source,target
" The simple analytical form of the adopted rotation curve (25)) allows us to calculate explicitly the value of the ""observed"" parameter «4, defined in Eq. (A13)):"," The simple analytical form of the adopted rotation curve \ref{paramprof}) ) allows us to calculate explicitly the value of the “observed"" parameter $\alpha_{obs}$ defined in Eq. \ref{alphaobs}) ):"
 where yx0.577 denotes the Euler gamma constant. thus Qop(t=1)1.59: the following discussion will be based on the use of this value of apy.," where $\gamma \approx 0.577$ denotes the Euler gamma constant, thus $\alpha_{obs}(\tau = 1) \approx 1.59$; the following discussion will be based on the use of this value of $\alpha_{obs}$."
 Note also that. for a given value of r. the rotation curve (25)) will admit a well-defined decomposition.," Note also that, for a given value of $\tau$, the rotation curve \ref{paramprof}) ) will admit a well-defined decomposition."
" In practice. before carrying out any detailed decomposition. we may introduce. as à simple definition of maximum-disk. the disk characterized by the value of the dimensionless weight £,,,.(7) that gives. without any dark matter contribution. the best fit to the inner rotation curve in the interval [O.Ro]."," In practice, before carrying out any detailed decomposition, we may introduce, as a simple definition of maximum-disk, the disk characterized by the value of the dimensionless weight $\beta_{max}(\tau)$ that gives, without any dark matter contribution, the best fit to the inner rotation curve in the interval $\left[0,R_{\Omega}\right]$."
 Note that this maximum-disk decomposition is designed in such a way to recover the central gradient of the rotation curve., Note that this maximum-disk decomposition is designed in such a way to recover the central gradient of the rotation curve.
 Sometimes a different definition is used. by referring to the stellar disk which reaches the asymptotic rotation velocity in correspondence of the maximum of its rotation curve.," Sometimes a different definition is used, by referring to the stellar disk which reaches the asymptotic rotation velocity in correspondence of the maximum of its rotation curve."
 This definition gives higher values ofB (Bing.310 for an exponential disk). but it is completely independent of the properties of the central part of the rotation curve.," This definition gives higher values of $\beta$ $\beta_{max}\approx 10$ for an exponential disk), but it is completely independent of the properties of the central part of the rotation curve."
 For r given by equation (26)). we find this value of B identifies an important reference value to which the results obtained from the self-consistent decomposition will thus be compared.," For $\tau$ given by equation \ref{taucorr}) ), we find this value of $\beta$ identifies an important reference value to which the results obtained from the self-consistent decomposition will thus be compared."
 We recall that 8=5 Is approximately in the middle of the parameter range discussed and explored in Sect. ?2.., We recall that $\beta=5$ is approximately in the middle of the parameter range discussed and explored in Sect. \ref{shaperc}.
 The properties of the self-consistent models constructed in the present paper are best illustrated by describing their ability to fit the just described representative idealized case in comparison to a fit performed by more standard parametric analyses., The properties of the self-consistent models constructed in the present paper are best illustrated by describing their ability to fit the just described representative idealized case in comparison to a fit performed by more standard parametric analyses.
 For both methods the goodness of a disk-halo decomposition. defined by a pair (α.8). is quantified by the function that is the integrated squared residuals between the “observed rotation curve and the rotation curve calculated from the model ωνηVpas ," For both methods the goodness of a disk-halo decomposition, defined by a pair $(\alpha,\beta)$, is quantified by the function that is the integrated squared residuals between the “observed"" rotation curve and the rotation curve calculated from the model $V_{mod} = \sqrt{{V}^2_D + V_{DM}^2}$."
The cut of the integration at seven exponential lengths is a reasonable choice. consistent with the analysis of Sect. 22...," The cut of the integration at seven exponential lengths is a reasonable choice, consistent with the analysis of Sect. \ref{flat} ."
 In this preliminary test we do not treat the asymptotic velocity as an additional free parameter of the model., In this preliminary test we do not treat the asymptotic velocity as an additional free parameter of the model.
 In other words. we just analyze the deviations defined by Eq. (," In other words, we just analyze the deviations defined by Eq. ("
29) in the (o.f) plane. at fixed V.,"29) in the $(\alpha, \beta)$ plane, at fixed $V_{\infty}$."
 The asymptotic velocity will be kept as a free parameter in Sect., The asymptotic velocity will be kept as a free parameter in Sect.
 5.2. for the case of NGC 3198.," 5.2, for the case of NGC 3198."
 The results obtained from the standard parametric decomposition are shown in Fig. 10..," The results obtained from the standard parametric decomposition are shown in Fig. \ref{parametric},"
 which clearly exhibits the disk-halo degeneracy pattern., which clearly exhibits the disk-halo degeneracy pattern.
 In particular. consider the contour marked by 0.02.," In particular, consider the contour marked by $0.02$."
 A sizable diagonal strip in parameter space consists of points that are basically equivalent from the point of view of the quality of the fit. even though they correspond to models that are physically very different. ranging from fairly light disks up to maximum-disk solutions (with 8 changing by a factor higher than ten. from =0.5 to = 6.5).," A sizable diagonal strip in parameter space consists of points that are basically equivalent from the point of view of the quality of the fit, even though they correspond to models that are physically very different, ranging from fairly light disks up to maximum-disk solutions (with $\beta$ changing by a factor higher than ten, from $\approx 0.5$ to $\approx 6.5$ )."
 In contrast. Fig.," In contrast, Fig."
 11. shows the contours of function (29)) for the case in which the model rotation curve is calculated using the self-consistent method presented in this paper., \ref{nparametric} shows the contours of function \ref{deviat}) ) for the case in which the model rotation curve is calculated using the self-consistent method presented in this paper.
 The plot ranges and the values of the solid line contours plotted in Fig., The plot ranges and the values of the solid line contours plotted in Fig.
 10. and Fig., \ref{parametric} and Fig.
 ΤΙ are the same., \ref{nparametric} are the same.
 The self-consistent models give a better disk-halo decomposition for three distinct, The self-consistent models give a better disk-halo decomposition for three distinct
the GGHz light curve.,the GHz light curve.
 The UMRAO monitoring of aat GGHz and GGHz started respectively in 1974 and in 1978., The UMRAO monitoring of at GHz and GHz started respectively in 1974 and in 1978.
 The 5GGHz and the GGHz light curves contain mainly these observations., The GHz and the GHz light curves contain mainly these observations.
 Details on the instrumentation and the calibration used at the UMRAO are given by Aller et al. (1985)), Details on the instrumentation and the calibration used at the UMRAO are given by Aller et al. \cite{AAL85}) )
 together with the data obtained until 1984., together with the data obtained until 1984.
 We do not include here the polarization observations. which are publicly available at the UMRAO Database Interface on the WWW at http://www.astro.Isa.umich.edu/obs/radiotel/umrao.html.," We do not include here the polarization observations, which are publicly available at the UMRAO Database Interface on the WWW at http://www.astro.lsa.umich.edu/obs/radiotel/umrao.html."
 Shorter wavelengths radio observations at 22.2 and GGHz were performed since 1980 both with the mm telescope of the Metsiihhovi Radio Observatory. Finland and with the 22mm telescope of the Crimean Astrophysical Observatory. Ukraine.," Shorter wavelengths radio observations at 22.2 and GHz were performed since 1980 both with the m telescope of the Metsähhovi Radio Observatory, Finland and with the m telescope of the Crimean Astrophysical Observatory, Ukraine."
 The GGHz and GGHz light curves are very well sampled since 1986 except for a gap in the summer of 1994 due to the replacement of the Metsihhovi antenna (see Fig. 2))., The GHz and GHz light curves are very well sampled since 1986 except for a gap in the summer of 1994 due to the replacement of the Metsähhovi antenna (see Fig. \ref{lcrmm}) ).
 The observations during 1980-85 and during 1985-90 are respectively published in Salonen et al. (1987)), The observations during 1980–85 and during 1985–90 are respectively published in Salonen et al. \cite{STU87}) )
 and in Terássranta et al. (1992)).," and in Terässranta et al. \cite{TTV92}) ),"
 together with details on the measurement methods and the calibrations., together with details on the measurement methods and the calibrations.
 Calibrations at GGHz were usually performed with the nearby source 2274 AA. M887). whose flux was taken to be Hy.," Calibrations at GHz were usually performed with the nearby source 274 A, 87), whose flux was taken to be Jy."
 Since there might have been a recent outburst in 2274. the GGHz data from Metsiihhovi presented here are only calibrated with the primary calibrator 221.," Since there might have been a recent outburst in 274, the GHz data from Metsähhovi presented here are only calibrated with the primary calibrator 21."
 We therefore have the same calibration procedure at 22 and GGHz., We therefore have the same calibration procedure at 22 and GHz.
 The differences between the two calibrations are generally within the uncertainties., The differences between the two calibrations are generally within the uncertainties.
 Daily observations of wwere performed by the Green Bank Interferometer (GBI) at GGHz and at GGHz from 1979 to 1988., Daily observations of were performed by the Green Bank Interferometer (GBI) at GHz and at GHz from 1979 to 1988.
 This huge data set was published by Waltman et al. (1991))., This huge data set was published by Waltman et al. \cite{WFJ91}) ).
 Additional observations carried out with new receivers at GGHz and at GGHz from 1989 to 1994 are also included in the database., Additional observations carried out with new receivers at GHz and at GHz from 1989 to 1994 are also included in the database.
 The GBI light curves display brightness dips. which occur when the sun is too close to oon the sky.," The GBI light curves display brightness dips, which occur when the sun is too close to on the sky."
 Since the GBI is an interferometer. 1t does not measure the total flux of an extended source like 273c. It is therefore difficult to compare the GBI measurements with single dish telescope observations.," Since the GBI is an interferometer, it does not measure the total flux of an extended source like c. It is therefore difficult to compare the GBI measurements with single dish telescope observations."
 For clarity. the GBI data are stored in separate files.," For clarity, the GBI data are stored in separate files."
 Other repeated radio observations from. the. literature were added to the database., Other repeated radio observations from the literature were added to the database.
 Observations at 2.7. 4.75 and GGHz from the mm telescope at Effelsberg. Germany reported in von Montigny et al. (1997))," Observations at 2.7, 4.75 and GHz from the m telescope at Effelsberg, Germany reported in von Montigny et al. \cite{VAA97}) )"
 were added to the GGHz. the GGHz and the GGHz light curves respectively.," were added to the GHz, the GHz and the GHz light curves respectively."
 The GGHz and 10GGHz light curves also contall earlier observations at GGHz and at GGHz from the mm telescope of the Algonquin Radio Observatory (Medd et al. 1972:;, The GHz and GHz light curves also contain earlier observations at GHz and at GHz from the m telescope of the Algonquin Radio Observatory (Medd et al. \cite{MAH72};
 Andrew et al. 1978))., Andrew et al. \cite{AMH78}) ).
 Observations at 7.8. 7.9 and GGHz from the mm antenna of the Haystack Radio Observatory are included in the GGHz and in the GGHz light curves (Allen Barrett 1966:; Dent Kapitzky 1976:: Dent Kojoian 1972:: Dent et al. 1974)).," Observations at 7.8, 7.9 and GHz from the m antenna of the Haystack Radio Observatory are included in the GHz and in the GHz light curves (Allen Barrett \cite{AB66}; Dent Kapitzky \cite{DK76}; Dent Kojoian \cite{DK72}; Dent et al. \cite{DKK74}) )."
 We also added to the GGHz and GGHz light curves the 22 and GGHz observations from the mm Itapetinga radio telescope. Brazil (Botti Abraham 1988)) and the GGHz observations from the UMRAO (Haddock et al. 1987)).," We also added to the GHz and GHz light curves the 22 and GHz observations from the m Itapetinga radio telescope, Brazil (Botti Abraham \cite{BA88}) ) and the GHz observations from the UMRAO (Haddock et al. \cite{HAA87}) )."
 Finally. we included in the GGHz light curve a few earlier observations at 31.4GGHz made with the mm antenna of the National Radio Astronomical Observatory (NRAO) at Kitt Peak (Dent Hobbs 1973)).," Finally, we included in the GHz light curve a few earlier observations at GHz made with the m antenna of the National Radio Astronomical Observatory (NRAO) at Kitt Peak (Dent Hobbs \cite{DH73}) )."
 We did not include all the isolated observations from early radio catalogues., We did not include all the isolated observations from early radio catalogues.
 We added only the flux measurements reported by Kühhr et al. (1981)).," We added only the flux measurements reported by Kühhr et al. \cite{KWP81}) ),"
 since they are all recalibrated to the scale of Baars et al. (1977)).," since they are all recalibrated to the scale of Baars et al. \cite{BGP77}) ),"
 and the total flux densities (core plus jet) reported by Conway et al. (1993))., and the total flux densities (core plus jet) reported by Conway et al. \cite{CGP93}) ).
 At very low frequency (< 330MMHz). we added the observations fron= Braude et al. (1979)).," At very low frequency $<$ MHz), we added the observations from Braude et al. \cite{BMS79}) ),"
 but multiplied by the scaling factor of 1.23 used for other objects by Kühhr et al. (1981))., but multiplied by the scaling factor of 1.23 used for other objects by Kühhr et al. \cite{KWP81}) ).
 In the MMHz range other isolated observations are from Artyukh (1984)). Dennison et al. (1981)).," In the MHz range other isolated observations are from Artyukh \cite{A84}) ), Dennison et al. \cite{DBL81}) ),"
 Fanti et al. (1979.. 1981)).," Fanti et al. \cite{FFM79}, , \cite{FFF81}) ),"
 Fisher Erickson (1980)) and Hunstead (1972))., Fisher Erickson \cite{FE80}) ) and Hunstead \cite{H72}) ).
 Above GGHz. some isolated radio observations were found in Jones et al. (1981)).," Above GHz, some isolated radio observations were found in Jones et al. \cite{JRO81}) ),"
 Landau et al. (1983)), Landau et al. \cite{LJE83}) )
 and Lichti et al. (1995))., and Lichti et al. \cite{LBC95}) ).
 All these data were included in the respective light curves., All these data were included in the respective light curves.
 The radio light curves of aat GGHz. GGHz and GGHz are shown in Fig. 2..," The radio light curves of at GHz, GHz and GHz are shown in Fig. \ref{lcrmm}."
 The contribution from the jet 2273A) was derived from Fig., The contribution from the jet 273A) was derived from Fig.
 Al of Conway et al. (1993))., A1 of Conway et al. \cite{CGP93}) ).
 It is a broken power law with a spectral index oj of 0.67 below MMHz (29.0JJy) and of 0.85 at higher frequencies., It is a broken power law with a spectral index $\alpha\dmrm{jet}$ of 0.67 below MHz Jy) and of 0.85 at higher frequencies.
 The flux density of 2273A declines strongly in the infrared-to-optical domain with εντον 7 44. as shown in Fig.," The flux density of 273A declines strongly in the infrared-to-optical domain with $\alpha\dmrm{jet}$ $\sim$ 4, as shown in Fig."
 Af of Meisenheimer et al. (1989))., 4f of Meisenheimer et al. \cite{MRH89}) ).
 Fig., Fig.
 6 shows that the jet component is dominant below ~ GGHz. whereas it becomes negligible (< All the millimetre/submillimetre (mm/submm) observations of wwere grouped together into seven light curves: mmm GGHz). mmm GGHz). mmm GGHz). mmm. mmm. mmm and mmm (see Table 1).," \ref{avspect} shows that the jet component is dominant below $\sim$ GHz, whereas it becomes negligible $<$ All the millimetre/submillimetre (mm/submm) observations of were grouped together into seven light curves: mm GHz), mm GHz), mm GHz), mm, mm, mm and mm (see Table \ref{tabrmm}) )."
 The mmm light curve is shown in Fig. 2.., The mm light curve is shown in Fig. \ref{lcrmm}.
 All the submillimetre observations. as well as most observations at. mmm. 1.3mmm and 2.0mmm were performed on Mauna Kea. Hawai.," All the submillimetre observations, as well as most observations at mm, mm and mm were performed on Mauna Kea, Hawaii."
 The QMC/Oregor photometer (Ade et al. 1954)), The QMC/Oregon photometer (Ade et al. \cite{AGC84}) )
 was used on the 3.8mm United Kingdom Infrared Telescope (UKIRT) until 1985., was used on the m United Kingdom Infrared Telescope (UKIRT) until 1985.
 Since January 1986. à new common user photometer UKT14 (Dunean et al. 1990))," Since January 1986, a new common user photometer UKT14 (Duncan et al. \cite{DSR90}) )"
 was installed on the UKIRT. before being moved in March 1988 to the 15mm James Clerk Maxwell Telescope (JCMT).," was installed on the UKIRT, before being moved in March 1988 to the m James Clerk Maxwell Telescope (JCMT)."
 Finally. in July 1996. UKT14 was replacec on the JCMT by the Submillimetre Common-User Bolometer Array (SCUBA). described by Robson et al. (1998)).," Finally, in July 1996, UKT14 was replaced on the JCMT by the Submillimetre Common-User Bolometer Array (SCUBA), described by Robson et al. \cite{R98}) )."
 Details οἱ the observations performed with the UKTI4 photometer both on the JCMT and the UKIRT. as well as calibration techniques are given by Robson et al. (1993)).," Details on the observations performed with the UKT14 photometer both on the JCMT and the UKIRT, as well as calibration techniques are given by Robson et al. \cite{RLG93}) )."
 The earlier observatior techniques with the QMC/Oregon photometerare described i Robson et al. (1983))., The earlier observation techniques with the QMC/Oregon photometerare described in Robson et al. \cite{RGC83}) ).
made by registering to the V frame then binning 3x3.,made by registering to the $V$ frame then binning 3x3.
 An example of a spatial map is shown in Figure 1., An example of a spatial map is shown in Figure 1.
 It is also possible to plot spatial color versus surface brightness (i.e. pixel color versus that pixels surface brightness in V)., It is also possible to plot spatial color versus surface brightness (i.e. pixel color versus that pixels surface brightness in $V$ ).
 An example of that type of analysis is shown in 833.5., An example of that type of analysis is shown in 3.5.
" A subset of the sample had been previously imaged in V—I (Pildis, Schombert Eder 1997)."," A subset of the sample had been previously imaged in $V-I$ (Pildis, Schombert Eder 1997)."
" While those colors are less accurate, their total values will be compared to the B—V colors in 833.4 and are found listed in Table 1."," While those colors are less accurate, their total values will be compared to the $B-V$ colors in 3.4 and are found listed in Table 1."
 Spatial V—I color maps are made and re-pixeled to the same orientation and scale of the newer B—V frames., Spatial $V-I$ color maps are made and re-pixeled to the same orientation and scale of the newer $B-V$ frames.
" This allows for a comparison of B—V and V—I not only in total colors and color profiles, put also on a pixel-by-pixel basis."," This allows for a comparison of $B-V$ and $V-I$ not only in total colors and color profiles, put also on a pixel-by-pixel basis."
Figure 7 is a “residual map”. demonstrating the difference between the observed 2 tuage aud a modelled one consisting of pure elliptical isophotes.,"Figure \ref{resid} is a ""residual map"", demonstrating the difference between the observed $R$ image and a modelled one consisting of pure elliptical isophotes."
 The “residual maps in all four filters are similar aud look like the Fig.," The ""residual maps"" in all four filters are similar and look like the Fig."
 3b from the paper of Wirth et al. (1985)), 3b from the paper of Wirth et al. \cite{wsb85}) )
 though Wirth et al., though Wirth et al.
 subtracted mediau-snoothed images. not modelled oues.," subtracted median-smoothed images, not modelled ones."
 With et al. (1985)), Wirth et al. \cite{wsb85}) )
 have interpreted the spiral absorption features of their Fig., have interpreted the spiral absorption features of their Fig.
 3b as dust arms., 3b as dust arms.
 We reach the same conclusion., We reach the same conclusion.
 Figure 6 is fully cousistent with earlier pliotoietric results for the central part of (see. for example. CFUT data in the work of Bacon et al. 1991)).," Figure \ref{isopar} is fully consistent with earlier photometric results for the central part of (see, for example, CFHT data in the work of Bacon et al. \cite{bemn94}) ),"
 though we would like to no| that boxiuess of the iuner isoplotes of is shown here for he first time., though we would like to note that boxiness of the inner isophotes of is shown here for the first time.
 There are also soie details of the radia profiles of PA. aud (1bía) which were not discussed earlier., There are also some details of the radial profiles of $P.A.$ and $(1-b/a)$ which were not discussed earlier.
 Over al the four spectral bands the major seni-axis ranee of Hs characterized by a local mast of ellipticity which reaches 0.2 auc by a local minima iu the position angle which oscillates between aand cclose enough to the oricutation of the line of nodes of the disk. PA.= 387.," Over all the four spectral bands the major semi-axis range of is characterized by a local maximum of ellipticity which reaches 0.2 and by a local minimum in the position angle which oscillates between and close enough to the orientation of the line of nodes of the disk, $P.A.=38\degr$ ."
 The same radius interval is characterized by a αια higher than outside. eq/0 is less hanLI.," The same radius interval is characterized by a $a_4/a$ higher than; outside, $a_4/a$ is less than."
.. This neaus that in the radius rauge of Wwe νου. a stellar disk. whose plane ds close tfo or even coincides with the global aue of the Ooealaxy., This means that in the radius range of we see a stellar disk whose plane is close to or even coincides with the global plane of the galaxy.
 One ist ↘↽↸∖↸∖↻↕∐∐∐∐≼↧↑∐⋜↧↑↑↕∐∖↸⊳↸∖∐⊓⋅⋜↧↕↥⋅↸∖∶↴⋁↕∪↕∪↕⋟ is) photometrically dominated by the bulee (ijimaetal. 1976))., One must keep in mind that the central region of is photometrically dominated by the bulge \cite{jap76}) ).
" At the distance of the major seuii-axi« of ccorresponds to a imetric radius of 85 pc. therefore we deal with a so called nuclear disk: simular disks were earlier found in some other emlv-tvpe spiral galaxies. particularly, i (Burkhead 19913)."," At the distance of the major semi-axis of corresponds to a metric radius of 85 pc, therefore we deal with a so called nuclear disk; similar disks were earlier found in some other early-type spiral galaxies, particularly, in \cite{burk}) )."
 In Fig., In Fig.
 7 one can see two dark (dust?), \ref{resid} one can see two dark (dust?)
 spiral müniuius located also in the same radius rauge., spiral miniarms located also in the same radius range.
" Besides that. over the same radius range a noticeable eiission line |OITI|A5007 is seen in our spectra (in the very center of31. r«D"". enission lines are abseut according to the claims of Bacon ( al. 199 D)."," Besides that, over the same radius range a noticeable emission line $\lambda 5007$ is seen in our spectra (in the very center of, $r < 5\arcsec$, emission lines are absent according to the claims of Bacon et al. \cite{bemn94}) )."
 We cau conclude that the nuclear stellar disk of contains also dust and ionized gas., We can conclude that the nuclear stellar disk of contains also dust and ionized gas.
 Lonizatiou nuelt be due to shocks because. according to Ciardullo ct al. (1988)).," Ionization might be due to shocks because, according to Ciardullo et al. \cite{ciar}) ),"
 the nitrogen emission line AG583 is everywhere stronger than fa inside kc=1’., the nitrogen emission line $\lambda 6583$ is everywhere stronger than $H\alpha$ inside $r=1\arcmin$.
 Thouel3... the most nearby spiral galaxy. has been studied for a lone time and with munatched spatial resolution. the true structure of its central region is still a puzzle.," Though, the most nearby spiral galaxy, has been studied for a long time and with unmatched spatial resolution, the true structure of its central region is still a puzzle."
 The large amount of accumulated observational data hasled to reject mau models. even regarded earlier ax reasonable ones.," The large amount of accumulated observational data hasled to reject many models, even regarded earlier as reasonable ones."
 Our work contributes to this process., Our work contributes to this process.
 found in a few clusters incliding MBS7/Virgo (Forman ot 22005). Indra A (Nulseu ct 220054). Hercules A (Nulseu et 22005b). aud MS0735.6|72121 (AI¢eNamara et 22005).," found in a few clusters including M87/Virgo (Forman et 2005), Hydra A (Nulsen et 2005a), Hercules A (Nulsen et 2005b), and MS0735.6+7421 (McNamara et 2005)."
 These shocks were fairly sveak with Mach uunbers iu the rauge of 1.2 aud 1.7 (see MeNiuuara Nulseu 2007 for a review)., These shocks were fairly weak with Mach numbers in the range of 1.2 and 1.7 (see McNamara Nulsen 2007 for a review).
 Ripple features in the N-rav surface brightness resulting from the propagation of veak shocks or sound waves as seeu iu a loug observation of Perseus (Fabian et 22003. 2006) may also coutribute to heating.," Ripple features in the X-ray surface brightness resulting from the propagation of weak shocks or sound waves as seen in a long observation of Perseus (Fabian et 2003, 2006) may also contribute to heating."
 Energy iuput from buovautlv rising bubbles of relativistic plasina (6.2.. Churazov ct 22002). weak shocks (c.g.. Revnolds. Heinz. Beegchuan 2001). and the propagation of sound or pressure waves are able to offset cooling.," Energy input from buoyantly rising bubbles of relativistic plasma (e.g., Churazov et 2002), weak shocks (e.g., Reynolds, Heinz, Begelman 2001), and the propagation of sound or pressure waves are able to offset cooling."
 Abell 2052 is a moderately rich. cooling flow cluster at a redshift of τ=04019815.," Abell 2052 is a moderately rich, cooling flow cluster at a redshift of $z=0.0348$."
 A powerful radio source. 3C 317. is hosted by the central cD galaxy. UGC 09799.," A powerful radio source, 3C 317, is hosted by the central cD galaxy, UGC 09799."
 Abell 2052 was previously observed in the N-vav with Einstein (White. Jones. Forman 1997).ROSA (Peres et 11998. Rizza et 22000). (White 2000). andChandra (Blanton ot 22001. 2003).," Abell 2052 was previously observed in the X-ray with $Einstein$ (White, Jones, Forman 1997), (Peres et 1998, Rizza et 2000), (White 2000), and (Blanton et 2001, 2003)."
 We present a deep observation of Abell 2052. combining the earlier Cvele 1 data with data from Cycle 6.," We present a deep observation of Abell 2052, combining the earlier Cycle 1 data with data from Cycle 6."
 This longer observation reveals probable shock features exterior to the bubble rius that contribute to heating im the cluster center., This longer observation reveals probable shock features exterior to the bubble rims that contribute to heating in the cluster center.
" We assume ZI,=10 kan + Πο |. Qa,—0.3. and Q4—0.7 (1""=0.69 κος at += 0.0318) throughout."," We assume $H_{\circ}=70$ km $^{-1}$ $^{-1}$ , $\Omega_{M}=0.3$, and $\Omega_{\Lambda}=0.7$ $1\arcsec = 0.69$ kpc at $z = 0.0348$ ) throughout."
 Errors are given at the 90% confidence level unless otherwise stated., Errors are given at the $90\%$ confidence level unless otherwise stated.
 Abcll 2052 was observed withChandra using the ACTS- detector on 2000 September 3 for a total of 36.751 seconds aud ou 2006 March 21 for 128.630 seconds.," Abell 2052 was observed with using the ACIS-S detector on 2000 September 3 for a total of 36,754 seconds and on 2006 March 24 for 128,630 seconds."
 The events from the 2000 data were telemietered in Faint mode and the eveuts from thelonger exposure were, The events from the 2000 data were telemetered in Faint mode and the events from thelonger exposure were
These successful first applications of the FGLR-method for distance determinations indicate the very promising potential of the method to provide an independent constraint on the extragalactic distance scale.,These successful first applications of the FGLR-method for distance determinations indicate the very promising potential of the method to provide an independent constraint on the extragalactic distance scale.
" In this section we use the results from the BSG studies to discuss Cepheid distances and the ""standard"" approach for their metallicity correction.", In this section we use the results from the BSG studies to discuss Cepheid distances and the “standard” approach for their metallicity correction.
 We start with M81 (the discussion presented here closely follows the one given by Kudritzkietal. 2011))., We start with M81 (the discussion presented here closely follows the one given by \citealt{kud11}) ).
 In addition to the HST Key Project work on M81 (Freedmanetal.1994.2001) there are two recent Cepheid studies by MeCommiasetal.(2009) and by Gerkeetal.(2010.," In addition to the HST Key Project work on M81 \citep{freedman94, freedman01} there are two recent Cepheid studies by \citet{mccommas09} and by \citet{gerke11}."
.. MeCommasetal.(2009) use HST light curves of 11 fundamental and two first overtone short period Cepheids 1n the outer disk of M8] at ~ 13.5 kpe galactocentric distance., \citet{mccommas09} use HST light curves of 11 fundamental and two first overtone short period Cepheids in the outer disk of M81 at $\sim$ 13.5 kpc galactocentric distance.
 Gerkeetal.(2011) investigate 107 long period Cepheids observed with the LBT in a galactocentric range of 3.5 to 10.5 kpe with ground-based B. V. I photometry.," \citet{gerke11} investigate 107 long period Cepheids observed with the LBT in a galactocentric range of 3.5 to 10.5 kpc with ground-based B, V, I photometry."
 Applying the Wesenheit VI method. both studies obtain a distance modulus relative to the LMC which is 0.17 mag longer than the BSG result.," Applying the Wesenheit VI method, both studies obtain a distance modulus relative to the LMC which is 0.17 mag longer than the BSG result."
 However. this is based on a metallicity correction Ate = YZ] - rare). which is motivated by the fact that the inner field Cepheids observed by the KP yield a distance modulus. which is 0.23 mag shorter relative to the outer fields without such a correction applied.," However, this is based on a metallicity correction $\Delta \mu$ = $\gamma$ ([Z] - $_{LMC}$ ), which is motivated by the fact that the inner field Cepheids observed by the KP yield a distance modulus, which is 0.23 mag shorter relative to the outer fields without such a correction applied."
 They use Zaritskyetal.(1994). for metallicity [Z] and the metallicity gradient and rage —-0.19 for the LMC oxygen abundance (see section 4. 2nd to last paragraph).," They use \citet{zaritsky94} for metallicity [Z] and the metallicity gradient and $_{LMC}$ =-0.19 for the LMC oxygen abundance (see section 4, 2nd to last paragraph)."
 This metallicity gradient requires a highly negative value of y. y = -0.55 mag dex7!. to account for the inner and outer field Cepheid distance moduli differences.," This metallicity gradient requires a highly negative value of $\gamma$, $\gamma$ = -0.55 mag $^{-1}$, to account for the inner and outer field Cepheid distance moduli differences."
 Applying the BSG metallicity gradient would require an even more negative value of y. namely y= -0.65 mag .," Applying the BSG metallicity gradient would require an even more negative value of $\gamma$, namely $\gamma$ = -0.65 mag $^{-1}$."
 Moreover. the LMC oxygen abundance in these corrections is too large compared with the LMC oxygen abundance of B-stars found by Hunteretal.(2007). ([Z]rajc = -0.36 dex). the iron abundances of LMC Cepheids determined by Romanielloetal.(2008) and Lucketal.(1998) με -0.33 dex). and the LMC region oxygen abundances obtained by Bresolin(2011). ϱΖ]ιμο = -0.33 dex).," Moreover, the LMC oxygen abundance in these corrections is too large compared with the LMC oxygen abundance of B-stars found by \citet{hunter07} $_{LMC}$ = -0.36 dex), the iron abundances of LMC Cepheids determined by \citet{romaniello08} and \citet{luck98} $_{LMC}$ = -0.33 dex), and the LMC region oxygen abundances obtained by \citet{bresolin11} $_{LMC}$ = -0.33 dex)."
 This means that with the BSG metallicity values in M81 the Cepheids in the outer field have a metallicity 0.11 dex higher than the LMC., This means that with the BSG metallicity values in M81 the Cepheids in the outer field have a metallicity 0.11 dex higher than the LMC.
 If one would apply the metallicity correction with y = -0.65 mag dex7! accordingly. this would enlarge the distance modulus by another 0.07 mag.," If one would apply the metallicity correction with $\gamma$ = -0.65 mag $^{-1}$ accordingly, this would enlarge the distance modulus by another 0.07 mag."
 However. with such a large negative value of y It is important to note that this empirical correction. which claims that Cepheids become brighter with increasing metallicity. is in striking disagreement with pulsation theory. which predicts exactly the opposite. namely that the Cepheid brightness decreases with increasing metallicity (FiorentinoBonoetal.2008).," However, with such a large negative value of $\gamma$ it is important to note that this empirical correction, which claims that Cepheids become brighter with increasing metallicity, is in striking disagreement with pulsation theory, which predicts exactly the opposite, namely that the Cepheid brightness decreases with increasing metallicity \citep{fiorentino02, marconi05, fiorentino07, bono08}."
. It also disagrees with the recent high S/N. high spectral resolution quantitative spectroscopy in the Milky Way and the LMC carried out by Romanielloetal.(2008).. which confirms the prediction by pulsation theory.," It also disagrees with the recent high S/N, high spectral resolution quantitative spectroscopy in the Milky Way and the LMC carried out by \citet{romaniello08}, which confirms the prediction by pulsation theory."
 According to this work. the value of y should be positive and not negative.," According to this work, the value of $\gamma$ should be positive and not negative."
 We also note that Uetal.(2009) have demonstrated from their quantitative spectroscopy of blue supergiants in M33 that the difference of distance moduli between inner field and outer field Cepheids found by Scoweroft would require a y-value of -0.55 mag dex7!., We also note that \citet{u09} have demonstrated from their quantitative spectroscopy of blue supergiants in M33 that the difference of distance moduli between inner field and outer field Cepheids found by \citet{scowcroft09} would require a $\gamma$ -value of -0.55 mag $^{-1}$.
 Even worse. Bresolinetal.(2010) re-determined region abundances in M33 using auroral lines and applying their abundance gradient to the Cepheid fields in M33 yields y = - 1.2 mag dex”!] (see discussion in Bresolin201 1)).," Even worse, \cite{bresolin10} re-determined region abundances in M33 using auroral lines and applying their abundance gradient to the Cepheid fields in M33 yields $\gamma$ = - 1.2 mag $^{-1}$ (see discussion in \citealt*{bresolin11}) )."
 Another galaxy where the comparison of Cepheids in the inner and outer fields leads to a significantly different distance modulus is the maser galaxy NGC 4258., Another galaxy where the comparison of Cepheids in the inner and outer fields leads to a significantly different distance modulus is the maser galaxy NGC 4258.
 This galaxy is of particular importance. since it has been used as the new anchor point for the extragalactic distance scale by Riessetal.(2009a.b.2011) because of its accurately known distance from the Keplerian motion of water masers orbiting the central black hole (Humphreysetal.2008).," This galaxy is of particular importance, since it has been used as the new anchor point for the extragalactic distance scale by \citet{riess09a, riess09b, riess11} because of its accurately known distance from the Keplerian motion of water masers orbiting the central black hole \citep{humphreys08}."
. Maerietal.(2006) based on the region strong line method oxygen abundances by Zaritskyetal.(1994) derived a y- value of -0.29 mag dex~!., \citet{macri06} based on the region strong line method oxygen abundances by \citet{zaritsky94} derived a $\gamma$ -value of -0.29 mag $^{-1}$ .
 However. most recently. Bresolin(2011) re-determined the region metallicities 1n. this galaxy including the observation of auroral lines in a few cases.," However, most recently, \cite{bresolin11} re-determined the region metallicities in this galaxy including the observation of auroral lines in a few cases."
 This led to a downward substantial revision of the metallicity. which seems to be close to the LMC and not strongly super-solar. and a very shallow abundance gradient.," This led to a downward substantial revision of the metallicity, which seems to be close to the LMC and not strongly super-solar, and a very shallow abundance gradient."
 Based on these results. Bresolin(2011) show that y = - 0.69 mag dex-! would be needed to explain the distance modulus difference between inner and outer fields. again a value much too negative. when compared with pulsation theory and observational work on Milky Way and LMC Cepheids.," Based on these results, \cite{bresolin11} show that $\gamma$ = - 0.69 mag $^{-1}$ would be needed to explain the distance modulus difference between inner and outer fields, again a value much too negative, when compared with pulsation theory and observational work on Milky Way and LMC Cepheids."
 While the improved region work on this important galaxy still awaits an independent confirmation through a study of BSGs. it is an additional clear indication of a systematic effect on Cepheid distance moduli. not understood at this point.," While the improved region work on this important galaxy still awaits an independent confirmation through a study of BSGs, it is an additional clear indication of a systematic effect on Cepheid distance moduli not understood at this point."
 Majaessetal.(2011) discussthe large metallicity corrections suggested by Gerkeetal. and by the recent HST/ACS Cepheid study of M101, \citet{majaess11} discussthe large metallicity corrections suggested by \citet{gerke11} and by the recent HST/ACS Cepheid study of M101
between radial bins.,between radial bins.
 Another is the fact that such a scheme results in necessarily wider radial bins. which causes the clustering signal to be diluted.," Another is the fact that such a scheme results in necessarily wider radial bins, which causes the clustering signal to be diluted."
 We do not feel that either is a large problem., We do not feel that either is a large problem.
 Applying the more traditional top-hat binning scheme to photometric surveys necessarily results in overlapping radial bins (due to photometric redshift errors) and there will always be considerable covariance between radial bins selected with photometric redshifts — we do not think that pair-centre binning will make this problem considerably worse., Applying the more traditional top-hat binning scheme to photometric surveys necessarily results in overlapping radial bins (due to photometric redshift errors) and there will always be considerable covariance between radial bins selected with photometric redshifts — we do not think that pair-centre binning will make this problem considerably worse.
 The dilution effect can be mitigated by imposing a maximum separation between the pairs included in a pair-centre bin: we call this constrained pair-centre binning., The dilution effect can be mitigated by imposing a maximum separation between the pairs included in a pair-centre bin: we call this constrained pair-centre binning.
 As can be seen by comparing the middle and right-hand panels of Figs., As can be seen by comparing the middle and right-hand panels of Figs.
 14 and 15. imposing such a constraint increases the expected signal while not causing a significant change in the effects of redshift-space distortions.," \ref{fig:xi-des}
 and \ref{fig:xi-dess}, imposing such a constraint increases the expected signal while not causing a significant change in the effects of redshift-space distortions."
 More detailed studies of these effects are warranted. but we are confident that the reduction in the redshift distortion effect we observe when utilising pair-centre binning wil make this scheme considerably preferable to a top-hat binning scheme.," More detailed studies of these effects are warranted, but we are confident that the reduction in the redshift distortion effect we observe when utilising pair-centre binning will make this scheme considerably preferable to a top-hat binning scheme."
 Pair-centre binning completely removes the effect of redshif distortions when given a uniform galaxy distribution., Pair-centre binning completely removes the effect of redshift distortions when given a uniform galaxy distribution.
 Such perfec distributions do not exist — most galaxy samples selections are based on an apparent magnitude limit — and thus realistic radia distributions of galaxies are more complicated., Such perfect distributions do not exist — most galaxy samples selections are based on an apparent magnitude limit — and thus realistic radial distributions of galaxies are more complicated.
 However. we have argued that if galaxy samples selected based on an apparen magnitude limit are cut back so that no galaxies A-corrected galaxies are missing from the sample. then this does not matter: the boundaries of the bins are either in real-space. or based on pair- neither of which introduces redshift distortion effects.," However, we have argued that if galaxy samples selected based on an apparent magnitude limit are cut back so that no galaxies $k$ -corrected galaxies are missing from the sample, then this does not matter: the boundaries of the bins are either in real-space, or based on pair-centres, neither of which introduces redshift distortion effects."
 We have argued. and it is clear from previous work. that any interpretation of projected clustering measurements must account for redshift space distortions.," We have argued, and it is clear from previous work, that any interpretation of projected clustering measurements must account for redshift space distortions."
 In fact. comparing correlation functions calculated using different binning schemes might actually prove to provide a mechanism for measuring the amplitude of the redshift-space distortions.," In fact, comparing correlation functions calculated using different binning schemes might actually prove to provide a mechanism for measuring the amplitude of the redshift-space distortions."
 This is beyond the scope of our current draft. and we leave this for subsequent work.," This is beyond the scope of our current draft, and we leave this for subsequent work."
 To quantify the effect of redshift-space distortions for future survevs. we have used the expected radial selection. function and photometric redshift distribution for the Dark Energy Survey ο. predict the effect of redshift-space distortions on projected clustering measurements.," To quantify the effect of redshift-space distortions for future surveys, we have used the expected radial selection function and photometric redshift distribution for the Dark Energy Survey to predict the effect of redshift-space distortions on projected clustering measurements."
 This analysis is also relevant to other jxlanned surveys such as PanStarrs and the LSST. which will have similar radial selection functions.," This analysis is also relevant to other planned surveys such as PanStarrs and the LSST, which will have similar radial selection functions."
 We have contrasted two differen ypes of binning: top-hat — in which we only allow galaxies between a given radial bound to enter our sample— and pair-centre — in which we only count galaxy pairs with an average radia yosition that Hes within our bounds., We have contrasted two different types of binning: top-hat — in which we only allow galaxies between a given radial bound to enter our sample— and pair-centre — in which we only count galaxy pairs with an average radial position that lies within our bounds.
 For typical bin widths that wil be applied to these surveys. we find that top-hat binning in the radia direction leaves a strong signal from redshift-space distortions.," For typical bin widths that will be applied to these surveys, we find that top-hat binning in the radial direction leaves a strong signal from redshift-space distortions."
 Using a pair-centre binning scheme reduces the redshift-space distortion signal. by as much as 80% in realistic situations (see Fig. 145) ," Using a pair-centre binning scheme reduces the redshift-space distortion signal, by as much as $\%$ in realistic situations (see Fig. \ref{fig:xi-des}) )"
and should therefore allow the measurements to be more sensitive to the cosmological parameters one wishes to constrain., and should therefore allow the measurements to be more sensitive to the cosmological parameters one wishes to constrain.
 In this analysis. we have only considered the simplitied situation where the redshift-space distortions act along one axis of a Cartesian basis.," In this analysis, we have only considered the simplified situation where the redshift-space distortions act along one axis of a Cartesian basis."
 However. the arguments we have put forward in favour of pair-centre binning do not rely on this assumption. and will remain valid even when wide-angle effects are included in any analysis.," However, the arguments we have put forward in favour of pair-centre binning do not rely on this assumption, and will remain valid even when wide-angle effects are included in any analysis."
 The authors thank the UK Science and Technology Facilities Research Council for financial support., The authors thank the UK Science and Technology Facilities Research Council for financial support.
 WIP is also grateful for support from the Leverhulme Trust and the European Research Council., WJP is also grateful for support from the Leverhulme Trust and the European Research Council.
 Simulated data was ealeulated. and analysed using the COSMOS Altix 3700 supercomputer. a UK-CCC facility supported by HEFCE and STFC in cooperation with CGI/Intel.," Simulated data was calculated and analysed using the COSMOS Altix 3700 supercomputer, a UK-CCC facility supported by HEFCE and STFC in cooperation with CGI/Intel."
 We thank the DES Large-Scale Structure working group members. and especially Enrique Gaztanaga. for many helpful discussions.," We thank the DES Large-Scale Structure working group members, and especially Enrique Gaztanaga, for many helpful discussions."
 We also thank the referee for carefully reading our manuscript and providing excellent suggestions for improvements., We also thank the referee for carefully reading our manuscript and providing excellent suggestions for improvements.
WD.,WD.
" Ποπονα, the issue of whether the debris disk cau sustain the high metal accretion rates Mz up to several S10) os} inferred iu some systems lias not been clear for a long time."," However, the issue of whether the debris disk can sustain the high metal accretion rates $\dot M_Z$ up to several $\times 10^{10}$ g $^{-1}$ inferred in some systems has not been clear for a long time."
 Receutly Rafikov (20112: hereafter R11) showed that coupling of the disk to stellar radiation via the Povuting-Robertson (PR) effect (Burns L979) can result in metal accretion rates Mz~10s gs Ll., Recently Rafikov (2011a; hereafter R11) showed that coupling of the disk to stellar radiation via the Poynting-Robertson (PR) effect (Burns 1979) can result in metal accretion rates $\dot M_Z \sim 10^8$ g $^{-1}$.
 Later Rafikov (2011b) has also demoustrated that under certain circumstances even higher values of Mz cau arise from the interaction between the debris disk aud metal eas that is produced by the sublimation at ει, Later Rafikov (2011b) has also demonstrated that under certain circumstances even higher values of $\dot M_Z$ can arise from the interaction between the debris disk and metal gas that is produced by the sublimation at $R_{in}$.
 The model of radiatively driven accretion of R11 did not cover the huge scale evolution of the debris disk resulting from the PR drag. and made certain assuniptious (c.e. hieh optical depths of the disk) which were not rigorously verified.," The model of radiatively driven accretion of R11 did not cover the large scale evolution of the debris disk resulting from the PR drag, and made certain assumptions (e.g. high optical depths of the disk) which were not rigorously verified."
 The goal of this work is to extend the analysis of R11 and to develop a detailed elobal model of the compact debris disk evolution caused by the PR drag., The goal of this work is to extend the analysis of R11 and to develop a detailed global model of the compact debris disk evolution caused by the PR drag.
 The paper is organized as follows., The paper is organized as follows.
 Iu refsectitheorv owe outline the basic picture of the PR-driven debris aceretiou and derive master equation (18)) that describes elobal evolution of the disk., In \\ref{sect:theory} we outline the basic picture of the PR-driven debris accretion and derive master equation \ref{eq:1}) ) that describes global evolution of the disk.
 We then explore in refsectilow both analytically and nuuerieallv the evolution of a low mass. optically thin disk of debris.," We then explore in \\ref{sect:low} both analytically and numerically the evolution of a low mass, optically thin disk of debris."
" In refsectihieh πο study global evolution of massive. optically thick debris disks starting with different initial spatial distributions of debris around the WD (vine-like. retsubsectilarec, arrow... LAO. ordishkοι refsubsect :disk)ytosccthecf feetoutheglobaldishecolution"," In \\ref{sect:high} we study global evolution of massive, optically thick debris disks starting with different initial spatial distributions of debris around the WD (ring-like, \\ref{subsect:large_narrow}, \ref{subsect:small}, or disk-like, \\ref{subsect:disk}) ) to see the effect on the global disk evolution."
 W etlscussourresultsumltheirobservationalimplicationsint disc., We discuss our results and their observational implications in \\ref{sect:disc}.
" Iu the following we consider an axisviunietrie disk of particles extending frou R;, to Rove in radius.", In the following we consider an axisymmetric disk of particles extending from $R_{in}$ to $R_{out}$ in radius.
" The ier radius nav coincide with the sublimation radius A, at which the effective temperature of particles equals the sublimation temperature Ti: 2 2 3.) where (δὲ, is the WD radius. 7,z:1500 Is for silicate erains. and Z,,=T,/(10! Is) is the normalized stellar temperature 7i."," The inner radius may coincide with the sublimation radius $R_s$ , at which the effective temperature of particles equals the sublimation temperature $T_s$: 22 ^2 )^2, where $R_\star$ is the WD radius, $T_s\approx 1500$ K for silicate grains, and $T_{\star,4}\equiv T_\star/(10^4$ K) is the normalized stellar temperature $T_\star$."
" Taking R,zO.OLR.. one funds Ryzm0.2 Ro. in agreement with observationallv iuferred mner radii of compact debris disks (Jura 2007. 20092)."," Taking $R_\star\approx 0.01R_\odot$ one finds $R_s\approx 0.2$ $_\odot$, in agreement with observationally inferred inner radii of compact debris disks (Jura 2007, 2009a)."
 When particles reach the sublimation radius they produce metallic eas. which joius the gaseous disk extending down to the WD surface.," When particles reach the sublimation radius they produce metallic gas, which joins the gaseous disk extending down to the WD surface."
 Metal accretion outo the WD surface proceeds through this clisk., Metal accretion onto the WD surface proceeds through this disk.
 Although this metal gas also spreads outward frou the sublination radius (CMelis 2010) aud under certain eireunistauces ean substantially affect debris disk evolution (Bafikov 2011b). in this work. following R11. we concentrate onlv on effects associated with the PR drag.," Although this metal gas also spreads outward from the sublimation radius (Melis 2010) and under certain circumstances can substantially affect debris disk evolution (Rafikov 2011b), in this work, following R11, we concentrate only on effects associated with the PR drag."
 Thus. here we neelect presence of the eas exterior of Fouad its iuteraction with the debris disk.," Thus, here we neglect presence of the gas exterior of $R_s$ and its interaction with the debris disk."
 According to Rafikov (2011b) this is a valid approxiuation as long as the viscous timescale in the gaseous disk is shorter than the time on which this disk cau be replenished by the sublimation of debris., According to Rafikov (2011b) this is a valid approximation as long as the viscous timescale in the gaseous disk is shorter than the time on which this disk can be replenished by the sublimation of debris.
" Then the eas does not acciuulate at rzFR, aud its density is always low cuough for the eas drag to not affect the debris disk appreciably.", Then the gas does not accumulate at $r\approx R_{in}$ and its density is always low enough for the gas drag to not affect the debris disk appreciably.
 We characterize the disk at cach point by its surface density X(r) aud optical depth where p ds the bulk ceusity of particles aud «is their characteristic size., We characterize the disk at each point by its surface density $\Sigma(r)$ and optical depth = where $\rho$ is the bulk density of particles and $a$ is their characteristic size.
 The particle size e is not well constrained by the existing observations. but its actual value becomes important only for low mass disks with stnall 7. see §3..," The particle size $a$ is not well constrained by the existing observations, but its actual value becomes important only for low mass disks with small $\tau$, see \ref{sect:low}."
" Following Friedjung (1985) aud RIL we represent iracdiation of the disk by the WD using a single incidence auele à at each radius + from the disk (the so-called ""h]unp-post dhunination model described iu R11): attr) where R&R, is the radius of the star.", Following Friedjung (1985) and R11 we represent irradiation of the disk by the WD using a single incidence angle $\alpha$ at each radius $r$ from the disk (the so-called “lamp-post” illumination model described in R11): (r) where $R_{\star}$ is the radius of the star.
 We can then introduce 7| according to the following definition:, We can then introduce $\tau_\parallel$ according to the following definition:.
 This variable is very important for our subsequent analysis., This variable is very important for our subsequent analysis.
 In the following we will call the disk optically thick or thin based ou whether 7) aud uot 7 is greater or sunaller than uit., In the following we will call the disk optically thick or thin based on whether $\tpar$ and not $\tau$ is greater or smaller than unity.
" R11 demoustrated that the mass accretion rate AL through the disk of solids dviven by the PR drag may be written as Tere L, is the WD Iuuinuosity. € is the speed of light and function eives the fraction of incoming starlight that is absorbed by thedisk."," R11 demonstrated that the mass accretion rate $\dot M$ through the disk of solids driven by the PR drag may be written as M(r)= (r) Here $L_{\star}$ is the WD luminosity, $c$ is the speed of light and function _r = 1 - gives the fraction of incoming starlight that is absorbed by thedisk."
 It is iustructive to examine different hnuuits of the expression (5))., It is instructive to examine different limits of the expression \ref{eq:mdot}) ).
 If the disk isoptically thick to iucideut stellar radiation. 7)291 (which cannot be the case everywhere at all times. as we will see below). then the," If the disk isoptically thick to incident stellar radiation, $\tau_\parallel\gg 1$ (which cannot be the case everywhere at all times, as we will see below), then the"
(2008).,.
". In order to take into account the isotopic effect. we correct the energies of the P,» and of the Ps;s levels of “Lit using the values of the isotopic shifts in the Dj and Ds lines listed in Table 1.."," In order to take into account the isotopic effect, we correct the energies of the$^2$ $_{1/2}$ and of the $^2$ $_{3/2}$ levels of $^6$ Li using the values of the isotopic shifts in the $_1$ and $_2$ lines listed in Table \ref{tab:phys-prop}."
 The HFS Hamiltonian. describing the interaction between the nuclear spin and the electronic angular momentum. can be expressed as a series of electric and magnetic multipoles (see.forexample.Kopfermann1958).," The HFS Hamiltonian, describing the interaction between the nuclear spin and the electronic angular momentum, can be expressed as a series of electric and magnetic multipoles \citep[see, for example,][]{Kop58}."
 We calculate the energies of the HFS F-levels using the values of the magnetic dipole and of the electric quadrupole HFS constants (usually indicated with the symbols <A and 8. respectively) listed in Table I..," We calculate the energies of the HFS $F$ -levels using the values of the magnetic dipole and of the electric quadrupole HFS constants (usually indicated with the symbols $\mathcal{A}$ and $\mathcal{B}$, respectively) listed in Table \ref{tab:phys-prop}."
 We recall that in the absence of magnetic fields. using Dirac’s notation. the energy eigenvectors can be written in the form ja//Ff>. where « represents a set of inner quantum numbers (specifying the configuration and. if the atomic system is deseribed by the L-S coupling scheme. the total electronic orbital and spin angular momenta). / is the total electronic angular momentum quantum number. while F and f are the quantum numbers associated with the total angular momentum operator (electronic plus nuclear: and with its projection along the quantization axis. respectively.," We recall that in the absence of magnetic fields, using Dirac's notation, the energy eigenvectors can be written in the form $|\alpha J I F f >$, where $\alpha$ represents a set of inner quantum numbers (specifying the configuration and, if the atomic system is described by the $L$ $S$ coupling scheme, the total electronic orbital and spin angular momenta), $J$ is the total electronic angular momentum quantum number, while $F$ and $f$ are the quantum numbers associated with the total angular momentum operator (electronic plus nuclear: ), and with its projection along the quantization axis, respectively."
"ΤΠ). The Grotrian diagrams showing the various HFS F-levels of the two isotopes. and the HFS components of the D, and D» lines are shown in the upper panel of Figure 2.."," The Grotrian diagrams showing the various HFS $F$ -levels of the two isotopes, and the HFS components of the $_1$ and $_2$ lines are shown in the upper panel of Figure \ref{fig:grotrian}."
 In the lower panels of Figure 2. the laboratory positions of the various HFS components are shown., In the lower panels of Figure \ref{fig:grotrian} the laboratory positions of the various HFS components are shown.
" Since the isotopic shifts are of the same order of magnitude às the frequency separation between the two D-lines. the D, line of “Li falls almost at the same wavelength as the D» line of °Li (see panels and c of Figure 2)."," Since the isotopic shifts are of the same order of magnitude as the frequency separation between the two D-lines, the $_1$ line of $^7$ Li falls almost at the same wavelength as the $_2$ line of $^6$ Li (see panels and of Figure \ref{fig:grotrian}) )."
 We observe that in both isotopes the ground level splits into two HFS F-levels., We observe that in both isotopes the ground level splits into two HFS $F$ -levels.
 The splitting between these two levels is much larger than that, The splitting between these two levels is much larger than that
"instantly removed as it arrives, while (ii) the outer grid point is placed at such a large radius, typically 1015 cm, that during the course of the run the outer edge of the spreading fall-back disk never reaches it.","instantly removed as it arrives, while (ii) the outer grid point is placed at such a large radius, typically $10^{13}$ cm, that during the course of the run the outer edge of the spreading fall-back disk never reaches it."
 The range in disk radii necessitates ~large1500dynamic—3000 grid points., The large dynamic range in disk radii $r_{\rm outer}/r_{\rm inner}$ necessitates $\sim1500-3000$ grid points.
" In addition, no router/Tinnerfresh material is added during a run."," In addition, no fresh material is added during a run."
" Thus the evolution is set entirely by gradients within the disk, unlike the standard Shakura-Sunyaev disk fed at a constant rate in the outer edge which approaches a steady-state M(r)= constant with time."," Thus the evolution is set entirely by gradients within the disk, unlike the standard Shakura-Sunyaev disk fed at a constant rate in the outer edge which approaches a steady-state ${\dot M}(r)=$ constant with time."
" -0.065 cm LGRBs are thought to be associated with the explosions of massive stars (MacFadyen Woosley 1999, Woosley Heger 2006)."," -0.065 cm LGRBs are thought to be associated with the explosions of massive stars (MacFadyen Woosley 1999, Woosley Heger 2006)."
 The initial failure of the SN is the reason for the GRB in the collapsar model., The initial failure of the SN is the reason for the GRB in the collapsar model.
" The hosts for IGRBs tend to be subluminous, irregular galaxies rich in star formation (Fruchter et al."," The hosts for lGRBs tend to be subluminous, irregular galaxies rich in star formation (Fruchter et al."
 2006)., 2006).
 If the long-term X-ray light curves of GRBs are indicative of feeding from a fall-back accretion, If the long-term X-ray light curves of GRBs are indicative of feeding from a fall-back accretion
The damping of Neptune’s eccentricity ew or inclination iw affects the secular excitation of the planetesimals in two regimes: slow and fast.,The damping of Neptune's eccentricity $e_N$ or inclination $i_N$ affects the secular excitation of the planetesimals in two regimes: slow and fast.
" We summarize constraints on Neptune’s eccentricity and inclination in Table 1 In the slow regime, ey or iw damps on a timescale Το or τι, respectively, longer than the time (527/gKBO) for e or i to reach its maximum value."," We summarize constraints on Neptune's eccentricity and inclination in Table \ref{tab:constrain}
 In the slow regime, $e_N$ or $i_N$ damps on a timescale $\tau_e$ or $\tau_i$, respectively, longer than the time $\frac{1}{2} 2\pi/g_{\rm KBO}$ ) for $e$ or $i$ to reach its maximum value."
" Because each planetesimal has an initial =0)0, its free inclination ifree and eccentricityi(£=0) ege,=e(t are set by Neptune’s initial en(t=0) and in(t=0)."," Because each planetesimal has an initial $i (t=0) = e (t=0)= 0$ , its free inclination $\ifree$ and eccentricity $\efree$ are set by Neptune's initial $e_N (t=0)$ and $i_N (t=0)$."
" In this slow regime, the planetesimal's ife¢ and ege, are conserved."," In this slow regime, the planetesimal's $\ifree$ and $\efree$ are conserved."
" As ey and iy damp, the planetesimal’s forced eccentricity eforceqa and inclination iforceq decrease, and the total eccentricity e and inclination i of the planetesimal approach ege, and 5free-"," As $e_N$ and $i_N$ damp, the planetesimal's forced eccentricity $\eforced$ and inclination $\iforced$ decrease, and the total eccentricity $e$ and inclination $i$ of the planetesimal approach $\efree$ and $\ifree$."
" Thus, in the slow regime, the planetesimals will evolve to a value below i«6? if iw<6°."," Thus, in the slow regime, the planetesimals will evolve to a value below $i < 6^\circ$ if $i_N < 6^\circ$."
" To satisfy our conservative criteria established in Section 3.1,, which requires planetesimals with 42.5«a45 AU to remain at e«0.1, Neptune's eccentricity must stay below 0.18 at 20 AU and 0.12 at 30 AU."," To satisfy our conservative criteria established in Section \ref{sec:obs}, which requires planetesimals with $42.5 < a < 45$ AU to remain at $e<0.1$, Neptune's eccentricity must stay below 0.18 at 20 AU and 0.12 at 30 AU."
" Thus in the slow damping case, there is a strong constraint 1)) on the maximum eccentricity and inclination at(Table which Neptune can remain over long timescales."," Thus in the slow damping case, there is a strong constraint (Table \ref{tab:constrain}) ) on the maximum eccentricity and inclination at which Neptune can remain over long timescales."
 Note that these values are twice the values given in Section 4.2.., Note that these values are twice the values given in Section \ref{subsec:evolve}.
" This is because in the slow damping regime, the planetesimals will evolve to Cfree=Cforcea(t and Uree=forced0), whereas if ey and iy remain0) high indefinitely, the(t planetesimals’ e and i continue to oscillate, reaching a maximum of 2€forced and 2itorced-"," This is because in the slow damping regime, the planetesimals will evolve to $\efree = \eforced(t=0)$ and $\ifree = \iforced(t=0)$, whereas if $e_N$ and $i_N$ remain high indefinitely, the planetesimals' $e$ and $i$ continue to oscillate, reaching a maximum of $2\eforced$ and $2\iforced$."
" If ew and iy damp in the fast regime, on a timescale shorter than the secular excitation time, ifree and etree are not conserved."," If $e_N$ and $i_N$ damp in the fast regime, on a timescale shorter than the secular excitation time, $\ifree$ and $\efree$ are not conserved."
 The planetesimal's total e and i are frozen at the values they reach after approximately one damping time., The planetesimal's total $e$ and $i$ are frozen at the values they reach after approximately one damping time.
 Fig., Fig.
 9 illustrates the behavior of the planetesimals in this regime in integrations in which Neptune's eccentricity orinclination damps., \ref{fig:idamp} illustrates the behavior of the planetesimals in this regime in integrations in which Neptune's eccentricity orinclination damps.
" Neptune's orbit could have been even more eccentric and inclined than in the slow regime if ey and iy damped quickly (Table 1,, right column)."," Neptune's orbit could have been even more eccentric and inclined than in the slow regime if $e_N$ and $i_N$ damped quickly (Table \ref{tab:constrain}, right column)."
" If the planetesimal has not yet reached the maximum of its secular cycle after one damping time, instead of converging to the ege, and ifree Set by initial conditions, the planetesimal evolves to €fnal=free and gna]=freesin(gknoTi) (see?,foradetailedsin(gKBOTe)explanationand"," If the planetesimal has not yet reached the maximum of its secular cycle after one damping time, instead of converging to the $\efree$ and $\ifree$ set by initial conditions, the planetesimal evolves to $e_{\rm final} = \efree \sin(\gkbo \tau_e )$ and $i_{\rm final} =\ifree \sin(\gkbo \tau_i )$ \citep[see][for a detailed explanation and justification]{2012D}."
 Consider again a planetesimal at 42.5 AU., Consider again a planetesimal at 42.5 AU.
" If justification)..Neptune's eccentricity and inclination damp on timescale of 7= 0.32 Myr,the final eccentricity and ainclination of the planetesimal are reduced by a factorof sin(gkgoT)= compared to the slow damping case."," If Neptune's eccentricity and inclination damp on a timescale of $\tau = $ 0.32 Myr,the final eccentricity and inclination of the planetesimal are reduced by a factorof $\sin(\gkbo \tau) = 0.5$ compared to the slow damping case."
" Thus the planetesimals will evolve to a value below i«6? if iw«6°/0.5= 12°.To satisfy our conservative criteria established in Section 3.1,, which requires planetesimals with 42.5«a45 AU to remain at e« 0.1, ey must stay below 0.18/0.5—0.36 at 20 AU and 0.12/0.5—0.24 "," Thus the planetesimals will evolve to a value below $i < 6^\circ$ if $i_N < 6^\circ/0.5 = 12^\circ$ To satisfy our conservative criteria established in Section \ref{sec:obs}, , which requires planetesimals with $42.5 < a < 45$ AU to remain at $e < 0.1$ $e_N$ must stay below $0.18/0.5 = 0.36$ at 20 AU and $0.12/0.5 = 0.24$ "
about the absolute level of obscuration (the embedded prolostars show comparable silicate feature depths).,about the absolute level of obscuration (the embedded protostars show comparable silicate feature depths).
 An alternative explanation might be that deeply obsenrecd ULIRGs and our z: 422 sources simply have a higher proportion of hydrocarbons., An alternative explanation might be that deeply obscured ULIRGs and our $z$ $\sim$ 2 sources simply have a higher proportion of hydrocarbons.
 For example. bombardinent with II atoms can hydrogenate amorphous carbon grains increasing the ILAC-to-silicate ratio (seee.g.Grishko&Dulev2000;Duleyetal. 2005).," For example, bombardment with H atoms can hydrogenate amorphous carbon grains increasing the HAC-to-silicate ratio \citep[see e.g.][]{gd00,duley05}."
. Various other processes can be important. s...," Various other processes can be important, s.a."
 UV radiation processing of ice mantles can lead to relractory materials on (he grain surfaces (hat lead to the aabsorption feature (Greenbergetal.1995).. consistent wilh the somewhat weaker ice features.," UV radiation processing of ice mantles can lead to refractory materials on the grain surfaces that lead to the absorption feature \citep{greenberg95}, consistent with the somewhat weaker ice features."
 Ultimately. the degree of WAC absorption depends on the balance of processes that support hydrocarbon generation to those that suppress it (s.a.," Ultimately, the degree of HAC absorption depends on the balance of processes that support hydrocarbon generation to those that suppress it (s.a."
 converte hydrocarbons (o aromatics)., converting hydrocarbons to aromatics).
 It is not unreasonable to suppose that such processes might be more efficient in our sources (han the tvpical Milkv Way sources., It is not unreasonable to suppose that such processes might be more efficient in our sources than the typical Milky Way sources.
 The geometric explanation is simpler ancl therefore favored. however. a difference in composition cannot be excluded.," The geometric explanation is simpler and therefore favored, however, a difference in composition cannot be excluded."
 refice;ZshowstheratioofIhe3.0 Πορ feature optical depth to the ssilicate dust optical depth., \\ref{ice_si} shows the ratio of the ice feature optical depth to the silicate dust optical depth.
 As before. we compare our sample with both local ULIRGs and ihe data for MW stars.," As before, we compare our sample with both local ULIRGs and the data for MW stars."
 We find that unlike the case lor the ILAC-to-silicate ratio which is remarkably similar across [or all available MW. sources. the ice-to-silieate ratio shows a wide spread of more (han an order of magnitude.," We find that unlike the case for the HAC-to-silicate ratio which is remarkably similar across for all available MW sources, the ice-to-silicate ratio shows a wide spread of more than an order of magnitude."
 This ratio is strongly. dependent on the ice mantle (hickuess (e.g.Ossenkopf&Henning1994:Zinoveva2005).. but radiative (ransler details following the arguments presented in (he previous section likely dominate.," This ratio is strongly dependent on the ice mantle thickness \citep[e.g.][]{oss94,zinoveva05}, but radiative transfer details following the arguments presented in the previous section likely dominate."
 When we consider only the sources with red sspectra. and where both ice and silicate optical depths are available. we find that IRASO8572+3915 has T.9/7o.7 00.08. and IRAS19254-7245 has 744/794; 00.15.," When we consider only the sources with red spectra, and where both ice and silicate optical depths are available, we find that IRAS08572+3915 has $\tau_{3.0}/\tau_{9.7}$ 0.08, and IRAS19254-7245 has $\tau_{3.0}/\tau_{9.7}$ 0.15."
 Although a much Larger sampling is needed. (his suggests (especially in conjunction wilh our own sample) Chat sources with redder sslopes have lower observed ssilicate ratios.," Although a much larger sampling is needed, this suggests (especially in conjunction with our own sample) that sources with redder slopes have lower observed silicate ratios."
[daG65s83 map (Fig. 10)) (,6583 map (Fig. \ref{fig:otherlines}) ) (
for which the surrounding continuum is essentially featureless).,for which the surrounding continuum is essentially featureless).
 Phe match is excellent (see Fig. 11)).," The match is excellent (see Fig. \ref{fig:NImap}) ),"
 particularly when considering the low Lo-noise ratio of the residual Ica55200 line spectra., particularly when considering the low signal-to-noise ratio of the residual 5200 line spectra.
 The rratio ranges from 21 at the centre to z1.4-1.5 in the arms. corresponding to electron densities IN. of 500 aand less than 100 ((low density. limit). respectively.," The / ratio ranges from $\simeq$ 1 at the centre to $\simeq$ 1.4-1.5 in the arms, corresponding to electron densities $N_e$ of 500 and less than 100 (low density limit), respectively."
 Lhe rratio ds roughly constant over the Ποιά of view. with values between 2 and 2.2.," The / ratio is roughly constant over the field of view, with values between 2 and 2.2."
 This seems to contracict the measurements made by Zeilinger et al. (, This seems to contradict the measurements made by Zeilinger et al. (
1996). who reported vvalues as high as SN at the centre. a factor of two higher han ours at the centre.,"1996), who reported / values as high as 8 at the centre, a factor of two higher than ours at the centre."
 We suggest that this cliscrepaney is mainlv due to the fact that Zeilinger et al. (, We suggest that this discrepancy is mainly due to the fact that Zeilinger et al. (
1996). cid not flux-calibrate their spectra (which were taken for the »urpose of measuring eas kinematics) anc did not correct hem for the underlving (Ho) stellar absorption.,1996) did not flux-calibrate their spectra (which were taken for the purpose of measuring gas kinematics) and did not correct them for the underlying $\alpha$ ) stellar absorption.
 The Bux distribution of the lines is less centrally peaked than that of the lines. with the rratio ranging from 0.4 at the location of the nucleus to 7«0.65 in the armis.," The flux distribution of the lines is less centrally peaked than that of the lines, with the / ratio ranging from $\simeq$ 0.4 at the location of the nucleus to $\simeq$ 0.65 in the arms."
 This is usually interpreted as a decrease of the comission in the dense nuclear regions. due to the lower critical electronic densities of the ines with respect to the ine doublet. (NO=1.9 Wwe. 1: and 5 Tor the u]AGTIT.. aand ines. respectively).," This is usually interpreted as a decrease of the emission in the dense nuclear regions, due to the lower critical electronic densities of the lines with respect to the line doublet $N_e^{crit} = 
1.9$ $\times$, 1.2 $\times$ and 8 $\times$ for the , and lines, respectively)."
 The flux integrated over à rraciius from the nucleus is c 1.9. is ΑΝ μα ο Ετος is W contribution from the central unresolved. peak.," The flux integrated over a radius from the nucleus is $\simeq$ 1.9 $\times$ $^2$ W, with a $\simeq$ 4.7 $\times$ $^2$ W contribution from the central unresolved peak."
 Assuming a uniform electron density IN. = 100 aand a pure hydrogen gas. this corresponds to a mass of ionized.. σας in. the arms of ⋅⋅GS ssolar masses.," Assuming a uniform electron density $N_e$ = 100 and a pure hydrogen gas, this corresponds to a mass of ionized gas in the arms of 6.8 $\times$ solar masses."
 For the central unresolved peak and assuming this time an electron density of 500 we obtain à mass of ionized gas of 4.43. ssolar masses.," For the central unresolved peak and assuming this time an electron density of 500, we obtain a mass of ionized gas of 4.4 $\times$ solar masses."
 Note that the quoted ionized eas masses are inversely proportional to the value of IN..., Note that the quoted ionized gas masses are inversely proportional to the value of $N_e$.
 The emission-line velocity and velocity dispersion. maps are shown in Fie. 12.., The emission-line velocity and velocity dispersion maps are shown in Fig. \ref{fig:gaskin}.
 The velocity field exhibits strong disturbances following the spiral-Hike distribution of the gas., The velocity field exhibits strong disturbances following the spiral-like distribution of the gas.
 There is a strong hint lor eas streaming on the inner side of the south-western arm. where the emission lines exhibit a complex structure probably resulting from the superposition of several kinematical components (Fig. 9)).," There is a strong hint for gas streaming on the inner side of the south-western arm, where the emission lines exhibit a complex structure probably resulting from the superposition of several kinematical components (Fig. \ref{fig:NIIwithspec}) )."
 This widening of the lines (m4.250 13) is also observed on the inner side of the north-castern arm. as emphasized in the dispersion map (Fig. 12)).," This widening of the lines $\sigma_{\rm gas} > 250$ ) is also observed on the inner side of the north-eastern arm, as emphasized in the dispersion map (Fig. \ref{fig:gaskin}) )."
 Using the high-resolution. ΛΕΡΟΣ narrow-banel image of NGC 2974 shown in Fig. 3..," Using the high-resolution /WFPC2 narrow-band image of NGC 2974 shown in Fig. \ref{fig:HSTimages},"
 we applied the method pioneered by Ferruit (1999) to deconvolve our merged clelatacube (see also Emisellem Ferruit 2000)., we applied the method pioneered by Ferruit (1999) to deconvolve our merged datacube (see also Emsellem Ferruit 2000).
 Pwo methocs were tested: a pure. Lucy. deconvolution. and a weakly euicded” Luey deconvolution. in which the narrow-band HST/NVPC2 image is used to constrain the integrated Lux in the deatacube.," Two methods were tested: a pure Lucy deconvolution, and a “weakly guided” Lucy deconvolution in which the narrow-band /WFPC2 image is used to constrain the integrated flux in the datacube."
 In both cases. we performed 300 iterations after which the gain in resolution was found not to compensate the increase in noise level.," In both cases, we performed 300 iterations after which the gain in resolution was found not to compensate the increase in noise level."
 Dilferences between the results of the two deconvolutions were not significant. except for a slight reduction of the high-frequeney features in the weakly euiced case.," Differences between the results of the two deconvolutions were not significant, except for a slight reduction of the high-frequency features in the weakly guided case."
 We therefore favour the latter. the analysis of which will be presented here.," We therefore favour the latter, the analysis of which will be presented here."
 The final resolution of the cdeconvolved clatacube. evaluated from the central peak (unresolved in the WEPC2 |Lea image). isΠΡΙ HM.," The final resolution of the deconvolved datacube, evaluated from the central peak (unresolved in the WFPC2 $+$ image), is $0\farcs35$ FWHM."
" ALapso fthedceconvol veddatacube. namelythe aandlla [flidistribition. thegasveloci yanddispersionmaps. areshouniniig, 13.."," Maps of the deconvolved datacube, namely the and flux distribution, the gas velocity and dispersion maps, are shown in Fig. \ref{fig:decmaps}."
 The two spiral arms are nicely revealed. as well as the central concentration which is now highly: contrasted.," The two spiral arms are nicely revealed, as well as the central concentration which is now highly contrasted."
 The velocity field shows strong streaming motions along the arms. with peak velocities of 211 and 264+.," The velocity field shows strong streaming motions along the arms, with peak velocities of $-$ 211 and 264."
 More interestingly. the dispersion is very high on the inner side of both arms. confirming the picture seen before deconvolution (sce Fig. 12)).," More interestingly, the dispersion is very high on the inner side of both arms, confirming the picture seen before deconvolution (see Fig. \ref{fig:gaskin}) ),"
 reaching values greater than 300., reaching values greater than 300.
.. The eas kinematics will be further discussed in Sect., The gas kinematics will be further discussed in Sect.
 4.3. in view of a density wave model., \ref{sec:wave} in view of a density wave model.
 In this Section. we present new cvnamical models for the stellar and. gas components in the central region of NGC 2074. using our new two-dimensional data as well as published. kinematics.," In this Section, we present new dynamical models for the stellar and gas components in the central region of NGC 2974, using our new two-dimensional data as well as published kinematics."
 The first step in this modelling process is to obtain a realistic threec-dimensional representation of the luminosity and mass distribution of the galaxy [from the very centre to the outer region., The first step in this modelling process is to obtain a realistic three-dimensional representation of the luminosity and mass distribution of the galaxy from the very centre to the outer region.
 We used the Multi-Gaussian. Expansion method. (Monnet. Bacon Emsellem1992: Emisellen 1994) to build a photometric for the cleconvolved surface. brightness of Νας 2974.," We used the Multi-Gaussian Expansion method (Monnet, Bacon Emsellem1992; Emsellem 1994) to build a photometric for the deconvolved surface brightness of NGC 2974."
 the combination of a ground-based. £ band image taken at, the combination of a ground-based $I$ band image taken at
formed in the wake of the runaway star DN.,formed in the wake of the runaway star BN.
 From the proper motion of BN and the projected separation from the Northern tip of Stream X we can infer a timescale of 200 vr., From the proper motion of BN and the projected separation from the Northern tip of Stream A we can infer a timescale of 200 yr.
 This may correspon to à cooling time. a formation time for OLL or a time for population inversion to be established Following the passage of BN.," This may correspond to a cooling time, a formation time for OH, or a time for population inversion to be established following the passage of BN."
 Fie., Fig.
 l shows tha the proper motions of BN ancl sources ] and n project back to à position on the sky near the base of Stream A. in a reeion largely clear of OLL masers.," \ref{ra-dec} shows that the proper motions of BN and sources I and n project back to a position on the sky near the base of Stream A, in a region largely clear of OH masers."
 This position is significanty displaced 7 aresec Northwest of the centre of the OLI maser torus., This position is significantly displaced $\sim$ 4 arcsec Northwest of the centre of the OH maser torus.
 I has been suggested that BN and sources Land n originally belonged to a multiple stellar system that. clisintegrated 7500. vr ago., It has been suggested that BN and sources I and n originally belonged to a multiple stellar system that disintegrated $\sim$ 500 yr ago.
 The disintegration could have due to a close dvnamical interaction. as suggested bv Gómez et al. (," The disintegration could have due to a close dynamical interaction, as suggested by Gómmez et al. ("
in. press). or it could have been due to a merger event that also produced the molecular outflow. as suggested. by Bally Zinnecker (2005).,"in press), or it could have been due to a merger event that also produced the molecular outflow, as suggested by Bally Zinnecker (2005)."
 Alternatively. Tan (2004) has proposed that BN was ejected [rom the 4! Ori € system ~4000 vr ago.," Alternatively, Tan (2004) has proposed that BN was ejected from the $\theta^{1}$ Ori C system $\sim$ 4000 yr ago."
 Our data do not distinguish unambiguously between these possibilities., Our data do not distinguish unambiguously between these possibilities.
 Llowever the fact that the large-scale OLL maser torus is centred. on source ] slightly favours Tan's scenario. with BN being a passing runaway from the 6+ Ori C svsten.," However the fact that the large-scale OH maser torus is centred on source I slightly favours Tan's scenario, with BN being a passing runaway from the $\theta^{1}$ Ori C system."
 The other large-scale feature Are D encloses Hic6. which is one of the cooler mid-LHt sources. with polarization that is consistent with external illumination and with no evidence ob embedded bright stars (Shuping et al.," The other large-scale feature Arc B encloses IRc6, which is one of the cooler mid-IR sources, with polarization that is consistent with external illumination and with no evidence of embedded bright stars (Shuping et al."
 2004 and references therein)., 2004 and references therein).
 This suggests that Are D might be associated with a photodissociation zone around UG., This suggests that Arc B might be associated with a photodissociation zone around IRc6.
" In further support of this there is strong emission from CIIGCII at the position of Htc6. implying densities of at. leas 10"" ? (Wilner. Wright Plambeck 1996)."," In further support of this there is strong emission from $_{3}$ CH at the position of IRc6, implying densities of at least $^{6}$ $^{-3}$ (Wilner, Wright Plambeck 1996)."
 The large-scale maser structures found in Orion-BN/IXL are similar in scale to OLL maser structures recently reported in W3(COLD., The large-scale maser structures found in Orion-BN/KL are similar in scale to OH maser structures recently reported in W3(OH).
 Wright et al. (, Wright et al. (
2004a.b) noted several ares of 18-cm masers. which they interpreted as propagating shocks.,"2004a,b) noted several arcs of 18-cm masers, which they interpreted as propagating shocks."
 Llarvey-Smiuth Cohen (2005) found a low brightness filament of excited. OLL 4765-MlIz emission. stretching for ~2200 au and clearly related. in its morphology to some of the erounc-state OLL ares at. 18-0. wavelength., Harvey-Smith Cohen (2005) found a low brightness filament of excited OH 4765-MHz emission stretching for $\sim$ 2200 au and clearly related in its morphology to some of the ground-state OH arcs at 18-cm wavelength.
 The structures seen in Orion are similar in linear scale., The structures seen in Orion are similar in linear scale.
 The individual maser spots in Stream A and Are B are. well separated on the sky for the most part. but are nevertheless likely to be simply the high-gain cores of an extended stream of maser emission.," The individual maser spots in Stream A and Arc B are well separated on the sky for the most part, but are nevertheless likely to be simply the high-gain cores of an extended stream of maser emission."
 The tvpical flux densities of ~O.1 Jv correspond to brightness temperatures ofat least ~3. 107 Ix. All these large-scale features in Orion and W3(OLLD) are relatively weak and therefore below the sensitivies of earlier surveys. for the most part.," The typical flux densities of $\sim$ 0.1 Jy correspond to brightness temperatures of at least $\sim$ $\times$ $^{5}$ K. All these large-scale features in Orion and W3(OH) are relatively weak and therefore below the sensitivies of earlier surveys, for the most part."
 Deeper observations ofother well-known OLL maser sources are needed to establish just how common such features are., Deeper observations of other well-known OH maser sources are needed to establish just how common such features are.
 The ΟΗ 1612-Mllz masers have ao more widespread distribution. than the other ΟΙ masers. and cilferent kinematics (Section 3.2)).," The OH 1612-MHz masers have a more widespread distribution than the other OH masers, and different kinematics (Section \ref{kinematics}) )."
 This suggests that they trace a region with dillerent physical conditions., This suggests that they trace a region with different physical conditions.
" Gray. Field Docl (1992) eive the following conditions for strong 1612-MllIz masers: molecular hydrogen density ng, 5 nog 60 eas kinetic temperature {ος Wk. dust emperature at maser site Zi 30 Ix. external radiation field Tí SOW and. velocity shift AV 2.0 +."," Gray, Field Doel (1992) give the following conditions for strong 1612-MHz masers: molecular hydrogen density $n_{\rm H_{2}}$ $^{-3}$, $n_{\rm OH}$ 60 $^{-3}$, gas kinetic temperature $T_{\rm k}$ =30 K, dust temperature at maser site $T_{\rm d}$ 30 K, external radiation field $T_{\rm x}$ 80 K and velocity shift $\Delta V$ 2.0 $^{-1}$."
 This is cooler han tvpical for OLL masers. but is consistent with the ocation of these particular 1612-MlIz masers further than normal from the main source of infrared. luminosity.," This is cooler than typical for OH masers, but is consistent with the location of these particular 1612-MHz masers further than normal from the main source of infrared luminosity."
 “Phe velocity. eracient needed for strong maser action is also consistent with the association of these masers with shocked eas in the molecular outllow (Section 3.3.2))., The velocity gradient needed for strong maser action is also consistent with the association of these masers with shocked gas in the molecular outflow (Section \ref{nearIR}) ).
 We note a further possible positional association between the 1612-MlIz masers and the methanol 6.7-Cillz masers recently discovered. by Voronkoy et al. (, We note a further possible positional association between the 1612-MHz masers and the methanol 6.7-GHz masers recently discovered by Voronkov et al. (
2005).,2005).
 In Fig., In Fig.
 11 we show the positions ancl velocities of the two species., \ref{methanol} we show the positions and velocities of the two species.
" There is a clear region of overlap centred around RA (J2000) = 0535"" 14255. Dee. (92000) = -05°222/44599 and Yi,— [75 km s!."," There is a clear region of overlap centred around RA (J2000) = $^{\rm h}$ $^{\rm m}$ 5, Dec. (J2000) = 9 and $V_{\rm lsr}$ = +7.5 km $^{-1}$."
 The 6.7-Gllz positions have errors of ~2 arcsec., The 6.7-GHz positions have errors of $\sim$ 2 arcsec.
 Lt will be important. to make 6.7- measurements of higher precision to examine this correspondence more. closely., It will be important to make 6.7-GHz measurements of higher precision to examine this correspondence more closely.
 “Phe positions of 25-Cillz masers from Johnston et al. (, The positions of 25-GHz masers from Johnston et al. (
L997. 1992) are also shown in the figure for completeness.,"1997, 1992) are also shown in the figure for completeness."
 Only one of these falls in the region of interest., Only one of these falls in the region of interest.
 We note that there is no association with the OLI mainline masers., We note that there is no association with the OH mainline masers.
 This is consistent with the 25-CGllz masers being class E masers. which are thought to be collisionally pumped (cf.," This is consistent with the 25-GHz masers being class I masers, which are thought to be collisionally pumped (cf."
 Crage et al., Cragg et al.
 2002)., 2002).
 The 6.7-Gllz maser transition is the prototype class Lb maser. usually thought to be radiatively pumped.," The 6.7-GHz maser transition is the prototype class II maser, usually thought to be radiatively pumped."
 The 6.7-CGllz masers in Orion are of therefore of interest. because of their apparent association with 25-Gllz masers., The 6.7-GHz masers in Orion are of therefore of interest because of their apparent association with 25-GHz masers.
 Voronkov et al., Voronkov et al.
 have considered. the pumping requirements for the coexistence of both types of methanol maser and find. that both tvpes can occur simultaneously. at. low temperature (~60 Ix) and low molecular hydrogen density (107 em.?)., have considered the pumping requirements for the coexistence of both types of methanol maser and find that both types can occur simultaneously at low temperature $\sim$ 60 K) and low molecular hydrogen density $\sim$ $^{5}$ $^{-3}$ ).
 These conditions are not too cdissimilar to those needed for strong 1612-Mllz masers. as given earlier.," These conditions are not too dissimilar to those needed for strong 1612-MHz masers, as given earlier."
 In. summary. it appears that in Orion we may have the first examples of both methanol class HL and OLL ground. state masers located far from the main source of infrared luminosity. and. associated instead with the interaction between the molecular outflow and the surrounding gas.," In summary, it appears that in Orion we may have the first examples of both methanol class II and OH ground state masers located far from the main source of infrared luminosity, and associated instead with the interaction between the molecular outflow and the surrounding gas."
" The proplyvds originally designated LV. 16 within the Orion '""Trapezium. cluster are those most likely to exhibit. maser emission for they are irradiated by the intense field of the O6.5 star 65 Ori C. Of these LV. 1. now resolved as a binary proplvd (168326 NW SE) by ODell Wen (1904). and LV 2 (proplvd. 167-317 of O'Dell Wen 1994) have been most intensively observed. (Graham ct al."," The proplyds originally designated LV 1–6 within the Orion Trapezium cluster are those most likely to exhibit maser emission for they are irradiated by the intense field of the O6.5 star $\theta^{1}$ Ori C. Of these LV 1, now resolved as a binary proplyd (168–326 NW SE) by O'Dell Wen (1994), and LV 2 (proplyd 167-317 of O'Dell Wen 1994) have been most intensively observed (Graham et al."
 2002: Henney et al., 2002; Henney et al.
 2002 respectively)., 2002 respectively).
 The S. 101. em radius LY 2 was shown by Hennev et al. (, The $\times$ $^{14}$ cm radius LV 2 was shown by Henney et al. (
2002) to be irradiated by a fux of 10t em7 ! Lyman photons.,2002) to be irradiated by a flux of $\times$ $^{4}$ $^{-2}$ $^{-1}$ Lyman photons.
 These. produce an ionisee skin with, These produce an ionised skin with
particle acceleration case.,particle acceleration case.
 The harder spectrum could suggest non-linear shock effects in jets where the CR pressure is nonnegligible (Ellison2001)., The harder spectrum could suggest non-linear shock effects in jets where the CR pressure is nonnegligible \citep{ell01}.
. This 15 consistent with the fact that the necessary CR energy is comparable to the total energy of jets. E—Ej.," This is consistent with the fact that the necessary CR energy is comparable to the total energy of jets, $E \sim E_j$."
 In Figure 3.. we also show the synchrotron and IC emission from decaypositrons in. equation. (11)). which have an energy comparable to that of decay gamma-rays.," In Figure \ref{fig:flux}, we also show the synchrotron and IC emission from decaypositrons in equation \ref{eq:Cob+}) ), which have an energy comparable to that of decay gamma-rays."
" The positron spectrum is dN,xz,""dz, for Duacccy and dN,xoPde, for 7,«oe<Say.", The positron spectrum is $dN_e \propto \varepsilon_e^{-p} d\varepsilon_e$ for $\Gamma m_e c^2< \varepsilon_e < \varepsilon_p$ and $dN_e \propto \varepsilon_e^{-p-1} d\varepsilon_e$ for $\varepsilon_p < \varepsilon_e < \varepsilon_{\max}$.
" Thesynchrotron frequency is ο—007¢(2./0.1TeVY eV while the IC frequency is p~9ecypgCosΠω].109(5,/0.ITeV eV where we consider cosmic microwave background (CMB). às main target photons (lokaetal.2004)."," Thesynchrotron frequency is $\nu^{\rm syn}=q B \varepsilon_e^2/2\pi m_e^3 c^5
\sim 10^{-4} B_{-6} (\varepsilon_e/0.1{\rm TeV})^2$ eV while the IC frequency is $\nu^{\rm IC} \sim 9 \epsilon_{\rm CMB} (\varepsilon_e/m_e c^2)^2
\sim 10^8 (\varepsilon_e/0.1{\rm TeV})^2$ eV where we consider cosmic microwave background (CMB) as main target photons \citep{ioka04}."
". However the cooling time {=mzloepz.U—107(,/0.1TeVyUl yr. is. usually longer than the decay time £. in equation (13) for s,«sg~10 TeV where U is the total energy density of magnetic fields and CMB."," However the cooling time $t_c = 3 m_e^2 c^3/4 \sigma_T \varepsilon_{e} U
\sim 10^7 (\varepsilon_e/0.1{\rm TeV})^{-1} U_{-12}^{-1}$ yr is usually longer than the decay time $t_\gamma$ in equation \ref{eq:tga}) ) for $\varepsilon_e < \varepsilon_{\max} \sim 10$ TeV where $U$ is the total energy density of magnetic fields and CMB."
" Then the luminosity is suppressed by [fto1007(e10yr)c,/0.TTeV)U.45 compared with decay gamma-rays in equation. (15))."," Then the luminosity is suppressed by $t_\gamma/t_c \sim 10^{-2} (t_\gamma/10^5{\rm yr}) 
(\varepsilon_e/0.1{\rm TeV}) U_{-12}$ compared with decay gamma-rays in equation \ref{eq:lumi}) )."
 This is favorable for the interpretation of such sources as TeV unlDs., This is favorable for the interpretation of such sources as TeV unIDs.
 Note that the ~eV photons by decay positrons come from an extended region in. which the optical background dominates the remnant flux., Note that the $\sim$ eV photons by decay positrons come from an extended region in which the optical background dominates the remnant flux.
 The accelerated RI CRs may suffer the adiabatic energy losses during the expansion of the remnant (Rachen&Mészáros 1998).. which will greatly suppress the RI emission.," The accelerated RI CRs may suffer the adiabatic energy losses during the expansion of the remnant \citep{Rachen:1998fd}, which will greatly suppress the RI emission."
 This is a potential problem for the RI decay model., This is a potential problem for the RI decay model.
 However the CR escape from a remnant is not fully understood yet., However the CR escape from a remnant is not fully understood yet.
 For instance. it is common to assume the free escape of CRs in models where the GRB reverse shocks are the sites for the ultra high energy CR production (e.g..Waxman2006;etal. 2008)..," For instance, it is common to assume the free escape of CRs in models where the GRB reverse shocks are the sites for the ultra high energy CR production \citep[e.g.,][]{Waxman:2004ez,minn08}. ."
 In the same sense. the RI decay model is a viable possibility for TeV unIDs.," In the same sense, the RI decay model is a viable possibility for TeV unIDs."
 We have discussed the TeV gamma-ray emission from the z decay. 3 decay and the radio-isotope (RI) decay mechanisms in GRB and/or hypernova remnants. in. their possible role as TeV unIDs.," We have discussed the TeV gamma-ray emission from the $\pi^0$ decay, $\beta$ decay and the radio-isotope (RI) decay mechanisms in GRB and/or hypernova remnants, in their possible role as TeV unIDs."
 There is evidence that typical GRBs predominantly occur in galaxies with less metals than our own (Fruchteretal.2006:Stanek2006).. although the correlation between the host metallicity and the GRB energy Is not confirmed (Savaglioetal.2008a.b).," There is evidence that typical GRBs predominantly occur in galaxies with less metals than our own \citep{fru06,sta06}, although the correlation between the host metallicity and the GRB energy is not confirmed \citep{sav08a,sav08b}."
. On the other hand broad-lined SNe Ie also inhabit more metal-rich galaxies (Modjazetal.2008).. suggesting that at least hypernovae and possibly GRB/SNe with LL Jets can occur in our Galaxy.," On the other hand broad-lined SNe Ic also inhabit more metal-rich galaxies \citep{mod08}, suggesting that at least hypernovae and possibly GRB/SNe with LL jets can occur in our Galaxy."
 In addition. the evidence that GRBs occur in low metal regions could be biased because the GRBs in the metal rich region tend to have no optical afterglows due to the dust absorption (1.e.. dark GRBs. which ts about half of all GRBs).," In addition, the evidence that GRBs occur in low metal regions could be biased because the GRBs in the metal rich region tend to have no optical afterglows due to the dust absorption (i.e., dark GRBs, which is about half of all GRBs)."
 Then it becomes difficult to identify the hosts for measuring the metal abundance., Then it becomes difficult to identify the hosts for measuring the metal abundance.
 To discrimmate amongst these models. the imaging of the gamma-ray morphology would be useful.," To discriminate amongst these models, the imaging of the gamma-ray morphology would be useful."
" The z"" decay model predicts a shell structure. since the density inside the remnants is low, while the |. decay model predicts an elongated structure. and the RI decay model predicts a center-filled structure."," The $\pi^0$ decay model predicts a shell structure, since the density inside the remnants is low, while the $\beta$ decay model predicts an elongated structure, and the RI decay model predicts a center-filled structure."
 For remnant ages fa<10 yr. the SNR may be observed also at other wavelengths.," For remnant ages $t_{\rm age}< 10^5$ yr, the SNR may be observed also at other wavelengths."
" HESS J1731-347 may be such an example. which ts likely to be an old SNR with a large gamma-ray to radio flux ratio [ων/Fa,~33 (Tianetal.2008)."," HESS J1731-347 may be such an example, which is likely to be an old SNR with a large gamma-ray to radio flux ratio $F_{\rm TeV}/F_{\rm radio}\sim 33$ \citep{tian08}."
 HESS 11834-087 may be also an old remnant with an elongated gamma-ray emission outside the SNR (Aharonianetal.2006).. which could be interpreted in the conetxt of a ./-decay model (but see also Mukherjeeet(2008))).," HESS J1834-087 may be also an old remnant with an elongated gamma-ray emission outside the SNR \citep{aha06}, which could be interpreted in the conetxt of a $\beta$ -decay model (but see also \citet{muk08}) )."
 The x? decay model predicts detectable GeV emission if the spectral index of 2.1-2.4 continues down to the GeV region (see Fig. 3))., The $\pi^0$ decay model predicts detectable GeV emission if the spectral index of $2.1$ $2.4$ continues down to the GeV region (see Fig. \ref{fig:flux}) ).
" Other models predict relatively low levels of GeV emission (Fig.3::2006). although rare young remnants may be bright if ©,~20GeV(rIOyr) in the RI model."," Other models predict relatively low levels of GeV emission \citep[Fig.~\ref{fig:flux};, although rare young remnants may be bright if $\varepsilon_p \sim 20 {\rm GeV} (t/10^4 {\rm yr})$ in the RI model."
 This may be tested by the Fermi satellite., This may be tested by the Fermi satellite.
" Note that the GRB prompt and afterglow emission. will mask the very early RI decay emission, which becomes prominent later."," Note that the GRB prompt and afterglow emission will mask the very early RI decay emission, which becomes prominent later."
 The implied TeV neutrino flux (~ gamma-ray flux) is not enough for detection by current facilities., The implied TeV neutrino flux $\sim$ gamma-ray flux) is not enough for detection by current facilities.
 However. in thefuture one may in principle test models through the flavor ratio.," However, in thefuture one may in principle test models through the flavor ratio."
" We expect z.»ptt,>+rἘνtu, in the z decay model. no neutrinos in the .} decay model (since neutrinos are beamed and usually off-axis). and Re”Ee*p, in the RI decay model."," We expect $\pi^{+} \to \mu^{+} + \nu_{\mu}
\to e^+ + \nu_e + \bar \nu_{\mu} + \nu_{\mu}$ in the $\pi^0$ decay model, no neutrinos in the $\beta$ decay model (since neutrinos are beamed and usually off-axis), and ${}^{56}{\rm Co} \to {}^{56}{\rm Fe}^{*} + e^{+} + \nu_e$ in the RI decay model."
 As discussed at the end of 22.. the radio observations limit the (e/p)joc;v ratio to S10 in the z decay model.," As discussed at the end of \ref{sec:pi}, the radio observations limit the $(e/p)_{10{\rm GeV}}$ ratio to $\lesssim 10^{-3}$ in the $\pi^0$ decay model."
 For the RI decay model. the CRs need to freely escape from the acceleration site before suffering the adiabatic energy losses (see the end of ??)).," For the RI decay model, the CRs need to freely escape from the acceleration site before suffering the adiabatic energy losses (see the end of \ref{sec:ri}) )."
 The implied 8$CR energy budget is less than ~10%(10timesenergy)«(107rate) of the standard SN CR energy budget in our models.," The implied CR energy budget is less than $\sim 10\%
\sim (10\ {\rm times}\ {\rm energy}) \times (10^{-2}\ {\rm times}\ 
{\rm rate})$ of the standard SN CR energy budget in our models."
 The CRs above the knee at 3«I0P eV. however. could be produced mainly by extragalactic and/or Galactic GRBs/hypernovae (Wicketal. 2008)..," The CRs above the knee at $\sim 3 \times 10^{15}$ eV, however, could be produced mainly by extragalactic and/or Galactic GRBs/hypernovae \citep{wic04,minn06,wan07,bud08}. ."
 The chemical composition is increasingly richerin heavy nuclei above the knee ~3«10 eV to the second knee ~6«10! eV (Antonietal.2005:Abbasi 2005).. and possibly above ~3«10'? eV (Ungeretal. 2007)..," The chemical composition is increasingly richerin heavy nuclei above the knee $\sim 3 \times 10^{15}$ eV to the second knee $\sim 6 \times 10^{17}$ eV \citep{ant05,abb05}, , and possibly above $\sim 3 \times 10^{19}$ eV \citep{ung07}. ."
 These may be accelerated by Jets as in the RI decay model., These may be accelerated by jets as in the RI decay model.
 The GRB remnants may be also responsible. for the excesses of cosmic-ray positrons and electrons recently observed by the PAMELA and ATIC/PPB-BETS experiments, The GRB remnants may be also responsible for the excesses of cosmic-ray positrons and electrons recently observed by the PAMELA and ATIC/PPB-BETS experiments
The Cold Neutral Medii: (CNM) is easily studied with the 21-cu line absorption because the II opacity .OAXUIDS shove N(WD is the column density aud T the temperature.,"The Cold Neutral Medium (CNM) is easily studied with the 21-cm line absorption because the HI opacity $\propto {N({\rm HI}) \over T}$, where $N({\rm HI})$ is the column density and $T$ the temperature."
 The CNALD has been au inportaut subfield for the interstellar medi (ISM) in general aud radio astronomy in particular., The CNM has been an important subfield for the interstellar medium (ISM) in general and radio astronomy in particular.
 Theoretically the CNAL is understood as being oue of two thermal equilibria states of the neutral medimu (Fieldetal.1969:Melee&Os-triker1977:Wolfireetal. 2003).," Theoretically the CNM is understood as being one of two thermal equilibrium states of the neutral medium \citep{Field69,McKee77a,Wolfire03}."
". McIvee&Ostriker(1977) sununarized the expected properties for the CNAL clouds: a coustaut deusitv of 12 αμὉ, temperature of 80 I. cloud size between 0.1 aud 10 pe (with the mean value of 1.6 pc). the III cobuuu density ranging between 6.5s107? aud 1273«1079 cur2. with the mean value of 27<Lat? cm7."," \cite{McKee77a} summarized the expected properties for the CNM clouds: a constant density of 42 $^{-3}$, temperature of 80 K, cloud size between 0.4 and 10 pc (with the mean value of 1.6 pc), the HI column density ranging between $6.5\times10^{19}$ and $173\times10^{19}$ $^{-2}$, with the mean value of $27\times10^{19}$ $^{-2}$."
 Although thermal properties of the CNA aro VON well understood theoretically and observationally. its other aspects remain iuvsterious and not wellbstudied. primarily because of a paucity of observational knowledge.," Although thermal properties of the CNM are very well understood theoretically and observationally, its other aspects remain mysterious and not well-studied, primarily because of a paucity of observational knowledge."
 This observational paucity inchides such very basics as cloud shapes (morphology) aud the coblunn-deusity distribution: acconrpauiviug it is the theoretical paucity involving production mechanism of the CNAL. the dynamic equilibriuu between the CNAL and its enviroment (specifically. condensation. evaporation. aud turbulent musing). aud the time scales for formation aud destruction.," This observational paucity includes such very basics as cloud shapes (morphology) and the column-density distribution; accompanying it is the theoretical paucity involving production mechanism of the CNM, the dynamic equilibrium between the CNM and its environment (specifically, condensation, evaporation, and turbulent mixing), and the time scales for formation and destruction."
 Two important recent observational works are stimulating further work on this topic., Two important recent observational works are stimulating further work on this topic.
 One is the \Gllennimu Survey of 21-àà line absorption. of which he latest paper(Ileiles Trolaud 2005: ITT05) provides statistical distributions of the fundamental parameters: cohunn density. temperature. turbulence. aud magnetic field.," One is the Millennium Survey of 21-cm line absorption, of which the latest paper (Heiles Troland 2005; HT05) provides statistical distributions of the fundamental parameters: column density, temperature, turbulence, and magnetic field."
" The secoud is the detection of reliable. very weak "" ibsorption lines towards three high-latitude sources mBraun&Ἱναιοκα(2001) aud Braun [auckar DR05)."," The second is the detection of reliable, very weak HI absorption lines towards three high-latitude sources by \cite{Braun04} and Braun Kanekar (2005; BK05)."
 These latest very seusitive. HT absorption observations were undertaken with the Westerbork radio elescope. in the directions of four continuni sources. all located at high Calactic latitude (b~ 8073) aud relatively close to each other.," These latest very sensitive HI absorption observations were undertaken with the Westerbork radio telescope, in the directions of four continuum sources, all located at high Galactic latitude $b\sim80$ ) and relatively close to each other."
 The peak HI cussion iu hese cirections is van low. 25 I& oulv.," The peak HI emission in these directions is very low, 2–5 K only."
 For three out of our sources multiple absorption lines were detected. with he peak optical depth of only 0.1 to2%.," For three out of four sources multiple absorption lines were detected, with the peak optical depth of only 0.1 to."
. DIx05 discovered. cold IIT. clouds with the lowest III column densities ever detected for cold iuterstellar clouds. nore than 30 times lower than what is expected for the smallest CNALD clouds.," 	BK05 discovered cold HI clouds with the lowest HI column densities ever detected for cold interstellar clouds, more than 30 times lower than what is expected for the smallest CNM clouds."
 Fascinated by the discoveries of DI&05. and desiring to confirm their reality. we repeated heir observations for two sources; 3C286 and 3C287. with he Arecibo telescope.," Fascinated by the discoveries of BK05, and desiring to confirm their reality, we repeated their observations for two sources, 3C286 and 3C287, with the Arecibo telescope."
 We casily coufirmed fincdines by BISOS for 3€286., We easily confirmed findings by BK05 for 3C286.
 Against 30287 we see only a weak feature with too little signal/noise to iuclude im our discussion., Against 3C287 we see only a weak feature with too little signal/noise to include in our discussion.
 Iu this paper we report on the Arecibo observations of 30286 and 3C287 and discuss müplicatious of these findiugs., 	In this paper we report on the Arecibo observations of 3C286 and 3C287 and discuss implications of these findings.
 Our main ain is to cuphasize the existence of cold CNAL clouds with the IIT cola deusities ~1055 7. to discuss these. data in the context of previous observational results. and to initiate discussion on the possible origin of these clouds. as well as their importance in the ISAL.," Our main aim is to emphasize the existence of cold CNM clouds with the HI column densities $\sim10^{18}$ $^{-2}$, to discuss these data in the context of previous observational results, and to initiate discussion on the possible origin of these clouds, as well as their importance in the ISM."
 Iu Section 2 we briefly outline our observing and data processing methods., In Section 2 we briefly outline our observing and data processing methods.
 Section presents basic properties of cold HI clouds iu he directious of 3C286 and 30287., Section 3 presents basic properties of cold HI clouds in the directions of 3C286 and 3C287.
 À comparison of frese Clouds with CNM compoucuts forud iu previous observational studies is even m Section 1., A comparison of these clouds with CNM components found in previous observational studies is given in Section 4.
 Iu Section5 we discuss several different possibilities for he formation of these clouds., In Section 5 we discuss several different possibilities for the formation of these clouds.
 The observations were conducted with t1ο Arecibo, 	The observations were conducted with the Arecibo.
 Several hours of observiug tine were erauted at the discretion o “the Arecibo Observatory Director Sixto Gonzalez to evaluate the viability of future very seusitive III absorption measurements., Several hours of observing time were granted at the discretion of the Arecibo Observatory Director Sixto Gonzalez to evaluate the viability of future very sensitive HI absorption measurements.
 The observing procedure was the same as in Ποιος&Trolaud(2003a)., The observing procedure was the same as in \cite{Heiles03a}.
. A specific observing pattern. developed in Heiles&Trolaud(2003a).. was performed to cstimate the expected? TL cussion profile.," A specific observing pattern, developed in \cite{Heiles03a}, was performed to estimate the `expected' HI emission profile."
 This pattern geuerates oue on-source spectrum and 16 off-source spectra which are used to derive first aud second derivatives of the ITE emission on the sky., This pattern generates one on-source spectrum and 16 off-source spectra which are used to derive first and second derivatives of the HI emission on the sky.
subject of a future paper.,subject of a future paper.
" The equivalent widths of the H, emission components are related to the mass loss rates in OB stars (Leitherer 1988).", The equivalent widths of the $_{\alpha}$ emission components are related to the mass loss rates in OB stars (Leitherer 1988).
" The H, emission component in [22023 has an equivalent width (W, = ) comparable to that of the OSI star. HD152408 (W, = )."," The $_{\alpha}$ emission component in I22023 has an equivalent width $_{\lambda}$ = ) comparable to that of the O8I star, HD152408 $_{\lambda}$ = )."
" From this. we estimate a mass loss rate of 1.23 107? Mayr""! (Leitherer 1988)."," From this, we estimate a mass loss rate of $\times$ $^{-5}$ $_{\odot}$ $^{-1}$ (Leitherer 1988)."
 However. this value may be treated with caution.," However, this value may be treated with caution."
" In 122023. the large equivalent width of the H, emission component may be due to a large amount of gas in its circumstellar envelope or the presence of a bipolar envelope (Volk et al."," In I22023, the large equivalent width of the $_{\alpha}$ emission component may be due to a large amount of gas in its circumstellar envelope or the presence of a bipolar envelope (Volk et al."
 2004) and may not be directly related to the mass loss rate., 2004) and may not be directly related to the mass loss rate.
 DIBs.5780.410A.... . —.. and were identified in the spectrum of the star (Table 2).," DIBs, and were identified in the spectrum of the star (Table 2)."
 They have also been identified in other hot post-AGB stars e.g. IRASO1005+7910 (Klochkova et al., They have also been identified in other hot $-$ AGB stars e.g. IRAS01005+7910 (Klochkova et al.
 2002). IRAS13266-5551] IRASI7311—4924 (Sarkar et al.," 2002), $-$ 5551 $-$ 4924 (Sarkar et al."
 2005)., 2005).
sample calculated by this method: mesL<0.4.,sample calculated by this method: $\frac{L_{bol.}}{L_{Edd}} \lesssim 0.4$.
 The lower part ofM ligure 5 shows the histogram ol the Eddington ratios calculated in this section., The lower part of figure \ref{fig5} shows the histogram of the Eddington ratios calculated in this section.
" The results from the (wo methods of black hole mass caleulation agree: radio-Ioud AGN are powered by very massive central black holes. (vpically with M,>107.. and more often wilh A,~10M..."," The results from the two methods of black hole mass calculation agree: radio-loud AGN are powered by very massive central black holes, typically with $M_{\bullet} > 10^8 M_{\odot}$, and more often with $M_{\bullet} \sim 10^9 M_{\odot}$."
 These results are generally consistent with the black hole masses derived [or luminous raciio-loud AGN in other studies., These results are generally consistent with the black hole masses derived for luminous radio-loud AGN in other studies.
 Falomo.Ixotilaànen&Treves(2002) [ind masses in the range 5x10M. to 9xLOSAL. [or their sample of 7 low-redshift (2<0.055) BL Lacs. calculated from spectroscopic measurements of stellar velocity dispersion.," \citet{Falomo} find masses in the range $5\times 10^7 M_{\odot}$ to $9 \times 10^8 M_{\odot}$ for their sample of 7 low-redshift $z < 0.055$ ) BL Lacs, calculated from spectroscopic measurements of stellar velocity dispersion."
 These fall within the range of masses found for our sample of BL Lacs via the velocity dispersion relation. although they tend toward the low-mass end of that range.," These fall within the range of masses found for our sample of BL Lacs via the velocity dispersion relation, although they tend toward the low-mass end of that range."
 This may indicate an evolutionary or selection effect. between (he (wo epochs studied., This may indicate an evolutionary or selection effect between the two epochs studied.
 MeLure&Dunlop(2001). find black hole masses in the range 2x10M. to 2x10M. [or a sample of 22 radio-loud quasars. determined through reverberation mapping.," \citet{McLure3} find black hole masses in the range $2\times 10^8
M_{\odot}$ to $2\times 10^9 M_{\odot}$ for a sample of 22 radio-loud quasars, determined through reverberation mapping."
 These are consistent will the masses found for our high-power sample., These are consistent with the masses found for our high-power sample.
 Our results support the idea that. although some radio-quiet objects may host very massive central black holes (Dunlopetal.2002).. luminous radio sources may require them.," Our results support the idea that, although some radio-quiet objects may host very massive central black holes \citep{Dunlop}, luminous radio sources may require them."
 Dunlop οἱ al., Dunlop et al.
 suggest a black hole mass threshold [or radio-Ioud AGN of 5x109... which is supported by the black hole masses derived [rom bulge Iuminosity in this study.," suggest a black hole mass threshold for radio-loud AGN of $5 \times 10^8 M_{\odot}$, which is supported by the black hole masses derived from bulge luminosity in this study."
" Masses derived in this study via the M, σ, relation suggest a threshold of ~1x10M...", Masses derived in this study via the $M_{\bullet}$ $\sigma_e$ relation suggest a threshold of $\sim 1\times 10^8 M_{\odot}$.
 Whatever its value. we find that neither the threshold nor the distribution of black hole masses in raclio-loud AGN depends on the actual level of radio emission. within the range represented bv these radio sources. or on the overall energv output of the nucleus.," Whatever its value, we find that neither the threshold nor the distribution of black hole masses in radio-loud AGN depends on the actual level of radio emission, within the range represented by these radio sources, or on the overall energy output of the nucleus."
 As a consequence. radio-Ioud AGN exhibit an extremely broad range of accretion rates: from petσοκ10 to fen~1.0.," As a consequence, radio-loud AGN exhibit an extremely broad range of accretion rates; from $\frac{L_{bol.}}{L_{Edd}} \lesssim 2\times 10^{-4}$ to $\frac{L_{bol.}}{L_{Edd}} \sim 1.0$."
 Across this range the host galaxies span a remarkably light range of high stellar Iuminosities all within one magnitude of brightest. cluster galaxies suggesting that. al least for raclio-loud AGN. there is al most a very weak relation between (he properties of (he host galaxy and both the overall rate ancl the efficiency ol fuelling of the black hole.," Across this range the host galaxies span a remarkably tight range of high stellar luminosities — all within one magnitude of brightest cluster galaxies — suggesting that, at least for radio-loud AGN, there is at most a very weak relation between the properties of the host galaxy and both the overall rate and the efficiency of fuelling of the black hole."
 (5) Ίσα (08).,= ( ] ( ).
" so long as E.>me*/2h?z13.7eV.? Here, the factor Ce=7.40x10!!(n./cm?) eV. In this case, σεεοςE?lnE, so heating is somewhat more important at high energies, although σεε Still falls off by one power of energy faster than the ionization and excitation cross-sections."," so long as $E > me^4/2 \hbar^2 \approx 13.7 \eV$ Here, the factor $\zeta_e = 7.40 \times 10^{-11} (n_e/{\rm cm}^{-3})$ eV. In this case, $\sigma_{ee} \propto E^{-2} \ln E$, so heating is somewhat more important at high energies, although $\sigma_{ee}$ still falls off by one power of energy faster than the ionization and excitation cross-sections."
" Note that, when plasma effects are included, the cross-section is independent of the temperature of the gas, so we need not specify it in our calculations."," Note that, when plasma effects are included, the cross-section is independent of the temperature of the gas, so we need not specify it in our calculations."
" We use equation (12)) in our fiducial calculations, following ?.."," We use equation \ref{eq:coul-log}) ) in our fiducial calculations, following \citet{xu91}."
" Ignoring collective effects reduces the fraction of incident energy deposited as heat at E=100eV by a few percent, and it correspondingly increases the fractions of energy deposited in ionization and excitation."," Ignoring collective effects reduces the fraction of incident energy deposited as heat at $E \ga 100 \eV$ by a few percent, and it correspondingly increases the fractions of energy deposited in ionization and excitation."
 The density can also play a second role in collisional de-excitation of the target atoms and in populating the upper levels of the atoms (provided also that the temperature is sufficiently large)., The density can also play a second role in collisional de-excitation of the target atoms and in populating the upper levels of the atoms (provided also that the temperature is sufficiently large).
 This requires n>>10?cm? so is not important for the IGM., This requires $n \gg 10^8 \cmden$ so is not important for the IGM.
 But we caution readers against trusting our results in such environments., But we caution readers against trusting our results in such environments.
 We now present our main results., We now present our main results.
" As a reminder, we use 10° Monte Carlo trials for each electron energy (which ranges from 10-9900 eV), and we explicitly follow all secondary electrons and photons."," As a reminder, we use $10^5$ Monte Carlo trials for each electron energy (which ranges from $10$ –9900 eV), and we explicitly follow all secondary electrons and photons."
" We take f=0.05 and set the density of the background gas to be the mean cosmic density at z=10, but we saw above that the results are very insensitive to these parameters."," We take $f=0.05$ and set the density of the background gas to be the mean cosmic density at $z=10$, but we saw above that the results are very insensitive to these parameters."
 The primary input parameters are then the initial electron energy and the ionization fractions., The primary input parameters are then the initial electron energy and the ionization fractions.
" For the latter, we let x; be the density of HII relative to the total hydrogen density and assume that this is also the fraction of helium in the form of Hell, with zero Helll."," For the latter, we let $x_i$ be the density of HII relative to the total hydrogen density and assume that this is also the fraction of helium in the form of HeII, with zero HeIII."
" We present our results in terms of energy deposition fractions, with fion, feat, and fexcite the fractions of the initial energy that goes into ionization, heating, and HI line photons generated by collisional (Note that line photons from helium are transformed into ionizing photons and so deposit their energy in other ways, implicit in our code.)"," We present our results in terms of energy deposition fractions, with $f_{\rm ion}$, $f_{\rm heat}$, and $f_{\rm excite}$ the fractions of the initial energy that goes into ionization, heating, and HI line photons generated by collisional (Note that line photons from helium are transformed into ionizing photons and so deposit their energy in other ways, implicit in our code.)"
 We also let fLya be the fraction of energy deposited in HI photons., We also let $f_{\rm Ly\alpha}$ be the fraction of energy deposited in HI photons.
 We have verified explicitly that our code conserves energy throughout the entire interaction cycle., We have verified explicitly that our code conserves energy throughout the entire interaction cycle.
" Figure 1 shows these fractions, as a function of photon energy, in a medium with σι=0.01."," Figure \ref{fig:xh099} shows these fractions, as a function of photon energy, in a medium with $x_i=0.01$."
" The thick solid, dashed, and dotted curves Show fion, fheat, and fexcite, respectively."," The thick solid, dashed, and dotted curves show $f_{\rm ion}$, $f_{\rm heat}$, and $f_{\rm excite}$, respectively."
" The thin solid and dot-dashed curves show explicitly the fractions of energy going into HI and Hel ionization, respectively. ("," The thin solid and dot-dashed curves show explicitly the fractions of energy going into HI and HeI ionization, respectively. ("
The fraction going into Hell ionization is <1% throughout.),The fraction going into HeII ionization is $\ll 1\%$ throughout.)
" Finally, the thin dotted curve Shows frya."," Finally, the thin dotted curve shows $f_{\rm Ly\alpha}$."
 The structure of the curves is relatively easy to understand., The structure of the curves is relatively easy to understand.
" Electrons with E«10.2eV are unable to interact with any atoms or ions, so all of the energy is deposited as heat."," Electrons with $E<10.2 \eV$ are unable to interact with any atoms or ions, so all of the energy is deposited as heat."
" As F increases, more and more excitation and ionization processes become available, so the energy injected as heat decreases."," As $E$ increases, more and more excitation and ionization processes become available, so the energy injected as heat decreases."
" Interestingly, even with this large of a neutral fraction, the individual line thresholds do not introduce discrete features into the deposition fractions, and all of the parameters depend smoothly on energy."," Interestingly, even with this large of a neutral fraction, the individual line thresholds do not introduce discrete features into the deposition fractions, and all of the parameters depend smoothly on energy."
" At higher energies, where no additional processes become available, the fractions vary only slowly, eventually approaching reasonably constant values at E~ 1-10keV, where ionization, heating, and excitation split roughly equally."," At higher energies, where no additional processes become available, the fractions vary only slowly, eventually approaching reasonably constant values at $E \sim 1$ $10 \keV$, where ionization, heating, and excitation split roughly equally."
" As pointed out by ?,, the naive expectation from the Bethe approximation(with c;,«cxE~'lnE for ionization and excitation and σεεο.E~*?InE for heating), that less and less heating should occur at high photon energies, is false."," As pointed out by \citet{shull85}, the naive expectation from the Bethe approximation(with $\sigma_{i,e} \propto E^{-1} \ln E$ for ionization and excitation and $\sigma_{ee} \propto E^{-2} \ln E$ for heating), that less and less heating should occur at high photon energies, is false."
" This is because each ionization produces a moderate energy secondary electron (typically ~10eV, but occasionally much larger)."," This is because each ionization produces a moderate energy secondary electron (typically $\sim 10 \eV$, but occasionally much larger)."
" A large fraction of the primary's energy is lost through these intermediaries, who in turn lose most of their energy to heat, making the behavior at high energies much less variable than one would expect."," A large fraction of the primary's energy is lost through these intermediaries, who in turn lose most of their energy to heat, making the behavior at high energies much less variable than one would expect."
 Figures 2 and 3 show the energy deposition fractions for a range of z;., Figures \ref{fig:ion-heat} and \ref{fig:excite-lya} show the energy deposition fractions for a range of $x_i$.
 The first panel shows fios., The first panel shows $f_{\rm ion}$.
" For small x;, the ionization thresholds imprint features on the curves."," For small $x_i$, the ionization thresholds imprint features on the curves."
" At high energies, fion~0.4 at small ionized fractions and rapidly approaches zero as x; increases."," At high energies, $f_{\rm ion} \sim 0.4$ at small ionized fractions and rapidly approaches zero as $x_i$ increases."
 The behavior at very high energies sets an upper limit to the total energy invested in ionization., The behavior at very high energies sets an upper limit to the total energy invested in ionization.
 The left panel of Figure 3 shows the corresponding fractions lost to collisionally excited HI line photons., The left panel of Figure \ref{fig:excite-lya} shows the corresponding fractions lost to collisionally excited HI line photons.
 Note the line structure apparent at z;<10?; the features are separated by ~10eV and correspond to multiple excitations of HI atoms., Note the line structure apparent at $x_i \le 10^{-3}$; the features are separated by $\sim 10 \eV$ and correspond to multiple excitations of HI atoms.
" Although the structure around these features appears noisy, it is real and remains unchanged in other Monte Carlo tests."," Although the structure around these features appears noisy, it is real and remains unchanged in other Monte Carlo tests."
" However, as noted above these features blend together by x;~ 10?."," However, as noted above these features blend together by $x_i \sim 10^{-2}$ ."
" Note that collisional excitation becomes important at lower photon energies than does ionization, because the lines require less energy; in nearly neutral"," Note that collisional excitation becomes important at lower photon energies than does ionization, because the lines require less energy; in nearly neutral"
"using the RMS value of pv?/(poc2), to correspond to the SPH average.","using the RMS value of $\rho v^{2}/(\rho_{0} c_{s}^{2})$, to correspond to the SPH average."
 The Mach number evolution (Fig. 1)), The Mach number evolution (Fig. \ref{fig:vrms}) )
" is similar in both codes and at all resolutions up to around 4 tg, at which point all calculations show variations of order from each other."," is similar in both codes and at all resolutions up to around 4 $t_{d}$, at which point all calculations show variations of order from each other."
" No clear trends either between codes or with resolution are apparent, indicating that the variation observed is due to the stochastic nature of fully-developed turbulence producing different though statistically similar evolution (see Fig."," No clear trends either between codes or with resolution are apparent, indicating that the variation observed is due to the stochastic nature of fully-developed turbulence producing different though statistically similar evolution (see Fig."
 3 for the evidence for this in the density field)., \ref{fig:coldens512} for the evidence for this in the density field).
" It is these intermittent fluctuations that make turbulence code comparisons based on snapshot-to-snapshot comparison difficult, because the instantaneous turbulence field will quickly diverge between different codes in the fully developed regime because of the chaotic nature of the turbulence (see projections and slices for t22ta comparing the SPH and grid results)."," It is these intermittent fluctuations that make turbulence code comparisons based on snapshot-to-snapshot comparison difficult, because the instantaneous turbulence field will quickly diverge between different codes in the fully developed regime because of the chaotic nature of the turbulence (see projections and slices for $t \gtrsim 2 t_{d}$ comparing the SPH and grid results)."
 The evolution of maximum density (Fig. 2)), The evolution of maximum density (Fig. \ref{fig:rhomax}) )
" shows strong time variability in all six calculations, similar to the results shown in ?,Fig.2 and ?,Fig.2.."," shows strong time variability in all six calculations, similar to the results shown in \citet[][Fig.~2]{kritsuketal07} and \citet[][Fig.~2]{FederrathKlessenSchmidt2009}."
" For isothermal flows arbitrarily large density fluctuations can be produced, though with vanishingly small probability as can be inferred from the log-normal form of the PDF."," For isothermal flows arbitrarily large density fluctuations can be produced, though with vanishingly small probability as can be inferred from the log-normal form of the PDF."
" This simply reflects the highly intermittent nature of the density fluctuations in supersonic, turbulent flows."," This simply reflects the highly intermittent nature of the density fluctuations in supersonic, turbulent flows."
" The maximum density is a clear function of resolution in each code, showing no signs of convergence, as one might expect seeing as we are sampling the very highest data point in the PDF."," The maximum density is a clear function of resolution in each code, showing no signs of convergence, as one might expect seeing as we are sampling the very highest data point in the PDF."
 The results also demonstrate the evidently higher mass resolution in the SPH code: at 128? particles the maximum density resolvable in SPH is roughly similar to that resolved at 512? on the grid., The results also demonstrate the evidently higher mass resolution in the SPH code: at $128^{3}$ particles the maximum density resolvable in SPH is roughly similar to that resolved at $512^{3}$ on the grid.
 Using 512? SPH particles the maximum density resolved at RMS Mach 10 is roughly three-and-a-half orders of magnitude above the mean density which one might therefore expect to be similar to the mass resolution in a 2048? grid-based calculation., Using $512^{3}$ SPH particles the maximum density resolved at RMS Mach 10 is roughly three-and-a-half orders of magnitude above the mean density which one might therefore expect to be similar to the mass resolution in a $2048^{3}$ grid-based calculation.
" The projected column density fields at the highest resolution (512?) are shown forPHANTOM,, and the density field computed from the tracer particles in Fig."," The projected column density fields at the highest resolution $512^{3}$ ) are shown for, and the density field computed from the tracer particles in Fig."
" 3 (left, middle and right columns, respectively), at intervals of At—1t4 for the first four dynamical times."," \ref{fig:coldens512} (left, middle and right columns, respectively), at intervals of $\Delta t= 1 t_{d}$ for the first four dynamical times."
 The column density plots for SPH have been produced directly from the particles to a 2D pixel map using the visualisation tool (?) whilst the grid based results have been integrated through the grid., The column density plots for SPH have been produced directly from the particles to a 2D pixel map using the visualisation tool \citep{splashpaper} whilst the grid based results have been integrated through the grid.
 We show the integration through the z-direction in the codes., We show the integration through the $z$ -direction in the codes.
" At early times the calculations show clear agreement in the location of individual shocks (£=lta, top row) and in the development of large scale structures (&.=2t4, second row)."," At early times the calculations show clear agreement in the location of individual shocks $t=1 t_{d}$, top row) and in the development of large scale structures $t=2 t_{d}$, second row)."
" By t=Atq (fourth row) there is no longer clear correspondence even at the largest scales between codes, in agreement with the observed deviations in the time evolution of the RMS Mach number around this time (Fig. 1))."," By $t=4 t_{d}$ (fourth row) there is no longer clear correspondence even at the largest scales between codes, in agreement with the observed deviations in the time evolution of the RMS Mach number around this time (Fig. \ref{fig:vrms}) )."
" In terms of resolution, high-density structures appear better resolved in the SPH calculations at the same number of computational elements."," In terms of resolution, high-density structures appear better resolved in the SPH calculations at the same number of computational elements."
" However, the grid results tend to show better resolution of features in low density regions, as one might expect since in SPH the resolution is preferentially shifted from low density regions towards high density regions."," However, the grid results tend to show better resolution of features in low density regions, as one might expect since in SPH the resolution is preferentially shifted from low density regions towards high density regions."
 The excellent agreement between codes in the development of individual shock structures within the first dynamical times (top row) enabled us to make a very detailed comparison of features between codes which proved to be very helpful in the comparison process., The excellent agreement between codes in the development of individual shock structures within the first dynamical times (top row) enabled us to make a very detailed comparison of features between codes which proved to be very helpful in the comparison process.
" In particular it highlighted that, with the parameters we were initially using, some of the dense structures created by the collision of one or more shocks were rapidly losing definition in the SPH results, resulting in a noisy density field that was rather unlike the grid results (this is shown in more detail in Appendix A))."," In particular it highlighted that, with the parameters we were initially using, some of the dense structures created by the collision of one or more shocks were rapidly losing definition in the SPH results, resulting in a noisy density field that was rather unlike the grid results (this is shown in more detail in Appendix \ref{sec:viscosity}) )."
" The problem could be easily traced to be caused by particles penetrating or “overshooting” the shock front in these high Mach number shocks, a problem which the non-linear 3 (von-Neumann-Richtmyer) term in the SPH artificial viscosity (Eqs. 9--10))"," The problem could be easily traced to be caused by particles penetrating or “overshooting” the shock front in these high Mach number shocks, a problem which the non-linear $\beta$ (von-Neumann-Richtmyer) term in the SPH artificial viscosity (Eqs. \ref{eq:qvisc}- \ref{eq:vsig}) )"
 was designed to prevent (see?).., was designed to prevent \citep[see][]{monaghan89}.
" The problem was thus easily fixed by using a larger value for 2,;,..", The problem was thus easily fixed by using a larger value for $\beta_{visc}$.
" We have therefore used υιοε=4 throughout the paper, rather than the nominal B,;;.=2 which is widely used — and sufficient — for low Mach number calculations."," We have therefore used $\beta_{visc} = 4$ throughout the paper, rather than the nominal $\beta_{visc} = 2$ which is widely used — and sufficient — for low Mach number calculations."
 It should be noted that this makes very little difference to the overall dissipation rate since the linear viscosity term (o) dominates the numerical dissipation rate almost everywhere except at very strong divergence in the velocity field (where particle penetration can occur)., It should be noted that this makes very little difference to the overall dissipation rate since the linear viscosity term $\alpha$ ) dominates the numerical dissipation rate almost everywhere except at very strong divergence in the velocity field (where particle penetration can occur).
 Comparing the projected column density fields calculated using the tracer particles in the calculation (right column) to, Comparing the projected column density fields calculated using the tracer particles in the calculation (right column) to
 as a whole., as a whole.
 The IL I A 1215 absorption line iu Damped a svstenis. (DLAs. loge NOI 1)220.3). aud sub-DLAs 01ος. N(II I):20.3) can be fit for accurate colin density imcasurcuicuts due to the exteuded damping wines in the profile.," The H I $\lambda$ 1215 absorption line in Damped $\alpha$ systems (DLAs, log N(H $>$ 20.3) and sub-DLAs $<$ log N(H $<$ 20.3) can be fit for accurate column density measurements due to the extended damping wings in the profile."
 DLAs and sub-DLA svsteiis have been shown to contain the majority of the neutral gas in the Universe (Wolfeetal.1995:Péroux2003h:al. 2009)..," DLAs and sub-DLA systems have been shown to contain the majority of the neutral gas in the Universe \citep{Wol95, Per03b, Pro05, Not09b}."
 The DLAs are of particular importance for galactic chemical evolution studies., The DLAs are of particular importance for galactic chemical evolution studies.
" With such hieh cobhuun densities. the absorption lines from metal atoms are easily visible,"," With such high column densities, the absorption lines from metal atoms are easily visible."
 Also. svstenis with high column deusities are expected to remain mainly neutral due to self shiclding. alleviating the need for uucertaiu ionization corrections to the abundances.," Also, systems with high column densities are expected to remain mainly neutral due to self shielding, alleviating the need for uncertain ionization corrections to the abundances."
 There is still nmumeh debate as to the nature of the ealaxies hosting DLAs and sub-DLAs., There is still much debate as to the nature of the galaxies hosting DLAs and sub-DLAs.
 Even at low redshift. finding a faint galaxy near the bright poiut source of the QSO is challenging.," Even at low redshift, finding a faint galaxy near the bright point source of the QSO is challenging."
 At higher redshift. the cosmological dimaningof surface brielituess (jiX(L| :)!) makes galaxy detectious even more difficult.," At higher redshift, the cosmological dimming of surface brightness $\mu\propto(1+z)^4$ ) makes galaxy detections even more difficult."
 Nonetheless. these svstenis are a unique laboratory to study the ISM of galaxies over a wide range of redshifts.," Nonetheless, these systems are a unique laboratory to study the ISM of galaxies over a wide range of redshifts."
Gaussian lies along the .r-axis and the shortest axis along the z- so that 0.σα<p1.,"Gaussian lies along the $x$ -axis and the shortest axis along the $z$ -axis, so that $0\le q\le p\le 1$."
 The two usual polar coordinates (8.0) define the orientation of the line-of-sight with respect to the principal axes of the object.," The two usual polar coordinates $(\theta,\phi)$ define the orientation of the line-of-sight with respect to the principal axes of the object."
 Another angle c is required to specify the rotation of the object around the line-of-sight. and uniquely detine the orientation in space of the Gr.jy.2) coordinate system.," Another angle $\psi$ is required to specify the rotation of the object around the line-of-sight, and uniquely define the orientation in space of the $(x,y,z)$ coordinate system."
 This angle c is defined by the requirement that the + axis project onto the ;/ axis. or equivalently that the ο axis lies in the Gr.y) plane.," This angle $\psi$ is defined by the requirement that the $z$ axis project onto the $y'$ axis, or equivalently that the $x'$ axis lies in the $(x,y)$ plane."
 Once the viewing angles (4.0.c) have been assiumed.. given the observed axial ratio q' forthe Gaussian. the intrinsic axial ratios p and q ean be found using relations valid for general ellipsoidal bodies (e.g.. de Zeeuw Franx 1989) where 0=1.q'7.," Once the viewing angles $(\theta,\phi,\psi)$ have been , given the observed axial ratio $q'$ for the Gaussian, the intrinsic axial ratios $p$ and $q$ can be found using relations valid for general ellipsoidal bodies (e.g., de Zeeuw Franx 1989) where $\delta'=1-q'^2$."
 It should be noted that in general a solution may not be found for all assumed viewing angles (e.g.. Bertola et 11991).," It should be noted that in general a solution may not be found for all assumed viewing angles (e.g., Bertola et 1991)."
 If a triaxial deprojection is sought for the galaxy. then the viewing angles have to be the same for all the Gaussians and the permissible viewing angles for the object. assumed to be triaxial. will lie in the intersection of the permissible viewing angles of euch Gaussian (cf.," If a triaxial deprojection is sought for the galaxy, then the viewing angles have to be the same for all the Gaussians and the permissible viewing angles for the object, assumed to be triaxial, will lie in the intersection of the permissible viewing angles of each Gaussian (cf."
 Williams 198, Williams 1981).
 If an acceptable MGE model can be obtained by fixing the PA wy of all the Gaussians to the same value c. then the object can be deprojected by assuming it is axisymmetric (triaxial solutions yowever can be excluded FFranx 1988].," If an acceptable MGE model can be obtained by fixing the PA $\psi_j$ of all the Gaussians to the same value $\psi$, then the object can be deprojected by assuming it is axisymmetric (triaxial solutions however can be excluded Franx 1988])."
 In this case the ormulae of the previous section simplify considerabuc, In this case the formulae of the previous section simplify considerably.
 In the oblate axisymmetric case (p— 1). once an inclination i>0 (for?= Othe deprojection is degenerate) has been assumed or the galaxy 6.=90° corresponding to edge-on). one has: while in the prolate axisymmetric case (p= q) The oblate MGE deprojection above is only defined if cosseq7 for all Gaussians.," In the oblate axisymmetric case $p=1$ ), once an inclination $i>0$ (for $i=0$ the deprojection is degenerate) has been assumed for the galaxy $i=90^\circ$ corresponding to edge-on), one has: while in the prolate axisymmetric case $p=q$ ) The oblate MGE deprojection above is only defined if $\cos^2 i<q'^2_j$ for all Gaussians."
 This means that the flattest Gaussian in an MGE fit dictates the minimum possible inclination for which the MGE model ean be used in a dynamical model., This means that the flattest Gaussian in an MGE fit dictates the minimum possible inclination for which the MGE model can be used in a dynamical model.
 However since the Gaussian components don't necessarily have physical significance one don't want to base any conclusion of a dynamical model on this minimum inclination., However since the Gaussian components don't necessarily have physical significance one don't want to base any conclusion of a dynamical model on this minimum inclination.
 One simple way to avoid this problem consists in trying to increase the minimum axial ratio q' allowed in the MGE fit until the X7 increases significantly or the galaxy contour cannot be accurately reproduced any more with any number of Gaussians., One simple way to avoid this problem consists in trying to increase the minimum axial ratio $q'$ allowed in the MGE fit until the $\chi^2$ increases significantly or the galaxy contour cannot be accurately reproduced any more with any number of Gaussians.
 This Gi Will provide a good estimate of the minimum inclination for which the given galaxy. assumed to be axisymmetric. can be deprojected.," This $q'_{\rm max}$ will provide a good estimate of the minimum inclination for which the given galaxy, assumed to be axisymmetric, can be deprojected."
 Independently from an actual MGE tit. the limit to the above (duas is Set by the axial ratio q’ of the ellipse having the same curvature of the galaxy isophotes along the major axis. at the point of maximum curvature.," Independently from an actual MGE fit, the limit to the above $q'_{\rm max}$ is set by the axial ratio $q'$ of the ellipse having the same curvature of the galaxy isophotes along the major axis, at the point of maximum curvature."
 In fact there has to be at least one Gaussian flat enough to reproduce the maximum curvature along the major axis., In fact there has to be at least one Gaussian flat enough to reproduce the maximum curvature along the major axis.
 The potential generated by a triaxial Gaussian mass distribution of the form given in equation (62). can be evaluated using the classical Chandrasekhar (1969) formulae for densities stratified on similar concentric ellipsoids (see Binney Tremaine 1987. p. 61).," The potential generated by a triaxial Gaussian mass distribution of the form given in equation \ref{eq:density}) ), can be evaluated using the classical Chandrasekhar (1969) formulae for densities stratified on similar concentric ellipsoids (see Binney Tremaine 1987, p. 61)."
 In the MGE case the potential can be written as a one-dimensional 1) integral wheres =1ιοί q.Gisthe gravitational constant and Y is the mass-to-light-ratio.," In the MGE case the potential can be written as a one-dimensional (1D) integral where $\delta=1-p^2$, $\epsilon=1-q^2$, G is the gravitational constant and $\Upsilon$ is the mass-to-light-ratio."
 For oblate axisymmetric models (p= 1) this reduces to In the spherical ease (p=q 1) to Already for So&[i the error function ertRB(2σ)] —]to 16 digits accuracy and the spherical MGE potential can be replaced with high precision by the potential of a point mass enclosing the total mass 4=YL of the Gaussian component., For oblate axisymmetric models $p=1$ ) this reduces to In the spherical case $p=q=1$ ) to Already for $8\sigma\la R$ the error function ${\rm erf}[R/(\sqrt{2}\ \sigma)]=1$ to 16 digits accuracy and the spherical MGE potential can be replaced with high precision by the potential of a point mass enclosing the total mass ${\cal M}=\Upsilon L$ of the Gaussian component.
 Since the σ of the Gaussians in an MGE fit span various orders of magnitude in size. asymptotic expressions can also be conveniently used to estimate the triaxial or axisymmetric potential of equations CLE) and (123) at very small and very large radii as done in Cappellari et (2002).," Since the $\sigma$ of the Gaussians in an MGE fit span various orders of magnitude in size, asymptotic expressions can also be conveniently used to estimate the triaxial or axisymmetric potential of equations \ref{eq:pot_tri}) ) and \ref{eq:pot_axis}) ) at very small and very large radii as done in Cappellari et (2002)."
 We start by considering the MGE fit to. galaxies without isophote twists., We start by considering the MGE fit to galaxies without isophote twists.
" The determination of an axisymmetric MGE parametrization from the photometry. namely the fit of à sum of Gaussians with the same centre and PA. to a galaxy image seems to be a very simple problem that can be efficiently solved with general nonlinear minimization algorithms,"," The determination of an axisymmetric MGE parametrization from the photometry, namely the fit of a sum of Gaussians with the same centre and PA, to a galaxy image seems to be a very simple problem that can be efficiently solved with general nonlinear minimization algorithms."
 We assume for simplicity that the PA cof all Gaussians is known., We assume for simplicity that the PA $\psi$ of all Gaussians is known.
 We don't fit c since it is very easily measured before fitting., We don't fit $\psi$ since it is very easily measured before fitting.
 We found it fast and accurate to determine it fromthe weighted second moments of the surface brightness above a given level. as done by automatic galaxy extraction. packages (e.g. Bertin Arnouts 1996).," We found it fast and accurate to determine it fromthe weighted second moments of the surface brightness above a given level, as done by automatic galaxy extraction packages (e.g., Bertin Arnouts 1996)."
 It may also be measured with standard, It may also be measured with standard
layer of dust causes a large temperature gradient.,layer of dust causes a large temperature gradient.
 Following this result. we attributed a value of 0.01 W K! m' to the thermal conductivity of a crust composed only of silicatic particles.," Following this result, we attributed a value of 0.01 W $^{-1}$ $^{-1}$ to the thermal conductivity of a crust composed only of silicatic particles."
" In. the case of the ""organic"" distribution. lacking for direct measurements. we deduced the physical properties from the results of the laboratory experiments conducted at the Space Research Institute of Graz (Kómmle et al. 1996))."," In the case of the ""organic"" distribution, lacking for direct measurements, we deduced the physical properties from the results of the laboratory experiments conducted at the Space Research Institute of Graz (Kömmle et al. \cite{koemle}) )."
 The thermal evolution of an analogue of cometary material composed of a mixture of minerals. ices and hydrocarbons has been studied. obtaining a sort of cohesive crust composed of minerals glued together by organics.," The thermal evolution of an analogue of cometary material composed of a mixture of minerals, ices and hydrocarbons has been studied, obtaining a sort of cohesive crust composed of minerals glued together by organics."
 This kind of crust has a thermal conductivity higher than that of silicatic crust. and also has a greater cohesive strength: an admixture with organic material raises crust conductivity of one order of magnitude or more with respect to a crust composed of silicatic grains.," This kind of crust has a thermal conductivity higher than that of silicatic crust, and also has a greater cohesive strength: an admixture with organic material raises crust conductivity of one order of magnitude or more with respect to a crust composed of silicatic grains."
" So. our ""organic"" crust is characterized by a higher thermal conductivity than the ""silicatic one: we attributed to a crust mainly composed of organic particles a value of 0.2 W K! m*'. At the beginning of computations the dust particles are embedded in the porous ice."," So, our ""organic"" crust is characterized by a higher thermal conductivity than the ""silicatic"" one: we attributed to a crust mainly composed of organic particles a value of 0.2 W $^{-1}$ $^{-1}$ At the beginning of computations the dust particles are embedded in the porous ice."
 When the ice sublimates the embedded particles become free. in a number proportional to the amount of sublimated ice. and can undergo the drag exerted by the gas flux.," When the ice sublimates the embedded particles become free, in a number proportional to the amount of sublimated ice, and can undergo the drag exerted by the gas flux."
" Average pore size is increasing due to the ice sublimation: a “pore widening factor"" proportional to the amount of sublimated ice is locally applied to the pore average size."," Average pore size is increasing due to the ice sublimation: a ""pore widening factor"" proportional to the amount of sublimated ice is locally applied to the pore average size."
 In this way we are taking into account that a sublimating ice produces holes and cavities. and as a consequence free particles can move towards the surface (particles can move and be blown off only if their size is less than the local average pore size!).," In this way we are taking into account that a sublimating ice produces holes and cavities, and as a consequence free particles can move towards the surface (particles can move and be blown off only if their size is less than the local average pore size!)."
 Free particles that are found close to the surface can move toward the surface and be blown off or accumulate to form a dust mantle., Free particles that are found close to the surface can move toward the surface and be blown off or accumulate to form a dust mantle.
 Free particles are noving under the opposite effects of gravity and gas flux: only grains smaller than the pore average size can move toward the surface in the pore system., Free particles are moving under the opposite effects of gravity and gas flux; only grains smaller than the pore average size can move toward the surface in the pore system.
 When the 1ce is condensing. a proportional amount of free particles become embedded and the pores becomes smaller (porosity To determine how many particles can be blown off to contribute to dust flux. and how many can instead be accumulated on the surface. the different forees acting on the single grain are compared. obtaining for each distribution a critical radius. depending on grain density.," When the ice is condensing, a proportional amount of free particles become embedded and the pores becomes smaller (porosity To determine how many particles can be blown off to contribute to dust flux, and how many can instead be accumulated on the surface, the different forces acting on the single grain are compared, obtaining for each distribution a critical radius, depending on grain density."
" The critical radius represents the radius of the largest particle that can leave the surface of the comet: G is the gravitational constant. M, the mass of the comet. R, its radius. w its angular rotation velocity. ο the dust grain density. Φ/ο is the gas flux. and Vy, the velocity of the gas flux."," The critical radius represents the radius of the largest particle that can leave the surface of the comet: where $G$ is the gravitational constant, $M_n$ the mass of the comet, $R_n$ its radius, $\omega$ its angular rotation velocity, $\rho_{dust}$ the dust grain density, $\Phi_{H_{2}O}$ is the gas flux, and $V_{H_{2}O}$ the velocity of the gas flux."
 In the Eq. (5)), In the Eq. \ref{rstar}) )
 the numerator represents the lifting force exerted by the outflowing gases. and the denominator represents the gravitational attraction. corrected by the centrifugal force.," the numerator represents the lifting force exerted by the outflowing gases, and the denominator represents the gravitational attraction corrected by the centrifugal force."
 At each time step the number of free dust particles for each size class and the value of the critical radius are computed., At each time step the number of free dust particles for each size class and the value of the critical radius are computed.
 All the free particles with radius à.<a are considered ejected (blown off) and contribute to the dust flux. while those with &.>e accumulate on the surface.," All the free particles with radius $a~<~a^*$ are considered ejected (blown off) and contribute to the dust flux, while those with $a~\geq~a^*$ accumulate on the surface."
 This refractory surface layer (dust mantle) is not necessarily stable. and can be later on blown off if the gas flux is strong enough.," This refractory surface layer (dust mantle) is not necessarily stable, and can be later on blown off if the gas flux is strong enough."
 It could also increase in thickness 1f more and more particles are not able to leave the surface. substantially reducing and then quenching the gas flux.," It could also increase in thickness if more and more particles are not able to leave the surface, substantially reducing and then quenching the gas flux."
" Dust mantle compaction due to a volume reduction when ice is sublimated ts taken into account,", Dust mantle compaction due to a volume reduction when ice is sublimated is taken into account.
 If the dust mantle is not too thick the gas flux from the interior is able to entrain a dust flux. so it is possible to have a dust flux even when there is no ice left on the In this way. even an originally homogeneous body becomes quickly highly inhomogeneous: composition. density and porosity are changing with depth.," If the dust mantle is not too thick the gas flux from the interior is able to entrain a dust flux, so it is possible to have a dust flux even when there is no ice left on the In this way, even an originally homogeneous body becomes quickly highly inhomogeneous: composition, density and porosity are changing with depth."
 A thermal model depends not only on the assumptions of the model itself. but also on the values attributed to the initial parameters.," A thermal model depends not only on the assumptions of the model itself, but also on the values attributed to the initial parameters."
 These parameters describe the orbit. the initial state of the body and the properties of the matter of which it is composed.," These parameters describe the orbit, the initial state of the body and the properties of the matter of which it is composed."
 They are defined or derived. when possible. from observation and laboratory experiments.," They are defined or derived, when possible, from observation and laboratory experiments."
" A given set of these parameters define a ""Case""."," A given set of these parameters define a ""Case""."
 By changing a small number of these parameters. and keeping fixed all the rest. we can build different Cases that are the subject of the To apply the above described model to a real case we need to define the characteristics of the body that we want to simulate. assuming an mitial structure and composition.," By changing a small number of these parameters, and keeping fixed all the rest, we can build different Cases that are the subject of the To apply the above described model to a real case we need to define the characteristics of the body that we want to simulate, assuming an initial structure and composition."
 As for the real case. we chose to simulate the behaviour of P/2005 Ul] (Read).," As for the real case, we chose to simulate the behaviour of P/2005 U1 (Read)."
 The results of this simulation can be applied also to the other MBCs known until now. because orbits and sizes are reasonably similar.," The results of this simulation can be applied also to the other MBCs known until now, because orbits and sizes are reasonably similar."
 As written before. we start from the assumption that the model body has a cometary nature. that is 1t is composed of ice and dust grains.," As written before, we start from the assumption that the model body has a cometary nature, that is it is composed of ice and dust grains."
 A further assumption is being made that the surface of the body is covered by a devolatilized mantle. and that a recently happened impact has opened a crater in this mantles.," A further assumption is being made that the surface of the body is covered by a devolatilized mantle, and that a recently happened impact has opened a crater in this mantles."
 As a consequence. the heat from the Sun is now able to reach ice-rich layers. so triggering a cometary-like activity (sublimating gas entraining dust particles).," As a consequence, the heat from the Sun is now able to reach ice-rich layers, so triggering a cometary-like activity (sublimating gas entraining dust particles)."
 At the beginning of the simulation. the immediate effects of the impact (release of heat) have already As for the composition and physical properties. it is difficult to make safe assumptions.," At the beginning of the simulation, the immediate effects of the impact (release of heat) have already As for the composition and physical properties, it is difficult to make safe assumptions."
 We have no reason to think. anyway. that these bodies are absolutely similar to the classical comets (Jupiter-family. Halley-family and Long Period comets). because their origin and evolution history ts different.," We have no reason to think, anyway, that these bodies are absolutely similar to the classical comets (Jupiter-family, Halley-family and Long Period comets), because their origin and evolution history is different."
 They formed closer to the Sun than the comets now stocked in the Kuiper Belt or Oort cloud., They formed closer to the Sun than the comets now stocked in the Kuiper Belt or Oort cloud.
 During the Solar System formation period materials from different distances, During the Solar System formation period materials from different distances
using ¢ Gem data.,using $\zeta$ Gem data.
 In this case we used photometry from Wisniewski&Johnson(1968). and Aloffeti&Barnes (1984).., In this case we used photometry from \citet{wj68} and \citet{mb84}. .
 In Table 8. we compare the derived surface brightness relations to similar relations from work based on non-variable supergiants (Fouque&Gieren1997) and other Cepheid observations (Nordegrenetal.2001)., In Table \ref{tab:sb} we compare the derived surface brightness relations to similar relations from work based on non-variable supergiants \citep{fg97} and other Cepheid observations \citep{nordgren01}.
. The Fy vs. V—HR fits can also be compared with the Gieren(1988) result Chat the slope of the V—H surface brightness relation (c) is weakly dependent on pulsational period (2?) according to which for a Aql predicts e=—0.376 and for ¢ Gem ¢=—0.319., The $F_{V}$ vs. $V-R$ fits can also be compared with the \citet{gieren88} result that the slope of the $V-R$ surface brightness relation (c) is weakly dependent on pulsational period $P$ ) according to which for $\eta$ Aql predicts $c = -0.376$ and for $\zeta$ Gem $c = -0.379$.
 These comparisons reveal generally good agreement between (he various relations in Table &.., These comparisons reveal generally good agreement between the various relations in Table \ref{tab:sb}.
 The relation between pulsational period and Cepheid radius has received considerable altention in the literature. primarily because early results based on dillerent techniques were discrepant (Fernie1984:Molfett&Barnes1987).," The relation between pulsational period and Cepheid radius has received considerable attention in the literature, primarily because early results based on different techniques were discrepant \citep{fernie84,mb87}."
. Period-radius relations are also useful in that they can indicate pulsation mode., Period-radius relations are also useful in that they can indicate pulsation mode.
 This is important for calibrating period-Iuminosity relations since different modes will vield different relations (Feast )..," This is important for calibrating period-luminosity relations since different modes will yield different relations \citep{fc97,nordgren01}."
 In Fig., In Fig.
 5. we compare our measured Cepheicl diameters to (he values predicted from a range of techniques: Dono.Caputo.&Marconi(1998) calculate a period-radius relation from [ull-amplitude. nonlinear. convective models for a range of metallicities ancl stellar masses.," \ref{fig:rad} we compare our measured Cepheid diameters to the values predicted from a range of techniques: \citet{bono98} calculate a period-radius relation from full-amplitude, nonlinear, convective models for a range of metallicities and stellar masses."
 Gieren.Molffett.&Barnes(1999) use the surface brightness technique based on W aud V—£2 photometry and (he Fouque&Gieren(1997). result to derive radii lor 116 Cepheids in the Galaxy and the Magellanie Clouds., \citet{gmb99} use the surface brightness technique based on $V$ and $V-R$ photometry and the \citet{fg97} result to derive radii for 116 Cepheids in the Galaxy and the Magellanic Clouds.
 They find an intrinsic width in their relationof z:0.03 in log h. Lanev&Stobie(1995) also use the surface brightness techuique for estimating, They find an intrinsic width in their relationof $\pm 0.03$ in log R. \citet{laney95} also use the surface brightness technique for estimating
of galaxies ancl even among the YSC's formed within one global galaxy-wide starburst.,of galaxies and even among the YSCs formed within one global galaxy-wide starburst.
 During a strong burst. typically lasting a few 100 vr in a massive gas-rich. ealaxy. a significant. increase of the ISM abundance may occur (Eritzev. Alvensleben Gerhardt 1994. their Fig.," During a strong burst, typically lasting a few $\times 10^8$ yr in a massive gas-rich galaxy, a significant increase of the ISM abundance may occur (Fritze–v. Alvensleben Gerhardt 1994, their Fig."
 12b)., 12b).
 Meanwhile. some fraction of the gas enriched. by dying first-generation. burst stars may well be shock-compressed to cool fast enough to be built into later generations of stars or clusters produced in the burst.," Meanwhile, some fraction of the gas enriched by dying first-generation burst stars may well be shock-compressed to cool fast enough to be built into later generations of stars or clusters produced in the burst."
 The same effect may occur when multiple bursts occur in a series of close encounters between two galaxies before their final merger., The same effect may occur when multiple bursts occur in a series of close encounters between two galaxies before their final merger.
 Hence. in extended: starburst: episodes. metallicity differences between YSC's formed carly on and [ate in the burst phase may be expected.," Hence, in extended starburst episodes metallicity differences between YSCs formed early on and late in the burst phase may be expected."
 Precise (relative) metallicity determinations for individual YSCs are not only important to study the questions raised. above. but also for the correct. derivation of ages [from broad-band colours.," Precise (relative) metallicity determinations for individual YSCs are not only important to study the questions raised above, but also for the correct derivation of ages from broad-band colours."
 Dust extinction is often very important in YSC systems., Dust extinction is often very important in YSC systems.
 In particular the voungest post-burst. galaxies ancl galaxies with ongoing starbursts often show strong ancl patchy dust structures ancl morphologies., In particular the youngest post-burst galaxies and galaxies with ongoing starbursts often show strong and patchy dust structures and morphologies.
 For instance. the voungest clusters in the overlap region of the two ealactic clises in the Antennac galaxies are completely obscurecl in the optical anc can only be detected. in near or miüd-infrared observations (Mirabel et al.," For instance, the youngest clusters in the overlap region of the two galactic discs in the Antennae galaxies are completely obscured in the optical and can only be detected in near or mid-infrared observations (Mirabel et al."
 1998. Mengel et al.," 1998, Mengel et al."
 2001)., 2001).
 Older merger remnants like NGC 7252 or NGC 3921 seem to have own their inner regions clear of all the gas left over from intense star formation during the burst (e.g... Schweizer et al.," Older merger remnants like NGC 7252 or NGC 3921 seem to have blown their inner regions clear of all the gas left over from intense star formation during the burst (e.g., Schweizer et al."
 1996)., 1996).
 Extinction estimates towards individual YSC's are therefore as important as individual metallicity estimates in order to obtain reliable ages and to be able to derive an age-normatised CLE or YSC mass function., Extinction estimates towards individual YSCs are therefore as important as individual metallicity estimates in order to obtain reliable ages and to be able to derive an age-normalised CLF or YSC mass function.
 Inclividual YSC spectroscopy. feasible today with Sm-class telescopes for the nearest systems. is very time-consuming. since observations of large numbers of clusters are required to obtain statistically significant results.," Individual YSC spectroscopy, feasible today with 8m-class telescopes for the nearest systems, is very time-consuming, since observations of large numbers of clusters are required to obtain statistically significant results."
 Multi-passbauxd imaging is à very interesting and useful alternative. as we will show below. in particular if it includes coverage of near-infrared (NIR) and/or ultraviolet. (UV) wavelengths.," Multi-passband imaging is a very interesting and useful alternative, as we will show below, in particular if it includes coverage of near-infrared (NIR) and/or ultraviolet (UV) wavelengths."
 The large majority of extragalactic star cluster studies done to date have essentially used two or three-passbancl aperture photometry. combined with theoretical stellar population synthesis models to obtain age estimates.," The large majority of extragalactic star cluster studies done to date have essentially used two or three-passband aperture photometry, combined with theoretical stellar population synthesis models to obtain age estimates."
 Phe accuracy to which this can be done obviously depends on the nuniber of different (broac-band) filters available as well as. crucially. on the actual wavelengths and wavelength range. covered by the observations. and on the PSE size compared to the cluster surface density. profile (ie. on how close to the observations were taken to the confusion limit for these clusters).," The accuracy to which this can be done obviously depends on the number of different (broad-band) filters available as well as, crucially, on the actual wavelengths and wavelength range covered by the observations, and on the PSF size compared to the cluster surface density profile (i.e., on how close to the observations were taken to the confusion limit for these clusters)."
 In this paper we assess the systematic uncertainties in age. extinction and metallicity determinations for YSC systems inherent to the use of broad-band. integrated colours.," In this paper we assess the systematic uncertainties in age, extinction and metallicity determinations for YSC systems inherent to the use of broad-band, integrated colours."
 We have ceveloped an evolutionary svnthesis optimisation technique that can be applied to photometric nmieasurements in à given number NON&4) of broad-band passbands., We have developed an evolutionary synthesis optimisation technique that can be applied to photometric measurements in a given number $N (N \ge 4)$ of broad-band passbands.
 “Phe optimisation routine then. simultaneously determines the best combination of age. extinction. and metallicity. from a comparison with the most. up-to-date Gotttingen simple stellar population (SSP) mocdels (Schulz et al.," The optimisation routine then simultaneously determines the best combination of age, extinction and metallicity from a comparison with the most up-to-date Götttingen simple stellar population (SSP) models (Schulz et al."
 2002). to which we have added the contributions of an exhaustive set of gaseous emission. lines. ancl gaseous continuum emission. GXndeors. Eritzev. Alvensleben cle Cirijs 2002. Anders Fritzev. Alvensleben 2003).," 2002), to which we have added the contributions of an exhaustive set of gaseous emission lines and gaseous continuum emission (Anders, Fritze–v. Alvensleben de Grijs 2002, Anders Fritze–v. Alvensleben 2003)."
 We also compare these results with similar determinations based on w Starburst99 SSP models (Leitherer et al., We also compare these results with similar determinations based on the Starburst99 SSP models (Leitherer et al.
 1999). but assuming fixed. solar metallicity for our sample clusters.," 1999), but assuming fixed, solar metallicity for our sample clusters."
 Although this is an often-used assumption. we will show that us introduces significant systematic cllects in the final age istribution. and therefore also in the mass clistribution.," Although this is an often-used assumption, we will show that this introduces significant systematic effects in the final age distribution, and therefore also in the mass distribution."
 We decided to focus our ellorts on the nearby. well-studied starburst galaxy NGC 3310. known to harbour large numbers of voung star clusters. for which multi-passband observations from the near-UV to the NIU are. reaclily available from theHS Data Archive (Section 2:: see also Elmeercen et al.," We decided to focus our efforts on the nearby, well-studied starburst galaxy NGC 3310, known to harbour large numbers of young star clusters, for which multi-passband observations from the near-UV to the NIR are readily available from the Data Archive (Section \ref{obs.sect}; see also Elmegreen et al."
 2002. hereafter. E02).," 2002, hereafter E02)."
 In Section 4d. we first place the NGC 3310 starburst in its physical context., In Section \ref{ngc3310.sect} we first place the NGC 3310 starburst in its physical context.
 We then discuss the derived age distribution of the cluster population. which we extend compared to previous work. in terms of the evolution of the CLE and the interaction stage of its parent galaxy in Sections 5. and 6...," We then discuss the derived age distribution of the cluster population, which we extend compared to previous work, in terms of the evolution of the CLF and the interaction stage of its parent galaxy in Sections \ref{agedet.sec} and \ref{interpretation.sec}. ."
 We summarise our main results and conclusions in Section 7.., We summarise our main results and conclusions in Section \ref{summary.sect}.
 Finally. we will apply our knowledge of the svstematic uncertainties eained in this paper to a larger sample of nearby starburst and interacting galaxies drawn from theUST GO-s5645 programme (Winclhorst ct al.," Finally, we will apply our knowledge of the systematic uncertainties gained in this paper to a larger sample of nearby starburst and interacting galaxies drawn from the GO-8645 programme (Windhorst et al."
 2002) in Papers HE ancl HI (de Cirijs et al..," 2002) in Papers II and III (de Grijs et al.,"
 in prep.)., in prep.).
 NGC 3310 is a representative member of the class of galaxies often showing signs of active starbursts and recently formed star clusters., NGC 3310 is a representative member of the class of galaxies often showing signs of active starbursts and recently formed star clusters.
 The galaxy may have been a normal. quiescent Sbe-tvpe galaxy before it started to produce large numbers of new stars. possibly due to the merger with a gas-rich metallicity companion (cf.," The galaxy may have been a normal, quiescent Sbc-type galaxy before it started to produce large numbers of new stars, possibly due to the merger with a gas-rich low-metallicity companion (cf."
 Ixobulnicky Skillman 1995)., Kobulnicky Skillman 1995).
 As part ofHST programme CGO-8645.. we. obtained observations of NGC 3310 through the E300. ΟΡΝΤΟ and Fsi4Ww filters (Winchorst ct al.," As part of programme GO-8645, we obtained observations of NGC 3310 through the F300W (“UV”) and F814W filters (Windhorst et al."
 2002). with the galaxy centre located on chip 3 of the Wide Field. Planetary Camera 2 (WEPC?).," 2002), with the galaxy centre located on chip 3 of the Wide Field Planetary Camera 2 )."
 Observations in aclelitional passbancds were obtained from theHST Data Archive., Observations in additional passbands were obtained from the Data Archive.
 ln order to obtain the largest common Ποιά of view (FoV) in the optical wavelength range. we restricted these archival data to be taken with theWEPC2.," In order to obtain the largest common field of view (FoV) in the optical wavelength range, we restricted these archival data to be taken with the."
 In addition. we obtained archival. NIIS. images taken with the Near-IEnfrared. Cameraand. Multi-Object. Spectrometers. (NICAIOS) camera. 2.," In addition, we obtained archival NIR images taken with the Near-Infrared Cameraand Multi-Object Spectrometer's (NICMOS) camera 2,"
The results for our cosmological parameters are shown in Fieure 6.. where we plot the nunmber of supernovae that could be observed per vear ancl per square degree.,"The results for our cosmological parameters are shown in Figure \ref{fig:snr}, where we plot the number of supernovae that could be observed per year and per square degree."
 Note that this ligure does not incorporate magnitude limits or observational selection functions. but does simply show the predicted number of supernovae (hat can in principle be observed.," Note that this figure does not incorporate magnitude limits or observational selection functions, but does simply show the predicted number of supernovae that can in principle be observed."
 The redshift distribution of SNe follows the star formation rate. peaking αἱ 25 for Pop II. and showing the same break al 2=30 lor PISNe as in Figure 2..," The redshift distribution of SNe follows the star formation rate, peaking at $z\sim5$ for Pop II, and showing the same break at $z=30$ for PISNe as in Figure \ref{fig2}."
 We expect the transition from preclominantiv PISNe to Pop II SNe to occur around a redshift of 2~15—20 (see Figure 4)). and we therelore show the rates for both tvpes of supernova in this redshift range.," We expect the transition from predominantly PISNe to Pop II SNe to occur around a redshift of $z\sim
15-20$ (see Figure \ref{fig:metal}) ), and we therefore show the rates for both types of supernova in this redshift range."
 As this transition occurs. we expect the Pop II SN rate to gradually drop below the solid line towards hieher redshifts as Pop II star formation switches off.," As this transition occurs, we expect the Pop II SN rate to gradually drop below the solid line towards higher redshifts as Pop II star formation switches off."
 Similarly we expect the Pop HI (Pop IL5) rate to drop below the dashed (dotted) line towards lower recdshilts as Pop III star formation ceases., Similarly we expect the Pop III (Pop II.5) rate to drop below the dashed (dotted) line towards lower redshifts as Pop III star formation ceases.
 We do not expect anv VAISs at ο<15. but we extend our caleulation down to z=7 because the reionization of the universe al roughly this recshilt provides a robust lower limit for the end of VAIS formation (e.g..Ohetal.2001).," We do not expect any VMSs at $z\la 15$, but we extend our calculation down to $z=7$ because the reionization of the universe at roughly this redshift provides a robust lower limit for the end of VMS formation \citep[e.g.,][]{Ohetal01}."
. That the PISN and Pop IE ον rates are so similar ad the transition redshilts is because the star mamation rate for Pop III al z15 which we predict analytically is similar (o the rate (for Pop II) found in the simulations of Springel&IHernequist. (see Figure 1))., That the PISN and Pop II SN rates are so similar at the transition redshifts is because the star formation rate for Pop III at $z\sim15$ which we predict analytically is similar to the rate (for Pop II) found in the simulations of \citeauthor{SprHer02} (see Figure \ref{fig1}) ).
 Again. we Mnphasize (hat the break in the VMS supernova rate at z=30 is artificially sharp. reflecting the abrupt transition in (he underlving star formation rate.," Again, we emphasize that the break in the VMS supernova rate at $z=30$ is artificially sharp, reflecting the abrupt transition in the underlying star formation rate."
 In terms of total numbers of supernovae. we predict ~2x10 PISNe per vear over je whole skv(above 2= 15). or about 50 per square degree per vear.," In terms of total numbers of supernovae, we predict $\sim 2\times10^6$ PISNe per year over the whole sky(above $z=15$ ), or about 50 per square degree per year."
 This still comprises only ~0.4 of all supernovae. as we find ~4x105 SNell per νου (all skv). a value comparable (ο previous estimates (Miralda-Escudé&Rees1997:Macdauetal.1993).," This still comprises only $\sim 0.4$ of all supernovae, as we find $\sim 4\times 10^8$ SNeII per year (all sky), a value comparable to previous estimates \citep{MirRee97,MadDelPan98}."
.. This number can be understood by a simple order of magnitude estimate as follows., This number can be understood by a simple order of magnitude estimate as follows.
" About of the barvons in (he universe are in stus by the present time. giving a local density in stus of p,c0.10rpua0GX105NL,/Mpc* for our cosmological parameters (Peebles1993)."," About of the baryons in the universe are in stars by the present time, giving a local density in stars of $\rho_* \simeq 0.1\Omega_b \rho_{\rm crit}
 \sim 6\times 10^8 \;\msun/{\rm Mpc^3}$ for our cosmological parameters \citep{Pee93}."
. The size ol the observable universe is 10 Gpe out to z=5 (most of the star formation happens later (han 2=5 because there is very little physical time belore (his). so the total mass in stars in (his volume. ignoring redshift evolution effects. is ~107M...," The size of the observable universe is $\sim 10$ Gpc out to $z=5$ (most of the star formation happens later than $z=5$ because there is very little physical time before this), so the total mass in stars in this volume, ignoring redshift evolution effects, is $\sim 10^{21.5}\;\msun$."
" About of the lass in stars goes into stars which can explode. sothe mass in supernovae is ~107ML,,"," About of the mass in stars goes into stars which can explode, sothe mass in supernovae is $\sim 10^{20.5}\;\msun$."
 The mass weighted average for a supernova progenitors mass is e30 M... and (he age of (he universe is 14 Gyr.," The mass weighted average for a supernova progenitor's mass is $\sim30\;\msun$ , and the age of the universe is $14\;{\rm Gyr}$ ."
 The number of supernovae per vear is then, The number of supernovae per year is then
NSERC and ολα.,NSERC and CIfAR.
 CAV acknowledges support from NSF eraut. AST-0909198., GW acknowledges support from NSF grant AST-0909198.
 Facilities:S," Facilities:,"
 Facilities:Sp," Facilities:,"
 Facilities:Spi," Facilities:,"
 Facilities:Spit," Facilities:,"
 Facilities:Spitz," Facilities:,"
 Facilities:Spitze," Facilities:,"
 Facilities:Spitzer," Facilities:,"
 Facilities:Spitzer.," Facilities:,"
 Facilities:Spitzer..," Facilities:,"
 Facilities:Spitzer...," Facilities:,"
be quantified by a luminosity-weighted age fractional change right).,be quantified by a luminosity-weighted age fractional change ).
 However. these galaxies can still accomodate the tight CM relation found in local clusters right).," However, these galaxies can still accomodate the tight CM relation found in local clusters )."
 In the framework of current models of star formation. one could accomodate this trend with lower star formation efficiencies in fainter galaxies. also resulting in a significant change with redshift of the slope of the correlation between mass-to-light ratio and mass (Ferreras Silk 2000).," In the framework of current models of star formation, one could accomodate this trend with lower star formation efficiencies in fainter galaxies, also resulting in a significant change with redshift of the slope of the correlation between mass-to-light ratio and mass (Ferreras Silk 2000)."
 This would imply that in the latest merging stages the less massive early-type systems could still undergo some star formation. whereas more massive galaxies would just merge stars and hot gas. without triggering star formation.," This would imply that in the latest merging stages the less massive early-type systems could still undergo some star formation, whereas more massive galaxies would just merge stars and hot gas, without triggering star formation."
 The fact that the method presented here ts very sensitive to small fractions of young stars poses a strong constraint on recent star formation in massive ellipticals., The fact that the method presented here is very sensitive to small fractions of young stars poses a strong constraint on recent star formation in massive ellipticals.
 We should emphasize that our claim only applies to the scatter at faint magnitudes. since red faint galaxies might lie beyond the detection limit of the archival F300W images used here.," We should emphasize that our claim only applies to the scatter at faint magnitudes, since red faint galaxies might lie beyond the detection limit of the archival F300W images used here."
 There are two possible alternatives to explain the blueness of these faint early-type systems., There are two possible alternatives to explain the blueness of these faint early-type systems.
 However. one can argue against them for the following reasons:," However, one can argue against them for the following reasons:"
since strong HICN emission is detected.,since strong HCN emission is detected.
 has a CLII;CN 11)/7CO (2.1) integrated intensitv ratio of 0.005. in good agreement with the value of 0.043 in 2008).," has a $_3$CN $^{13}$ CO (2–1) integrated intensity ratio of 0.058, in good agreement with the value of 0.043 in \citep{he08}."
 Strong C'S emission has been detected in our survey., Strong CS emission has been detected in our survey.
 According to (1993).. CS can be rapidly destroved by shocks which might occur after a star leaves the AGB stage and ejects material in a very fast wind (Ilerpinetal.2002).," According to \citet{willacy98}, CS can be rapidly destroyed by shocks which might occur after a star leaves the AGB stage and ejects material in a very fast wind \citep{herpin02}."
. Therefore. the high abundance of CS in suggests that shocks are not important for the chemistry in this C-rich envelope.," Therefore, the high abundance of CS in suggests that shocks are not important for the chemistry in this C-rich envelope."
 Three refractory Si-bearing species (SiO. SiS. and S1Cs) were detected in 6.," Three refractory Si-bearing species (SiO, SiS, and $_2$ ) were detected in ."
. Although other Si-bearing species were detected in (Cernicharoetal.2000).. emission from the other Si-bearing species is relatively faint and should be below the detection limit of our observations of 6.," Although other Si-bearing species were detected in \citep{cernicharo00}, emission from the other Si-bearing species is relatively faint and should be below the detection limit of our observations of ."
. We find that the abunclances of SiO and SiCs in are similar to those in determined by Ileetal.(2008)., We find that the abundances of SiO and $_2$ in are similar to those in determined by \citet{he08}.
. Although the situation may be complicated by optical depth effects. the WON/SiO line intensity ratio has (he potential to provide a useful tool to discriminate between C-riehi and O-rich envelopes and is a good (racer of mass loss rate for AD and ο stars (seee.g.Diegingetal.2000).," Although the situation may be complicated by optical depth effects, the HCN/SiO line intensity ratio has the potential to provide a useful tool to discriminate between C-rich and O-rich envelopes and is a good tracer of mass loss rate for M and S stars \citep[see e.g.][]{bieging00}."
. The HCN (82)/SiO (65) intensity ratio in is 8.4. in good agreement the value of 9.7 in (IIeetal.2008).," The HCN (3–2)/SiO (6–5) intensity ratio in is 8.4, in good agreement the value of 9.7 in \citep{he08}."
. There is no evidence showing that the ION/SiO line intensity ratio has dependance on (he mass loss rate of C-rich stars., There is no evidence showing that the HCN/SiO line intensity ratio has dependance on the mass loss rate of C-rich stars.
 GonzálezDelgadoetal.(2003) ancl Schoieretal.(2006) found a correlation between the mass loss rate and the SiO abundance for AGB stars., \citet{gonzalez03} and \citet{schoier06} found a correlation between the mass loss rate and the SiO abundance for AGB stars.
 This is described as of SiO molecules onto dust grains., This is described as freeze-out of SiO molecules onto dust grains.
 The similarity of the SiO abundances in and suggests that the depletion of SiO onto dust grains might be insignificant for the two C-rich envelopes., The similarity of the SiO abundances in and suggests that the depletion of SiO onto dust grains might be insignificant for the two C-rich envelopes.
 Our observations show that the SiS abundance in is lower than that in IRC+10216., Our observations show that the SiS abundance in is lower than that in .
. The Sis (14.13)/SiO (65) intensity ratio in is 1.1. about half of that in found by IIeetal. (2008)..," The SiS (14–13)/SiO (6–5) intensity ratio in is 1.1, about half of that in found by \citet{he08}. ."
 Schóieretal.(2007) cidnot finda strong correlation between tlie massloss rate and the SiS abundance. suggesting," \citet{schoier07} didnot finda strong correlation between the massloss rate and the SiS abundance, suggesting"
stars in individual LMC clusters as given in Grocholski et al.,stars in individual LMC clusters as given in Grocholski et al.
 have not been corrected for age and metallicity according to the formulation given by those authors. as this actually. increases the dispersion in distance modulus.," have not been corrected for age and metallicity according to the formulation given by those authors, as this actually increases the dispersion in distance modulus."
 Combining the mean Weyiss magnitudes for. the solar. neighbourhood and the LALC gives an uncorrected LAIC clistance modulus of 1S.505+0.019., Combining the mean $_{2MASS}$ magnitudes for the solar neighbourhood and the LMC gives an uncorrected LMC distance modulus of $\pm$ 0.019.
 Applying Ix-band corrections for the age and. metallicity cillerences between LAIC ancl solar-neighborhooc red. clump populations of -0.03 (Salaris Cirarcli 2002) gives a truc LALC Ix-band distance modulus of LS.4A75-40.0 21. where we have somewhat arbitrarily allowed for an uncertainty of 0.01. mag in the population correction.," Applying K-band corrections for the age and metallicity differences between LMC and solar-neighborhood red clump populations of -0.03 (Salaris Girardi 2002) gives a 'true' LMC K-band distance modulus of $\pm$ 0.021, where we have somewhat arbitrarily allowed for an uncertainty of 0.01 mag in the population correction."
 The only L-band mean magnitude for LMC red clump stars currently available in the literature is ονiss=17.03+0.06 from Ixoerwer (2009)., The only H-band mean magnitude for LMC red clump stars currently available in the literature is $H_{2MASS} = 17.03\pm0.06$ from Koerwer (2009).
 On the assumption that H-Ix. is about equal in LMC anc solar neighborhoot red clump stars (given that H-Ix. is insensitive to. both temperature and metallicity). we apply the same population correction as for Ix to get an L-band LAC modulus of 1S8.49+0.06. in good agreement with the K-band value bu much less tightly. constrained.," On the assumption that H-K is about equal in LMC and solar neighborhood red clump stars (given that H-K is insensitive to both temperature and metallicity), we apply the same population correction as for K to get an H-band LMC modulus of $\pm$ 0.06, in good agreement with the K-band value but much less tightly constrained."
 For LMC red clump stars in the J band. we have use the values given by Szewezvk et al. (," For LMC red clump stars in the J band, we have used the values given by Szewczyk et al. ("
2008). as neither Alves et al. (,"2008), as neither Alves et al. ("
2002) nor CGrocholski et al. (,2002) nor Grocholski et al. (
2007) provide J-baux measurements.,2007) provide J-band measurements.
 We get a mean Joyass for LMC red clump stars of 4040.02. and hence anuncorrcehed LM clistance nmiocdulus of 15.950.009.," We get a mean $_{2MASS}$ for LMC red clump stars of $\pm$ 0.02, and hence an LMC distance modulus of $\pm$ 0.03."
 Ehe ciscrepaney between this ane the corrected. Ix-band: modulus is unsurprising. since the mean οτί for τος clump stars in the LAIC is about 0.13 bluer than in the solar neighbourhood. indicating that a substantial population correction would. be required.," The discrepancy between this and the corrected K-band modulus is unsurprising, since the mean J-K for red clump stars in the LMC is about 0.13 bluer than in the solar neighbourhood, indicating that a substantial population correction would be required."
 Our results suggest that this correction would lie roughly halfway between the value for E (0.2. Cirardi Salaris 2001) and Ix (-0.03. Salaris Cirardi 2002).," Our results suggest that this correction would lie roughly halfway between the value for I (0.2, Girardi Salaris 2001) and K (-0.03, Salaris Girardi 2002)."
 The mean red clump absolute magnitude in Ix derived above is consistent with that of Alves (2000). although an exact comparison is dillicult. given the absence of a well-defined: standard svstem in the data used there.," The mean red clump absolute magnitude in K derived above is consistent with that of Alves (2000), although an exact comparison is difficult given the absence of a well-defined standard system in the data used there."
 Our result is. however. somewhat brighter than that derived. by CGroenewegen (2008).," Our result is, however, somewhat brighter than that derived by Groenewegen (2008)."
 This is not surprising in view of the rend toward fainter absolute magnitude with decreasing »wallax seen in our own data., This is not surprising in view of the trend toward fainter absolute magnitude with decreasing parallax seen in our own data.
 Alves’ sample include a range of parallaxes similar to that used here. while CGroenewegen's sample included. only. stars more. distan han those we observed.," Alves' sample included a range of parallaxes similar to that used here, while Groenewegen's sample included only stars more distant than those we observed."
 The hypothesis considered. by CGroenewegen. that a bias might be present in his resul »ecause ofa lack of data for bright nearby rec clump stars. is hus confirmed.," The hypothesis considered by Groenewegen, that a bias might be present in his result because of a lack of data for bright nearby red clump stars, is thus confirmed."
 As all three studies use the same definition of the red clump (ice. Paezvisski Stanck 1998). this is no a [actor in the comparison.," As all three studies use the same definition of the red clump (i.e. Paczyńsski Stanek 1998), this is not a factor in the comparison."
 Thecorrected distance to the LMC derived: above is in good agreement with the Ix-band. red. clump distance derived by Alves ct al. (, The distance to the LMC derived above is in good agreement with the K-band red clump distance derived by Alves et al. (
2002) (18.494+0.03). which includes the same Salaris Girardi (2002) population correction.,"2002) $\pm$ 0.03), which includes the same Salaris Girardi (2002) population correction."
 Our distance is in excellent. agreement with Dietrzvsski. Gieren and Uelalski (2003) (18.50+0.01). who applied no correction for population dillerences.," Our distance is in excellent agreement with Pietrzyńsski, Gieren and Udalski (2003) $\pm$ 0.01), who applied no correction for population differences."
 Red clump LMC distances derived. using V. and | magnitudes would need. much larger anc more uncertain corrections [ου abundance and age cllects. and are best excluded. from comparison (Pictrzvisski et al.," Red clump LMC distances derived using V and I magnitudes would need much larger and more uncertain corrections for abundance and age effects, and are best excluded from comparison (Pietrzyńsski et al."
 2010)., 2010).
 While the K-band correction undoubtedly has some uncertainty attached. the correction itself is quite small.," While the K-band correction undoubtedly has some uncertainty attached, the correction itself is quite small."
 Thewnecorrected Ix-band. Cepheicl distance moduli. of Is.48+0.04 (Benedict ct al., The K-band Cepheid distance moduli of $\pm$ 0.04 (Benedict et al.
 2007) and IS470.03 (van Lecuwen οἱ al., 2007) and $\pm$ 0.03 (van Leeuwen et al.
 2007) are [likewise in excellent. agreement. especially with our eorreched distance.," 2007) are likewise in excellent agreement, especially with our distance."
 Phe uncorrected V-band and. Wis; distance moduli from Beneclict et al. (, The uncorrected V-band and $_{VI}$ distance moduli from Benedict et al. (
2007). 18.50 0.03 ancl IS.520.06. and the Wi modulus from van Leeuwen et al. (,"2007), 18.50 $\pm$ 0.03 and $\pm$ 0.06, and the $_{VI}$ modulus from van Leeuwen et al. ("
2007). 18.52zE0.03. are slightly larger. but LAIC Cepheids have long been known to be bluer at a given. period than Cepheids in the solar neighbourhood (Gascoigne Iron 1965. Laney Stobie 150. 1904). so this small dillerence is in the expected sense. though hardly significant.,"2007), $\pm$ 0.03, are slightly larger, but LMC Cepheids have long been known to be bluer at a given period than Cepheids in the solar neighbourhood (Gascoigne Kron 1965, Laney Stobie 1986, 1994), so this small difference is in the expected sense, though hardly significant."
 Agreement with the Cepheid moduli apparently also implies good agreement with the most recent RR Lyrac results from LIST parallaxes (Benedict AleArthur 2011)., Agreement with the Cepheid moduli apparently also implies good agreement with the most recent RR Lyrae results from HST parallaxes (Benedict McArthur 2011).
 bor Twpe Ib Cepheids. the latest results (Alatsunaga. Feast Alenzies 2009) give LS4640.10. which is in. very good agreement although considerably less precise.," For Type II Cepheids, the latest results (Matsunaga, Feast Menzies 2009) give $\pm$ 0.10, which is in very good agreement although considerably less precise."
 This supersedes the earlier result (Feast ct al., This supersedes the earlier result (Feast et al.
 2008). which eave a rather smaller nioclulus.," 2008), which gave a rather smaller modulus."
 Results from LMC eclipsing binaries are rather sparse. and only one result is available for a binary where empirical surface brightnesses are available (Pietrzvásski ct al.," Results from LMC eclipsing binaries are rather sparse, and only one result is available for a binary where empirical surface brightnesses are available (Pietrzyńsski et al."
 2009)., 2009).
 Agreement between their value for the LMC modulus (18.50+0.06) anc ours is reasonable enough. but a [final comparison will have to wait until results for the remaining seven binaries in that phase of the Araucaria Project are available.," Agreement between their value for the LMC modulus $\pm$ 0.06) and ours is reasonable enough, but a final comparison will have to wait until results for the remaining seven binaries in that phase of the Araucaria Project are available."
 Neat-LR. observations of 226 red clump stars as bright as A=0.3 have resulted in a determination of the local mean absolute magnitude in οντως and Keayyess accurate to +0.02 mag.," Near-IR observations of 226 red clump stars as bright as $K =
-0.3$ have resulted in a determination of the local mean absolute magnitude in $_{2MASS}$ and $_{2MASS}$ accurate to $\pm0.02$ mag."
 A comparison with Ix-band absolute magnitudes for LMC red. clump stars from the literature implies an LAIC distance. modulus. of 18.5030.02. (uncorrected). or 18.472E0.02 (corrected by the value given in Salaris Girardi 2002).," A comparison with K-band absolute magnitudes for LMC red clump stars from the literature implies an LMC distance modulus of $\pm0.02$ (uncorrected), or $\pm0.02$ (corrected by the value given in Salaris Girardi 2002)."
 Comparison of this result touncorrecled Copheid. PL-relation clistance moduli in the Ix-band. (van Leeuwen et al., Comparison of this result to Cepheid PL-relation distance moduli in the K-band (van Leeuwen et al.
 2007. )onedict et al.," 2007, Benedict et al."
 2007) suggests that metallicity corrections to distance moduli derived [rom near-H Cepheid PL relations may not be very significant. at least for abundances between those in the solar neighbourhood and in the LAIC.," 2007) suggests that metallicity corrections to distance moduli derived from near-IR Cepheid PL relations may not be very significant, at least for abundances between those in the solar neighbourhood and in the LMC."
 1n addition. the agreement between our cistance moclulus and those derived from Cepheid Wy; PL relations (van Lecuwen et al.," In addition, the agreement between our distance modulus and those derived from Cepheid $_{VI}$ PL relations (van Leeuwen et al."
 2007. Denedict et al.," 2007, Benedict et al."
 2007) suggests that )ono et al. (, 2007) suggests that Bono et al. (
2010) may be correct in arguing that metallicity corrections to distances from. Cepheid. Wesenheit (VI) PL relations may be fairly negligible.,2010) may be correct in arguing that metallicity corrections to distances from Cepheid Wesenheit (VI) PL relations may be fairly negligible.
 Aluch the sameholds for the V-band PLrelation (Benedict ο al., Much the sameholds for the V-band PLrelation (Benedict et al.
 2007). and these conclusions are strengthened by the recent results from RR Lyraes. Type LH," 2007), and these conclusions are strengthened by the recent results from RR Lyraes, Type II"
simplicity. we retain only the scattering term in. equation (7)). reducing it to In the 3l limit. equations (9)) and (10)) lead to an exponential growth of the pairdensity ancl velocity: for .r29r. where is the leneth-seale for pair loading.,"simplicity, we retain only the scattering term in equation \ref{dPdxa}) ), reducing it to In the $\beta \ll 1$ limit, equations \ref{dndxb}) ) and \ref{dPdxb}) ) lead to an exponential growth of the pairdensity and velocity: for $x > x_\pm$, where is the length-scale for pair loading."
" For a GRB of isotropic-cquivalent output energy. £-. equation (5)) gives for the acceleration length-scale at racius r where A=efl|2) is the geometrical thickness of he GARB front. % being the observed burst. duration. 2 the GIUDs redshift. and the usual scaling .X,,=V/10"" was used."," For a GRB of isotropic-equivalent output energy $E_\gamma$, equation \ref{lambda}) ) gives for the acceleration length-scale at radius $r$ where $\Delta = cT/(1+z)$ is the geometrical thickness of the GRB front, $T$ being the observed burst duration, $z$ the GRB's redshift, and the usual scaling $X_n = X/10^n$ was used."
 From equation (11)) we see that the wind acceleration ength-scale wv... defined by +Grae)=2 isa factor of a [ow arecr than wa.," From equation \ref{nb}) ) we see that the wind acceleration length-scale $x_{acc}$, defined by $\gamma (x_{acc}) = 2$ is a factor of a few larger than $x_\pm$ ."
" A simple estimate of uric. can be obtained ον equating the momentum deposited by photon scattering Dacelerpraes)PyzomeoeccEie)2=DacezynoscerefA} (considering that all photons have the same energy mocz,) with the momentum (acct|pectpemye of the medium. (assuming that the wind mass density. is dominated by the protons. Gru)Kp(rocnpsme). and that nyCroce) 8): Then equation (13)) shows that the wind is accelerated to a relativistic speed for radii smaller than >Meee We Can solve the pair density ancl momentun equations together to obtain nGr) ων"," A simple estimate of $x_{acc}$ can be obtained by equating the momentum deposited by photon scattering $\npair_{acc} (\sigma_T x_{acc})
(F_p \epsilon_p m_e c^2/c^2) = \npair_{acc}\epsilon_p(m_e c)(x_{acc}/\lambda)$ (considering that all photons have the same energy $m_e c^2 \epsilon_p$ ) with the momentum $(\npair_{acc} m_e +
n_{p,acc} m_p) c \sim \next m_p c$ of the medium (assuming that the wind mass density is dominated by the protons, $\npair (x_{acc}) \ll n_p(x_{acc})
(m_p/m_e)$, and that $n_p(x_{acc}) \approx \next$ ): Then equation \ref{xpm}) ) shows that the wind is accelerated to a relativistic speed for radii smaller than For $x \gg x_{acc}$ we can solve the pair density and momentum equations together to obtain $\npair(x)$ $\gamma(x)$."
" We consider a power-law solution of the form Substituting this into equations (9)) and (10)). and assuming that the mass density is dominated by protons Lc. the number of pairs per proton is much less than mpm... we obtain where yourfoc. og]Lmoraesfru is à constant independent of c. and inu;s ds determined. by the condition that the pair creation optical depth for a photon scattered at a; of energy ~cy. is unity between vii, and ir tine ds determined by thefollowing equation ὃν substituting (16)) in the above equation we find Minin explicitly Or Lt follows from equation (18)) that Furthermore. there are two cases to be considered. for the integral in equation (17)) | one of which is ej2(aDaszc 1."," We consider a power-law solution of the form Substituting this into equations \ref{dndxb}) ) and \ref{dPdxb}) ), and assuming that the mass density is dominated by protons i.e., the number of pairs per proton is much less than $m_p/m_e$, we obtain where $y\equiv x/x_{acc}$ , $\eta\equiv x_{acc}/x_\pm$ is a constant independent of $x$, and $x_{min}$ is determined by the condition that the pair creation optical depth for a photon scattered at $x_{min},
$ of energy $\sim \epsilon_p$, is unity between $x_{min}$ and $x$ ; $x_{min}$ is determined by thefollowing equation By substituting \ref{sola}) ) in the above equation we find $x_{min}$ explicitly or It follows from equation \ref{dPdxc}) ) that Furthermore, there are two cases to be considered for the integral in equation \ref{dndxc}) ) – one of which is $a_1-2(\alpha+1)a_2>-1$ ."
 The integral in this case is dominated by the upper limit. and by equating the exponents of y on the two sides of the equation we find ad=1.," The integral in this case is dominated by the upper limit, and by equating the exponents of $y$ on the two sides of the equation we find $\alpha a^2 = 1$."
 This together with equation (22)) implies that a<1/2. which is not a case of interest for GRBs since the high energy spectral index. for GRBs has à2 1.," This together with equation \ref{rela}) ) implies that $\alpha<1/2$, which is not a case of interest for GRBs since the high energy spectral index for GRBs has $\alpha>1$ ."
 The other possibility is that αι2(al)ro<— l.andinthis case pair production is dominated by photons scattered at the smallest. ie. at ai.," The other possibility is that $a_1-2(\alpha+1)a_2<-1$ , and in this case pair production is dominated by photons scattered at the smallest $x$ i.e. at $x_{min}$."
" Making use of the expression for ric, (eq. 21))", Making use of the expression for $x_{min}$ (eq. \ref{xmin}) )
" in equation (17)). and setting the exponent of y to zero results in Solving for e, and e» from equations (22)) and (23)) we lind In other words the solution for n and 5 are given by with ol)~expt). the density at ra... and clo~ 4."," in equation \ref{dndxc}) ), and setting the exponent of $y$ to zero results in Solving for $a_1$ and $a_2$ from equations \ref{rela}) ) and \ref{relb}) ) we find In other words the solution for $\npair$ and $\gamma$ are given by with $A_1\sim n\exp(\eta)$, the density at $x_{acc}$, and $A_2\sim 4$ ."
 X somewhat more accurate expression for ely ancl ele can beobtained by combining equations (17)). (18)) (24)).," A somewhat more accurate expression for $A_1$ and $A_2$ can beobtained by combining equations \ref{dndxc}) ), \ref{dPdxc}) ) \ref{solb}) )."
 The result in Beloborocdoy (2002)is à special case (a= 1) of the solution presented. here., The result in Beloborodov (2002)is a special case $\alpha=1$ ) of the solution presented here.
 Equations (4)) and (7)) were derived under the assumptions of planar ecometry and. stationary solution in the a, Equations \ref{dndxa}) ) and \ref{dPdxa}) ) were derived under the assumptions of planar geometry and stationary solution in the $x$ -coordinate.
 Dueto the spherical expansion.the rate of momentum deposition decreases as r while the rate," Dueto the spherical expansion,the rate of momentum deposition decreases as $r^{-2}$ , while the rate"
to the carbon detected in the hieh-: IGAL particularly: at;Z6.,"to the carbon detected in the $z$ IGM, particularly at $z \ga 6$."
 Àn alternate interpretation of Table 1. assuniug that the ICAL is relatively uniforiilv euxielied by volume. is that Z= stars (1100 37.) created the ICM metals aud consequently. reionization may occur early.," An alternate interpretation of Table 1, assuming that the IGM is relatively uniformly enriched by volume, is that $Z=0$ stars (1–100 $M_\odot$ ) created the IGM metals and consequently, reionization may occur early."
 This is because the values of NyeNy (0 30.220) generated by these stars In association with the detected: Zj well exceeds that required for a late IT I reionization at :~6., This is because the values of $N_{\rm Lyc}/N_{\rm b}$ $\sim$ 30–220) generated by these stars in association with the detected $Z_{\rm IGM}$ well exceeds that required for a late H I reionization at $z \sim 6$.
 If clusters of such stars are respousible for both the reiouization ancl inetal eurichiment of the ICONE. they should be easily detected by future missions such as the IWST (Tiuuulinsouetal.2003. 2001).. aud the amount of star formation at 29 is potentially significant (81).," If clusters of such stars are responsible for both the reionization and metal enrichment of the IGM, they should be easily detected by future missions such as the JWST \citep{tsv,tgs}, and the amount of star formation at $z \ga 9$ is potentially significant 1)."
 Lastly. despite their lieh ionizing photonrete. VAISS are efficicut at ecnerating total ionizing radiationmass than are ποτάπου stars in a prescut-dav IME. owing to the ercatly boosted metal vield from a top-heavy IMFE. (," Lastly, despite their high ionizing photon, VMSs are efficient at generating total ionizing radiation than are metal-free stars in a present-day IMF, owing to the greatly boosted metal yield from a top-heavy IMF. ("
Both of these stellar populations. however. have approximately equal ο the difference being largest when IMSs are excluded. or equivaleutly at 2= 6.),"Both of these stellar populations, however, have approximately equal $\eta_{\rm Lyc, C}$, with the difference being largest when IMSs are excluded, or equivalently at $z
\ga 6$ .)"
 Therefore. VMSs are not necessarily preferred as a more efficient source of ionizing radiation at carly epochs ou nucleosvuthetie grounds in association with a eiven detected level of IGM. cuvichmenut. auc possibly based ou reionization requirements as well (sec. e.g.. SomervilleLivio 2003)).," Therefore, VMSs are not necessarily preferred as a more efficient source of ionizing radiation at early epochs on nucleosynthetic grounds in association with a given detected level of IGM enrichment, and possibly based on reionization requirements as well (see, e.g., \citealt{somerville2}) )."
 Furthermore. recent studies (e.g... Sclineideretal 2002)) indicate that the transition from a top- to a preseut-dav IMIF occurs at gas metallicities of about 10τσ.," Furthermore, recent studies (e.g., \citealt{schneider}) ) indicate that the transition from a top-heavy to a present-day IMF occurs at gas metallicities of about $10^{-4} Z_\odot$."
 If this were true. then we can scale the uuubers for VMSs in Table 1 down by 1.5 orders of magnitude. and derive that VMSS may produce oulv ~ 0.35 jonizine photous per barvou for au ICAL metallicity of 10.!Z.. before they pollute thei cuviromments aud cease forming.," If this were true, then we can scale the numbers for VMSs in Table 1 down by 1.5 orders of magnitude, and derive that VMSs may produce only $\sim$ 0.35 ionizing photons per baryon for an IGM metallicity of $10^{-4} Z_\odot$ before they pollute their environments and cease forming."
 We eniplasize. however. that VMSs may still be iuportaut for reiouization alone. given the right combination of conditions. owing to their hieh ioniziug rates.," We emphasize, however, that VMSs may still be important for reionization alone, given the right combination of conditions, owing to their high ionizing rates."
 The conversion between νο and NiveNy does not account for the relative propagation timescales of metals and photons from starforiiing reeious to the ICAL which will nupact the evolution of ICAL abundance ratios between individual elements. c.g.. [C/O].," The conversion between $\eta_{\rm Lyc}$ and $N_{\rm Lyc}/N_{\rm b}$ does not account for the relative propagation timescales of metals and photons from starforming regions to the IGM, which will impact the evolution of IGM abundance ratios between individual elements, e.g., [C/O]."
 Furthenuiore. the definition of gp nupliitle assumes the instantancous creation of the metals.," Furthermore, the definition of $\eta_{\rm Lyc}$ implicitly assumes the instantaneous creation of the metals."
 This is not necessarily true at high redshifts. c.g. to generate sufficicut carbon at 2— 36 requires the star formation to have occurred at 2 69.," This is not necessarily true at high redshifts, e.g., to generate sufficient carbon at $z \sim$ 3–6 requires the star formation to have occurred at $z \ga$ 6–9."
 As we noted earlier. this becomes particularly problematic for the transport of the carbon to the ICM through SN-driven winds.," As we noted earlier, this becomes particularly problematic for the transport of the carbon to the IGM through SN-driven winds."
 We explore the cosmological relevance of these timescale issucs in inore detail in a forthcoming paper., We explore the cosmological relevance of these timescale issues in more detail in a forthcoming paper.
 We are grateful το Jason Tunliuson for valuable input aud calculations., We are grateful to Jason Tumlinson for valuable input and calculations.
 We thank Alike Shull aud Jessica Roscuberg for mau helpful discussions. and Danicl Schaerer. Alessandro Chief. Oscar Straniero aud Sara Ellisou for useful correspoudence.," We thank Mike Shull and Jessica Rosenberg for many helpful discussions, and Daniel Schaerer, Alessandro Chieffi, Oscar Straniero and Sara Ellison for useful correspondence."
 We thank our anonviuous referee for helpful sugeestious which improved the manuscript., We thank our anonymous referee for helpful suggestions which improved the manuscript.
 À. V. eratefullv acknowledges the support of NSF eraut. AST-0201670., A. V. gratefully acknowledges the support of NSF grant AST-0201670.
. J. W. T. acknowledges the support of DOE eraut. DE-ECGO2-91ER10606 in Nuclear Physics and Astrophysics at The University of Chicago., J. W. T. acknowledges the support of DOE grant DE-FG02-91ER40606 in Nuclear Physics and Astrophysics at The University of Chicago.
the calculation of optical depths.,the calculation of optical depths.
" This calculation requires a specification of the density field at all locations, which can be given by the SPH formalism."," This calculation requires a specification of the density field at all locations, which can be given by the SPH formalism."
" The definition of a scalar field using an SPH particle distribution is where is the value of at the location of particlejj., is the mass of particle77,, is the density of particlej7,, and )isthesmoothingkernel(orinterpolatingkernel)."," The definition of a scalar field using an SPH particle distribution is where is the value of at the location of particle, is the mass of particle, is the density of particle, and is the smoothing kernel (or interpolating kernel)."
"Thesummationisty, ~~ nearest neighbour particles to the location ).", The summation is typically over nearest neighbour particles to the location.
".Thesmoothing lengthof particlejj,,hh;,, is defined such that a sphere of radius will contain the nearest neighbour particles tojj."," The of particle, is defined such that a sphere of radius will contain the nearest neighbour particles to."
". For example, to calculate density, substitute):: The sphere that contains the nearest neighbours (i.e. a sphere of radius 22h;)) is referred to as the volume..There is a subtlety to equation (16)) that should be noted, relating to which value of to use."," For example, to calculate density, substitute: The sphere that contains the nearest neighbours (i.e. a sphere of radius ) is referred to as the .There is a subtlety to equation \ref{eq:rhocalc}) ) that should be noted, relating to which value of to use."
" There are now two means by which to estimate density: the first is the so-called ""gather"" method, where the smoothing length is defined for the locationTTj, and Where the index refers to all particles which are contained within a radius of the locationrr;."," There are now two means by which to estimate density: the first is the so-called “gather” method, where the smoothing length is defined for the location, and Where the index refers to all particles which are contained within a radius of the location."
". The second method (which is used in this work and in ?)) is the ""scatter"" method.", The second method (which is used in this work and in \citealt{SPHRAY}) ) is the “scatter” method.
" The smoothing length is used - in this formalism, the density at any one location is calculated by adding the contributions from particles whose smoothing volume intersects the location: In the context of ray tracing, the density along the ray is affected only by particles with smoothing volumes that intersect it (see Figure 2))."," The smoothing length is used - in this formalism, the density at any one location is calculated by adding the contributions from particles whose smoothing volume intersects the location: In the context of ray tracing, the density along the ray is affected only by particles with smoothing volumes that intersect it (see Figure \ref{fig:scatter}) )."
" By determining which particles intersect the ray, the rest of the particle distribution can be ignored for the purposes of calculating optical depth, reducing computational expense (whereas with the gather method, the ensemble of particles contributing to the calculation changes significantly with position, and requires the inclusion of a larger subset of SPH particles to perform the calculation)."," By determining which particles intersect the ray, the rest of the particle distribution can be ignored for the purposes of calculating optical depth, reducing computational expense (whereas with the gather method, the ensemble of particles contributing to the calculation changes significantly with position, and requires the inclusion of a larger subset of SPH particles to perform the calculation)."
" Using the scatter method, the column density Jalongtherayis Which can be rearranged to give The integral is now decomposed into integrals, where is the number of particles intersected by the ray."," Using the scatter method, the column density along the ray is Which can be rearranged to give The integral is now decomposed into integrals, where is the number of particles intersected by the ray."
 Each integral is defined by the impact parameter (see Figure 2))., Each integral is defined by the impact parameter (see Figure \ref{fig:scatter}) ).
" The calculation itself can be performed for a smoothing volume of1,, and scaled upwards (this is due to the construction of the smoothing kernel)."," The calculation itself can be performed for a smoothing volume of, and scaled upwards (this is due to the construction of the smoothing kernel)."
 The entire optical depth calculation has been decomposed into the repetition of a single algorithm for calculating the optical depth through a single smoothing volume., The entire optical depth calculation has been decomposed into the repetition of a single algorithm for calculating the optical depth through a single smoothing volume.
 This calculation will nowbe expounded., This calculation will nowbe expounded.
 Consider Figure 3.., Consider Figure \ref{fig:sphere}.
 The ray (with direction vector )))intersectsthespherewithimpactparameterbb., The ray (with direction vector ) intersects the sphere with impact parameter.
". If the ray penetrates a distance into the sphere (out of total possible distance ss)), then the integral can be defined analytically,a given the functional form of )."," If the ray penetrates a distance into the sphere (out of a total possible distance ), then the integral can be defined analytically, given the functional form of ."
.defining, defining
of that clement was maintained. as a free parameter. ancl the process repeated to determine the clement providing the next most significant improvement.,"of that element was maintained as a free parameter, and the process repeated to determine the element providing the next most significant improvement."
 1n agreement with the results for AIST and NGC 4696. we find that the most significant. improvements in the fit to the NGC 4636 data are obtained by including the abundances of Si. Mg and S as free fit parameters (the measured 47.2 value is. reduced from. -722.6 to 475.0. for the introduction. of only three extra fit) parameters)," In agreement with the results for M87 and NGC 4696, we find that the most significant improvements in the fit to the NGC 4636 data are obtained by including the abundances of Si, Mg and S as free fit parameters (the measured $\chi^2$ value is reduced from 722.6 to 475.0, for the introduction of only three extra fit parameters)."
 At this »ont. including the abundances of further elements as fit xuvameters did. not lead to such significant. improvements and. due to the already complex nature of the best-fit moc1. we forced the abuncanees of all other elements to vary with he same ratio relative to their solar values (cllectively tving he abundances to that of iron. the clement to which the ASCA cata are most. sensitive).," At this point, including the abundances of further elements as fit parameters did not lead to such significant improvements and, due to the already complex nature of the best-fit model, we forced the abundances of all other elements to vary with the same ratio relative to their solar values (effectively tying the abundances to that of iron, the element to which the ASCA data are most sensitive)."
 We note. however. that including the abundances of Na and. O as further free fit xwameters did. lead. to formally significant improvements. with reductions in X7 of ~20 and 30. respectively.," We note, however, that including the abundances of Na and O as further free fit parameters did lead to formally significant improvements, with reductions in $\chi^2$ of $ \sim 20$ and 30, respectively."
 Llowever. due to the systematic uncertainties in the NCC 4636 spectra at low energies (Section 3.3). which elfect the measured O abundance. and the fact that the Na abundance fits to an un-physically high. value (5 times solar). the metallicities of these elements were not included as free. parameters in our final analysis).," However, due to the systematic uncertainties in the NGC 4636 spectra at low energies (Section 3.3), which effect the measured O abundance, and the fact that the Na abundance fits to an un-physically high value $\sim 5$ times solar), the metallicities of these elements were not included as free parameters in our final analysis)."
 Phe measured. clement abundances for NGC 4636. as a fraction of their solar photospheric values defined by Anders Crevesse (1989). are Zp.=0.62un οσο Zu=0.96fr and Za=149.525.," The measured element abundances for NGC 4636, as a fraction of their solar photospheric values defined by Anders Grevesse (1989), are $Z_{\rm Fe} = 0.62^{+0.13}_{-0.09}$, $Z_{\rm Mg} =
0.93^{+0.19}_{-0.15}$, $Z_{\rm Si} = 0.96^{+0.18}_{-0.12}$ and $Z_{\rm
S} = 1.49^{+0.27}_{-0.22}$."
 These results are in reasonable agreement with those of Matsushita C1997) and. Buote (1999)., These results are in reasonable agreement with those of Matsushita (1997) and Buote (1999).
 Scaling our measured abundance ratios to the meteoric abundance scale of Anders Crevesse (1989) we determine Me/Fe] ~0.00. διο ~0.02 and. S/Ee]-0.16.," Scaling our measured abundance ratios to the meteoric abundance scale of Anders Grevesse (1989) we determine [Mg/Fe] $\sim 0.00$, [Si/Fe] $\sim 0.02$ and $\sim 0.16$."
 Comparing these values with the supernova vield. models of Nagataki Sato (1998). our observed Si/Fe] ratio implies a mass fraction of the iron enrichment due to type Ia supernova. MiosniafMerete in the range 0.55rr0.9 (where the limits cover the full range of models examined by these authors).," Comparing these values with the supernova yield models of Nagataki Sato (1998), our observed [Si/Fe] ratio implies a mass fraction of the iron enrichment due to type Ia supernova, $M_{\rm Fe,SNIa}/M_{\rm Fe,total}$, in the range $0.55-0.9$ (where the limits cover the full range of models examined by these authors)."
 For spherical type HE supernovae. a mass fraction in the range AlpeNia/MpeaonavOT0.85 is preferred.," For spherical type II supernovae, a mass fraction in the range $M_{\rm Fe,SNIa}/M_{\rm Fe,total} \sim 0.7-0.85$ is preferred."
 Further comparison of our Si/Fe] constraint with the supernovae nmicdels. discussed. by Gibson (1997). also. requires Miosnia~0.50.7.," Further comparison of our [Si/Fe] constraint with the supernovae models discussed by Gibson (1997) also requires $M_{\rm Fe,SNIa} \sim 0.5-0.7$."
 However. the observed S/Ec] and Me/Fe] ratios favour a mass fraction due to type la supernovae of &0.5 (Gibson 1991).," However, the observed [S/Fe] and [Mg/Fe] ratios favour a mass fraction due to type Ia supernovae of $\approxlt 0.5$ (Gibson 1997)."
 We have presented detections of harc N-rav emission components in the spectra of six. nearby giant elliptical ealaxies observed. with ASC'A.," We have presented detections of hard X-ray emission components in the spectra of six, nearby giant elliptical galaxies observed with ASCA."
" The galaxies exhibit clear. dynamical evidence for supermassive (107 afew 10"" )) black holes in their nuclei."," The galaxies exhibit clear, dynamical evidence for supermassive $10^8-$ a few $10^9$ ) black holes in their nuclei."
 Phe hare X-ray. emission can be parameterizecl by power-law mocels with photon indices. DL-061.5 (mean value 1.2). and luminosities. Exi407.26.H107is)215 5. or thermal bremsstrahlung models with electron. temperatures. AT10 keV. Such properties identify these galaxies as a new class of accreting X-ray source. with X-ray. spectra significantly harder than those of Seyfert nuclei. typical binary X-ray sources and low-luminosity AGN. and bolometric luminosities comparatively dominated bv their X-ray emission.," The hard X-ray emission can be parameterized by power-law models with photon indices, $\Gamma =
0.6-1.5$ (mean value 1.2), and luminosities, $L_{\rm X,1-10} \sim 2.6
\times 10^{40}-2.1 \times 10^{42}$ , or thermal bremsstrahlung models with electron temperatures, $kT > 10$ keV. Such properties identify these galaxies as a new class of accreting X-ray source, with X-ray spectra significantly harder than those of Seyfert nuclei, typical binary X-ray sources and low-luminosity AGN, and bolometric luminosities comparatively dominated by their X-ray emission."
 We have argued. that the hard X-ray. emission. is likely to be due to acerction onto the central. supermassive black holes. via low-racliative cllicicney Lows. coupled with strong outllows.," We have argued that the hard X-ray emission is likely to be due to accretion onto the central, supermassive black holes, via low-radiative efficiency flows, coupled with strong outflows."
 Within such models. the hard. X-ray emission. originates [rom bremsstrahlung processes in the racliatively-clominant. outer regions of the accretion lows. (," Within such models, the hard X-ray emission originates from bremsstrahlung processes in the radiatively-dominant, outer regions of the accretion flows. ("
Detailed modeling. and discussion of these issues are presented by Di Matteo 1999.,Detailed modeling and discussion of these issues are presented by Di Matteo 1999b).
 For the case of M87. the lux of the hard component was shown to be in good agreement with the nuclear X-rav [lux determined from earlier ROSAT LIBRI observations. which were able to resolve knot A in the jet from the nuclear emission component.," For the case of M87, the flux of the hard component was shown to be in good agreement with the nuclear X-ray flux determined from earlier ROSAT HRI observations, which were able to resolve knot A in the jet from the nuclear emission component."
 We have stressed the importance of accounting for the complex temperature structure. intrinsic absorption and variable clement abundance ratios in the analysis of the ASC'X spectra.," We have stressed the importance of accounting for the complex temperature structure, intrinsic absorption and variable element abundance ratios in the analysis of the ASCA spectra."
 We confirmed results showing that the application of such models leads to measurements of approximately solar emission-weighted. metallicities for the X-ray gas in the galaxies., We confirmed results showing that the application of such models leads to measurements of approximately solar emission-weighted metallicities for the X-ray gas in the galaxies.
 We also presented detailed results on the individual element abundances in NGC 4636., We also presented detailed results on the individual element abundances in NGC 4636.
 Future observations at high spatial resolution with the Chandra Observatory will be crucial in establishing the contributions [from the various N-ray emission. mechanisms esent in elliptical galaxies and unambiguously identifving he origin of the hard. N-rav. components., Future observations at high spatial resolution with the Chandra Observatory will be crucial in establishing the contributions from the various X-ray emission mechanisms present in elliptical galaxies and unambiguously identifying the origin of the hard X-ray components.
 Decp X-ray spectroscopy with NMM ancl ASTRO-E will allow us to examine variability. in the X-ray emission. (which. should x: slower in sources where the X-rav emission originates rom the outer regions of low racliative-cllicicney accretion lows than in typical Sevfert nuclei) and to search for road. iron emission features associated with the power-law components.," Deep X-ray spectroscopy with XMM and ASTRO-E will allow us to examine variability in the X-ray emission (which should be slower in sources where the X-ray emission originates from the outer regions of low radiative-efficiency accretion flows than in typical Seyfert nuclei) and to search for broad, iron emission features associated with the power-law components."
 The detection of such broad emission features would argue against the simple. low-racliative ellicienev accretion models discussed. here. ancl require the presence of significant amounts of cold. reflecting material close to the central black holes.," The detection of such broad emission features would argue against the simple, low-radiative efficiency accretion models discussed here, and require the presence of significant amounts of cold, reflecting material close to the central black holes."
 The discovery of hard X-ray emission components in the spectra of nearby elliptical galaxies containing supermassive jack holes provides important new constraints on the accretion processes in these systenis., The discovery of hard X-ray emission components in the spectra of nearby elliptical galaxies containing supermassive black holes provides important new constraints on the accretion processes in these systems.
 Our results are relevant o understanding the demise of quasars (which could Xausiblv be due to a change in the dominant. acerction mode in ellipticals over the history of the Universe) and. ultimately. the origin of the hard (DL~ 1.4) Cosmic X-ray Backeround Di Matteo Fabian 1997b).," Our results are relevant to understanding the demise of quasars (which could plausibly be due to a change in the dominant accretion mode in ellipticals over the history of the Universe) and, ultimately, the origin of the hard $\Gamma \sim 1.4$ ) Cosmic X-ray Background Di Matteo Fabian 1997b)."
 These issues. and others. will be explored in future papers (Di Matteo 1990b: Di Matteo Allen 1999).," These issues, and others, will be explored in future papers (Di Matteo 1999b; Di Matteo Allen 1999)."
Upon examination of the one-dimensional beta fits and their reduced y statistics. it appeared as though the beta model fits derived from Sherpa were not statistically robust.,"Upon examination of the one-dimensional beta fits and their reduced $\chi^{2}$ statistics, it appeared as though the beta model fits derived from Sherpa were not statistically robust."
 The reduced y for these fits was often above 2. and although others have used similar results (2).. 1t was judged necessary to find a second method used as to of independently verify the profiles.," The reduced $\chi^{2}$ for these fits was often above 2, and although others have used similar results \citep{Sakelliou}, it was judged necessary to find a second method used as to of independently verify the profiles."
 Therefore. a second set of temperature and iron profiles were calculated with the same set of data.," Therefore, a second set of temperature and iron profiles were calculated with the same set of data."
 The second method used was to divide the cluster into radial regions not by a constant length scale. but instead by giving each region a constant number of counts.," The second method used was to divide the cluster into radial regions not by a constant length scale, but instead by giving each region a constant number of counts."
" The furthest extent of spectral extraction was also determined by the net counts in a 2.55 wide region,", The furthest extent of spectral extraction was also determined by the net counts in a 5 wide region.
" If the net counts next the 2.""55 wide region out ever dropped below 20 for or 100 for data. then this defined the edge of the cluster due to their low signal-to-noise ratio of the regions beyond this point."," If the net counts next the 5 wide region out ever dropped below 20 for or 100 for data, then this defined the edge of the cluster due to their low signal-to-noise ratio of the regions beyond this point."
 The four calculated counts regions for each cluster are listed in Table 3.., The four calculated counts regions for each cluster are listed in Table \ref{Table3}.
 Dividing the cluster in this manner also allows for all of the spectra for one cluster to be comparably significant instead of having a wide disparity in spectral quality., Dividing the cluster in this manner also allows for all of the spectra for one cluster to be comparably significant instead of having a wide disparity in spectral quality.
 The spectra were extracted in exactly the same manner as the core radius spectra. which will be described in detail in $2.5...," The spectra were extracted in exactly the same manner as the core radius spectra, which will be described in detail in \ref{spectrasec}."
 This process of sub-dividing the cluster will be called the counts profile or counts hereafter.," This process of sub-dividing the cluster will be called the counts profile or counts radius, hereafter."
 They will also be listed às 7j. 7s.73.and ry as an abbreviation in the tables. particularly in Table 3 The radial profiles in each cluster are compared in two ways in Tables 3 4..," They will also be listed as $r_{\rm{1}}, r_{\rm{2}}, r_{\rm{3}}$, and $r_{\rm{4}}$ as an abbreviation in the tables, particularly in Table \ref{Table3}
 The radial profiles in each cluster are compared in two ways in Tables \ref{Table3} \ref{Table4}."
 Table 3 shows the extents of each individual counts region as well as the calculated core radius and virial radius fgg 1n areseconds., Table \ref{Table3} shows the extents of each individual counts region as well as the calculated core radius and virial radius $r_{200}$ in arcseconds.
 Table 4. shows the average core and counts regions in terms of kpe., Table \ref{Table4} shows the average core and counts regions in terms of kpc.
 It was found that there were insignifica5 differences between the two radit on average. except foSB the very outer region.," It was found that there were insignificant differences between the two radii on average, except for the very outer region."
 The outermost counts regions are usually much wider than 2r. (see the averages given 1 Table 4 )., The outermost counts regions are usually much wider than $_{\rm c}$ (see the averages given in Table \ref{Table4}) ).
 Therefore. the average temperature and iro abundance measurements should be strongly correlatec between the core and counts radius. with differences only being expected in the outermost regions.," Therefore, the average temperature and iron abundance measurements should be strongly correlated between the core and counts radius, with differences only being expected in the outermost regions."
 Also included i Table 3is the calculated virial radius in are seconds., Also included in Table \ref{Table3} is the calculated virial radius in arc seconds.
 The virial radius is calculated as found in ?.. divided by 1.4 to take into account the difference between cosmologies (Ho=S0 km s! Mpe7! in ?. while Ho=71 km s Mpc! here).," The virial radius is calculated as found in \cite{Jones}, divided by 1.4 to take into account the difference between cosmologies ${H}_{0} = 50$ km $^{-1}$ $^{-1}$ in \cite{Jones} while $H_{0} = 71$ km $^{-1}$ $^{-1}$ here)."
 The formula itself is given as and the temperature used was the overall temperature measured by the procedure described in § 2.5.., The formula itself is given as and the temperature used was the overall temperature measured by the procedure described in $\S$ \ref{spectrasec}. .
 This, This
Both cases were evaluated together with the CPL parametrization (Eq. 7)).,Both cases were evaluated together with the CPL parametrization (Eq. \ref{eq:cpl}) ).
 We performed a MCMC run by introducing the modified CAMB routines and the new parametrization for w(z) in the COSMOMC code., We performed a MCMC run by introducing the modified CAMB routines and the new parametrization for $w(z)$ in the COSMOMC code.
" The total parameter space directly constrained was then p={Q,h?,Q.h7,0,T,Aj,n, wo,w1)."," The total parameter space directly constrained was then $\{\Omega_b h^2, \Omega_c h^2, \theta, \tau, A_s, n_s,$ $w_0, w_1 \}$."
 We used the matter power spectrum from Tegmarketal.2006 to account for the SDSS LRG data., We used the matter power spectrum from \cite{T06} to account for the SDSS LRG data.
 The modeling for non linear effects and scale dependent bias was done with a Q-model (Coleetal. 2005)) as explained above., The modeling for non linear effects and scale dependent bias was done with a Q-model \cite{Cole05}) ) as explained above.
" Since we are interested in models with w(z)«—1 in order to determine a valid figure of merit, dark energy perturbations were ""turned off"" when solving for CMB and matter power spectrum."," Since we are interested in models with $w(z)<-1$ in order to determine a valid figure of merit, dark energy perturbations were “turned off” when solving for CMB and matter power spectrum."
 The obtained results on all parameters are summarized in Table 1.., The obtained results on all parameters are summarized in Table \ref{Tablew0w1}.
 All these constraints on individual parameters were obtained by marginalization over other parameters., All these constraints on individual parameters were obtained by marginalization over other parameters.
" For comparison reasons, the last column shows the results where w is a constant value (no evolution)."," For comparison reasons, the last column shows the results where $w$ is a constant value (no evolution)."
 The constraints on nearly all parameters remain essentially identical., The constraints on nearly all parameters remain essentially identical.
" Of course, the main exception regards parameters that govern the equation of state itself, which have a bigger uncertainty compared to a constant w."," Of course, the main exception regards parameters that govern the equation of state itself, which have a bigger uncertainty compared to a constant $w$ ."
" Considering the parametrization of a smooth transition with either Il=1 or Γ=0.85 results in some small changes in the preferred values and the uncertainties, which seem to be smaller when Γ=0.85."," Considering the parametrization of a smooth transition with either $\Gamma=1$ or $\Gamma=0.85$ results in some small changes in the preferred values and the uncertainties, which seem to be smaller when $\Gamma=0.85$."
 The 2D marginalized contours at and 95 confidence level are presented in Fig. 3.., The 2D marginalized contours at and 95 confidence level are presented in Fig. \ref{fig:w0w1}.
" Again, the slightly different values of the Γ parameter have an effect on the derived constraints on wo— wi, although it is rather small."," Again, the slightly different values of the $\Gamma$ parameter have an effect on the derived constraints on $w_0-w_1$ , although it is rather small."
" Finally, we notice that using the parametrization given by Eq."," Finally, we notice that using the parametrization given by Eq."
 8 with Γ=0.85 provides very similar constraints to a pure CPL parametrization., \ref{wqz} with $\Gamma=0.85$ provides very similar constraints to a pure CPL parametrization.
 The Dark Energy Task Force report (Albrechtetal. 2006)) introduced a numerical quantity to determine the capacity of future surveys in constraining dark energy models., The Dark Energy Task Force report \cite{DETF}) ) introduced a numerical quantity to determine the capacity of future surveys in constraining dark energy models.
 This numerical quantity is referred to as the figure of merit (f.o.m.), This numerical quantity is referred to as the figure of merit (f.o.m.)
 for a given experiment or combination of experiments and is defined as the reciprocal of the area of the marginalized 2D region contour at 95 confidence in the wo—w; parameter space., for a given experiment or combination of experiments and is defined as the reciprocal of the area of the marginalized 2D region contour at 95 confidence in the $w_0-w_1$ parameter space.
 In terms of the f.o.m., In terms of the f.o.m.
" for the present day data, the obtained values are summarized in the following table These values can thus be used to compare the improvement of future experiments in constraining dark energy evolution on Hubble timescales."," for the present day data, the obtained values are summarized in the following table These values can thus be used to compare the improvement of future experiments in constraining dark energy evolution on Hubble timescales."
" For more rapid transitions, one has to consider higher values of I, which is done in the next section."," For more rapid transitions, one has to consider higher values of $\Gamma$, which is done in the next section."
" In this section we examine what constraints can be derived when a rapid transition in the equation of state of dark energy (T=5) is considered, using the full data sets presented above."," In this section we examine what constraints can be derived when a rapid transition in the equation of state of dark energy $\Gamma=5$ ) is considered, using the full data sets presented above."
 Only models with w(z)>—1 were constrained by including DE perturbations when solving the total perturbations equations with CAMB., Only models with $w(z)>-1$ were constrained by including DE perturbations when solving the total perturbations equations with CAMB.
" For each case we ran one long chain, using the Rafetery-Lewis diagnostic to check for convergence."," For each case we ran one long chain, using the Rafetery-Lewis diagnostic to check for convergence."
" As for the LRG SDSS data, we used the data on the matter power spectrum as implemented in COSMOMC with a Q-model to correct for non-linear effects."," As for the LRG SDSS data, we used the data on the matter power spectrum as implemented in COSMOMC with a Q-model to correct for non-linear effects."
" Finally, we restricted ourselves to a flat Universe (€),=0) for simplicity reasons."," Finally, we restricted ourselves to a flat Universe $\Omega_k=0$ ) for simplicity reasons."
" As seen above, for transitions to w..=—1, the matter correlation function shows a different sensitivity to the initial value w,."," As seen above, for transitions to $w_-=-1$, the matter correlation function shows a different sensitivity to the initial value $w_+$."
" We considered then three distinct transitions by setting w_=—1 and three low values for w, (0,—0.1 and —0.2)."," We considered then three distinct transitions by setting $w_-=-1$ and three low values for $w_+$ $0, -0.1$ and $-0.2$ )."
 In each case the objective is to get constraints on the transition epoch (αι). the value a;=0 corresponding to the standard concordance model.," In each case the objective is to get constraints on the transition epoch $a_t$ ), the value $a_t= 0$ corresponding to the standard concordance model."
" As w, approaches 0 the contribution of dark energy at high redshifts remains non vanishing, allowing us to investigate its possible influence at earlier epochs."," As $w_+$ approaches $0$ the contribution of dark energy at high redshifts remains non vanishing, allowing us to investigate its possible influence at earlier epochs."
" Four different data combinations were used to constrain this model, CMB, CMB+SN Ia, CMB+P(k) and finally CMB+P(k)+ SN Ia. The results of the mean posterior values and confidence intervals on each parameter are summarized in Table 2.."," Four different data combinations were used to constrain this model, CMB, CMB+SN Ia, CMB+P(k) and finally CMB+P(k)+ SN Ia. The results of the mean posterior values and confidence intervals on each parameter are summarized in Table \ref{Table_wi02wf1}."
" The posterior distribution in some parameter is clearly non-Gaussian, so in some cases the lo error bars are quoted using asymmetrical limits."," The posterior distribution in some parameter is clearly non-Gaussian, so in some cases the $\sigma$ error bars are quoted using asymmetrical limits."
 Fig., Fig.
" 4 shows the contours in the space of Oo—a;, on which the effect of the different data combinations on these two parameters can be appreciated."," \ref{fig:Ol_at_1} shows the contours in the space of $\Omega_Q-a_t$, on which the effect of the different data combinations on these two parameters can be appreciated."
" This figure shows that the combination of the WMAPS data on the CMB with supernovae already constrains the possible transition to be at a;«0.6 at the two sigma level confidence region), or in redshift space z,>0.7."," This figure shows that the combination of the WMAP5 data on the CMB with supernovae already constrains the possible transition to be at $a_t<0.6$ at the two sigma level confidence region), or in redshift space $z_t>0.7$."
" When the matter power spectrum data is added, some small reduction on the allowed region in the transition parameter a, is observed."," When the matter power spectrum data is added, some small reduction on the allowed region in the transition parameter $a_t$ is observed."
" Surprisingly, the combination CMB+P(k) without supernovae leads to a better constraint on the transition epoch."," Surprisingly, the combination CMB+P(k) without supernovae leads to a better constraint on the transition epoch."
" This result is not intuitive, sinceas demonstrated in the previous section, one obtains only negligible differences in the matter correlation function shape by changing the transition epoch."," This result is not intuitive, sinceas demonstrated in the previous section, one obtains only negligible differences in the matter correlation function shape by changing the transition epoch."
 The cause for this reduction of the allowed transition redshift is actuallydue, The cause for this reduction of the allowed transition redshift is actuallydue
In FigureOo 3.. we show a selection of two-point correlation fictions derived from theWAZAP. data.,"In Figure \ref{fig:twopt_auto}, we show a selection of two-point correlation functions derived from the data."
 Specifically. all available Wa. Q and V. auto-correlatious are shown. in addition to the eross-correlations between the Wwe aud VW bands.," Specifically, all available $Ka$ , $Q$ and $V$ auto-correlations are shown, in addition to the cross-correlations between the $Ka$ and $W$ bands."
 Table 1 shows the \? sieuificauces for all possible two-point fuuctious from the available data. (," Table \ref{tab:twopt}
 shows the $\chi^2$ significances for all possible two-point functions from the available data. ("
Note that ouly unique combinations are actually shown: empty table cells iudicate that the same colubinatious may be fouud elsewhere iu the table.,Note that only unique combinations are actually shown; empty table cells indicate that the same combinations may be found elsewhere in the table.
 For example. TQ aud QI are ideutical for auto-correlatious. but ciffereut for cross-correlations.)," For example, IQ and QI are identical for auto-correlations, but different for cross-correlations.)"
 Starting with the pure intensity correlations shown in the top row of Figure 3.. we recognize the by now well-known behavior of the CAIB temperature two-poiut function. observed both byCOBE (e.s..Bennettctal.1991) audWAZAP (c.e..Spereeletal. 2003): at small aneular separations. it is slightly low compared to the ACDM inodel. and at separations lareer than 607. very close to zero.," Starting with the pure intensity correlations shown in the top row of Figure \ref{fig:twopt_auto}, we recognize the by now well-known behavior of the CMB temperature two-point function, observed both by \citep[e.g.,][]{bennett:1994} and \citep[e.g.,][]{spergel:2003}: : at small angular separations, it is slightly low compared to the $\Lambda$ CDM model, and at separations larger than $60^{\circ}$, very close to zero."
 This peculiar behavior has attracted the interest of both experimentalists aud theorists. aud some have suggested that this could be the signature of a closed topological space.," This peculiar behavior has attracted the interest of both experimentalists and theorists, and some have suggested that this could be the signature of a closed topological space."
 However. from the view of a simple 4? test. this function remains consistent with the simplest ACDALT model at the level.," However, from the view of a simple $\chi^2$ test, this function remains consistent with the simplest $\Lambda$ CDM model at the level."
 Next. looking at the tempcrature-polarization (IL-Q/U) cross-correlations we see that the overall behavior of the Q-. V. and Wa«W band functions are quite different.," Next, looking at the temperature-polarization (I-Q/U) cross-correlations we see that the overall behavior of the $Q$ -, $V$, and $Ka \times W$ band functions are quite different."
 This indicates that theWAZAP data still are too noise dominated to extract high-sensitivity cosmological information from individual bands., This indicates that the data still are too noise dominated to extract high-sensitivity cosmological information from individual bands.
 This is also reflected in the second and third cohuuus of Table 1.. where there is a significant scatter between the different results.," This is also reflected in the second and third columns of Table \ref{tab:twopt}, where there is a significant scatter between the different results."
 Towever. we do see that all results are iu good agereemoenut with the expectations. indicating that the noise model is satisfactory.," However, we do see that all results are in good agreement with the expectations, indicating that the noise model is satisfactory."
 The three bottoni rows of Figure 2. show the pure polarization correlation functions. which are the main target in this paper.," The three bottom rows of Figure \ref{fig:twopt_auto} show the pure polarization correlation functions, which are the main target in this paper."
 And here we see several interesting features., And here we see several interesting features.
 First. we recognize a sharp feature in the UU correlation function at ~111.," First, we recognize a sharp feature in the UU correlation function at $\sim141^{\circ}$."
 This is the angular separation between the A- and D sides ofthe differcutialWALA detectors. and it was also seen in the pure noise teiiperatureP two-point correlation function in the WAZAP data (Eriksenetal.2005).," This is the angular separation between the A- and B sides of the differential detectors, and it was also seen in the pure noise temperature two-point correlation function in the first-year data \citep{eriksen:2005}."
. However. even nore interesting ds the overall very pronounced large-scale excesses seen iu the QQ and UU fictions: both the Q- aud V-baud functions lie mostly within the 26-3e confidence regious. aud the overall aerectuent with the simulations appears quite poor.," However, even more interesting is the overall very pronounced large-scale excesses seen in the QQ and UU functions: both the $Q$ - and $V$ -band functions lie mostly within the $2\sigma$ $3\sigma$ confidence regions, and the overall agreement with the simulations appears quite poor."
 Again. this is strongly reflected in Table 1: all OQ correlations are anomalous at iiore than couficence. and all UU correlations at more than confidence.," Again, this is strongly reflected in Table \ref{tab:twopt}: all QQ correlations are anomalous at more than confidence, and all UU correlations at more than confidence."
 In the case of the TT band. which happens to be the most anomalous of any band. we have good reasons to expect such behavior.," In the case of the $W-$ band, which happens to be the most anomalous of any band, we have good reasons to expect such behavior."
 This band has a significantly higher 1/7 kuce frequency than any other baud (Jarosiketal.2003).. with the IL differencing assenibly. haviug the highest.," This band has a significantly higher $1/f$ knee frequency than any other band \citep{jarosik:2003}, with the $W$ 4 differencing assembly having the highest."
 As a result. theWAZAP team has chosen not to use this baud for cosmological analysis in polarization.," As a result, the team has chosen not to use this band for cosmological analysis in polarization."
 But the anomalous behavior of the Q aud V. bands is a priori not expected: these are used for cosinological analysis by theWALA team aud should be clean., But the anomalous behavior of the $Q$ and $V$ bands is a priori not expected; these are used for cosmological analysis by the team and should be clean.
 We Phave also generated an ensemble of noisc-oulv simulations. and computed the tvo-poiut fictions from hese.," We have also generated an ensemble of noise-only simulations, and computed the two-point functions from these."
 The corresponding 4? fractions are listed) in xmwentheses in Table 1 for the pure polarization modes.," The corresponding $\chi^2$ fractions are listed in parentheses in Table \ref{tab:twopt}
 for the pure polarization modes."
 Tere we see that. eenerallv speaking. the noisc-oulv wpothesis performs almost. but not quite. as well as he signal-plus-uoise hypothesis.," Here we see that, generally speaking, the noise-only hypothesis performs almost, but not quite, as well as the signal-plus-noise hypothesis."
 This is simply due to he fact that theWAZAP polarization data are stronely dominated by the correlated noise. and it is very difficult roni a correlation fiction point of view to distinguish yetwoeen a small signal component aud a large-scale noise Huctuation.," This is simply due to the fact that the polarization data are strongly dominated by the correlated noise, and it is very difficult from a correlation function point of view to distinguish between a small signal component and a large-scale noise fluctuation."
 The anomalous behavior seen in the Q- aud V-baud two-point functions clearly ueeds an explanation., The anomalous behavior seen in the $Q$ - and $V$ -band two-point functions clearly needs an explanation.
 Aud typically. when such unexpected behavior is observed. oue of the the first issues fo consider is residual foregrounds.," And typically, when such unexpected behavior is observed, one of the the first issues to consider is residual foregrounds."
 To check whether this may be a relevant issue. we first sinplwv compute the cross-correlation fictions between each of the three frequency bauds (va. Q. aud V) aud the two available foreground templates (svuchrotron aud dust).," To check whether this may be a relevant issue, we first simply compute the cross-correlation functions between each of the three frequency bands $Ka$, $Q$, and $V$ ) and the two available foreground templates (synchrotron and dust)."
 This is done both for the realWALAP data aud the simulated cuscuibles. aud the agreement between the (pure CAMIB | noise) sinulatious aud theWAZAP data is again quoted iu terms of a 47 fraction.," This is done both for the real data and the simulated ensembles, and the agreement between the (pure CMB $+$ noise) simulations and the data is again quoted in terms of a $\chi^2$ fraction."
 The results from these calculations are as follows: or the Wa baud. we find that the 47 siguificauces are 451 and 0.21 for svuchrotron and dust. respectively. indicating no significaut foreground detection iu this case.," The results from these calculations are as follows: for the $Ka$ band, we find that the $\chi^2$ significances are 0.51 and 0.24 for synchrotron and dust, respectively, indicating no significant foreground detection in this case."
" dElowever. for the (Q band the corresponding Munbers are (0.05. and ~0.005. corresponding to correlations statistically significant at 26 and ~3 respectively,"," However, for the $Q$ band the corresponding numbers are 0.05 and $\sim0.005$, corresponding to correlations statistically significant at $2\sigma$ and $\sim3\sigma$, respectively."
 For the V. baud. the uunbers are 0.05 and 1.02. sienificant at 20 or more.," For the $V$ band, the numbers are 0.05 and 0.02, significant at $2\sigma$ or more."
" To study theseforeeround correlations further. we conrpute the two-poiut functions from the foreground cluplates directly, and fit these to the observed correlation functions with a single free ampltucle for cach cluplate. A, and Aq. bv minimizine Tere. αμ.) is the correlation function mean aud οι=—(GC)p)Cu)pU) ds the covariance iatrix. both quantities obtained from the noise simuulatious."," To study theseforeground correlations further, we compute the two-point functions from the foreground templates directly, and fit these to the observed correlation functions with a single free amplitude for each template, $A_{\textrm{s}}$ and $A_{\textrm{d}}$, by minimizing Here, $C_{\textrm{sim}}(b)$ is the correlation function mean and $\Sigma_{\textrm{sim}}(b, b') = \bigl<(C(b) -\mu(b))(C(b')-\mu(b'))\bigr>$ is the covariance matrix, both quantities obtained from the noise simulations."
 The iudices 6.0% run over all possible pure polarization two-poiut bius (.6.. both angular bius and QQ. QU. and UU correlations).," The indices $b, b'$ run over all possible pure polarization two-point bins (i.e., both angular bins and QQ, QU, and UU correlations)."
 The resulting best-fit amplitudes from this caleulatiou for [να Q- aud V. bands are shown in Table 2..," The resulting best-fit amplitudes from this calculation for $Ka$ -, $Q$ - and $V$ bands are shown in Table \ref{tab:amp_marg_conf}."
 Tere. we again see that the /va-hand amplitudes are ecucrally significantly lower than those of the Q and V lands. (," Here, we again see that the $Ka$ -band amplitudes are generally significantly lower than those of the $Q$ and $V$ bands. ("
Note that the uncertainties quoted iu this table ouly iuchide statistical errors. not systematic errors.,"Note that the uncertainties quoted in this table only include statistical errors, not systematic errors."
The sienificances should thereforenot be considered as true detection levels. but are only sugecstive.},"The significances should thereforenot be considered as true detection levels, but are only suggestive.)"
 In Figure L.the fitted correlation functious are compared to the observed functions.," In Figure \ref{fig:amp_tp}, the fitted correlation functions are compared to the observed functions."
 First. the red curve shows the functions derived from the actual WAZAP data. with grav bands iudicatiung the lo uncertainties derived from smniulatious.," First, the red curve shows the functions derived from the actual data, with gray bands indicating the $1\sigma$ uncertainties derived from simulations."
 The blue curve shows the mean correlation function of the simnulatious. Cu tb).," The blue curve shows the mean correlation function of the simulations, $C_{\textrm{sim}}(b)$ ,"
The principal obstacle to the development of three-dimensional turbulence ancl a cascade to small scales is the stable stratification.,The principal obstacle to the development of three-dimensional turbulence and a cascade to small scales is the stable stratification.
 The kinetic energy. available in the vertical wind shear must be greater (han the potential energy. requirecl to mix the atmosphere., The kinetic energy available in the vertical wind shear must be greater than the potential energy required to mix the atmosphere.
 The ratio of these energies is quantified bv the Richardson number £2;=N?/(0U/Or). where N is the frequency and U is the horizontal velocity.," The ratio of these energies is quantified by the Richardson number $Ri\equiv N^2/(\partial U/\partial r)^2$, where $N$ is the frequency and $U$ is the horizontal velocity."
 A requirement for XII instability in vertical planes is that 227<1/4 somewhere in the flow. at least under adiabatic ancl inviscid conditions (Drazin&Reid1981).," A requirement for KH instability in vertical planes is that $Ri<1/4$ somewhere in the flow, at least under adiabatic and inviscid conditions \citep{Drazin_Reid81}."
. It would be Πορ if numerical researchers would report the values of Aj achieved in their simulations., It would be helpful if numerical researchers would report the values of $Ri$ achieved in their simulations.
" For an isothermal atmosphere with density and pressure scale height /7,=c2/59. the condition Ri«+ is equivalent to so Wilh 5zz7/5 as for nondegenerate molecular hydrogen. the flow must be (ransonic or else change on a scale smaller (han the scale height in order (hat A27<1/4."," For an isothermal atmosphere with density and pressure scale height $H_p=\cs^2/\gamma g$, the condition $Ri<\frac{1}{4}$ is equivalent to so with $\gamma\approx 7/5$ as for nondegenerate molecular hydrogen, the flow must be transonic or else change on a scale smaller than the scale height in order that $Ri<1/4$."
 But it is possible (hat instability max occur at larger Richardson number in the presence of radiative diffusion., But it is possible that instability may occur at larger Richardson number in the presence of radiative diffusion.
 Other instabilities that may be relevant are the baroclinic instability (Pecllosky1987:Vallis 2006).. the Goldreich-Schubert-Fricke instability (Goldreich&Sehubert1967:Fricke1968). and perhaps even (he magnetorotational instability. (Balbus&Lawley1991) if the shear extends {ο such a depth that the atmosphere becomes substantially conducting. aud if the shear has the right sign.," Other instabilities that may be relevant are the baroclinic instability \citep{Pedlosky_book,Vallis_book}, the Goldreich-Schubert-Fricke instability \citep{GoldreichSchubert67,Fricke68}, and perhaps even the magnetorotational instability \citep{balbus91} if the shear extends to such a depth that the atmosphere becomes substantially conducting, and if the shear has the right sign."
 It is bevond the scope of this note to assess the importance of these instabilities for controlling the speed of the circulation., It is beyond the scope of this note to assess the importance of these instabilities for controlling the speed of the circulation.
 Nevertheless. we will discuss the GSF instability briefly because it is illustrative and must surely occur at some level.," Nevertheless, we will discuss the GSF instability briefly because it is illustrative and must surely occur at some level."
 The GSF instability is enabled by thermal diffusion in baroclinic atmospheres of negligible viscosity that do not rotate on evlinders. 0O/0z40. even if the atmosphere is dynamically. stable according to Hollands Criterion (Tassoul1973).. i.e. baroclinically stable.," The GSF instability is enabled by thermal diffusion in baroclinic atmospheres of negligible viscosity that do not rotate on cylinders, $\partial\Omega/\partial z\ne0$, even if the atmosphere is dynamically stable according to lland's Criterion \citep{Tassoul78}, i.e. baroclinically stable."
" The instability is aNISVInInelric., and the maximum erowth rate is expressed in terms of the evlindrical radius zc and angular momentum per unit mass j=zOQ by but this is approached only al wavelengths A<2z(,/N)*7. where y=166T""/35qPe,ep)paa/p) is the thermal diffusivitv. so that radiative diffusion undercuts the restoring force of buovancv."," The instability is axisymmetric, and the maximum growth rate is expressed in terms of the cylindrical radius $\varpi$ and angular momentum per unit mass $j=\varpi^2\Omega$ by but this is approached only at wavelengths $\lambda\lesssim2\pi(\chi/N)^{1/2}$, where $\chi=16\sigma
T^3/3\kappa\rho^2c_v\sim (c/\kappa\rho)(p_{\rm rad}/p)$ is the thermal diffusivity, so that radiative diffusion undercuts the restoring force of buoyancy."
 Thus A<LHkm(íp/bar)Is/fone!) ΙΩΝ)”.," Thus $\lambda\lesssim 1\,{\rm km}\,(p/{\rm
 bar})^{-1}(\kappa/{\rm cm^2\,g^{-1}})^{-1/2} (T/10^3{\rm K})^2$ ."
 Such a wavelength would not be resolved by elobal simulations., Such a wavelength would not be resolved by global simulations.
" One müght expect the GSF instabilities {ο saburate nonlinearly at displacements £~A due to nonaxisvmmetric IKelvin-IHelmholtz instabilities acting on the risingand falling ""fingers. which carry opposilely signed eulerian"," One might expect the GSF instabilities to saturate nonlinearly at displacements $\xi\sim\lambda$ due to nonaxisymmetric Kelvin-Helmholtz instabilities acting on the risingand falling “fingers,” which carry oppositely signed eulerian"
One possibility is that the emission is extended beyond the slit adopted in these observations.,One possibility is that the emission is extended beyond the slit adopted in these observations.
 Spatially extended emission can certainly arise in outflow sources. as demonstrated by vanBoekeletal.(2009) ancl by our sample of optically thick dust disks (see Sect. ??)).," Spatially extended emission can certainly arise in outflow sources, as demonstrated by \citet{van09} and by our sample of optically thick dust disks (see Sect. \ref{Sect:thick}) )."
 However. no jets have been reported toward TW Iva and T Cha (Azevedo1993) and only a compact (8-LOmimas) outflow in Ha has been detected toward CS Cha (Takamietal.2003).," However, no jets have been reported toward TW Hya and T Cha \citep{azevedo07,alcala93} and only a compact mas) outflow in $\alpha$ has been detected toward CS Cha \citep{takami03}."
. In Sect., In Sect.
 ?? we also show (hat jets/oullows are not likely to be the main source of emission in transition objects., \ref{sect:jets} we also show that jets/outflows are not likely to be the main source of emission in transition objects.
 Another explanation for the Spitzer-VLT {his dilference is line and/or continuum variability., Another explanation for the Spitzer-VLT flux difference is line and/or continuum variability.
 At least for CS Cha and TW Ilva we know that line/contimmun variability measured from 2-epochs of Spitzer spectra is ~30%.. similar to the {his differences from the VLT and Spitzer spectra.," At least for CS Cha and TW Hya we know that line/continuum variability measured from 2-epochs of Spitzer spectra is $\sim$, similar to the flux differences from the VLT and Spitzer spectra."
 We should also keep in mind that at the distance of TW Iva and T. Cha (Table 4)) our slit just covers out to 10 AAU from the central stars., We should also keep in mind that at the distance of TW Hya and T Cha (Table \ref{table:modelparameters}) ) our slit just covers out to $\sim$ AU from the central stars.
 As discussed later even emission from the disk surface can extend bevond several tens of AU., As discussed later even emission from the disk surface can extend beyond several tens of AU.
 Further observations with wider slits and different orientation angles are necessary to constrain the spatial extension of the emission., Further observations with wider slits and different orientation angles are necessary to constrain the spatial extension of the emission.
 The most important result from the VISIR spectra is that the measured lines of transilion disks are relatively narrow (ranging [rom ~14kkin/s to 740 kkin/s) and peaked near the stellar velocity (see Table 3))., The most important result from the VISIR spectra is that the measured lines of transition disks are relatively narrow (ranging from $\sim$ km/s to $\sim$ km/s) and peaked near the stellar velocity (see Table \ref{table:results}) ).
 These line characteristics are consistent with a cisk origin [or the emission?., These line characteristics are consistent with a disk origin for the .
. We note that TW IIva. whose disk is almost seen face-on (441°. Pontoppidanetal. 2008)). has (he narrower line width.," We note that TW Hya, whose disk is almost seen face-on $4\pm 1^{\circ}$, \citealt{pontoppidan08}) ), has the narrower line width."
 The inclinations of the disks around Cs Cha and T Cha are not well constrained but likely closer to edge-on., The inclinations of the disks around CS Cha and T Cha are not well constrained but likely closer to edge-on.
 successfully model the SED of CS Cha with a disk viewed at aninclination of 607., \citet{espaillat07} successfully model the SED of CS Cha with a disk viewed at aninclination of $^\circ$ .
The star formation history (SEID) of galaxies is a key ingredient in describing thei evolution.,The star formation history (SFH) of galaxies is a key ingredient in describing their evolution.
 From an observational point of view. the SELL can be studied: by measuring the integrated. light of the galaxy population as a whole or of a homogeneous sample of galaxies at cilferent redshifts. at wavelengths associated with massive star formation (e.g.. Madau. Pozzetti Dickinson 1998: Lilly et al.," From an observational point of view, the SFH can be studied by measuring the integrated light of the galaxy population as a whole or of a homogeneous sample of galaxies at different redshifts, at wavelengths associated with massive star formation (e.g., Madau, Pozzetti Dickinson 1998; Lilly et al."
 1998)., 1998).
 An alternative method. which avoids the dillieulties in selecting a homogeneous sample of galaxies. determines the SELL of a specific galaxy using multi-band. photometry and chemical abuncances combined. with population synthesis models.," An alternative method, which avoids the difficulties in selecting a homogeneous sample of galaxies, determines the SFH of a specific galaxy using multi-band photometry and chemical abundances combined with population synthesis models."
 In. the case of the Milky Way (MW the large amount of available data. allows to qualitatively constrict the input SEES of these methods with some accuracy (e.g.. Prantzos Aubert 1995: Chiappini. AMatteucci. Gratton 1997: C'arigi 1997: Boissier Prantzos 1999).," In the case of the Milky Way (MW), the large amount of available data allows to qualitatively constrict the input SFHs of these methods with some accuracy (e.g., Prantzos Aubert 1995; Chiappini, Matteucci, Gratton 1997; Carigi 1997; Boissier Prantzos 1999)."
 On the same line of multi-band. photometry. but with higher precision. the SEL of à system can be. obtained through the study. of its resolved. stellar population.," On the same line of multi-band photometry, but with higher precision, the SFH of a system can be obtained through the study of its resolved stellar population."
 This allows to construct colour-magnituce cliagrams. which contain detailed information on the SELL behind such diagrams.," This allows to construct colour-magnitude diagrams, which contain detailed information on the SFH behind such diagrams."
 LInverting the problem however. is not. trivial. with the answer depending sensitively on the assumed metallicity of the object being studied at every time. ic.. the enrichment history.," Inverting the problem however, is not trivial, with the answer depending sensitively on the assumed metallicity of the object being studied at every time, i.e., the enrichment history."
 The accuracy of these infercnees being aso crucially determined by the depth and error level of he observations. these requirements have so far severely constrained the applicability. of such direct. inferences to only a handful of astrophysical systems.," The accuracy of these inferences being also crucially determined by the depth and error level of the observations, these requirements have so far severely constrained the applicability of such direct inferences to only a handful of astrophysical systems."
 Still. such methods jwe recently been applied to svstems where the metallicity ws been independently determined. and where high quality data exist.," Still, such methods have recently been applied to systems where the metallicity has been independently determined, and where high quality data exist."
 Examples being the works of Chiosi et al. (, Examples being the works of Chiosi et al. (
1989). Aparicio et al. (,"1989), Aparicio et al. ("
1990) ancl Mould ct al. (,1990) and Mould et al. (
1997) using Alagellanie and local star clusters. ancl Mighell Butcher (1992). Smeecker-Llane et al. (,"1997) using Magellanic and local star clusters, and Mighell Butcher (1992), Smecker-Hane et al. ("
1994). Tolstoy Saha (1996). Aparicio CGallart (1995). Mighell (1997) and Lernancdez et al. (,"1994), Tolstoy Saha (1996), Aparicio Gallart (1995), Mighell (1997) and Hernandez et al. ("
2000a) using local dSph's.,2000a) using local dSph's.
 With the coming of high equality photometric data from the Llipparcos satellite. colour magnitude diagram inversion methods using rigorous statistical analysis Clolstov," With the coming of high quality photometric data from the Hipparcos satellite, colour magnitude diagram inversion methods using rigorous statistical analysis (Tolstoy"
lind a value of XN~0.8.,find a value of $\rm X \simeq 0.8$.
 This caleulation also requires an extrapolation from the CO(2-1) measurements to the CO(1-0) luminosity., This calculation also requires an extrapolation from the CO(2-1) measurements to the CO(1-0) luminosity.
" Assuming constant brightness temperature and using a value of X appropriate to ULIRGs leads to molecular gas masses of about 5x10!"" AL. for the CO emitting components in 12020725 and 13350417.", Assuming constant brightness temperature and using a value of X appropriate to ULIRGs leads to molecular gas masses of about $5\times10^{10}$ $_\odot$ for the CO emitting components in 1202–0725 and 1335–0417.
 We can also calculate the gravitational masses using the observed sizes and line widtlis for the sources. and assuming a disk of gas in Ixeplerian rotation.," We can also calculate the gravitational masses using the observed sizes and line widths for the sources, and assuming a disk of gas in Keplerian rotation."
" For 120201725 south we use a line width of 190 lan ! and a radius corresponding to half the separation of the two components = 0.15"" = 1.1 kpc. leading to an enclosed mass of 0.23x10!"" 707) M..."," For 1202–0725 south we use a line width of 190 km $^{-1}$ and a radius corresponding to half the separation of the two components = $''$ = 1.1 kpc, leading to an enclosed mass of $0.23 \times 10^{10}$ $^{-2}(i)$ $_\odot$."
" For 13350417 we do not have spatially resolved spectroscopy. so we adopt a line width of 420 km | and a radius of half the separation of the two components = 0.65"" = 4.7 kpc. leading to an enclosed mass of 4.8xLOM 26) M."," For 1335–0417 we do not have spatially resolved spectroscopy, so we adopt a line width of 420 km $^{-1}$ and a radius of half the separation of the two components = $''$ = 4.7 kpc, leading to an enclosed mass of $4.8 \times 10^{10}$ $^{-2}(i)$ $_\odot$."
 An upper limit to / can be derived by assuming that the molecular gas mass dominates the total enclosed mass., An upper limit to $i$ can be derived by assuming that the molecular gas mass dominates the total enclosed mass.
 Using X=0.8 for 12020725 south we find 7<12. while for 13350417 we lind 7<43°.," Using $\rm X = 0.8$ for 1202–0725 south we find $i \le 12^o$, while for 1335–0417 we find $i \le 43^o$."
 These small angles lead (o a sienilicant problem in thatthe implied rotational velocities are then extremely large. > 400 km 4.," These small angles lead to a significant problem in thatthe implied rotational velocities are then extremely large, $\ge$ 400 km $^{-1}$."
 To obtain rotational velocities of ~250 km !. more typical of large spiral galaxies. would require a further reduction in the conversion factor to X.<0.2.," To obtain rotational velocities of $\sim 250$ km $^{-1}$, more typical of large spiral galaxies, would require a further reduction in the conversion factor to $\rm X \le 0.2$."
 IIowever. such a low X value would violate (he minimun mass conditions dictated by optically Chin CO emission. for which X~0.35 for an excitation temperature of 50 Ix. and assuming a Galactic CO abundance (Solomon οἱ al.," However, such a low X value would violate the minimum mass conditions dictated by optically thin CO emission, for which $\rm X \sim 0.35$ for an excitation temperature of 50 K and assuming a Galactic CO abundance (Solomon et al."
 1997)., 1997).
 It max be that these svstems are extremely massive. or perhaps that (he apparent CO lIunminosities are magnified by gravitational lensing (see section 6).," It may be that these systems are extremely massive, or perhaps that the apparent CO luminosities are magnified by gravitational lensing (see section 6)."
" We now consider the continuunrto-line ratio: —552—,", We now consider the continuum-to-line ratio: ${{L_{\rm FIR}}\over{L'_{\rm CO(1-0)}}}$ .
 A non-linear relationship, A non-linear relationship
»oint that it is possible for gas physics to significantly change the Einstein racius of massive clusters. even without caving a central barvon concentration.,"point that it is possible for gas physics to significantly change the Einstein radius of massive clusters, even without leaving a central baryon concentration."
 Finally. we note that rani pressure stripping of hot accreted barvons. which make up the majority (~80hanvon ) o£ he cluster barvons. may help to reduce the central raction.," Finally, we note that ram pressure stripping of hot accreted baryons, which make up the majority $\sim 80\%$ ) of the cluster baryons, may help to reduce the central baryon fraction."
 Indeed. cluster simulations find a reduced barvon Traction atorMeir20.2 (c.g.]xravtsovetal.2005:Dolagal.2009) and match better the barvonie fraction. inferred rom X-rav observations (Vikhlininetal.," Indeed, cluster simulations find a reduced baryon fraction at $r/\rv \la 0.2$ \citep[e.g.,][]{Kravtsov,Dolag} and match better the baryonic fraction inferred from X-ray observations \citep{Vikhlinin}."
206)9).. RB is grateful. for the kind. hospitality of the. at the Larvarel-Smithsonian CLA. ancl also acknowledges support by the Moore. Distinguished Scholar program at Caltech ancl the John Simon Guggenheim Memorial Foundation.," RB is grateful for the kind hospitality of the at the Harvard-Smithsonian CfA, and also acknowledges support by the Moore Distinguished Scholar program at Caltech and the John Simon Guggenheim Memorial Foundation."
 This work was supported in part by NASBA grant. NNNOSALA3Cἐν by Harvard. University funcls and by BSE grant. 2004386," This work was supported in part by NASA grant NNX08AL43G, by Harvard University funds and by BSF grant 2004386."
The 1.4 Gllz VLA image of ? shows a faint jet-like extension to the southeast. while the 8.4 Gllz VLA map of ? shows only the unresolved core.,"The 1.4 GHz VLA image of \citet{Giroletti04a} shows a faint jet-like extension to the southeast, while the 8.4 GHz VLA map of \citet{Patnaik92} shows only the unresolved core."
 The source is quite core-dominated in our VLDI image (Fig. 6)).," The source is quite core-dominated in our VLBI image (Fig. \ref{fig:0929}) ),"
 but also shows a clear jet to the southeast. well aligned with the structure observed by 2..," but also shows a clear jet to the southeast, well aligned with the structure observed by \citet{Giroletti04a}."
" The VLBI core displavs the verv hieh fractional polarization of m,=15%. while no polarization was detected in the jet."," The VLBI core displays the very high fractional polarization of $m_c=15\%$, while no polarization was detected in the jet."
"SED model does not, on average, seem to provide a closer fit.","SED model does not, on average, seem to provide a closer fit."
 The relatively good fit provided by the isothermal SED model is probably due to most of our sample consisting of low redshift galaxies and therefore that we do not probe much of the Wien part of the galaxy SED., The relatively good fit provided by the isothermal SED model is probably due to most of our sample consisting of low redshift galaxies and therefore that we do not probe much of the Wien part of the galaxy SED.
 In Fig., In Fig.
" 2, we summarize our results and compare the H-ATLAS dust temperatures with dust temperatures in the literature for a variety of sub-mm bright galaxies."," 2, we summarize our results and compare the H-ATLAS dust temperatures with dust temperatures in the literature for a variety of sub-mm bright galaxies."
 These samples are: (i) the sources in BLAST detected above 5c in at least one of the BLAST bands with either a COMBO-17 (Wolf et al., These samples are: (i) the sources in BLAST detected above $\sigma$ in at least one of the BLAST bands with either a COMBO-17 (Wolf et al.
 2004) or a SWIRE photometric redshift (Rowan-Robinson et al., 2004) or a SWIRE photometric redshift (Rowan-Robinson et al.
 2008) and Spitzer-MIPS 70 and 160 um fluxes (Dye et al.," 2008) and -MIPS $70$ and $160\,\mu$ m fluxes (Dye et al."
 2009; 6=1.5 fixed); (ii) local ULIRGS observed with SCUBA at 450 and 850 um and complemented with IRAS 60 and 100 um fluxes (Clements et al.," 2009; $\beta=1.5$ fixed); (ii) local ULIRGS observed with SCUBA at $450$ and $850\,\mu$ m and complemented with IRAS $60$ and $100\,\mu$ m fluxes (Clements et al."
 2010; 6 varied); (iii) SCUBA sub-mm galaxies detected at better than 3σ at 850 um and having redshifts determined from Keck-I spectroscopy (Chapman et al.," 2010; $\beta$ varied); (iii) SCUBA sub-mm galaxies detected at better than $\sigma$ at $850\,\mu$ m and having redshifts determined from Keck-I spectroscopy (Chapman et al."
 2005; 6=1.5 fixed); and (iv) local IRAS-selected galaxies with 60 and 100 um fluxes complemented with SCUBA 850 um (Dunne et al.," 2005; $\beta=1.5$ fixed); and (iv) local IRAS-selected galaxies with 60 and $100\,\mu$ m fluxes complemented with SCUBA $850\,\mu$ m (Dunne et al."
 2000; β varied)., 2000; $\beta$ varied).
" In Table 1, we list average dust temperatures as a function of redshift for several bins in redshift for both H-ATLAS only and all of the combined sub-mm galaxy samples, including H-ATLAS, plotted in Fig."," In Table 1, we list average dust temperatures as a function of redshift for several bins in redshift for both H-ATLAS only and all of the combined sub-mm galaxy samples, including H-ATLAS, plotted in Fig."
 2., 2.
" We do not find any evolution in the H-ATLAS dust temperature with redshift, though some evolution is inferred by BLAST measurements (Dye et al."," We do not find any evolution in the H-ATLAS dust temperature with redshift, though some evolution is inferred by BLAST measurements (Dye et al."
 2009; Pascale et al., 2009; Pascale et al.
" 2009), where sources at higher redshift had higher temperature in agreement with the radio-identified submillimeter-selected galaxies (SMGs) found with SCUBA (Chapman et al."," 2009), where sources at higher redshift had higher temperature in agreement with the radio-identified submillimeter-selected galaxies (SMGs) found with SCUBA (Chapman et al."
 2005; Ivison et al., 2005; Ivison et al.
 2010; Kovacs et al., 2010; Kovacs et al.
 2006; Coppin et al., 2006; Coppin et al.
 2008)., 2008).
" While we find remarkable consistency between the average dust temperatures for our H-ATLAS sample as a function of redshift, these average values are not necessarily in agreement with other sub-mm galaxy subsamples in the literature, mostly due to selection effects."," While we find remarkable consistency between the average dust temperatures for our H-ATLAS sample as a function of redshift, these average values are not necessarily in agreement with other sub-mm galaxy subsamples in the literature, mostly due to selection effects."
" For example, the SCUBA ULIRGS have an average temperature of (43+7)K. These sources were selected using IRAS 60um data and IRAS selected sources are known to be biased towards higher temperatures."," For example, the SCUBA ULIRGS have an average temperature of $(43 \pm 7)$ K. These sources were selected using IRAS $60\,\mu$ m data and IRAS selected sources are known to be biased towards higher temperatures."
" Optically-selected low-redshift sub-mm galaxies are known to have colder temperatures consistent with our findings (e.g., Willmer et al."," Optically-selected low-redshift sub-mm galaxies are known to have colder temperatures consistent with our findings (e.g., Willmer et al."
 2009; Vlahakis et al., 2009; Vlahakis et al.
 2005)., 2005).
" The large expected sample of sources from the 550 deg.? of H-ATLAS will enable more detailed studies in the future, without the biases associated with selections of various sub-samples, including our own."," The large expected sample of sources from the 550 $^2$ of H-ATLAS will enable more detailed studies in the future, without the biases associated with selections of various sub-samples, including our own."
" While we show results here with B=1.5 fixed, when fitting for & and Ty we found 8=1.4+0.1, consistent with 6=1.3 found in Dunne et al. ("," While we show results here with $\beta=1.5$ fixed, when fitting for $\beta$ and $T_{\rm d}$ we found $\beta = 1.4 \pm 0.1$, consistent with $\beta=1.3$ found in Dunne et al. ("
2000).,2000).
 In Fig., In Fig.
" 3, we plot the dust temperature versus FIR luminosity by integrating model SEDs between 8 and 1100 um for the H-ATLAS subsample."," 3, we plot the dust temperature versus FIR luminosity by integrating model SEDs between 8 and 1100 $\mu$ m for the H-ATLAS subsample."
 Luminosities for other samples are from the literature., Luminosities for other samples are from the literature.
" Fitting for a relation of the form Ty=+alog(Lrig/ Lo), we find Το= —20.5K and a=4.4 (see, Fig."," Fitting for a relation of the form $T_{\rm d}={T_{\rm 0}}+\alpha\log(L_{FIR}/L_{\odot})$ , we find ${T_{\rm 0}}=-20.5$ K and $\alpha=4.4$ (see, Fig."
 4)., 4).
 The value of log(Lr;g/Lo) is on average 10.9+0.8 for our sample., The value of $\log(L_{FIR}/L_{\odot})$ is on average $10.9\pm0.8$ for our sample.
 This relation is consistent with the BLAST data (Dye et al., This relation is consistent with the BLAST data (Dye et al.
 2009)., 2009).
" Since most of our sources lack redshifts, we consider another example application of our colour diagram and infer the statistical redshift distribution N(z) for the source samples plotted in Fig."," Since most of our sources lack redshifts, we consider another example application of our colour diagram and infer the statistical redshift distribution $N(z)$ for the source samples plotted in Fig."
 1., 1.
 We do this by first gridding the colour-colour plane along the SED tracks into redshift bins., We do this by first gridding the colour-colour plane along the SED tracks into redshift bins.
 We then convert the number of sources within a grid region of colours to a binned redshift distribution (Hughes et al., We then convert the number of sources within a grid region of colours to a binned redshift distribution (Hughes et al.
 2002)., 2002).
 This method is equivalent to extracting the redshift probability distribution function for the whole sample if we had simply fitted SEDs to individual fluxes and taken the sum of the redshift probabilities of each source., This method is equivalent to extracting the redshift probability distribution function for the whole sample if we had simply fitted SEDs to individual fluxes and taken the sum of the redshift probabilities of each source.
" While the redshift for an individual galaxy is largely uncertain, and sensitive to the SEDs used, the statistical redshift distribution we extract should be a reasonable estimate of the true distribution of the source sample."," While the redshift for an individual galaxy is largely uncertain, and sensitive to the SEDs used, the statistical redshift distribution we extract should be a reasonable estimate of the true distribution of the source sample."
 Figure 4 shows the redshift distribution for SPIRE sources detected in all 3 bands (Fig., Figure 4 shows the redshift distribution for SPIRE sources detected in all 3 bands (Fig.
 1(a))., 1(a)).
" For the sample of 1686 sources with flux densities above 35 mJy at 350 um and above 3o0 at 250 and 500m, we find the average redshift to be 2.2+ 0.6."," For the sample of 1686 sources with flux densities above 35 mJy at $350\,\mu$ m and above $\sigma$ at $250$ and $500\,\mu$ m, we find the average redshift to be $2.2 \pm 0.6$ ."
 This is consistent with the average redshift of, This is consistent with the average redshift of
For these objects. most of the euergv radiated bv the central star is absorbed by the circumstellar dust shell and recadiatedoas thermal cutission. predonmiünautlv by amorphous silicates.,"For these objects, most of the energy radiated by the central star is absorbed by the circumstellar dust shell and re-radiated as thermal emission, predominantly by amorphous silicates."
 Amorphous silicates have strong catures at 10 and LS jan. The current objects cau be ordered by increasing optical depth of those features. which aerees with ordering bv increasing waveleugth of he peak of he SED.," Amorphous silicates have strong features at 10 and 18 $\mu$ m. The current objects can be ordered by increasing optical depth of those features, which agrees with ordering by increasing wavelength of the peak of the SED."
 When the 10-1. feature becomes optically thick. the enerev from the central star must ve re-raciated at even longer wavoeleugths. therefore the )ea position shifts towards 30 gan (seo Fig. 1)).," When the $\mu$ m feature becomes optically thick, the energy from the central star must be re-radiated at even longer wavelengths, therefore the peak position shifts towards 30 $\mu$ m (see Fig. \ref{fig1}) )."
 It is yvclieved that the low amass loss rate Miras evolve iuto Yeh mass loss rate ΟΠΠ stars. while the IRAS colors indicate that the peak of the dust emission shifts towards ouecr waveleneths (van der Veen Παπιο 198s)).," It is believed that the low mass loss rate Miras evolve into high mass loss rate OH/IR stars, while the IRAS colors indicate that the peak of the dust emission shifts towards longer wavelengths (van der Veen Habing \cite{vanderveen}) )."
 With Increasing nass loss rate the characteristic density in the wind will increase. increasing the optical depth towards he ceutral star.," With increasing mass loss rate the characteristic density in the wind will increase, increasing the optical depth towards the central star."
 This evolution can be found im the oxygen-rich AGB stars in our sample., This evolution can be found in the oxygen-rich AGB stars in our sample.
 Iu Fig., In Fig.
 6 the objects are plotted iu the same order as in Fig. 1.. ," \ref{ovcrystal} the objects are plotted in the same order as in Fig. \ref{fig1}, ,"
"however. the intensities are now in £, units. and normalized with respect to the measured maximal intensity."," however, the intensities are now in $F_\nu$ units, and normalized with respect to the measured maximum intensity."
 The 10-410 feature of Mira is completely in cluission: for WAN Pse and CRL 2199. the 10-10 feature is partially self-absorbed.," The $\mu$ m feature of Mira is completely in emission; for WX Psc and CRL 2199, the $\mu$ m feature is partially self-absorbed."
 For the OIT/IR. stars OITIO1.9. OITI27.5. OII26.5. AFGL 5379 and OID32.8. the 10-412 feature is completely in absorption. with optical depths rangiug fron l.l for OIILOLO to 3.6 for OID2.5.," For the OH/IR stars OH104.9, OH127.8, OH26.5, AFGL 5379 and OH32.8, the $\mu$ m feature is completely in absorption, with optical depths ranging from 1.1 for OH104.9 to 3.6 for OH32.8."
 A detailed aualvsis of the amorphous silicate features will be presented in a future paper (Ikeniper et al. in preparation).," A detailed analysis of the amorphous silicate features will be presented in a future paper (Kemper et al, in preparation)."
 As the optical depth increases. some structure becomes apparent iu the 20.15 pau region.," As the optical depth increases, some structure becomes apparent in the 20–45 $\mu$ m region."
 Iu the lower iass-loss rate objects. strong enuüssiou features due to amorphous silicates are present. but there are no obvious uarrow features at AN>20 μπι. For the redder objects. we fud that the amorphous silicates features are(self-)absorbed.. and that ποιο structure is apparent at wavelengths Αα.>20 san. These narrow features can be identified as crystalline silicates. both olivines aud pyroxenes (Waters ct al. 1996)).," In the lower mass-loss rate objects, strong emission features due to amorphous silicates are present, but there are no obvious narrow features at $\lambda > 20$ $\mu$ m. For the redder objects, we find that the amorphous silicates features are, and that some structure is apparent at wavelengths $\lambda > 20$ $\mu$ m. These narrow features can be identified as crystalline silicates, both olivines and pyroxenes (Waters et al. \cite{waters96}) )."
 The identifications are based on laboratory spectra of crystalline silicates (Jaeecr ct al. 1998:, The identifications are based on laboratory spectra of crystalline silicates (Jägger et al. \cite{jaeger};
 voile et al. 1993..," Koike et al. \cite{koike},"
 I&oike Shibai 1998)) aud simular bauds secu in other objects on which detailed studies have been performed. ie. AFGL 1106 (Molster et al. 1999a)}) ," Koike Shibai \cite{koike98}) ) and similar bands seen in other objects on which detailed studies have been performed, i.e. AFGL 4106 (Molster et al. \cite{molster}) )"
aud to ΠΟ 15677 (Voors 1999))., and to HD 45677 (Voors \cite{voors}) ).
 The dashed lines iu Fie., The dashed lines in Fig.
 6 represent the position of some muportaut crvstalliue silicate complexes. which are listed in Table L. ," \ref{ovcrystal} represent the position of some important crystalline silicate complexes, which are listed in Table \ref{xtab}. ."
These crystalline silicate features are found i clussion at the longest waveleugths but sometimes in absorption at somewhat shorter wavelengths. for example the 23.6 pau olivine feature in OIT32.8 and in OII26.5 (see Fig. 6)).," These crystalline silicate features are found in emission at the longest wavelengths but sometimes in absorption at somewhat shorter wavelengths, for example the 23.6 $\mu$ m olivine feature in OH32.8 and in OH26.5 (see Fig. \ref{ovcrystal}) )."
 The OILI/IR stars presented here are the oulv objects Known to exhibit crystalline silicates in absorption outside the 8-13 pon waveleneth region., The OH/IR stars presented here are the only objects known to exhibit crystalline silicates in absorption outside the 8-13 $\mu$ m wavelength region.
 For OT32.8 this was already reported by Waters Molster (1999)) iu compariso- with AFCGL 1106., For OH32.8 this was already reported by Waters Molster \cite{wamo}) ) in comparison with AFGL 4106.
 The presence of the most nuportaut crystalline silicate features is mdicated im Table l1 for all he sources im our sample., The presence of the most important crystalline silicate features is indicated in Table \ref{xtab} for all the sources in our sample.
 Note that those features are detected bv close examination of the spectrum: not all catures are visible iu the overview figures preseuted im his paper., Note that those features are detected by close examination of the spectrum; not all features are visible in the overview figures presented in this paper.
 Detailed modelling of the wealth of crystalline 4.ilicate features shown by the individual objects is deferred o a future paper., Detailed modelling of the wealth of crystalline silicate features shown by the individual objects is deferred to a future paper.
 The crystalline silicate features tend to appear iu hose sources having ereater optical depth at 10 san. However. the sharpucss of the crystalline silicate features shows a large variation.," The crystalline silicate features tend to appear in those sources having greater optical depth at 10 $\mu$ m. However, the sharpness of the crystalline silicate features shows a large variation."
 The sharpucss is expected to be determined by properties of the crystalline silicates. such as the presence of impurities. the shape of the dust grains. and ureenlaritics iu the lattice structure.," The sharpness is expected to be determined by properties of the crystalline silicates, such as the presence of impurities, the shape of the dust grains, and irregularities in the lattice structure."
 The spectra. of AFGL 5379 does not show the sharp crystalline peaks ound in the spectra of the other OIL/IR stars auc in the spectra of AFGL 1106 and ΠΟ 15677. but the shapes of its catures do resemble the laboratory spectra of crystalline silicates (Jaeecrao ot al. 1998)).," The spectrum of AFGL 5379 does not show the sharp crystalline peaks found in the spectra of the other OH/IR stars and in the spectra of AFGL 4106 and HD 45677, but the shapes of its features do resemble the laboratory spectra of crystalline silicates (Jägger et al. \cite{jaeger}) )."
 This sueecstsee hat the dust eraius around these objects exhibit differences im he properties of the lattice structure. such as inpurities. roles. aud edge effects due to erain size.," This suggests that the dust grains around these objects exhibit differences in the properties of the lattice structure, such as impurities, holes, and edge effects due to grain size."
 The appearauce of the crystalline silicate cussion features iu the redder sources in our sample confirms the relationship between dust crystallinity and cuvelope colour temperature. and hence mass-loss rate. identified by Waters et al. (1996)).," The appearance of the crystalline silicate emission features in the redder sources in our sample confirms the relationship between dust crystallinity and envelope colour temperature, and hence mass-loss rate, identified by Waters et al. \cite{waters96}) )."
" Specifically, there secius to be a threshold value for the lass loss rate above which the crystalline silicate features appear in the spectrum."," Specifically, there seems to be a threshold value for the mass loss rate above which the crystalline silicate features appear in the spectrum."
" Ποπονο, above this threshold value. the streneth and width of the features secu to be uncorrelated to the mass loss rate."," However, above this threshold value, the strength and width of the features seem to be uncorrelated to the mass loss rate."
 Fie., Fig.
 7 prescuts a inore detailed overview of the location ofthe crystalline silicate features., \ref{oh104} presents a more detailed overview of the location ofthe crystalline silicate features.
 Tn the upper panel. theupper spectrum is that of OTLOL9.," In the upper panel, theupper spectrum is that of OH104.9."
 The solid line represents the coutinuu fit obtained using the method described above., The solid line represents the continuum fit obtained using the method described above.
 At longer wavelcneths the, At longer wavelengths the
increases by a factor 16.,increases by a factor 16.
 This is in reasonable agreement with the theoretical value and the expected behaviour with changing resolution. confirming that the NTST is triggered in our simulations.," This is in reasonable agreement with the theoretical value and the expected behaviour with changing resolution, confirming that the NTSI is triggered in our simulations."
 Fig., Fig.
 8 also shows that the saturation amplitude is somewhat smaller as the resolution is increased (compare also the bottom left and right panels of Fig. 7)), \ref{fig:NTSI} also shows that the saturation amplitude is somewhat smaller as the resolution is increased (compare also the bottom left and right panels of Fig. \ref{fig:evolution}) )
 and that it converges to a resolution- value., and that it converges to a resolution-independent value.
 The numerical simulations show that the initial perturbations are preferentially located off the binary axis. have an oscillatory behaviour with a small wavelength and grow faster when the spatial resolution is increased (Fig. 7)).," The numerical simulations show that the initial perturbations are preferentially located off the binary axis, have an oscillatory behaviour with a small wavelength and grow faster when the spatial resolution is increased (Fig. \ref{fig:evolution}) )."
 The rapid development of these perturbations is consistent with a linear instability., The rapid development of these perturbations is consistent with a linear instability.
 These properties are reminiscent of the TAI., These properties are reminiscent of the TAI.
 The TAT studied by ?? is an overstability with an oscillation frequency of the velocity perturbations x1/A.," The TAI studied by \citet{1993A&A...267..155D,1996ApJ...461..927D} is an overstability with an oscillation frequency of the velocity perturbations $\propto 1/\lambda$."
 The growth timescale is xV/A and indeed smaller wavelength perturbations grow faster at higher resolution., The growth timescale is $\propto \sqrt{\lambda}$ and indeed smaller wavelength perturbations grow faster at higher resolution.
 ? noted that the growth is limited by pressure effects and that the TAI grows faster than the NTSI when Here. / is the minimum distance along the contact discontinuity (/=0 on the binary axis) beyond which the TAT can develop for a given wavelength A.," \citet{1994ApJ...428..186V} noted that the growth is limited by pressure effects and that the TAI grows faster than the NTSI when Here, $l$ is the minimum distance along the contact discontinuity $l=0$ on the binary axis) beyond which the TAI can develop for a given wavelength $\lambda$."
" The relevant wavelengths are smaller than #2, and larger than the shell width L~42, /A4>. with the smaller scales growing faster."," The relevant wavelengths are smaller than $R_s$ and larger than the shell width $L\sim R_s/\mathcal{M}^2$ , with the smaller scales growing faster."
 The instability develops preferentially along the wings (?).., The instability develops preferentially along the wings \citep{1998NewA....3..571B}.
 The presence of the TAI closer to the binary axis at the highest resolution may explain why the growth rate of the NTSI (see Fig. 8)), The presence of the TAI closer to the binary axis at the highest resolution may explain why the growth rate of the NTSI (see Fig. \ref{fig:NTSI}) )
 does not perfectly match the theoretical value., does not perfectly match the theoretical value.
 Despite the similarities. we could not formally identify the TAT.," Despite the similarities, we could not formally identify the TAI."
 One difficulty is that we were not able to quantify the growth rates as several modes interact quickly and make the linear phase very short., One difficulty is that we were not able to quantify the growth rates as several modes interact quickly and make the linear phase very short.
 Another is that we found that our initial velocity profile along the shock is inconsistent with the equilibrium solution proposed by ?.., Another is that we found that our initial velocity profile along the shock is inconsistent with the equilibrium solution proposed by \citet{1993A&A...267..155D}.
 This was corrected by ? but they concluded that the set of equations used by ?. led to inconsistencies in the dispersion relations. casting doubt on the theoretical rates to expect.," This was corrected by \citet{1998MNRAS.298.1021M} but they concluded that the set of equations used by \citet{1993A&A...267..155D} led to inconsistencies in the dispersion relations, casting doubt on the theoretical rates to expect."
 We suggest that it 1s not possible to neglect. as was done. the derivatives 0/00 in the equations (6 corresponds to the polar angle to the binary axis with the origin at the stagnation point). since there is a significant change in the azimuthal speed of the incoming flow as it is decelerated and redirected along the shock.," We suggest that it is not possible to neglect, as was done, the derivatives $\partial/\partial \theta$ in the equations $\theta$ corresponds to the polar angle to the binary axis with the origin at the stagnation point), since there is a significant change in the azimuthal speed of the incoming flow as it is decelerated and redirected along the shock."
 Although our results still support the presence in the simulations of some form of the TAT. the simulations also show that the saturation amplitude of this instability is low compared to the NTSI.," Although our results still support the presence in the simulations of some form of the TAI, the simulations also show that the saturation amplitude of this instability is low compared to the NTSI."
 In all the simulations we performed. the non-linear evolution was dominated by the large scale. high amplitude perturbations induced by the NTSI.," In all the simulations we performed, the non-linear evolution was dominated by the large scale, high amplitude perturbations induced by the NTSI."
 At best. the TAI may play a role in the early stages as a seed instability for the NTST. as described in refntsi..," At best, the TAI may play a role in the early stages as a seed instability for the NTSI, as described in \\ref{ntsi}."
 In real systems the velocities of the winds are never exactly equal and the contact discontinuity is subject to the KHI., In real systems the velocities of the winds are never exactly equal and the contact discontinuity is subject to the KHI.
 Even or a 1 velocity difference between the winds. this instability jeoretically has a larger growth rate than the TAI and NTSI.," Even for a $1\%$ velocity difference between the winds, this instability theoretically has a larger growth rate than the TAI and NTSI."
 Fig., Fig.
 9 compares simulations for ;j=1 with equal winds or ey.=Brox. ραubject to the KHI.," \ref{fig:NTSI_KH} compares simulations for $\eta=1$ with equal winds or $v_{1\infty}=2v_{2\infty}$, subject to the KHI."
 We also include here a map of the r.m.s., We also include here a map of the r.m.s.
 of 18. Velocity fluctuations observed over a long averaging period., of the velocity fluctuations observed over a long averaging period.
 There is little difference in the outcome between equal winds and rx=25x. either in the appearance of the turbulent region op row) or in the r.m.s.," There is little difference in the outcome between equal winds and $v_{1\infty}=2v_{2\infty}$, either in the appearance of the turbulent region (top row) or in the r.m.s."
 of the perturbations (second row)., of the perturbations (second row).
 If anything. the KHI seems to increase slightly the region where strong fluctuations occur.," If anything, the KHI seems to increase slightly the region where strong fluctuations occur."
 The NTSI dominates the final non-linear phase even when the KHI is initially present., The NTSI dominates the final non-linear phase even when the KHI is initially present.
 The r.m.s., The r.m.s.
 values close to one are the expected outcome of the NTSI (2).., values close to one are the expected outcome of the NTSI \citep{1994ApJ...428..186V}.
 We found the same results for simulations with 7=1/16 0.0625., We found the same results for simulations with $\eta=1/16=0.0625$ .
 The corresponding density maps and velocity perturbations are given in the bottom two rows of Fig. 9.., The corresponding density maps and velocity perturbations are given in the bottom two rows of Fig. \ref{fig:NTSI_KH}.
 The NTSI was studied theoretically for planar shocks but the ;j=0.0625 simulations show it is also present and dominant when the shock is curved. although following it requires high numerical resolutions.," The NTSI was studied theoretically for planar shocks but the $\eta=0.0625$ simulations show it is also present and dominant when the shock is curved, although following it requires high numerical resolutions."
 The simulations were performed with ο=12S and 5 levels of refinement in a box of size Sa., The simulations were performed with $n_x=128$ and 5 levels of refinement in a box of size $8a$.
 For lower resolutions the NTSI is not triggered and the final result is stable (the same is observed for η= 1)., For lower resolutions the NTSI is not triggered and the final result is stable (the same is observed for $\eta=1$ ).
 The density maps for equal winds and ep.=204 look similar., The density maps for equal winds and $v_{1\infty}=2v_{2\infty}$ look similar.
 The highest velocity perturbations are at the same location but the r.m.s values are higher when an initial shear is present., The highest velocity perturbations are at the same location but the r.m.s values are higher when an initial shear is present.
 We conclude that having a velocity shear in a thin shell increases the amplitude of the perturbations but does not affect much the morphology of the unstable flow. which is mostly set by the NTSI.," We conclude that having a velocity shear in a thin shell increases the amplitude of the perturbations but does not affect much the morphology of the unstable flow, which is mostly set by the NTSI."
 This is consistent with ? who concluded from their simulations of perturbed slabs that the KHI does not strongly modify the outcome of the NTSI., This is consistent with \citet{1996NewA....1..235B} who concluded from their simulations of perturbed slabs that the KHI does not strongly modify the outcome of the NTSI.
 Pressure has a stabilising effect on both instabilities., Pressure has a stabilising effect on both instabilities.
 We performed a simulation. with αι Μο with all other physical and numerical parameters identical to those of the jj= lori.=rox simulations.," We performed a simulation with $\mathcal{M}_1$ $\mathcal{M}_2$ $6$ with all other physical and numerical parameters identical to those of the $\eta=1$, $v_{1\infty}=v_{2\infty}$ simulations."
 Both instabilities are seen to develop but more slowly., Both instabilities are seen to develop but more slowly.
 Keeping the wind velocity constant. a lower Mach number implies a higher sound speed but the thickness of the shell increases faster so that the growth timescale of the NTSI ονἐςx 1/.MD is longer.," Keeping the wind velocity constant, a lower Mach number implies a higher sound speed but the thickness of the shell increases faster so that the growth timescale of the NTSI $\propto L/c_s\propto 1/{\cal M}$ ) is longer."
 The NTSI is also harder to trigger as it requires a perturbation of amplitude comparable to the size of theshell., The NTSI is also harder to trigger as it requires a perturbation of amplitude comparable to the size of theshell.
 The TAT develops more slowly as pressure suppresses the development, The TAI develops more slowly as pressure suppresses the development
In the case of dy angle the situation is more complicated.,In the case of $\delta_D$ angle the situation is more complicated.
 Iowever. if we restrict our analvsis only to the case of the absolute value of dy angle. then we could neglect As; and Aso coellicients. because (they are equal to zero (see also (Flin2004.2005.2006. 2007))).," However, if we restrict our analysis only to the case of the absolute value of $\delta_D$ angle, then we could neglect $\Delta_{21}$ and $\Delta_{22}$ coefficients, because they are equal to zero (see also \citep{f4,Aryal04,Aryal05a,Aryal06,Aryal07}) )."
" In that case Ay is reduced to |Ay]. while A. now denoted as A... is (he function of coefficients Ay, ancl Ay only."," In that case $\Delta_1$ is reduced to $|\Delta_{11}|$, while $\Delta$, now denoted as $\Delta_c$, is the function of coefficients $\Delta_{11}$ and $\Delta_{12}$ only."
 However. please note that 244 and Ays are not independent of each other (Gocdlowski1994).," However, please note that $\Delta_{11}$ and $\Delta_{12}$ are not independent of each other \citep{g3}."
. We also performed the investigation of the linear regression given by y=αν+h counted for various parameters., We also performed the investigation of the linear regression given by $y=aN+b$ counted for various parameters.
 These were carried out [ον each investigated angle separately., These were carried out for each investigated angle separately.
" We studied the linear regression between: the values of different statistics A7. A,σκι). A/o(A) and the number of analvzed galaxies in each particular cluster."," We studied the linear regression between: the values of different statistics $\chi^2$, $\Delta_1/\sigma(\Delta_1)$, $\Delta/\sigma(\Delta)$ and the number of analyzed galaxies in each particular cluster."
 In the case of dp. the values of statistics: A7. Nga/oGNu). Ap/o0GN) and the number of analyzed galaxies in each particular cluster were considered.," In the case of $\delta_D$, the values of statistics: $\chi^2$, $|\Delta_{11}/\sigma(\Delta_{11})|$, $\Delta_c/\sigma(\Delta_c)$ and the number of analyzed galaxies in each particular cluster were considered."
 We assumed that the theoretical. uniform. random distribution contains the same number of objects as the observed one.," We assumed that the theoretical, uniform, random distribution contains the same number of objects as the observed one."
 Our null hvpothesis ff) is that the distribution is a random one., Our null hypothesis $H_0$ is that the distribution is a random one.
 In such a case the statistics /=a/o(a) has Students distribution with u—2 degrees of freedom. where vw is the number of analvzed clusters.," In such a case the statistics $t=a/\sigma(a)$ has Student's distribution with $u-2$ degrees of freedom, where $u$ is the number of analyzed clusters."
 It means (hat we tested Lf) hypothesis that /=0 against //4 hypothesis that />0., It means that we tested $H_0$ hypothesis that $t=0$ against $H_1$ hypothesis that $t>0$.
" In order to reject the Lf) hypothesis. (he value of the observed statistics / should be greater than /,,.."," In order to reject the $H_0$ hypothesis, the value of the observed statistics $t$ should be greater than $t_{cr}$."
 Our sample has PAT clusters., Our sample has 247 clusters.
" For this sample. at the significance level a= 0.05. the value /,,.= 1.651. while for the sample of OF clusters with known values of velocity dispersion. the value /,,.=1.660."," For this sample, at the significance level $\alpha=0.05$ , the value $t_{cr} = 1.651$ , while for the sample of 97 clusters with known values of velocity dispersion, the value $t_{cr} = 1.660$."
 Sinularly. using linear regression we looked lor possible relations between the values of applied statistics: A7. Ay/o(Ay) and A/o(A) (or A7. Nu/o(Au) and a./o(6N.) in the ease of dp angle) and the DM type of each cluster.," Similarly, using linear regression we looked for possible relations between the values of applied statistics: $\chi^2$, $\Delta_1/\sigma(\Delta_1)$ and $\Delta/\sigma(\Delta)$ (or $\chi^2$, $|\Delta_{11}/\sigma(\Delta_{11})|$ and $\Delta_c/\sigma(\Delta_c)$ in the case of $\delta_D$ angle) and the BM type of each cluster."
 The linear regression between values of above mentioned statistics ancl velocity dispersion of galaxies inside cluster was also examined., The linear regression between values of above mentioned statistics and velocity dispersion of galaxies inside cluster was also examined.
 The linearregression analvses were performedindependently for (he sample containing, The linearregression analyses were performedindependently for the sample containing
Nuclear radio emission ts almost invariably associated with the presence of an active galactic nucleus (AGN) and this is an indication that the process of accretion onto a supermassive black hole (SMBH) naturally produces a signature in the form of radiation in the radio domain.,Nuclear radio emission is almost invariably associated with the presence of an active galactic nucleus (AGN) and this is an indication that the process of accretion onto a supermassive black hole (SMBH) naturally produces a signature in the form of radiation in the radio domain.
 The separation between radio-loud (RL) and radio-quiet (RQ) AGNs ts in fact only a measure of the relative flux in the radio band with respect to the optical or X-ray nucleus (Kellermannetal.1994;Terashima&Wilson 2003):: but also RQ AGNs. when studied at sufficient depth. usually show the presence at least of a nuclear radio component (e.g..Ulvestad&Wilson1989:Na-garetal. 2005).," The separation between radio-loud (RL) and radio-quiet (RQ) AGNs is in fact only a measure of the relative flux in the radio band with respect to the optical or X-ray nucleus \citep{kellermann94,terashima03}; but also RQ AGNs, when studied at sufficient depth, usually show the presence at least of a nuclear radio component \citep[e.g.,][]{ulvestad89,nagar05}."
. For RL AGNs the radio core results from synchrotron emission produced by the unresolved base of their jets: for RQ AGNSs the situation is more controversial and it has been recently proposed. besides the possibility of a Jet origin. that their radio nuclei are the manifestation of the presence of a thermal outflow or of an active disk corona (Blundell&Kuncic2007;LaorBehar2008) When combined to the very limited effects that absorption has on radio waves. the study of radio emission provides. in principle. a very powerful tool to detect accretion onto SMBH and. consequently. to establish when a SMBH is present in à given galaxy.," For RL AGNs the radio core results from synchrotron emission produced by the unresolved base of their jets; for RQ AGNs the situation is more controversial and it has been recently proposed, besides the possibility of a jet origin, that their radio nuclei are the manifestation of the presence of a thermal outflow or of an active disk corona \citep{blundell07,laor08}
 When combined to the very limited effects that absorption has on radio waves, the study of radio emission provides, in principle, a very powerful tool to detect accretion onto SMBH and, consequently, to establish when a SMBH is present in a given galaxy."
" However. to take full advantage of this approach. we must reach a much deeper understanding of what determines the radio luminosity of a given galaxy and how this ts related to its level of accretion,"," However, to take full advantage of this approach, we must reach a much deeper understanding of what determines the radio luminosity of a given galaxy and how this is related to its level of accretion."
 A large effort has been dedicated to explore the connection between the host properties (mostly from an optical point of view) and its radio emission., A large effort has been dedicated to explore the connection between the host properties (mostly from an optical point of view) and its radio emission.
 Already. from the pioneering study by Auriemmaetal.(1977) it was clear that more massive galaxies have on average a higher radio lummosity than smaller galaxies. while apparently there are no distinctions between clusters and non-clusters members (Ledlow&Owen1996).," Already from the pioneering study by \citet{auriemma77} it was clear that more massive galaxies have on average a higher radio luminosity than smaller galaxies, while apparently there are no distinctions between clusters and non-clusters members \citep{ledlow96}."
 The radio luminosity functions (RLFs) of galaxies of different optical magnitudes are similar but they differ strongly in their scaling., The radio luminosity functions (RLFs) of galaxies of different optical magnitudes are similar but they differ strongly in their scaling.
 More recent studies confirm the early results. indicating that the normalization of the RLF scales with the host luminosity as L? (e.g.Bestetal.2005:Mauch&Sadler 2007).," More recent studies confirm the early results, indicating that the normalization of the RLF scales with the host luminosity as $\sim$ $^{2.5}$ \citep[e.g.,][]{best05b,mauch07}."
. However. galaxies of given optical magnitude show a very large range of radio power. more than 5 orders of magnitude. and the relation between the radio and optical luminosity can only be described in terms of a probability distribution.," However, galaxies of given optical magnitude show a very large range of radio power, more than 5 orders of magnitude, and the relation between the radio and optical luminosity can only be described in terms of a probability distribution."
 These studies focused mostly on massive galaxies and had a relatively high threshold for the radio detection., These studies focused mostly on massive galaxies and had a relatively high threshold for the radio detection.
 The analysis reaching the lowest level of luminosity (in both bands) were, The analysis reaching the lowest level of luminosity (in both bands) were
is secun to cole from the region sinated heween the two iiti sources (see Fig. ll..,"is seen to come from the region situated between the two initial sources (see Fig. \ref{fig11},"
 right punel). which is also tvpic:d of microwave spikes (Altvutsev et al.," right panel), which is also typical of microwave spikes (Altyntsev et al."
 1996)., 1996).
 This nxw dudicate the formation of a oop WIt[um ootpolits situatec a the two initial microwave sources., This may indicate the formation of a loop with footpoints situated at the two initial microwave sources.
s. According o Fig. 11.," According to Fig. \ref{fig11},"
 the spatial location of one of tl1ο footpolits is close to the epicentre of the burst on 20j| λίαν M. uodulatec by οι oscillations (sec Fig. 9)).," the spatial location of one of the footpoints is close to the epicentre of the burst on 2005 May 04, modulated by 3-min oscillations (see Fig. \ref{fig9}) )."
 The lexyp-ike reeion of the maxima eniission iu the sp1se-like ptIsc is also apxweutlv located perpendicular to the coronal uaenetic fau structure orieldating in the suns]vot. Which is üghllighte Lby the αλα narrowband map of he event on 2005 May. L.," The loop-like region of the maximum emission in the spike-like pulse is also apparently located perpendicular to the coronal magnetic fan structure originating in the sunspot, which is highlighted by the 3-min narrowband map of the event on 2005 May 4."
 In this case. again. the energy release can be rigecredOO |w the 3-auin oscilations guided by a magnetic jdlasma structure originating iu the sunspot.," In this case, again, the energy release can be triggered by the 3-min oscillations guided by a magnetic plasma structure originating in the sunspot."
 The microwave light curves of solu fares oun 2005 April 28 aud 2005 Alay [contain pronounced variations with periods of about 3Mi niu., The microwave light curves of solar flares on 2005 April 28 and 2005 May 4 contain pronounced variations with periods of about 3 min.
 This behaviour indicates that there is au apparent relationship with πα oscillations in the sunspot situated close to the flare sites., This behaviour indicates that there is an apparent relationship with 3-min oscillations in the sunspot situated close to the flare sites.
 The ain of this paper was to understand this relationship., The aim of this paper was to understand this relationship.
 Our analysis of dvuamical featres in the nücrowave. EUV. white light. and A-rav inaene data of AR 10756 acquire caine its passage through the solar disk from 2005 Apri 28 to 2005 May . duferred he dvuauical morphology of the active region.," Our analysis of dynamical features in the microwave, EUV, white light, and X-ray imaging data of AR 10756 acquired during its passage through the solar disk from 2005 April 28 to 2005 May 4, inferred the dynamical morphology of the active region."
 The 3aun1 narrowband signals detectec over the sunspot and in the flare site are all well localised. which exchules tcir possibe link with the iustruneuta artifacts. such as sidelobes of the image svuthesis. auk icnce are vatural.," The 3-min narrowband signals detected over the sunspot and in the flare site are all well localised, which excludes their possible link with the instrumental artifacts, such as sidelobes of the image synthesis, and hence are natural."
 The 3-1win narrowband maps of the active rogki. coustructed with the use of PWE show he preseuce of exchided V-shaped sources situated over he suuspot. with arius extended towards the fleue site.," The 3-min narrowband maps of the active region, constructed with the use of PWF show the presence of extended V-shaped sources situated over the sunspot, with arms extended towards the flare site."
 We interpret these srYlas as evidence of the ninenetic doas channels hat link. the SHlspo and t1C flare site bv οπήας maegnuctolvdrodvuamic waves., We interpret these arms as evidence of the magnetic plasma channels that link the sunspot and the flare site by guiding magnetohydrodynamic waves.
" The 3-uinu xxiodicities of euπουν releases are then lieecreao by the aauiu oscillations leaking otut from the sunspot aong the naenetie structures,", The 3-min periodicities of energy releases are then triggered by the 3-min oscillations leaking out from the sunspot along the magnetic structures.
 Ou the basis of our findings. we educe that the ouwsieal imechauisin res]xyusible for the relationship jetween Jmm suuspot os‘ations and 3-anin QPP in rearby flares can be as felows.," On the basis of our findings, we deduce that the physical mechanism responsible for the relationship between 3-min sunspot oscillations and 3-min QPP in nearby flares can be as follows."
 The cuerey of 3auiu oscillations leaks out of fhe sunspots iu the form of, The energy of 3-min oscillations leaks out of the sunspots in the form of
 Nimptl750. and multiplets. which are very difficult todeblend.,"$\lambda$ 1750, and multiplets, which are very difficult todeblend."
 Nun11750 would also be useful to estimate the metallicity in addition to Nv.tl240 (Shields et al., $\lambda$ 1750 would also be useful to estimate the metallicity in addition to $\lambda$ 1240 (Shields et al.
 1976: Baldwin Netzer 1978: Hamann et al., 1976; Baldwin Netzer 1978; Hamann et al.
 2002: Dietrich. et al., 2002; Dietrich et al.
 2003). but we did not take 1t into account because of the difficulty in deblending it from broad emission.," 2003), but we did not take it into account because of the difficulty in deblending it from broad emission."
fluctuations (note that this includes the noise)).,fluctuations (note that this includes the noise).
 This will become more clear in the following., This will become more clear in the following.
 If the sky Uuetuations where ever shown to be nongaussian (or an experiment contained an important component. of nongaussian noise). then the band.power estimates would. need to be recalculated. potentially changing Figure 1.," If the sky fluctuations where ever shown to be non–gaussian (or an experiment contained an important component of non–gaussian noise), then the band–power estimates would need to be recalculated, potentially changing Figure 1."
 A common approach to estimation applies the x7. statistic to the band.power estimatesparameter of Figure 1., 	A common approach to parameter estimation applies the $\chi^2$ –statistic to the band–power estimates of Figure 1.
 This technique. however. is not strictly applicable in this context because the points in Figure 1 are not eaussian distributed.," This technique, however, is not strictly applicable in this context because the points in Figure 1 are not gaussian distributed."
 This is true even if the underlving sky [uctuations. the pixel values (including noise). are in fact random variables.," This is true even if the underlying sky fluctuations, the pixel values (including noise), are in fact gaussian random variables."
 Power estimates the of thegaussian temperature I[uctuations. and an estimate ofrepresent the variance of gaussian variables is not itself gaussian.," Power estimates represent the of the temperature fluctuations, and an estimate of the variance of gaussian variables is not itself gaussian."
 The 47 statistic. which assumes gaussianity. is therefore not the correct approach.," The $\chi^2$ –statistic, which assumes gaussianity, is therefore not the correct approach."
 A analysis of the data in 1 requires that the correct likelihood rigorousfunction be calculated for eachFigure, 	A rigorous analysis of the data in Figure 1 requires that the correct likelihood function be calculated for each experiment.
 Even with the present data set. this is à time consuming task.experiment. due to the variety. of dillerent experimental set.ups represented. and for the next generation with tens of thousands of pixels. it becomes experiments. in the extreme: for example. analysis of BOONMIZILANCGcomputationallys Northdemanding American Hight (30.000 requires 10 hours on a Cray T3I2 (Borril 1998).," Even with the present data set, this is a time consuming task, due to the variety of different experimental set–ups represented, and for the next generation experiments, with tens of thousands of pixels, it becomes computationally demanding in the extreme; for example, analysis of BOOMERANG's North American flight (30,000pixels) requires $\sim 10$ hours on a Cray T3E (Borril 1998)."
 lt is therefore pixels)important to find. useful to likelihood. functions (Dond et al., It is therefore important to find useful approximations to experimental likelihood functions (Bond et al.
 1998: approximationsWanelelt ct al., 1998; Wandelt et al.
 1998)., 1998).
experimental Llere. we describe our clforts to derive a reasonable ," Here, we describe our efforts to derive a reasonable approximation."
Some results from its application to current data approximation.can be found in Bartlettpreliminary ct al. (, Some preliminary results from its application to current data can be found in Bartlett et al. (
1998b).,1998b).
 2 APPRONIAIATE LIIELILIOOD FUNCTION For (gaussian noise is assumed throughout). we may write the gaussianlikelihood anisotropiesfunction for a set of parameters. represented. by a vector ©. once given the data. à set of pixel values arranged in a vector d: C is the covariance matrix C; The average is understood to be over the theoretical ensemble of all possible anisotropy. patterns rcalizable with the given parameter set. 9. of which the actual data set is but one realization.," \bsk ∋ 2 APPROXIMATE LIKELIHOOD FUNCTION \ssk ∋ 	For gaussian anisotropies (gaussian noise is assumed throughout), we may write the likelihood function for a set of parameters, represented by a vector $\Teta$, once given the data, a set of pixel values arranged in a vector $\vd$: where $\mC$ is the covariance matrix The average is understood to be over the theoretical ensemble of all possible anisotropy patterns realizable with the given parameter set $\Teta$, of which the actual data set is but one realization."
 The has two contributions. one intrinsic to the sky [uctuations. 'P(O). a covariancefunction of the parameter vector. and the other due to the noise. IN.," The covariance has two contributions, one intrinsic to the sky fluctuations, $\mT(\Teta)$, a function of the parameter vector, and the other due to the noise, $\mN$."
" For a data vector consisting of simple pixel values. from a map of the sky. we further have where. as usual. the power spectrum is the ensemble of €. D, describes the beam (assumed symmetric). P is the Legendre polynomial of experimentalorder / and 8;; is the angle sphericallyseparating pixels / and j."," For a data vector consisting of simple pixel values, from a map of the sky, we further have where, as usual, the power spectrum is the ensemble of $C_l$ $B_l$ describes the experimental beam (assumed spherically symmetric), $P_l$ is the Legendre polynomial of order $l$ and $\theta_{ij}$ is the angle separating pixels $i$ and $j$."
 The likelihood is a function of the O. which be either the Cy or the world.model constants. such as O. parametersete... In the maylatter situation. the parameter dependence enters the likelihood function through relations of the kind € by the adopted theory. e.g... inflation.," The likelihood is a function of the parameters $\Teta$, which may be either the $C_l$ or the world–model constants, such as $\Omega$, etc... In the latter situation, the parameter dependence enters the likelihood function through relations of the kind $C_l[\Teta]$ , specified by the adopted theory, e.g., inflation."
 In either case.the best 9].estimates specilied.for the parameter values are found by maximizing," In either case,the best estimates for the parameter values are found by maximizing"
 The conventional wisdom based on the staucare theory of structure formation says tliat he universe was reionized sometime in the redshilt range z=6—12 (Barkaua Loeb 2001)., The conventional wisdom based on the standard theory of structure formation says that the universe was reionized sometime in the redshift range $z=6-12$ (Barkana Loeb 2001).
 The relatively large uncertain range iu recshift reflecs our iuperfect knowledge of the deusity luctuatious on sinall scales. star formatio1 processes (e.g.. efficiency. INE. ete.)," The relatively large uncertain range in redshift reflects our imperfect knowledge of the density fluctuations on small scales, star formation processes (e.g., efficiency, IMF, etc.)"
 aud feedback oocesses at. high redshift., and feedback processes at high redshift.
" The latest observations of |igh redshift quasars (e.g.. Fan 2001) are begiuning to probe the lower bouud of hat wildosv and st@eestiousMD have beeu mace that we uay be witnessiug the eud phase of the cosiuologic:| 'ejonization. process at 5~6. based solely ou tlie appearauce of a precipitous drop of t""ansiulted flux at he rest-Draiue wavelength near zo6 ina single quasar spectrum (Becker 2001. 1jereal[te: BOL: Barkaua 2001)."," The latest observations of high redshift quasars (e.g., Fan 2001) are beginning to probe the lower bound of that window and suggestions have been made that we may be witnessing the end phase of the cosmological reionization process at $z\sim 6$, based solely on the appearance of a precipitous drop of transmitted flux at the rest-frame wavelength near $z\sim 6$ in a single quasar spectrum (Becker 2001, hereafter B01; Barkana 2001)."
 In thisLetter we present an analysis of ile lonizine backe‘ound radiation field iu the redshift range 7=19—6.1. using the absorption measurements in BO!L.," In this we present an analysis of the ionizing background radiation field in the redshift range $z=4.9-6.1$, using the absorption measurements in B01."
 Combining[n] with previous data at lower redshift. we ind that. coming from hiel recsult. the ionizing radiatiou intensity displays a sharp rise at 26 peaking at z= 2.6. a sighificant clewuturn [rom 52.6 to 25.2 by a factor of ~0.6. aud subseqtently a consistent ascent [rom z=5.0 to 2=2.4 by a factor of ~E.," Combining with previous data at lower redshift, we find that, coming from high redshift, the ionizing radiation intensity displays a sharp rise at $z\sim 6$ peaking at $z=5.6$ , a significant downturn from $z\sim 5.6$ to $5.2$ by a factor of $\sim 0.6$, and subsequently a consistent ascent from $z=5.0$ to $z=2.4$ by a factor of $\sim 4$."
 All these three features are consistent witl a picture that the cosmological reionization was near completion al 276., All these three features are consistent with a picture that the cosmological reionization was near completion at $z\sim 6$.
 The first feature (i.e.. the i1itial sharp rise) has been predicted by several authors previously (Cen Ostriker 1993: Cinediu 2000a: Miralda-Escudé.. Haehnelt. Rees 2001).," The first feature (i.e., the initial sharp rise) has been predicted by several authors previously (Cen Ostriker 1993; Gnedin 2000a; Miralda-Escudé,, Haehnelt, Rees 2001)."
 At present. the Primary uncertainty for its determinaion observationally is the possibility that the high level of absorption in the single observed quasar at 2=6.28 is some kind of anomaly. (we show that it canuot be a simple statistica Πιctuation in the absorption level).," At present, the primary uncertainty for its determination observationally is the possibility that the high level of absorption in the single observed quasar at $z=6.28$ is some kind of anomaly (we show that it cannot be a simple statistical fluctuation in the absorption level)."
 Additional observed quasars at 2203»ga will be critical in this regarc., Additional observed quasars at $z\gtrsim 6.3$ will be critical in this regard.
 Here we focus our attention ou the relatively more robust measurements of the ionizing racdiatior field at z«6 and show that the observed pause in the rise of the amplitude of theionizing radiation field from z~5.6 to 5.0 could bedue to suppression of star formation following relonizatiou a I0€ 6., Here we focus our attention on the relatively more robust measurements of the ionizing radiation field at $z<6$ and show that the observed pause in the rise of the amplitude of theionizing radiation field from $z\sim 5.6$ to $5.0$ could bedue to suppression of star formation following reionization at $z\sim 6$ .
As was discussed in sect. 3..,"As was discussed in sect. \ref{sec:comparison},"
 the global accretion rate in the present model is limited by the rate at which the hot layer can flow over the cool disk., the global accretion rate in the present model is limited by the rate at which the hot layer can flow over the cool disk.
 The surface density and temperature of the hot layer are in turn narrowly constrained by the physics of the Coulomb interaction which allow the layer to form and the energy balance between it and the underlying disk., The surface density and temperature of the hot layer are in turn narrowly constrained by the physics of the Coulomb interaction which allow the layer to form and the energy balance between it and the underlying disk.
 There are thus two ways to increase the flow rate in the hot layer: by increasing the effective viscosity or providing another mechanism besides viscous dissipation to transport angular momentum., There are thus two ways to increase the flow rate in the hot layer: by increasing the effective viscosity or providing another mechanism besides viscous dissipation to transport angular momentum.
 The interaction between the ion supported ADAF and the hot layer provides such a mechanism., The interaction between the ion supported ADAF and the hot layer provides such a mechanism.
 The 10n supported flow is partially suppoted against gravity by gas pressure and rotates slower than Keplerian., The ion supported flow is partially suppoted against gravity by gas pressure and rotates slower than Keplerian.
 The mass condensing from the ADAF on the hot layer thus acts as a sink of angular momentum. which increases the mass flux in the hot layer.," The mass condensing from the ADAF on the hot layer thus acts as a sink of angular momentum, which increases the mass flux in the hot layer."
 This effect was not included in DSOS and the calculations above., This effect was not included in DS05 and the calculations above.
 An estimate of its importance can be made by evaluating the angular momentum exchange from the solutions in sect., An estimate of its importance can be made by evaluating the angular momentum exchange from the solutions in sect.
 3., 3.
 We find that. for the viscosity parameter c.=0.2 assumed for the hot layer. the effect increases the mass flux by a factor 2-3.," We find that, for the viscosity parameter $\alpha=0.2$ assumed for the hot layer, the effect increases the mass flux by a factor 2–3."
 The effect is thus significant. but not sufficient to increase the mass flux by the factors indicated by the comparison with observations in sect.," The effect is thus significant, but not sufficient to increase the mass flux by the factors indicated by the comparison with observations in sect."
 3., 3.
 The missing ingredient most likely to lead to the higher mass fluxes inferred from the observations may well be a strong magnetic field., The missing ingredient most likely to lead to the higher mass fluxes inferred from the observations may well be a strong magnetic field.
 Strong ordered magnetic fields in the inner regions of the flow are implied by the presence of jets. especially in the hard X-ray states discussed here.," Strong ordered magnetic fields in the inner regions of the flow are implied by the presence of jets, especially in the hard X-ray states discussed here."
 A bundle of strong ordered magnetic field held together by a disk (?) can have field strengths well above those produced by magnetorotational turbulence., A bundle of strong ordered magnetic field held together by a disk \citep{1974Ap&SS..28...45B} can have field strengths well above those produced by magnetorotational turbulence.
 The angular momentum exchange by interaction of such a bundle with the disk (222?) can be much more effective than turbulence parametrized with à viscosity parameter a~].," The angular momentum exchange by interaction of such a bundle with the disk \citep{2001MNRAS.323..587S, 2003ApJ...592.1042I,
2003PASJ...55L..69N,2005ApJ...620..878D} can be much more effective than turbulence parametrized with a viscosity parameter $\alpha\sim
1$."
 This aspect is beyond the present study. and is a promising field for further study.," This aspect is beyond the present study, and is a promising field for further study."
 The spectrum from the hot ring in our model is hard. to predict. without à more detailed model., The spectrum from the hot ring in our model is hard to predict without a more detailed model.
 The uncertainty lies chiefly in the distribution and number of seed photons available for cooling., The uncertainty lies chiefly in the distribution and number of seed photons available for cooling.
 The more photon-starved the hot ring 1s. the higher its temperature will be. and (since the evaporation rate into an ADAF scales with 77) the smaller its contribution to the overall spectrum.," The more photon-starved the hot ring is, the higher its temperature will be, and (since the evaporation rate into an ADAF scales with $T_{\rm{e}}^2$ ) the smaller its contribution to the overall spectrum."
 The temperature we assumed for the hot ring in practice could be much lower. which would bring it more in line with observations of the high energy cutoff observed in some spectra (which suggest a maximum temperature of about KT.-150 keV).," The temperature we assumed for the hot ring in practice could be much lower, which would bring it more in line with observations of the high energy cutoff observed in some spectra (which suggest a maximum temperature of about $kT_{\rm{e}} \sim 150$ keV)."
 Additionally. the geometric distribution of seed photons will change the structure of the Compton spectrum.," Additionally, the geometric distribution of seed photons will change the structure of the Compton spectrum."
 This is because photons that scatter once preferentially scatter back in the direction they were originally travelling. and there is a deficit of photons in the first scattering hump in the spectrum.," This is because photons that scatter once preferentially scatter back in the direction they were originally travelling, and there is a deficit of photons in the first scattering hump in the spectrum."
 This effect is most pronounced in the plane-parallel case (e.g. ?)). but there will also be some anisotropy in the hot ring's spectrum if the seed photons are primarily from the disk.," This effect is most pronounced in the plane-parallel case (e.g. \cite{1991ApJ...380L..51H}) ), but there will also be some anisotropy in the hot ring's spectrum if the seed photons are primarily from the disk."
 We have considered only seed photons from the disk. but there may also be photons produced from other processes (such as synchrotron emission) which would allow the hot ring to cool more efficiently and make the effects of anisotropy less pronounced (since the seed photons would be travelling through the hot ring in essentially random directions).," We have considered only seed photons from the disk, but there may also be photons produced from other processes (such as synchrotron emission) which would allow the hot ring to cool more efficiently and make the effects of anisotropy less pronounced (since the seed photons would be travelling through the hot ring in essentially random directions)."
 Finally. in this paper we have neglected the spectral contribution from the ADAF.," Finally, in this paper we have neglected the spectral contribution from the ADAF."
 Depending on its radiative efficiency. its contribution could also harden the observed high-energy Comptonized spectrum considerably.," Depending on its radiative efficiency, its contribution could also harden the observed high-energy Comptonized spectrum considerably."
" Our model of a disk truncated at 15-20 Rs and surrounding corona Is qualitatively very different from the untruncated disk (with R5,~ [Rs) models fit by ? and ?.. and it is natural to ask how the observed soft excess can be so small when the radiating area is so much larger."," Our model of a disk truncated at 15-20 $R_{\rm S}$ and surrounding corona is qualitatively very different from the untruncated disk (with $R_{in} \sim 1 R_{\rm S}$ ) models fit by \cite{2006ApJ...652L.113M} and \cite{2006ApJ...653..525M}, and it is natural to ask how the observed soft excess can be so small when the radiating area is so much larger."
 The answer lies in several points., The answer lies in several points.
 The most important of these is that the temperature in our disks ts about a factor 2 smaller than is found by ?.. so that the flux is intrinsically much smaller and (even after the correction 1s applied) most of the flux is cut off by interstellar absorption.," The most important of these is that the temperature in our disks is about a factor 2 smaller than is found by \cite{2006ApJ...652L.113M}, , so that the flux is intrinsically much smaller and (even after the colour-correction is applied) most of the flux is cut off by interstellar absorption."
 There ts a further reduction from the hot surface layer. which upscatters about two-thirds of the photons.," There is a further reduction from the hot surface layer, which upscatters about two-thirds of the photons."
 Finally. the shape of the upscattered photons deviates from a power law at low energies. so that measuring the temperature of the soft excess depends very sensitively on modelling the Comptonized spectrum correctly.," Finally, the shape of the upscattered photons deviates from a power law at low energies, so that measuring the temperature of the soft excess depends very sensitively on modelling the Comptonized spectrum correctly."
 The effects of trradiation on the measured truncation radius have also been studied using a more phenomenological approach in ?.. who re-analyzed the data from J1817-330 (?) to demonstrate that irradiation can increase the measured truncation radius in. this. source (although they assume continual stress at the inner boundary of the truncated disk. which we have not done here).," The effects of irradiation on the measured truncation radius have also been studied using a more phenomenological approach in \cite{2008MNRAS.tmp..717G}, who re-analyzed the data from J1817-330 \citep{2007ApJ...666.1129R} to demonstrate that irradiation can increase the measured truncation radius in this source (although they assume continual stress at the inner boundary of the truncated disk, which we have not done here)."
 In particular. they. note future plans to test the effects of incomplete thermalization from incident radiation (cf.," In particular, they note future plans to test the effects of incomplete thermalization from incident radiation (cf."
 sect. 2.4.1)).," sect. \ref{sec:cooldisk}) ),"
 which ean. further increase the truncation radius., which can further increase the truncation radius.
 Several well-studied sources show some evidence of deviations from a single power law., Several well-studied sources show some evidence of deviations from a single power law.
 ? notes that spectra from Cyg X-] have additional structure. in their spectra that can be fit with an additional very soft Comptonizing component. while both the source GX 339-4 and Cyg X-I sometimes show an excess of very high energy photons compared to a fit with a single power law. which suggests a second site for Comptonization that ts naturally explained with this model.," \cite{2007A&ARv..15....1D} notes that spectra from Cyg X-1 have additional structure in their spectra that can be fit with an additional very soft Comptonizing component, while both the source GX 339-4 and Cyg X-1 sometimes show an excess of very high energy photons compared to a fit with a single power law, which suggests a second site for Comptonization that is naturally explained with this model."
 For GX 339-4. ? detected a broad Fe-K line. which they fitted with a relativistically broadened profile. implying an untruncated disk and a spinning black hole.," For GX 339-4, \cite{2006ApJ...653..525M} detected a broad Fe-K line, which they fitted with a relativistically broadened profile, implying an untruncated disk and a spinning black hole."
 However. the observation of a broadened Fe-K line mayalso be consistent," However, the observation of a broadened Fe-K line mayalso be consistent"
WZ See is (he prototvpe of a class of cataclysmic variables (hat exhibit extreme characteristics: short orbital periods. extremely large dwarl nova outbursts. long outburst recurrence (ies. and lowmass companion stars.,"WZ Sge is the prototype of a class of cataclysmic variables that exhibit extreme characteristics: short orbital periods, extremely large dwarf nova outbursts, long outburst recurrence times, and low–mass companion stars."
 WZ dee displavs ~7.5 mag outbursts separated by ~2 3 decades aud has a stellar mass ratio of 1325: 1 with a companion star (hat is less than 0.11 AL. and perhaps as low as 0.03 M... (Steeghs et al., WZ Sge displays $\sim$ 7.5 mag outbursts separated by $\sim$ 2–3 decades and has a stellar mass ratio of 13–25: 1 with a companion star that is less than 0.11 $\Msun$ and perhaps as low as 0.03 $\Msun$ (Steeghs et al.
 2001. Ciardi et al.," 2001, Ciardi et al."
 1998)., 1998).
 These extreme characteristics make WZ See an ideal proving ground [ον accretion disk theory., These extreme characteristics make WZ Sge an ideal proving ground for accretion disk theory.
 Among the many challenges WZ See offers is the origin of the rapid 27.87 s and 28.96 s oscillations., Among the many challenges WZ Sge offers is the origin of the rapid 27.87 s and 28.96 s oscillations.
 First seen in (he optical by Robinson. Nather Patterson. (LOTS). (hese oscillations have been detected in the UV. (Welsh et al.," First seen in the optical by Robinson, Nather Patterson (1978), these oscillations have been detected in the UV (Welsh et al."
 1997. Skidmore οἱ al.," 1997, Skidmore et al."
 1999). infrared (Skidmore et al.," 1999), infrared (Skidmore et al."
 2002) and in the X-ray (Patterson οἱ al., 2002) and in the X-ray (Patterson et al.
 1993). though weakly.," 1998), though weakly."
 The oscillations are complex. with large changes in amplitude. phase jitter. and (ransient signals al nearby periods.," The oscillations are complex, with large changes in amplitude, phase jitter, and transient signals at nearby periods."
 Sometimes both periodicities are present in the light curve., Sometimes both periodicities are present in the light curve.
 Robinson et al. (, Robinson et al. (
"1978) proposed that the oscillations are due to nonradial gy mode pulsations of the white dwarl, a hypothesis supported by the simultaneous presence of (he incommensurate 27.87 s and 28.96 s periodicities.","1978) proposed that the oscillations are due to non–radial $g$ –mode pulsations of the white dwarf, a hypothesis supported by the simultaneous presence of the incommensurate 27.87 s and 28.96 s periodicities."
 Further support comes from analoev with GW Lib. a cataclysmic variable (hat almost. certainly is afide pulsating white dwarl (van Zyl et al.," Further support comes from analogy with GW Lib, a cataclysmic variable that almost certainly is a pulsating white dwarf (van Zyl et al."
 2000. szkody et al.," 2000, Szkody et al."
 2002)., 2002).
 An alternative hypothesis. proposed by Patterson (1930). attributed the oscillations to a maegnetized white dwar! channelling the accretion flow.," An alternative hypothesis, proposed by Patterson (1980), attributed the oscillations to a magnetized white dwarf channelling the accretion flow."
 The white dwarfs rotation provides the stable clock driving the 27.87 s fundamental periodicity., The white dwarf's rotation provides the stable clock driving the 27.87 s fundamental periodicity.
 The other complex. transient oscillations are due to reprocessing of radiation in the accretion disk (see Patterson et al.," The other complex, transient oscillations are due to reprocessing of radiation in the accretion disk (see Patterson et al."
 1998 for more details)., 1998 for more details).
 WZ See would then be a member of the DC) Herculis (or intermediate polar) class of cataclysmic variables., WZ Sge would then be a member of the DQ Herculis (or intermediate polar) class of cataclysmic variables.
 The detection of a 27.87 s periodicity in observations added much support to this magnetic accretor model., The detection of a 27.87 s periodicity in observations added much support to this magnetic accretor model.
" However. despite the success of this ""oblique rotator” model in other cataclvsmüc variables. the presence of the simultaneous incommensurale periodicities in WZ See remains an obstacle for this interpretatioΕν"," However, despite the success of this “oblique rotator” model in other cataclysmic variables, the presence of the simultaneous incommensurate periodicities in WZ Sge remains an obstacle for this interpretation."
 In their investigation of quasiperiodic oscillations in cataclysmic variables. Warner Woudt (2002) developed the “low inertia magnetic accretor (LIMA) model and this vields a third. possibility for the origin of the oscillations.," In their investigation of quasi–periodic oscillations in cataclysmic variables, Warner Woudt (2002) developed the “low inertia magnetic accretor” (LIMA) model and this yields a third possibility for the origin of the oscillations."
 The model contains two elements: (1) mmagnelicallycontrolled accretion onto a rapidly rotating belt on the white dwarf and (11) a prograde travelling wave at the inner edge of the disk that produces a vertical thickening which acts as a site for reprocessing and ean also occult part of the disk and/or white dwarl., The model contains two elements: (i) magnetically–controlled accretion onto a rapidly rotating belt on the white dwarf and (ii) a prograde travelling wave at the inner edge of the disk that produces a vertical thickening which acts as a site for reprocessing and can also occult part of the disk and/or white dwarf.
 In (his scenario. the 27.87 s periodicity arises [rom magnetic accretion onto the white dwart. but unlike the DQ Ier model. the belt can slip on the white dwarls surface and hence the oscillation can vary in phase. amplitude and even period quite naturally.," In this scenario, the 27.87 s periodicity arises from magnetic accretion onto the white dwarf, but unlike the DQ Her model, the belt can slip on the white dwarf's surface and hence the oscillation can vary in phase, amplitude and even period quite naturally."
 The 23.96 s signal, The 28.96 s signal
observations were taken with the 2.5-m [Isaac Newton Telescope (LNT) on La Palma over several nights in 1990 April and June.,observations were taken with the 2.5-m Isaac Newton Telescope (INT) on La Palma over several nights in 1990 April and June.
 Ehe uncertainty in the orbital period leads to à possible phase error of ten per cent after four days., The uncertainty in the orbital period leads to a possible phase error of ten per cent after four days.
 On combining data with a smaller temporal separation than this. the resulting datasets have approximately eighty per cent orbital phase coverage.," On combining data with a smaller temporal separation than this, the resulting datasets have approximately eighty per cent orbital phase coverage."
 The second set of imaging data we obtained at the 2.4- Lliltner telescope at. Michigan.Dartmouth.MET. (ΛΗΔΑ) observatory using a Sloan Digital Sky Survey (SDSS) i-band filter., The second set of imaging data we obtained at the 2.4-m Hiltner telescope at Michigan–Dartmouth–MIT (MDM) observatory using a Sloan Digital Sky Survey (SDSS) -band filter.
 Lt consists of twenty-seven 60-5 exposures and seventy-eight. 180-8 exposures taken over four nights curing 2009 Julv., It consists of twenty-seven 60-s exposures and seventy-eight 180-s exposures taken over four nights during 2009 July.
 The field of view was 3.32 aremin? while the images had à tvpical seeing of about 1.6 arcesec., The field of view was $\times$ 3.32 $^2$ while the images had a typical seeing of about 1.6 arcsec.
 This dataset had approximately fifty per cent orbital phase coverage., This dataset had approximately fifty per cent orbital phase coverage.
 All images were prepared ον de-biasing. trimming and Uat-fielcing with the routine inIRAF.," All images were prepared by de-biasing, trimming and flat-fielding with the routine in."
. For the spectral images. an aperture was selected around the target on each image and the spectrum was extracted: using routines in the package inIRAF.," For the spectral images, an aperture was selected around the target on each image and the spectrum was extracted using routines in the package in."
. Phe wavelength-calibration arc-Iamp spectra (CuNe for the red. and. Cur for the blue) were extracted. using the same parameters as for the corresponding target spectra., The wavelength-calibration arc-lamp spectra (CuNe for the red and CuAr for the blue) were extracted using the same parameters as for the corresponding target spectra.
 The are spectra were fitted with a high-orcer cubic spline to remove the shape of the continuum of the illuminating arc-lamip., The arc spectra were fitted with a high-order cubic spline to remove the shape of the continuum of the illuminating arc-lamp.
 The wavelength solutions for the target spectra were calculated using the lines identified in the are spectra and ehecked using the sky lines in a sky spectrum extracted. from a source-free region of the spectral image containing the target., The wavelength solutions for the target spectra were calculated using the lines identified in the arc spectra and checked using the sky lines in a sky spectrum extracted from a source-free region of the spectral image containing the target.
 With only three blue spectra for which we had. enough signal-to-noise (S/N) to obtain a trace for extraction on the spectral image. we summed the spectra and removed cosmic ravs (which were located on the continuum) manually inIRAF.," With only three blue spectra for which we had enough signal-to-noise (S/N) to obtain a trace for extraction on the spectral image, we summed the spectra and removed cosmic rays (which were located on the continuum) manually in."
. We also summed the red spectra and again removed cosmic ravs manually. checking for consistency against the meclian-combined cosmic-rav-Lilterecl spectrum.," We also summed the red spectra and again removed cosmic rays manually, checking for consistency against the median-combined cosmic-ray-filtered spectrum."
 Finally. we measured equivalent widths of any emission lines in the summed spectrum by fitting with a Gaussian line profile inIRAF.. excluding from the fits data from any spectrum which hacl been alfected by a cosmic rav hit on that emission line.," Finally, we measured equivalent widths of any emission lines in the summed spectrum by fitting with a Gaussian line profile in, excluding from the fits data from any spectrum which had been affected by a cosmic ray hit on that emission line."
 For the imaging data. profile-fitting photometry was performed with the (StetsonLOST) package inIRAF.," For the imaging data, profile-fitting photometry was performed with the \citep{stetson87} package in."
. A set of bright. isolated stars is required to mocel the stellar. profiles arising from the point spread. function (PSE) of the light in an image.," A set of bright, isolated stars is required to model the stellar profiles arising from the point spread function (PSF) of the light in an image."
 In a crowded field where no well-isolated stars are available. an iterative procedure is required to build the PSE.," In a crowded field where no well-isolated stars are available, an iterative procedure is required to build the PSF."
 The following is the procedure we used to construct the PSE of our images., The following is the procedure we used to construct the PSF of our images.
 First. à Gaussian function. was fitted. to a sample of reasonably uncrowcded stars with good. signal-to-noise ancl no defects. in an attempt to model the PSE.," First, a Gaussian function was fitted to a sample of reasonably uncrowded stars with good signal-to-noise and no defects, in an attempt to model the PSF."
 A constant PSE model was initially computed. and fitted to the chosen PSE stars and their neighbours in order to subtract them from the image. revealing in the process previously invisible faint neighbouring stars — these were subsequently added to the star list. had. photometry performed. on them. and were finally subtracted from the image.," A constant PSF model was initially computed and fitted to the chosen PSF stars and their neighbours in order to subtract them from the image, revealing in the process previously invisible faint neighbouring stars – these were subsequently added to the star list, had photometry performed on them and were finally subtracted from the image."
 The process was Iterated upon until a fairly complete list. of PSE-star. neighbours had been found. and these were then subtractecl from the original image to produce an image containing the PSE stars but excluding their close neighbours., The process was iterated upon until a fairly complete list of PSF-star neighbours had been found and these were then subtracted from the original image to produce an image containing the PSF stars but excluding their close neighbours.
 From this image a PSE model which varied. linearly across the image was computed., From this image a PSF model which varied linearly across the image was computed.
 This new model was used to fit ancl subtract (more cleanly) the PSE stars and their neighbours [rom he original image in the same way as before. iterating on he process to eliminate the close neighbours of the PSE stars and finally produce an image containing only the PSE stars. which at this stage had. become well-isolated enough o compute a sulliciently accurate model of the PSE to use or photometry.," This new model was used to fit and subtract (more cleanly) the PSF stars and their neighbours from the original image in the same way as before, iterating on the process to eliminate the close neighbours of the PSF stars and finally produce an image containing only the PSF stars, which at this stage had become well-isolated enough to compute a sufficiently accurate model of the PSF to use for photometry."
 It was from this image that the final PSE model was mace., It was from this image that the final PSF model was made.
 This model was then fitted to the source (the CV. M5 VIOTI) and several comparison stars to obtain heir instrumental magnitudes.," This model was then fitted to the source (the CV, M5 V101) and several comparison stars to obtain their instrumental magnitudes."
 The process was repeated for cach image and a light eurve was constructed using the same xiehter comparison star in each image (with constancy checked. against several other comparison stars)., The process was repeated for each image and a light curve was constructed using the same brighter comparison star in each image (with constancy checked against several other comparison stars).
 The light curves were folded on the orbital period ancl plotted against orbital phase., The light curves were folded on the orbital period and plotted against orbital phase.
 Phase zero is arbitrary since the ephemoeris was not known., Phase zero is arbitrary since the ephemeris was not known.
 Our light. curve (Pie. 5)), Our light curve (Fig. \ref{fig:flux}) )
 shows a —15-d. outburs in theV. band. during 2004 May. the only large outburs seen in nine months of monitoring.," shows a $\sim$ 15-d outburst in the band during 2004 May, the only large outburst seen in nine months of monitoring."
 The rise to maximum takes place over at least five days. fading over another ten days. approximately.," The rise to maximum takes place over at least five days, fading over another ten days, approximately."
 Phe actual peak of the outburs may have been missed in the —24-hr sampling gaps., The actual peak of the outburst may have been missed in the $\sim$ 24-hr sampling gaps.
 We were unable to calibrate the outburst amplitude on the magnitude scale due to severe crowcding elleets. combine with the apparent faintness of the CV., We were unable to calibrate the outburst amplitude on the magnitude scale due to severe crowding effects combined with the apparent faintness of the CV.
 Phe outburst was also caught in the Z-band: however. due to the aforementionec cilliculty in calibrating the flux. it is unclear if the lower L-band flus-levels compared to the V-hancl are real or not.," The outburst was also caught in the -band; however, due to the aforementioned difficulty in calibrating the flux, it is unclear if the lower -band flux-levels compared to the -band are real or not."
 The best available reference image to use for the D-bane reductions came from the end of May. when the {lux leve Πας more or less reached quiescent levels again however. there may still have been some activity of the object a this time. which would. in elfect. reduce the Ες measure in the subtractecl images.," The best available reference image to use for the -band reductions came from the end of May when the flux level had more or less reached quiescent levels again – however, there may still have been some activity of the object at this time, which would, in effect, reduce the flux measured in the subtracted images."
 Inspecting the full dataset. we see low-level Hiekering-like variability. typical of CVs. which appears to be present at a level above the noise bu again. caution is required in interpreting this feature withou proper calibration.," Inspecting the full dataset, we see low-level flickering-like variability, typical of CVs, which appears to be present at a level above the noise – but again, caution is required in interpreting this feature without proper calibration."
 Following the 1999 event recorded by Sahuctal.(2001).. the system was observed in a bright state about once per vear up until 2004.," Following the 1999 event recorded by \citet{sahu01}, the system was observed in a bright state about once per year up until 2004."
 Pictrukowiezetal.(2005). estimated the outburst recurrence time for the svstem to be greater than 150 d based on their own observations as well as the 1999 event., \citet{piet05} estimated the outburst recurrence time for the system to be greater than 150 d based on their own observations as well as the 1999 event.
 Our observations are in agreement with this estimate., Our observations are in agreement with this estimate.
 1n nine months of monitoring we saw only one outburst of duration 15 d. The sampling was every second. night for most of the observing programme. but after discarding the images with the worst seeing. we are left with gaps in the data of up to 17 d. This means there is a possibility we may have missed another sipilar outburst: also. there is a stronger likelihood of any shorter outbursts of only a few davs curation if present having gone undetectect.," In nine months of monitoring we saw only one outburst of duration $\sim15$ d. The sampling was every second night for most of the observing programme, but after discarding the images with the worst seeing, we are left with gaps in the data of up to 17 d. This means there is a possibility we may have missed another similar outburst; also, there is a stronger likelihood of any shorter outbursts of only a few days duration – if present – having gone undetected."
Alultiftequeney data or resolved VLBI observations would be required to test these hypotheses. while higher sensitivity would allow us to make higher-time resolution lightcurves in linear polarization. and more accurately probe how well the polarized. emission followed. the total intensity.,"Multifrequency data or resolved VLBI observations would be required to test these hypotheses, while higher sensitivity would allow us to make higher-time resolution lightcurves in linear polarization, and more accurately probe how well the polarized emission followed the total intensity."
 Upcoming facilities such as EVLA and eMERLIN will provide. the required. increases in sensitivity. ancl fractional bandwidth to make such observations., Upcoming facilities such as EVLA and eMERLIN will provide the required increases in sensitivity and fractional bandwidth to make such observations.
 Imaging at 43€Cllz with the VLA in A-configuration eives an angular resolution of order 50mmas., Imaging at GHz with the VLA in A-configuration gives an angular resolution of order mas.
 This would be sullicient to resolve arcsecond-scale extensions such as those seen by. Marthetal.(2001)... if present. curing our observations.," This would be sufficient to resolve arcsecond-scale extensions such as those seen by \citet{Mar01}, if present during our observations."
 Llowever. given the time-variable nature of the source. the variability had. to be removed prior to imaging the source in order to search for any potential faint extensions.," However, given the time-variable nature of the source, the variability had to be removed prior to imaging the source in order to search for any potential faint extensions."
 Imaging without removing the variability showed no extension to an level of1., Imaging without removing the variability showed no extension to an level of.
.. An automated procedure was written usingPARSELTONGUE. à Python interface toAPS. to remove the time-variable core bv making images of l-min time chunks. anc subtracting the fitted core component in the «c-plane before recombining and imaging the core-subtractec data from all time intervals.," An automated procedure was written using, a Python interface to, to remove the time-variable core by making images of 1-min time chunks, and subtracting the fitted core component in the -plane before recombining and imaging the core-subtracted data from all time intervals."
 At GOLIz. there was no observable extension down to an rms of1.," At GHz, there was no observable extension down to an rms of."
.. Phe subtraction did not work as well at 43€GGllIz. possibly due to atmospheric distortions shifting the source position slightly.," The subtraction did not work as well at GHz, possibly due to atmospheric distortions shifting the source position slightly."
 The central source was not Cully removed. although no evidence for extension was seen down to an rms of," The central source was not fully removed, although no evidence for extension was seen down to an rms of."
 The dillerent. proper motion measurements quoted. in the literature (Mioduszewskietal.2001:MartíMiller-Jonesetal.2004) all predict that a flare would take several davs to become sullicientlv extended to be resolved at GGlIz by the VLA in its A-configuration.," The different proper motion measurements quoted in the literature \citep{Mio01,Mar01,Mil04} all predict that a flare would take several days to become sufficiently extended to be resolved at GHz by the VLA in its A-configuration."
 Phe 400-m.]y are at the start of our observations could not therefore have been resolved., The 400-mJy flare at the start of our observations could not therefore have been resolved.
 Lhe Ryle Telescope monitoring show no [lares with 15-CGllz Hlux densities exceeding mm. between the 2001 September outburst (Miller-Jonesetal.2004) and the beginning of our observations., The Ryle Telescope monitoring show no flares with 15-GHz flux densities exceeding mJy between the 2001 September outburst \citep{Mil04} and the beginning of our observations.
 The lack of extended: emission down to our rms limit of mmJv then constrains the e-folding time for the decay of any low-level Hares to be <5.2« lc. and that for the 2001 September giant flare to be «12.5 dd. The overall radio spectrum was sulliciently well-sampled on four occasions over the course of the January 2002 observing run to generate broadband spectra (Fig. 3)).," The lack of extended emission down to our rms limit of mJy then constrains the e-folding time for the decay of any low-level flares to be $<5.2$ d, and that for the 2001 September giant flare to be $<12.5$ d. The overall radio spectrum was sufficiently well-sampled on four occasions over the course of the January 2002 observing run to generate broadband spectra (Fig. \ref{fig:radio_spectra}) )."
 The spectra are consistent with canonical svnchrotron spectra alfected by absorption at the lower frequencies., The spectra are consistent with canonical synchrotron spectra affected by absorption at the lower frequencies.
 The overall Dux density. decreases with time and the spectral turnover moves to lower frequencies., The overall flux density decreases with time and the spectral turnover moves to lower frequencies.
 This is the behaviour expected for the decay of the 400-mJy Mare at the start of the observations. as the cjecta move outwards from the core and expand.," This is the behaviour expected for the decay of the 400-mJy flare at the start of the observations, as the ejecta move outwards from the core and expand."
 The lower-level variability seen in Fig., The lower-level variability seen in Fig.
 is à secondary. effect. superposed on the general decrease. indicative of multiple emitting components in the source.," is a secondary effect superposed on the general decrease, indicative of multiple emitting components in the source."
 As noted in Section 2.1.. the lower-frequeney. lighteurve ds a smoothed ancl delaved: version of the emission at. the higher frequeney. a clear indication of the existence of opacity. cllects. as commonly. observed in. Πας sources such as AGN (e.g.Allerctal.LOS5).. supernovae LOSG).. and gamma-ray bursts (c.g.Soder-bergctal. 2006).," As noted in Section \ref{sec:lcs}, the lower-frequency lightcurve is a smoothed and delayed version of the emission at the higher frequency, a clear indication of the existence of opacity effects, as commonly observed in flaring sources such as AGN \citep[e.g.][]{All85}, supernovae \citep[e.g.][]{Wei86}, and gamma-ray bursts \citep[e.g.][]{Sod06}."
. Since the optical depth for both Lree- absorption ancl synchrotron self-absorption decreases with increasing frequency. we probe more compact regions at high frequencies. with lower-frequency. emission. being delayed: until the source has either expanded or moved out [rom behind the absorbing medium and the optical depth has decreased to order unity.," Since the optical depth for both free-free absorption and synchrotron self-absorption decreases with increasing frequency, we probe more compact regions at high frequencies, with lower-frequency emission being delayed until the source has either expanded or moved out from behind the absorbing medium and the optical depth has decreased to order unity."
 Molnaretal.(1984). observec similar low-level activity in Cve N-3 with small Dares which peaked later ancl with smaller amplitudes at. lower frequencies., \citet{Mol84} observed similar low-level activity in Cyg X-3 with small flares which peaked later and with smaller amplitudes at lower frequencies.
 “Pheyv measured a delay of 1525 mmin between 22 and CLIz. increasing to 239ET mmin between 15 and GCGlLIz.," They measured a delay of $15\pm5$ min between 22 and GHz, increasing to $239\pm7$ min between 15 and GHz."
" ""ον also claimed evidence for a periodicity in the range hh. although such a periodicity has not since been detected. (c.g.John-periodicphenomenoninthedataofMolnaretal. is less thanmm."," They also claimed evidence for a periodicity in the range h, although such a periodicity has not since been detected \citep[e.g.][who note that in fact the amplitude of any periodic
phenomenon in the data of \citeauthor{Mol84} is less than."
Js). To search for any periodicitv in our data. we constructed the power spectra of the lightcurves at the νο frequencies. which are shown in Fig. 4..," To search for any periodicity in our data, we constructed the power spectra of the lightcurves at the two frequencies, which are shown in Fig. \ref{fig:powerspectra}. ."
NGC objects aud. galaxies clusters). Masellauic Clouds targets or crowded areas (6.8. AIS1).,"NGC objects and galaxies clusters), Magellanic Clouds targets or crowded areas (e.g. M31)."
 Finally. from the remaining fields. we choose sources with offaxis angles between 3 and 15 arcu.," Finally, from the remaining fields, we choose sources with off–axis angles between 3 and 15 arcmin."
 To sunuuarize. we restricted to 501 fields (~90 deg?) and 3.161 sources.," To summarize, we restricted to 501 fields $\sim 90$ $^{2}$ ) and 3,161 sources."
 The survey is inhomogencous (because of the worsening of the PSF with the offaxis) thus iu the computation of the flux distribution different sources have different weights., The survey is inhomogeneous (because of the worsening of the PSF with the off–axis) thus in the computation of the flux distribution different sources have different weights.
 The weight is defined as the inverse of the area iu which the source has a non-zero probability of being detected., The weight is defined as the inverse of the area in which the source has a non-zero probability of being detected.
 Our results are compared in Fig., Our results are compared in Fig.
 8 with those of the ROSAT Deep Survey. (IIasiuger et al. 1998))., 8 with those of the ROSAT Deep Survey (Hasinger et al. \cite{hasinger98}) ).
 We derive our distribution down toc1.2«10.teresbem7 where the surveved area corresponds to S of the total (2& deg?)., We derive our distribution down to $\simeq 1.2 \times 10^{-14} \ergs \cmdue$ where the surveyed area corresponds to $8 \%$ of the total $\simeq 8$ $^{2}$ ).
 The ROSAT Deep Survey extends to fainter fluxes anc it is well fitted by a broken power law. with the break at ~2.10HHCrestom3 (IIasiuger et al. 1998)).," The ROSAT Deep Survey extends to fainter fluxes and it is well fitted by a broken power law, with the break at $\sim 2 \times 10^{-14} \ergs \cmdue$ (Hasinger et al. \cite{hasinger98}) )."
 The BAIW-URI distribution is very siuilar both iu steepness alc in normalization to the ROSAT Deep Survey. but extends to brighter fluxes. a factor of 2 after the break point.," The BMW-HRI distribution is very similar both in steepness and in normalization to the ROSAT Deep Survey, but extends to brighter fluxes, a factor of 2 after the break point."
 Iu order to compare the two distributions. we exclude from the BAIW-TIRT distribution the fainter fluxes ⋖↼∕∖∣∖↓∩⊔-0.σονoTem7: this ⋅≻⋅⋅is why we cannot coustrain⋅ he power law below the break with such few poiuts) aud we compared the DMW-ITRI distribution with the bright wat of the ROSAT Deep Survey.," In order to compare the two distributions, we exclude from the BMW-HRI distribution the fainter fluxes $< 7 \times 10^{-14} \ergs \cmdue$; this is why we cannot constrain the power law below the break with such few points) and we compared the BMW-HRI distribution with the bright part of the ROSAT Deep Survey."
 By mieuus of a maxi ikelihood munimization fit we fud that. assuming a single oower law for the differential cistribution. the best fit for he exponential is given by a=2.75+0.11 with a tormalization of 229.8!d (in units of 10.44).," By means of a maximum likelihood minimization fit we find that, assuming a single power law for the differential distribution, the best fit for the exponential is given by $\alpha = -2.75\,\pm\,0.11$ with a normalization of $229.8^{+69}_{-60}$ (in units of $10^{-14}$ )."
 This value is in very eood aegrecinent with the bright part of the ROSAT Deep Survey fux distribution (a=2.72 and a normalization of 238.1: Hasiuger et al. 1998))., This value is in very good agreement with the bright part of the ROSAT Deep Survey flux distribution $\alpha = -2.72$ and a normalization of 238.1; Hasinger et al. \cite{hasinger98}) ).
 We compared the DNIW-IIRI with the ROSAT source catalogue of pointed observations with the Teh Resolution Imager (ROSIIRICAT/IRXII. ROSAT Team 2001).," We compared the BMW-HRI with the ROSAT source catalogue of pointed observations with the High Resolution Imager (ROSHRICAT/1RXH, ROSAT Team 2001)."
 This catalogue. derived by reprocessing the public IIRI dataset (a otal of 5.393 poiutiues covering 1.910( of the skv) through the SASS. provides aresecond positions aud count rates for 131.902 sources.," This catalogue, derived by reprocessing the public HRI dataset (a total of 5,393 pointings covering $\%$ of the sky) through the SASS, provides arcsecond positions and count rates for 131,902 sources."
" This version includes detections which were classified as false after a visual Inspection (""f detections). multiple detections of the sale source within the same observation (""w detections) aud 331 obvious sources which were not detected bv the SASS and added manually (see Appendix À.2)."," This version includes detections which were classified as false after a visual inspection (“f” detections), multiple detections of the same source within the same observation (“u” detections) and 331 obvious sources which were not detected by the SASS and added manually (see Appendix A.2)."
" After removing ""u and ""f detections. 56.101 entries are left (ROSHRICAT lone version)."," After removing “u” and “f” detections, 56,401 entries are left (ROSHRICAT long version)."
 Additionally. applviug a SN>d vields to 13.152 Heh confidence detections (ROSHRICAT short We compared the BNIW-IIRI catalogue with the ROSIIRICAT. both in its short and its lone version (hereafter ROSURICAT-short aud ROSTRICAT-loug. respectively) by cross-correlating the eutries in the two catalogues.," Additionally, applying a $S/N\,>4$ yields to 13,452 high confidence detections (ROSHRICAT short We compared the BMW-HRI catalogue with the ROSHRICAT, both in its short and its long version (hereafter ROSHRICAT-short and ROSHRICAT-long, respectively) by cross-correlating the entries in the two catalogues."
 The results of these cross-correlatious are μπιτσος]. in this section while a detailed description of specific checks is given in Appendix A. For cousisteucy. we applied to the ROSURICAT catalogues the Sue selection criteria applied iu the compilations ofthe BAIW-IIRI (see section 3).," The results of these cross-correlations are summarized in this section while a detailed description of specific checks is given in Appendix A. For consistency, we applied to the ROSHRICAT catalogues the same selection criteria applied in the compilations of the BMW-HRI (see section 3)."
 Moreover. we filtered out from the ROSATURICAT catalogues the 331 entries which were uot detected bv tlic SASS (uo flux information). plus sone detections with a wrong declination (1 sources for the short version and 61 sources for the long version).," Moreover, we filtered out from the ROSATHRICAT catalogues the 331 entries which were not detected by the SASS (no flux information), plus some detections with a wrong declination (4 sources for the short version and 64 sources for the long version)."
 We remain with 10.708 and 13.252 entries for the ROSIIRICAT-«hort aud long respectively.," We remain with 10,708 and 43,252 entries for the ROSHRICAT-short and long respectively."
 To compute tle cross-correlation radius we fist calculated he positional error corresponding to the 95% of the sources both for 1 DMW-IIRI and for the ROSIIRICAT catalogues., To compute the cross-correlation radius we first calculated the positional error corresponding to the $\%$ of the sources both for the BMW-HRI and for the ROSHRICAT catalogues.
 By ddiug in quadrature the two errors we obtain radii of 8 nd 12 aresec. to be used for the cross-correlations with 16 ROSATURICAT short aud loug. respectively.," By adding in quadrature the two errors we obtain radii of 8 and 12 arcsec, to be used for the cross-correlations with the ROSATHRICAT short and long, respectively."
 As the iuuber of the ROSIIBICAT sources that cross-correlate with each DAI-ITRI sources can be. in several cases. riore iu one. we decided to choose the nearest ROSURICAT source (nini distance approach).," As the number of the ROSHRICAT sources that cross-correlate with each BMW-HRI sources can be, in several cases, more than one, we decided to choose the nearest ROSHRICAT source (minimum distance approach)."
region. or that the optical coustauts we used do not adequately represent the circumstellar materials.,"region, or that the optical constants we used do not adequately represent the circumstellar materials."
 The sources i which we detect the ice enission features are the four stars with the deepest 10-11 silicate absorption. aud heuce presumably the lighest niass-loss rates.," The sources in which we detect the ice emission features are the four stars with the deepest $\mu$ m silicate absorption, and hence presumably the highest mass-loss rates."
 These sane stars also show the 3.1-an absorption baud (see Fie. 2))., These same stars also show the $\mu$ m absorption band (see Fig. \ref{nir}) ).
 OII32.8 was too faint at 3 qun to be detected by the SWS. but the 3.1-;24. ice absorption feature has been detected im ground-based spectra (Roche Aitken 1981)).," OH32.8 was too faint at 3 $\mu$ m to be detected by the SWS, but the $\mu$ m ice absorption feature has been detected in ground-based spectra (Roche Aitken \cite{roche}) )."
 The sources with selt-absorbed silicate cussion features. do not appear to show ice features.," The sources with self-absorbed silicate emission features, do not appear to show ice features."
 OIIIOL9. which shows a relatively shallow silicate absorption. may show a weak 23.1-ju absorption. ut it is hard to discern. because the spectrum is woisy at short wavelengths.," OH104.9, which shows a relatively shallow silicate absorption, may show a weak $\mu$ m absorption, but it is hard to discern, because the spectrum is noisy at short wavelengths."
 The 6.0-sau baud of water ice is siguificautlv weaker han the 3.1421. baud (see c.g. Moore 19993)., The $\mu$ m band of water ice is significantly weaker than the $\mu$ m band (see e.g. Moore \cite{moore}) ).
 The spectra 6 Lour most heavilv-obscured sources. OIT32.5. APCL 5379 and OII26.5. show a weak depression around 6 sau. but his waveleneth reeion is verv rich in gaseous TO lines. nakine it difficult to ascribe the observed feature to ice sorption.," The spectra of our most heavily-obscured sources, OH32.8, AFGL 5379 and OH26.5, show a weak depression around 6 $\mu$ m, but this wavelength region is very rich in gaseous $_2$ O lines, making it difficult to ascribe the observed feature to ice absorption."
 Ice formation requires cool temperatures and sufücieut shiclding from stellar and interstellar radiation (e.g. Whittet et al. L988))., Ice formation requires cool temperatures and sufficient shielding from stellar and interstellar radiation (e.g. Whittet et al. \cite{whittet}) ).
 The high densitics iu the (ecucral) outflow that accompany large miass-loss rates may provide he required shiclding., The high densities in the (general) outflow that accompany large mass-loss rates may provide the required shielding.
" Alternatively. cuhanuced densities could be provided by the formation of a circmuustellar disk iu the superwiud phase. or by inhomogeneous mass oss. stich as is apparent in studies of HI5O and ΟΠ mascr chuups (οιο, Richards et al. 1999))."," Alternatively, enhanced densities could be provided by the formation of a circumstellar disk in the superwind phase, or by inhomogeneous mass loss, such as is apparent in studies of $_2$ O and OH maser clumps (e.g. Richards et al. \cite{richards}) )."
 As discussed by Ounout et al. (1990)).," As discussed by Omont et al. \cite{omont}) ),"
 the presence of the 63-4211 band requires that he water ice is at least partially crystalline. iuplviug that he ice remained relatively wari (2100 I) for long enough o allow crystalline reorganization to take place.," the presence of the $\mu$ m band requires that the water ice is at least partially crystalline, implying that the ice remained relatively warm $\ga$ 100 K) for long enough to allow crystalline reorganization to take place."
 Optical depths and column deusities for the detected 3.1-;nn features are given in Table 3.., Optical depths and column densities for the detected $\mu$ m features are given in Table \ref{icetab}. .
 Meyer et al. (1998)), Meyer et al. \cite{meyer}) )
 iive proposed that the ice coluun density correlates otter with the ratio of mass-loss rate to LDunünositv (AL/L) than with 37 alone., have proposed that the ice column density correlates better with the ratio of mass-loss rate to luminosity $\dot{M}/L$ ) than with $\dot{M}$ alone.
 Adypting reasonable estimates (based ou values in the literature) for these parameters. our results support the relation between ice coluun density and logML proposed by Alever et al (see heir Fie.," Adopting reasonable estimates (based on values in the literature) for these parameters, our results support the relation between ice column density and $\log{\dot{M}/L}$ proposed by Meyer et al (see their Fig."
 3)., 3).
" ILowever. eiven the uncertainties in both xuwanmeters, aud that the Iuminositv changes siguificautlv with the variability phase. the relationship should be reated with some caution."," However, given the uncertainties in both parameters, and that the luminosity changes significantly with the variability phase, the relationship should be treated with some caution."
 OU32.8 shows the μι ice baud. and au Έτ μι absorption feature in the wing of the silicate absorption ‘cature (Roche Aitken 198D) which was attributed to he libration mode of water ice.," OH32.8 shows the $\mu$ m ice band, and an $\mu$ m absorption feature in the wing of the silicate absorption feature (Roche Aitken \cite{roche}) ) which was attributed to the libration mode of water ice."
 Justtanont Ticleus (19021) were able to model ground-based aud IRAS observations ofthis source using silicate erains with water-ice nautles. which give auch broader 10-7221 absorption feature than do bare silicate eraius.," Justtanont Tielens \cite{justtiel}) ) were able to model ground-based and IRAS observations of this source using silicate grains with water-ice mantles, which give a much broader $\mu$ m absorption feature than do bare silicate grains."
 The broad 11-420 feature is clearly seen in the five sources withstrong 10-j00 absorption (Fig. 1))., The broad $\mu$ m feature is clearly seen in the five sources with strong $\mu$ m absorption (Fig. \ref{fig1}) ).
 It appears stronely in OII26.5. OIIIOL.9.. OITI27.5 and OID32.5. and as an inflection Lear 11.5 gon in AFGL 5379.," It appears strongly in OH26.5, OH104.9, OH127.8 and OH32.8, and as an inflection near 11.5 $\mu$ m in AFGL 5379."
 The coutribution of this feature to the overall 10-11 absorption profile therefore docs not appear to correlate fully with the presence of the other water ice bands: AFGL 5379 shows strong far-IR ice cussion aud jaa absorption. but only weak L1-jan absorption. while OULOL9 shows strong μαι absorption but has weak or absent f£u-IR aud 3.1-pau features.," The contribution of this feature to the overall $\mu$ m absorption profile therefore does not appear to correlate fully with the presence of the other water ice bands: AFGL 5379 shows strong far-IR ice emission and $\mu$ m absorption, but only weak $\mu$ m absorption, while OH104.9 shows strong $\mu$ m absorption but has weak or absent far-IR and $\mu$ m features."
 Smith UWerman (1990)) found an 11-12 absorption feature in the spectrum of another OIT/IR star. OITIL38.0|7.3. which does not show any ice absorption at 3.1 on. Since the 3.1-42n stretching mode is intrinsically stronger than the libration imd0dde. Suuth Uerman concluded. that the Li-jnu feature observed towards OIIL38.0 is not produced by water icc. iud suggestedOO that it is due to partialh-crvstalliue. silicates.," Smith Herman \cite{smith}) ) found an $\mu$ m absorption feature in the spectrum of another OH/IR star, OH138.0+7.3, which does not show any ice absorption at 3.1 $\mu$ m. Since the $\mu$ m stretching mode is intrinsically stronger than the libration mode, Smith Herman concluded that the $\mu$ m feature observed towards OH138.0 is not produced by water ice, and suggested that it is due to partially-crystalline silicates."
 Another possibility is that spectra like that of OIII38.0 are the absorption couuterpar of the Little-\Tarenin Little (1990)) Sil]| or “Broad” emission features. which show au emission componueut at 11 gan ou the wing of the silicate feature.," Another possibility is that spectra like that of OH138.0 are the absorption counterpart of the Little-Marenin Little \cite{lml}) ) `Sil++' or `Broad' emission features, which show an emission component at $\sim$ 11 $\mu$ m on the wing of the silicate feature."
 These features have been ascribed to crystalline silicates or amorphous alumina grains (see e.g. Sloan Price 1998))., These features have been ascribed to crystalline silicates or amorphous alumina grains (see e.g. Sloan Price \cite{sloan}) ).
" Clearly. full raciative-trauster modelling would be useful to determine whether ice mautles can indeed explain the range of μι features seen. or whether other grain components are necessary,"," Clearly, full radiative-transfer modelling would be useful to determine whether ice mantles can indeed explain the range of $\mu$ m features seen, or whether other grain components are necessary."
 The presence of strong water ice features in our spectra indicates that a substantial amount of the TeO in the circunistellar envelopes may be depleted into the solid phase., The presence of strong water ice features in our spectra indicates that a substantial amount of the $_2$ O in the circumstellar envelopes may be depleted into the solid phase.
 This would decrease the amount of gas-phase TL.0 (ancl shotodissociated OIL) iu the outer regions of the ciretuustellar cuvelope which cau be detected by maser aud thermal cussion. Water maser lues are observed to be relatively weaker in OII/IR stars than in objects with lower mass-loss rates (e.g. Likkel 19893).," This would decrease the amount of gas-phase $_2$ O (and photodissociated OH) in the outer regions of the circumstellar envelope which can be detected by maser and thermal emission, Water maser lines are observed to be relatively weaker in OH/IR stars than in objects with lower mass-loss rates (e.g. Likkel \cite{likkel}) )."
 Collisional quenching due to the ligh deusitics iu the immer parts of the outflow is thought to suppress the maser action: our results indicate that depletion iuto the solid. (1c0) phase may also play a vole., Collisional quenching due to the high densities in the inner parts of the outflow is thought to suppress the maser action; our results indicate that depletion into the solid (ice) phase may also play a role.
 CO ice shows features near L7 nu (e.g. Cliar et al. 19953):, CO ice shows features near 4.7 $\mu$ m (e.g. Chiar et al. \cite{chiar}) ):
 these are not seen iu our spectra. but a broad absorption band around 13 san. due to gas-pliase CO is seen.," these are not seen in our spectra, but a broad absorption band around 4.3 $\mu$ m, due to gas-phase CO is seen."
 This baud is significantly broader than the 127-24 CO» ice absorption feature seen im molecularclouds (o.8. de Ciara et al. 1996b))., This band is significantly broader than the $\mu$ m $_2$ ice absorption feature seen in molecularclouds (e.g. de Graauw et al. \cite{degraauwco2}) ).
 We see no evideuce of CO» ice at L27 pau. CO» ice shows another strong feature at 15 fna: our spectra show some structure near this wavelength (Fig. 6)).," We see no evidence of $_2$ ice at 4.27 $\mu$ m. $_2$ ice shows another strong feature at 15 $\mu$ m; our spectra show some structure near this wavelength (Fig. \ref{ovcrystal}) ),"
 but this may be au artefact of the imstiriuneut or data-reduction process., but this may be an artefact of the instrument or data-reduction process.
content. has the corTOC magnitude. although the detailed shaoe has uo reason to be exact a priori,"content, has the correct magnitude, although the detailed shape has no reason to be exact a priori."
 Iu particular. at low masses. 6>-10. which represent a πια fraction of the total matter density field aud «lo not significantly contribute to the iiteeral (27)). the wormalization (27)) becmues lareely irclevaut (since large changes of bCAL) would uot significaitlv chanee the oveyall uormalization) so that there is no τίson a priori to trst our model.," In particular, at low masses, $\sigma>10$, which represent a small fraction of the total matter density field and do not significantly contribute to the integral \ref{b-fnu}) ), the normalization \ref{b-fnu}) ) becomes largely irrelevant (since large changes of $b(M)$ would not significantly change the overall normalization) so that there is no reason a priori to trust our model."
 Thus. it may happen tha at very low nasses the bias goes to zero. for mstance as a power law over M.," Thus, it may happen that at very low masses the bias goes to zero, for instance as a power law over $M$."
 However. this is bevonud the reach o current nunerica simulations and it is not a serious pracical problems. for t1ο sale reason that this only concerns a small fractio Lot the matter coutenut aud of the halo population.," However, this is beyond the reach of current numerical simulations and it is not a serious practical problem, for the same reason that this only concerns a small fraction of the matter content and of the halo population."
" As is well known. the deperdence ou redshift. at fixed ofAL). is quite weak over fie range Oxlox2.5,"," As is well known, the dependence on redshift, at fixed $\sigma(M)$, is quite weak over the range $0\leq z \leq 2.5$."
 There appears to be a slight exowth of the bias at lareer redshift. iu the regine of rare halos (a(AL)« 0.5).," There appears to be a slight growth of the bias at larger redshift, in the regime of rare halos $\sigma(M)<0.5$ )."
 This is most clearly seen by the comparison with the dashed line associated with the fit from ?.. whicli ds independent of > and is ideutical in the three panels.," This is most clearly seen by the comparison with the dashed line associated with the fit from \citet{SMT2001}, which is independent of $z$ and is identical in the three panels."
 This znall growth is also reproduced by otY Luoel (26)). as shown bv the solid line.," This small growth is also reproduced by our model \ref{bM-def}) ), as shown by the solid line."
 This confirms he validitv of this approach. aud more generally of such models that follow ?..," This confirms the validity of this approach, and more generally of such models that follow \citet{Kaiser1984}."
" Towever. for practical purposes it is probabY sufficieut to neglect the dependence ou redshift i this ra1σο,"," However, for practical purposes it is probably sufficient to neglect the dependence on redshift in this range."
" It is interesting fo 1te that the bias obtaimed from Eq.(8) of ? behaves a larec asses as bo~ad,--ση. with a parameter 0cTOUT obtained from fits to the halo miss function (tluxmel the| peak-backeround split arguinent). whereas we have noiced in Sect."," It is interesting to note that the bias obtained from Eq.(8) of \citet{SMT2001}
 behaves at large masses as $b \sim a \delta_c/\sigma_q^2$, with a parameter $a\simeq 0.707$ obtained from fits to the halo mass function (through the peak-background split argument), whereas we have noticed in Sect."
" 2.3 that (21) yields b—(612/07(0,ubσα.)"," \ref{Normalization} that \ref{b2-def}) ) yields $b \sim (\delta_{L*}/\sigma_q^2) (\sigma_{q,q}(s)/\sigma_{0,0}(x))$."
 In order to explain whl bohn predictions are rather close (especially at z0 in FieB. 1)), In order to explain why both predictions are rather close (especially at $z=0$ in Fig. \ref{figbiasM_D200}) )
" despite these different forms. aud wihout introdicing such a parameter & in Eq.(21)). we have also plotted the curves obtained by setting 5=u (i.c. neelecting ilo motions) or ór=0,. with the usual value ó,=1.686."," despite these different forms, and without introducing such a parameter $a$ in \ref{b2-def}) ), we have also plotted the curves obtained by setting $s=x$ (i.e. neglecting halo motions) or $\deltaLs=\delta_c$, with the usual value $\delta_c=1.686$."
" We can see that the change frou 8, to dp. makes amost no difference for the halo bias (for é.= 200). while taking into account halo motions leads"," We can see that the change from $\delta_c$ to $\deltaLs$ makes almost no difference for the halo bias (for $\deltas=200$ ), while taking into account halo motions leads"
"cluster lass estimates can in turn provide tightcr constraints on cosmological parameters. aud therefore it is of kev inportauce to reduce the errors iu cluster mass estimates,","cluster mass estimates can in turn provide tighter constraints on cosmological parameters, and therefore it is of key importance to reduce the errors in cluster mass estimates."
 For example. the primary source of error in clister-sed deteriunuations of oy is the error iu the iass-cluperature relation for relaxed clusters (e.g. 77?77)].," For example, the primary source of error in cluster-based determinations of $\sigma_8$ is the error in the mass-temperature relation for relaxed clusters (e.g., \citealt{PI03.1,HE04.2,VO05.1}) )."
 Receut studies show that an παν indepeudent mass approach such as eravitational lensing provides a unique ool to calibrate the mass - temperature relation (6.9.. ΑΟ. H," Recent studies show that an X-ray independent mass approach such as gravitational lensing provides a unique tool to calibrate the mass - temperature relation (e.g., \citealt{SM05.1, MA08.1, ZH08.1}) )."
ere. we use strong eravitational lensing mass ueasurecleuts of a sample of cight strong lensing clusters at 0.5«2<0.8 to accurately mcasure the galaxy cluster uass-teniperature relation.," Here, we use strong gravitational lensing mass measurements of a sample of eight strong lensing clusters at $0.3 < z 
< 0.8$ to accurately measure the galaxy cluster mass-temperature relation."
" We also include the effects of cluster concentrations in an effort to further reduce the scatter in the cluster mass-temiperature relation. which would ultimately enable tighter coustraiuts on σς,"," We also include the effects of cluster concentrations in an effort to further reduce the scatter in the cluster mass-temperature relation, which would ultimately enable tighter constraints on $\sigma_8$."
 Iu addition to the correlations that exist between cluster properties. some observational properties of brightest cluster ealaxies (BCCs) also scale with properties of the host clusters.," In addition to the correlations that exist between cluster properties, some observational properties of brightest cluster galaxies (BCGs) also scale with properties of the host clusters."
 Whereas scalings between cluster properties are sensitive to cosmological paralcters. scalings between BCCs and their host clusters provide constraints on BC'G formation aud the evolution of clusters.," Whereas scalings between cluster properties are sensitive to cosmological parameters, scalings between BCGs and their host clusters provide constraints on BCG formation and the evolution of clusters."
 BCGs are a unique population: they are the most nassive and bhunduous galaxies m the Universe., BCGs are a unique population: they are the most massive and luminous galaxies in the Universe.
 They are typically located near the ceuters of clusters. which sugeests that a BCCos formation history is intricately iuked to the formation of the cluster itself.," They are typically located near the centers of clusters, which suggests that a BCG's formation history is intricately linked to the formation of the cluster itself."
 However. the ormation of BCCs is still poorly understood.," However, the formation of BCGs is still poorly understood."
 BCCs may form after their lost clusters assemble iu oue of two wavs., BCGs may form after their host clusters assemble in one of two ways.
 First.a BCC may be the first galaxy to v0 drageed iu by dvuaimical friction to the center of the dark matter halo destined to become a cluster. where it then erows through galactic caunibalizii by merging with subsequent galaxies that fall to the center (e.e.. ?7)).," First, a BCG may be the first galaxy to be dragged in by dynamical friction to the center of the dark matter halo destined to become a cluster, where it then grows through galactic cannibalism by merging with subsequent galaxies that fall to the center (e.g., \citealt{OS75.1,HA78.1}) )."
 However. this scenario typically requires more than a IIubble time to form à BCC because unich of the mass of the παπας galaxy is tidally stripped. which reduces the dynamical friction effect and slows the imfall (?)..," However, this scenario typically requires more than a Hubble time to form a BCG because much of the mass of the infalling galaxy is tidally stripped, which reduces the dynamical friction effect and slows the infall \citep{ME85.1}."
 BCC formation may also occur after cluster formation if the host clusters central cooling flow forms stars at the cluster center aud those stars build the BCC (?).., BCG formation may also occur after cluster formation if the host cluster's central cooling flow forms stars at the cluster center and those stars build the BCG \citep{CO77.1}.
 There are several instances of ongoing or recent star formation in BCGs that occupy cooling-fow clusters (c.g. 2?77)). but it is unclear whether the star formation is fueled by the cooling flows or by cold gas brought in through receut ealaxy mergers (?7)..," There are several instances of ongoing or recent star formation in BCGs that occupy cooling-flow clusters (e.g., \citealt{CA98.1,CR99.1, HI05.1,MC06.1}) ), but it is unclear whether the star formation is fueled by the cooling flows or by cold gas brought in through recent galaxy mergers \citep{BI08.2}."
 Iu another scenario. BCGs müght form iu coucert with them host custers.," In another scenario, BCGs might form in concert with their host clusters."
" A BCC αν begin with several galaxies miereiug together m a group to form a dluge galaxw. aud then when groups icerec as luerarchical structire formation continues. this large ealaxy eventually beconmnies a BCC in a massive cluster (ee. 2224), "," A BCG may begin with several galaxies merging together in a group to form a large galaxy, and then when groups merge as hierarchical structure formation continues, this large galaxy eventually becomes a BCG in a massive cluster (e.g., \citealt{ME85.1, DU98.1, BO06.1}) )."
Iere. we examιο. the. correlation between BCC ΠΠ and chster inass in cight strong leusine clusters at 0.3κ«08.," Here, we examine the correlation between BCG luminosity and cluster mass in eight strong lensing clusters at $0.3 < z 
<0.8$."
 This will enable coustraiuts not oulv on BCC aid cluster formation in geucral. but also on how the DC in strong lensing clusters may have formed and evolved differently than DCCs in the general cluster population.," This will enable constraints not only on BCG and cluster formation in general, but also on how the BCGs in strong lensing clusters may have formed and evolved differently than BCGs in the general cluster population."
 The rest of this paper is organized as follows., The rest of this paper is organized as follows.
 Iu Section 2 we describe the selection of our cluster saluple. aud Section 3. gives the masses. dynamical states. auc N-vav temperatures for these clusters.," In Section \ref{sample} we describe the selection of our cluster sample, and Section \ref{properties} gives the masses, dynamical states, and X-ray temperatures for these clusters."
 Iu Section | we find the AJT relation for the relaxed clusters in our sample and show how the inclusion of cluster concentrations both significantly reduces the scatter in the AYT relation aud lifts the restriction on cluster dyvuanüca state., In Section \ref{mtrelation} we find the $M-T$ relation for the relaxed clusters in our sample and show how the inclusion of cluster concentrations both significantly reduces the scatter in the $M-T$ relation and lifts the restriction on cluster dynamical state.
 Iu. Section 55o we ideutity the BCGs iu our sample and measure their Inninosities., In Section \ref{bcgprop} we identify the BCGs in our sample and measure their luminosities.
 We use these luninositics in Section 6 to measure the correlation between BCC Iuuinositv aud cluster mass. and we find preliminary evidence that stroug lensing clusters Ίαν lave more active merge histories than the general cluster population.," We use these luminosities in Section \ref{lm} to measure the correlation between BCG luminosity and cluster mass, and we find preliminary evidence that strong lensing clusters may have more active merging histories than the general cluster population."
 Section 7 preseuts our conclusions., Section \ref{conclude} presents our conclusions.
" Throughout this paper. we adopt a spatially flat cosmological model dominated by cold dark matter and a cosmological coustant (0,4,=0.3. O4=07. h—U.)."," Throughout this paper, we adopt a spatially flat cosmological model dominated by cold dark matter and a cosmological constant $\Omega_{\rm m}=0.3$, $\Omega_\Lambda=0.7$, $h=0.7$ )."
 We base our sample on 10 well-kuown strong lensing clusters analyzed in ?.., We base our sample on 10 well-known strong lensing clusters analyzed in \cite{CO06.1}.
 All 10 clusters haveTelescope (LIST) inaging. which make possible the mass deteruiuations and photometry nieasurenmenuts central to this paper.," All 10 clusters have ) imaging, which make possible the mass determinations and photometry measurements central to this paper."
 However. there are no published arc redshitts for two of the clusters. Cl | 1609 and Cl 0051. 27. which limits the strong lensing determination of their cluster niasses to the unknown factor Dl/Di. the ratio of the angular diameter distances to the source and between the leus aud source.," However, there are no published arc redshifts for two of the clusters, Cl $+$ 1609 and Cl $-$ 27, which limits the strong lensing determination of their cluster masses to the unknown factor $D_{\rm s}/D_{\rm ls}$, the ratio of the angular diameter distances to the source and between the lens and source."
 Consequently we remove these two clusters. and our sample consists of the remnainiue cielt clusters atf 0.3«2<0.8: ClG 2211 02. Abell 370. 3C 220.1. MS 2353. NIS 0151.6. 0305. MS | 6625. C] | 17123. aud ZwCI 002111652.," Consequently we remove these two clusters, and our sample consists of the remaining eight clusters at $0.3 < z < 0.8$: ClG $-$ 02, Abell 370, 3C 220.1, MS $-$ 2353, MS $-$ 0305, MS $+$ 6625, Cl $+$ 4713, and ZwCl $+$ 1652."
 Strong correlatious are found between cluster observables. and the resultant scaling relations clearly eucapsulate key information about cosmological parameters and the assembly history— of clusters.," Strong correlations are found between cluster observables, and the resultant scaling relations clearly encapsulate key information about cosmological parameters and the assembly history of clusters."
 Cluster masses are a component of may cluster scaling relations. and we measure strong lensing masses for our siuuple of clusters and compare these to mass estimates from the distributions of cluster N-arav gas.," Cluster masses are a component of many cluster scaling relations, and we measure strong lensing masses for our sample of clusters and compare these to mass estimates from the distributions of cluster X-ray gas."
 Dased on these comparisous and other observable properties of the cluster. we determine the οπιασα] state of each cluster as relaxed or uurelaxed.," Based on these comparisons and other observable properties of the cluster, we determine the dynamical state of each cluster as relaxed or unrelaxed."
 We also present cluster N-ray temperatures. which are another couponent of cluster scaling relations.," We also present cluster X-ray temperatures, which are another component of cluster scaling relations."
 We inodel each cluster mass distributiou with an (Jliptieal Naviuro-Freuk-White (NEW: 773) dark matter ido centered on the BCC. using the best-fit NEW xuanieters found by ον," We model each cluster mass distribution with an elliptical Navarro-Frenk-White (NFW; \citealt{NA96.1, NA97.1}) ) dark matter halo centered on the BCG, using the best-fit NFW parameters found by \cite{CO06.1}."
 Stroug leusine arcs with neasured redshifts observed iu a cluster coustrai its nass distribution. aud ? use the arcs to characterize vost-fit ΣΕΝ ellipsoids to cach cluster.," Strong lensing arcs with measured redshifts observed in a cluster constrain its mass distribution, and \cite{CO06.1} use the arcs to characterize best-fit NFW ellipsoids to each cluster."
 With the NFAW 6lark matter halos completely defined in this wav. we cau 6letermune auv cluster radius ray as the radius at which he density of the halo is A times the critical density at he cluster redshift.," With the NFW dark matter halos completely defined in this way, we can determine any cluster radius $r_{\Delta}$ as the radius at which the density of the halo is $\Delta$ times the critical density at the cluster redshift."
 Lack of information about the clusters threc- shapes prevents us frou calculating— their, Lack of information about the clusters' three-dimensional shapes prevents us from calculating their
All the svinbols are standard.,All the symbols are standard.
" We orient the coordinate svstem with é. parallel to OQ». 6, pointing radially. and δι pointing along the azimuthal background flow."," We orient the coordinate system with $\vect{\hat e}_z$ parallel to $\vect{\Omega}_F$, $\vect{\hat e}_x$ pointing radially, and $\vect{\hat e}_y$ pointing along the azimuthal background flow."
 We shall treat a small domain compared to £j. ancl clisregard the curvature terms in equations (2))-(5)).," We shall treat a small domain compared to $R_0$, and disregard the curvature terms in equations \ref{hd_eq1}) \ref{hd_eq4}) )."
" In addition to gas with density p,. the flow contains a component of solids (dust + ice)."," In addition to gas with density $\rho_g$, the flow contains a component of solids (dust + ice)."
" We assstune that the gas and solids are strongly coupled. so v;=v,v."," We asssume that the gas and solids are strongly coupled, so $\vect{v}_d = \vect{v}_g = \vect{v}$."
" In the strongly coupled limit. the dust component of the mixture adds inertia to the flow so that p—p,+pa in equations (2)) and (3)) but the solids do not contribute to the pressure (P=c?p,. where ος ls the isothermal sound speed) aud energy density in equations (4)) aud (5))."," In the strongly coupled limit, the dust component of the mixture adds inertia to the flow so that $\rho = \rho_g + \rho_d$ in equations \ref{hd_eq1}) ) and \ref{hd_eq2}) ) but the solids do not contribute to the pressure $P = c_s^2 \rho_g$, where $c_s$ is the isothermal sound speed) and energy density in equations \ref{hd_eq3}) ) and \ref{hd_eq4}) )."
 The dust component also separately obevs a continuity. equation For an axisvnunetric ecuilibrium. (he x and z components of the momentum equation read Ilere. Odo/(ORvQ7.dyfg. where On ls ihe keljxlerian orbital frequency.I and we approximatePl OD/O2zxOF:MUN ," The dust component also separately obeys a continuity equation For an axisymmetric equilibrium, the $x$ and $z$ components of the momentum equation read Here, $\partial \Phi / \partial R \approx \Omega_K^2 R$, where $\Omega_K$ is the keplerian orbital frequency, and we approximate $\partial \Phi / \partial z \approx \Omega_K^2 z$."
From equation (7)). the orbital velocity ofthe flow in equilibrium depends on (he dust abundance.," From equation \ref{momr_eq}) ), the orbital velocity ofthe flow in equilibrium depends on the dust abundance."
 Ii order to further specify our coordinate svstem. let us define O7 as (he orbital frequency of dust-Iree gas with a relerence value of density al 2=0 of pj.," In order to further specify our coordinate system, let us define $\Omega_F$ as the inertial-frame orbital frequency of dust-free gas with a reference value of density at $z=0$ of $\rho_{g0}$ ."
 With, With
Aloran. Halpern & Lelfancl (1996). after careful spectroscopy of a sample based. on the cross-correlation of the LIGAS SC and. All Sky Survey. reported the cliscovery of an “anomalous” class of objects.,"Moran, Halpern $\&$ Helfand (1996), after careful spectroscopy of a sample based on the cross-correlation of the IRAS PSC and All Sky Survey, reported the discovery of an “anomalous” class of objects."
 The optical spectra of hese sources are dominated by the features of starburst galaxies. based on the emission line diagnostic cliagranis (Veilleux & Osterbrock LOST). vet their X-ray luminosities are typical of Sevfert 2 galaxies.," The optical spectra of these sources are dominated by the features of starburst galaxies, based on the emission line diagnostic diagrams (Veilleux $\&$ Osterbrock 1987), yet their X-ray luminosities are typical of Seyfert 2 galaxies."
" Close examination of heir optical spectra reveals some weak Sevlert-like features: ΟΙ) significantly broader than all other narrow lines in the spectrum. and in some cases à weak broad. HL, component.", Close examination of their optical spectra reveals some weak Seyfert-like features: [OIII] significantly broader than all other narrow lines in the spectrum and in some cases a weak broad $_\alpha$ component.
" The authors designated. these objects ""starburst/Sevfert composite"" galaxies and presented. them as a new class of X-ray luminous source.", The authors designated these objects “starburst/Seyfert composite” galaxies and presented them as a new class of X-ray luminous source.
" Simülar ""composite"" objects. have also been noticed by Veron et al. ("," Similar ""composite"" objects have also been noticed by Veron et al. ("
1997).,1997).
 Indeed. they oesented observations of 15 objects with transition spectra ic showing the simultaneous presence of a strong star-orming component and an active nucleus and they showed hat fall either on the starburst region or on the borderlines »etween the dillerent classes.," Indeed, they presented observations of 15 objects with transition spectra ie showing the simultaneous presence of a strong star-forming component and an active nucleus and they showed that fall either on the starburst region or on the borderlines between the different classes."
 Hereafter. we will refer to these objects as composite galaxies and we will distinguish them. rom the Sv2/Starburst galaxies that show emission from roth components at all wavelengths.," Hereafter, we will refer to these objects as composite galaxies and we will distinguish them from the Sy2/Starburst galaxies that show emission from both components at all wavelengths."
 The composite galaxies bear close resemblance to he narrow-line X-ray galaxies (NLACGs) detected in large numbers in deep surveys (eg Bovle 1995. ΟΠπας 1996).," The composite galaxies bear close resemblance to the narrow-line X-ray galaxies (NLXGs) detected in large numbers in deep surveys (eg Boyle 1995, Griffiths 1996)."
 These NLNCGs again have spectra composite of Sevfert and starburst galaxies. (Bovle 1995) with luminosities Loqos~1077ores-, These NLXGs again have spectra composite of Seyfert and starburst galaxies (Boyle 1995) with luminosities $_{2-10 keV} \sim 10^{42-43}$.
 Unfortunately the faint [uxes of these NLXCGs do not allow their detailed study in either optical or X-ray wavelengths., Unfortunately the faint fluxes of these NLXGs do not allow their detailed study in either optical or X-ray wavelengths.
" Although it is unclear whether these nearby. ""composites? are the same class of objects as those found in deep Ποια NUNGs. their high luminosities need to be explained."," Although it is unclear whether these nearby “composites” are the same class of objects as those found in deep field NLXGs, their high luminosities need to be explained."
 It is unclear how their intense X-ray emission can be reconciled with weak or absent Sevfert characteristics., It is unclear how their intense X-ray emission can be reconciled with weak or absent Seyfert characteristics.
 Only a few composite galaxies have been studied so far in X-, Only a few composite galaxies have been studied so far in X-rays.
" Specifically. LX8S00317-2142 (Georgantopoulos 2000) jw been observed with and is the most. [uminous object (L,=~1OMeres lin the 0.1-2 keV. band) in the Aloran (1996) sample."," Specifically, IRAS00317-2142 (Georgantopoulos 2000) has been observed with and is the most luminous object $_x=\sim10^{43}$ in the 0.1-2 keV band) in the Moran (1996) sample."
 The spectrum is represented wea power-law with E—1.76 and there is no evidence for absorption above the CGalactic value., The spectrum is represented by a power-law with $\Gamma \sim 1.76$ and there is no evidence for absorption above the Galactic value.
 Strong variability in he 1-2 keV band (by. a factor of three) is detected between he and observations., Strong variability in the 1-2 keV band (by a factor of three) is detected between the and observations.
 These characteristics indicate an AGN origin for the X-ray emission., These characteristics indicate an AGN origin for the X-ray emission.
" However no iron line is detected and the 90 per cent upper limit on the equivalent width is 0.9 keV. Phe ratio faxο ~ 2-5 rule out the Compton thick interpretation for 11,N8500317-2142.", However no iron line is detected and the 90 per cent upper limit on the equivalent width is 0.9 keV. The ratio $f_{HX}/f_{[OIII]}$ $\sim$ 2.5 rule out the Compton thick interpretation for IRAS00317-2142.
 Llowever. the precise nature of this object and the relative," However, the precise nature of this object and the relative"
the effects of chemical composition and finite entropy ancl derive slightly more complex relations than (1.. 2)). in particular an exponent closer to 4.13 [or me. in (2)).,"the effects of chemical composition and finite entropy and derive slightly more complex relations than \ref{mp}, , \ref{mdot}) ), in particular an exponent closer to 4.13 for $m_2$ in \ref{mdot}) )."
 Hlowever their Fig.l shows that the deviations are small enough (hat the polovtropic approximation is adequate for the purposes of this paper. particularly for larger values of the white clwarl nass (han considered by Bildsten Delove.," However their Fig.1 shows that the deviations are small enough that the poloytropic approximation is adequate for the purposes of this paper, particularly for larger values of the white dwarf mass than considered by Bildsten Deloye."
 The important result here is (hat the mass (ransler rate could have been much hieher in (he past. when AM» was lareer.," The important result here is that the mass transfer rate could have been much higher in the past, when $M_2$ was larger."
 The initial white dwarl mass in à UCXD is set bv its prior evolution., The initial white dwarf mass in a UCXB is set by its prior evolution.
 UCABs presumably result. from some kind of common envelope evolution ollowing the dvnanmical capture by the neutron star primary of an evolved companion star., UCXBs presumably result from some kind of common envelope evolution following the dynamical capture by the neutron star primary of an evolved companion star.
 The degenerate core mass of the companion can range from x0.1—0.4M. for helium. and up to 20.6M. for carbon/oxvgen. depending sensitivelv on how [ar the companion has evolved at the epoch of capture.," The degenerate core mass of the companion can range from $\simeq
0.1 - 0.4\msun$ for helium, and up to $\simeq 0.6\msun$ for carbon/oxygen, depending sensitively on how far the companion has evolved at the epoch of capture."
 It is clear that mass transfer rates well above the Eddington value are easily possible in UCXDs., It is clear that mass transfer rates well above the Eddington value are easily possible in UCXBs.
 Note (hat Liga is (vice the usual value since we expect hydrogenpoor accretion here. i.e. This implies an Exldington accretion rate Compact objects accreting above their Edcdington rates probably appear as ultraluminous Xorav sources (ULLXNs). and it is now generally accepted thal a large [fraction of ULXs are of (his (vpe.," Note that $\le$ is twice the usual value since we expect hydrogen–poor accretion here, i.e. This implies an Eddington accretion rate Compact objects accreting above their Eddington rates probably appear as ultraluminous X–ray sources (ULXs), and it is now generally accepted that a large fraction of ULXs are of this type."
 Disc accretion in this regime was first described by Shakura Sunvaev (1973)., Disc accretion in this regime was first described by Shakura Sunyaev (1973).
" In their picture. radiation pressure becomes important at the spherization radius Haa0ZR.4. where im ds the local accretion rate in units of the Eddington value. and R=2CAL,/e7 is the Schwarzschild radius of the aceretor."," In their picture, radiation pressure becomes important at the spherization radius $R_{\rm sph} \simeq 27\dot m R_s/4$, where $\dot
m$ is the local accretion rate in units of the Eddington value, and $R_s = 2GM_1/c^2$ is the Schwarzschild radius of the accretor."
 Shakira Sunvaev explicitly considered only black hole accretors. but their picture also applies to other accretors provided that ris sufficiently large to ensure Zhi> accretor radius (this always holds lor neutron stars with mi>l1 [or example).," Shakura Sunyaev explicitly considered only black hole accretors, but their picture also applies to other accretors provided that $\dot m$ is sufficiently large to ensure $R_{\rm sph} >$ accretor radius (this always holds for neutron stars with $\dot m >1$ for example)."
" Inside 72,5 the disc remains close to the local radiation pressure limit and blows gas away so that the accretion rate decreases with disc radius aV. MUR)©MUSRon)£MianGR/Rs)."," Inside $R_{\rm sph}$ the disc remains close to the local radiation pressure limit and blows gas away so that the accretion rate decreases with disc radius as $\dot M(R) \simeq \dot M(R/R_{\rm sph})
\simeq \me(R/R_s)$."
 The dise wind has the local escape velocity at each radius. so mass Conservation shows that the wind is dense near 7/54 and tenuous near thT inner disc edge.," The disc wind has the local escape velocity at each radius, so mass conservation shows that the wind is dense near $R_{\rm sph}$ and tenuous near the inner disc edge."
 The centrifugal barrier along the dise axis creates a vacuum funnel throng[un which the Iuminositv.escapes., The centrifugal barrier along the disc axis creates a vacuum funnel through which the luminosityescapes.
"In this paper we proposed a novel approach to the design of follow-up observations of low-cadence photometric surveys, in a way that will maximize the chances to detect planetary transits.","In this paper we proposed a novel approach to the design of follow-up observations of low-cadence photometric surveys, in a way that will maximize the chances to detect planetary transits."
" Examples of such surveys areHipparcos,,ASAS,, and as successor."," Examples of such surveys are, and as successor."
" The strategy may also be beneficial for the Large Synoptic Survey Telescope (Jurié&Ivezié2011),, and for Pan-STARRS ground-based survey, especially for directing follow-up observations of hot Jupiters transiting M-dwarf stars in the Medium Deep survey (Dupuy&Liu2009;Fordetal.2008).."," The strategy may also be beneficial for the Large Synoptic Survey Telescope \citep{2011EAS....45..281J}, and for Pan-STARRS ground-based survey, especially for directing follow-up observations of hot Jupiters transiting M-dwarf stars in the Medium Deep survey \citep[][]{2009ApJ...704.1519D, 2008AIPC.1082..275F}."
 We tested our proposed procedure on two stars with transiting planets that were observed by during transits: HD 209458 and HD 189733., We tested our proposed procedure on two stars with transiting planets that were observed by during transits: HD 209458 and HD 189733.
" We showed that without any prior information regarding the orbital elements of the planets, it was possible to use the available data base of to direct follow-up observations for both stars and thus detect the planetary transits in minimal observational effort."," We showed that without any prior information regarding the orbital elements of the planets, it was possible to use the available data base of to direct follow-up observations for both stars and thus detect the planetary transits in minimal observational effort."
" This makes use of the fact that the Bayesian approach allows the inclusion of new data, that reflect new state of knowledge, in an easy and straightforward fashion."," This makes use of the fact that the Bayesian approach allows the inclusion of new data, that reflect new state of knowledge, in an easy and straightforward fashion."
 The examples we analyzed are only test cases to demonstrate the algorithm capabilities., The examples we analyzed are only test cases to demonstrate the algorithm capabilities.
" Using in such fashion to detect planets is already impractical, due to the long time that elapsed since the completion of the mission."," Using in such fashion to detect planets is already impractical, due to the long time that elapsed since the completion of the mission."
 The effect of the elapsing time is clearly seen in the way the ITP decreases during 10 yr (Fig. 2))., The effect of the elapsing time is clearly seen in the way the ITP decreases during $10$ yr (Fig. \ref{fig.HD209458followup10years}) ).
" We have shown that one year afterHipparcos,, it was possible to use its data to direct photometric follow-up observations that could have detected the planetary transits in only one follow-up observation for HD 209458, and in five observations for HD 189733."," We have shown that one year after, it was possible to use its data to direct photometric follow-up observations that could have detected the planetary transits in only one follow-up observation for HD 209458, and in five observations for HD 189733."
" In cases where only the Wald statistic has high significance, but the ITP is relatively low, we might recommend performing spectroscopic follow-up instead of photometric one, since RV search is less dependent on precise knowledge of the transit phase, because the goal is then to sample all phases of the orbit."," In cases where only the Wald statistic has high significance, but the ITP is relatively low, we might recommend performing spectroscopic follow-up instead of photometric one, since RV search is less dependent on precise knowledge of the transit phase, because the goal is then to sample all phases of the orbit."
" Since observations were performed almost two decades ago, and due to the fact that the ITP lost its significance, it may be more productive to perform RV follow-up observation for potential stars found in alone."," Since observations were performed almost two decades ago, and due to the fact that the ITP lost its significance, it may be more productive to perform RV follow-up observation for potential stars found in alone."
 We will explore this option in future work., We will explore this option in future work.
" Obviously, the procedure suggested here should not only be confined to the search for transiting planets, but can also be applied for searching other kinds of periodic variables, such as eclipsing binaries and Chepeids."," Obviously, the procedure suggested here should not only be confined to the search for transiting planets, but can also be applied for searching other kinds of periodic variables, such as eclipsing binaries and Chepeids."
 This will probably require some modifications of the procedure and algorithm., This will probably require some modifications of the procedure and algorithm.
" In this context, it is important to mention a similar approach of adaptive scheduling, which Tom Loredo proposed for the purpose of optimizing RV observations."," In this context, it is important to mention a similar approach of adaptive scheduling, which Tom Loredo proposed for the purpose of optimizing RV observations."
" The approach, adaptive Bayesian exploration (ABE; Loredo (2004))), is much more general, attempting to optimize"," The approach, adaptive Bayesian exploration (ABE; \citet{2004AIPC..707..330L}) ), is much more general, attempting to optimize"
where e; are the observed. racial velocities.,where $v_i$ are the observed radial velocities.
 The methods. described. in. this paper both use. the peculiar velocity correlation function and likelihood analysis described above., The methods described in this paper both use the peculiar velocity correlation function and likelihood analysis described above.
 This Section describes how we apply these techniques to the peculiar velocity data in practice., This Section describes how we apply these techniques to the peculiar velocity data in practice.
 The gridding method. is à way of averaging together the peculiar velocities of spatially close galaxies by laving a eric across the survey., The gridding method is a way of averaging together the peculiar velocities of spatially close galaxies by laying a grid across the survey.
 Averaging over a number of galaxies should allow the lincar signal to dominate., Averaging over a number of galaxies should allow the linear signal to dominate.
 Ht is similar to à countscin-cells approach used in galaxy surveys., It is similar to a counts-in-cells approach used in galaxy surveys.
 We discuss a simple way to bin the velocity fiel ancl detail a practical approach to take account of the binning accurately in the VCP., We discuss a simple way to bin the velocity field and detail a practical approach to take account of the binning accurately in the VCF.
 The technique we implement here is designed to be simple and fast., The technique we implement here is designed to be simple and fast.
 The likelihood analysis outlined in Section 2.2. above uses the individual galaxy peculiar velocities. ο). as the data.," The likelihood analysis outlined in Section \ref{section:like} above uses the individual galaxy peculiar velocities, $v_i$, as the data."
 Determining cosmological parameters in this way does not ake account of the nonlinear part of the peculiar velocity signal because. as stated above. we make our prediction or the VCE based. only on linear theory.," Determining cosmological parameters in this way does not take account of the nonlinear part of the peculiar velocity signal because, as stated above, we make our prediction for the VCF based only on linear theory."
 Phe density ield becomes nonlinear only on small scales. above a wave number (&) of about 0.25 i," The density field becomes nonlinear only on small scales, above a wave number $k$ ) of about $h$ $^{-1}$."
" We lav down a grid across the survey ancl average ogether all the peculiar velocities within cach grid. cell so hat where ef,"" is the racial peculiar velocity of the cell and c, is the error on the velocity. of the cell: the angle brackets denote an average over all galaxies 7 within the cell m.", We lay down a grid across the survey and average together all the peculiar velocities within each grid cell so that where $v_m^{\prime}$ is the radial peculiar velocity of the cell and $\epsilon_{m}^{\prime}$ is the error on the velocity of the cell; the angle brackets denote an average over all galaxies $i$ within the cell $m$.
 lere there is the approximation that the grid cells are small enough so the radial components to cach galaxy within each eid cell are parallel., Here there is the approximation that the grid cells are small enough so the radial components to each galaxy within each grid cell are parallel.
 This is tested when we apply the method to both linear and nonlinear simulations and we clo not see a significant. problem from this approximation., This is tested when we apply the method to both linear and nonlinear simulations and we do not see a significant problem from this approximation.
" Note that e; is the contribution to the correlation function fron the random velocity errors of cach galaxy and therefore the remaining contribution c;, to the binned correlation function is reduced by the square root of the number of galaxies.", Note that $\epsilon_i$ is the contribution to the correlation function from the random velocity errors of each galaxy and therefore the remaining contribution $\epsilon^{\prime}_m$ to the binned correlation function is reduced by the square root of the number of galaxies.
 Averaging the cata over a volume. of space wil essentially smooth the velocity field. which is equivalent to damping the small scale. contributions., Averaging the data over a volume of space will essentially smooth the velocity field which is equivalent to damping the small scale contributions.
 This reduces the observed. correlations because we average away some of the signal., This reduces the observed correlations because we average away some of the signal.
 Lf the data is averaged. on a grid. ancl insertec directly into the equations in Section 2 without accounting for the averaging in the correlation function. then the cosmological parameters will be biased., If the data is averaged on a grid and inserted directly into the equations in Section \ref{section:pre} without accounting for the averaging in the correlation function then the cosmological parameters will be biased.
 This is illustratec in Figure 1.., This is illustrated in Figure \ref{fig:psi}.
 The smoothed parallel ancl perpendicular correlation functions (dotted lines) are more similar to the parallel ancl perpendicular correlation functions with a lower os (dashed lines) than the unsmoothed functions with the same os (solid lines)., The smoothed parallel and perpendicular correlation functions (dotted lines) are more similar to the parallel and perpendicular correlation functions with a lower $\sigma_8$ (dashed lines) than the unsmoothed functions with the same $\sigma_8$ (solid lines).
 This type of binning is then taken account of bv multiplying the power spectrum in Eq., This type of binning is then taken account of by multiplying the power spectrum in Eq.
 4 and 5 with a window function corresponding to the size and. shape of the ericl cell., \ref{eq:psi} and \ref{eq:diag} with a window function corresponding to the size and shape of the grid cell.
 Ehis is because the binning in real space can be written as a convolution with a kernel followed by a sampling at the bin centres., This is because the binning in real space can be written as a convolution with a kernel followed by a sampling at the bin centres.
 The convolution kernel VM(x) is uniform within a bin centered on the origin. is zero outside ancl normalised to have unit integral.," The convolution kernel $W({\bf x})$ is uniform within a bin centered on the origin, is zero outside and normalised to have unit integral."
 In. Fourier space this convolution is simplv a multiplication. and the Fourier space window function is the Fourier transform of the real space window function," In Fourier space this convolution is simply a multiplication, and the Fourier space window function is the Fourier transform of the real space window function"
the RNPL--PCA data.,the -PCA data.
 We fitted a constant ancl a linear model to the eclipse measurements between MJD 52182 54410., We fitted a constant and a linear model to the eclipse measurements between MJD 52132 - 54410.
 Vhe results of the fit are given in Table 2., The results of the fit are given in Table 2.
 We obtained an orbital period of0.1367109674. (3) cl (epoch ALJD 51250.924540 (4)) and have derived. 10 limits of 0.2 10 dd + and -1.6 10 17 4 dto on the orbital period. derivative (Pin).," We obtained an orbital period of 0.1367109674 (3) d (epoch MJD 51250.924540 (4)) and have derived $\sigma$ limits of 0.2 $\times$ 10 $^{-12}$ d $^{-1}$ and -1.6 $\times$ 10 $^{-12}$ d $^{-1}$, on the orbital period derivative $\dot{P}_{orb}$ )."
 The- us of the lit was 74 for 51 cd.o.L., The $\chi^{2}$ of the fit was 74 for 51 d.o.f.
 Before and after the above mentioned. MJD range. we found shifts in the mid-eclipse times.," Before and after the above mentioned MJD range, we found shifts in the mid-eclipse times."
 We refer to these shifts as three epochs in the orbital period., We refer to these shifts as three epochs in the orbital period.
" Figure 2 shows the ""observed minus calculated” (O - €) diagram for all the eclipse measurements of N'TIS J1T10-281. obtained after subtracting the linear component obtained from epoch 2."," Figure 2 shows the $``$ observed minus calculated"" (O - C) diagram for all the eclipse measurements of XTE J1710-281, obtained after subtracting the linear component obtained from epoch 2."
 The three dillerent epochs of orbital. period is evident., The three different epochs of orbital period is evident.
" Ht is obvious from the figure that a polynomial function consisting of linear (1). quadratic (Popa). cubic (D, ϱ) etc terms cannot be fitted to the observed. dataset."," It is obvious from the figure that a polynomial function consisting of linear $_{orb}$ ), quadratic $\dot{P_{orb}}$ ), cubic $\ddot{P_{orb}}$ ) etc terms cannot be fitted to the observed dataset."
 A piecewise linear function. could be more appropriate., A piecewise linear function could be more appropriate.
 jut. there are few observations in epoch 1 and 3. hence one cannot determine the orbital period. during epoch-1 and epoch-3 with very high accuracy.," But, there are few observations in epoch 1 and 3, hence one cannot determine the orbital period during epoch-1 and epoch-3 with very high accuracy."
 However. from our observations. we have put lower limits on orbital period 'hanges of XP = 1.4 ms 10 7 d) between and epoch-2: and a AP — v09 ms “rection(1.1 « 10. 7 d) between epoch-2 and epoch-3.," However, from our observations, we have put lower limits on orbital period changes of $\Delta P$ = 1.4 ms (1.7 $\times$ 10 $^{-8}$ d) between epoch-1 and epoch-2; and a $\Delta P$ = 0.9 ms (1.1 $\times$ 10 $^{-8}$ d) between epoch-2 and epoch-3."
 ‘The significance of the two orbital period. glitches are 11σ and 4o respectively., The detection significance of the two orbital period glitches are $\sigma$ and $\sigma$ respectively.
 We have also created average eclipse profiles for the iee epochs bv combining all the corresponding: eclipse light curves., We have also created average eclipse profiles for the three epochs by combining all the corresponding eclipse light curves.
 The eclipse light curves were co-added: using 16 orbital period and epoch given in Table 2., The eclipse light curves were co-added using the orbital period and epoch given in Table 2.
 Ehe folded profiles are shown in the top panel of Figure 3., The folded profiles are shown in the top panel of Figure 3.
 The best fit ramp function is also shown for the eclipse profile of epoch , The best fit ramp function is also shown for the eclipse profile of epoch 2.
The best fit had a v of 689 for 650 degrees of [reedom (d.o.£)., The best fit had a $ \chi^{2} $ of 689 for 650 degrees of freedom (d.o.f).
 Ehe bottom panels of the same figure shows the eclipse ingress and ceress profiles., The bottom panels of the same figure shows the eclipse ingress and egress profiles.
 It is clear from Figure 3y that the time of ingress ancl egress of eclipse. during the three epochs is shifted in phase while the eclipse duration has remained. nearly. sanie.," It is clear from Figure 3 that the time of ingress and egress of eclipse, during the three epochs is shifted in phase while the eclipse duration has remained nearly same."
 Aleasurements of change in orbital period of an LMND. is a crucial diagnostic to understand. the accretion processes occuring in a binary svstem: and their οσο on. the system parameters.," Measurements of change in orbital period of an LMXB, is a crucial diagnostic to understand the accretion processes occuring in a binary system; and their effect on the system parameters."
 And the orbital period can be very wel determined by time connecting a stable fiducial marker in he light curve of the binary system., And the orbital period can be very well determined by time connecting a stable fiducial marker in the light curve of the binary system.
 We have. analvzec 57 full X-ray eclipses of NPE J1T10-281. observed by the RNTL satellite.," We have analyzed 57 full X-ray eclipses of XTE J1710-281, observed by the $RXTE$ satellite."
 Phe observations cover more than 30000 jnarv orbits spreac over 11 vears., The observations cover more than 30000 binary orbits spread over $\sim$ 11 years.
 A’ five-componen model was fit to cach eclipse profile ancl the mid-eclipse ines and the corresponding errors. determined., A five-component model was fit to each eclipse profile and the mid-eclipse times and the corresponding errors determined.
" We have determined an orbital period. of (1361710967. (3) d anc imits on the period derivative o£ -1.6 « 10. I dd. 1+ and 0.2 10 del c.. limits on the MN of secular orbita serlocl evolution. {δν""irb. OL nu2 103 vr for a perioc decay and 18.7 107 vr fora increase."," We have determined an orbital period of 0.1367109674 (3) d and limits on the period derivative of -1.6 $\times$ 10 $^{-12}$ d $^{-1}$ and 0.2 $\times$ 10 $^{-12}$ d $^{-1}$, i.e., limits on the timescale of secular orbital period evolution, ${P}_{orb}/\dot{P_{orb}}$ , of 2.34 $\times$ 10 $^{8}$ yr for a period decay and 18.7 $\times$ 10 $^{8}$ yr for a period increase."
 respectively. during the period from MJD 52132 to MJD 54410," respectively, during the period from MJD 52132 to MJD 54410."
" The variation in the orbital ephemerides of NPE J1710- is significantly cillerent from that seen in most of the other "" systems. such as. 40° 1820-3(4 &Crind-av 2001)..ru SAN JISQOS.4-3658 (Jainet2MarChale).. Her. N-1 (Paulet 2007).. X 2127|119 (Llomer&1905) and 4U 1822-37 (Jainetal. 2010).."," The variation in the orbital ephemerides of XTE J1710-281, is significantly different from that seen in most of the other LMXB systems, such as, 4U 1820-303 \citep{Chou01}, SAX J1808.4-3658 \citep{Jain07}, Her X-1 \citep{Paul07}, , X 2127+119 \citep{Homer98} and 4U 1822-37 \citep{Jain10}. ."
" During the period rom AJL) 52132 to. ALJD 54410. thelimits on the orbital »eriod derivative of NTE JIT10-281. is more than an order of magnitude smaller than those measured in the other LAINDs (400 1820-303 (3.5 10. vxr ty SAN JISOS4-3658 (1.3 1O 7 vr 4).1 Ler N-1( 1822.3710 ""ovr 1) N 2127|119 (9 10 r and 4U ( (2.0 10."" 1)."," During the period from MJD 52132 to MJD 54410, thelimits on the orbital period derivative of XTE J1710-281, is more than an order of magnitude smaller than those measured in the other LMXBs (4U 1820-303 (3.5 $\times$ 10 $^{-8}$ $^{-1}$ ), SAX J1808.4-3658 (1.3 $\times$ 10 $^{-8}$ $^{-1}$ ), Her X-1 (-2 $\times$ 10 $^{-7}$ $^{-1}$ ), X 2127+119 (9 $\times$ 10 $^{-7}$ $^{-1}$ ) and 4U 1822-37 (2.0 $\times$ 10 $^{-7}$ $^{-1}$ ))."
 Outside he above ALJD range. the observed trend in the residual (O - €) behaviour of NTE J1710-281. is also different from that seen in the aforementioned LAINDs.," Outside the above MJD range, the observed trend in the residual (O - C) behaviour of XTE J1710-281, is also different from that seen in the aforementioned LMXBs."
" The ""- variation d resemble the one seen in EXOMANDUXI( uh""(WoLnumctal.9).", The observed O - C variation strongly resemble the one seen in EXO 0748-676 \citep{Wolff09}.
. Interestingly. of well eclipse times. EXO dips.n°Yr48-676 knownand NTE J1710-281 have shortest duration of the making it easier to monitor with X-ray observatories.," Interestingly, of the known LMXBS with well determined eclipse times, EXO 0748-676 and XTE J1710-281 have shortest duration of the eclipse, making it easier to monitor with X-ray observatories."
" Though fewer eclipses have been observed in NLL J1710-281. as nu»to more than 400 complete eclipses seen rom EXO""men(M (Wollctal.2009).. the mid-eclipse inies ΗΝΤΙΑΔ are accurate enough to enable detection of very small orbital period. glitches."," Though fewer eclipses have been observed in XTE J1710-281, as opposed to more than 400 complete eclipses seen from EXO 0748-676 \citep{Wolff09}, the mid-eclipse times measured with RXTE-PCA are accurate enough to enable detection of very small orbital period glitches."
 Magnetic field eveling of the secondary star is assumed o be the meecause For the observed orbital period glitches in ENOt+ etel(Wolfetal.2009)., Magnetic field cycling of the secondary star is assumed to be the likely cause for the observed orbital period glitches in EXO 0748-676 \citep{Wolff09}.
. It is proposed. that magnetic activity with the secondary star could ος responsible for sudden changes in the orbital period., It is proposed that magnetic activity associated with the secondary star could be responsible for sudden changes in the orbital period.
 If the secondary. star associated with NTE 1710-281 has strong. changing. magnetic activity. it can lead to changes in the structure of secondary star.," If the secondary star associated with XTE J1710-281 has strong, changing, magnetic activity, it can lead to changes in the structure of secondary star."
 A changing eravitational quadrapole moment can result into changes inthe orbital period ofthe binary system (Lanza&Itodono1999:&vandenLeuvel2006) .," A changing gravitational quadrapole moment can result into changes inthe orbital period ofthe binary system \citep{Lanza99, Tauris06}. ."
 Mowever. in case of NPE the optical counterpart has been discovered(Itatti but the tvpe of the companion star is not vet known.," However, in case of XTE J1710-281, the optical counterpart has been discovered\citep{Ratti10} but the type of the companion star is not yet known."
The fluxes were measured on flux-calibrated integrated spectra using a Gaussian fit and a flat continuum.,The fluxes were measured on flux-calibrated integrated spectra using a Gaussian fit and a flat continuum.
 These fluxes have been corrected for dust reddening using the extinction coefficient derived from the SED fitting (see??)..," These fluxes have been corrected for dust reddening using the extinction coefficient derived from the SED fitting \citep[see][]{contini11, vergani11}."
 The line ratios. on the other hand. were determined from the integrated spectra in counts.," The line ratios, on the other hand, were determined from the integrated spectra in counts."
 Indeed. the flux calibration procedure would have added noise on top of the already low SNR data.," Indeed, the flux calibration procedure would have added noise on top of the already low SNR data."
 Further. the lines of interest (namely. and n]6584)) are close enough in wavelength to assume that the sensitivity curve is constant over the wavelength range of interest.," Further, the lines of interest (namely, and ) are close enough in wavelength to assume that the sensitivity curve is constant over the wavelength range of interest."
 The same argument justifies the fact that we did not correct the emission-line ratios for differential extinction., The same argument justifies the fact that we did not correct the emission-line ratios for differential extinction.
 Table 2 lists our final integrated flux. N2 emission line ratio (V2=log([Nu]6584/H«) and star formation rates (SER. corrected or not for dust reddening).," Table \ref{eml} lists our final integrated flux, N2 emission line ratio $N2 = \log(\mathrm{\niia{}}/\mathrm{H\alpha})$ and star formation rates (SFR, corrected or not for dust reddening)."
 Among the 44 galaxies detected in with SINFONI. we have been able to measure the emission-line in 34 galaxies and hence derive integrated N2 emission-line ratio and metallicity for these objects.," Among the 44 galaxies detected in with SINFONI, we have been able to measure the emission-line in 34 galaxies and hence derive integrated N2 emission-line ratio and metallicity for these objects."
 ].40mm For many galaxies in our sample. the low SNR of the data cubes prevents us from measuring in each spaxel. with high confidence. the emission lines surrounding: namelyu]6584..]6717.31.. and textsci]]G300 which is detected only in. one galaxy: VVDS1400960045.," 1.40mm For many galaxies in our sample, the low SNR of the data cubes prevents us from measuring in each spaxel, with high confidence, the emission lines surrounding: namely, and ]6300 which is detected only in one galaxy: VVDS140096645."
 These lines might either not be bright enough to be detected. or a bright OH sky-line ts too close.," These lines might either not be bright enough to be detected, or a bright OH sky-line is too close."
 To increase the SNR of our finalsspectra. we summed the spectra of the spaxels gatheredin a specified region. and measured the line fluxes in the resulting spectra.," To increase the SNR of our final spectra, we summed the spectra of the spaxels gathered in a specified region, and measured the line fluxes in the resulting spectra."
 We developed a specific procedure to do this analysis within our data cubes., We developed a specific procedure to do this analysis within our data cubes.
 The program allowed to define a region spaxel-by-spaxel. or to define a region with contours on 2D maps (such as flux. SNR. ete maps).," The program allowed to define a region spaxel-by-spaxel, or to define a region with contours on 2D maps (such as flux, SNR, etc maps)."
 In a given region. the spaxel-to-spaxel line shift due to the rotation velocity of the gas along the line-of-sight was fully corrected for (see refintfl).," In a given region, the spaxel-to-spaxel line shift due to the rotation velocity of the gas along the line-of-sight was fully corrected for (see \\ref{intfl}) )."
 The integrated spectrum in a defined region was then fitted with a flat continuum and two Gaussians. one for and one for (the sulfur doublet was neglected for this analysis as it was detected in a few cases only).," The integrated spectrum in a defined region was then fitted with a flat continuum and two Gaussians, one for and one for (the sulfur doublet was neglected for this analysis as it was detected in a few cases only)."
 The width of each Gaussian was set to be the same as the emission of the collisional and recombination lines traces the same tonised gas in the galaxies., The width of each Gaussian was set to be the same as the emission of the collisional and recombination lines traces the same ionised gas in the galaxies.
 The fit was weighted using the corresponding non sky-subtracted spectrum. Le. giving a lower weight to the channels affected by the subtraction of a strong sky-line.," The fit was weighted using the corresponding non sky-subtracted spectrum, i.e. giving a lower weight to the channels affected by the subtraction of a strong sky-line."
 We then estimated the Io error on the fluxes with a Monte-Carlo technique. in which the fit was considered to be a “noise-free” model. to which we added a Gaussian noise with a standard deviation corresponding to the residuals from the initial spectrum minus the “noise-free” model.," We then estimated the $1\sigma$ error on the fluxes with a Monte-Carlo technique, in which the fit was considered to be a “noise-free” model, to which we added a Gaussian noise with a standard deviation corresponding to the residuals from the initial spectrum minus the “noise-free” model."
 This operation was repeated a hundred of times. which gave a set of parameters on which the Lc deviation was computed.," This operation was repeated a hundred of times, which gave a set of parameters on which the $1\sigma$ deviation was computed."
 shows a result of our fits in different regions for two galaxies., shows a result of our fits in different regions for two galaxies.
 Finally. we estimate spatially-resolved aand," Finally, we estimate spatially-resolved and"
in the optical and are characterized by large values of R.,in the optical and are characterized by large values of $R$.
 Steep UV curves remain steep 1n the optical and are characterized by small values of R., Steep UV curves remain steep in the optical and are characterized by small values of $R$.
 The CCM curve for R=3.1 is shown in Figure | by the dotted line., The CCM curve for $R=3.1$ is shown in Figure 1 by the dotted line.
 The results of CCM are important in 3 ways: (1) They indicate that some of the spatial variations seen in extinction curves behave coherently and systematically over a wide wavelength range. thus potentially allowing for the consistent dereddening of multiwavelength energy distributions. (," The results of CCM are important in 3 ways: (1) They indicate that some of the spatial variations seen in extinction curves behave coherently and systematically over a wide wavelength range, thus potentially allowing for the consistent dereddening of multiwavelength energy distributions. ("
2) The observed dependence on R allows for the definition of a meaningful average Galactic extinction curve.,2) The observed dependence on $R$ allows for the definition of a meaningful average Galactic extinction curve.
" Existing datasets of extinction curves. particularly for the UV. are biased toward ""interesting"" regions where extinction properties are extreme."," Existing datasets of extinction curves, particularly for the UV, are biased toward “interesting” regions where extinction properties are extreme."
 Computing a simple mean curve from these data does not necessarily yield a reasonable estimate of a Galactic mean., Computing a simple mean curve from these data does not necessarily yield a reasonable estimate of a Galactic mean.
 Since it is well-established. however. that the appropriate mean value of AR for the diffuse ISM its —3.1 (e.g.. Schultz Wiemer 1975; Whittet van Breda 1980; Rieke Lebofsky 1985). a reasonable definition of a mean Galactic extinction law is that which corresponds to the case where R=3.1. (," Since it is well-established, however, that the appropriate mean value of $R$ for the diffuse ISM is $\sim$ 3.1 (e.g., Schultz Wiemer 1975; Whittet van Breda 1980; Rieke Lebofsky 1985), a reasonable definition of a mean Galactic extinction law is that which corresponds to the case where $R = 3.1$. ("
3) They demonstrate a general correlation between dust grain environment and the wavelength dependence of extinction. since large values of are generally found in dense environments where dust grain growthR is thought to occur.,"3) They demonstrate a general correlation between dust grain environment and the wavelength dependence of extinction, since large values of $R$ are generally found in dense environments where dust grain growth is thought to occur."
" The ""greyness"" of the UV/optical extinction curves for large R is consistent with a larger than normal dust grain. population.", The “greyness” of the UV/optical extinction curves for large $R$ is consistent with a larger than normal dust grain population.
 These results have an important bearing on how to correct for the effects of extinction. discussed in the following section.," These results have an important bearing on how to correct for the effects of extinction, discussed in the following section."
 Given the observed complexity of Galactic UV extinction. what is the best way to deredden an observed energy distribution?," Given the observed complexity of Galactic UV extinction, what is the best way to deredden an observed energy distribution?"
 There are three different possibilities. which involve the use of a global mean extinction curve. an R-dependent curve. and a sightline-specific curve.," There are three different possibilities, which involve the use of a global mean extinction curve, an $R$ -dependent curve, and a sightline-specific curve."
 These three alternatives and their inherent uncertainties are discussed below. and a new derivation of the shape of the average IR-through-UV extinction curve is presented.," These three alternatives and their inherent uncertainties are discussed below, and a new derivation of the shape of the average IR-through-UV extinction curve is presented."
 A more thorough discussion of the uncertainties involved in UV= extinction corrections is given by Massa (1987)., A more thorough discussion of the uncertainties involved in UV extinction corrections is given by Massa (1987).
 If there is no specific information available about the wavelength dependence of the extinction along a sightline of interest then the only alternative is to adopt some globally defined mean curve and perform a realistic error. analysis., If there is no specific information available about the wavelength dependence of the extinction along a sightline of interest then the only alternative is to adopt some globally defined mean curve and perform a realistic error analysis.
 This is the least attractive of the three cases discussed here. but is by far the most commonly used.," This is the least attractive of the three cases discussed here, but is by far the most commonly used."
 The average Galactic extinction curves from either Seaton (1979; see Figure 1) or Savage Mathis (1979) are often adopted for dereddening UV data., The average Galactic extinction curves from either Seaton (1979; see Figure 1) or Savage Mathis (1979) are often adopted for dereddening UV data.
 These should now be superseded by the use of an R-dependent curve computed for the case R=3.1 (see $2.2)., These should now be superseded by the use of an $R$ -dependent curve computed for the case $R = 3.1$ (see 2.2).
 Figure | shows the R=3.1 curve from CCM (dotted line) and a new determination of the R=3.1 case (solid line) which is deseribed in the Appendix to this paper., Figure 1 shows the $R = 3.1$ curve from CCM (dotted line) and a new determination of the $R = 3.1$ case (solid line) which is described in the Appendix to this paper.
 This new curve aims to reproduce the detailed wavelength dependence of the R=3.1 extinction law and has been constructed to account for bandpass effects properly in optical/IR extinction data and to reproduce the observed broad-. intermediate-. and narrow- band extinction measurements.," This new curve aims to reproduce the detailed wavelength dependence of the $R = 3.1$ extinction law and has been constructed to account for bandpass effects properly in optical/IR extinction data and to reproduce the observed broad-, intermediate-, and narrow- band extinction measurements."
 The curve is thus suitable for dereddening multiwavelength spectrophotometric observations and can be used to derive the average extinction relationships in any photometrie system., The curve is thus suitable for dereddening multiwavelength spectrophotometric observations and can be used to derive the average extinction relationships in any photometric system.
 A complete evaluation of the likely error in à dereddened relative energy distribution 7(À—V) requires the propagation of the uncertainty in E(8—V) and the often-neglected but often-dominant uncertainty in the adopted mean curve., A complete evaluation of the likely error in a dereddened relative energy distribution $m(\lambda-V)$ requires the propagation of the uncertainty in $E(B-V)$ and the often-neglected but often-dominant uncertainty in the adopted mean curve.
 This is given by where &(À—V) represents the normalized extinction. curve E(A—V)/E(B—V)., This is given by where $k(\lambda-V)$ represents the normalized extinction curve $E(\lambda-V)/E(B-V)$.
 If absolute fluxes are desired. then the uncertainty in the assumed value of R must also be incorporated (two additional terms on the righthand side of eq.," If absolute fluxes are desired, then the uncertainty in the assumed value of $R$ must also be incorporated (two additional terms on the righthand side of eq."
 1. similar to the current terms but with R substituted for &(À—V)).," 1, similar to the current terms but with $R$ substituted for $k(\lambda-V)$ )."
 The large database of satellite extinction measurements from Savage et al. (, The large database of satellite extinction measurements from Savage et al. (
1985) shows that the 1-6 scatter at 1500 18 σι)=0.74. based on ~400 sightlines with E(B—V):Iv0.5. (,"1985) shows that the $\sigma$ scatter at 1500 is $\sigma_{k(15-V)} = 0.74$, based on $\sim$ 400 sightlines with $E(B-V)
\ge 0.5$ . ("
Only relatively large values of E(B—V) were considered in order to minimize the effects of spectral mismatch error and random noise on the σ measurement.),Only relatively large values of $E(B-V)$ were considered in order to minimize the effects of spectral mismatch error and random noise on the $\sigma$ measurement.)
 To extend this analysis to other wavelengths. we computed the standard deviation at each wavelength point for the 80 curves shown in Figure 2. and then scaled the result to mateh theANS value at 1500A.. (," To extend this analysis to other wavelengths, we computed the standard deviation at each wavelength point for the 80 curves shown in Figure 2, and then scaled the result to match the value at 1500. ("
The actual standard deviation at 1500 for the 80 curves is somewhat higher than theANS result because of the bias in Figure 2 toward extreme extinetior curves).,The actual standard deviation at 1500 for the 80 curves is somewhat higher than the result because of the bias in Figure 2 toward extreme extinction curves).
" The resultant values of o;xv, are shown by the thick dotted curve near the bottom of Figure 2 (labeled ""67) anc are listed at selected wavelengths in the third column of Table I.", The resultant values of $\sigma_{k(\lambda-V)}$ are shown by the thick dotted curve near the bottom of Figure 2 (labeled $\sigma$ ”) and are listed at selected wavelengths in the third column of Table 1.
" This estimate of o;4v, should be adopted whenever the average Galactic extinction curve is used for dereddening ar observed energy distribution.", This estimate of $\sigma_{k(\lambda-V)}$ should be adopted whenever the average Galactic extinction curve is used for dereddening an observed energy distribution.
 The uncertainties approach zero for 1/\«3 qr! due to the curve normalization.," The uncertainties approach zero for $1/\lambda < 3$ $\mu
m^{-1}$ due to the curve normalization."
" The quantity E(B—V) is usually derived directly from photometry and ofter has an easily quantifiable uncertainty: thus the computation of 07vy, from eq.", The quantity $E(B-V)$ is usually derived directly from photometry and often has an easily quantifiable uncertainty; thus the computation of $\sigma^2_{m(\lambda-V)}$ from eq.
 | is straightforward., 1 is straightforward.
 Sometimes £(B—V) is not known and is estimated by “ironing out” the 2175 extinction bump using an assumed extinction curve shape (e.g.. see Massa. Savage. Fitzpatrick 1983).," Sometimes $E(B-V)$ is not known and is estimated by “ironing out” the 2175 extinction bump using an assumed extinction curve shape (e.g., see Massa, Savage, Fitzpatrick 1983)."
 In. many cases. uncertainties in E(B-V) às small as 0.01-0.02 mag for moderately reddened objects have been quoted from this process.," In many cases, uncertainties in $E(B-V)$ as small as 0.01-0.02 mag for moderately reddened objects have been quoted from this process."
 This is incorrect!, This is incorrect!
" The normalized ""height"" of the 2175 extinction bump — which is the quantity that is important in the ironing-out process — has a I-o scatter of about +20% around its mean value (from the data in Figure 2 and Savage et al.", The normalized “height” of the 2175 extinction bump — which is the quantity that is important in the ironing-out process — has a $\sigma$ scatter of about $\pm$ around its mean value (from the data in Figure 2 and Savage et al.
 1985)., 1985).
 Thus the uncertainty in an £(B8—V) measurement derived from the bump must be considered to have à similar relative uncertainty., Thus the uncertainty in an $E(B-V)$ measurement derived from the bump must be considered to have a similar relative uncertainty.
 Since bump strength does not correlate well with other aspects of UV extinction. such as the slope of the linear component or the strength of the far-UV rise (FM). the uncertainty in an energy distribution dereddened this way can be estimated by using eq.," Since bump strength does not correlate well with other aspects of UV extinction, such as the slope of the linear component or the strength of the far-UV rise (FM), the uncertainty in an energy distribution dereddened this way can be estimated by using eq."
" | with o5,5v,&20% and the values of o;v, from Table 1.", 1 with $\sigma_{E(B-V)} \simeq 20\%$ and the values of $\sigma_{k(\lambda-V)}$ from Table 1.
 The result of this calculation needs tobe modified somewhat by removing the signature of the 2175 bump., The result of this calculation needs tobe modified somewhat by removing the signature of the 2175 bump.
 The final estimate of 0y computed this way ts listed in the last column of Table 1., The final estimate of $\sigma^2_{m(\lambda-V)}$ computed this way is listed in the last column of Table 1.
 Multiplying these values by E(B—V) gives the uncertainty in a dereddened relative energy distribution., Multiplying these values by $E(B-V)$ gives the uncertainty in a dereddened relative energy distribution.
" The values inTable 1 agree well with estimates 8vy, at 1500. 1800. 2200. 2500. and 3300 derived from the data of Savage et al (1985). and are"," The values inTable 1 agree well with estimates $\sigma^2_{m(\lambda-V)}$ at 1500, 1800, 2200, 2500, and 3300 derived from the data of Savage et al (1985), and are"
ions with IT. This process gradually removes aud the abundance of Lill reaches a coustaut value.,ions with H. This process gradually removes $^-$ and the abundance of LiH reaches a constant value.
 Tn order to make accurate comparisons with the results obtained iu previous studies. we have run models with the same reaction rates adopted in our standard case. but differing cosmological paraiucters to reproduce exactly the thoices of the various authors listed in Table 7.," In order to make accurate comparisons with the results obtained in previous studies, we have run models with the same reaction rates adopted in our standard case, but differing cosmological parameters to reproduce exactly the choices of the various authors listed in Table 7."
 The results are shown in Fig., The results are shown in Fig.
 7. where we compare the predictions of our model (solid lines) with those of Palla et al. (," 7, where we compare the predictions of our model (solid lines) with those of Palla et al. ("
1995) (upper left panel). Lepp Shull (1981) (upper right panel). Puy et al. (,"1995) (upper left panel), Lepp Shull (1984) (upper right panel), Puy et al. ("
1993). (lower loft. panel). and Black (1991) (lower right panel). all mdicated bx dashed lines.,"1993) (lower left panel), and Black (1991) (lower right panel), all indicated by dashed lines."
 A common feature in the first three cases is a dramatic reduction of the abundance of LiII by 79 orders of maeguitudoe. due to the replacement of the semiclassical estimate of the rate of radiative association (Lepp Shull 1981) with the quautal calculations by Dalgarno ct al. (," A common feature in the first three cases is a dramatic reduction of the abundance of LiH by 7–9 orders of magnitude, due to the replacement of the semiclassical estimate of the rate of radiative association (Lepp Shull 1984) with the quantal calculations by Dalgarno et al. ("
1996) and Cüanturco Con Ciorei (1996a).,1996) and Gianturco Gori Giorgi (1996a).
 With respect to our earlier study of primordial omistrv. hne iore accurate treatinent of II recolubination results iun ai decreased residual electron fraction by a factor 23 (see also Table 5).," With respect to our earlier study of primordial chemistry, the more accurate treatment of H recombination results in a decreased residual electron fraction by a factor 2–3 (see also Table 5)."
" This. in turn. has a direct inpact on the IT; and UD abundances. which are lower bv a factor ~5,"," This, in turn, has a direct impact on the $_2$ and HD abundances, which are lower by a factor $\sim 5$."
 Otherwise. the evolution with redshift of these two species follows the same behaviour.," Otherwise, the evolution with redshift of these two species follows the same behaviour."
 Sinular considerations apply to the comparison wit1 the results obtained earlier by Lepp Shull (1981) for II. ID! and Ils.," Similar considerations apply to the comparison with the results obtained earlier by Lepp Shull (1984) for H, $^+$ and $_2$."
 Iowever. it is worth noticing that in their model the formation of ID occurs through the analogues of tlicTE and IE) channels. at rates ciniuished by the cosinological D/II ratio. plus a ueeheible coutributioi from direct radiative association of IT and D. Iu coutrast. we have found that the main reaction responsible for the formation of ΠΟ is the isotope exchange reacion (Ds) which has no counterpart in the lyvdrogen chewical network.," However, it is worth noticing that in their model the formation of HD occurs through the analogues of the $^-$ and $_2^+$ channels, at rates diminished by the cosmological D/H ratio, plus a negligible contribution from direct radiative association of H and D. In contrast, we have found that the main reaction responsible for the formation of HD is the isotope exchange reaction (D8) which has no counterpart in the hydrogen chemical network."
 Therefore. despite their higher residual electron fraction. them asvuiptotic abuudance of IID is 1nderestinated by about oue order of magnitude.," Therefore, despite their higher residual electron fraction, their asymptotic abundance of HD is underestimated by about one order of magnitude."
 Puy et al. (, Puy et al. (
1993) «υιός abundances of IT; aud ΠΟ about one order of magnitude larger than ours. owing to their uurealistie choice ΟΕ the photodissociation rate (II9),"1993) obtained abundances of $_2$ and HD about one order of magnitude larger than ours, owing to their unrealistic choice of the photodissociation rate (H9)"
observations.,observations.
 The cata were reduced bv using the software package NewStar of Nobevamia Raclio Observatory and IDL of Research Systems. Inc. Prior to our observations. sixtv-three low-mass molecular cloud cores have been observed in Noll by Casellietal.(20026).. but with lower angular resolution (54 arcsec).," The data were reduced by using the software package NewStar of Nobeyama Radio Observatory and IDL of Research Systems, Inc. Prior to our observations, sixty-three low-mass molecular cloud cores have been observed in $_2$ $^+$ by \citet{cac02}, but with lower angular resolution (54 arcsec)."
 We will refer to their results to secure our discussion on the basis of our observations toward the eieht cores but withbetter angular resolution (18/6 beam and 20755 grid)., We will refer to their results to secure our discussion on the basis of our observations toward the eight cores but withbetter angular resolution $\farcs$ 6 beam and $\farcs$ 55 grid).
 Since the typical radius of (he molecular cloud core is about 50 arcsec in the region. (he improvement in spatial resolution helps us to derive the physical parameters more precisely.," Since the typical radius of the molecular cloud core is about 50 arcsec in the region, the improvement in spatial resolution helps us to derive the physical parameters more precisely."
 Figure 1 shows that the distribution of the velocitv-integrated. intensity of the main Noll J—1-0 component (F4. F = 2. 341. 2) toward the eight molecular cloud cores.," Figure 1 shows that the distribution of the velocity-integrated intensity of the main $_2$ $^+$ $J = 1\rightarrow0$ component $F_1$, $F$ = 2, $\rightarrow$ 1, 2) toward the eight molecular cloud cores."
 The core associated with L1551 IRS5 (L1551) is 2-3 times as intense as the other cores. and we double the contour interval for this source For clarity.," The core associated with L1551 IRS5 (L1551) is $-$ 3 times as intense as the other cores, and we double the contour interval for this source for clarity."
 We use (he main component rather than the optically thinner components (to obtain better signal-to-noise ratios., We use the main component rather than the optically thinner components to obtain better signal-to-noise ratios.
 For checking. we have also made (he integrated intensity map of the Fy. F = 0. lol. 2 component (not shown. (he map quality is much worse). and have confirmed that the intensity peak position is consistent in general.," For checking, we have also made the integrated intensity map of the $F_1$, $F$ = 0, $\rightarrow$ 1, 2 component (not shown, the map quality is much worse), and have confirmed that the intensity peak position is consistent in general."
 As shown later. the optical depth is not very large even for (he main component ( unitv).," As shown later, the optical depth is not very large even for the main component $\sim$ unity)."
 The positions of the intensity maxima of the cores are summarized in Table 1., The positions of the intensity maxima of the cores are summarized in Table 1.
 The core name with the prefix of Miz relers to the core number in (1994)., The core name with the prefix of Miz refers to the core number in \citet{miz94}.
. Core Mizsb is newly found in our observations., Core Miz8b is newly found in our observations.
 Core L1527 is associated with a Class 0 protostar. while cores Mizr. Mizs. and. L1551 are associated with Class I protostars.," Core L1527 is associated with a Class 0 protostar, while cores Miz7, Miz8, and, L1551 are associated with Class I protostars."
" These are ""cores with stars.”", These are “cores with stars.”
 Furthermore. a Class 0 protostar L1551 NE 1993) is located near (he core boundary of L1551. but its relationship to the Noll core is nol clear in our map (see Saitoetal.(2001):Yokogawa(2003) [or a detailed study of this region in CO and CS).," Furthermore, a Class 0 protostar L1551 NE \citep{bar93} is located near the core boundary of L1551, but its relationship to the $_2$ $^+$ core is not clear in our map (see \citet{sai01,yok03} for a detailed study of this region in $^{18}$ O and CS)."
" Cores Mizl. Miz2. LI521F. and Mizsb are ""starless cores."," Cores Miz1, Miz2, L1521F, and Miz8b are “starless cores”."
 The basic physical parameters of the cores are summarized in Table 2., The basic physical parameters of the cores are summarized in Table 2.
 The IIWIIM core radius A is measured as VS/n (59 is the core area S at the half maximum). and then corrected for the telescope beam size.," The HWHM core radius $R$ is measured as $\sqrt{S}/\pi$ $S$ is the core area S at the half maximum), and then corrected for the telescope beam size."
 There is no remarkable difference in core radius between starless cores (22 = 0.03540.004 pe) and core with stars (2 = 0.0312z:0.006 pc)., There is no remarkable difference in core radius between starless cores $R$ = $\pm$ 0.004 pc) and core with stars $R$ = $\pm$ 0.006 pc).
 The study ol Casellietal.(2002€). shows that cores with stars are slightly larger than starless cores. but difference is not large.," The study of \citet{cac02} shows that cores with stars are slightly larger than starless cores, but difference is not large."
 Our result is in marked contrast with that of in IPCO . in which cores with stars tend to be more compact.," Our result is in marked contrast with that of \citet{miz94} in $^{13}$ $^+$ , in which cores with stars tend to be more compact."
 Depletion of IPCO — will be a plausible explanation. because it is known that Noll is more robust for depletion than WCCO — (Berginetal.2001:Caselli2002b:Lee 2003)..," Depletion of $^{13}$ $^+$ will be a plausible explanation, because it is known that $_2$ $^+$ is more robust for depletion than $^{13}$ $^+$ \citep{ber01,cab02,lee03}. ."
 It is suggested that, It is suggested that
counterpart. aud sugecstCoco that it is a cataclysinic variable (private commnuulcation).,"counterpart, and suggest that it is a cataclysmic variable (private communication)."
 We note that it is curious that the period of the signal from NMMU J121129.7630107 is within 20 of being a factor of 2 longer than the period of the sigual from AMAMU J185330.7012815., We note that it is curious that the period of the signal from XMMU J124429.7–630407 is within $\sigma$ of being a factor of 2 longer than the period of the signal from XMMU J185330.7–012815.
 We have not been able to identify anv svstenmatic effect that uuelt explain both sienals., We have not been able to identify any systematic effect that might explain both signals.
 In our search. we did not fiud simular siguificaut sienals from any of the thousands of other sources that we examined.," In our search, we did not find similar significant signals from any of the thousands of other sources that we examined."
 The signals are uulikelv to be detector artifacts. because they are detected in the pu and both MOS cameras.," The signals are unlikely to be detector artifacts, because they are detected in the pn and both MOS cameras."
 Uavineg failed to identify iiv causcs intrinsic to the spacecraft. on-board computers. or data processing. we believe that they are astroplivsical. and that the factor of two difference between thems is simply a coincidence.," Having failed to identify any causes intrinsic to the spacecraft, on-board computers, or data processing, we believe that they are astrophysical, and that the factor of two difference between them is simply a coincidence."
 The periodic signals that we have detected. from xeviouxlv-uuideuti&ed sources all have periods louger han 100 5. Although there is a chance that some of these systelus are neutron stars. we expect that most of thoi »long to the nmch-lareer population of magneticallv-accretiug. white dwarfs. either polars or intermediate »olars (e.g...Norton&Watson1989:Sclavarzetal.2002:Ramsay&Cropper2003:Mimoetal. 2003).," The periodic signals that we have detected from previously-unidentified sources all have periods longer than 100 s. Although there is a chance that some of these systems are neutron stars, we expect that most of them belong to the much-larger population of magnetically-accreting white dwarfs, either polars or intermediate polars \citep[e.g.,][]{nw89,sch02,rc03,mun03}."
.. Accreting white dwarfs typically have luuinosities of 107—Ll. so that given their count rates. they could be ocated as close as 50 pe (for NMMU J185330.7.012815) or as far as 5 kpc (for NMMU. J121129.7.630107).," Accreting white dwarfs typically have luminosities of $10^{30}-10^{32}$, so that given their count rates, they could be located as close as 50 pc (for XMMU J185330.7–012815) or as far as 5 kpc (for XMMU J124429.7–630407)."
 As members of the local Calactic ncieliborliood. they will be distributed over the ecutive slaw. not just within [b|57.. our targeted survey of the Galactic plaue is iof particularly efficieut at finding cataclysmic variables.," As members of the local Galactic neighborhood they will be distributed over the entire sky, not just within $|b|$$<$, our targeted survey of the Galactic plane is not particularly efficient at finding cataclysmic variables."
 Therefore. we do not discuss them further.," Therefore, we do not discuss them further."
 Iu the context of a search for maeguctars. it ix notable hat no new source was found to exhibit periodic variability with periods iu the rauge of known imagnuetars hat are pulsed iu N-ravs. 512 s. To uuderstaud the ack of detections of obvious candidate neutron stars. we reed to compute the fraction of the Galaxy that was covered by our survey.," In the context of a search for magnetars, it is notable that no new source was found to exhibit periodic variability with periods in the range of known magnetars that are pulsed in X-rays, 5–12 s. To understand the lack of detections of obvious candidate neutron stars, we need to compute the fraction of the Galaxy that was covered by our survey."
 If the properties of maguctars as a population were better known. we would do so * assume distributions for thei ΕΠο aud oulse amplitudes. aud carry out a maximau-likelihood or Monte-Carlo calculation to model the observed yopulation (c.e..Faucher-Caenere&Ixaspi2006:Lorimeretal.2006).," If the properties of magnetars as a population were bettern known, we would do so by assuming distributions for their luminosities and pulse amplitudes, and carry out a maximum-likelihood or Monte-Carlo calculation to model the observed population \citep[e.g.,][]{fgk06, lor06}."
. Tlowever. the intrinsic distributions for he huuinosities aud pulse fractious of magnetars are o»orlv coustrainted.," However, the intrinsic distributions for the luminosities and pulse fractions of magnetars are poorly constrainted."
 Some guidauce cau be obtained roni models that explain the pulsatiousas originating roni single bright spots on their surfaces;, Some guidance can be obtained from models that explain the pulsationsas originating from single bright spots on their surfaces.
 Ozel(2002) fud that the fractional amplitudes of pulsations are argest when the hot spot is located ou the equator. aud viewed from the equator.," \citet{ozel02}
 find that the fractional amplitudes of pulsations are largest when the hot spot is located on the equator, and viewed from the equator."
 However. the amplitude drops veh when the spot aud viewer have a latitude >50°.," However, the amplitude drops by $\approx$ when the spot and viewer have a latitude $>$."
". ""Therefore. we roughly estimate that any given magnetar will be easily detectable over 265% of the sk."," Therefore, we roughly estimate that any given magnetar will be easily detectable over $\approx$ of the sky."
 Uufortuutelv. as we describe below. the luminosities of magnetars are highlv variable. aud cannot be predicted by first principles because the mechanism causing the variability is uot understood (6...Woodsetal.2001:Minoetal. 2007).," Unfortuntely, as we describe below, the luminosities of magnetars are highly variable, and cannot be predicted by first principles because the mechanism causing the variability is not understood \citep[e.g.,][]{wood04, mun07}."
. Therefore. in the following we oulv preseut some representativo cases.," Therefore, in the following we only present some representative cases."
 The total Galactic populations for our fiducial examples are then calculated in two steps. first computing the depth along the Iinc-ofsieht through the Galaxy to which our observatious were scusitive. aud second cstimating the fraction of the stellar mass in the Galactic spiral aris that was euclosed by our observations.," The total Galactic populations for our fiducial examples are then calculated in two steps, first computing the depth along the line-of-sight through the Galaxy to which our observations were sensitive, and second estimating the fraction of the stellar mass in the Galactic spiral arms that was enclosed by our observations."
 We compute the depth (D) through the Galaxy that cach observation was seusitive for any given hunuinositv (Lx) and limiting total umber of counts (Cu) frou: where Gtar(Null.b.D]) is the couversion factor between flux aud count rate for cach detector.," We compute the depth $D$ ) through the Galaxy that each observation was sensitive for any given luminosity $L_{\rm X}$ ) and limiting total number of counts $C_{\rm lim}$ ) from: where $\xi_{\rm det}(N_{\rm H}[l,b,D])$ is the conversion factor between flux and count rate for each detector."
 This factor depends additionally upon the Galactic absorption Nyy. which iu turn is a function of the distance D to a source and its position iu the Galactic plane. 7.b.," This factor depends additionally upon the Galactic absorption $N_{\rm H}$ , which in turn is a function of the distance $D$ to a source and its position in the Galactic plane, $l,b$."
 We computed FONT)for both the AACIS-I and for the EEPIC pu behind the medimm &lter using the Portable. Tuteractive Milti-Missiou assimine several trial spectra aud a rauge of Ny.," We computed $f(N_{\rm H})$for both the ACIS-I and for the EPIC pn behind the medium filter using the Portable, Interactive Multi-Mission assuming several trial spectra and a range of $N_{\rm H}$."
 We have neglected some other factors that do not siguificautlv affect our results. the choice of filters for (fan 25% effect on £). aud livdrocarbon build-up on t[ume ACIS (negligible for sources with NgZ1077 2).," We have neglected some other factors that do not significantly affect our results, the choice of filters for (an $\approx$ effect on $\xi$ ), and hydrocarbon build-up on the ACIS (negligible for sources with $N_{\rm
H}$$\ga$$10^{22}$ $^{-2}$ )."
 Vienctting as à function of offset from the aimi point is a stuall effect forChandra. reducing the count rate from a source by 220% at au offset of s...," Vignetting as a function of offset from the aim point is a small effect for, reducing the count rate from a source by $\approx$ at an offset of ."
 We have neglected, We have neglected
"be, this choice first advocated by is supported by laboratory experiments where the instability takes the form of salt fingers (?).","be, this choice first advocated by is supported by laboratory experiments where the instability takes the form of salt fingers ."
". Also and contrary to the “blob assumption"", the “finger prescription"" leads to a very good description of the surface abundances in low-metallicity stars as shown in CZ07, as well as in solar-metallicity stars as will be discussed in 4."," Also and contrary to the “blob assumption"", the “finger prescription"" leads to a very good description of the surface abundances in low-metallicity stars as shown in CZ07, as well as in solar-metallicity stars as will be discussed in 4."
 Unfortunatly and as mentionned by the 3D simulation by did not have the resolution to give clues on the aspect ratio of the fingers., Unfortunatly and as mentionned by the 3D simulation by did not have the resolution to give clues on the aspect ratio of the fingers.
" As a test we have however run a 1.25 Me model without rotation-induced mixing but with C,—104 instead of the value of 10? used in all the other computations presented in the present paper.", As a test we have however run a 1.25 $_{\odot}$ model without rotation-induced mixing but with $_{\rm t} = 10^4$ instead of the value of $10^3$ used in all the other computations presented in the present paper.
 The predictions for the evolution of the surface abundances up to the RGB tip are shown in Fig.6 (red lines in left panels) and 10.., The predictions for the evolution of the surface abundances up to the RGB tip are shown in \ref{fig:surfaceabundances1p25} (red lines in left panels) and \ref{fig:Li_1p25_V0_Ct1e3_Ct1e4}.
" As expected, increasing the thermohaline diffusion coefficient by a factor of 10 leads to faster and substantially stronger processing of material on the RGB: At the RGB tip, the surface abundances of ?He and of ""Li are reduced respectively by a factor of 2 and by ~ 1.5 dex compared to the C,—10? assumption."," As expected, increasing the thermohaline diffusion coefficient by a factor of 10 leads to faster and substantially stronger processing of material on the RGB: At the RGB tip, the surface abundances of $^3$ He and of $^7$ Li are reduced respectively by a factor of 2 and by $\sim$ 1.5 dex compared to the $_{\rm t} = 10^3$ assumption."
 The impact on the carbon and oxygen isotopic ratios and on the surface abundance of !N is more moderate., The impact on the carbon and oxygen isotopic ratios and on the surface abundance of $^{14}$ N is more moderate.
 Even in that case there remains enough ?He to drive thermohaline mixing when the star is on the TP-AGB., Even in that case there remains enough $^3$ He to drive thermohaline mixing when the star is on the TP-AGB.
" The Li production during that phase is higher than in the Οι=10? case, with the final surface abundance N(Li)=2 instead of 0.9."," The Li production during that phase is higher than in the $_{\rm t} = 10^3$ case, with the final surface abundance N(Li)=2 instead of 0.9."
 The final ?He abundance and carbon isotopic ratio are 1.8x107* (in mass fraction) and 8 respectively (instead of 3.15x107 and 9.65)., The final $^3$ He abundance and carbon isotopic ratio are $1.8 \times 10^{-4}$ (in mass fraction) and 8 respectively (instead of $3.15 \times 10^{-4}$ and 9.65).
 In the present computations we have not included the effects of atomic diffusion., In the present computations we have not included the effects of atomic diffusion.
" In particular we do not consider radiative levitation that may lead to accumulation of heavy elements and thus to thermohaline instability in the outer layers of peculiar, slowly-rotating main sequence A-type stars?).."," In particular we do not consider radiative levitation that may lead to accumulation of heavy elements and thus to thermohaline instability in the outer layers of peculiar, slowly-rotating main sequence A-type stars."
" This simplification has no effect on our conclusions, since the thermohaline instability induced by iron accumulation affects only the very external regions of these atypical main sequence stars and has no direct impact on the nuclear burning occuring much deeper inside the star, nor on the RGB chemical properties."," This simplification has no effect on our conclusions, since the thermohaline instability induced by iron accumulation affects only the very external regions of these atypical main sequence stars and has no direct impact on the nuclear burning occuring much deeper inside the star, nor on the RGB chemical properties."
" We do not consider either the effect of atomic diffusion on the RGB, although pointed out that at that phase He gravitational settling may eventually lead to a larger µ- inversion than ?He-burning on the outskirts of the HBS."," We do not consider either the effect of atomic diffusion on the RGB, although pointed out that at that phase $^4$ He gravitational settling may eventually lead to a larger $\mu$ -inversion than $^3$ He-burning on the outskirts of the HBS."
" In their computations, however, thermohaline mixing is not taken into account."," In their computations, however, thermohaline mixing is not taken into account."
 Consequently the effects of concentration variations on µ they get from pure atomic diffusion are maximum compared to reality where thermohaline mixing (induced by ?He-burning and eventually by He-settling) counteracts atomic diffusion., Consequently the effects of concentration variations on $\mu$ they get from pure atomic diffusion are maximum compared to reality where thermohaline mixing (induced by $^3$ He-burning and eventually by $^4$ He-settling) counteracts atomic diffusion.
" Michaud and collaborators have estimated that a value of Dine of the order of 107 cm? s~! is able to substantially reduce (by a factor of 10) the small gradients of He caused by atomic diffusion on the RGB for a 0.95Mo, Z=0.004 model."," Michaud and collaborators have estimated that a value of $_{\rm thc}$ of the order of $^7$ $^2$ $^{-1}$ is able to substantially reduce (by a factor of 10) the small gradients of He caused by atomic diffusion on the RGB for a $_{\odot}$, Z=0.004 model."
 Given that this number is smaller than Di obtained in our RGB models (see Fig., Given that this number is smaller than $_{\rm thc}$ obtained in our RGB models (see Fig.
" 4 and 9)), we can safely assume that the effects of atomic diffusion must be wiped out by turbulence and that ?He-burning is the dominating process inducing thermohaline instability between the HBS and the convective envelope in RGB stars."," \ref{fig:Dthc_X_1p25} and \ref{fig:Dtot_Dthc_1p25_105_deltaM}) ), we can safely assume that the effects of atomic diffusion must be wiped out by turbulence and that $^3$ He-burning is the dominating process inducing thermohaline instability between the HBS and the convective envelope in RGB stars."
" We are aware that some He settling may remain even under the counteracting action of thermohaline mixing, although this should be confirmed by computations that are out of the scope of the present paper."," We are aware that some $^4$ He settling may remain even under the counteracting action of thermohaline mixing, although this should be confirmed by computations that are out of the scope of the present paper."
" One may note, however, that this should simply slightly re-inforce the LL-inversion induced by ?He-burning (although to a much lower extent than in Michaud's computations), and thus strengthen the thermohaline transport compared to the present models."," One may note, however, that this should simply slightly re-inforce the $\mu$ -inversion induced by $^3$ He-burning (although to a much lower extent than in Michaud's computations), and thus strengthen the thermohaline transport compared to the present models."
" Table 1 gives the luminosity of the bump as well as the luminosity Let, at which the thermohaline instability ""contacts"" the base of the convective envelope for all the low-mass stellar models computed both without and with rotation for the present study."," Table 1 gives the luminosity of the bump as well as the luminosity $_{\rm c, th}$ at which the thermohaline instability “contacts"" the base of the convective envelope for all the low-mass stellar models computed both without and with rotation for the present study."
" As we have just seen, for RGB stars less massive than ~1.5 Mo, thermohaline mixing starts changing the surface abundances soon after the bump."," As we have just seen, for RGB stars less massive than $\sim$ 1.5 $_{\odot}$, thermohaline mixing starts changing the surface abundances soon after the bump."
" However, for RGB stars with initial mass higher than 1.5 Mo computed without rotation-induced mixing, the thermohaline instability is long quenched into a very thin region, and is able to connect the external wing of the HBS with the convective envelope only when the star reaches already very high luminosity, close from"," However, for RGB stars with initial mass higher than 1.5 $_{\odot}$ computed without rotation-induced mixing, the thermohaline instability is long quenched into a very thin region, and is able to connect the external wing of the HBS with the convective envelope only when the star reaches already very high luminosity, close from"
"is modelled νvith re.=6"" and i3=0.65.",is modelled with $r_c = 6''$ and $\beta =0.65$.
" This result is in goox agreement with the fit ο NGC 1399 by O'Sullivan (2003). who find ες=6.6£0.6"" aud 3=0.59+0.1. althougl they use au elliLrοσα] beta model with axis ratio 1.23 ratier than our splerically syiumetric oue."," This result is in good agreement with the fit to NGC 1399 by O'Sullivan (2003), who find $r_c = 6.6 \pm 0.6''$ and $\beta=0.59 \pm 0.1$, although they use an elliptical beta model with axis ratio $1.23$ rather than our spherically symmetric one."
 Surface brightness profiles at. larger radii have been measured by Joues (1995) aud Paolillo (2003) using ROSAT PSPC «ata., Surface brightness profiles at larger radii have been measured by Jones (1995) and Paolillo (2003) using ROSAT PSPC data.
" Joues (1997) found the surface xiglituess xolile beyond the core of NGC 1399 well 'epresented by a single beta model wit1 core racdius re=1"" and 820.35 out to a radius of 0020 kkpe).", Jones (1997) found the surface brightness profile beyond the core of NGC 1399 well represented by a single beta model with core radius $r_c = 45''$ and $\beta = 0.35$ out to a radius of $40'$ $220$ kpc).
 Paolilo (2003) modelle Lihe surface xiehtuess profile of NGC 1399 and the Foriax IC with a three component beta nodel. whose hird (cluster) component dominated emission beyond L7.," Paolillo (2003) modelled the surface brightness profile of NGC 1399 and the Fornax ICM with a three component beta model, whose third (cluster) component dominated emission beyond $7'$."
 Their model is consistent with the model ‘Jones (1997) lor radii rs 200kkpce. where tie ROSAT PSPC corrections are well kOWLL. out. falls off 1uore rapidly at lareer raclii.," Their model is consistent with the model of Jones (1997) for radii $r \lesssim 200$ kpc, where the ROSAT PSPC corrections are well known, but falls off more rapidly at larger radii."
 Similarly. we find our daa equally well described by either a two or three component beta nodel over he radial rauge of our observation.," Similarly, we find our data equally well described by either a two or three component beta model over the radial range of our observation."
" The left pauel of Figure 6 models the data with a wo component beta model wlere the outer component is parameterized by r.=125"" and 38=0.35. iereafter called ICM. as fourd by Jones (1997)."," The left panel of Figure \ref{fig:n1399rprof} models the data with a two component beta model where the outer component is parameterized by $r_c=45''$ and $\beta=0.35$, hereafter called ICM1, as found by Jones (1997)."
 The right panel shows a {νου component )ela moclel fit to the saue data. where the surface brightuess at large radii is described by the sum of a central compotent with (ry. 3) the same as above aud two additioual components. the," The right panel shows a three component beta model fit to the same data, where the surface brightness at large radii is described by the sum of a central component with $r_c, \beta$ ) the same as above and two additional components, the"
"for quiet Sun | intensity of such values reported by Magoetal.(LOTS) πας used as a natural ""standard light source for absolute radiomoetric calibrations of SERTS-59. SERTS-91. SERTS-93. aud SERTS-95 (Thomas&Neupert1991:Brosiusctal.1996:Brosius.Davila.&Thomas— 19098b).","for quiet Sun + intensity of such values reported by \citet{man78} was used as a natural “standard” light source for absolute radiometric calibrations of SERTS-89, SERTS-91, SERTS-93 and SERTS-95 \citep{tho94, bro96, bro98b}."
. SERTS-9T was civectly calibrated at RAL in the same facility used to characterize the CDS aud EUNIS instimueuts. and provided the calibration update for CDS NIS-l first-order and NIS-2 second-order lines.," SERTS-97 was directly calibrated at RAL in the same facility used to characterize the CDS and EUNIS instruments, and provided the calibration update for CDS NIS-1 first-order and NIS-2 second-order lines."
 SERTS-97pointed at two locatious diving its observation (Swartzctal. 1999)., SERTS-97pointed at two locations during its observation \citep{swa99}.
. The slit position iu pointing 1 was in the cuet region with average intensity of τις cre temτα |. while it covered the “quiet suzroundines” of an AR in pointing 2 with average intensity 8270 ore tem αι | (Brosiusetal.20001).," The slit position in pointing 1 was in the quiet region with average intensity of 7400 erg $^{-1}$ $^{-2}$ $^{-1}$, while it covered the “quiet surroundings"" of an AR in pointing 2 with average intensity 8270 erg $^{-1}$ $^{-2}$ $^{-1}$ \citep{bro00b}."
 The quict-Sun radiauce measured by SERTS-97 is consistent with thei value measured near the disk ceuter w Mangoetal.(1978). from Skvlab. aud is also well consistent with those measured by CDS NIS 2 during 19961998 (e.g.Brekkeetal.2000:Warren—-2005: 2006).," The quiet-Sun radiance measured by SERTS-97 is consistent with the value measured near the disk center by \citet{man78} from Skylab, and is also well consistent with those measured by CDS NIS 2 during 1996–1998 \citep[e.g.][]{bre00, war05, brk06}."
" However, we fud that the quiet Sun radiances uecasured by EUNIS-07 on the order of 5000 cre stem js to which is about a factor of L.L smaller han that measured by SERTS-97 aud about a factor of 1.6 smaller than the old measurements in 1960τος (see Table 5))."," However, we find that the quiet Sun radiances measured by EUNIS-07 on the order of 5000 erg $^{-1}$ $^{-2}$ $^{-1}$, which is about a factor of 1.4 smaller than that measured by SERTS-97 and about a factor of 1.6 smaller than the old measurements in 1960–70s (see Table \ref{tabhe}) )."
 Note that the old measurements iuclude he blending cussion from line. but the blending vpically contributes less than of the total intensity of these two lines in the quiet Sun. so cannot explain the ie difference from the EUNIS-07 measurement.," Note that the old measurements include the blending emission from line, but the blending typically contributes less than of the total intensity of these two lines in the quiet Sun, so cannot explain the big difference from the EUNIS-07 measurement."
 Based ou the lone-teriu monitoriug of CDS NIS ivraciances roni 1998 to 2010. DelZanua&Audretta(2011) sugeested that the Skvlab values of the 301 line in the quiet Sun were overestimated. aud so cid for hose by SERTS-59. SERTS-91. SERTS-93 aud SERTS-95 whose absolute radiometric calibration was based on he Skylab measurements.," Based on the long-term monitoring of CDS NIS irradiances from 1998 to 2010, \citet{del11} suggested that the Skylab values of the 304 line in the quiet Sun were overestimated, and so did for those by SERTS-89, SERTS-91, SERTS-93 and SERTS-95 whose absolute radiometric calibration was based on the Skylab measurements."
" Whereas the large difference vetween the SERTS-97 and EUNIS-07 iicasurenmeuts which were both based on the direct lab-calibration sugeests that the large dispersion of measurements roni different iustruimnents may be partially ascribed to rue variations depending on observed locations if the average is limited in a small FOV. and on observing ines (e.g. differcut phases of a solar ονο]ο, or cdiffercut solar cycles}."," Whereas the large difference between the SERTS-97 and EUNIS-07 measurements which were both based on the direct lab-calibration suggests that the large dispersion of measurements from different instruments may be partially ascribed to true variations depending on observed locations if the average is limited in a small FOV, and on observing times (e.g. different phases of a solar cycle, or different solar cycles)."
" For example. the iucusity of the 301 lue in ""quiet surroundings” of an active region lay be siguificant larger than that iu the very quiet region."," For example, the intensity of the 304 line in “quiet surroundings"" of an active region may be significant larger than that in the very quiet region."
" EUNIS-06 showed that the ""quiet surroundigs have the values of 8OO0 ere eii Zr. |; while the very"," EUNIS-06 showed that the “quiet surroundings"" have the values of $-$ 8000 erg $^{-1}$ $^{-2}$ $^{-1}$ , while the very"
as θ]οι Or Εριους) in the above analysis.,as $\theta_{jet}$ or $\epo$ ) in the above analysis.
" The inclusion of all 33 bursts (by fixing the parameters with lower or upper limits to the values given) in G07, however, results in an even higher dispersion and lower correlation coefficient in the Ghirlanda relation as compared to the Amati relation: TK,A=0.67+0.07(5.60) TK,¢=0.66+0.07(5.50) with oa—0.18 σας0.23."," The inclusion of all 33 bursts (by fixing the parameters with lower or upper limits to the values given) in G07, however, results in an even higher dispersion and lower correlation coefficient in the Ghirlanda relation as compared to the Amati relation: $\tau_{K,A}=0.67\pm 0.07 ~(5.6\sigma)$ $\tau_{K,G}=0.66\pm 0.07 ~(5.5\sigma)$ with $\sigma_{A}=0.18$ $\sigma_{G}=0.23$."
" The same arguments in a yet stronger form hold for thecomparison of the collimation-corrected peak luminosity (Ly) with Ep,ine correlation and the Liso—Ep,ine relation (Ghirlanda et al.", The same arguments in a yet stronger form hold for thecomparison of the collimation-corrected peak luminosity $L_{\gamma}$ ) with $\epi$ correlation and the $L_{iso}-\epi$ relation (Ghirlanda et al.
" 2005b, hereafter G05b)."," 2005b, hereafter G05b)."
respectively). How important are the «0.696 of certain outliers to the Ghirlanda relation?, How important are the $<$ of certain outliers to the Ghirlanda relation?
" Unlike the case for the Amati relation, the method given by NP05a to determine the number of certain outliers, cannot be regarded as rigorous test of the Ghirlanda relation, since it requires a aknowledge of the jet opening angle distribution function as well as the redshift distribution of the bursts."," Unlike the case for the Amati relation, the method given by NP05a to determine the number of certain outliers, cannot be regarded as a rigorous test of the Ghirlanda relation, since it requires a knowledge of the jet opening angle distribution function as well as the redshift distribution of the bursts."
 Several attempts have been made so far to determine the distribution of jet opening angles (e.g. Frail et al., Several attempts have been made so far to determine the distribution of jet opening angles (e.g. Frail et al.
 2001; Norris 2001; Ghirlanda et al., 2001; Norris 2001; Ghirlanda et al.
 2005a; Guetta et al., 2005a; Guetta et al.
" 2005; Friedman Bloom 2005), even given the sparse number of bursts with measured jet opening angles."," 2005; Friedman Bloom 2005), even given the sparse number of bursts with measured jet opening angles."
" However, as indicated by Band Preece (2005), also by Perna, Sari Frail (2003), a major problem with the current observed distribution of 6;., is that it is affected by another type of selection effect on its head and tail (i.e. very high and very low θ1ει). which is related to the current limited ability of observing very early and late breaks in the afterglow evolution of the bursts."," However, as indicated by Band Preece (2005), also by Perna, Sari Frail (2003), a major problem with the current observed distribution of $\theta_{jet}$ is that it is affected by another type of selection effect on its head and tail (i.e. very high and very low $\theta_{jet}$ ), which is related to the current limited ability of observing very early and late breaks in the afterglow evolution of the bursts."
" Nevertheless, all obtained distribution functions imply a range of θες«40° for the jet opening angle with the peak of the distributions being around 5?—10?."," Nevertheless, all obtained distribution functions imply a range of $\theta_{jet}<40^{\circ}$ for the jet opening angle with the peak of the distributions being around $5^{\circ}-10^{\circ}$."
" Therefore, the extreme assumption that we made at the beginning of this section (ie. fp=1, corresponding to θ1οι= 90°) in order to determine the number of outliers to the Ghirlanda relation appears to be unrealistically generous."," Therefore, the extreme assumption that we made at the beginning of this section (i.e. $f_{b}=1$, corresponding to $\theta_{jet}=90^{\circ}$ ) in order to determine the number of outliers to the Ghirlanda relation appears to be unrealistically generous."
" By this, we have assumed that the outflows of all bursts are essentially isotropic."," By this, we have assumed that the outflows of all bursts are essentially isotropic."
" Even if the relativistic outflows are not highly collimated, some beaming is expected in most cases, since the energy channels mainly along the rotation axis of the inrushing material into the newly created black hole (Woosley, 1993)."," Even if the relativistic outflows are not highly collimated, some beaming is expected in most cases, since the energy channels mainly along the rotation axis of the inrushing material into the newly created black hole (Woosley, 1993)."
" We therefore conclude that the use of fj;=1 in the method given by NP05a, severely underestimates the number of outliers to the Ghirlanda relation."," We therefore conclude that the use of $f_{b}=1$ in the method given by NP05a, severely underestimates the number of outliers to the Ghirlanda relation."
" In order to show how the apparent consistency of the bursts with Ghirlanda relation exacerbates using f,<1, we also find the Ghirlanda relation limit at >3c using the latest update of the relation (G07) and assuming 0;4=25? as the upper value of the jet opening angle — twice as large as the largest reported angle in the GRB sample of G07 — for which we find inconsistency given the BATSE sample of LGRBs considered in this work."," In order to show how the apparent consistency of the bursts with Ghirlanda relation exacerbates using $f_{b}<1$, we also find the Ghirlanda relation limit at $>3\sigma$ using the latest update of the relation (G07) and assuming $\theta_{jet} = 25^{\circ}$ as the upper value of the jet opening angle – twice as large as the largest reported angle in the GRB sample of G07 – for which we find inconsistency given the BATSE sample of LGRBs considered in this work."
 Another consistency check can be performed by estimating the beaming fractions (fy) of bright BATSE LGRBs via the relation proposed by Norris (2001) between the spectral lag of LGRBs and their beaming fractions., Another consistency check can be performed by estimating the beaming fractions $f_{b}$ ) of bright BATSE LGRBs via the relation proposed by Norris (2001) between the spectral lag of LGRBs and their beaming fractions.
" Even though we make generous assumptions in the calculation of the number of certain outliers, we find at least 34% of 1310 bright BATSE LGRBs to be certain >3c outliers to the Ghirlanda relation (Eqn."," Even though we make generous assumptions in the calculation of the number of certain outliers, we find at least $34\%$ of 1310 bright BATSE LGRBs to be certain $>3\sigma$ outliers to the Ghirlanda relation (Eqn."
 3 of G07)., 3 of G07).
" In addition, the redshift that maximizes the redshift-dependent term A(z,o,8,6,c) of NPO05a's method in equation is at Zmas>10 for the Ghirlanda relation."," In addition, the redshift that maximizes the redshift-dependent term $A(z,\alpha, \beta, \xi, \sigma)$ of NP05a's method in equation is at $z_{max}>10$ for the Ghirlanda relation."
 This redshift(3) is much larger than the maximum detectable redshift by BATSE that Cohen Piran (1995) report (z—2.1*1.) assuming no evolution inthe luminosity function of the bursts., This redshift is much larger than the maximum detectable redshift by BATSE that Cohen Piran (1995) report $z=2.1^{+1}_{-0.7}$ ) assuming no evolution inthe luminosity function of the bursts.
" Moreover, Norris Gehrels (2008), have recently estimated the redshift distribution of SWIFT GRBs with unknown redshifts to be the same as the rest (1/3) of the SWIFT sample with measured redshifts resulting in an average z~2.1 for the whole sample of SWIFT bursts."," Moreover, Norris Gehrels (2008), have recently estimated the redshift distribution of SWIFT GRBs with unknown redshifts to be the same as the rest $1/3$ ) of the SWIFT sample with measured redshifts resulting in an average $z\sim 2.1$ for the whole sample of SWIFT bursts."
 Knowing that BATSE LADs were on average 5 times less sensitive than BAT (Fenimore et al., Knowing that BATSE LADs were on average 5 times less sensitive than BAT (Fenimore et al.
" 2004), we can use this as an upper limit for the average redshift of BATSE GRBs which results in an A(z) that is a factor of two smaller than what was used to obtain the limits given in previous paragraph, leading to an increase in the number of certain outliers to the Ghirlanda relation."," 2004), we can use this as an upper limit for the average redshift of BATSE GRBs which results in an $A(z)$ that is a factor of two smaller than what was used to obtain the limits given in previous paragraph, leading to an increase in the number of certain outliers to the Ghirlanda relation."
" 'The consistency checks for this relation are, however, uncertain so long as the accurate unbiased redshift and jet angle distributions of the whole sample of BATSE bursts are not known."," The consistency checks for this relation are, however, uncertain so long as the accurate unbiased redshift and jet angle distributions of the whole sample of BATSE bursts are not known."
" The significant frequency, at over19%,, of >3c outliers to the Amati relation found here is in contrast to the complete lack of outliers reported in G08 and the ~6% outlier frequency reported in N08."," The significant frequency, at over, of $>3\sigma$ outliers to the Amati relation found here is in contrast to the complete lack of outliers reported in G08 and the $\sim6\%$ outlier frequency reported in N08."
 The presently reported outlier frequency is comparable to the ~25% outlier frequency reported by ΝΡθδα but still less than the ~88% outlier frequency reported by Band Preece (2005)., The presently reported outlier frequency is comparable to the $\sim 25\%$ outlier frequency reported by NP05a but still less than the $\sim 88\%$ outlier frequency reported by Band Preece (2005).
" We find a similar outlier frequency to the Liso—Ep,int relation, >8% at >30, which is again in stark contrast to the findings of N08 with only ~0.2% at >3c outliers to this relation."," We find a similar outlier frequency to the $L_{iso}-\epi$ relation, $>8\%$ at $>3\sigma$, which is again in stark contrast to the findings of N08 with only $\sim 0.2\%$ at $>3\sigma$ outliers to this relation."
" All of these discrepancies can be attributable to two sources: either an old version of the Amati relation was being used, or a different subsample of BATSE LGRBs was being used."," All of these discrepancies can be attributable to two sources: either an old version of the Amati relation was being used, or a different subsample of BATSE LGRBs was being used."
 A third possibility raised initially by Ghirlanda et al. (, A third possibility raised initially by Ghirlanda et al. (
"20052), that the apparent high frequency of outliers found by the method given in NP05a, could be due to the assumption of a low scatter in the Amati relation, is rejected.","2005a), that the apparent high frequency of outliers found by the method given in NP05a, could be due to the assumption of a low scatter in the Amati relation, is rejected."
" Were it true, the practical uses of the Amati relation, as well as other correlations intimately connected with, most importantly the Ghirlanda relation, would be limited."," Were it true, the practical uses of the Amati relation, as well as other correlations intimately connected with, most importantly the Ghirlanda relation, would be limited."
" Even if the Amati relation as given by G08 is exact, it is not a significantly more accurate estimator of redshifts than random, since the positions of the bursts relative to these relations appear to be indifferent to a wide range of z. (Left) shows the of a sample of LGRBs used by Figure[]G08 to define the Amati— relation together with their trajectories on this plane for a wide range of redshifts (0.2«z« 20)."," Even if the Amati relation as given by G08 is exact, it is not a significantly more accurate estimator of redshifts than random, since the positions of the bursts relative to these relations appear to be indifferent to a wide range of z. Figure \ref{AG08} ) shows the of a sample of LGRBs used by G08 to define the Amati relation together with their trajectories on this plane for a wide range of redshifts $0.2<z<20$ )."
 Inspection of the plot indicates that the scatter and correlation strength of the relation depends very weakly on the redshifts of the bursts., Inspection of the plot indicates that the scatter and correlation strength of the relation depends very weakly on the redshifts of the bursts.
 The same sample of bursts (black dots in the Left plot of Figure pp» also define a strong correlation in the observer plane (green dots in the Right plot of Figure py., The same sample of bursts (black dots in the plot of Figure \ref{AG08}) ) also define a strong correlation in the observer plane (green dots in the plot of Figure \ref{AG08}) ).
" The trajectories are however, different at lower redshifts and deviate from the Amati relation in"," The trajectories are however, different at lower redshifts and deviate from the Amati relation in"
"cause a black hole to become radio-loud or radio-quiet are currently unclear, but may include black hole mass (Best 2006),, black hole spin (Sikoraetal. 2007),, magnetic field (Ye&Wang2005),, merger history or a combination of these factors.","cause a black hole to become radio-loud or radio-quiet are currently unclear, but may include black hole mass \citep{Best2006}, black hole spin \citep{Sikora07}, , magnetic field \citep{Ye05}, merger history \citep{Wilson95} or a combination of these factors."
 Also missing from this description is the merger status of the two original black holes., Also missing from this description is the merger status of the two original black holes.
" The timescale for the black hole merger is extremely uncertain (e.g.Komossa2003;WilsonSpolaor2011) and so it is not clear at what stage of the above process the black holes merge, nor what the scale effect, if any, of that merger will be."," The timescale for the black hole merger is extremely uncertain \citep[e.g.][]{Komossa03, Wilson95, Khan11, Preto11, Burke11} and so it is not clear at what stage of the above process the black holes merge, nor what the large-scale effect, if any, of that merger will be."
" We note a possible secondary peak discussed in §3, but defer further speculation until we have a higher resolution, higher dynamic-range, VLBI image."," We note a possible secondary peak discussed in 3, but defer further speculation until we have a higher resolution, higher dynamic-range, VLBI image."
" Eventually enough energy is deposited into the cool inflowing gas, both from radio jets and star formation, to heat and disrupt the gas, resulting in the cessation of star-forming activity and a much less efficient accretion mode known as radio-mode or hot-mode accretion."," Eventually enough energy is deposited into the cool inflowing gas, both from radio jets and star formation, to heat and disrupt the gas, resulting in the cessation of star-forming activity and a much less efficient accretion mode known as radio-mode or hot-mode accretion."
" The end product of this process is an elliptical galaxy, with little or no star formation, whose central black hole slowly accretes the hot interstellar medium."," The end product of this process is an elliptical galaxy, with little or no star formation, whose central black hole slowly accretes the hot interstellar medium."
" 00183 appears to be a rare example of an object caught at an early phase of the process of forming a quasar, in the brief period after the merging starburst, as the black hole ramps up to “quasar mode” activity."," 00183 appears to be a rare example of an object caught at an early phase of the process of forming a quasar, in the brief period after the merging starburst, as the black hole ramps up to “quasar mode” activity."
 The radio source has already grown to a luminosity La.scu:=3x10? W Hz! (Roy&Norris1997).., The radio source has already grown to a luminosity $L_{4.8GHz}=3\times10^{25}$ W $^{-1}$ \citep{Roy:1997p29162}.
" A parallel, observational, description is given by Spoonetal.(2007) who propose an evolutionary scenario in which 00183 (located in their class ""2A"") is in a short-lived evolutionary transition from fully obscured buried nuclei to an AGN with a clumpy torus geometry."," A parallel, observational, description is given by \cite{Spoon2007} who propose an evolutionary scenario in which 00183 (located in their class ""2A"") is in a short-lived evolutionary transition from fully obscured buried nuclei to an AGN with a clumpy torus geometry."
" Norrisetal.(2006) identified a class of galaxies, subsequently christened PRONGS (Powerful Radio Objects Nested in Galaxies with Star-formation) by Maoetal. (2010),, that consist of a radio-loud AGN buried within a galaxy that appears at optical/infrared wavelengths as a star-forming galaxy."," \citet{Norris:2006p6530} identified a class of galaxies, subsequently christened PRONGS (Powerful Radio Objects Nested in Galaxies with Star-formation) by \cite{Mao2010}, that consist of a radio-loud AGN buried within a galaxy that appears at optical/infrared wavelengths as a star-forming galaxy."
" Although AGNs are widely found within star-forming galaxies (e.g. Seyfert galaxies), such AGNs are relatively weak (~10?! W !), three orders of magnitude weaker than PRONGS."," Although AGNs are widely found within star-forming galaxies (e.g. Seyfert galaxies), such AGNs are relatively weak $\sim 10^{21}$ W $^{-1}$ ), three orders of magnitude weaker than PRONGS."
" Furthermore, Seyfert galaxies typically fall on the far-infrared-radio correlation (FRC:Royetal.1998) whereas 00183 and other PRONGS are typically ~ 10 times too radio-luminous to follow the FRC."," Furthermore, Seyfert galaxies typically fall on the far-infrared-radio correlation \citep[FRC:][]{Roy98} whereas 00183 and other PRONGS are typically $\sim$ 10 times too radio-luminous to follow the FRC."
" PRONGS are rare in the local Universe, with only two known examples (NGC612&0313-192:Ekersetal.1978; but seem to be increasingly common at high redshifts, with ~50 identified by Mao et al."," PRONGS are rare in the local Universe, with only two known examples \citep[NGC 612 \& 0313-192: ][]{Ekers:1978p30180, Emonts2008, Ledlow:2001p30193,Keel:2006p30187} but seem to be increasingly common at high redshifts, with $\sim 50$ identified by Mao et al."
 in the ATLAS survey of seven square degrees (Norrisetal.2006;Middelberg2008).," in the ATLAS survey of seven square degrees \citep{Norris:2006p6530, Middelberg2008}."
". The PRONGS studied so far are smaller («50 kpc to 200 kpc) than standard radio galaxies, which range from hundreds of kpc to 4.5 Mpc(Schilizzietal.2001),, suggesting that they may be either young or frustrated radio-loud galaxies."," The PRONGS studied so far are smaller $< $ 50 kpc to 200 kpc) than standard radio galaxies, which range from hundreds of kpc to 4.5 \citep{Schilizzi01}, suggesting that they may be either young or frustrated radio-loud galaxies."
 00183 is clearly an extreme example of the class of PRONGS., 00183 is clearly an extreme example of the class of PRONGS.
" If, as Maoetal.(2010) suggest, PRONGS are an early evolutionary stage of radio-loud galaxies, then 00183 may represent a short-lived extreme phase at the start of this process."," If, as \citet{Mao2010} suggest, PRONGS are an early evolutionary stage of radio-loud galaxies, then 00183 may represent a short-lived extreme phase at the start of this process."
 Gigahertz-Peaked Spectrum (GPS) and Compact Steep Spectrum (CSS) sources are similar to PRONGS in that they have a very small but powerful radio AGN at their centre., Gigahertz-Peaked Spectrum (GPS) and Compact Steep Spectrum (CSS) sources are similar to PRONGS in that they have a very small but powerful radio AGN at their centre.
" GPS sources are typically < 1 kpc in size, and are widely thought to mark the earliest evolutionary phase of large-scale radio sources (Polatidis&Conway2003;Tinti&DeZotti2006;Fanti 2009)."," GPS sources are typically $<$ 1 kpc in size, and are widely thought to mark the earliest evolutionary phase of large-scale radio sources \citep{Polatidis03, Tinti06, Fanti09}."
". CSS sources are one to several tens of kpc in size (O’Dea1998;Snellenεἰal.1998;Randalletal.2011) and represent an intermediate stage between GPS sources and the largest radio sources, FRI/II galaxies (Snellenetal.1999)."," CSS sources are one to several tens of kpc in size \citep{ODea:1998p10573, Snellen:1998, Randall2011} and represent an intermediate stage between GPS sources and the largest radio sources, FRI/II galaxies \citep{Snellen99}."
". PRONGS differ from CSS/GPS sources in that they are immersed in a star-forming galaxy, whereas most CSS/GPS sources are hosted by luminous red galaxies or quasars (O’Dea1998;Randalletal. 2011)."," PRONGS differ from CSS/GPS sources in that they are immersed in a star-forming galaxy, whereas most CSS/GPS sources are hosted by luminous red galaxies or quasars \citep{ODea:1998p10573, Randall2011}."
". CSS sources have a steep (a<--0.δ) spectral index across the GHz frequency range, while GPS sources reach a maximum brightness at a few GHz, with the spectral index becoming positive below the maximum (Randalletal. 2011)."," CSS sources have a steep $\alpha < -0.8$ ) spectral index across the GHz frequency range, while GPS sources reach a maximum brightness at a few GHz, with the spectral index becoming positive below the maximum \citep{Randall2011}."
". The positive spectral index at low frequencies is thought to be caused by synchrotron self absorption, although free-free absorption may also be significant (Fanti 2009)."," The positive spectral index at low frequencies is thought to be caused by synchrotron self absorption, although free-free absorption may also be significant \citep{Fanti09}."
. Fig., Fig.
 4 shows the spectral energy distribution (SED) of 00183., \ref{fig:figsed} shows the spectral energy distribution (SED) of 00183.
" 00183 is intermediate between these two classes, with the spectrum noticeably flattening at low frequencies without actually reaching a maximum."," 00183 is intermediate between these two classes, with the spectrum noticeably flattening at low frequencies without actually reaching a maximum."
 We can estimate whether free-free absorption could be causing the observed turnover in this source., We can estimate whether free-free absorption could be causing the observed turnover in this source.
" We assume a constant synchrotron spectral index a=—1.38 (i.e. the value at high frequencies), and a flux density of 14.7 mJy at 19.513 GHz, which implies an un-absorbed synchrotron flux density of 1120 mJy at 843 MHz."," We assume a constant synchrotron spectral index $\alpha = -1.38 $ (i.e. the value at high frequencies), and a flux density of 14.7 mJy at 19.513 GHz, which implies an un-absorbed synchrotron flux density of 1120 mJy at 843 MHz."
" If the turnover is caused by free-free absorption by the surrounding starburst, modelled as a foreground slab of ionised gas, then the slab has an opacity of ~ 1 at 843 MHz."," If the turnover is caused by free-free absorption by the surrounding starburst, modelled as a foreground slab of ionised gas, then the slab has an opacity of $\sim$ 1 at 843 MHz."
" Assuming an electron temperature of 8000K, and an electron density of 10° to 10* cm? (Anantharamaiahetal.1997),, the required path length to produce the observed spectral flattening is 1.5 to 15 pc, with a covering factor of unity."," Assuming an electron temperature of 8000K, and an electron density of $10^{3}$ to $10^{4}$ $^{-3}$ \citep{Anant97}, the required path length to produce the observed spectral flattening is 1.5 to 15 pc, with a covering factor of unity."
" This is reasonable given the intense starburst, and demonstrates that, at least in this source, the turnover can easily be caused by free-free absorption in the surrounding starburst."," This is reasonable given the intense starburst, and demonstrates that, at least in this source, the turnover can easily be caused by free-free absorption in the surrounding starburst."
" In summary, the radio luminosity, size (1.7 kpc), and spectral shape mark 00183 as similar to CSS and GPS sources, but differing in that it is hosted by a star-forming ULIRG."," In summary, the radio luminosity, size (1.7 kpc), and spectral shape mark 00183 as similar to CSS and GPS sources, but differing in that it is hosted by a star-forming ULIRG."
" According to the standard CSS/GPS scenario (Randalletal.2011), the radio jets have just turned on, and are now boring their way through the dense dust and gas."," According to the standard CSS/GPS scenario \citep{Randall2011}, the radio jets have just turned on, and are now boring their way through the dense dust and gas."
 00183 is surrounded by an enormous mass of cold molecular gas(My2>2.4x10? Mo)) (Norrisetal.2011) so clearly the jets have a difficult task ahead of them., 00183 is surrounded by an enormous mass of cold molecular gas$> 2.4 \times 10^{10} $ ) \citep{Norris11} so clearly the jets have a difficult task ahead of them.
" They will eventually emerge as fully-fledged giant radio lobes, at which point 00183 will probably become a classical FRII galaxy or quasar."," They will eventually emerge as fully-fledged giant radio lobes, at which point 00183 will probably become a classical FRII galaxy or quasar."
for GO-LOT75. the ACS Survey of Galactic Globular Clusters. as described by (2008).,"for GO-10775, the ACS Survey of Galactic Globular Clusters, as described by \citet{an08}."
. The observing strategy in (he current program was designed to follow the identical pattern of exposure times and dithers as GO-10775., The observing strategy in the current program was designed to follow the identical pattern of exposure times and dithers as GO-10775.
 Since Andersonetal.(2003). give an extremely detailed description of the data reduction process. only those aspects that have changed in the interim will be mentioned here.," Since \citet{an08} give an extremely detailed description of the data reduction process, only those aspects that have changed in the interim will be mentioned here."
 Belore performing photometry on the individual images. thev were corrected for charge transfer efficiency using the algorithm developed by Anderson&Beclin(2010).," Before performing photometry on the individual images, they were corrected for charge transfer efficiency using the algorithm developed by \citet{an10}."
. The instrumental photometry was then calibrated to the IST VEGAmag svstem following Bedinet and using (he aperture corrections from Siriannielal.(2005) as described by. Sarajedinielal.(2007) and Andersonetal.(2008)., The instrumental photometry was then calibrated to the HST VEGAmag system following \citet{be05} and using the aperture corrections from \citet{si05} as described by \citet{sa07} and \citet{an08}.
. The VEGAÀmasg photometric zeropoints were obtained from Bohlin(2007)., The VEGAmag photometric zeropoints were obtained from \citet{bo07}.
. The photometric catalogs and supporting data files from the reduction process of the 6 GC's presented herein will be made publicly available through the same archive that will host the ACS GC Treasury database., The photometric catalogs and supporting data files from the reduction process of the 6 GCs presented herein will be made publicly available through the same archive that will host the ACS GC Treasury database.
 The F606W.F6061—δι] CAIDs are presented in Figures 1. through 6..," The $F606W,F606W-F814W$ CMDs are presented in Figures \ref{rupr106} through \ref{palmr15}."
 Typical photometric errors are demonstrated. (towards the left side of each figure., Typical photometric errors are demonstrated towards the left side of each figure.
 In cases where eronnc-based V.7 data are available. we also make a direct comparison with the ACS data converted to V. and J using (he empirical (ranusformatious provided by Sirianniοἱal.(2005).," In cases where ground-based $V,I$ data are available, we also make a direct comparison with the ACS data converted to $V$ and $I$ using the empirical transformations provided by \citet{si05}."
. The eround-based comparisons indicate. in all cases. that the LST photometric system maintains a high degree of homogeneity post-SAl4 and that the transformations to V. and J magnitudes perform well.," The ground-based comparisons indicate, in all cases, that the HST photometric system maintains a high degree of homogeneity post-SM4 and that the transformations to ground-based $V$ and $I$ magnitudes perform well."
 The CMDs reveal several striking5 features., The CMDs reveal several striking features.
 In particular. it can be seen that Rarprecht 106 and IC 4499 have strong binary and blue strageler sequences.," In particular, it can be seen that Ruprecht 106 and IC 4499 have strong binary and blue straggler sequences."
 NGC 6426. Palomar 15. and Pyxis show signs5 of differential reddening5 and. indeed. these are (he most recldened clusters in (he present sample.," NGC 6426, Palomar 15, and Pyxis show signs of differential reddening and, indeed, these are the most reddened clusters in the present sample."
 Palomar 15 and Pyxis are sparsely populated clusters: (he red giant branch (RGB) of Pyxis loses coherence for F606<19., Palomar 15 and Pyxis are sparsely populated clusters; the red giant branch (RGB) of Pyxis loses coherence for $F606W \la 19$.
 This section provides a brief review of noteworthy studies targeting the GCs considered in the present study., This section provides a brief review of noteworthy studies targeting the GCs considered in the present study.
 A few basic parameters awe collected in Table 2.., A few basic parameters are collected in Table \ref{basic}. .
The authors are grateful for support. provided. by NASA. erant ADP/NNNOODADO2ZC.⇁⇁ for.⋅ the⊲⊀ Sloan Digital Sky. Survey. (SDSS)on 2005.)usarello been dby (he Alfred M Sloan Foundation. ) Participating Institutions.providi the National Acronautics LT Space Ac- ministration. the National Seicnes 15cm Foundation. the U.S. Department of Enerey. the Japanese AMonbukagakusho. and the Alax Planck Society.,"The authors are grateful for support provided by NASA grant ADP/NNX09AD02G. Funding for the Sloan Digital Sky Survey (SDSS) has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Ad- ministration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society."
 The SDSS Web site is http://wwwesdss.ore/. Phe SDSS is managed by the Astrophysical Research ConsortiumParticipating (ARC) [or the Participat- ing Institutions., The SDSS Web site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participat- ing Institutions.
" The Institutions are The University of Chicago. Fermilab. the Institute for Advanced Study. the Japan Participation Group. “Phe Johns Llopkins University. the lxorecan Scientist. Group. Los Alamos National Laboratory. the AMas-Planek-lostitute for. Astronomy (AIPLA). the Alax-Planck-lnstitute for Astrophysics (AIPA). New Alexico State University. University of Pittsburgh. University of Portsmouth. Princeton University. the United States Naval Observatory, and the University of Washington."," The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, the Korean Scientist Group, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington."
 0.15em Adelman-MeC'arthy ct al.," 0.15cm Adelman-McCarthy et al.,"
 2006. ApJS. 162. 38.," 2006, ApJS, 162, 38."
 V.15cem Adelman-MeCarthy et al., 0.15cm Adelman-McCarthy et al.
 2008. PUN 175. 297.," 2008, ApJS, 175, 297."
" 15cm Bernardi M. 2009. AAS. Al"". 1491."," 0.15cm Bernardi M., 2009, MNRAS, 395, 1491."
 ).15cem Bernardi M. et al;," 0.15cm Bernardi M., et al."
" ""2003. 1882."," 2003, AJ, 125, 1882."
 Vi5em Dernardi AL. lt. Nichol IC... Schneider D... Brinkmann J.. 2005. AJ. 129. 61.," 0.15cm Bernardi M., Sheth R.K., Nichol R.C., Schneider D.P., Brinkmann J., 2005, AJ, 129, 61."
 15cm Dernardi M... Nichol B.C... Sheth B.Ix... Miller C.J.. Brinkmann J.. 2006. XJ. 131. 1288.," 0.15cm Bernardi M., Nichol R.C., Sheth R.K., Miller C.J., Brinkmann J., 2006, AJ, 131, 1288."
 Μια Bernardi M. Hyde J.D.. Sheth RoW... Miller C... Nichol R.C.. 2007. AJ. 133. 1741.," 0.15cm Bernardi M., Hyde J.B., Sheth R.K., Miller C.J., Nichol R.C., 2007, AJ, 133, 1741."
 15cm. Dovlan-Ixolchin. AL. Ala Chung-Pei. Quatacrt E.. 2006. MINRAS. 369. 1081.," 0.15cm Boylan-Kolchin M., Ma Chung-Pei, Quataert E., 2006, MNRAS, 369, 1081."
 15cm Druzual Αίας. and. Charlot S... 2003. NINILAS. 344. 1000.," 0.15cm Bruzual A.G. and Charlot S., 2003, MNRAS, 344, 1000."
 15cm De Lucia G. and Blaizot J.. 2007. NINILAS. 375. 2," 0.15cm De Lucia G. and Blaizot J., 2007, MNRAS, 375, 2."
 lem Di Matteo P.. Pipino A. Lehnert M.D.. Combes E... Semelin D.. 2009. AAA. 499. 427.," 0.1cm Di Matteo P., Pipino A., Lehnert M.D., Combes F., Semelin B., 2009, A, 499, 427."
 15cm Gallazzi A. Charlot S.. Brinchmann J.. White S.D.M.. Tremionti CLA... 2005. AINRAS. 362. 41.," 0.15cm Gallazzi A., Charlot S., Brinchmann J., White S.D.M., Tremionti C.A., 2005, MNRAS, 362, 41."
 ). AL. S.. Brinchmann J.. White S.D.NL.M2006. οNUNMNILAS. 370. MMPen," 0.15cm Gallazzi A., Charlot S., Brinchmann J., White S.D.M., 2006, MNRAS, 370, 1106."
man110 .l5em s D.A.. Tu. 1999. NINILAS.: 623.," 0.15cm Forbes D.A., Ponman T.J., 1999, MNRAS, 309, 623."
 .15em Friaca ολοοι. Verlevieh tJ. 1999. NINILAS. 425. 435.," 0.15cm Friaca A.C.S., Terlevich R.J., 1999, MNRAS, 325, 335."
 Sem Loee D.. Baldry L. Blanton M. Eisenstein D.. 2002. astro-ph/0210394 Sem Livde J. and Bernardi M.. 2009. AINRAS. 394 ," 0.15cm Hogg D., Baldry I., Blanton M., Eisenstein D., 2002, astro-ph/0210394 0.15cm Hyde J. and Bernardi M., 2009, MNRAS, 394, 1978."
Sem Jimenez I... B.. Haiman Z.. Panter D.. Heavens κο 2007. ApJ.Lian669. Ma947.," 0.15cm Jimenez R., Mariangela B., Haiman Z., Panter B., Heavens A.F., 2007, ApJ, 669, 947."
 Sem Jorgensen L.. Al. Wjaergaarc P... 1995. AINRAS. 276. 1341.," 0.15cm rgensen I., Franx M., Kjaergaard P., 1995, MNRAS, 276, 1341."
 Sem Ixo J. and Im M. 2005. Journal of the Ixorean Astronomical Society. 38. 149.," 0.15cm Ko J. and Im M., 2005, Journal of the Korean Astronomical Society, 38, 149."
" ).15em Ixobavashi C..mu"" ,2004. MINAS. "" τμ)."," 0.15cm Kobayashi C., 2004, MNRAS, 347, 740."
 VISMN KoesterMCMn 1.1., 0.15cm Koester B.P. et al.
  Mm ApJ.Pn 660. 239.," 2007, ApJ, 660, 239."
: ≱⊳⋅⋉↛⊔↓∟⋜↧⋯↓∣⋊⊾↓⋜↧↓⊲↦≺ . Gal. DII.p >en∙ aes∙L19. PL.⊀↴⊲eq Capaccioli M..⊲∙⊽⋰↴⊲ Djorgovski S.C.. Funding ApJ. 626.," 0.15cm La Barbera F., Carvalho R.R., Gal R.R., Busarello G., Merluzzi P., Capaccioli M., Djorgovski S.G., 2005, ApJ, 626, L19."
" Barbera has bem"" E. Carvalho II. 2009. ApJ. 699 the"," 0.15cm La Barbera F., Carvalho R.R., 2009, ApJ, 699, L76."
 and Liu ES. Nia NY. Shude M. Wa HL. Dene ZC. 2008. MNILAS. 385. 23.," 0.15cm Liu F.S, Xia X.Y, Shude M., Wu H., Deng Z.G., 2008, MNRAS, 385, 23."
" Sem MoehlertD... VPhomas D.. Saglia 1... Bender I1.. Weener G.. 2003. AA, ae"," 0.15cm MehlertD., Thomas D., Saglia R.P., Bender R., Wegner G., 2003, A, 407, 423."
 a Sem Miller €.. et al.," 0.15cm Miller C., et al."
 2A AJ. di 968.," 2005, AJ, 130, 968."
 Sem Michard 1t... 2005. AA. 451.," 0.15cm Michard R., 2005, A, 441, 451."
 Sem Naab T.. Ikhochfar οι Burkert Α.. 2006. ApJ. 636. 51.," 0.15cm Naab T., Khochfar S., Burkert A., 2006, ApJ, 636, 81."
 5cm Roche N. Bernardi AL. Hye J. 2009. MINAS. 398. 1549 (Paper 1).," 0.15cm Roche N. Bernardi M., Hyde J. 2009, MNRAS, 398, 1549 (Paper I)."
 k15em Rogers D.. Ferreras. LL. Pasquali A. Bernardi AL. Lahay O.. Ixaviraj οι. 2010. MNILCAS. in press (astro-ph1002.0835) Sem Sheth νι. Jimenez lt. Panter B.. Heavens ALF. 2006. ApJ. 650. 1. L25.," 0.15cm Rogers B., Ferreras I., Pasquali A., Bernardi M., Lahav O., Kaviraj S., 2010, MNRAS, in press (astro-ph/1002.0835) 0.15cm Sheth R.K., Jimenez R., Panter B., Heavens A.F., 2006, ApJ, 650, 1, L25."
 Sem Skelton It... Bell E. Somerville It... 2009. ApJ. 699. L9.," 0.15cm Skelton R.E., Bell E., Somerville R.S., 2009, ApJ, 699, L9."
 Sem Spolaor AL. Proctor ILN..Forbes D.. Couch WJ... 2009. ApJ. 691. LI38," 0.15cm Spolaor M., Proctor R.N., Forbes D., Couch W.J., 2009, ApJ, 691, L138."
 Vi5em Suh LL. Jeong H.. Oh Il... Yi S.J. Ferras LL. Schawinski Ix.. 2010. XpJS. in press. (," 0.15cm Suh H., Jeong H., Oh K., Yi S.K, Ferras I., Schawinski K., 2010, ApJS, in press. ("
astro-ph/1002.3424) 15cm Tamura N.. IXobavashi €... Arimoto N.. Ixocdama νι Ἱνου]ί O.. 2000. XJ. 119. 2134.,"astro-ph/1002.3424) 0.15cm Tamura N., Kobayashi C., Arimoto N., Kodama T., Kouji O., 2000, AJ, 119, 2134."
 15cm Tamura N.. Ohta Ix.. 2003. XJ. 126. 596.," 0.15cm Tamura N., Ohta K., 2003, AJ, 126, 596."
 15cm Tamura N.. Ohta Ix.. 2004. MNIUAS. 355. 617.," 0.15cm Tamura N., Ohta K., 2004, MNRAS, 355, 617."
 k15em Tran We-V. van Dokkum DP. Franx AL. Hlinhworth €.. Ixelson D.. Natascha M.. Schreiber E... 2005 ApJ. 627. L25.," 0.15cm Tran K.-V., van Dokkum P., Franx M., Illinhworth G., Kelson D., Natascha M., Schreiber F., 2005, ApJ, 627, L25."
" Vi5em ""ran W.-V.. Moustakas J. Mx ALL. Anthony HL. Bai L.. Zaritsky D. Iautsch 8.J.. 2008. ApJ. 683."," 0.15cm Tran K.-V., Moustakas J., Gonzalez A.H., Anthony H., Bai L., Zaritsky D., Kautsch S.J., 2008, ApJ, 683."
 )15cm van der Wel A. Holden D.. Zirn AAV. Frans AM. Rettura A.. Hlingworth €i. Ford LL. 2008. Ap.J. 68S. 4s.," 0.15cm van der Wel A., Holden B., Zirm A.W., Franx M., Rettura A., Illingworth G., Ford H., 2008, ApJ, 688, 48."
 15cm Wu IL. Shao Z.. Xia N.. Deng Z.. 2005. ApJ. 622. 244.," 0.15cm Wu H., Shao Z., Xia X., Deng Z., 2005, ApJ, 622, 244."
 15cm. Yamauchi Οι. Goto T... 2005.. ΑΝΜο. 359. 1557.," 0.15cm Yamauchi C., Goto T., 2005, MNRAS, 359, 1557."
The increasingly strong evidence that the bursts detected by BeppoSAX originate in galaxies undergoing star formation. and may oceur near or in the star-forming regions themselves. favors the collapsar model and disfavors the binary merger model as the explanation for long. softer. smoother bursts.,"The increasingly strong evidence that the bursts detected by BeppoSAX originate in galaxies undergoing star formation, and may occur near or in the star-forming regions themselves, favors the collapsar model and disfavors the binary merger model as the explanation for long, softer, smoother bursts."
 Simulations of the kicks given to NS-NS and NS-BH binaries by the SNe that form them shows that most binary mergers are expected to occur well outside any galaxy (Bulik Belezynski 1999)., Simulations of the kicks given to NS-NS and NS-BH binaries by the SNe that form them shows that most binary mergers are expected to occur well outside any galaxy (Bulik Belczynski 1999).
 This is particularly the case. given that the GRB host galaxies identified so far have small masses. as discussed earlier. and therefore low escape velocities.," This is particularly the case, given that the GRB host galaxies identified so far have small masses, as discussed earlier, and therefore low escape velocities."
 The fact that all of the optical afterglows of the BeppoSAX bursts are coincident with the disk of the host galaxy therefore also disfavors the binary merger model as the explanation for the long. softer. smoother bursts.," The fact that all of the optical afterglows of the BeppoSAX bursts are coincident with the disk of the host galaxy therefore also disfavors the binary merger model as the explanation for the long, softer, smoother bursts."
 Current models of the bursts themselves fall into three general categories: Those that invoke a central engine. those that invoke internal shock waves in a relativistically expanding wind. and those that invoke a relativistic external shock wave.," Current models of the bursts themselves fall into three general categories: Those that invoke a central engine, those that invoke internal shock waves in a relativistically expanding wind, and those that invoke a relativistic external shock wave."
 Dermer (1999) argued that the external shock wave model explains many of the observed properties of the bursts., Dermer (1999) argued that the external shock wave model explains many of the observed properties of the bursts.
 By contrast. Fenimore (1999; see also Fenimore et al.," By contrast, Fenimore (1999; see also Fenimore et al."
 1999) argued that several features of GRBs. such as the large gaps seen in burst time histories. cannot be explained by the external shock wave model. and that the bursts must therefore be due either to a central engine or to internal shocks in a relativistically expanding wind.," 1999) argued that several features of GRBs, such as the large gaps seen in burst time histories, cannot be explained by the external shock wave model, and that the bursts must therefore be due either to a central engine or to internal shocks in a relativistically expanding wind."
 Either way. the intensity and spectral variations seen during the burst must originate at a central engine.," Either way, the intensity and spectral variations seen during the burst must originate at a central engine."
 This implies that the lifetime of the central engine must in many cases be fuueine2LOO1000 s. which poses a severe difficulty for NS-NS or NS-BH binary merger models. if such models are invoked to explain the long. softer. smoother bursts. and may pose a problem for the collapsar model.," This implies that the lifetime of the central engine must in many cases be $t_{\rm
engine} \gtrsim 100 - 1000$ s, which poses a severe difficulty for NS-NS or NS-BH binary merger models, if such models are invoked to explain the long, softer, smoother bursts, and may pose a problem for the collapsar model."
 Fenimore (1999) reported at this meeting that he finds no evidence of relativistic expansion in the tme histories and spectra of the GRBs themselves. presenting a possible difficulty for the internal shock wave model.," Fenimore (1999) reported at this meeting that he finds no evidence of relativistic expansion in the time histories and spectra of the GRBs themselves, presenting a possible difficulty for the internal shock wave model."
 One puzzle about the bursts themselves is: Why are GRB spectra so smooth?, One puzzle about the bursts themselves is: Why are GRB spectra so smooth?
 The shock synchrotron model agrees well with observed burst spectra., The shock synchrotron model agrees well with observed burst spectra.
" But this agreement is surprising. since strong deviations from the simplest spectral shape are expected due to inverse Compton scattering. and 1f forward and reverse shock contributions to the prompt gamma-ray emission occur simultaneously or at different times (Tavani 1999),"," But this agreement is surprising, since strong deviations from the simplest spectral shape are expected due to inverse Compton scattering, and if forward and reverse shock contributions to the prompt gamma-ray emission occur simultaneously or at different times (Tavani 1999)."
 Another puzzle 1s: Why is the spread in the peak energy Ly of the burst spectra so narrow?, Another puzzle is: Why is the spread in the peak energy $E_{\rm peak}$ of the burst spectra so narrow?
 In the external shock model. this requires that all GRBs have nearly the same ultra-relativistic value of E.," In the external shock model, this requires that all GRBs have nearly the same ultra-relativistic value of $\Gamma$."
" The narrow range in Ej,oak is. dm] anything. more difficult to understand in the internal shock model."," The narrow range in $E_{\rm peak}$ is, if anything, more difficult to understand in the internal shock model."
" If AT/T<<<1 in the relativistic outflow. the range in FL, will be narrow. but then it is hard to understand why most of the energy of the relativistic outflow is dissipated during the burst rather than in the afterglow."," If $\Delta 
\Gamma/\Gamma << 1$ in the relativistic outflow, the range in $E_{\rm
peak}$ will be narrow, but then it is hard to understand why most of the energy of the relativistic outflow is dissipated during the burst rather than in the afterglow."
 Conversely. if AT/T>>1 in the relativistic outflow. most of the energy of the relativistic outflow is dissipated during the burst rather than in the afterglow. but then one expects a wide range of Eos. This is a hint — like the problem discussed earlier that one would expect strong beaming to produce a large special relativistic Doppler redshift. yet this is not seen in burst spectra — that there may be something missing 1n our picture of the dissipation and radiation mechanisms in GRBs.," Conversely, if $\Delta \Gamma/\Gamma >>
1$ in the relativistic outflow, most of the energy of the relativistic outflow is dissipated during the burst rather than in the afterglow, but then one expects a wide range of $E_{\rm peak}$ 's. This is a hint – like the problem discussed earlier that one would expect strong beaming to produce a large special relativistic Doppler redshift, yet this is not seen in burst spectra – that there may be something missing in our picture of the dissipation and radiation mechanisms in GRBs."
 Most theorists GRBs to be significantly beamed — many energetic astrophysical phenomena are (examples include young protostars: the so-called “microquasars.” which are black hole binaries in the Galaxy; radio galaxies: and AGN).," Most theorists GRBs to be significantly beamed – many energetic astrophysical phenomena are (examples include young protostars; the so-called “microquasars,” which are black hole binaries in the Galaxy; radio galaxies; and AGN)."
 And theorists beaming because it saves their models., And theorists beaming because it saves their models.
" Several speakers at this workshop have emphasized these points (see. e.g.. Dar 1999, Fargion 1999, and Rees 1999)."," Several speakers at this workshop have emphasized these points (see, e.g., Dar 1999, Fargion 1999, and Rees 1999)."
 Strong beaming probably requires strong magnetic fields. but no detailed physical model of how this might happen has been put forward as yet.," Strong beaming probably requires strong magnetic fields, but no detailed physical model of how this might happen has been put forward as yet."
 One can ask: Where is the observational evidence for beaming...?, One can ask: Where is the observational evidence for beaming...?
 Fenimore (1999) told us that there is none in the time histories of the bursts themselves., Fenimore (1999) told us that there is none in the time histories of the bursts themselves.
" Worse yet. Greiner (1999) reported that fonp/Fgf,7<m| from an analysis of the ROSAT all sky survey."," Worse yet, Greiner (1999) reported that $f_{\rm
GRB}/f^{\rm X-ray}_{\rm afterglow} \gtrsim 1$ from an analysis of the ROSAT all sky survey."
 This constraint may not be as strong as it appears. because the duration of the temporal exposure in the ROSAT all-sky survey is only a few hundred seconds. and thus the sensitivity of the survey is relatively poor.," This constraint may not be as strong as it appears, because the duration of the temporal exposure in the ROSAT all-sky survey is only a few hundred seconds, and thus the sensitivity of the survey is relatively poor."
 Consequently. soft X-ray afterglows would be detectable by the ROSAT all-sky survey only within a day or so after the burst. when (in the relativistic external shock model of afterglows — see below) the soft X-ray emission is still highly beamed.," Consequently, soft X-ray afterglows would be detectable by the ROSAT all-sky survey only within a day or so after the burst, when (in the relativistic external shock model of afterglows – see below) the soft X-ray emission is still highly beamed."
" Constraints on so-called ""orphan"" optical afterglows. and therefore on the beaming of GRBs. will be strengthened by new low-: SN la searches that will soon be underway."," Constraints on so-called “orphan” optical afterglows, and therefore on the beaming of GRBs, will be strengthened by new $z$ SN Ia searches that will soon be underway."
 These searches will monitor an area of the sky that is roughly ten, These searches will monitor an area of the sky that is roughly ten
Both the spatial ancl kinematic distributions of halo elobular clusters differ from those of halo field stars.,	Both the spatial and kinematic distributions of halo globular clusters differ from those of halo field stars.
 Harris (1976) and Zinn (1985) found that the spatial distribution of the full cluster. system goes as A7 [or 4<Ro«X20kpc. in good agreement with the profile of halo. field stars (Freeman 1996).," Harris (1976) and Zinn (1985) found that the spatial distribution of the full cluster system goes as $R^{-3.5}$ for $4\leq R\leq20 \kpc$ , in good agreement with the profile of halo field stars (Freeman 1996)."
 At smaller radii the profile becomes shallower and [lattens into a core (Ostriker. Binney Saha 1989).," At smaller radii the profile becomes shallower and flattens into a core (Ostriker, Binney Saha 1989)."
 Similarlv. while the distribution of halo field. star orbits appears to have significant radial bias (Beers Sommer-Larsen 1995). the distribution of halo cluster orbits appears to be nearly isotropic refseciorbagun)).," Similarly, while the distribution of halo field star orbits appears to have significant radial bias (Beers Sommer-Larsen 1995), the distribution of halo cluster orbits appears to be nearly isotropic \\ref{sec:orb_dyn}) )."
Ourresullsfromthepresent f ibsalsocchibillhediscrepanegbetweenthespaltialdistribulionskdduilpebesher ampiéicduldbelelistipst, Our results from the present-day fits also exhibit the discrepancy between the spatial distributions of halo clusters and halo field stars.
iblepbwper lawprofilederivedusinglhicMcstelsphercappearsconsiderably because we have included. elusters with 77x4tkpe in the data set., The power-law profile derived using the Mestel sphere appears considerably flatter than $R^{-3.5}$ because we have included clusters with $R\leq 4\kpc$ in the data set.
 Ehe. Exldington sphere best represents the clistribution over the Pull racial range., The Eddington sphere best represents the distribution over the full radial range.
 Lt has a core. density pxROT at small radius. a steep drop bevond 20kpe with density px42.077 and the expected. power-law decline with density px42/7 at intermediate raclii.," It has a core, density $\rho\propto R^{-2.5}$ at small radius, a steep drop beyond $20 \kpc$ with density $\rho\propto R^{-4.5}$ and the expected power-law decline with density $\rho\propto R^{-3.5}$ at intermediate radii."
 Based on the estimates of initial conditions. we conclude that cluster evolution can account for the dillerence between the spatial distributions of halo clusters and field stars.," 	Based on the estimates of initial conditions, we conclude that cluster evolution can account for the difference between the spatial distributions of halo clusters and field stars."
 The estimated. initial density profile px&SosIULS in both spherical and two-component models over the full racial range of the data., The estimated initial density profile $\rho\propto R^{-3.38\pm0.3}$ in both spherical and two-component models over the full radial range of the data.
 This is in good agreement with the halo field star profile px3.20.2! recently determined by Sommer-Larsen Zhen (1990) as well as the conventionally accepted value of 2/7," This is in good agreement with the halo field star profile $\rho\propto
R^{-3.29\pm0.24}$ recently determined by Sommer-Larsen Zhen (1990) as well as the conventionally accepted value of $R^{-3.5}$."
 Evolution also accounts for at least some cilferences in halo cluster and field star kinematics., 	Evolution also accounts for at least some differences in halo cluster and field star kinematics.
 As cliscussed in refsecznit.. the predicted. initial halo cluster population in the 2-component model has a strong radial bias which diminishes over time due to the preferential. evaporation of clusters on eccentric orbits.," As discussed in \\ref{sec:init}, the predicted initial halo cluster population in the 2-component model has a strong radial bias which diminishes over time due to the preferential evaporation of clusters on eccentric orbits."
 Approximately 41% of the kinetic enerey of this component is initially in radial motions., Approximately $41\%$ of the kinetic energy of this component is initially in radial motions.
 Compared to 33% implied. by the isotropy of the observed halo cluster clistribution. this is closer to the value of 54% derived for halo field stars bv Beers Sonmumoer-Larsen (1995) and is roughly consistent with he value of 44% derived by Norris (1986).," Compared to $33\%$ implied by the isotropy of the observed halo cluster distribution, this is closer to the value of $54\%$ derived for halo field stars by Beers Sommer-Larsen (1995) and is roughly consistent with the value of $44\%$ derived by Norris (1986)."
 The preclictec initial clisk population. by contrast. is unlike the observed stellar thick disk.," 	The predicted initial disk population, by contrast, is unlike the observed stellar thick disk."
 Phe estimates indicate hat the present-day high.5 angular5 momentum. population developed from a nearly isotropic initial distribution through he selective evaporation of clusters on. eccentric. orbits., The estimates indicate that the present-day high angular momentum population developed from a nearly isotropic initial distribution through the selective evaporation of clusters on eccentric orbits.
 Although the model. underestimates the size of the disk population. any resulting kinematic bias predicts. higher angular momentum. in the svstem because. lower angular momentum members cannot be distinguished from the halo clusters.," Although the model underestimates the size of the disk population, any resulting kinematic bias predicts higher angular momentum in the system because lower angular momentum members cannot be distinguished from the halo clusters."
 Evidence for a flattened: component with nearly random kinematics may exist in the sample of halo clusters studied by Zinn (1993) and in the halo field star sample stucied by Sommer-Larsen Zhen (1990)., Evidence for a flattened component with nearly random kinematics may exist in the sample of halo clusters studied by Zinn (1993) and in the halo field star sample studied by Sommer-Larsen Zhen (1990).
 Overall. the results of this paper point to a scenario which correlates the origin of halo field stars and. clusters during Galaxy formation.," 	Overall, the results of this paper point to a scenario which correlates the origin of halo field stars and clusters during Galaxy formation."
 The predicted. disk cluster system is less clearly correlated. with observed. disk stellar populations but may be related to an intermediate. phase of the clissipative collapse which is thought to have given tise to the disk (Larson 1990: Zinn 1993)., The predicted disk cluster system is less clearly correlated with observed disk stellar populations but may be related to an intermediate phase of the dissipative collapse which is thought to have given rise to the disk (Larson 1990; Zinn 1993).
 The results clo not contradict merecr-incduced heating of an initially cold disk (Quinn. Lernquist Fullager 1993). provided: that initially circular disk cluster orbits can be isotropized. by he accretion event.," The results do not contradict merger-induced heating of an initially cold disk (Quinn, Hernquist Fullager 1993), provided that initially circular disk cluster orbits can be isotropized by the accretion event."
 Finally. we emphasize that our predictions describe the initial population of clusters which evolve quasi-statically hrough relaxation and tidal heating.," 	Finally, we emphasize that our predictions describe the initial population of clusters which evolve quasi-statically through relaxation and tidal heating."
 Since clusters probably ormed with a range of initial densities. some would have 1).," Since clusters probably formed with a range of initial densities, some would have been prey to rapid tidal disruption (Paper I)."
 However. flatboctbsgnlitcalite of such initial conditions cannot be divined rom the observed. population because. excepting a few clusters such as Pal 5 (Cuclworth 1993). the majority. of observed. clusters must have formed with initial densities which allowed quasi-static evolution and long-term survival.," However, the significance of such initial conditions cannot be divined from the observed population because, excepting a few clusters such as Pal 5 (Cudworth 1993), the majority of observed clusters must have formed with initial densities which allowed quasi-static evolution and long-term survival."
 Consequently. the importance of tidal disruption in shaping the cluster population at an early epoch can be described only through models of the initial conditions of the cluster system in a proto-Galactic or cosmological context (Paper 1).," Consequently, the importance of tidal disruption in shaping the cluster population at an early epoch can be described only through models of the initial conditions of the cluster system in a proto-Galactic or cosmological context (Paper I)."
 Vhe main conclusions of this work are as follows:, 	The main conclusions of this work are as follows:
By design. most of the next-generation panoramic surveys will involve simple continuum imaging.,"By design, most of the next-generation panoramic surveys will involve simple continuum imaging."
 However. many projects will be complemented by ancillary sub-surveys that will accrue more (deeper) imaging and spectroscopic observations over smaller areas.," However, many projects will be complemented by ancillary sub-surveys that will accrue more (deeper) imaging and spectroscopic observations over smaller areas."
 The largest surveys that cover most of the sky will necessarily overlap with fields that have already undergone significant observational investments., The largest surveys that cover most of the sky will necessarily overlap with fields that have already undergone significant observational investments.
 Several of these tthe Great Observatories Origins Deep Survey. Chandra Deep Fields. Cosmological Evolution Survey [COSMOS] tield and the like) have been targeted with deep imaging from virtually all terrestrial and space-based facilities. and often have been subject to extensive spectroscopic campaigns. providing very large. deep redshift catalogues LLilly et 22007).," Several of these the Great Observatories Origins Deep Survey, Chandra Deep Fields, Cosmological Evolution Survey [COSMOS] field and the like) have been targeted with deep imaging from virtually all terrestrial and space-based facilities, and often have been subject to extensive spectroscopic campaigns, providing very large, deep redshift catalogues Lilly et 2007)."
 As time goes on. the interplay between overlapping surveys will become more important as we move towards a truly holistic picture of the sky.," As time goes on, the interplay between overlapping surveys will become more important as we move towards a truly holistic picture of the sky."
 Artiticial neural networks. or more generally the technique of “machine learning’. has been used as a tool in astronomy (ας well as other scientitic disciplines and industrial applications) for some time SStorrie-Lombardi et 11992: Lahav et 1995): the estimation of galaxy redshifts from photometry is a classic example.," Artificial neural networks, or more generally the technique of `machine learning', has been used as a tool in astronomy (as well as other scientific disciplines and industrial applications) for some time Storrie-Lombardi et 1992; Lahav et 1995); the estimation of galaxy redshifts from photometry is a classic example."
 Perhaps the most successful application of neural networks in an astronomical setting in the past few years has been he ‘crowd sourcing’ technique of Galaxy Zoo (Raddick et 22008: Lintott et 22008). which exploits thousands of humans © perform visual classification of galaxies from the SDSS. relying on the superior capabilities of the human brain aareal neura network) for pattern recognition.," Perhaps the most successful application of neural networks in an astronomical setting in the past few years has been the `crowd sourcing' technique of Galaxy Zoo (Raddick et 2008; Lintott et 2008), which exploits thousands of humans to perform visual classification of galaxies from the SDSS, relying on the superior capabilities of the human brain a neural network) for pattern recognition."
 Many of the established machine earning techniques employ supervised learning. where the neura network is trained using a series of input pairs.," Many of the established machine learning techniques employ supervised learning, where the neural network is trained using a series of input pairs."
 A common example is the multi-layer perceptron. where each input pair consists of a vector (a set of photometry for example) and a known outpu (a spectroscopic redshift).," A common example is the multi-layer perceptron, where each input pair consists of a vector (a set of photometry for example) and a known output (a spectroscopic redshift)."
 The network then attempts to find the mapping that successfully converts the input vectors to the requirec output in this sense. it is “supervised” learning.," The network then attempts to find the mapping that successfully converts the input vectors to the required output – in this sense, it is `supervised' learning."
 After training. new input vectors— (e.g. photometry) ean be passed through the network ο predict their output (redshifts. CCollister 22004).," After training, new input vectors (e.g. photometry) can be passed through the network to predict their output (redshifts, Collister 2004)."
 An alternative approach is to use the input vectors themselves o find the mapping. since if such a mapping between parameters (or combinations of parameters) exists. this information should be latent in the input catalogue.," An alternative approach is to use the input vectors themselves to find the mapping, since if such a mapping between parameters (or combinations of parameters) exists, this information should be latent in the input catalogue."
 In this paper. I will describe a specific type of unsupervised machine learning — the Kohonen self-organising map (SOM. 11982. 2001) — as a tool or data mining in astronomy.," In this paper, I will describe a specific type of unsupervised machine learning – the Kohonen self-organising map (SOM, 1982, 2001) – as a tool for data mining in astronomy."
 SOMs have found application in other scientific disciplines. notably geophysics and genetics. and other disparate areas. especially those where some form of »uttern recognition is required.," SOMs have found application in other scientific disciplines, notably geophysics and genetics, and other disparate areas, especially those where some form of pattern recognition is required."
 While there has been some use of self-organisation and SOMs in astronomical applications NuikzmarkmainBodyEnd799mainBodyStart8O0Oneez 22003. 22011). the technique is not in widespread=— use.," While there has been some use of self-organisation and SOMs in astronomical applications N\'u\\tikzmark{mainBodyEnd799}\~\tikzmark{mainBodyStart800}neez 2003, 2011), the technique is not in widespread use."
 In essence. a SOM is a neural network that takes as input a large raining set (in this case large astronomical catalogues). and maps it by a process of competitive learning. where neurons compete to become more like members of the training set.," In essence, a SOM is a neural network that takes as input a large training set (in this case large astronomical catalogues), and maps it by a process of competitive learning, where neurons compete to become more like members of the training set."
 The resulting map is a representation of the topology of the input parameter space. encoding correlations between parameters. and allowing one to visualise the high-dimensional properties of a parameter volume in a low-resolution. lower-dimensional way.," The resulting map is a representation of the topology of the input parameter space, encoding correlations between parameters, and allowing one to visualise the high-dimensional properties of a parameter volume in a low-resolution, lower-dimensional way."
 This self-organised mapping has often been described as a form of non-linear principle component analysis. and is a variant of &-means clustering algorithms.," This self-organised mapping has often been described as a form of non-linear principle component analysis, and is a variant of -means clustering algorithms."
 It allows one to identify special features (for instance. clustering) in the input catalogue.," It allows one to identify special features (for instance, clustering) in the input catalogue."
 As the algorithm itself is effectively classifying new input data based on previously seen specimens. after training SOMs be used to ‘classify’ new inputs. even if they only contain a sub-set of the original information used to train the original map.," As the algorithm itself is effectively classifying new input data based on previously seen specimens, after training SOMs be used to `classify' new inputs, even if they only contain a sub-set of the original information used to train the original map."
 The method is unsupervised in the sense that the user is not required to specify the desired output. as the “mapping” of components of the input vectors is a natural outcome of the learning.," The method is unsupervised in the sense that the user is not required to specify the desired output, as the `mapping' of components of the input vectors is a natural outcome of the learning."
 Indeed. perhaps the most fascinating aspect of large SOMs is the potential for emergent behaviour 22007) allowing one to discover new properties of the input data that would be imperceptible otherwise.," Indeed, perhaps the most fascinating aspect of large SOMs is the potential for emergent behaviour 2007) allowing one to discover new properties of the input data that would be imperceptible otherwise."
 In summary. the SOM is an extremely versatile tool. and could have several possible uses. however in this paper we demonstrate two of its main applications: object. selection and parameter estimation.," In summary, the SOM is an extremely versatile tool, and could have several possible uses, however in this paper we demonstrate two of its main applications: object selection and parameter estimation."
 In $22 we describe the algorithm. including a toy example and in $33 we present the two practical examples using data from the the COSMOS (Scoville et 22007).," In 2 we describe the algorithm, including a toy example and in 3 we present the two practical examples using data from the the COSMOS (Scoville et 2007)."
 At the end of the paper we provide a brief list of common SOM terminology for convenience., At the end of the paper we provide a brief list of common SOM terminology for convenience.
 The SOM algorithm used here as a Python class is made available at w.physics.megill.ca/7-jimgeaeh/som. or from the author on request.," The SOM algorithm used here as a Python class is made available at $\sim$ jimgeach/som, or from the author on request."
 The SOM can be considered as a collection of “nodes” arranged in a grid of arbitrary dimension. although for visualisation purposes two dimensions are most common.," The SOM can be considered as a collection of `nodes' arranged in a grid of arbitrary dimension, although for visualisation purposes two dimensions are most common."
" Each node is attached to avector of ""weights w with the same dimension as an input “training” vector. t."," Each node is attached to avector of `weights' ${\mathbf w}$ with the same dimension as an input `training' vector, ${\mathbf t}$."
 In the case of a galaxy survey for example. a t could comprise of five measurements of photometry.," In the case of a galaxy survey for example, a ${\mathbf t}$ could comprise of five measurements of photometry."
 In fact. the input data neec not actually be vectorised: any input — provided it can be digitizec — way could be considered.," In fact, the input data need not actually be vectorised; any input – provided it can be digitized – way could be considered."
 A further example to consider migh be a digital astronomical image. where we might expect the SOM to help perform morphological classitications.," A further example to consider might be a digital astronomical image, where we might expect the SOM to help perform morphological classifications."
 Througout this work however. we will consider the case of inputs that are representec as vectors. with each vector component made up from standare ‘catalogue data’ such as photometry and redshift information.," Througout this work however, we will consider the case of inputs that are represented as vectors, with each vector component made up from standard `catalogue data' such as photometry and redshift information."
 The map can be considered as a set of “component planes’. with a given node in the ;' plane taking the value of ;.," The map can be considered as a set of `component planes', with a given node in the $i^{\rm th}$ plane taking the value of $w_i$."
 In the two dimensiona representation. plotting two or more component planes next to each other provides a low-resolution visual representation of the dimensional topology of the input data.," In the two dimensional representation, plotting two or more component planes next to each other provides a low-resolution visual representation of the higher-dimensional topology of the input data."
 How does the SOM achieve this mapping?, How does the SOM achieve this mapping?
 To start. each node is initialised with a random weight: this can be selected from a uniform distribution. or an arbitrary probability distribution (limited according to a sensible physical range of values). or even randomly sampled from the input training set.," To start, each node is initialised with a random weight; this can be selected from a uniform distribution, or an arbitrary probability distribution (limited according to a sensible physical range of values), or even randomly sampled from the input training set."
 The learning process is then a set of iterations. and follows a simple philosophy: each node ‘competes’ to be the best match to a randomly selected vector from the training set.," The learning process is then a set of iterations, and follows a simple philosophy: each node `competes' to be the best match to a randomly selected vector from the training set."
 The winning node — called the Best Matching Unit (BMU) — is rewarded by being allowed to become more like the input vector., The winning node – called the Best Matching Unit (BMU) – is rewarded by being allowed to become more like the input vector.
 In addition. nodes in the vicinity of the BMU. rpare. are also allowed to be altered in the same direction. but to à lesser extent than the BMU>.," In addition, nodes in the vicinity of the BMU, $r_{\rm BMU}$, are also allowed to be altered in the same direction, but to a lesser extent than the ."
. After many samplings. the nodes can learn to become," After many samplings, the nodes can learn to become"
We have also performed a few experiments with more centrally concentrated (6S) initial haloes. C,We have also performed a few experiments with more centrally concentrated $c\sim 8$ ) initial haloes. (
Ehese would » more appropriate models to use if the true cosmology isQ=1. A=0: on the other hand. low-Q models. can xocduce less concentrated haloes more in line with our e4 runs.),"These would be more appropriate models to use if the true cosmology is $\Omega=1$, $\Lambda=0$; on the other hand, $\Omega$ models can produce less concentrated haloes more in line with our $c\sim 4$ runs.)"
 The clear outcome of these runs (99€. S6Ea) is hat even if we exaggerate the strength of halo pinching » making the disk more massive ancl more centrally concentrated during the growth phase. we are barely able to oduce a central core of the required size. and the overall it to the observed. rotation curve is extremely poor.," The clear outcome of these runs (99Ca, 86Ea) is that even if we exaggerate the strength of halo pinching by making the disk more massive and more centrally concentrated during the growth phase, we are barely able to produce a central core of the required size, and the overall fit to the observed rotation curve is extremely poor."
 We must therefore. conclude that. our scenario only explains he observed rotation curve of if the elfective concentration of the dark matter halo was closer to ὁ=4 han (ο ὃςδ., We must therefore conclude that our scenario only explains the observed rotation curve of if the effective concentration of the dark matter halo was closer to $c=4$ than to $c=8$.
 Aurkert (1995). has pointed out that the core structure of the dark matter halo in appears to be shared w other galaxies in its class. and questioned the ability of the mass ejection hypothesis to produce the fine-tuning hat he claims is necessary to turn. NEWs one-parameter zunilv of cuspy N-body halo profiles into the cilfercnt one-xwameter family of observed. profiles.," Burkert \shortcite{B95} has pointed out that the core structure of the dark matter halo in appears to be shared by other galaxies in its class, and questioned the ability of the mass ejection hypothesis to produce the fine-tuning that he claims is necessary to turn NFW's one-parameter family of cuspy $N$ -body halo profiles into the different one-parameter family of observed profiles."
 In. this regard we would like to point out that we obtain reasonable fits to he rising part of the rotation curve for a rather wide range of ejected mass Lractions: the real challenge is rather to it thedeclining part of 1547s rotation curve., In this regard we would like to point out that we obtain reasonable fits to the rising part of the rotation curve for a rather wide range of ejected mass fractions; the real challenge is rather to fit the part of 's rotation curve.
 Of the rotation curves in Burkert’s (1995) sample. only ls extends sulliciently far outwards to provide such a stringent est.," Of the rotation curves in Burkert's \shortcite{B95} sample, only 's extends sufficiently far outwards to provide such a stringent test."
 While his argument about fine-tuning is undoubtedly. interesting. we do not find it entirely compelling given the current paucity of observational data.," While his argument about fine-tuning is undoubtedly interesting, we do not find it entirely compelling given the current paucity of observational data."
 Our numerical experiments confirm that it is not. very easy to give a satisfactory account of the observed rotation curve, Our numerical experiments confirm that it is not very easy to give a satisfactory account of the observed rotation curve
 Mp;~1067109ML. 2005).," $M_{BH} \sim 10^6-10^9\,\msun$ \citep{ferrarese2005}."
. ~dos10°AL. (eie.Schódelet," $\simeq 4\times10^6\,M_\odot$ \citep[e.g.,][]{Schodel2003,Ghez2005}."
 ~107AZ. (Barthetal.2001:2005).. (VanWasseulove2010).. (Volouterictal.2008).. (AlagorrianMarconi&Πιν2003:HaringRix2001). [σονFerrarese&Merrittetal.2009).," $\sim 10^5\,M_\odot$ \citep{Barth2004,Peterson2005}. \citep{svanwas2010}. \citep{VLN2008}. \citep{Magorrian1998,MarconiHunt2003,Haring2004}. \citep[``M-$\sigma$"",][]{Ferrarese2000,Gebhardt2000, Tremaine2002, Graham2008,Gultekin2009}."
. Laueretal.(2007) (butseeetal.2007:Graham2008)... (Cureeneetal.2008).," \cite {Lauer2007} \citep[but see][]{Bernardi2007,Tundo2007,Graham2008}. \citep{Greene2008},"
. due to changes in the accretion properties (Mathur&(προ2005).. dwnamical effects (Volouteri2007).. or a cosunic bias (Volonteri&Natarajan2009:VanWasscu-hoveetal. 2010).," due to changes in the accretion properties \citep{Mathur2005}, dynamical effects \citep{Volonteri2007}, or a cosmic bias \citep{VN09,svanwas2010}."
. It has also been proposed (e.g..PortegiesZwartetal.2001:Ciürkan2001). that black holes of intermediate mass (between the stella mass range. ~ few tens M... and the supermassive black hole range. >LOAD). can form im the couter of deuse voung star clusters.," It has also been proposed \citep[e.g.,][]{PZ2004,Ato2004} that black holes of intermediate mass (between the stellar mass range, $\sim$ few tens $\msun$, and the supermassive black hole range, $\gta 10^5\msun$ ), can form in the center of dense young star clusters."
 It is proposed that the formation of the black hole is fostered by the tendeney of the most massive stars to concentrate into the cluster core through mass segregation., It is proposed that the formation of the black hole is fostered by the tendency of the most massive stars to concentrate into the cluster core through mass segregation.
 The iereiue of mail-sequence stars via direct plivsical collisions can cuter iuto a runaway phase. fornuue a verv inassive star. which can then collapse to form a black hole (Begehuan&Rees1978:Ebisuzalietal.2006b.a:Ciürkau2001. 2006).," The merging of main-sequence stars via direct physical collisions can enter into a runaway phase, forming a very massive star, which can then collapse to form a black hole \citep{Begelman1978, ebisuzaki2001,Miller2002,PZ2002,PZ2004,freitag2006a,freitag2006b,Ato2004,ato2006}."
. Observational evidences for intermediate mass black holes iu globular clusters are scant (e.g.vanderMarel&Anderson2010:Pasquato2010.andreferences therein)..," Observational evidences for intermediate mass black holes in globular clusters are scant \citep[e.g.,][and references therein]{vandermarel2010,Pasquato2010}."
. Dynamical lüueasurenmients are hampered by the small size of the sphere of influence of these black holes. aud ouly four candidates have curreutly been identified. iu MIS. ADSL. CU and w Coeutaun (Cerssenetal.2002:Ibata2009:Cebhardtetal.2005:Novola 2008).," Dynamical measurements are hampered by the small size of the sphere of influence of these black holes, and only four candidates have currently been identified, in M15, M54, G1 and $\omega$ Centauri \citep{Gerssen2002,Ibata2009,Gebhardt2005,Noyola2008}."
. The radio aud N-rav cluission detected from Gl make this cluster the stronecst candidate. although alternative explanations. such as an X-ray binary are possible (Ulyestadetal.2007:Pooley&Rappaport 2006).," The radio and X-ray emission detected from G1 make this cluster the strongest candidate, although alternative explanations, such as an X-ray binary are possible \citep{Ulvestad2007,Pooley2006}."
". ""Massive black holes (nore massive than stellar mass black holes) are therefore expected to be widespread iu stellar syvsteis. ο those of the lowest to highest mass."," `Massive' black holes (more massive than stellar mass black holes) are therefore expected to be widespread in stellar systems, from those of the lowest to highest mass."
 Oulv a πια] fraction of these massive black holes are active at levels that are expected for ACNs. aud. indeed. most massive black holes at the preseut dav are ‘quiescent’.," Only a small fraction of these massive black holes are active at levels that are expected for AGNs, and, indeed, most massive black holes at the present day are `quiescent'."
 I[owever. because. MDIIS are embedded in stellar svstems. they are unlikelytoever become completely inactive.," However, because MBHs are embedded in stellar systems, they are unlikelytoever become completely inactive."
 A massive black hole surrounded by stars could be accreting material.either strippedfrom a colupalion star or available as recycled material via mass," A massive black hole surrounded by stars could be accreting material,either strippedfrom a companion star or available as recycled material via mass"
dependence. guiding shifts. cosmic rays. dark. ancl gain.,"dependence, guiding shifts, cosmic rays, dark, and gain."
 We then corrected. forghosls. a common artefact in EPdatal. using the method. of 2.," We then corrected for, a common artefact in FP, using the method of ."
.. Fourth. we applied a spectral smoothing using a Llanning function. and then sky subtracted the data.," Fourth, we applied a spectral smoothing using a Hanning function, and then sky subtracted the data."
 We then combined all data cubes over all the eveles and nights observed to create a total integrated cube., We then combined all data cubes over all the cycles and nights observed to create a total integrated cube.
 X spatial smoothing of 5.5 pixels was applied to allow better identification of cilfuse gas., A spatial smoothing of $5\times5$ pixels was applied to allow better identification of diffuse gas.
 Finally. we fitted the line profiles with a single gaussian component and then corrected for the filter dependence. with a mean temperature of LOC. We were then able to extract the final velocity. dispersion and Ho integrated maps.," Finally, we fitted the line profiles with a single gaussian component and then corrected for the filter dependence, with a mean temperature of $^o$ C. We were then able to extract the final velocity, dispersion and $\alpha$ integrated maps."
 For each galaxy. we show an image. summed over the 40 channels. of the raw data in Fig.," For each galaxy, we show an image, summed over the 40 channels, of the raw data in Fig."
 2. (before applying the 5-5 pixel binning and gaussian fits to the spectra)., \ref{a2raw} (before applying the $5\times5$ pixel binning and gaussian fits to the spectra).
 ‘This figure shows that there is a contaminating rellection in the top and right side of the data (see rectangles outlined in red)., This figure shows that there is a contaminating reflection in the top and right side of the data (see rectangles outlined in red).
 This reflection arises from light rellected olf the detector. ancl depended on the light present in the clome. vicl was therefore brighter when taking the Lats at twilight han when observing the galaxies.," This reflection arises from light reflected off the detector, and depended on the light present in the dome, and was therefore brighter when taking the flats at twilight than when observing the galaxies."
 The data cubes were Uat-eorrected by dividing them with the normalized Lat-fielcl image., The data cubes were flat-corrected by dividing them with the normalized flat-field image.
 The continuum of the data cubes. in. the regions of reflection. can therefore be inferior to that of the rest of the cube. and is not representative of the true continuum.," The continuum of the data cubes, in the regions of reflection, can therefore be inferior to that of the rest of the cube, and is not representative of the true continuum."
 This parasitic rellection only allected areas. of dilfuse emission., This parasitic reflection only affected areas of diffuse emission.
 Section 3 shows in more detail how this reflection was accounted for in the analysis of the dilluse extended. emission., Section 3 shows in more detail how this reflection was accounted for in the analysis of the diffuse extended emission.
 We applied. the reduction steps outlined in Section 2. and for each emission line we obtained the radial velocity nmieasurement. standard: deviation and integrated. [lux by fitting a gaussian function.," We applied the reduction steps outlined in Section 2, and for each emission line we obtained the radial velocity measurement, standard deviation and integrated flux by fitting a gaussian function."
 These respectively gave. the full resolution velocity fields. dispersion. maps and. Uux-calibrated Ho integrated maps shown in Fig.," These respectively gave the full resolution velocity fields, dispersion maps and flux-calibrated $\alpha$ integrated maps shown in Fig."
 3. (NGC 247) and bie., \ref{a2f3} (NGC 247) and Fig.
 4. (NGC 300)., \ref{a2f4} (NGC 300).
 We also obtained lower resolution velocity fields (see Fig., We also obtained lower resolution velocity fields (see Fig.
 3. and Fig. 4..," \ref{a2f3} and Fig. \ref{a2f4},"
" middle-right panels). » applving an additional gaussian spatial smoothing of wy=55"". where wy ds the width of the smoothing unction."," middle-right panels), by applying an additional gaussian spatial smoothing of $w_{\rm \lambda}=55''$, where $w_{\rm \lambda}$ is the width of the smoothing function."
 These low resolution maps were used to extract the kinematical parameters of the galaxies. which would. have xen dillieult to do with the original full resolution velocity ields because of perturbations in the field gas).," These low resolution maps were used to extract the kinematical parameters of the galaxies, which would have been difficult to do with the original full resolution velocity fields because of perturbations in the field )."
 By using these less disturbed kinematical xwamoeters. we then used the original full resolution velocity ields to extract the rotation curves.," By using these less disturbed kinematical parameters, we then used the original full resolution velocity fields to extract the rotation curves."
 Excessive smoothing could induce ai bias in the determination. of the inclination towards lower values., Excessive smoothing could induce a bias in the determination of the inclination towards lower values.
 determined that a rotation curve starts to properly trace the kinematies of a galaxy when the scale of the galaxy is more than 7 times the resolution of the data., determined that a rotation curve starts to properly trace the kinematics of a galaxy when the scale of the galaxy is more than 7 times the resolution of the data.
 Since our smoothing corresponds to less than 1/10 of the scale of the galaxies. the values we determine for the inclination should not be wlected significantlv.," Since our smoothing corresponds to less than 1/10 of the scale of the galaxies, the values we determine for the inclination should not be affected significantly."
 uh and succeeded. in detecting dilluse ionized. gas in NGC 253 by binning the data into annular rings., Both and succeeded in detecting diffuse ionized gas in NGC 253 by binning the data into annular rings.
 Since NGC 247 is also highly. inclined. (7~747). we can apply the same kind of binning.," Since NGC 247 is also highly inclined $i\sim74^o$ ), we can apply the same kind of binning."
 Phe annular rings were centred along the major axis in the plane of the image and. about the galaxys dynamical centre., The annular rings were centred along the major axis in the plane of the image and about the galaxy's dynamical centre.
 For a given opening angle. different regions corresponding to dillerent. racial intervals were binned together.," For a given opening angle, different regions corresponding to different radial intervals were binned together."
" We chose an opening angle of ~20"" 10"" on each side of the major axis). so that we would not overlap on too large a portion of sky. and mace the binning intervals erow with radius. since dilfuse emission. becomes more clillicult to detect as the radius increases (see Fig. 5))."," We chose an opening angle of $\sim20^o$ $10^o$ on each side of the major axis), so that we would not overlap on too large a portion of sky, and made the binning intervals grow with radius, since diffuse emission becomes more difficult to detect as the radius increases (see Fig. \ref{a2f5}) )."
 As seen [from our raw data in Fig. 2..," As seen from our raw data in Fig. \ref{a2raw},"
 the extended part of the northern arm of NGC 247 (bevond a radius of 11) foll cürectly into the areas allectecl by the contaminating reflections., the extended part of the northern arm of NGC 247 (beyond a radius of $'$ ) fell directly into the areas affected by the contaminating reflections.
 Tere. it became crucial to determine if any emission line detected. was the result. of dilluse emission or of the rellection.," Here, it became crucial to determine if any emission line detected was the result of diffuse emission or of the reflection."
 The continuum observed. in. the allected regions was also not representative of dis true value. ancl could amount to a negative value since it. had been previously overcorrected. for during sky. subtraction.," The continuum observed in the affected regions was also not representative of its true value, and could amount to a negative value since it had been previously overcorrected for during sky subtraction."
 l]lowever. the spectrum. of the reflection. did. πο vary significantly.," However, the spectrum of the reflection did not vary significantly."
" By applying another annular ring binning. this time with opening angle of SO"" to smooth sullicientlv. over 1e alfected. areas. we were able to obtain a typical response μα»ectrum Lor the contaminating rellection."," By applying another annular ring binning, this time with opening angle of $80^o$ to smooth sufficiently over the affected areas, we were able to obtain a typical response spectrum for the contaminating reflection."
" Loan emission line was onlv seen in the first (opening angle of 20°) and not the second (opening angle of SO"") binning. then it was considered to be truly associated with ciuse emission."," If an emission line was only seen in the first (opening angle of $^o$ ) and not the second (opening angle of $^o$ ) binning, then it was considered to be truly associated with diffuse emission."
 Using this method. we were able to identify. two extended racial intervals on the northern side of NGC 247 which had faint Ho emission (c= 11.27. r= 13.1’).," Using this method, we were able to identify two extended radial intervals on the northern side of NGC 247 which had faint $\alpha$ emission $r=11.2'$ , $r=13.1'$ )."
 Four kinematical parameters must be determined from the velocity. Ποια to derive the rotation curve., Four kinematical parameters must be determined from the velocity field to derive the rotation curve.
 They. are the cdvnanmical centre Gro and yo). the svstemic velocity Vi... the inclination 7. and the position angle PA of the major axis.," They are the dynamical centre $x_{\rm 0}$ and $y_{\rm 0}$ ), the systemic velocity $V_{\rm sys}$, the inclination $i$, and the position angle PA of the major axis."
 We use the program and task to derive then., We use the program and task to derive them.
 These programs are based on a least square fitting method that best reproduces the observed. velocity field., These programs are based on a least square fitting method that best reproduces the observed velocity field.
(?).. Using the lower resolution velocity: fields (ey=55” ). we first find. the dynamical centre anc Vi by. keeping 7 and PA fixed.," Using the lower resolution velocity fields $w_{\rm \lambda}=55''$ ), we first find the dynamical centre and $V_{\rm sys}$ by keeping $i$ and PA fixed."
 The initial values are chosen as those derived in the study (Carignan Puche 1990 for. NGC 247: Puche et al., The initial values are chosen as those derived in the study (Carignan Puche 1990 for NGC 247; Puche et al.
 1990 for NGC300)., 1990 for NGC.
". To minimize errors due to deprojection effects. we exclude data in an opening angle of 60"" around the minor axis lor NGC 247 and 35"" [or NGC 300."," To minimize errors due to deprojection effects, we exclude data in an opening angle of $^o$ around the minor axis for NGC 247 and $^o$ for NGC 300."
 We use a cosine-square weighting function on the remaining data of NGC 247. where each point is weighted by cos(8)7 with& being the angle from the major axis.," We use a cosine-square weighting function on the remaining data of NGC 247, where each point is weighted by $\cos(\theta)^2$ with$\theta$ being the angle from the major axis."
 This maximizes the weight of the points around the major axis., This maximizes the weight of the points around the major axis.
"frequeney emission al low angular resolution (>10"") is probably from dust. but associated with the large-scale. overlving molecular cloud.","frequency emission at low angular resolution $\geq 10^{\prime\prime}$ ) is probably from dust, but associated with the large-scale, overlying molecular cloud."
" ο, Ixurtz acknowledges support from UNAM. DGAPA project INI06107."," S. Kurtz acknowledges support from UNAM, DGAPA project IN106107."
An issue that is relevant for ACS observations is the degradation of the charge transfer efficiency (CTE) with time.,An issue that is relevant for ACS observations is the degradation of the charge transfer efficiency (CTE) with time.
 Over time. cosmic rays cause an increasing number of defects in the detector.," Over time, cosmic rays cause an increasing number of defects in the detector."
 During read-out. these defects can trap charges for a while.," During read-out, these defects can trap charges for a while."
 The delayed transfer of charge leads to a trail of electrons in the read-out direction. causing objects to appear elongated.," The delayed transfer of charge leads to a trail of electrons in the read-out direction, causing objects to appear elongated."
 The effect is strongest for faint objects. because brighter objects quickly fill the traps.," The effect is strongest for faint objects, because brighter objects quickly fill the traps."
 ? provide a detailed discussion of CTE effects and their impact on weak lensing studies., \cite{Rhodes07} provide a detailed discussion of CTE effects and their impact on weak lensing studies.
 Similar to? we derive an empirical correction for CTE. but our adopted approach differs in a number of ways.," Similar to \cite{Rhodes07}
 we derive an empirical correction for CTE, but our adopted approach differs in a number of ways."
 The presence of CTE in our data leads to a slight modification of our lensing analysis., The presence of CTE in our data leads to a slight modification of our lensing analysis.
 First. we note that CTE affects only οι and that the change in shape occurs during the read-out stage.," First, we note that CTE affects only $e_1$ and that the change in shape occurs during the read-out stage."
" Hence the measured value for e, needs to be corrected for CTE the correction for PSF anisotropy and eireularization: where ef! is the predicted change in polarization given by the model derived in the Appendix.", Hence the measured value for $e_1$ needs to be corrected for CTE the correction for PSF anisotropy and circularization: where $e_1^{\rm CTE}$ is the predicted change in polarization given by the model derived in the Appendix.
 To derive our CTE model. we used observations of the star cluster NGC 104 as well as 100 exposures from the COSMOS survey (?)..," To derive our CTE model, we used observations of the star cluster NGC 104 as well as 100 exposures from the COSMOS survey \citep{Scoville07}."
 The observations of a star cluster allow us to study the effect of CTE as a function of position. time and signal-to-noise ratio with high precision. because stars are intrinsically round after correction for PSF anisotropy.," The observations of a star cluster allow us to study the effect of CTE as a function of position, time and signal-to-noise ratio with high precision, because stars are intrinsically round after correction for PSF anisotropy."
 We find that the CTE effect increases linearly with time and distance from the read-out electronics., We find that the CTE effect increases linearly with time and distance from the read-out electronics.
 The amplitude of the effect is observed to be proportional to \/S/N., The amplitude of the effect is observed to be proportional to $\sqrt{S/N}$.
 We use 100 exposures from COSMOS to examine how the CTE effect dependsS on source size., We use 100 exposures from COSMOS to examine how the CTE effect depends on source size.
" We findled an strongsfr size; dependence.. withae ejCTLxr"" (wherephere r,pq is the dispersion of the Gaussian weight function used to measure the quadrupole moments)."," We find a strong size dependence, with $e_1^{\rm CTE}\propto
r_g^{-2}$ (where $r_g$ is the dispersion of the Gaussian weight function used to measure the quadrupole moments)."
 Once the CTE effect has been subtracted for all objects (including stars). the lensing analysis proceeds as described in ?..," Once the CTE effect has been subtracted for all objects (including stars), the lensing analysis proceeds as described in \cite{Hoekstra98}."
 Hence the next step is to correct both polarization components for PSF anisotropy., Hence the next step is to correct both polarization components for PSF anisotropy.
 The ACS PSF is time dependent and therefore a different PSF model is required for each observation., The ACS PSF is time dependent and therefore a different PSF model is required for each observation.
 An added complication is the fact that only a limited number of stars are observed in each image., An added complication is the fact that only a limited number of stars are observed in each image.
 To estimate the spatial variation of the PSF anisotropy a number of procedures have been proposed (???)..," To estimate the spatial variation of the PSF anisotropy a number of procedures have been proposed \citep{Rhodes07,Schrabback07,Schrabback10}."
 Here we opt for a simple approach. similar to the one used in ?..," Here we opt for a simple approach, similar to the one used in \cite{Hoekstra98}."
 We use observations of the star cluster ΝΟ10Η to derive an adequate model for PSF anisotropy., We use observations of the star cluster NGC104 to derive an adequate model for PSF anisotropy.
 These data were taken at the start of ACS operations (PID 9018). and therefore do not suffer from CTE effects.," These data were taken at the start of ACS operations (PID 9018), and therefore do not suffer from CTE effects."
 We model the PSF anisotropy by a third order polynomial in both x and v., We model the PSF anisotropy by a third order polynomial in both $x$ and $y$.
 Such a model would not be well constrained by our galaxy cluster data. but it is thanks to the high number density of stars in NGCIOA.," Such a model would not be well constrained by our galaxy cluster data, but it is thanks to the high number density of stars in NGC104."
 We select one of the models as our reference. because the PSF pattern varied only mildly from exposure to exposure.," We select one of the models as our reference, because the PSF pattern varied only mildly from exposure to exposure."
 The resulting reference model is shown in Figure 2.., The resulting reference model is shown in Figure \ref{psfmod}.
 The PSF anisotropy is fairly small. but can reach ~4% towards the edges of the field.," The PSF anisotropy is fairly small, but can reach $\sim 4\%$ towards the edges of the field."
 Most of the variation in the ACS PSF arises from focus changes. which are the result of changes in the telescope temperature as it orbits the Earth.," Most of the variation in the ACS PSF arises from focus changes, which are the result of changes in the telescope temperature as it orbits the Earth."
 We therefore expect that a scaled version of our model can capture much of the spatial, We therefore expect that a scaled version of our model can capture much of the spatial
"in the field and in some young clusters (e.g., Kraus&Hillenbrand 2009)) may be a consequence of formation mechanisms unique to VLM stars and brown dwarfs (e.g., embryonic dynamical ejection: Reipurth&Clarke2001;Bateetal. 2002;; fragmentation of circumstellar disks: Boss2001;Jiangetal. 2004)) or dynamical evolution within and/or outside the natal cloud (e.g., Closeetal. 2007)).","in the field and in some young clusters (e.g., \citealt{2009arXiv0908.1385K}) ) may be a consequence of formation mechanisms unique to VLM stars and brown dwarfs (e.g., embryonic dynamical ejection: \citealt{2001AJ....122..432R, 2002MNRAS.332L..65B}; fragmentation of circumstellar disks: \citealt{2001ApJ...551L.167B, 2004AJ....127..455J}) ) or dynamical evolution within and/or outside the natal cloud (e.g., \citealt{2007ApJ...660.1492C}) )."
" In addition, wide VLM pairs are often found to be triples or quadruples (e.g,. Phan-Baoetal.2006;;"," In addition, wide VLM pairs are often found to be triples or quadruples (e.g,. \citealt{2006ApJ...645L.153P};"
" DDhital et 22009, in preparation), enabling studies of higher order multiplicity associated with star and brown dwarf formation."," Dhital et 2009, in preparation), enabling studies of higher order multiplicity associated with star and brown dwarf formation."
" In this article, we report the discovery of a new wide L dwarf pair,J15500845+1455180 (hereafterJ1550+1455; Cruzetal. 2007)) identified by direct imaging and resolved spectroscopy to be a 0.9, near-equal brightness binary."," In this article, we report the discovery of a new wide L dwarf pair, (hereafter; \citealt{2007AJ....133..439C}) ) identified by direct imaging and resolved spectroscopy to be a $\farcs$ 9, near-equal brightness binary."
" In Section 2 we describe imaging and spectroscopic observations of the source, and ascertain the separation, relative near-infrared magnitudes and individual spectral classifications of its components."," In Section 2 we describe imaging and spectroscopic observations of the source, and ascertain the separation, relative near-infrared magnitudes and individual spectral classifications of its components."
" In Section 3 we review evidence that this source is a physical binary based on constraints in common proper motion, common spectrophotometric distances and low probability of chance alignment."," In Section 3 we review evidence that this source is a physical binary based on constraints in common proper motion, common spectrophotometric distances and low probability of chance alignment."
" The properties ofJ1550+1455 are discussed in the context of other VLM binaries in Section 4, along with motivation to measure its age using the binary brown dwarf test."," The properties of are discussed in the context of other VLM binaries in Section 4, along with motivation to measure its age using the binary brown dwarf test."
 Resultsare summarized in Section 5., Resultsare summarized in Section 5.
 was originally identified by Cruz in a color- and magnitude-selected search of the Two Micron All Sky Survey (2MASS; Skrutskieetal. 2006)) for nearby late-type M and L dwarfs., was originally identified by \citet{2007AJ....133..439C} in a color- and magnitude-selected search of the Two Micron All Sky Survey (2MASS; \citealt{2006AJ....131.1163S}) ) for nearby late-type M and L dwarfs.
" It was selected as a near-infrared bright (K, = 13.26+0.04 mag) but optically faint source with red near-infrared colors (J—K, = 1.52+0.05 mag).", It was selected as a near-infrared bright $K_s$ = $\pm$ 0.04 mag) but optically faint source with red near-infrared colors $J-K_s$ = $\pm$ 0.05 mag).
 The epoch 2009 February 6 (UT) 2MASS images show an unresolved point source., The epoch 2009 February 6 (UT) 2MASS images show an unresolved point source.
" Cruzetal.(2007) reported an optical spectral classification of L2: on the Kirkpatricketal. scale, the uncertainty arising from low signal-to- (1999)data (I. RReid CCruz, 2009, private communication)."," \citet{2007AJ....133..439C} reported an optical spectral classification of L2: on the \citet{1999ApJ...519..802K} scale, the uncertainty arising from low signal-to-noise data (I. Reid Cruz, 2009, private communication)."
" has a relatively small proper motion, = 0.165+0.015 "" γι! (Jamesonetal. 2008), which combinedjj with the 31 pc distance estimate of Cruzetal.(2007) yields an estimated tangential velocity = 24s-!, typical for a “normal” thin disk L dwarf Fahertyetal. 2009))."," has a relatively small proper motion, $\mu$ = $\pm$ 0.015 $\arcsec$ $^{-1}$ \citep{2008MNRAS.384.1399J}, which combined with the 31 pc distance estimate of \citet{2007AJ....133..439C} yields an estimated tangential velocity = 24, typical for a “normal” thin disk L dwarf (e.g., \citealt{2009AJ....137....1F}) )."
" was also (e.g.,imaged and targeted for spectroscopy by the Sloan Digital Sky Survey (SDSS; Yorketal. 2000))", was also imaged and targeted for spectroscopy by the Sloan Digital Sky Survey (SDSS; \citealt{2000AJ....120.1579Y}) ).
" This source is morphologically classified in SDSS as a galaxy due to its extended point spread function (PSF), as shown in Figure 1.."," This source is morphologically classified in SDSS as a galaxy due to its extended point spread function (PSF), as shown in Figure \ref{fig_sdssimage}."
" Both i- and z-band images show a faint extension toward the north, which as discussed below is consistent with a faint, marginally resolved companion."," Both $i$ - and $z$ -band images show a faint extension toward the north, which as discussed below is consistent with a faint, marginally resolved companion."
 Spectroscopic data from SDSS Data Release 7 (DR7; Abazajianetal. 2009)) are shown in Figure 2.., Spectroscopic data from SDSS Data Release 7 (DR7; \citealt{2009ApJS..182..543A}) ) are shown in Figure \ref{fig_optspec}.
" These data are superior to those in the Cruzetal. study, and comparison to the Kirkpatricketal.(2007)(1999) spectral standards indicate an optical classification of L3 (an uncertainty of 0.5 subtypes is assumed)."," These data are superior to those in the \citet{2007AJ....133..439C} study, and comparison to the \citet{1999ApJ...519..802K} spectral standards indicate an optical classification of L3 (an uncertainty of 0.5 subtypes is assumed)."
" There is no indication of either Ha emission (6563 A) or absorption (6708 A) to limiting pseudo-equivalent of —1.8 and 1.2A, respectively."," There is no indication of either $\alpha$ emission (6563 ) or absorption (6708 ) to limiting pseudo-equivalent of –1.8 and 1.2, respectively."
" We infer a radial velocity for of —7+12 based on cross-correlation with similarly-typed L dwarf velocity templates also observed by SDSS SSchmidt et al.,"," We infer a radial velocity for of $-$ $\pm$ 12 based on cross-correlation with similarly-typed L dwarf velocity templates also observed by SDSS Schmidt et al.,"
 in preparation)., in preparation).
" was targeted with the 3 m NASA Infrared Telescope Facility (IRTF) SpeX spectrograph (Rayneretal.2003) on 2009 June 29 (UT), as part of a program to identify unresolved L dwarf/T dwarf spectral binaries Burgasseretal. 2008a))."," was targeted with the 3 m NASA Infrared Telescope Facility (IRTF) SpeX spectrograph \citep{2003PASP..115..362R} on 2009 June 29 (UT), as part of a program to identify unresolved L dwarf/T dwarf spectral binaries (e.g., \citealt{2008ApJ...681..579B}) )."
" Conditions were clear with (e.g.,excellent seeing of 04-05 at J- and K-", Conditions were clear with excellent seeing of $\farcs$ $\farcs$ 5 at $J$ - and $K$ -bands.
" Acquisition images obtained with SpeX's imaging channel revealed two point sources at the position of aligned along a north-south axis,"," Acquisition images obtained with SpeX's imaging channel revealed two point sources at the position of aligned along a north-south axis,"
oL neutral hydrogen (Putimanetal.1998).. unlikely to have survived a passage through the cluster core.,"of neutral hydrogen \citep{put1998}, unlikely to have survived a passage through the cluster core."
 Furthermore. observations of Fornax A in he subcluster (Ekersetal.1983) indicate that it las a projected velocity of approximately inorthiwards. consistent. with iufall.," Furthermore, observations of Fornax A in the subcluster \citep{eke1983} indicate that it has a projected velocity of approximately northwards, consistent with infall."
 Similarly. te subgroup seet in projectiou on the cluster core (seen in Fig.," Similarly, the subgroup seen in projection on the cluster core (seen in Fig."
 2 at )) is probably real aid infalline. although it was not ro)ustly identified yw the KMMN. algorithin.," \ref{fig_velocity} at ) is probably real and infalling, although it was not robustly identified by the KMM algorithm."
 TUs group contaius (GC LIOL whic1 has a distorted X-ray envelope indicative of infall (.Jonesetal.1997).. ancl the iregular galaxy GC ΟΤΑ. whic1 shows signs of eine cisrupted by Its first yassage through the cluster (Chana16.Infante.&Reisenegeer2000).," This group contains NGC 1404, which has a distorted X-ray envelope indicative of infall \citep{jon1997}, and the irregular galaxy NGC 1427A, which shows signs of being disrupted by its first passage through the cluster \citep*{cha2000}."
. The morphologies o “both tlese galaxies are iucicative of material blown olf behiid them as they nove towards the οἱuster celer., The morphologies of both these galaxies are indicative of material blown off behind them as they move towards the cluster center.
 The substructu'e that àve have identified iu Foruax bears o the cleterminatioLol its Cepheid distance., The substructure that we have identified in Fornax bears on the determination of its Cepheid distance.
 There are now th'ee Cepheid distauces to spirals in the Foruax region> NCC 1365 at itepimadi999.. GC 13264 at itepprol000.. awb NGC 1125 at citepmou2000..," There are now three Cepheid distances to spirals in the Fornax region: NGC 1365 at \\citep{mad1999}, NGC 1326A at \\citep{pro1999}, and NGC 1425 at \\citep{mou2000}."
" fould οἱ suggestMOD that tie mean of these cAv20Mpc) be adopted. but this may Sil not vield an ac""urate custer distance."," Mould et suggest that the mean of these $\approx20\Mpc$ ) be adopted, but this may still not yield an accurate cluster distance."
 Though seen in projection only ((~ 0.LMpc) from the cluster core aud with a similar velocity. NGC 1365 (see Fig. 2))," Though seen in projection only $\sim 0.4\Mpc$ ) from the cluster core and with a similar velocity, NGC 1365 (see Fig. \ref{fig_velocity}) )"
 may be situated uear the tuIn-arouid racius (22 OOL tor ~1O% in distance). eiven the teneucy of late-type galaxies to avokl the cluster core.," may be situated near the turn-around radius $\sim$ out or $\sim$ in distance), given the tendency of late-type galaxies to avoid the cluster core."
 If NGC 1365 were in the cluser core. it migit be expected to show morphological peculiarities like spi‘als in Virgo. Colua. alle other clusters (seeBravo-Alfaroetal.2000).. but it is symmetric at wavelenetls from optical to (Liudblad1999).," If NGC 1365 were in the cluster core, it might be expected to show morphological peculiarities like spirals in Virgo, Coma, and other clusters \citep[see][]{bra2000}, but it is symmetric at wavelengths from optical to \citep{lin1999}."
. With au ideutical Cepheicl distatce. aud as a member of the infalliug subgroup (Fig. 3)).," With an identical Cepheid distance, and as a member of the infalling Fornax-SW subgroup (Fig. \ref{fig_subcluster}) ),"
 NGC 1326À is aSO a doubtful indicator o ‘the distance to the FOrlax Core., NGC 1326A is also a doubtful indicator of the distance to the Fornax core.
 NGC 1125 is perhaps a better gauge of he cluster disance. but it is 0266 (~2 Mpe) or 10 core radii removed from the cluster ceuter: it is not even clear whetler NGC 1125 belougs t| Foruax or the nearby Eridanus cluster (Mould et a.).," NGC 1425 is perhaps a better gauge of the cluster distance, but it is 6 $\sim 2\Mpc$ ) or $\sim 10$ core radii removed from the cluster center; it is not even clear whether NGC 1425 belongs to Fornax or the nearby Eridanus cluster (Mould et al.)."
 While a simpler svsteu than the Virgo cluser. Fornax nevertheless preseuts its own difficulties for au accurae distance measurement using €'epheids: a secure result awaits observations of addiional spirals iπροsly residiug iu the clisler core.," While a simpler system than the Virgo cluster, Fornax nevertheless presents its own difficulties for an accurate distance measurement using Cepheids; a secure result awaits observations of additional spirals unambiguously residing in the cluster core."
 We are very grateful to Holman. Brown aud tje st alfo Eie UINST for observing assistance aud Ryan for the caustic caleulatious.," We are very grateful to Holman, Brown and the staff of the UKST for observing assistance and Ryan for the caustic calculations."
 We thauk Geller. Aoore. Thomas aud Webster for helpful discussions.," We thank Geller, Moore, Thomas and Webster for helpful discussions."
 Part of this work was done at the Insti1]te of Cieophysies aud Planetary Physics. under the auspices of the DDepartiuent of Euergy  Lawrence Livermore National Laboratory (contract W-7105-Ene-15).," Part of this work was done at the Institute of Geophysics and Planetary Physics, under the auspices of the Department of Energy by Lawrence Livermore National Laboratory (contract W-7405-Eng-48)."
 This material is based upor work supported by the National, This material is based upon work supported by the National
As pointed out by ?.. à large fraction of the X-ray emission due to the accretion shock may be absorbed by the gas present 1 the surrounding stellar atmosphere or by the accretion colum itself.,"As pointed out by \cite{Drake2005ESASP}, a large fraction of the X-ray emission due to the accretion shock may be absorbed by the gas present in the surrounding stellar atmosphere or by the accretion column itself."
 The absorption from the stellar atmosphere mainly depends on the location of the emitting plasma., The absorption from the stellar atmosphere mainly depends on the location of the emitting plasma.
 For a give shocked slab of material rooted in the chromosphere. photons emitted from plasma located at the base of the slab (deep intc the chromosphere) travel through higher density gas layers tha photons from plasma located im the shallower portion of the slab.," For a given shocked slab of material rooted in the chromosphere, photons emitted from plasma located at the base of the slab (deep into the chromosphere) travel through higher density gas layers than photons from plasma located in the shallower portion of the slab."
" The deepness of the emitting plasma in the chromosphere depends on the thickness of the slab /,, and on the sinking of the slab in the chromosphere /ri,, (Sect. 2.2))", The deepness of the emitting plasma in the chromosphere depends on the thickness of the slab $l_{\rm ps}$ and on the sinking of the slab in the chromosphere $h_{\rm sink}$ (Sect. \ref{par:spacepar}) )
 to the position at which the ram pressure of the post-shock plasma equals the thermal pressure of the chromosphere., to the position at which the ram pressure of the post-shock plasma equals the thermal pressure of the chromosphere.
 As discussed in Sect. 2.2..," As discussed in Sect. \ref{par:spacepar},"
" our simulations explore a wide range of values for /,, and hag (see Table 1).", our simulations explore a wide range of values for $l_{\rm ps}$ and $h_{\rm sink}$ (see Table \ref{tab:Par_space}) ).
 In order to estimate the effect of the absorption on the observed X-ray emission. we calculate the X-ray luminosities by assuming that only the emission from plasma located in the shallower layers of the shocked slab can be observed (see also ? for a previous application of this method to estimate absorption effects).," In order to estimate the effect of the absorption on the observed X-ray emission, we calculate the X-ray luminosities by assuming that only the emission from plasma located in the shallower layers of the shocked slab can be observed (see also \citealt{Drake2005ESASP} for a previous application of this method to estimate absorption effects)."
 Specifically. we assume that all the emission due to plasma located at s.«Sa. d8 fully absorbed. while the emission. produced from plasma located ats>sap. Is fully transmitted.," Specifically, we assume that all the emission due to plasma located at $s<s_{\rm abs}$ is fully absorbed, while the emission produced from plasma located at $s>s_{\rm abs}$ is fully transmitted."
" The threshold s,,, 1s defined as the height. in the unperturbed stellar chromosphere. at which the overlying atmosphere absorbs of the energy of a trial X-ray spectrum (see also Fig. 1))."," The threshold $s_{\rm abs}$ is defined as the height, in the unperturbed stellar chromosphere, at which the overlying atmosphere absorbs of the energy of a trial X-ray spectrum (see also Fig. \ref{fig:cartoon}) )."
 We considered as trial X- spectrum that produced by a plasma at 7=1 MMK., We considered as trial X-ray spectrum that produced by a plasma at $T=1$ MK.
" The plasma temperature does not influence the threshold 5j, used for calculating the and the resonance line luminosities. while it slightly influences the thresholds used for the [0.5—8.0| KkeV band."," The plasma temperature does not influence the threshold $s_{\rm abs}$ used for calculating the and the resonance line luminosities, while it slightly influences the thresholds used for the $[0.5-8.0]$ keV band."
 However. we found that the results of only a few of the parameter configurations considered here. specifically those leading to [ps~sing. slightly depend on the particular choice of the trial X-ray spectrum.," However, we found that the results of only a few of the parameter configurations considered here, specifically those leading to $l_{ps}\sim h_{sink}$, slightly depend on the particular choice of the trial X-ray spectrum."
 For these configurations a more detailed description of the absorption effect. including the dependence on the wavelength. a more smooth transition between the full absorption and the full transmission and a dependence of the angle of view should be performed to give a more precise answer to the observability issue.," For these configurations a more detailed description of the absorption effect, including the dependence on the wavelength, a more smooth transition between the full absorption and the full transmission and a dependence of the angle of view should be performed to give a more precise answer to the observability issue."
" The values of sj&, for the three X-ray bands and for the three metal abundances are reported in Table ]..", The values of $s_{\rm abs}$ for the three X-ray bands and for the three metal abundances are reported in Table \ref{tab:threshold}.
" The value of sy, obviously depends on the chromospheric metal abundances. that we assume to be equal to the abundances of the accreting material."," The value of $s_{\rm abs}$ obviously depends on the chromospheric metal abundances, that we assume to be equal to the abundances of the accreting material."
 However. chromospheric abundances may be different from accretion stream abundances.," However, chromospheric abundances may be different from accretion stream abundances."
 For instance. if the chromospheric abundance i$ higher or lower than the accretion stream abundance. then we underestimate or overestimate the absorptiol effect. respectively.," For instance, if the chromospheric abundance is higher or lower than the accretion stream abundance, then we underestimate or overestimate the absorption effect, respectively."
 A better knowledge of metal abundances of the different components of the star-disk system ts required to better address this issue., A better knowledge of metal abundances of the different components of the star-disk system is required to better address this issue.
" We found that s4,, does not change significantly if we consider the absorbed X-ray emission in the [0.5—8.0| kkeV band or in the resonance line. because the absorption in the softer part of the [0.5—8.0] kkeV band (which is the same of the line) is dominant."," We found that $s_{\rm abs}$ does not change significantly if we consider the absorbed X-ray emission in the $[0.5-8.0]$ keV band or in the resonance line, because the absorption in the softer part of the $[0.5-8.0]$ keV band (which is the same of the line) is dominant."
" On the other hand. we found a significantly lower value of s4&, in the resonance line. this line forming at higher energy (where the absorption is lower) thanvir."," On the other hand, we found a significantly lower value of $s_{\rm abs}$ in the resonance line, this line forming at higher energy (where the absorption is lower) than."
" Therefore. we consider one set of thresholds ως for the synthesis of the luminosities in the [0.5—8.0] kkeV band and in the resonance line. and another set of sas, for the luminosities 1n the resonance line (see Table 1))."," Therefore, we consider one set of thresholds $s_{\rm abs}$ for the synthesis of the luminosities in the $[0.5-8.0]$ keV band and in the resonance line, and another set of $s_{\rm abs}$ for the luminosities in the resonance line (see Table \ref{tab:threshold}) )."
 In all the simulations. during the first 100—200 s. the system follows the same evolution as described in Paper I. Figure 3 shows. as an example. the evolution of plasma temperature. density. pressure and velocity for a stream with Hae=10! em. dace=400 km s! and z=1.0.," In all the simulations, during the first $100-200$ s, the system follows the same evolution as described in Paper I. Figure \ref{fig:oscillations}
 shows, as an example, the evolution of plasma temperature, density, pressure and velocity for a stream with $n_{\rm acc}=10^{11}$ $^{-3}$, $u_{\rm acc}=400$ km $^{-1}$ and $\zeta=1.0$."
 The aceretion stream penetrates the chromosphere and generates a transmitted shock and a reverse shock., The accretion stream penetrates the chromosphere and generates a transmitted shock and a reverse shock.
 After this transient phase. the chromosphere stops the flow penetration where the ram pressure of the post-shock plasma equals the thermal pressure of the chromosphere.," After this transient phase, the chromosphere stops the flow penetration where the ram pressure of the post-shock plasma equals the thermal pressure of the chromosphere."
 The reverse shock progressively builds up a nearly isothermal slab at the post-shock temperature (heating phase: left panels of Fig. 3)., The reverse shock progressively builds up a nearly isothermal slab at the post-shock temperature (heating phase; left panels of Fig. \ref{fig:oscillations}) ).
 During this. phase the intensity of the radiativecooling at the base of the slab, During this phase the intensity of the radiativecooling at the base of the slab
observations.,observations.
 Iu this paper we report on preliminary results of these observations., In this paper we report on preliminary results of these observations.
 Definitive results along with their iiplications will be the subject of another paper (Mascetti et al., Definitive results along with their implications will be the subject of another paper (Masetti et al.
 2000)., 2000).
 Iu the following. for the Iuniuositv estimates we will assume that the RB lies at a distance d = 8 kpe (Ortolani ct al.," In the following, for the luminosity estimates we will assume that the RB lies at a distance $d$ = 8 kpc (Ortolani et al."
 1996)., 1996).
 Dining TOOL. the RB was iu a stroie state of bursting activity.," During TOO1, the RB was in a strong state of bursting activity."
 The 2-10 keV heli curve obtained with MECS (sec FitB., The 2-10 keV light curve obtained with MECS (see Fig.
 l. right pawel. part a) showed 113 Type II Xorav bursts during 9157 seconds of eood observational data.," 1, right panel, part ) showed 113 Type II X–ray bursts during 9457 seconds of good observational data."
 Evidence of Type II musts was also observed im the 0.1-2 keV data obtained with LECS., Evidence of Type II bursts was also observed in the 0.1-2 keV data obtained with LECS.
" We divide he MECS TOOL data into two sumets persisteit oendssion (PE: below 5 couuts 21 7) and bursting emission (BE: above 5 counts Ly, ", We divided the MECS TOO1 data into two subsets: persistent emission (PE; below 5 counts $^{-1}$ ) and bursting emission (BE; above 5 counts $^{-1}$ ).
The MECS PE aud BE spectra οnud be well ftwitha plotoclectrically absorbe wo-component blackbody (2BB): hese BB collIOCifs may originate from the jeutron star (NS) surface. a boun«cary laver between tl16 NS and the inner edge of he accretion disk. or the inner region of the disk itself.," The MECS PE and BE spectra could be well fit with a photoelectrically absorbed two-component blackbody (2BB); these BB components may originate from the neutron star (NS) surface, a boundary layer between the NS and the inner edge of the accretion disk, or the inner region of the disk itself."
 The same model was usec Or he RB by Cuerriero et al. (, The same model was used for the RB by Guerriero et al. (
1998) who fouπ valies consisten with ours.,1998) who found values consistent with ours.
 In Table 1 we report the best-fit parauccrs along witit rein nfideunce errors, In Table 1 we report the best-fit parameters along with their confidence errors.
 The temperatire values of he two DD conponents were ightly higher during the PE tha lcming the BE. Wwile their luninosilos Were Auci higher (by a factor 20 for t1C €'o0ler DD ai 6! for the hotcr BB) duriug 16 BE than duriug he PE.," The temperature values of the two BB components were slightly higher during the PE than during the BE, while their luminosities were much higher (by a factor 20 for the cooler BB and 60 for the hotter BB) during the BE than during the PE."
 We al«) remark that dving the BE the hetter BB conrponeut was brighter (by more la vatactor 3) than the cooler DD. whiο durius ιο PE they had simuzar Iuuinosities.," We also remark that during the BE the hotter BB component was brighter (by more than a factor 3) than the cooler BB, while during the PE they had similar luminosities."
 This implies tla the BE iufhοςον nore the ieher temperature ος»uponent th: he other one., This implies that the BE influences more the higher temperature component than the other one.
 Tf the BE is che to spasinodic ccretion oito the compact object. je higher teurerature clupo1Cit should be 16 one comune from he NS surface.," If the BE is due to spasmodic accretion onto the compact object, the higher temperature component should be the one coming from the NS surface."
" The sotrco was also visible i ιο hard Nrav (15-100 keV) enc‘TeV τα1ος,", The source was also visible in the hard X–ray (15-100 keV) energy range.
 Ilowever hie statistics oft1C PDS lielit curve was muuch lower and di not allow cistiusuisu iefιο Tyo IT bursts., However the statistics of the PDS light curve was much lower and did not allow distinguishing the Type II bursts.
 Iu order to construct f16 BE spectra we 1sec he time iuervals iu which the IntYS nowere observed wit1i MECS., In order to construct the BE spectrum we used the time intervals in which the bursts were observed with MECS.
" A""C» we could rot derive he correct 15-10() keV. flux and spectrum of both BE aiC PE given he residua ""OIree contanunatioun by CX 351-0."," Also, we could not derive the correct 15-100 keV flux and spectrum of both BE and PE given the residual source contamination by GX 354-0."
 Thus. 1i order to overcome his xobleinm. we used as backgrouud level for he 1-100 xev BE spectrumt1C total count rate level ucasured dunue the PE time iuervals.," Thus, in order to overcome this problem, we used as background level for the 1-100 keV BE spectrum the total count rate level measured during the PE time intervals."
" The couined LECSAECS|PDS PE-subtraced ""nrstius specrun show iiu Fig."," The combined LECS+MECS+PDS PE-subtracted bursting spectrum, shown in Fig."
 2. was 10 longer fi with a 2BB nodel.," 2, was no longer fit with a 2BB model."
 By :vldiis a power lav* conrponent we obtained au acceptable fit (see Talle 1), By adding a power law component we obtained an acceptable fit (see Table 1).
 The furher addition of a Fe K emission line at 6.5 keV. slightly inproved he Bt. with parameter values foind for this Ine In general agreement wit ithe fudigsoe w Stella et al. (," The further addition of a Fe K emission line at 6.5 keV slightly improved the fit, with parameter values found for this line in general agreement with the findings by Stella et al. ("
1988) for Tye II bursts.,1988) for Type II bursts.
 Diving TOO2 the RD d:ustically recuced its bursting activity. axd the bursts were concentrated at the beginning of this TOO (Fie.," During TOO2 the RB drastically reduced its bursting activity, and the bursts were concentrated at the beginning of this TOO (Fig."
 Ll. zieht paucl. part 0).," 1, right panel, part )."
 AsO. he emission intensity level «ecreased.," Also, the emission intensity level decreased."
 The bestfit model was a plotoelectrically absorbed 2BB mocel (Table |)., The best–fit model was a photoelectrically absorbed 2BB model (Table 1).
 No evidence of a Fe emission line was prescut., No evidence of a Fe emission line was present.
"We consider a double cone mirror (Fig. B1)),","We consider a double cone mirror (Fig. \ref{fig:offax_scheme}) ),"
 with optical axis aligned with z and the intersection plane at z=0., with optical axis aligned with $z$ and the intersection plane at $z=0$ .
" We define Ro to be its radius at z=0, αρ the incidence angle for an source placed at infinity, and L;, Ly, lengths of the primary and secondary mirror segments."," We define $R_0$ to be its radius at $z =0$, $\alpha_0$ the incidence angle for anon-axis source placed at infinity, and $L_1$, $L_2$, lengths of the primary and secondary mirror segments."
 We assume αρ to be shallow and that the source is at the finite distance D>L4., We assume $\alpha_0$ to be shallow and that the source is at the finite distance $D \gg L_1$.
" If the source is on-axis, the beam impinges the primary segmentwith a nearly constant half-divergency 6=Ro/D."," If the source is on-axis, the beam impinges the primary segmentwith a nearly constant half-divergency $\delta = R_0/D$."
" We denote with ΤΙ, Q1, and z, the radial, azimuthal, and axial coordinates of the impact point on the primary segment, and r2, q», and z2 on the secondary."," We denote with $r_1$, $\varphi_1$, and $z_1$ the radial, azimuthal, and axial coordinates of the impact point on the primary segment, and $r_2$, $\varphi_2$, and $z_2$ on the secondary."
" We now assume the source to be moved off-axis by an angle 6, and choose the direction o,=y»0 in the tilt plane of the source (the xz plane, like in Fig. 1))."," We now assume the source to be moved off-axis by an angle $\theta$, and choose the direction $\varphi_1 = \varphi_2 = 0$ in the tilt plane of the source (the $xz$ plane, like in Fig. \ref{fig:mirror_section}) )."
" Our scope in this appendix is to determine analytically the incidence angles on the two mirrors, a, and a», and the vignetting for double reflection, V, as a function of ao, 6, 0, v1, more generally than we did in Appendix AppendixA:."," Our scope in this appendix is to determine analytically the incidence angles on the two mirrors, $\alpha_1$ and $\alpha_2$, and the vignetting for double reflection, $V$, as a function of $\alpha_0$, $\delta$, $\theta$, $\varphi_1$, more generally than we did in Appendix \ref{App_vign}."
". The two conical surfaces are described in polar coordinates by the equations The normal vectors to the two segments, directed inwards, are if the double cone approximation is valid, the normal vectors are only a function of the y’s angles."," The two conical surfaces are described in polar coordinates by the equations The normal vectors to the two segments, directed inwards, are if the double cone approximation is valid, the normal vectors are only a function of the $\varphi$ 's angles."
"{ the source were on-axis, the initial direction of the ray would have the expression Since the source is off-axis by 6, we have to tilt ko by an angle @ about the y axis."," the source were on-axis, the initial direction of the ray would have the expression Since the source is off-axis by $\theta$, we have to tilt $\underline{k}_0^*$ by an angle $\theta$ about the $y$ axis."
" The application of the rotation matrix returns the expression for the initial direction of the off-axis photon, ky, If a; is the cosincidence angle of the first reflection (measured from the surface), we can write the scalar product which becomes, after some algebra, In the limit of small ao, 6, 6, we can approximate the cosines with | and the sines with their arguments, yielding that is exactly Eq. (20))."," The application of the rotation matrix returns the expression for the initial direction of the off-axis photon, $\underline{k}_0$, If $\alpha_1$ is the incidence angle of the first reflection (measured from the surface), we can write the scalar product which becomes, after some algebra, In the limit of small $\alpha_0$, $\delta$, $\theta$, we can approximate the cosines with 1 and the sines with their arguments, yielding that is exactly Eq. \ref{eq:angles1}) )."
" To derive the incidence angle on the secondary mirror segment, we need to trace the exit direction of each ray, k,, after the first reflection."," To derive the incidence angle on the secondary mirror segment, we need to trace the exit direction of each ray, $\underline{k}_1$, after the first reflection."
" This is obtained from the vector equation because the parallel component to the surface is conserved, whilst the normal component reverses its sign in the reflection process."," This is obtained from the vector equation because the parallel component to the surface is conserved, whilst the normal component reverses its sign in the reflection process."
 By substitution of the Eqs. (B5)), By substitution of the Eqs. \ref{eq:k_0}) )
" and (B3), one obtains, as always in the small angles limit, A ray reflected at the generic point r, of the primary segment has equation r(t)=τι+tk,, with ¢>0."," and \ref{eq:normal}) ), one obtains, as always in the small angles limit, A ray reflected at the generic point $\underline{r}_1$ of the primary segment has equation $\underline{r}(t) = \underline{r}_1+ t \,\underline{k}_1$, with $t>0$."
" Therefore, the reflected ray intersects the secondary segment at a position το fulfillingthe condition r(t)= ry, iie. ryΤι=tk, for some t."," Therefore, the reflected ray intersects the secondary segment at a position $\underline{r}_2$ fulfillingthe condition $ \underline{r}(t)=\underline{r}_2 $ , i.e., $ \underline{r}_2 - \underline{r}_1 = t\, \underline{k}_1$ for some $t$ ."
 This is equivalent to constraining the two vectors to be parallel: wherery) Χ denotes a cross product., This is equivalent to constraining the two vectors to be parallel: where $\times$ denotes a cross product.
 Using both Eqs. (B1)), Using both Eqs. \ref{eq:z1}) )
" and (B2), Eq. (B11))"," and \ref{eq:z2}) ), Eq. \ref{eq:prod_vect}) )"
" can be developed into 3 scalar equations, only 2 of which are mutually independent, i.e.,"," can be developed into 3 scalar equations, only 2 of which are mutually independent, i.e.,"
ree parameter.,free parameter.
 In the secoud data segment (6 to 10 hours UT).— the 47 nfor the fit never converged to the straight. inc.," In the second data segment (6 to 10 hours UT), the $\chi^2$ for the fit never converged to the straight line."
 We therefore show the narrowest ft which attained P=L., We therefore show the narrowest fit which attained $\chi^2=1$.
 The values of IIWIIM for the fitted Gaussians aud IDWIIM of the corresponding Caussian source ou the sky are given iu. Table 3.., The values of HWHM for the fitted Gaussians and HWHM of the corresponding Gaussian source on the sky are given in Table \ref{srcsizes}. .
 Iu FigureOo 5Γ the rielit-Oo aud left-handed polarizations are shown separately for the time seemeuts 6-10 hours and 10 hours to the eud of the experiment., In Figure \ref{uvplt2} the right- and left-handed polarizations are shown separately for the time segments 6-10 hours and 10 hours to the end of the experiment.
 The Stokes LL data from Mauua Ikea were flageed during the last part of the experiucut. aud for his reason the lougest baseline is müssne frou the fina LL plo (lower neht-haud panel).," The Stokes LL data from Mauna Kea were flagged during the last part of the experiment, and for this reason the longest baseline is missing from the final LL plot (lower right-hand panel)."
 The enhanced brightening a RR cau be clearly seen., The enhanced brightening at RR can be clearly seen.
 Also clearly seeu is the fact tha LL does not xiehteu at all divine the second flare. whereas RR docs.," Also clearly seen is the fact that LL does not brighten at all during the second flare, whereas RR does."
 This is consistent with the lightcurve shown in Figure 3.., This is consistent with the lightcurve shown in Figure \ref{ttsvlalc}.
 We have determined upper limits to the source sizes for he separate RR aud LL data iu the sue way as described above., We have determined upper limits to the source sizes for the separate RR and LL data in the same way as described above.
 These are also listed in Table 3.., These are also listed in Table \ref{srcsizes}.
 T Tau N is not resolved in the VLA map. which has a asin baseline separation of ~300 kA. but is resolved-out bv the VLBI.," T Tau N is not resolved in the VLA map, which has a maximum baseline separation of $\sim$ 300 $\lambda$, but is resolved-out by the VLBI."
" This coustrains its size to be between roughly 20 mas zuid 300 mas,", This constrains its size to be between roughly 20 mas and 300 mas.
 A 20 mas source corresponda to 2:8 AU at 110 pe.which is huge enough to rule," A 20 mas source corresponds to 2.8 AU at 140 pc,which is large enough to rule"
of the ow-encitation lines.,of the low-excitation lines.
 For the lieh-excitatiou starbursting dwarts. such a discrepancy does not arise. aud hot stars remain an option.," For the high-excitation starbursting dwarfs, such a discrepancy does not arise, and hot stars remain an option."
 Again. the inconsisteney could be alleviated if regions with relatively stronger [OIV| eiissiou. were dispersed ina lower excitation background.," Again, the inconsistency could be alleviated if regions with relatively stronger ] emission were dispersed in a lower excitation background."
 In fact. such a scenario is qualitatively consistent with the observations. as are others with distributed local sources of [OV].," In fact, such a scenario is qualitatively consistent with the observations, as are others with distributed local sources of ]."
 The major reason to consider it uulikelv is that we have failed wp to now to detect [OV] enissiou even at asimdlar love in local star forming regions. while we would have to postulate regious withstronger cutission.," The major reason to consider it unlikely is that we have failed up to now to detect ] emission even at a level in local star forming regions, while we would have to postulate regions with emission."
 The Galactic ceuter. which is closest to starburst galaxies in lmauy aspects; still shows 1v]. though even fainter than in the starbursts (Lutz ct al. 1996b3).," The Galactic center, which is closest to starburst galaxies in many aspects, still shows ], though even fainter than in the starbursts (Lutz et al. \cite{lutz96b}) )."
 Iu the massive star foriumng reeious audDoracdus.. for which /[Nen] indicates high excitation. we were unable to detect [OI] at a level of «0.01 and <0.005 of ΝοΠη. respectively (Thornley et al.," In the massive star forming regions and, for which ] indicates high excitation, we were unable to detect ] at a level of $<$ 0.01 and $<$ 0.005 of ], respectively (Thornley et al.,"
 in preparation)., in preparation).
 Ilieh excitation planetary nebulae are a known source of [Or1v| ciission., High excitation planetary nebulae are a known source of ] emission.
 A young starburst will. of course. not contain planetary nebulae and it is easy to show that their --inteerated contribution from the old stellar population is too faint.," A young starburst will, of course, not contain planetary nebulae and it is easy to show that their integrated contribution from the old stellar population is too faint."
 Evolutionary caleulatious (e.g. Clarlot Druzual 19011) show that the contribution of post-ACD o the bolometric Inniuositv is less thau evel populations., Evolutionary calculations (e.g. Charlot Bruzual \cite{charlot91}) ) show that the contribution of post-AGB stages to the bolometric luminosity is less than even in old populations.
 Making the extreme assumptions at of the bolometric Iunuinositv is due to au old »pulatioun and that al PAGB objects are like. one of he highest excitation planetary nebulae. we estimate a robust upper init of 29 ? for the OV] e1iission from plauctary nebulae in82.. based on Ov] fux. huninosity aud distauce of as given w Shure ct al. (1983))," Making the extreme assumptions that of the bolometric luminosity is due to an old population and that all PAGB objects are like, one of the highest excitation planetary nebulae, we estimate a robust upper limit of $^{-20}$ $^{-2}$ for the ] emission from planetary nebulae in, based on ] flux, luminosity and distance of as given by Shure et al. \cite{shure83}) )"
 and Beintema et al. (1996))., and Beintema et al. \cite{beintema96}) ).
 There is ample evidence for ionizing shocks iu starburst ealaxies., There is ample evidence for ionizing shocks in starburst galaxies.
 Spatially exteuded. Liuer-tvpe optical cussion lines can be attributed to shocks. aud kinematic mapping soletimies provides direct evidence for outfowius Ssperwiuds (Πουπια ct al. 19903). ," Spatially extended, `Liner'-type optical emission lines can be attributed to shocks, and kinematic mapping sometimes provides direct evidence for outflowing `superwinds' (Heckman et al. \cite{heckman90}) ). ]"
column deusities approaching 7 are expected for modest velocity shocks (LO0-200kkin/s. e.g. Shull Melee 1979.. Dopita Sutherland 1996)).," column densities approaching $^{14}\,$ $^{-2}$ are expected for modest velocity shocks km/s, e.g. Shull McKee \cite{shull79}, Dopita Sutherland \cite{dopita96}) )."
 Assuming postshock values of 7 aud TIS. we estimate 25.090401 iuteuxity: of: ~ὃν.4105eergss t 2τσκ uro!Cn equivalent to ~3:«10.29 ccu.? for the SWS beam.," Assuming postshock values of $^{-3}$ and K, we estimate a $\mu$ m intensity of $\sim 3\times 10^{-5}$ $^{-1}$ $^{-2}$ $^{-1}$, equivalent to $\sim 3\times 10^{-20}$ $^{-2}$ for the SWS beam."
 For the assumed. conditions. the covering factor of such shocks iu the starburst region of would have to be of the order unity.," For the assumed conditions, the covering factor of such shocks in the starburst region of would have to be of the order unity."
 At higher shock velocities. the ΟΙ] cohunn would be increasingly dominated by material at rest’ in the photoionized precursor in the material aleacl of the shock frout (Dopita Sutherlaud 1996)).," At higher shock velocities, the ] column would be increasingly dominated by material `at rest' in the photoionized precursor in the material ahead of the shock front (Dopita Sutherland \cite{dopita96}) )."
 The shock models predict that intensities simular to those estimated for rv] are eiitted in optical shock tracers like66716/21AÀ., The shock models predict that intensities similar to those estimated for ] are emitted in optical shock tracers like.
 This is fully consistent with optical spectroscopy of (e.g. Góttz et al. 1900)., This is fully consistent with optical spectroscopy of (e.g. Göttz et al. \cite{goetz90}) ).
 We note that the faint shock cussion predicted for the aud 11] lines will be completely dominated by he emission from regions., We note that the faint shock emission predicted for the ] and ] lines will be completely dominated by the emission from regions.
 It is instructive to compare the [Ov] results for with the SWS observatious for103... a bright supernova remnant interacting with a dense molecular cloud (Oliva ct al..," It is instructive to compare the ] results for with the SWS observations for, a bright supernova remnant interacting with a dense molecular cloud (Oliva et al.,"
 in preparation)., in preparation).
 The 1v] iuteusities are very simular., The ] intensities are very similar.
 The ionic lines are just resolved at the SWS spectral resolving power. again simular to82.," The ionic lines are just resolved at the SWS spectral resolving power, again similar to."
. Ionizing shocks lence are a plausible origin for the Iv]. cimission if their total coveriug factor approaches unity in the ceutral starburst region of82., Ionizing shocks hence are a plausible origin for the ] emission if their total covering factor approaches unity in the central starburst region of.
. We have discussed various excitation iuechanisnis for ‘aint 1v]. cinission from starburst galaxies., We have discussed various excitation mechanisms for faint ] emission from starburst galaxies.
 Iu. general. starburst-related sources and in particular ionizing shocks xovide the most plausible explanation.," In general, starburst-related sources and in particular ionizing shocks provide the most plausible explanation."
 Weak buried AGNs mav be plausible for individual sources but cau v0 ruled out for the best studied case of whose Oly] enütting region has been spatially resolved., Weak buried AGNs may be plausible for individual sources but can be ruled out for the best studied case of whose ] emitting region has been spatially resolved.
 Iu addition. the fairly simall scatter iu. 1v| versus starburst ΠΕ favours a starburst-related origin. since no finetumine of two judependent iiechauisuis is required.," In addition, the fairly small scatter in ] versus starburst luminosity favours a starburst-related origin, since no finetuning of two independent mechanisms is required."
Stars form in giant molecular clouds (GMCs) whose primary constituent is molecular hydrogen.H».,"Stars form in giant molecular clouds (GMCs) whose primary constituent is molecular hydrogen,."
. Because llacks a permanent dipole moment. and the lowest lying excited state capable of quadrupole emission requires temperatures ~200 KK to be excited. the physical conditions in the cold (~10 K) molecular gas are typically probed via tracer molecules. rather than by direct detection ofΗ».," Because lacks a permanent dipole moment, and the lowest lying excited state capable of quadrupole emission requires temperatures $\sim 500$ K to be excited, the physical conditions in the cold $\sim 10$ K) molecular gas are typically probed via tracer molecules, rather than by direct detection of."
. Carbon Monoxide (7CÍO: hereafter. CO) is the second most abundant molecule in GMCs.," Carbon Monoxide $^{12}$ $^{16}$ O; hereafter, CO) is the second most abundant molecule in GMCs."
" Because the J=!-0 rotational transition of CO lies only 5 K above ground. has a relatively low effective density (~107.""em. ») for excitation 1999), and has a wavelength of ~3 mm which is readily observable from the ground. CO (J21-0) has historically been one of the most commonly used tracers of physical conditions in the molecular ISM."," Because the J=1-0 rotational transition of CO lies only $\sim5$ K above ground, has a relatively low effective density $\sim 10^{2-3}$ ) for excitation , and has a wavelength of $\sim3$ mm which is readily observable from the ground, CO (J=1-0) has historically been one of the most commonly used tracers of physical conditions in the molecular ISM."
 A large uncertainty in using CO to trace ggas is relating the observed CO line luminosity to the underlying ccolumn density., A large uncertainty in using CO to trace gas is relating the observed CO line luminosity to the underlying column density.
 However. despite the fact that aabundances vary strongly within GMCs2011). a multitude of observations suggests that the conversion factor between CO and iis reasonably constant in Galactic GMCs. following the relation: where iis the cconversion factor in units of ccolumn density divided by velocity-integrated CO linetensity!..," However, despite the fact that abundances vary strongly within GMCs, a multitude of observations suggests that the conversion factor between CO and is reasonably constant in Galactic GMCs, following the relation: where is the conversion factor in units of column density divided by velocity-integrated CO line."
 Lines of evidence for a relatively constant, Lines of evidence for a relatively constant
The figure of merit being compared is the nunber of square degrees of sky per 2l-hour period which can be surveyed for given source magnitude.,The figure of merit being compared is the number of square degrees of sky per 24-hour period which can be surveyed for given source magnitude.
 I demaud that at least of the sources at the chosen magniltide be measured with S/N>7 (recall that cosmic rays aud varyiug pixel phases make the S/N a random variable)., I demand that at least of the sources at the chosen magnitude be measured with $S/N\ge7$ (recall that cosmic rays and varying pixel phases make the $S/N$ a random variable).
 We cau reach the following couclusious: This of course is just a nolse analysis: there are systematic-error ancl cost isstes as well. the ormer favoringSNAP aud the latterL597.," We can reach the following conclusions: This of course is just a noise analysis; there are systematic-error and cost issues as well, the former favoring and the latter."
 Iu particular. note that the above analysis las assured isolated point sources—wlhich is appropriate to a time-domain search with perfect dillerence imagine.," In particular, note that the above analysis has assumed isolated point sources—which is appropriate to a time-domain search with perfect difference imaging."
 For crowdec-feld photometry. however (color-magnitude diagrams for distant. systems. Cepleicl ueasurement. etc.).," For crowded-field photometry, however (color-magnitude diagrams for distant systems, Cepheid measurement, etc.),"
 the space telescopes gain a large factor from better resolution., the space telescopes gain a large factor from better resolution.
 Note also that both observatories” desigus could be tweaked to improve performance on this ueasure. but the ultiuate restrictions ou FOV. telemetry rate. etc.," Note also that both observatories' designs could be tweaked to improve performance on this measure, but the ultimate restrictions on FOV, telemetry rate, etc."
 require a [ull engineering analysis., require a full engineering analysis.
 For lensing applications. pre-cleterminationu of supernova lost-ealaxy redshifts. aud a slew of ealaxy-evolution studies. photometric determination of galaxy redshifts will be of huge benefit.," For lensing applications, pre-determination of supernova host-galaxy redshifts, and a slew of galaxy-evolution studies, photometric determination of galaxy redshifts will be of huge benefit."
 We thus ueed to kuow the speed at which we cau measure colors of resolved objects to a nominal accuracy., We thus need to know the speed at which we can measure colors of resolved objects to a nominal accuracy.
 I take here a target S/N>20 for photo-z applications., I take here a target $S/N\ge20$ for photo-z applications.
We activate particle self-gravity in simulations of the streaming instability with inelastic NS collisions. at times when there is little particle concentration. to catch the simultaneous action of streaming instability and self-gravity during the next concentration event.,"We activate particle self-gravity in simulations of the streaming instability with inelastic NS collisions, at times when there is little particle concentration, to catch the simultaneous action of streaming instability and self-gravity during the next concentration event."
" In NNS we thus start self- at ¢=S527. while in NNS we start self-gravity at ¢=197,4, (see 7))."," In NS we thus start self-gravity at $t=52T_{\rm orb}$, while in NS we start self-gravity at $t=19 T_{\rm orb}$ (see )."
 We then evolve the simulation for another 5 orbits. either ignoring collisions or applying the usual variation of collision types (elastic. inelastic KS. inelastic NS).," We then evolve the simulation for another 5 orbits, either ignoring collisions or applying the usual variation of collision types (elastic, inelastic KS, inelastic NS)."
 Results of 64° simulations are shown in1., Results of $64^3$ simulations are shown in.
. Between 3 and 4 initially condense out of the dominantly axisymmetric filament forming by the streaming instability., Between 3 and 4 initially condense out of the dominantly axisymmetric filament forming by the streaming instability.
 These clumps have masses between a tenth and a third of the dwarf planet Ceres — corresponding to contracted radit between 220 and 330 km. assuming an internal density of 2 g/em*.," These clumps have masses between a tenth and a third of the dwarf planet Ceres – corresponding to contracted radii between 220 and 330 km, assuming an internal density of 2 $^3$."
 All the clumps form in a single planetesimal-formation event shortly after the onset of self-gravity., All the clumps form in a single planetesimal-formation event shortly after the onset of self-gravity.
 The clumps continue to grow mainly by accreting particles from the turbulent flow. but no new gravitationally bound clumps form.," The clumps continue to grow mainly by accreting particles from the turbulent flow, but no new gravitationally bound clumps form."
 Clumps eventually collide and merge in all simulations., Clumps eventually collide and merge in all simulations.
 Such clump merging is likely an unphysical effect driven by the large sizes of the planetesimals., Such clump merging is likely an unphysical effect driven by the large sizes of the planetesimals.
 The self-gravity solver does not allow gravitational structures to become smaller than a grid cell. and that leads to artificially large collisional cross sections.," The self-gravity solver does not allow gravitational structures to become smaller than a grid cell, and that leads to artificially large collisional cross sections."
 A more probable outcome of the real physical system is gravitational scattering and/or formation of binaries (Nesvornyetal..2010)., A more probable outcome of the real physical system is gravitational scattering and/or formation of binaries \citep{Nesvorny+etal2010}.
. Results at 128? are shown in12., Results at $128^3$ are shown in.
. At higher resolution the number of clumps condensing out is about twice as high compared to the lower resolution simulation., At higher resolution the number of clumps condensing out is about twice as high compared to the lower resolution simulation.
 However. the masses of the most massive clumps are very similar to lower resolution (although a bit higher — up to of Ceres). so it appears that higher resolution simply allows lower-mass clumps to condense out as well.," However, the masses of the most massive clumps are very similar to lower resolution (although a bit higher – up to of Ceres), so it appears that higher resolution simply allows lower-mass clumps to condense out as well."
 The masses of the clumps condensing out at 128? resolution correspond to contracted radii between 84 and 405 km., The masses of the clumps condensing out at $128^3$ resolution correspond to contracted radii between 84 and 405 km.
 The ability. to. form smaller clumps at higher resolution is expected from the picture that a radial contraction phase is needed before the Roche density can beachieved?., The ability to form smaller clumps at higher resolution is expected from the picture that a radial contraction phase is needed before the Roche density can be.
. Higher resolution allows contraction to narrower bands and thus formation of less massive planetesimals., Higher resolution allows contraction to narrower bands and thus formation of less massive planetesimals.
 It is nevertheless difficult to compare the planetesimal masses condensing out at the two resolutions as the initial conditions are not the same., It is nevertheless difficult to compare the planetesimal masses condensing out at the two resolutions as the initial conditions are not the same.
 Reinetal.(2010) observed in their 2-D sheanmng sheet simulations. that inclusion of collisions would lead to condensation. of fewer and more massive clumps. when compared to simulations without collisions.," \cite{Rein+etal2010} observed in their 2-D shearing sheet simulations that inclusion of collisions would lead to condensation of fewer and more massive clumps, when compared to simulations without collisions."
 Our also shows that the simulation with no collisions makes the highest number of clumps of all the four simulations., Our also shows that the simulation with no collisions makes the highest number of clumps of all the four simulations.
 evertheless the characteristic mass of the most massive clumps appears indifferent to the treatment of collisions., Nevertheless the characteristic mass of the most massive clumps appears indifferent to the treatment of collisions.
 Since G controls the relative strength of self-gravity. results obtained with a given G can not be sealed to other values of G.," Since $\tilde{G}$ controls the relative strength of self-gravity, results obtained with a given $\tilde{G}$ can not be scaled to other values of $\tilde{G}$."
 We vary the self-gravity parameter in 128? simulations in13. starting self-gravity at the same time as in 12.," We vary the self-gravity parameter in $128^3$ simulations in, starting self-gravity at the same time as in ."
. Weaker self-gravity gives lower clump masses. but gravitationally bound clumps of up to 0.01 Ceres masses (or 100 km radius) condense even at G=0.02.," Weaker self-gravity gives lower clump masses, but gravitationally bound clumps of up to $0.01$ Ceres masses (or 100 km radius) condense even at $\tilde{G}=0.02$."
 The solar nebula model of Hayashi(1981) has G=0.04 at 3 AU from the sun.," The solar nebula model of \cite{Hayashi1981}
 has $\tilde{G}\approx0.04$ at 3 AU from the sun."
 Thus the streaming instability allows planetesimal formation in dise models that are similar in mass to the solar nebula. in contrast to recent simulations of planetesimal formation in pressure bumps excited by the magnetorotational instability which required disc. masses up to 10 times the solar nebula (Johansenetal..2011).," Thus the streaming instability allows planetesimal formation in disc models that are similar in mass to the solar nebula, in contrast to recent simulations of planetesimal formation in pressure bumps excited by the magnetorotational instability which required disc masses up to 10 times the solar nebula \citep{Johansen+etal2011}."
. The presented simulations do not catch the transition from bound clump to solid planetesimal., The presented simulations do not catch the transition from bound clump to solid planetesimal.
 However. Nesvornyetal.(2010). simulated the gravitational collapse of spherical particle clouds and generally found formation of binary planetesimals. with the two largest bodies containing a significant fraction of the mass of the cloud.," However, \cite{Nesvorny+etal2010} simulated the gravitational collapse of spherical particle clouds and generally found formation of binary planetesimals, with the two largest bodies containing a significant fraction of the mass of the cloud."
 The fact that the masses of the most nassive bound clumps in our simulations are relatively independent of resolution allows us to eritically compare the mass distribution of the clumps to to the observed properties of the asteroid and Kuiper belts and extrasolar debris disces., The fact that the masses of the most massive bound clumps in our simulations are relatively independent of resolution allows us to critically compare the mass distribution of the clumps to to the observed properties of the asteroid and Kuiper belts and extrasolar debris discs.
 The physical mass of the clumps depends on location in the disc and on the self-gravity parameter C., The physical mass of the clumps depends on location in the disc and on the self-gravity parameter $\tilde{G}$.
 While the simulations are dimensionless. the translation to physical mass involves multiplication by the mass unit Mo=pol?GOH?/(AnG).," While the simulations are dimensionless, the translation to physical mass involves multiplication by the mass unit $M_0
= \rho_0 H^3 = \tilde{G} \varOmega^2 H^3/(4 \pi G) $."
" In a nebula with constant G and Τος+7"", the mass unit scales as Myo177. so re-scaling to the Kuiper gives planetesimal masses 5-6 times higher than in and12."," In a nebula with constant $\tilde{G}$ and $T\propto r^{-1/2}$, the mass unit scales as $M_0 \propto
r^{3/4}$, so re-scaling to the Kuiper gives planetesimal masses 5–6 times higher than in and."
. Contracted radii at the location of the Kuiper belt are approximately higher than in the asteroid belt. yielding planetesimal radit between 150 and 730 km.," Contracted radii at the location of the Kuiper belt are approximately higher than in the asteroid belt, yielding planetesimal radii between 150 and 730 km."
 The upper range is comparable to the masses of thelargest known Kuiper belt objects (Chiangetal..2007;Brown.2008).," The upper range is comparable to the masses of thelargest known Kuiper belt objects \citep{Chiang+etal2007,Brown2008}."
. This extrapolation is only valid for an assumed constant self-gravity parameter G., This extrapolation is only valid for an assumed constant self-gravity parameter $\tilde{G}$ .
" The minimum mass solar nebula. with ©x777, has G«rt."," The minimum mass solar nebula, with $\varSigma\propto r^{-3/2}$, has $\tilde{G}\propto r^{1/4}$."
 The weak dependence on radial distance from the star gives in the Kuiper belt at =30AU a 107=L8 times larger G than in the asteroid belt.," The weak dependence on radial distance from the star gives in the Kuiper belt at $r=30\,{\rm AU}$ a $10^{1/4}\approx1.8$ times larger $\tilde{G}$ than in the asteroid belt."
 From we read off an approximate doubling inplanetesimal mass when increasing G from 0.05 to 0.1., From we read off an approximate doubling inplanetesimal mass when increasing $\tilde{G}$ from $0.05$ to $0.1$ .
 We expect thatthis scaling holds for larger G as well., We expect thatthis scaling holds for larger $\tilde{G}$ as well.
 This way the minimum mass, This way the minimum mass
between stellar angular velocity Qy and temperature difference AT at r=ΟΕ. where AT=mas(7\(re.9))—min(Ti(r.8)).,"between stellar angular velocity $\Omega_0$ and temperature difference $\Delta T$ at $r=0.71R_\odot$, where $\Delta T =\max (T_1(r_\mathrm{bc},\theta))-\min
(T_1(r_\mathrm{bc},\theta))$."
 Although the temperature difference monotonously increases with larger stellar angular velocity values. it is not enough to make the rotational profile largely deviate from the Tavlor-Proudimnan state.," Although the temperature difference monotonously increases with larger stellar angular velocity values, it is not enough to make the rotational profile largely deviate from the Taylor-Proudman state."
 This can be explained by using the thermal wind equation. which is a steady state solution of eq. (45)):," This can be explained by using the thermal wind equation, which is a steady state solution of eq. \ref{therm01}) ):"
 The inertial terim and the diffusion terim are neglected here., The inertial term and the diffusion term are neglected here.
 This equation indicates that. for a given value of the NTP. we need an entropy gradient. proportional to Q7.," This equation indicates that, for a given value of the NTP, we need an entropy gradient proportional to $\Omega_0^2$."
" However. our simulation results show that ATxOt"". which means that as O0 increases. the thermal driving force becomes insufficient to push differential rotation away from the Tavlor-Proucdinan state."," However, our simulation results show that $\Delta T \propto \Omega_0^{0.58}$, which means that as $\Omega_0$ increases, the thermal driving force becomes insufficient to push differential rotation away from the Taylor-Proudman state."
 In other words. the latitudinal entropy. gracient in rapidly rotating stars is so small that differential rotation stavs close to the Tavlor-Prouchnan state.," In other words, the latitudinal entropy gradient in rapidly rotating stars is so small that differential rotation stays close to the Taylor-Proudman state."
 In our model. meridional flow generates latitudinal entropy gradient al the base of the convection zone.," In our model, meridional flow generates latitudinal entropy gradient at the base of the convection zone."
 It is conjectured that the insullident thermal drive is due to a slow meridional We next investigate the dependence of meridional flow on stellar angular velocity., It is conjectured that the insufficient thermal drive is due to a slow meridional We next investigate the dependence of meridional flow on stellar angular velocity.
 Fig., Fig.
 1l shows the radial profile of latitudinal velocity ορ at 0=457. using the results of cases 1. 2 and 9.," \ref{vari_some} shows the radial profile of latitudinal velocity $v_\theta$ at $\theta=45^\circ$, using the results of cases 1, 2 and 9."
 In case 2. stellar angular velocity is twice that of ease I (the solar value).," In case 2, stellar angular velocity is twice that of case 1 (the solar value)."
 In case 9. stellar angular velocity is equal to the solar value. and the amplitude of the X effect is (wo limes (he value in case 1.," In case 9, stellar angular velocity is equal to the solar value, and the amplitude of the $\Lambda$ effect is two times the value in case 1."
 Fig., Fig.
 11. shows that meridional flow does not depend on stellar angular velocity. while it correlates with the effect.," \ref{vari_some} shows that meridional flow does not depend on stellar angular velocity, while it correlates with the $\Lambda$ effect."
 Considering eq. (34)).," Considering eq. \ref{lambda}) ),"
 the X elfect increases with larger values of stellar angular velocity. since the amplitude of the A ellect is proportional to Qo.," the $\Lambda$ effect increases with larger values of stellar angular velocity, since the amplitude of the $\Lambda$ effect is proportional to $\Omega_0$."
 The reason why differential rotation in rapidly rotation stars is close to the Tavlor-Proudiman state is that meridional flow does not become [ast with large stellar angular velocity values., The reason why differential rotation in rapidly rotation stars is close to the Taylor-Proudman state is that meridional flow does not become fast with large stellar angular velocity values.
to those in red and «leac elliptieals than those in star forming disks.,to those in red and dead ellipticals than those in star forming disks.
 Furthermore it is possible to only select. galxies for which the light in t10 fiber is dominated by the stars in thefudge., Furthermore it is possible to only select galxies for which the light in the fiber is dominated by the stars in the.
 Ln order to «o this we use the catalog by Simardοἱ (2011).. who have performed a bulge-disk decomposition for galaxies in the SDSS.," In order to do this we use the catalog by \citet{simard}, who have performed a bulge-disk decomposition for galaxies in the SDSS."
 We now choose only those galaxies for which at least SYA of the light in the fiber is originated by bulge stars and repeat the analysis shown in Fig. s.., We now choose only those galaxies for which at least $80\%$ of the light in the fiber is originated by bulge stars and repeat the analysis shown in Fig. \ref{fig:hist}.
 lt is worth noting that the total number of elliptical (spiral) ealaxies is reduced by a ((52%))., It is worth noting that the total number of elliptical (spiral) galaxies is reduced by a ).
 Once again the metallicity seems. to be the only discrepant quantity. between the bulges of passive spirals and ellipticals at high significance (22~10. in all three bins)., Once again the metallicity seems to be the only discrepant quantity between the bulges of passive spirals and ellipticals at high significance $P\sim10^{-3}$ in all three bins).
 Phe distribution of age; and a-enhancement in both galaxy samples are relatively similar., The distribution of age and $\alpha$ -enhancement in both galaxy samples are relatively similar.
 Visual inspection of the distributions. as well as the INS test. probabilities. shows that the statistical evidence for a dillerence. between the samples is inconclusive.," Visual inspection of the distributions, as well as the KS test probabilities, shows that the statistical evidence for a difference between the samples is inconclusive."
 High spatial resolution ancl 3D spectroscopy. rather than increasing sample size. would. be more likely to test this conclusively.," High spatial resolution and 3D spectroscopy, rather than increasing sample size, would be more likely to test this conclusively."
 Our findings point to a scenario in which the stellar population properties in the bulges of quicscent spiral aud elliptical galaxies scale with the central velocity dispersion., Our findings point to a scenario in which the stellar population properties in the bulges of quiescent spiral and elliptical galaxies scale with the central velocity dispersion.
" We find the voungest. less metallic. less a-enhanced objects to be those with the lower values of @,."," We find the youngest, less metallic, less $\alpha$ -enhanced objects to be those with the lower values of $\sigma_v$."
 This result is in good qualitative agreement with that of Thomas&Davies (2006).. despite notable difference in sample selection ancl aperture definition.," This result is in good qualitative agreement with that of \citet{thomas06}, despite notable difference in sample selection and aperture definition."
 The main difference between the two works is the statistical significance reached. because we use a sample ~50 times Larger., The main difference between the two works is the statistical significance reached because we use a sample $\sim 50$ times larger.
 Our larger sample size could also be driving our main discrepancy., Our larger sample size could also be driving our main discrepancy.
 While they find 21Η. o-enhancement and age of spiral bulges to be equivalent to those in ellipticals at à given. velocity dispersion. we find that the metallicity in bulges of quiescent. spirals is higher than in elliptical galaxies.," While they find Z/H, $\alpha$ -enhancement and age of spiral bulges to be equivalent to those in ellipticals at a given velocity dispersion, we find that the metallicity in bulges of quiescent spirals is higher than in elliptical galaxies."
 llowever. it seems that the metallicity of those stellar populations«κο correlates with the total stellar mass of the ealaxv.," However, it seems that the metallicity of those stellar populations correlates with the total stellar mass of the galaxy."
 We know that there is a fundamental. correlation between the mass of a galaxy and its metal content (1οι.‘Tremontietal.2004:Gallazzictab... 2005).. and that its origin is likelv due to the higher capacity of more massive systems to retain metals in the presence of outllows.," We know that there is a fundamental correlation between the mass of a galaxy and its metal content \citep[i.e.,][]{tremonti, anna05}, and that its origin is likely due to the higher capacity of more massive systems to retain metals in the presence of outflows."
 ‘Taken together. our results imply that the formation epoch of galaxies and the duration of their. star-forming period are linked. to the mass of the bulge.," Taken together, our results imply that the formation epoch of galaxies and the duration of their star-forming period are linked to the mass of the bulge."
 The extent to which metals are retained within the galaxy. not being removed. as a result of outllows. is determined bv the total mass of the galaxy.," The extent to which metals are retained within the galaxy, not being removed as a result of outflows, is determined by the total mass of the galaxy."
 Alastersetal.(2010). studied the stellar populations of red spirals. finding them to be systematically older and with less recent. SE activity than blue spiral galaxies.," \citet{masters} studied the stellar populations of red spirals, finding them to be systematically older and with less recent SF activity than blue spiral galaxies."
 Combining their results with those presented. here. imply a scenario in which SkLIs of red spirals are more similar to those of ellipticals than those of star forming spirals.," Combining their results with those presented here, imply a scenario in which SFHs of red spirals are more similar to those of ellipticals than those of star forming spirals."
 We are very conservative in the selection of quiescen galaxies. so it is possible that a population of disk-like. level star formers do exist (and that is precisely what Wolfeal.(2009) and others report).," We are very conservative in the selection of quiescent galaxies, so it is possible that a population of disk-like, low-level star formers do exist (and that is precisely what \citet{wolf09} and others report)."
" However. a late quenching of the SE in disk galaxies could be reconciled with our results if, in spite of the relatively homogeneus color and lack of SE at:0.1. there are radial gradients present in the stellar populations ages."," However, a late quenching of the SF in disk galaxies could be reconciled with our results if, in spite of the relatively homogeneus color and lack of SF at $z \le 0.1$, there are radial gradients present in the stellar populations ages."
 La other words. if these. galaxies erow inside-out. (Bardenetab.2005) and the center of the objects. where the bulk of the stellar populations resides. was assembled at zl. the star formation per unit miss might be small enough to not to leave behind à strong imprint in the global colors of the object bv zx0.1. and make it into our sample.," In other words, if these galaxies grow inside-out \citep{barden} and the center of the objects, where the bulk of the stellar populations resides, was assembled at $z > 1$, the star formation per unit mass might be small enough to not to leave behind a strong imprint in the global colors of the object by $z \le 0.1$, and make it into our sample."
 Ixuntschneretal.(2006) make use of SAURON survey data in order to study the stellar populations of 48 carly-tvpe galaxies., \citet{sauron} make use of SAURON survey data in order to study the stellar populations of 48 early-type galaxies.
 They find that the [lattened component identified. in fast-rotators does actually show an increase in the metallicity and a mildly depressed. o /EFe] ratio with respect to the main body of the galaxy., They find that the flattened component identified in fast-rotators does actually show an increase in the metallicity and a mildly depressed $\alpha$ /Fe] ratio with respect to the main body of the galaxy.
" Unfortunately their maps do not typically cover regions much larger than 4, nor later morphological tvpes than SOs."," Unfortunately their maps do not typically cover regions much larger than $R_e$, nor later morphological types than S0s."
 Future survevs. like the recently started Calar Alto Large Integral. Field. Area (CALIPA) survey will provide 3D spectroscopy over the full optical extent of a statistically significant sample of galaxies of all morphological types (Sánchezctal...2012).. allowing to study the stellar populations of quiescent spirals at larger radii," Future surveys, like the recently started Calar Alto Large Integral Field Area (CALIFA) survey will provide 3D spectroscopy over the full optical extent of a statistically significant sample of galaxies of all morphological types \citep{sanchez}, allowing to study the stellar populations of quiescent spirals at larger radii."
 Assuming that similar a enhancements imply. similar star formation timescales. it seems reasonable to believe that whatever the reason is after the shorter typical SE timescales in elliptical galaxies. it is very likely that the stars in the bulges ofquicscent spirals share a common formation mocde with those in ellipticals.," Assuming that similar $\alpha-$ enhancements imply similar star formation timescales, it seems reasonable to believe that whatever the reason is after the shorter typical SF timescales in elliptical galaxies, it is very likely that the stars in the bulges of quiescent spirals share a common formation mode with those in ellipticals."
 Furthermore. the fact that the weighted ages are similar at a given e implies that the epoch of the star formation shut-olf must also be placed at the same epoch. and any subsequent. episode of star formation must have happened at a lookback time high enough for any trace of voung stellar populations to have dissapeared by today.," Furthermore, the fact that the light-weighted ages are similar at a given $\sigma_v$ implies that the epoch of the star formation shut-off must also be placed at the same epoch, and any subsequent episode of star formation must have happened at a lookback time high enough for any trace of young stellar populations to have dissapeared by today."
 We would like to remind that while at stellar masses above 1.2OHAI. the contribution of passive disks to the growth of the red. sequence is very small (vanderWeletal. 2009).. probably because of a nmerecr-cominated formation history at those masses (vancerWelοal.2009:Robainactal.. 2010).. there are many. passive clisks contributing to such a growth since z1 (Dundyetal.POLO:Holdenetab.POLL) at lower masses.," We would like to remind that while at stellar masses above $1-2 \times 10^{11}M_\odot$ the contribution of passive disks to the growth of the red sequence is very small \citep{arjen09}, probably because of a merger-dominated formation history at those masses \citep{arjen09,robaina10}, there are many passive disks contributing to such a growth since $z\sim 1$ \citep{bundy10, holden11} at lower masses."
 Therefore. it will be very important to understand when and how do spiral galaxies without noticeable star formation activity in the local Universe stopped forming stars.," Therefore, it will be very important to understand when and how do spiral galaxies without noticeable star formation activity in the local Universe stopped forming stars."
 Future models of ealaxv formation and evolution. would have to be able to reproduce the small difference in metallicity We have assembled a sample of galaxies with morphological classifications from Calaxy Zoo and photometry ancl light-profile fit parameters from the SDSS DRT. NYU-VAC.," Future models of galaxy formation and evolution would have to be able to reproduce the small difference in metallicity We have assembled a sample of galaxies with morphological classifications from Galaxy Zoo and photometry and light-profile fit parameters from the SDSS DR7, NYU-VAC."
 We perform a comparison between the stellar populations in the central regions of low inclination quiescent. spiral galaxies and those in elliptical galaxies over the redshift range 0.04< and for galaxies with stellar masses above 1011AZ.., We perform a comparison between the stellar populations in the central regions of low inclination quiescent spiral galaxies and those in elliptical galaxies over the redshift range $0.04<z<0.1$ and for galaxies with stellar masses above $10^{10.4}M_\odot$.
 Specifically. we compare their r-band. leht-weighted ages. stellar metallicities and. alpha-cnhancement (as traced. by A(Aleb/ 03). derived as in 605 and GO6.The main results of this analysis are:," Specifically, we compare their r-band light-weighted ages, stellar metallicities and alpha-enhancement (as traced by $\Delta$ $\langle$ $\rangle$ )), derived as in G05 and G06.The main results of this analysis are:"
Alternatively. if the density along the rotational axis is significantly lower than near the equator. then. ~0.03 along the axis would allow a more reasonable solution.,"Alternatively, if the density along the rotational axis is significantly lower than near the equator, then $A_* \sim 0.03$ along the axis would allow a more reasonable solution."
" As an illustrating example. oue possible solution for the reaming model parameters is e,0.1. ep~0.002 aud E~LT«107 ere (the value of p is hardly constrained by the peak time aud flux. aud could be estimated frou the ohserved spectral slope}."," As an illustrating example, one possible solution for the remaining model parameters is $\epsilon _e \sim 0.1$ , $\epsilon_B \sim 0.002$ and $E \sim 1.7\times
10^{50}\;$ erg (the value of $p$ is hardly constrained by the peak time and flux, and could be estimated from the observed spectral slope)."
 We lave constrained the size of the radio ejecta from 22008D at carly epochs., We have constrained the size of the radio ejecta from 2008D at early epochs.
 The source was unresolved in our nuages. with upper limits on the augular diameter size of O.L mas at 28 davs and 0.5 mas at 69 clays.," The source was unresolved in our images, with upper limits on the angular diameter size of 0.4 mas at 28 days and 0.5 mas at 69 days."
 These angular sizes result in upper Μπιτς ou the average apparent isotropic expansion velocity of 1.1e for the first 28 davs aud 0.57e for the first 69 davs after the stellar explosion., These angular sizes result in upper limits on the average apparent isotropic expansion velocity of $1.1c$ for the first 28 days and $0.57c$ for the first 69 days after the stellar explosion.
 From the upper Iit ou the proper motion of the radio source. we derive an average expausion velocity between the two epochs of 0.38c.," From the upper limit on the proper motion of the radio source, we derive an average expansion velocity between the two epochs of $0.38c$."
 For 220070 there is oulv a reliable upper Init ou the augular diameter size at 37 davs of 0.3 mas. resulting in auupper linut ou the average expausion velocity of 0.6Le.," For 2007uy there is only a reliable upper limit on the angular diameter size at 37 days of 0.3 mas, resulting in anupper limit on the average expansion velocity of $0.64c$."
 These upper limits for both SNe show that if there were a jet. it was moderately relativistic.," These upper limits for both SNe show that if there were a jet, it was moderately relativistic."
" This result is consistent with the analysis of the radio light curves of this source. and also iu aerecineut with conclusious derived frou VLBA aud HSA observations bv ?. aud ος,"," This result is consistent with the analysis of the radio light curves of this source, and also in agreement with conclusions derived from VLBA and HSA observations by \citet{soderberg2008nature} and \citet{bietenholz2009apj}."
 The light curves in Figures 1. and 2. show that sole data. m particular at the lower radio frequencies. deviate significautl from the best-Bt light curves.," The light curves in Figures \ref{fig:SN2008Dlcs} and \ref{fig:SN2007uylcs} show that some data, in particular at the lower radio frequencies, deviate significantly from the best-fit light curves."
 We have investigated whether this could be due to interstellar scintillation (ISS). ie. the effect of the iuterstellar ποτα imeddulating the radio fiuxes of sources that have angular sizes which are smaller than the typical scintillation scales.," We have investigated whether this could be due to interstellar scintillation (ISS), i.e. the effect of the interstellar medium modulating the radio fluxes of sources that have angular sizes which are smaller than the typical scintillation scales."
 There are three types of ISS. ic. weak. refractive aud diffractive.," There are three types of ISS, i.e. weak, refractive and diffractive."
 For 22008D and 22007uv the effects of weak scintillation are very small at most a few percent. while diffractive scintillation plavs an even less siguificant role.," For 2008D and 2007uy the effects of weak scintillation are very small, at most a few percent, while diffractive scintillation plays an even less significant role."
 The effects of refractive ISS are much larger. ranging up ο several teus of percent. depending on the observing requenucv and time.," The effects of refractive ISS are much larger, ranging up to several tens of percent, depending on the observing frequency and time."
 Details of the ISS calculations are given iu Appendix ??.., Details of the ISS calculations are given in Appendix \ref{sec:appendix}.
 The ISS effects are shown in Fieures 1 aud 2 as dashed lines. showine the asin and minima modulatious of our best fit uodel fluxes.," The ISS effects are shown in Figures \ref{fig:SN2008Dlcs} and \ref{fig:SN2007uylcs} as dashed lines, showing the maximum and minimum modulations of our best fit model fluxes."
 It is evident iu the Figures that ISS can explain iost of the scatter in the observed fiuxes of he two SNe. except for the 325 ΑΠΣ imicasureieuts at ~LOO davs.," It is evident in the Figures that ISS can explain most of the scatter in the observed fluxes of the two SNe, except for the 325 MHz measurements at $\sim 400$ days."
 From the current data-set it is nof clear if the latter deviations are iutrimsic or caused bv systematic observational effects., From the current data-set it is not clear if the latter deviations are intrinsic or caused by systematic observational effects.
 The temporal behavior of the modeled Lelt curves is mainly determined by the better sampled lieher radio frequencies. aud deviating behavior at later times aud lower frequencies is certainly possible.," The temporal behavior of the modeled light curves is mainly determined by the better sampled higher radio frequencies, and deviating behavior at later times and lower frequencies is certainly possible."
 ILoxcever. the fact that both SNe display the sale lieh fiux could be an indication of systematics. but future 325 MIIz observations with the GCAIRT aud at even lower frequencies with LOFAR (see Section ??)) will be able to solve this issue.," However, the fact that both SNe display the same high flux could be an indication of systematics, but future 325 MHz observations with the GMRT and at even lower frequencies with LOFAR (see Section \ref{sec:lofar}) ) will be able to solve this issue."
 SN progenitors are voung stars on ealactic timescales. so it is relevant to cousider the molecular component of the galactic eas where these stars form.," SN progenitors are young stars on galactic timescales, so it is relevant to consider the molecular component of the galactic gas where these stars form."
 Although the linear resolution of the single dish observations is ~8.6 kpe (and therefore much larecr than single eiaut molecular clouds). general statements about the star forming euvironnient are still possible.," Although the linear resolution of the single dish observations is $\sim$ 8.6 kpc (and therefore much larger than single giant molecular clouds), general statements about the star forming environment are still possible."
" There are several striking features in Figure 1,", There are several striking features in Figure \ref{fig:n2770-co}.
 The gas distribution is. uulike iu most spiral galaxies. asvunuuetric;," The gas distribution is, unlike in most spiral galaxies, asymmetric."
 The center position has. am απλοτής shape around the svstemic velocity of 1917 kin/s. There Is more σας at the NI position thanat 220071 (=S1). and more at S2 than at 22008D (=N2). while the SNe have occurred far too receutlv to affect molecular clouds ou the scale saampled by the 1211 beam.," The center position has an asymmetric shape around the systemic velocity of 1947 km/s. There is more gas at the N1 position than at 2007uy (=S1), and more at S2 than at 2008D (=N2), while the SNe have occurred far too recently to affect molecular clouds on the scale sampled by the 12m beam."
 To explore this asviunietrv further. we co-added the north aud south positions separatelv: the resulting spectra are the bottoni left aud right panels iu Figure L.," To explore this asymmetry further, we co-added the north and south positions separately; the resulting spectra are the bottom left and right panels in Figure \ref{fig:n2770-co}."
 The most interesting feature appears in the lower left of the Figure (total of the south positions)., The most interesting feature appears in the lower left of the Figure (total of the south positions).
 The eas following the ealaxy’s CO rotation curve (centered around ~1820 kui/s) is obvious. and typical of normal spiral galaxies (seee.g.ολ," The gas following the galaxy's CO rotation curve (centered around $\sim$ 1820 km/s) is obvious, and typical of normal spiral galaxies \citep[see e.g.][]{sage1993aa}."
 A second feature. centered around ~2125 kms. is also visible.," A second feature, centered around $\sim$ 2125 km/s, is also visible."
 The statistical significance of the feature is lo., The statistical significance of the feature is $4\sigma$.
" The physical significance. if oue accepts the lo detection. is that this indicates a counter-rotating componcut of eas,"," The physical significance, if one accepts the $4\sigma$ detection, is that this indicates a counter-rotating component of gas."
 No such counter-rotating feature is seen in the stunned north positions (lower right pancl of Figure 1)., No such counter-rotating feature is seen in the summed north positions (lower right panel of Figure \ref{fig:n2770-co}) ).
 To explore the significance of particular features in the CO results more thoroughly. we compared the data to 1e III line observed by 7? usine the Nancaay telescope in France. aud the WSRT III map from ?..," To explore the significance of particular features in the CO results more thoroughly, we compared the data to the HI line observed by \citet{matthews2001aa} using the Nançaay telescope in France, and the WSRT HI map from \citet{rhee1996aas}."
 The HII line roni ?.theirFigure1 shows the same asviunietry as 16 CO center position above., The HI line from \citet[][their Figure 1]{matthews2001aa} shows the same asymmetry as the CO center position above.
 Even more striking is the nap of 7.. which clearly shows the IIT rotating iu theopposite scuse of the CO. with high velocities south of ιο center.," Even more striking is the map of \citet{rhee1996aas}, which clearly shows the HI rotating in the sense of the CO, with high velocities south of the center."
 At the le level (second positive contour) rere is a counter-rotating TT component iu the south. at low velocities (ceutered. around 1850 kis).," At the $\sigma$ level (second positive contour) there is a counter-rotating HI component in the south, at low velocities (centered around $\sim1850$ km/s)."
 This counter-rotating HI is therefore co-rotating with the CO. although the direction of rotation of the stars has not 2ος. reported. but the usual assuuption is that the III and stars co-votate.," This counter-rotating HI is therefore co-rotating with the CO, although the direction of rotation of the stars has not been reported, but the usual assumption is that the HI and stars co-rotate."
 There is only oue other galaxy or Which counterrotating eas components have been reported. namely σι.," There is only one other galaxy for which counter-rotating gas components have been reported, namely 4546 \citep[][]{sage1994aj}."
 The oulv plausible source of counter-aotatiug gas is a collision or merger., The only plausible source of counter-rotating gas is a collision or merger.
 22770 does have a chwart companion. NGC22770D. and based upon recent work ou the local group of galaxies (e.g.2)... it is clear that collisions with dwarf galaxies are ongoing mto the present epoch.," 2770 does have a dwarf companion, 2770B, and based upon recent work on the local group of galaxies \citep[e.g.][]{mcconnachie2009nature}, it is clear that collisions with dwarf galaxies are ongoing into the present epoch."
 We accordingly conclude that 22770. has absorbed a dwarf galaxy at some point iu the last ~LO’ vr or so., We accordingly conclude that 2770 has absorbed a dwarf galaxy at some point in the last $\sim10^8$ yr or so.
 The resulting cloud-cloud collisions have iuduced star formation. aud we are now seciug the resulting SNe.," The resulting cloud-cloud collisions have induced star formation, and we are now seeing the resulting SNe."
 Although the SNe have occurred in differcut parts of 22770. studies of other galaxies have shown that collisions or mergers can affect the star formation inthe cutire galaxy (seee.g. ?)..," Although the SNe have occurred in different parts of 2770, studies of other galaxies have shown that collisions or mergers can affect the star formation inthe entire galaxy \citep[see e.g.][]{bureau2006mnras}. ."
 Using the inclination and absorption corrected ΕΟΝ colors. it is possible to estimate (rather crudely. and with a lot of asstuuptions) how long ago a burst of star," Using the inclination and absorption corrected UBV colors, it is possible to estimate (rather crudely, and with a lot of assumptions) how long ago a burst of star"
For the systems formed. during the cluster’s lifetime. we calculate the change in angular momentum with respect to the parental binary or and use the largest angle in ourcalculations.,"For the systems formed during the cluster's lifetime, we calculate the change in angular momentum with respect to the parental binary or and use the largest angle in our."
 As we are interested in the elfeet of cluster evolution on planetary svstemis (or protoplanctary disks). we define a periastron distance that allows for the formation of such a system without interference from the secondary component of the binary svstem.," As we are interested in the effect of cluster evolution on planetary systems (or protoplanetary disks), we define a periastron distance that allows for the formation of such a system without interference from the secondary component of the binary system."
 We take the standard. definition of periastron distance rio: where e& and e are the semi-major axis and the eccentricity of the binary system. respectively.," We take the standard definition of periastron distance $r_{\rm peri}$: where $a$ and $e$ are the semi-major axis and the eccentricity of the binary system, respectively."
 We determine rii lor cach svstem. and. assume that a stable planetary. system (or disk) could have developed for any binary with riosLOO AAU.," We determine $r_{\rm peri}$ for each system, and assume that a stable planetary system (or disk) could have developed for any binary with $r_{\rm peri} > 100$ AU."
 Of the 43. planets orbiting a binary component in the sample of 7.. only 5 are in binary systems with separations less than AAU.," Of the 43 planets orbiting a binary component in the sample of \citet{Desidera07}, only 5 are in binary systems with separations less than AU."
 Ifa binary exceeds this periastron threshold we determine its inclination angle from the change in the orbital angular momentum vector., If a binary exceeds this periastron threshold we determine its inclination angle from the change in the orbital angular momentum vector.
 We show the clistribution of inclination angles for svstenis with rues>100 XAU after MMyr in Fig. 1.., We show the distribution of inclination angles for systems with $r_{\rm peri} > 100$ AU after Myr in Fig. \ref{theta_dist}.
 Whilst only 1 per cent of systems have an inclination angle within the threshold range (39.237 to 140.777). many of the binaries are tight (< AAU) and hence not susceptible to dynamical processing (?)..," Whilst only 1 per cent of systems have an inclination angle within the threshold range $^\circ$ to $^\circ$ ), many of the binaries are tight $<$ AU) and hence not susceptible to dynamical processing \citep{Parker09a}."
 This is readily demonstrated. in. Fig. 2.," This is readily demonstrated in Fig. \ref{peri_kozai},"
" where we plot the fraction of binaries with inclination angles in the threshold range 4g, as a function. of ris.", where we plot the fraction of binaries with inclination angles in the threshold range $i_{\rm Koz}$ as a function of $r_{\rm peri}$ .
 Binaries with. Fes IOOAAU are. far more. likely to. have inclination angles in the range Zi; than the tighter svstems., Binaries with $r_{\rm peri} > 100$ AU are far more likely to have inclination angles in the range $i_{\rm Koz}$ than the tighter systems.
 Additionally. a binary with a periastron. distance rei<LOO AAU is unlikely to form a stable planetary system. as that system will be perturbed by the other component. of the binary system.," Additionally, a binary with a periastron distance $r_{\rm peri} < 100$ AU is unlikely to form a stable planetary system, as that system will be perturbed by the other component of the binary system."
 The contribution from binaries that are formed during the cluster’s evolution is minimal., The contribution from binaries that are formed during the cluster's evolution is minimal.
 As can be seen in Fig. 1..," As can be seen in Fig. \ref{theta_dist},"
 only four newly formed systems with rer 100.XAU Lie within the threshold range fig... compared to the many tens of primordial binarics.," only four newly formed systems with $r_{\rm peri} > 100$ AU lie within the threshold range $i_{\rm Koz}$, compared to the many tens of primordial binaries."
 OL the systems that have revi100 ΑΔ we determine the fraction of svstems that have an inclination anele between 39.237 and. 140.777.," Of the systems that have $r_{\rm peri} > 100$ AU, we determine the fraction of systems that have an inclination angle between $^\circ$ and $^\circ$."
 We show the evolution of this fraction during the cluster’s lifetime in Fig. 3.., We show the evolution of this fraction during the cluster's lifetime in Fig. \ref{kozai_frac}.
 We show the fraction of systems that could be subjected to the ]xozai mechanism for three different initial half-mass raclii: ppc (the solid line). ppe (the dashed line) and ppc (the dashec-dot line).," We show the fraction of systems that could be subjected to the Kozai mechanism for three different initial half-mass radii; pc (the solid line), pc (the dashed line) and pc (the dashed-dot line)."
 For the most dense clusters ενος=OL pe). the fraction of svstems that could potentially undergo the Ixozai mechanism is roughly constant. at  20 per cent.," For the most dense clusters $r_{1/2} = 0.1$ pc), the fraction of systems that could potentially undergo the Kozai mechanism is roughly constant, at $\sim$ 20 per cent."
 For the less dense clusters. the fraction is less: ~ 13 per cent for roe=0.2 pe. and ~ 10 per cent for kí»=0.4 pe.," For the less dense clusters, the fraction is less; $\sim$ 13 per cent for $r_{1/2} = 0.2$ pc, and $\sim$ 10 per cent for $r_{1/2} = 0.4$ pc."
 This decrease in allected systems with increasing half-mass radius is simply due to there being fewer interactions in the less-dense clusters., This decrease in affected systems with increasing half-mass radius is simply due to there being fewer interactions in the less-dense clusters.
 The fraction of svstems that could. be subjected to the Ixozai mechanism remains roughly constant after Myr for the most dense clusters (ryyo=0.1 0.2 pe)., The fraction of systems that could be subjected to the Kozai mechanism remains roughly constant after Myr for the most dense clusters $r_{1/2} = 0.1$ $0.2$ pc).
 This is entirely due to the crossing time of the cluster being only ~0.2 Myr (?) and therefore the cluster has relaxed ancl the majority of binaries have already reached. dynamical equilibrium., This is entirely due to the crossing time of the cluster being only $\sim 0.2$ Myr \citep{Parker09a} and therefore the cluster has relaxed and the majority of binaries have already reached dynamical equilibrium.
" A planet orbiting the component of a binary star will undergo Ixozai eveles on the following timescale (???):: where a, is the period of the binary. £2, is the period of theplanet. eig, is the eccentricity of the binary. 20, and me are the masses of the primary and secondary components of the binary respectively. and m, is the mass of the planet."," A planet orbiting the component of a binary star will undergo Kozai cycles on the following timescale \citep*{Kiseleva98,Takeda08,Verrier09}: where $P_{\rm bin}$ is the period of the binary, $P_p$ is the period of theplanet, $e_{\rm bin}$ is the eccentricity of the binary, $m_1$ and $m_2$ are the masses of the primary and secondary components of the binary respectively, and $m_p$ is the mass of the planet."
"dust emission is optically thin aud the Ravleigh-Jeans approximation is satisfied. the slope . of the dust opacity is related to the spectral index a of the observed disk cussion £, (B,xw') by the relation a=2|3.","dust emission is optically thin and the Rayleigh-Jeans approximation is satisfied, the slope $\beta$ of the dust opacity is related to the spectral index $\alpha$ of the observed disk emission $F_{\nu}$ $F_\nu \propto \nu^\alpha$ ) by the relation $\alpha=2+\beta$."
 This relation is only approxinate if the dust euissiou is optically thick at some radii., This relation is only approximate if the dust emission is optically thick at some radii.
 In Paper L we derived values for Jj of 0.5 and 0.7 for DC Tan and RY Tau respectively from an analysis of the SED. taking iuto account the optically thick contribution to the total dust enüssiou.," In Paper I, we derived values for $\beta$ of 0.5 and 0.7 for DG Tau and RY Tau respectively from an analysis of the SED, taking into account the optically thick contribution to the total dust emission."
 For the assumnued dust composition and structure. these values of 3 cau be reproduced with different choices of the maxima grain size ay aad the erain size slope q (sec Appendix Aj).," For the assumed dust composition and structure, these values of $\beta$ can be reproduced with different choices of the maximum grain size $a_{max}$ and the grain size slope $q$ (see Appendix \ref{app:A}) )."
 To investigate how the asswuptions on the erain size distribution affect the model fitting. we adopt two cifferent dust models that correspond to the extreme cases of low (£) aud high (JJ) opacity.," To investigate how the assumptions on the grain size distribution affect the model fitting, we adopt two different dust models that correspond to the extreme cases of low $L$ ) and high $H$ ) opacity."
 The corresponding dust opacities at both 1.3 nuu and 2.8 mun are given in Table 2.., The corresponding dust opacities at both 1.3 mm and 2.8 mm are given in Table \ref{tab:dust}.
" Finally, we assune that the dust opacity is constant throughout the disk."," Finally, we assume that the dust opacity is constant throughout the disk."
" This is indeed one of the main assumption we waut to test by modeling the observed dust cussion at 1.3 aaa aud 2.8 nua and will be discussed iu detail in Section 5.{,,", This is indeed one of the main assumption we want to test by modeling the observed dust emission at 1.3 mm and 2.8 mm and will be discussed in detail in Section \ref{sec:betavar}.
 Alodels απ observations are conrpared imn Fourier space to avoid the nou linear effects introduced by the cleaning process., Models and observations are compared in Fourier space to avoid the non linear effects introduced by the cleaning process.
" The best fit models are found by X? minimization with five free parzuueters the disk inclinationi /. the disk position angle PA. R,,;. Xj. aud p for the power law surface density (Equation 1)). aud ;. PA. Πε. NX, and 5 for the similarity solution (Equation 2))."," The best fit models are found by $\chi^2$ minimization with five free parameters: the disk inclination $i$ , the disk position angle PA, $R_{out}$, $\Sigma_{40}$ , and $p$ for the power law surface density (Equation \ref{eq:pow}) ), and $i$, PA, $R_t$, $\Sigma_t$ and $\gamma$ for the similarity solution (Equation \ref{eq:sim}) )."
" The disk iuuer radius RA, is fixed at 0.1. AU.", The disk inner radius $R_{in}$ is fixed at 0.1 AU.
 For both surface density models we find best fit solutions for both the high (77) aud low (£) dust opacity models., For both surface density models we find best fit solutions for both the high $H$ ) and low $L$ ) dust opacity models.
 The 1.3 wan aud 2.5 nuu data are fitted imdepeudently., The 1.3 mm and 2.8 mm data are fitted independently.
 Toj minimize∙∙∙ 42 and evaluate the coustraiuts: ou the model parameters. we use a Bayesian approach that adopts uniform prior probability distributions.," To minimize $\chi^2$ and evaluate the constraints on the model parameters, we use a Bayesian approach that adopts uniform prior probability distributions."
B Iu practiceB we sample the 47Di probabilityBm distribution bv varving the free parameters usus the Markov Chain Monte Carlo method described in Paper 1. Once a best fit solution is found. we confu that this indeed corresponds to an absolute ⋯∐∐∐∐∐⊔∪↕∖−∙⋜↕↴∖↴∪⋯⋯∖↴↸∖≼⊔∪⋜↧↕∪↸⊳⋜↧↕⋯∐∐∐∐∐⊔∙_ .. ⋅⋅ by ruuniue multiple Moute Carlo simmlatious with random initializations and veritving that they all converge to the same solution.," In practice we sample the $\chi^2$ probability distribution by varying the free parameters using the Markov Chain Monte Carlo method described in Paper I. Once a best fit solution is found, we confirm that this indeed corresponds to an absolute minimum of $\chi^2$, as opposed to a local minimum, by running multiple Monte Carlo simulations with random initializations and verifying that they all converge to the same solution."
 Each pariuneter is allowed to vary in a large range: ffor the inclination. £90° for the position angle. 101000 AU for Ry aud Roar El foy p aud 5. aud Q0.1000 e/cu for Mp and M.," Each parameter is allowed to vary in a large range: for the inclination, $\pm$ for the position angle, $10-1000$ AU for $R_t$ and $R_{out}$, $\pm4$ for $p$ and $\gamma$, and $0.1-1000$ $^2$ for $\Sigma_{40}$ and $\Sigma_t$."
 The best ft disk models found for high aud low dust opacities are listed in Table 3 and Table 1 respectively., The best fit disk models found for high and low dust opacities are listed in Table \ref{tab:res_clubs} and Table \ref{tab:res_spades} respectively.
 Each table lists the parameters for he sinüluitv solution disk model in the upper vat. and for the power law disk model in the ower part.," Each table lists the parameters for the similarity solution disk model in the upper part, and for the power law disk model in the lower part."
" The probability distributions for cach ree paralcter are shown in Figure { aud Figure 5 for RY Tau iu the case of the sinularity solution and power law respectively,", The probability distributions for each free parameter are shown in Figure \ref{fig:RYTau_SIM} and Figure \ref{fig:RYTau_POW} for RY Tau in the case of the similarity solution and power law respectively.
 The same quantities or DG Tan are shown in Figure 6 aud Figure 7.., The same quantities for DG Tau are shown in Figure \ref{fig:DGTau_SIM} and Figure \ref{fig:DGTau_POW}.
 Iu these figures.Oo the black aud red listoeramsC» indicate the probability distributions derived bv fittine the 1.3 nuu and 2.5 nuu observations. respectively: solid aud dashed curves represent the IT and £ dust opacity models.," In these figures, the black and red histograms indicate the probability distributions derived by fitting the 1.3 mm and 2.8 mm observations, respectively; solid and dashed curves represent the $H$ and $L$ dust opacity models."
 For cach parameter we derive the uncertainty range that correspouds o a likelihood of (30) bv fitting a normal distribution to the probabilities., For each parameter we derive the uncertainty range that corresponds to a likelihood of $\sigma$ ) by fitting a normal distribution to the probabilities.
 Finally. Figure & shows comparisons between he observed real part of the correlated flix (filled squares with error bars). the best fit models for he simüluitv solution (solid curve). and a power aw surface density (dashed curve).," Finally, Figure \ref{fig:uvamp_deproj_real} shows comparisons between the observed real part of the correlated flux (filled squares with error bars), the best fit models for the similarity solution (solid curve), and a power law surface density (dashed curve)."
 The best fit solutions for the fF aud £ dust opacity models are shown in Figure 5-6 with solid and dashed curves respectively., The best fit solutions for the $H$ and $L$ dust opacity models are shown in Figure \ref{fig:RYTau_POW}- \ref{fig:DGTau_SIM} with solid and dashed curves respectively.
" In all cases. II aud L models lead to very simulay values for the disk position angle. the disk inclination aud the racial profiles of the surface density defined byp aud Πε ta the case of the power law models. aud 5 aud A, for the similarity solution models."," In all cases, $H$ and $L$ models lead to very similar values for the disk position angle, the disk inclination and the radial profiles of the surface density defined by$p$ and $R_{out}$ in the case of the power law models, and $\gamma$ and $R_t$ for the similarity solution models."
 As discussed in Paper L these parameters are essentially indepeudent of the dust opacity.," As discussed in Paper I, these parameters are essentially independent of the dust opacity."
 This is mainlybecause the disk mid-plaue temperature TAR) varies by only a few percent between, This is mainlybecause the disk mid-plane temperature $T_i(R)$ varies by only a few percent between
extracted.,extracted.
" Along the y-axis, we can not estimate the error bars in the same way as the other points as the largest difference between the rotation curve of the whole galaxy and that of one of the sides or, if larger, the intrinsic error) since we only detect emission on the approaching side of the galaxy."," Along the y-axis, we can not estimate the error bars in the same way as the other points as the largest difference between the rotation curve of the whole galaxy and that of one of the sides or, if larger, the intrinsic error) since we only detect emission on the approaching side of the galaxy."
" The error bars were therefore chosen as the dispersion of the gaussian profile fitted to the emission line, since the largest uncertainty is on the location and shape of the profile, rather than on the kinematical parameters."," The error bars were therefore chosen as the dispersion of the gaussian profile fitted to the emission line, since the largest uncertainty is on the location and shape of the profile, rather than on the kinematical parameters."
 An error on the order of 20° for the inclination would be required to affect significantly the derived rotation velocities., An error on the order of $^o$ for the inclination would be required to affect significantly the derived rotation velocities.
" Finally, the error bars associated with the velocities determined for the receding side (red points in the bottom-right panel of Fig. 6)),"," Finally, the error bars associated with the velocities determined for the receding side (red points in the bottom-right panel of Fig. \ref{a2f6}) ),"
 were taken as those derived by the task., were taken as those derived by the task.
 In the bottom panels of Fig., In the bottom panels of Fig.
" 3 and Fig. 4,,"," \ref{a2f3} and Fig. \ref{a2f4},"
" we show the position-velocity (PV) diagrams for each galaxy, along with the final adopted rotation curves in red, and for NGC 247, we include in black the rotation curve derived for both sides, which is affected by the non-circular motions."," we show the position-velocity (PV) diagrams for each galaxy, along with the final adopted rotation curves in red, and for NGC 247, we include in black the rotation curve derived for both sides, which is affected by the non-circular motions."
 Observational data seem to favour flat core mass models rather than cuspy core models????7)., Observational data seem to favour flat core mass models rather than cuspy core models.
". We therefore choose to model a dark halo in the form of an isothermal sphere, which has a density profile as defined by Eq. 1.."," We therefore choose to model a dark halo in the form of an isothermal sphere, which has a density profile as defined by Eq. \ref{a2_eq1}."
 This model is parameterized by a central density po and core radius Τε., This model is parameterized by a central density $\rho_{\rm 0}$ and core radius $r_{\rm c}$ .
" The parameters are tied together by po=9c? /AnGr.?, where σ is the one dimensional velocity dispersion."," The parameters are tied together by $\rho_{\rm 0}=9\sigma^2/4\pi$ ${r_c}^2$, where $\sigma$ is the one dimensional velocity dispersion."
" Based on a least-square fitting procedure, three parameters must bedetermined during the mass model"," Based on a least-square fitting procedure, three parameters must bedetermined during the mass model"
Alter Anderson ancl Neddermever's 1936 discovery of the muon was confirmed by (1937).. I. L. Rabi famously quipped “who ordered (hat?.,"After Anderson and Neddermeyer's 1936 discovery of the muon was confirmed by \citet{street37}, I. I. Rabi famously quipped “who ordered that?”,"
" ie.. why was there a second ""electron""?"," i.e., why was there a second “electron”?"
" No sensible answer to (his question could even be attempted until the eeneral pattern of ""multiplicitv of ""fundamental particles was established.", No sensible answer to this question could even be attempted until the general pattern of “multiplicity” of “fundamental” particles was established.
 The emergence of a standard particle physics model does allow (his question to be al least properly framed., The emergence of a standard particle physics model does allow this question to be at least properly framed.
" In (his model. (here are exactly tree ""electrons"" (electron. muon. tau). and each is associated wilh ils corresponding neutrino. with identical quantum munbers except 1 extra unit of charge."," In this model, there are exactly three “electrons” (electron, muon, tau), and each is associated with its corresponding neutrino, with identical quantum numbers except 1 extra unit of charge."
 In parallel. there are exactly three “lower quarks” (clown. strange. bottoni). each with its corresponding “upper quark” (up. charm. top). also with identical quantum mnmunbers except 1 extra unit of charge.," In parallel, there are exactly three “lower quarks” (down, strange, bottom), each with its corresponding “upper quark” (up, charm, top), also with identical quantum numbers except 1 extra unit of charge."
 The standard model has demonstrated al least some predictive power (as opposed to being merely a post-facto classification scheme) because the top quark was firmlv established in the model well before its experimental confirmation., The standard model has demonstrated at least some predictive power (as opposed to being merely a post-facto classification scheme) because the top quark was firmly established in the model well before its experimental confirmation.
"(1999) calibration of Tipps vs. (D—V). rather than the recipe of Paper I. leads to a slightly better match in the base of the giant branch. but it worsens the match at V.—14. where our calibration provides a good match {ο (the data,","(1999) calibration of $T_{eff}$ s vs. $(B-V)$, rather than the recipe of Paper I, leads to a slightly better match in the base of the giant branch, but it worsens the match at $V \sim 14$, where our calibration provides a good match to the data."
" Such mismatches. if due to errors in the T, ys oL the isochrones. may have a non-negligible impact on the ages inferred from the fit of the integrated spectrum of the cluster. as we show below."," Such mismatches, if due to errors in the $T_{eff}$ s of the isochrones, may have a non-negligible impact on the ages inferred from the fit of the integrated spectrum of the cluster, as we show below."
 It is also important to notice that AGB stars are not included in the Salaris isochrones., It is also important to notice that AGB stars are not included in the Salaris isochrones.
 It willbe shown in Section 3. that this also has an important impact on the integrated line indices., It willbe shown in Section \ref{isoobs} that this also has an important impact on the integrated line indices.
 In Fieure 2 we repeat (he CMD of 47 Tuc. this Gime comparing the data with the Padova isochrones.," In Figure \ref{fig2} we repeat the CMD of 47 Tuc, this time comparing the data with the Padova isochrones."
 Theoretical quantities (7;jj and Mi) were (ranslormed into the observational plane following the same recipes as adopted to the Salaris isochrones shown in Figure 1.., Theoretical quantities $T_{eff}$ and $M_{bol}$ ) were transformed into the observational plane following the same recipes as adopted to the Salaris isochrones shown in Figure \ref{fig1}.
 The Padova isochrones were computed assuming (he same chemical composition as adopted in the computation of the Salaris isochrones., The Padova isochrones were computed assuming the same chemical composition as adopted in the computation of the Salaris isochrones.
 However. (he Padova isochrones do not consider the effect of diffusion of helium and heavier elements.," However, the Padova isochrones do not consider the effect of diffusion of helium and heavier elements."
 As explained by Vazdekis et al. (, As explained by Vazdekis et al. (
2001). inclusion of heavy-element diffusion results in a slightly cooler and fainter turn-olf [or a given stellar mass and chemical composition.,"2001), inclusion of heavy-element diffusion results in a slightly cooler and fainter turn-off for a given stellar mass and chemical composition."
 In fact. the turn-off of the 11 Gvirs isochrone from Salaris is about 0.16 mag [unter and 150 Ix cooler than the turn-olf of the Padova isochrone for a similar age (11.2 νι).," In fact, the turn-off of the 11 Gyrs isochrone from Salaris is about 0.16 mag fainter and 150 K cooler than the turn-off of the Padova isochrone for a similar age (11.2 Gyrs)."
 For this reason the age that best fits (he turn-olf color and magnitude of 47 Tuc. according to the Padova isochrones. is somewhere between 12.5 and 14.1 Gvrs. being thus slightly older than the one inferred [vom the Salaris isochrones (Figure 1)).," For this reason the age that best fits the turn-off color and magnitude of 47 Tuc, according to the Padova isochrones, is somewhere between 12.5 and 14.1 Gyrs, being thus slightly older than the one inferred from the Salaris isochrones (Figure \ref{fig1}) )."
 Evidence for the occurence of atomic diffusion in the Sun has been presented in a number of studies., Evidence for the occurence of atomic diffusion in the Sun has been presented in a number of studies.
 For instance. Basu. Pinsonneault Baheall (2000) show that diffusion of heavy elements is recuired if models are to fit the data on the profiles of sound speed. density. ancl acdiabatic index in (he Sun.," For instance, Basu, Pinsonneault Bahcall (2000) show that diffusion of heavy elements is required if models are to fit the data on the profiles of sound speed, density and adiabatic index in the Sun."
 For more stars. Lebreton et al. (," For more metal-poor stars, Lebreton et al. ("
1999) showed that the IER. diagram from IHipparcos data for stus wilh 1.05 <ΡΕ 0.45 can be reconciled with the predictions of stellar evolution onlv if diffusion of heavy elements is considered.,1999) showed that the HR diagram from Hipparcos data for stars with –1.05 $<$ $<$ –0.45 can be reconciled with the predictions of stellar evolution only if diffusion of heavy elements is considered.
 However. the extent to which atomic diffusion affects stellar structure and evolution is still under debate.," However, the extent to which atomic diffusion affects stellar structure and evolution is still under debate."
 It has been argued. Chat the constancy of the Li abundance in metal-poor dwarls wilh a wide range of metallicities (the so-called lithium plateau. Spite Spite 1952) suggests that diffusion effects may be partially inhibited (Delivannis Demarque 1991).," It has been argued that the constancy of the Li abundance in metal-poor dwarfs with a wide range of metallicities (the so-called lithium plateau, Spite Spite 1982) suggests that diffusion effects may be partially inhibited (Deliyannis Demarque 1991)."
 On the other hand. Salaris Weiss (2001) showed (hat models with fully efficient. diffusion may be consistent with the lithium plateau if the errors on lithium abundances and sample incompleteness are duly accounted for.," On the other hand, Salaris Weiss (2001) showed that models with fully efficient diffusion may be consistent with the lithium plateau if the errors on lithium abundances and sample incompleteness are duly accounted for."
 According to Vazdekis οἱ al. (, According to Vazdekis et al. (
2001). the consideration of atomic diffusion in its full extent reduces the turn-off age of 47 Tuc by ~ 1 Gyr.,"2001), the consideration of atomic diffusion in its full extent reduces the turn-off age of 47 Tuc by $\sim$ 1 Gyr."
 An important constraint on the extent of diffusion affects has also been placed by Gratton et al. (, An important constraint on the extent of diffusion affects has also been placed by Gratton et al. (
2001). who found that /Fe/// is the same for stars,"2001), who found that is the same for stars"
Precessing radio jets have been directly observed in Galactic X-ray binaries (e.g..?) and suggested to be present in Sevler( galaxies with curved jets like NGC 3516 (?)..,"Precessing radio jets have been directly observed in Galactic X-ray binaries \citep[e.g.,][]{Mioduszewski01} and suggested to be present in Seyfert galaxies with curved jets like NGC 3516 \citep{Veilleux93}."
 The detection of (wo pairs of orthogonallv-placed. sell-similar edge-brightened radio bubbles in the Sevlert galaxy Mrk 6. prompted ? (0 invoke two episodes of precessing radio jets to explain the radio structures.," The detection of two pairs of orthogonally-placed, self-similar edge-brightened radio bubbles in the Seyfert galaxy Mrk 6, prompted \citet{Kharb06} to invoke two episodes of precessing radio jets to explain the radio structures."
 Jet. precession could arise due to (he presence of binary black holes (?).. the relativistic Lense-Thirrine effect (?22).. or accretion disk warping due io non-axisvimmnmetrie radiation pressure forces (?)..," Jet precession could arise due to the presence of binary black holes \citep{Caproni04}, the relativistic Lense-Thirring effect \citep{Bardeen75,Caproni06}, or accretion disk warping due to non-axisymmetric radiation pressure forces \citep{Pringle96}."
" The Sevlert galaxy. Circinus has radio bubbles with bright. hiehly polarized edges (?7).. similar to the ""edge-brightened' Alrk 6 and NGC 6764. and a precessing accretion disk. as evidenced by the VLBI water maser observations of ?.."," The Seyfert galaxy Circinus has radio bubbles with bright, highly polarized edges \citep{Elmouttie95}, similar to the “edge-brightened” Mrk 6 and NGC 6764, and a precessing accretion disk, as evidenced by the VLBI water maser observations of \citet{Greenhill03}."
 A precessing disk and S-shaped radio jets with tightly correlated X-ray emission have also been observed in the Sevfert galaxy NGC 4258 (???)..," A precessing disk and S-shaped radio jets with tightly correlated X-ray emission have also been observed in the Seyfert galaxy NGC 4258 \citep{Sanders82, Cecil00,Wilson01}."
 Therefore. the presence of a precessing jet in (he radio-bubble galaxy. NGC 6764. is a viable possibility.," Therefore, the presence of a precessing jet in the radio-bubble galaxy, NGC 6764, is a viable possibility."
 ? presented a (hree-cimensional kinematic model to explain the proper motions of the precessing jet in (he ταν binary 55433., \citet{Hjellming81} presented a three-dimensional kinematic model to explain the proper motions of the precessing jet in the X-ray binary SS433.
 This model has since been successfully. applied to the radio morphologies of raclio-powerlul AGNs (e.g..?)..," This model has since been successfully applied to the radio morphologies of radio-powerful AGNs \citep[e.g.,][]{Gower82}."
 Following the relations in 2.. we have attempted to fit a precessing jet model to the radio structure in NGC 6764.," Following the relations in \citet{Hjellming81}, we have attempted to fit a precessing jet model to the radio structure in NGC 6764."
 We find (hat this model is able to fit (he radio structure from parsec to sub-kpe scales (see Figure 2)., We find that this model is able to fit the radio structure from parsec to sub-kpc scales (see Figure 2).
" The best-fit model parameters are: jet speed = 0.028e. jet PA. = 76°. inclination = 18”, precession cone hall-opening angle = 3. and angular velocity = 14x10? rad 1."," The best-fit model parameters are: jet speed = $c$ , jet P.A. = $\degr$ , inclination = $\degr$, precession cone half-opening angle = $\degr$, and angular velocity = $\times10^{-5}$ rad $^{-1}$."
 Apart from the radio morphology. this model is consistent with a couple of different observational fincines.," Apart from the radio morphology, this model is consistent with a couple of different observational findings."
" In the top panel of Figure 2. “A” marks the region with the llatter radio and harder X-rav spectrum. while ""D marks the location of a prominent. curved //a filament (??7).. seen here as coincident with the precessing radio counterjet."," In the top panel of Figure 2, “A” marks the region with the flatter radio and harder X-ray spectrum, while “B” marks the location of a prominent, curved $H{\alpha}$ filament \citep{Zurita00, HotaSaikia06,Leon07}, seen here as coincident with the precessing radio counterjet."
 ? were (he first (o present and discuss (he racdio—//a image overlavs., \citet{HotaSaikia06} were the first to present and discuss the $-H{\alpha}$ image overlays.
 The correspondence of the jet with these regions can explain both the spectral [lattening in the south (particle re-acceleration) ancl emission lines in the north (shock excitation)., The correspondence of the jet with these regions can explain both the spectral flattening in the south (particle re-acceleration) and emission lines in the north (shock excitation).
 Clearly. this study would greatly benefit [rom (shock-sensitive) Πα emission line observations of NGC 6764 (e.g..?)..," Clearly, this study would greatly benefit from (shock-sensitive) $\alpha$ emission line observations of NGC 6764 \citep[e.g.,][]{Sharp10}."
 While keeping in mind the uncertainties involved in the surface brightness values of the faint detected features. we estimated the observed jet-to-counterjet surface brightness ratio (?2-)↜⋅∕∣ ad three positions along5 the jet and counterjel.," While keeping in mind the uncertainties involved in the surface brightness values of the faint detected features, we estimated the observed jet-to-counterjet surface brightness ratio $R_{j}$ ) at three positions along the jet and counterjet."
 We note that if component 3 is a noise ⋅∕ ↽≻≼↲≀↧↴↳↽⋅⊔∐↲∐⊔∐↲∫↘⋝≼↲⊳∖⊽∐∐↓≀↧↴∥↲⋝∖⊽≀↧↴∣↽≻∪∖↽≼↲∐⋯⊳∖⇁↥∣↽≻≼↲↕⋅≼↲∩≀↧↴↕⋅≺," We note that if component 3 is a noise peak, then the $R_{j}$ estimates above must be regarded as lower limits."
⇂≼↲≼⇂≀↧↪∖⇁↥∪∖∖⊽≼↲↕⋅∐↕∐∐⊳∖⊽⋅↴⊺≀↧↴↳↽↕∐∩⊔∐↲↽≻≼↲≀↧↴↳↽⊳∖⇁⋯⋅↓⋟≀↧↴≺∢≼↲ S S brightness values of components 2 (jet) and 3 (counterjet). we derive an 22; 1.5.," Taking the peak surface brightness values of components 2 (jet) and 3 (counterjet), we derive an $R_{j}\sim$ 1.5."
 However. the peak positions of components 2 and 3 are not equidistant from the peak of component 1 (core).," However, the peak positions of components 2 and 3 are not equidistant from the peak of component 1 (core)."
 Therefore. taking5 the peak positionofcomponent 2 as a reference. we obtained the surface brightness ad a distance of ~4.5mas from the core (his being the distance between," Therefore, taking the peak positionofcomponent 2 as a reference, we obtained the surface brightness at a distance of $\sim4.5~mas$ from the core (this being the distance between"
in ,in .
"The process is repeated 10000 times, and the results (1988)..provide an estimate of the distribution of random cross-correlations for each time lag."," The process is repeated 10000 times, and the results provide an estimate of the distribution of random cross-correlations for each time lag."
" The results of the cross-correlation tests are summarized in Figure 5,, which shows the DCF for the data as black points and the 1-o (red), 2-σ and 3-e contours for the distribution of (yellow)random cross-correlations."," The results of the cross-correlation tests are summarized in Figure \ref{dcfs}, which shows the DCF for the data as black points and the $\sigma$ (red), $\sigma$ (yellow) and $\sigma$ (green) contours for the distribution of random cross-correlations."
(green) Using these values we find no highly significant cross-correlation., Using these values we find no highly significant cross-correlation.
 The most prominent peaks are located at -10 days (radio lagging) with an significance for B20134-370 and a peak at -240 days with a significance for B2023+336., The most prominent peaks are located at -10 days (radio lagging) with an significance for B2013+370 and a peak at -240 days with a significance for B2023+336.
" Additionally, the auto-correlation functions (not shown) were calculated separately for the gamma-ray and radio light curves, without finding any significant peak that could suggest periodic behavior."," Additionally, the auto-correlation functions (not shown) were calculated separately for the gamma-ray and radio light curves, without finding any significant peak that could suggest periodic behavior."
" Although statistically significant correlation between the gamma-raya and radio light curves would provide a definite identification, such identifications based on correlated variability have only been established for very bright gamma-ray blazars during short-lived flares2010a)."," Although a statistically significant correlation between the gamma-ray and radio light curves would provide a definite identification, such identifications based on correlated variability have only been established for very bright gamma-ray blazars during short-lived flares."
". If we only include the prominent gamma- flare of B2013+370 in 2009 the value of the cross-correlation peak at -10 days lag clearly increases, as shown in Figure 5.."," If we only include the prominent gamma-ray flare of B2013+370 in 2009 the value of the cross-correlation peak at -10 days lag clearly increases, as shown in Figure \ref{dcfs}."
" Assessing the statistical significance for very short light curves is difficult because the noise properties used for the statistical test are derived from longer time series and might not be appropriate for short periods of time, especially when these have been selected because of unusual source activity, a prominent gamma-ray flare in this case."," Assessing the statistical significance for very short light curves is difficult because the noise properties used for the statistical test are derived from longer time series and might not be appropriate for short periods of time, especially when these have been selected because of unusual source activity, a prominent gamma-ray flare in this case."
 The fact that the significance decreases as more data are included indicates that no robust claims about the physical significance of the apparent correlations can be made using time series dominated by a single event., The fact that the significance decreases as more data are included indicates that no robust claims about the physical significance of the apparent correlations can be made using time series dominated by a single event.
 Intrinsic long-term flux correlations might be washed out by the presence of extrinsic variability affecting only one of the frequency bands., Intrinsic long-term flux correlations might be washed out by the presence of extrinsic variability affecting only one of the frequency bands.
 showed that observations of extragalactic sources in (1998)the line of sight to B2013--370 and near B2023--336 show, showed that observations of extragalactic sources in the line of sight to B2013+370 and near B2023+336 show
":The and lines: are detected toward the TVLA 1 source upto. ~ £2i and I0|. respectively. [rom the svstemic velocity,","The and lines are detected toward the VLA 1 source upto $\sim$ 4.2 and 10, respectively, from the systemic velocity."
 In order to show how the envelope and disk structure changes with velocity. the line emission is divided into four velocity ranges: low (0—2.5 !)). medium (2.5—4.2 ')). high (4.25.8 !)). and very. high (5.8—10 !)) velocity ranges. on the redshifted and blueshifted sides.," In order to show how the envelope and disk structure changes with velocity, the line emission is divided into four velocity ranges: low $-$ 2.5 ), medium $-$ 4.2 ), high $-$ 5.8 ), and very high $-$ 10 ) velocity ranges, on the redshifted and blueshifted sides."
 In!|CO.. at low velocity. the redshifted emission is detected mainlv in the south and the blueshifted emission is mainlv in the north of the VLA | source (Fig.," In, at low velocity, the redshifted emission is detected mainly in the south and the blueshifted emission is mainly in the north of the VLA 1 source (Fig."
 τας). consistent with a rotation motion about the source.," \ref{fig:line}a a), consistent with a rotation motion about the source."
 As seen inCO.. the emission is contaminated bv the outflow emission. with the blueshifted emission also extending to the west and the reclshifted emission also extending to the east.," As seen in, the emission is contaminated by the outflow emission, with the blueshifted emission also extending to the west and the redshifted emission also extending to the east."
 In addition. the blueshiltecl emission shows a V-shaped structure opening to the north. spatially coincident with the cavity walls traced bv the reflection nebulae. suggesting that (he envelope material is piling up on the cavity walls as the cavity walls expand into the envelope.," In addition, the blueshifted emission shows a V-shaped structure opening to the north, spatially coincident with the cavity walls traced by the reflection nebulae, suggesting that the envelope material is piling up on the cavity walls as the cavity walls expand into the envelope."
 A similar V-shaped structure is also seen opening to the south in the redshilted. emission., A similar V-shaped structure is also seen opening to the south in the redshifted emission.
 At medium velocity. the emission shrinks to (he source. spatially coincident with the dusty disk (Fig.," At medium velocity, the emission shrinks to the source, spatially coincident with the dusty disk (Fig."
 τας aud Fig., \ref{fig:line}a a and Fig.
 6bb for a zoom-in)., \ref{fig:cont}b b for a zoom-in).
 The blueshifted emission peak is to the north and the redshilted emission peak is to the south in the equatorial plane. indicating that the motion there is highly dominated by the rotation about the VLA 1 source. as expected for a rotationally supported disk.," The blueshifted emission peak is to the north and the redshifted emission peak is to the south in the equatorial plane, indicating that the motion there is highly dominated by the rotation about the VLA 1 source, as expected for a rotationally supported disk."
 The two peaks. however. are not svmmnietric about (he source. with the northern peak at a distance ol ~ and southern peak al ~075.," The two peaks, however, are not symmetric about the source, with the northern peak at a distance of $\sim$ and southern peak at $\sim$."
 Two faint protrusions are also seen. one in the blue extending to the west from the northern part of the disk and one in the red extending to the east from the southern part. parallel to the jet axis.," Two faint protrusions are also seen, one in the blue extending to the west from the northern part of the disk and one in the red extending to the east from the southern part, parallel to the jet axis."
 These structures are similar to (hose seen in (he rotating molecular outflow in CD 26 (Launharcltetal.2009).. ancl (hus may trace material outflowing [rom the disk.," These structures are similar to those seen in the rotating molecular outflow in CB 26 \citep{Launhardt2009}, and thus may trace material outflowing from the disk."
 InPCO.. at low velocity. the blueshiltecl emission is mainly to the north and the recshiftecl emission is mainiv to the south. with V-shaped structures coincident with the cavitv walls (Fig.," In, at low velocity, the blueshifted emission is mainly to the north and the redshifted emission is mainly to the south, with V-shaped structures coincident with the cavity walls (Fig."
 Tec). similar to that seen in.," \ref{fig:line}c c), similar to that seen in."
CO... At medium velocity. the blueshifted enussion extends to (he west from the northern part of the disk while the redshifted emission extends to both the west and east [rom the southern part of the disk (Fig.," At medium velocity, the blueshifted emission extends to the west from the northern part of the disk while the redshifted emission extends to both the west and east from the southern part of the disk (Fig."
 τας and Fig., \ref{fig:line}d d and Fig.
 6cc for a zoom-in)., \ref{fig:cont}c c for a zoom-in).
 Note that the blueshiftecl emission ancl the recdshiltecl emission bevoncl ~ +1” from the source are contaminated by (the outflow shell emission. showing a cone-like structure with the Gp pointing toward the source.," Note that the blueshifted emission and the redshifted emission beyond $\sim$ $\pm$ from the source are contaminated by the outflow shell emission, showing a cone-like structure with the tip pointing toward the source."
 The blueshilted emission also shows an E-W elongation al ~ in the north (Fig., The blueshifted emission also shows an E-W elongation at $\sim$ in the north (Fig.
 τος). with an unknown origin.," \ref{fig:line}d d), with an unknown origin."
 At high velocity. the blueshiltecl and reclshifted emissions extend out [rom the inner radii of the disk (Fig.," At high velocity, the blueshifted and redshifted emissions extend out from the inner radii of the disk (Fig."
 Tee and Fig., \ref{fig:line}e e and Fig.
 6dd for a zoom-in)., \ref{fig:cont}d d for a zoom-in).
 The emissions within e from the source are not much, The emissions within $\sim$ from the source are not much
"6=7/4 then we will have correlation for k=2, but not for k=1.","$\delta=\pi/4$ then we will have correlation for $k=2$, but not for $k=1$."
" Practically speaking, for δέ1 we can have some particular symmetry, but not general symmetry A=4n."," Practically speaking, for $\delta \l \gg 1$ we can have some particular symmetry, but not general symmetry $\Delta=4n$."
 Conclusions concerning this rectangular model of GF are clearly seen in Fig.5., Conclusions concerning this rectangular model of GF are clearly seen in \ref{fign}.
". To understand how each sort of defects is related with corresponding 4n-correlation, we introduce the model of defects, which can be describe as a sum of peaks with amplitudes A; and coordinates 0;,9;."," To understand how each sort of defects is related with corresponding $4n$ -correlation, we introduce the model of defects, which can be describe as a sum of peaks with amplitudes $A_j$ and coordinates $\theta_j,\phi_j$."
" For analytical description of the model we neglect the beam convolution of the image of point sources (PS), but we include it in the numerical simulation."," For analytical description of the model we neglect the beam convolution of the image of point sources (PS), but we include it in the numerical simulation."
" For the model of defects For the dem coefficients of the spherical harmonics expansion from Eq.(6)) we get As for the rectangular model, we will assume that all 0;=1/2 and simply we will have agm~P;""(0) for £ó>> 1, as well as 05<1."," For the model of defects For the $\alm$ coefficients of the spherical harmonics expansion from \ref{ps}) ) we get As for the rectangular model, we will assume that all $\theta_j=\pi/2$ and simply we will have $a_{\l,m}\sim P_\l^m(0)$ for $\l\delta\gg 1$ , as well as $\l\delta\ll 1$."
" As it was shown in previous section, P;""(0) clearly demonstrate 4n correlation."," As it was shown in previous section, $P_\l^m(0)$ clearly demonstrate $4n$ correlation."
" We would like to point out that for the spots model this correlation now is strong, unlike the belt and rectangular models."," We would like to point out that for the spots model this correlation now is strong, unlike the belt and rectangular models."
" Moreover, implementation of the Gaussian shape of the PS which come from beam convolution does not change that symmetry at all."," Moreover, implementation of the Gaussian shape of the PS which come from beam convolution does not change that symmetry at all."
" To show that, in Fig.6 we plot the model of two PS with amplitudes in order to 10 mK, combined with the ILC map."," To show that, in \ref{ps} we plot the model of two PS with amplitudes in order to 10 mK, combined with the ILC map."
 The reason for such effect is quite obvious., The reason for such effect is quite obvious.
" The beam convolution does not change the symmetry of the but rescale the amplitudes of the PS by a factor exp[—mNM(t11)]/2c?, if we assume the Gaussian shape of the "," The beam convolution does not change the symmetry of the model, but rescale the amplitudes of the PS by a factor $\exp[-\l(\l+1)]/2\sigma^2$, if we assume the Gaussian shape of the beam."
"An important question is that is the symmetry of the Galaxy image in ¢ direction important for extraction of the brightest part of the signal, or is the effect simply determined by the symmetry of the Galaxy image in 0direction?"," An important question is that is the symmetry of the Galaxy image in $\phi$ direction important for extraction of the brightest part of the signal, or is the effect simply determined by the symmetry of the Galaxy image in $\theta$direction?"
" To answer this question, in Fig.7 we plot the result from the d? estimation in the model with 5 spots located at 0;=π/2 with different amplitudes and different ¢;."," To answer this question, in \ref{ps5} we plot the result from the $d^{\Delta}_{\l,m}$ estimation in the model with 5 spots located at $\theta_j=\pi/2$ with different amplitudes and different $\phi_j$."
 As one can see no symmetry in ϕ direction was assumed., As one can see no symmetry in $\phi$ direction was assumed.
 The result of reconstruction clearly shows that location of the sources in the Galactic plane in @ direction is crucial., The result of reconstruction clearly shows that location of the sources in the Galactic plane in $\phi$ direction is crucial.
" Unlike the model with symmetric location of the spots in Fig.6, now the residuals of the extraction of the spots dominate over the rest of the signal in the Galactic plane."," Unlike the model with symmetric location of the spots in \ref{ps}, , now the residuals of the extraction of the spots dominate over the rest of the signal in the Galactic plane."
"However, as is seen from Fig.7, the 4n-correlation of image exists.","However, as is seen from \ref{ps5}, , the $4n$ -correlation of image exists."
" The properties of the agm coefficients in the spots model are related with the sum (see Eq.(24))) Actually, Eq.(25)) determines the phases of the ag coefficients."," The properties of the $a_{\l,m}$ coefficients in the spots model are related with the sum (see \ref{ps1}) )) Actually, \ref{aa}) ) determines the phases of the $a_{\l,m}$ coefficients."
" Let us discuss the model of two symmetrically situated PS with the same amplitudes A;=A»and $1= 7/2, $3=2x—$1."," Let us discuss the model of two symmetrically situated PS with the same amplitudes $A_1=A_2$and $\phi_1=\pi/2$ , $\phi_2=2\pi-\phi_1$."
" For this particular case Im[S(m)]= 0, while Re[S(m)]=2Acos(7m/2).", For this particular case ${\rm Im}[ S(m)]=0$ while ${\rm Re} [S(m)]=2A\cos(\pi m/2) $.
" For m=2k+1,k0,12... we get Re[S(m)]=Im[S(m)]=0 and the contribution of the strong signal to the map ILC + two PS vanishes."," For $m=2k+1, k=0,1,2\ldots$ we get ${\rm Re} [S(m)]={\rm Im} [S(m)]=0$ and the contribution of the strong signal to the map ILC + two PS vanishes."
" This means that for amplitudes agm=Cem+pem; where Cem and pem correspond to the ILC and PS signals respectively) and phases Vp, of αρπι coefficients, we have where € are the ILC phases."," This means that for amplitudes $a_{\l,m}=c_{\l,m}+p_{\l,m}$, where $c_{\l,m}$ and $p_{\l,m}$ correspond to the ILC and PS signals respectively) and phases $\Psi_{\l,m}$ of $a_{\l,m}$ coefficients, we have where $\xi_{\l,m}$ are the ILC phases."
" As one can see, this is a particular example, when strong, but symmetric in $ direction signal do not contribute to the set of adem coefficients at least for the defined range of multipoles."," As one can see, this is a particular example, when strong, but symmetric in $\phi$ direction signal do not contribute to the set of $a_{\lm}$ coefficients at least for the defined range of multipoles."
" Let us discuss the other opposite model, in which the number of spots in the galactic plane is no fewer than 2, and their ¢; coordinates are random in some range o,27— Φ."," Let us discuss the other opposite model, in which the number of spots in the galactic plane is no fewer than 2, and their $\phi_j$ coordinates are random in some range $\Phi,2\pi-\Phi$ ."
 No specific assumptions about the amplitudes are needed., No specific assumptions about the amplitudes are needed.
" In this model the sum S(m) in Eq.(25)) mostly is representedby m=0 modes, S(0)=Yj Aj, while all mπε0 modesS(m)«S(0) becauseof randomness of the phases m@;."," In this model the sum $S(m)$ in \ref{aa}) ) mostly is representedby $m=0$ modes, $S(0)= \sum_j A_j$ , while all $m\neq 0$ modes$S(m)\ll S(0)$ becauseof randomness of the phases $m\phi_j$ ."
" This model,actually is close to the rectangular model, in which the width of rectangular sidein the ¢ direction now is ®,27— ®. At the end of this"," This model,actually is close to the rectangular model, in which the width of rectangular sidein the $\phi$ direction now is $\Phi,2\pi-\Phi$ At the end of this"
comparison with these isochrones (the selected metallicities οος from the isochrone metallicities because of the effects of observational scatter. as explained. in the previous section).,"comparison with these isochrones (the selected metallicities differ from the isochrone metallicities because of the effects of observational scatter, as explained in the previous section)."
 Fig., Fig.
 3 shows the MacDonald. isochrones overlaid on the colour magnitude diagram. of these three sets of stars from the sample., 3 shows the MacDonald isochrones overlaid on the colour magnitude diagram of these three sets of stars from the sample.
 ALL isochrone sets in what follows are shown for three dillerent ages. although age of course has very Little elect. for. the stars of the spectral type being considered (Ix chwarls).," All isochrone sets in what follows are shown for three different ages, although age of course has very little effect for the stars of the spectral type being considered (K dwarfs)."
 Solar metallicity stars are shown by open circles ancl the isochrones (for three ages) bv solid. lines., Solar metallicity stars are shown by open circles and the isochrones (for three ages) by solid lines.
 Sub-solar metallicity stars are shown by crosses and the sub-solar isochrones by dotted. lines. and the super-solar mictallicity stars by filled. squares ancl the super-solar metallicity isochrones by dashed: lines.," Sub-solar metallicity stars are shown by crosses and the sub-solar isochrones by dotted lines, and the super-solar metallicity stars by filled squares and the super-solar metallicity isochrones by dashed lines."
 Stars and isochrones are denoted in this svstem throughout the comparison (i.e. Figures 3. 4. 5. 6. S and 9).," Stars and isochrones are denoted in this system throughout the comparison (i.e. Figures 3, 4, 5, 6, 8 and 9)."
 The MacDonald. solar metallicity isochrones in figure 3 match the data quite well. and are execllent for the low metallicity case.," The MacDonald solar metallicity isochrones in figure 3 match the data quite well, and are excellent for the low metallicity case."
 Although the super-solar isochrones achieve eood agreement with the data for Ady26. stars more Iuminous than this appear to be hotter than the models (by about 200 Ix).," Although the super-solar isochrones achieve good agreement with the data for $M_V > 6$, stars more luminous than this appear to be hotter than the models (by about 200 K)."
 Before we discuss this disagreement in more detail it is worth noting that the MacDonald isochrones use ANYANZ=2.5. for the metallicity range considered (see also table 2).," Before we discuss this disagreement in more detail it is worth noting that the MacDonald isochrones use $\Delta Y/\Delta Z = 2.5$, for the metallicity range considered (see also table 2)."
 As it has been pointed out by several researchers (see c.g. Pagel ancl Portinari. 1998 anc references therein) the width of the main sequence at a fixed. luminosity. for dwarfs also depends on the value of AY/AZ although a similar effect is also due to variations with metallicity. in the mixing length parameter (e.g. Jimenez ancl MacDonald. 1906).," As it has been pointed out by several researchers (see e.g. Pagel and Portinari, 1998 and references therein) the width of the main sequence at a fixed luminosity for dwarfs also depends on the value of $\Delta Y/\Delta Z$ although a similar effect is also due to variations with metallicity in the mixing length parameter (e.g. Jimenez and MacDonald, 1996)."
 We have experimented with changing AY/AZ by +0.5., We have experimented with changing $\Delta Y/\Delta Z$ by $\pm 0.5$.
 ‘This experiment is qualitative only. because our starting point is isochrones which are not vet a good Lit to the super-solar metallicity stars.," This experiment is qualitative only, because our starting point is isochrones which are not yet a good fit to the super-solar metallicity stars."
 Adopting values. of A)/AZ in this range leads to no significant improvements in the overall fits of the isochrones., Adopting values of $\Delta Y/ \Delta Z$ in this range leads to no significant improvements in the overall fits of the isochrones.
 For example. increasing AYVSAZ to 3 fa very modest increase) helps to [fit the luminous metal rich. stars but the fit to the low luminosity. metal-rich chvarls deteriorates.," For example, increasing $\Delta Y/ \Delta Z$ to 3 (a very modest increase) helps to fit the luminous metal rich stars but the fit to the low luminosity metal-rich dwarfs deteriorates."
 An alternative explanation is that the mixing length. parameter. might change with luminosity (increase) for metal rich stars., An alternative explanation is that the mixing length parameter might change with luminosity (increase) for metal rich stars.
 Fig., Fig.
 4 shows a similar comparison as in Fig., 4 shows a similar comparison as in Fig.
 3 but this time using the PADOVA isochrones., 3 but this time using the PADOVA isochrones.
 The first thing to note is hat the solar isochrone provides a fit of nearly the same quality as the MacDonald. isochrones., The first thing to note is that the solar isochrone provides a fit of nearly the same quality as the MacDonald isochrones.
 On the other hand xh the low and high metallicity isochrones do not. provide adequate fits to the data., On the other hand both the low and high metallicity isochrones do not provide adequate fits to the data.
 The metal-rich isochrone does xovide a good fit to the luminous stars (Ady<6) but fails ο provide a good fit to the less Luminous dwarls., The metal-rich isochrone does provide a good fit to the luminous stars $M_V < 6$ ) but fails to provide a good fit to the less luminous dwarfs.
 Fhis can f traced. back to the large value of AY/AZ used (2.7 [or Z= 0.03) in these isochrones (we found the same elfect or the MacDonald. isochrones)., This can be traced back to the large value of $\Delta Y/ \Delta Z$ used (2.7 for $Z=0.03$ ) in these isochrones (we found the same effect for the MacDonald isochrones).
 Furthermore. for the low metallicity isochrone the adopted AY/AZ value is rather ow (1.8 for Z= 0.008). and may be the reason for the isochrone to be sub-Iuminous relative to the data.," Furthermore, for the low metallicity isochrone the adopted $\Delta
Y/ \Delta Z$ value is rather low (1.8 for $Z=0.008$ ), and may be the reason for the isochrone to be sub-luminous relative to the data."
 In Fig 5 the Siess et al (Siess. Dufour and Forestini. 2000) isochrones are shown compared. to the data.," In Fig 5 the Siess et al (Siess, Dufour and Forestini, 2000) isochrones are shown compared to the data."
 Lhe slope of these isochrones matches the data well and the metal weak isochrones are correctly locatecl. but the solar and the metal rich isochrones do not match the data as well. being systematically too faint.," The slope of these isochrones matches the data well and the metal weak isochrones are correctly located, but the solar and the metal rich isochrones do not match the data as well, being systematically too faint."
 Especially interesting is the solar composition metallicity isochrone which appears to be too faint by a few tenths of a magnitude. but given the small number of stars this dillerence may not be significant. (1.6. the error in these comparisons is dominated by systematic ellects which are plausibly at least a few 0.1 mag).," Especially interesting is the solar composition metallicity isochrone which appears to be too faint by a few tenths of a magnitude, but given the small number of stars this difference may not be significant (i.e. the error in these comparisons is dominated by systematic effects which are plausibly at least a few $\times$ 0.1 mag)."
 The disagreement is more severe for the metal rich case., The disagreement is more severe for the metal rich case.
 The Y72 (i.e. Yonsei-Yale) isochrones are compared in Fig., The $^2$ (i.e. Yonsei-Yale) isochrones are compared in Fig.
 6 with the Llippareos data. choosing the Lejeune et al. (," 6 with the Hipparcos data, choosing the Lejeune et al. ("
1998) library to transform from elfective temperature and luminosity to colour ancl absolute magnitude.,1998) library to transform from effective temperature and luminosity to colour and absolute magnitude.
 The solar metallicity isochrone provides a σους fit to the data and the overall slope matches the data well., The solar metallicity isochrone provides a good fit to the data and the overall slope matches the data well.
 On the other hand. the low and high metallicity isochrones do not match the data.," On the other hand, the low and high metallicity isochrones do not match the data."
 For the Y? isochrones AY7AZ=2 for the whole metallicity range.," For the $Y^2$ isochrones $\Delta Y / \Delta
Z = 2$ for the whole metallicity range."
 It would be very interesting to have these isochrones, It would be very interesting to have these isochrones
"We selected 59 non-passive (i.e. currently star-forming or hosting an AGN) BEG targets based on the scheme of Leeetal.(2008), using the spectroscopic sample of galaxies in the SDSS Data Release 4 (DR4;Adelman-McCarthyetal. 2006).","We selected 59 non-passive (i.e. currently star-forming or hosting an AGN) BEG targets based on the scheme of \citet{lee08}, using the spectroscopic sample of galaxies in the SDSS Data Release 4 \citep[DR4;][]{ade06}."
". We adopted the physical parameters of the galaxies from several value-added galaxy catalogs (VAGCs) drawn from the SDSS: photometric parameters from the SDSS pipeline (Stoughton 2002),, structural parameters estimated by Park&Choi(2005) and Choietal.(2007),, and spectroscopic parameters from Max-Planck-Institute for Astrophysics (MPA) / Johns Hopkins University(JHU) VAGC (Kauffmannetal.2003;Tremontietal.2004;Gallazzi 2006)."," We adopted the physical parameters of the galaxies from several value-added galaxy catalogs (VAGCs) drawn from the SDSS: photometric parameters from the SDSS pipeline \citep{sto02}, structural parameters estimated by \citet{par05} and \citet{cho07}, and spectroscopic parameters from Max-Planck-Institute for Astrophysics (MPA) / Johns Hopkins University(JHU) VAGC \citep{kau03,tre04,gal06}."
". Firstly, we selected the early-type galaxies from the SDSS galaxies using their distribution in the color, color gradient and light-concentration parameter space (Park&Choi2005)."," Firstly, we selected the early-type galaxies from the SDSS galaxies using their distribution in the color, color gradient and light-concentration parameter space \citep{par05}."
". Next, we divided the selected early-type galaxies into REGs and BEGs, using the method of Leeetal.(2006) based on the color distribution of bright early-type galaxies as a function of redshift?."," Next, we divided the selected early-type galaxies into REGs and BEGs, using the method of \citet{lee06} based on the color distribution of bright early-type galaxies as a function of redshift."
". The BEGs were classified using their flux ratios between several spectral lines (e.g.BPTdiagram;Baldwinetal.1981;Kewleyet2006) into passive, SF, Seyfert, and low ionization nuclear emission region (LINER) galaxies, among which passive BEGs were excluded."," The BEGs were classified using their flux ratios between several spectral lines \citep[e.g.~BPT diagram;][]{bal81,kew06} into passive, SF, Seyfert, and low ionization nuclear emission region (LINER) galaxies, among which passive BEGs were excluded."
" Finally, we dropped BEGs with conspicuous sub-structures or disk components in visual checks."," Finally, we dropped BEGs with conspicuous sub-structures or disk components in visual checks."
 Among the BEGs selected in this, Among the BEGs selected in this
in maeuituce lanited survevs.,in magnitude limited surveys.
 However. bv comparing photometry in overlapping fields where both CEITT aud IIubble Space Telescope inagiug is available. uo galaxies brighter than the magnitude lunt of Ryp=2L1 are found to be lost due to low surface brightuess (77).," However, by comparing photometry in overlapping fields where both CFHT and Hubble Space Telescope imaging is available, no galaxies brighter than the magnitude limit of $R_{AB} = 24.1$ are found to be lost due to low surface brightness \citep{Simard2002, Willmer2006}."
 ? come to similar conclusions regarding the loss of low surface brightuess galaxies frou deep miaeiug in the GOODS-N field., \citet{Melbourne2007} come to similar conclusions regarding the loss of low surface brightness galaxies from deep imaging in the GOODS-N field.
 Iu many previous studies. huuinositv has been taken as a proxy for muss (?7777777)..," In many previous studies, luminosity has been taken as a proxy for mass \citep{Kobulnicky2000, Pettini2001, Garnett2002, Kobulnicky2003a, Kobulnicky2004, Maier2004, Shapley2004, Shapley2005}."
 However. it has Όσσα recognized that the evolutiou iu the LZ relation caunot straighttforwardly be attributed to metallicity evolution. but that luminosity evolution must also be considered.," However, it has been recognized that the evolution in the LZ relation cannot straightforwardly be attributed to metallicity evolution, but that luminosity evolution must also be considered."
 By comparing figures 6 and 7.. we see that the offset in metallicity in the MZ relation is significantly smaller than the offset in the LZ relation.," By comparing figures \ref{fig:mz} and \ref{fig:lz}, we see that the offset in metallicity in the MZ relation is significantly smaller than the offset in the LZ relation."
 ? (among others) sugeest that the ditfereutial evolution in the LZ aud MZ relation results from au evolution iu the mass-to-lelt ratio., \citet{Lamareille2009} (among others) suggest that the differential evolution in the LZ and MZ relation results from an evolution in the mass-to-light ratio.
 They estimate the evolution such that where 0 is the slope of the LZ relation and Alog(O/HV aud Alog(O/II) are the differences. in metallicitv at a fixed stellar mass and fixed D-biud magnitude in the MZ and LZ relations. respectively.," They estimate the evolution such that where $a$ is the slope of the LZ relation and $\Delta log(O/H)^M$ and $\Delta log(O/H)^L$ are the differences in metallicity at a fixed stellar mass and fixed B-band magnitude in the MZ and LZ relations, respectively."
 Equation 10. assumes that the metallicity evolution is characterized by the MZ relation and that additional evolution inferred from the LZ relation is due to evolution of the luminosity., Equation \ref{eq:lzevol} assumes that the metallicity evolution is characterized by the MZ relation and that additional evolution inferred from the LZ relation is due to evolution of the luminosity.
 We estimate the evolution of the B-baud πιοντν as a function of stellar mass from equation 10.., We estimate the evolution of the B-band luminosity as a function of stellar mass from equation \ref{eq:lzevol}. .
 We ake the difference. between the local and DEEP2 LZ relation. AJogtO/II). to be the average difference jetween the binned DEEDP2 data and the fit to the ocal LZ relation over all maguitucdes (see Figure 7)).," We take the difference between the local and DEEP2 LZ relation, $\Delta log(O/H)^L$, to be the average difference between the binned DEEP2 data and the fit to the local LZ relation over all magnitudes (see Figure \ref{fig:lz}) )."
" Cousequently, Alog(O/IT)*0.20d0.03. dex and a=011."," Consequently, $\Delta log(O/H)^L = 0.20 \pm 0.03$ dex and $a = -0.11$."
 We take Alog(O/II) to be the difference )etween the DEEP? binned data aud local MZ relation fit., We take $\Delta log(O/H)^M$ to be the difference between the DEEP2 binned data and local MZ relation fit.
 The difference is piarzuneterized by where e=log(AL.)10., The difference is parameterized by where $x = log(M_{\ast}) - 10$.
 Were we have performed a linear least-squares fit using polyfit.pro aud the errors aredetermined from the residuals of the fit aud do uot account for observational uucertaiuties., Here we have performed a linear least-squares fit using $\emph{poly\_fit.pro}$ and the errors aredetermined from the residuals of the fit and do not account for observational uncertainties.
where (AyAy.A].Ad)=(50.3950.1050.1250)1983).,"where $(\lambda_1^-,\lambda_2^-,\lambda_1^+,\lambda_2^+)=(3750,3950,4050,4250)$."
. A definition using narrower contiuuun bands (AyAyA}Xd)—(3850.3950.1000.L100) was introduced by and is widely used.," A definition using narrower continuum bands $(\lambda_1^-,\lambda_2^-,\lambda_1^+,\lambda_2^+)=(3850,3950,4000,4100)$ was introduced by and is widely used."
 The advantage of the narrower bands is that the iudex is less scusitive to reddeniug., The advantage of the narrower bands is that the index is less sensitive to reddening.
" We adopt the narrow-band definition. aud denote this index as D,(1000)."," We adopt the narrow-band definition, and denote this index as $D_{\mathrm{n}}(4000)$."
" The resultaut Dy(1000) iudices ave L.1040.02 and 1.6340.08 for LEDA 81271 and IRAS 01250|2832. respectively,"," The resultant $D_{\mathrm{n}}(4000)$ indices are $\pm$ 0.02 and $\pm$ 0.08 for LEDA 84274 and IRAS 01250+2832, respectively."
" On the basis of these indices, LEDA 81271 has the spectimm of a late-tvpe ealaxy. and IRAS 01250|2832 that of an clliptical galaxy."," On the basis of these indices, LEDA 84274 has the spectrum of a late-type galaxy, and IRAS 01250+2832 that of an elliptical galaxy."
 The ANARI NIR spectroscopic observations display a steep red coutimmun in both, The $AKARI$ NIR spectroscopic observations display a steep red continuum in both
The non-equilibrium ionization fractions are calculated including the following processes: photoionization. collisional ionization. case Bo radiative recombination. dielectronic recombination for Hle. 1. and the coupling between Il and Lle caused by the radiation fields. from the Le | 24.6 eV recombination continuum and from the bound-bound transitions of He E (2)..,"The non-equilibrium ionization fractions are calculated including the following processes: photoionization, collisional ionization, case B radiative recombination, dielectronic recombination for He I, and the coupling between H and He caused by the radiation fields from the He I 24.6 eV recombination continuum and from the bound-bound transitions of He I \citep{Venkatesan:01}."
 The photoionization cross sections for HE E and and He 11 are taken from Spitzer (1978). and from Verner et al. (," The photoionization cross sections for H I and and He II are taken from Spitzer (1978), and from Verner et al. ("
"1996) for He 1. The ratio of the LE E to He E photoionization cross sections decreases with photon energy. ranging from about at LOO eV. to at 1 keV. This implies that an X-ray photon is ""seen? better by a He 1 atom than by a 11 E atom.","1996) for He I. The ratio of the H I to He I photoionization cross sections decreases with photon energy, ranging from about at 100 eV to at 1 keV. This implies that an X-ray photon is “seen"" better by a He I atom than by a H I atom."
 We also include secondary ionizations and. excitations of LE Ll and He L arising from the X-ravs (Shull van Steenberg 1985)., We also include secondary ionizations and excitations of H I and He I arising from the X-rays (Shull van Steenberg 1985).
" As notedin οι, à tvpical. X-ray photon is far more likely to be absorbed. by He L rather than LL ol. so that secondary ionization (rather than clirect photoionization) is most relevant for LE Lb when X-rays dominate photoionization."," As notedin \citet{Venkatesan:01}, a typical X-ray photon is far more likely to be absorbed by He I rather than H I, so that secondary ionization (rather than direct photoionization) is most relevant for H I when X-rays dominate photoionization."
 The resulting photoclectrons will ionize many more 11 1 atoms than Ile L 11 1 atoms being more numerous.," The resulting photoelectrons will ionize many more H I atoms than He I, H I atoms being more numerous."
 As the backerouncl ionization increases. the photoelectron deposits more ancl more of its energy in heat and less in collisional ionizations/excitations.," As the background ionization increases, the photoelectron deposits more and more of its energy in heat and less in collisional ionizations/excitations."
" Shull van Steenberg (1985) assumed that the ionization fractions of HE E and He L were equal. anc we have replaced the eencric ionization [fraction in their formulae with the electron Traction or, which is more cirectlv relevant for the IGM."," Shull van Steenberg (1985) assumed that the ionization fractions of H I and He I were equal, and we have replaced the generic ionization fraction in their formulae with the electron fraction $x_e$ which is more directly relevant for the IGM."
" The thermal evolution of the gas is computed including he following processes (?): photocleetric heating [rom he secondary electrons of LE and. Le. which is itself. a ""unction of the background. ionization levels (Shull van Steenberg 1985). and. heating from the LE 1 photoclectrons iberated. by the bound-bound transitions or the 24.6 eV recombination continuum of Hle 1. Cooling terms include raciative and cielectronic recombination (?. and references herein). thermal bremsstrahlung. Compton scattering. olf he CAIB. collisional ionization and excitation. and the adiabatic expansion of the ICM."," The thermal evolution of the gas is computed including the following processes \citep{Venkatesan:01}: photoelectric heating from the secondary electrons of H and He, which is itself a function of the background ionization levels (Shull van Steenberg 1985), and, heating from the H I photoelectrons liberated by the bound-bound transitions or the 24.6 eV recombination continuum of He I. Cooling terms include radiative and dielectronic recombination \citealt{Venkatesan:01} and references therein), thermal bremsstrahlung, Compton scattering off the CMB, collisional ionization and excitation, and the adiabatic expansion of the IGM."
 The contributions to reating and cooling from the scattering of the secondary Lye photons from X-ray ionization is negligible (77). and is not included here.," The contributions to heating and cooling from the scattering of the secondary $\alpha$ photons from X-ray ionization is negligible \citep{chen04,chen08} and is not included here."
 Our LD non-equilibrium ionization code includes all of the above ionization and heating processes. ancl solves for the evolution of the thermal and ionization state around the source as follows.," Our 1D non-equilibrium ionization code includes all of the above ionization and heating processes, and solves for the evolution of the thermal and ionization state around the source as follows."
 Phe IGM surrounding the source is divided up into a large number of concentric spherical shells., The IGM surrounding the source is divided up into a large number of concentric spherical shells.
 Unless otherwise noted. we use 1000 shells. spaced logarithmically in radius from 10 “to 10 Alpe.," Unless otherwise noted, we use 1000 shells, spaced logarithmically in radius from $10^{-4}$ to $10$ Mpc."
 These shells are initially »opulated with hydrogen and helium in a primordial ratio., These shells are initially populated with hydrogen and helium in a primordial ratio.
 When considering a uniform medium surrouncing he source. the gas is given initial tonizecl fractions as determined bv the recombination (7) or the appropriate cosmology and redshift.," When considering a uniform medium surrounding the source, the gas is given initial ionized fractions as determined by the recombination \citep{seager_how_2000} for the appropriate cosmology and redshift."
 “Phe initial emperature of the gas in cach shell is also determined by and each shell is initially set to be expanding with he Hubble Dow., The initial temperature of the gas in each shell is also determined by and each shell is initially set to be expanding with the Hubble flow.
 We then proceed to evolve the thermal and ionization states of these shells forwards in time in a series of short time steps., We then proceed to evolve the thermal and ionization states of these shells forwards in time in a series of short time steps.
 During cach time step we begin by computing the input spectrum ofphotons emitted by the central source (QSO. stars or both).," During each time step we begin by computing the input spectrum of photons emitted by the central source (QSO, stars or both)."
 Given this spectrum. we compute rates of ionization and heating in the innermost shell and solve for the evolution of its properties by integrating the appropriate set of differential equations as desribed. below.," Given this spectrum, we compute rates of ionization and heating in the innermost shell and solve for the evolution of its properties by integrating the appropriate set of differential equations as desribed below."
 The input spectrum is then attenuated by the optical depth of this first gaἸο ancl used as input for the second. shell., The input spectrum is then attenuated by the optical depth of this first shell and used as input for the second shell.
 This process is repeated: until the outermost shell is reached. (which is 'hosen to be at sulliciently [large radius that the radiation ficld is attenuated to close to zero at all times curing our calculation), This process is repeated until the outermost shell is reached (which is chosen to be at sufficiently large radius that the radiation field is attenuated to close to zero at all times during our calculation).
 In addition to changes in. temperature. and ionization state. the density of cach shell evolves as it expands or contracts due to anv initial velocity ane pressure forces.," In addition to changes in temperature and ionization state, the density of each shell evolves as it expands or contracts due to any initial velocity and pressure forces."
 This approach is similar to those in other recent papers. e.g.. Thomas Zaroubi (2008).," This approach is similar to those in other recent papers, e.g., Thomas Zaroubi (2008)."
 Our calculations of the ionization and thermal evolution ofeach shell use the same input physics as the IGM evolution model of ?.., Our calculations of the ionization and thermal evolution of each shell use the same input physics as the IGM evolution model of \cite{benson_galaxy_2010}.
 The censity of cach ionization. n;. state in a eiven shell is then given by where for each atomic species 11 or Ho. i refers to their jonization state (1.c.. 1 = 1 and 2 for Il and LE. and i = 3. 4 and 5 for He. and He? ). 7; is the number density. 7 is the temperature of the shell. Vis the volume of the shell. a; is the recombination rate for 7 (2).. Ly; is the collisional ionization rate coellicient for 7 (2). and E; is the ionization rate for 7 which is given by where a;i is an cllective photo-ionization Cross-section that accounts for the ellects of secondary ionizations and is given by 2? (as re-expressed by 23): where o(£) is the actual cross section (2). and In the above. SCLclé is the number of photons emitted per second in the energy range ££ to Le|clés by the central source ancl τζετ) is the optical depth to radius r at energy E.," The density of each ionization, $n_i$, state in a given shell is then given by where for each atomic species H or He, i refers to their ionization state (i.e., i = 1 and 2 for H and $^+$, and i = 3, 4 and 5 for He, $^+$ and $^{2+}$ ), $n_i$ is the number density, $T$ is the temperature of the shell, $V$ is the volume of the shell, $\alpha_i$ is the recombination rate for $i$ \citep{verner_atomic_1996}, $\Gamma_{e,i}$ is the collisional ionization rate coefficient for $i$ \citep{voronov_practical_1997} and $\Gamma_{\gamma,i}$ is the photo-ionization rate for $i$ which is given by where $\sigma_i^\prime$ is an effective photo-ionization cross-section that accounts for the effects of secondary ionizations and is given by \citet{shull85} (as re-expressed by \citealt{Venkatesan:01}) ): where $\sigma(E)$ is the actual cross section \citep{verner_analytic_1995} and In the above, $S(E) \d E$ is the number of photons emitted per second in the energy range $E$ to $E+\d E$ by the central source and $\tau(E;r)$ is the optical depth to radius $r$ at energy $E$ ."
 Similarly. the evolution of the temperature of each shell is given by," Similarly, the evolution of the temperature of each shell is given by"
We now compare our results for he weak-lensing power spectra with nuuerical simulations.,We now compare our results for the weak-lensing power spectrum with numerical simulations.
" In addition. we also consider the predictions obtaiue roni the popular ""halo-ft fittine function for the 3D density power προςτι eiven in ?.. to estimate the eaius tha can be reached by using a somewhat more svsteniaic approach."," In addition, we also consider the predictions obtained from the popular ``halo-fit'' fitting function for the 3D density power spectrum given in \cite{Smith2003}, to estimate the gains that can be reached by using a somewhat more systematic approach."
 We show our results for the convergeenceo power Spectruni. D). in Fig. 1..," We show our results for the convergence power spectrum, $\Pkappa(\ell)$, in Fig. \ref{fig_Pl}."
 For retereice we also plot the linear power and we can check that both simulations aud analytical models recover the lnear recoime on large scales., For reference we also plot the linear power and we can check that both simulations and analytical models recover the linear regime on large scales.
 The τιuerical error bars Hucrease on aree scales because of the finite size of the simulation box., The numerical error bars increase on large scales because of the finite size of the simulation box.
 Ou small scales the nuierea error is dominated Ww systenatic effects. due to the finite resolution. that leac O allluderestinate of the sanall-scale power (as clearly shown by the sharp decline at verv high ().," On small scales the numerical error is dominated by systematic effects, due to the finite resolution, that lead to an underestimate of the small-scale power (as clearly shown by the sharp decline at very high $\ell$ )."
 For each source recIshift we estimaed the scale (up to which the simulatiois have an accuracy of better than ! by colparing wih hieheraesolution simulations (with 512° particles insead of 256°)., For each source redshift we estimated the scale $\ell$ up to which the simulations have an accuracy of better than $5\%$ by comparing with higher-resolution simulations (with $512^3$ particles instead of $256^3$ ).
 This scale is shown by the verical arrow in Fie., This scale is shown by the vertical arrow in Fig.
 d. and we cau check that our model indeed aerees with the mmuerical simulations up to this iultipole., \ref{fig_Pl} and we can check that our model indeed agrees with the numerical simulations up to this multipole.
 We recover the well-kuown fact that on scales that are of interes for cosmological analysis of weak gravitational lensing. 10«ές10i. τιilinear terms significantly contribute to or dominate the oower spectrum (??)..," We recover the well-known fact that on scales that are of interest for cosmological analysis of weak gravitational lensing, $10^2 < \ell < 10^4$, nonlinear terms significantly contribute to or dominate the power spectrum \citep{Bartelmann2001,Munshi2008}."
 The overall shapes of the power spectra obtained from our model. described iu Sect. 2..," The overall shapes of the power spectra obtained from our model, described in Sect. \ref{Analytic},"
" aud from the fittine formula frou, 7.. are very simular."," and from the fitting formula from \cite{Smith2003}, are very similar."
" This ds expected since the latter “halo-fit™ also goes to the linear power on larec S‘ales ancl it is based on nuniperical simulatious for its Su-scale behavior. while the halo model that underlies ΟΥ approach on simall scales also agrees with simular siuulations Ga particular i --involves the ""NEW. profile aud a lnass-concentration relation that are derived from. sinations)."," This is expected since the latter “halo-fit” also goes to the linear power on large scales and it is based on numerical simulations for its small-scale behavior, while the halo model that underlies our approach on small scales also agrees with similar simulations (in particular it involves the “NFW” profile and a mass-concentration relation that are derived from simulations)."
 These similar shapes also coviri that the sharp falloff of the power at veh ( found iu 16 rav-tracing SHations is not plivsical but due to the fute resolution., These similar shapes also confirm that the sharp falloff of the power at high $\ell$ found in the ray-tracing simulations is not physical but due to the finite resolution.
 The iuprovenmeuts that can be expeced from our approach. as compared with a simpler fittine formula to nieasures of the 3D power. are hat i) on arge scales we are consistent with perturbation theory 1p to one-loop order. aud ii) on simall scales we directly use a plivsical halo model Gustead of using some forma or the power spectrin with free expoucuts that are fitted to a set of simulations).," The improvements that can be expected from our approach, as compared with a simpler fitting formula to measures of the 3D power, are that i) on large scales we are consistent with perturbation theory up to one-loop order, and ii) on small scales we directly use a physical halo model (instead of using some formula for the power spectrum with free exponents that are fitted to a set of simulations)."
 On large scales the error bars of our ray-tracine simulations (aud their lack of large-scale power) are too large to clearly see he benefit of the one-loop perturbative terms at low τν., On large scales the error bars of our ray-tracing simulations (and their lack of large-scale power) are too large to clearly see the benefit of the one-loop perturbative terms at low $z_s$.
 However. the higher accuracy duc to these higher-order rturbative contributions cau be see at τς= Land τς=1.5. as will be shown more clearly in Sect.," However, the higher accuracy due to these higher-order perturbative contributions can be seen at $z_s=1$ and $z_s=1.5$, as will be shown more clearly in Sect."
 G.1 below. (," \ref{Convergence-power-spectrum-1H}
 below. ("
The benefit of these terms las already been shown in studies of the 3D matter density power spectrum. especially or the accurate prediction of the xuvon acoustic oscillations. e.g. 277277???).,"The benefit of these terms has already been shown in studies of the 3D matter density power spectrum, especially for the accurate prediction of the baryon acoustic oscillations, e.g. \citet{Jeong2006,Nishimichi2007b,Nishimichi2009,Crocce2008,Matsubara2008,Taruya2009,Sato2011b,Valageas2011d,Valageas2011e}) )."
 In the weak-lensing context. this hieher accuracy could also be useful for the analysis of fuure observations such as the Enclicl nussion (?)..," In the weak-lensing context, this higher accuracy could also be useful for the analysis of future observations such as the Euclid mission \citep{Refregier2010}."
 Ou sinall scales. although the agreement of our model with the simulatioIs Is nO perfect we cau see a clear inrprovenient as conxwed with the fitting formula frou ?..," On small scales, although the agreement of our model with the simulations is not perfect we can see a clear improvement as compared with the fitting formula from \cite{Smith2003}."
 This is not surprisingOo since the latter was derived frou a set of older nuuerica sinnulatious with somewhat differeut costological nreers than the ones we consider iu this oper., This is not surprising since the latter was derived from a set of older numerical simulations with somewhat different cosmological parameters than the ones we consider in this paper.
" The uuderestimate of the power on sinall scales by his ""halo-fit formua. by about 30% around the peak for te=L. was already roticed in 2.."," The underestimate of the power on small scales by this “halo-fit” formula, by about $30\%$ around the peak for $z_s=1$, was already noticed in \cite{Hilbert2009}. ."
 The comparison of our nodel with the 3D power spectrum in 77 was also used on simulations with «iffereut cosmological parameters. bu WO!eh the explicit expression (7)) we automatically take oeito account the dependence on cosmology of the lnear OYOWh factor Dy(t) of the density flicuations aud of je linear threshold à; associated: with the nonlinear leusitv contrast of 200 (7)..," The comparison of our model with the 3D power spectrum in \cite{Valageas2011d,Valageas2011e} was also based on simulations with different cosmological parameters, but through the explicit expression \ref{Pk-1H}) ) we automatically take into account the dependence on cosmology of the linear growth factor $D_+(t)$ of the density fluctuations and of the linear threshold $\deltaLc$ associated with the nonlinear density contrast of $200$ \citep{Valageas2009}."
 We mostly neglect the lepeudeuce on cosmolosv of the halo profiles aud of 1011) niass-concentration relation., We mostly neglect the dependence on cosmology of the halo profiles and of their mass-concentration relation.
" However. even hough virialization processes do not reach complete relaxation. lat is. a violent relaxation ""à la Lyuden-Bell” ο) is rot complete in this cosmological contest aud docs no allow the halos to reach a statistical equilibrimm tha i» fulv independent of the initial conditions. iuterual alo sropertics are almost universal ancl dmdepenudenu of cosmological paraiucters up to a eood accuracy (for realistic CDM. scenarios)."," However, even though virialization processes do not reach complete relaxation, that is, a violent relaxation “à la Lynden-Bell” \citep{Lynden-Bell1967} is not complete in this cosmological context and does not allow the halos to reach a statistical equilibrium that is fully independent of the initial conditions, internal halo properties are almost universal and independent of cosmological parameters up to a good accuracy (for realistic CDM scenarios)."
" Similarly. deviations of he halo Lass ""unctiou from 7universality” have been detected bu aro Veuher weak (02?77).."," Similarly, deviations of the halo mass function from “universality” have been detected but are rather weak \citep{Tinker2008,More2011,Bhattacharya2011}."
" This is expecially true for our o»rpose as we mmteerate over the full halo mass ""unction (whic1 ds normalized o unity) aud we take iuto accoun he dependence ou cosinology of its largeanass cutoff.", This is especially true for our purpose as we integrate over the full halo mass function (which is normalized to unity) and we take into account the dependence on cosmology of its large-mass cutoff.
 This explains why our model is able to reach a good agreemoeu with he umunuerical simulations., This explains why our model is able to reach a good agreement with the numerical simulations.
 O1i the intermediae scales. which are seusitive to the interpolatioi (18)). we also obtain a satisfactory match to the nuuxvical simulations.," On the intermediate scales, which are sensitive to the interpolation \ref{P-tang-2}) ), we also obtain a satisfactory match to the numerical simulations."
 Within this range. around (oM300. the “halo-fit™ prediction happoeus Oo provide a siubu. or in a feay cases: slightly better. agreement with he simulations.," Within this range, around $\ell \sim 300$, the “halo-fit” prediction happens to provide a similar, or in a few cases slightly better, agreement with the simulations."
 These transition scales. where both the one-loop perturbative contribution aud the l1-halo teri ire stbdominant as shown in Fie.," These transition scales, where both the one-loop perturbative contribution and the 1-halo term are subdominant as shown in Fig."
 | )olow. are COVOYred hy he interpolation (] SJ).," \ref{fig_Pl_1H} below, are governed by the interpolation \ref{P-tang-2}) )."
 This menus that this 1iterpolation is uot fully satisfactory aud that there reallis rooliu for iuprovenient., This means that this interpolation is not fully satisfactory and that there remains room for improvement.
 However. to keep our inode as simple as possible and to remain consistent with our previous 3D studies we do not investigate here alternative prescriptions.," However, to keep our model as simple as possible and to remain consistent with our previous 3D studies we do not investigate here alternative prescriptions."
 We shall check in Sect., We shall check in Sect.
 7 below thatthe overall aereenmient found in Fie., \ref{Cosmology} below thatthe overall agreement found in Fig.
 1 roiunaius valid as we chauge the values of the cosinological parameters., \ref{fig_Pl} remains valid as we change the values of the cosmological parameters.
Astcroscismic Science Consortium (xASC) ahead. of public release and for their outstanding ellorts which have mace these results possible.,Asteroseismic Science Consortium (KASC) ahead of public release and for their outstanding efforts which have made these results possible.
 Funding for the, Funding for the
placed on a cubical Cartesian eric. aud are then perturbed according to a given power spectrmn Pik)=AR. by applving the Zeldovich (1970) approximation which also allows to selfconsistently assign initial velocities.,"placed on a cubical Cartesian grid, and are then perturbed according to a given power spectrum $P(k)=A k^{n}$, by applying the Zeldovich (1970) approximation which also allows to self-consistently assign initial velocities."
 The power-law iudex is sotton =2.5 which approximately describes the spectral behavior ou the scale ~LOSAL..., The power-law index is setto $n=-2.5$ which approximately describes the spectral behavior on the scale $\sim 10^{8}M_{\odot}$.
 To fix the amplitude A. we specify the initial variance of tle fluctuation amplitude The sunuuation is over all coutributing modes. where the miuinuun waveuuniber is given by the overall size of the Cartesian box. aud the maxima wavenumber by the Nyquist frequency.," To fix the amplitude $A$, we specify the initial variance of the fluctuation amplitude The summation is over all contributing modes, where the minimum wavenumber is given by the overall size of the Cartesian box, and the maximum wavenumber by the Nyquist frequency."
 Choosing σὲ~0.01. the ruis amplitude of fluctuations at the moment of collapse is approximately This choice eusures that the substructure develops on a simular timescale as the overall collapse of the backeround imedimn.," Choosing $\sigma_{i}^{2}\simeq 0.01$, the rms amplitude of fluctuations at the moment of collapse is approximately This choice ensures that the substructure develops on a similar timescale as the overall collapse of the background medium."
 Next. particles within a (propor) radius of f TiO pe are selected for the simulation.," Next, particles within a (proper) radius of $R_{i}=$ 776 pc are selected for the simulation."
 The resultiug umber of DAL particles is Ip=1707I.," The resulting number of DM particles is $N_{\rm
DM}=17074$."
 Finally. the particles are set iuto rigid rotation and are endowed with a uniform Iubble expansion (see also I&atz 1991).," Finally, the particles are set into rigid rotation and are endowed with a uniform Hubble expansion (see also Katz 1991)."
 Áugular momentum is added by asstuing a spin parameter A=L[E|/?/(GADP7)0 and 0.05. where L. E. aud M are the total angular momentum. euergx. and mass respectively.," Angular momentum is added by assuming a spin parameter $\lambda=L|E|^{1/2}/(G M^{5/2})=0$ and 0.05, where $L$, $E$, and $M$ are the total angular momentum, energy, and mass, respectively."
 The spin parameter is a nieasure of the degree of rotational support. such that the ratio of ceutritugal to eravitational acceleration is eiveu bv ~M at virialization.," The spin parameter is a measure of the degree of rotational support, such that the ratio of centrifugal to gravitational acceleration is given by $\sim \lambda^{2}$ at virialization."
 The second value corresponds to the average spin parameter found in cosmological simulatious (o.e.. Barnes Efstathiou 1987: Jaug-Condell Ieruquist 2001).," The second value corresponds to the average spin parameter found in cosmological simulations (e.g., Barnes Efstathiou 1987; Jang-Condell Hernquist 2001)."
 The collisional SPII particles (Αι= 32768) are randonilv placed to approximate a inifori initial density., The collisional SPH particles $N_{\rm SPH}=32768$ ) are randomly placed to approximate a uniform initial density.
 The SPIL particles follow the same IHubble expansion and rigid rotation as the DAI particles., The SPH particles follow the same Hubble expansion and rigid rotation as the DM particles.
 For the initial eas temperature at 7;=LOO we adopt the value of 200 Is (Teemark et al., For the initial gas temperature at $z_{i}=100$ we adopt the value of $200$ K (Tegmark et al.
 1997)., 1997).
" The fractional free-clectrou abundance is initialized as or,=L6«101. and the hydrogen molecule abundance. m the runs whereIL formation is allowed. as fin,=2«105 (Auninos Norman 1996)."," The fractional free-electron abundance is initialized as $x_{e}=4.6\times 10^{-4}$, and the hydrogen molecule abundance, in the runs where$_{2}$ formation is allowed, as $f_{\rm H_{2}}=2\times 10^{-6}$ (Anninos Norman 1996)."
 Iu Table 1l. we sunmunarize the parameters of the laree-scale simulations.," In Table 1, we summarize the parameters of the large-scale simulations."
 We will discuss the initial state of the refined. stuall-scale simulation in L2.," We will discuss the initial state of the refined, small-scale simulation in 4.2."
" We enipasize that the initial particle setup. and in particular the realization of the DM fluctuations. is identical for all runs which oulv differ in the choice of spin. iu the preseuce or absence of a soft UV. background. aud im whether IL, cooling is allowed or not."," We empasize that the initial particle setup, and in particular the realization of the DM fluctuations, is identical for all runs which only differ in the choice of spin, in the presence or absence of a soft UV background, and in whether $_{2}$ cooling is allowed or not."
 The runs with uo Πω cooling correspond to the limiting case iu which all the IT». has been radiatively destroved by a soft UV. backerouud., The runs with no $_{2}$ cooling correspond to the limiting case in which all the $_{2}$ has been radiatively destroyed by a soft UV background.
 Iu 2. we have discussed the possible eniergeuce of such au eficient feedback following the build-arp of the cosmic UV background close to the epoch of reionization.," In 2, we have discussed the possible emergence of such an efficient feedback following the build-up of the cosmic UV background close to the epoch of reionization."
 Tn this section. we onlv consider simulations where uo external UV background is included. and defer the discussion of its effect to 5.," In this section, we only consider simulations where no external UV background is included, and defer the discussion of its effect to 5."
 We carry out these simulations iu two separate steps., We carry out these simulations in two separate steps.
 First. we simulate the large-scale evolution on the scale of the host halo. ~l kpc. eudiug with the formation of high-density clumps on a scale of ~1 pe.," First, we simulate the large-scale evolution on the scale of the host halo, $\sim 1$ kpc, ending with the formation of high-density clumps on a scale of $\sim
1$ pc."
 Once the mass resolution of the siuulatioun becomes larger than the local Jeans mass. A;xAL... a sink particle is created.," Once the mass resolution of the simulation becomes larger than the local Jeans mass, $M_{J}\la M_{\rm res}$, a sink particle is created."
 Consequeuthy. the internal dynamics of a chuup cannot be studied any further in these coarse-erain smniulatious.," Consequently, the internal dynamics of a clump cannot be studied any further in these coarse-grain simulations."
 Second. we follow the evolution of a chuup to higher densities aud smaller spatial scales. by refining the resolution in the vicinity of the chunp to again resolve the Jeans mass.," Second, we follow the evolution of a clump to higher densities and smaller spatial scales, by refining the resolution in the vicinity of the clump to again resolve the Jeans mass."
 We begin with a discussion of the large-scale evolution., We begin with a discussion of the large-scale evolution.
 We first describe the run with no spin aud with suppressed Ho formation (Run A) in more detail. and subsequently explore what happens uuder variations of these asstuuptious.," We first describe the run with no spin and with suppressed $_{2}$ formation (Run A) in more detail, and subsequently explore what happens under variations of these assumptions."
 In Figure 1. we show the initial configuration at 2;—100. which is ideutical for all runs.," In Figure 1, we show the initial configuration at $z_{i}=100$ , which is identical for all runs."
 The overdense region initially expauds with the IIubble flow at a reduced rate. subsequently turus around at traον 16. and eventually collapses.," The overdense region initially expands with the Hubble flow at a reduced rate, subsequently turns around at $z_{\rm ta}\sim 16$ , and eventually collapses."
envelopes.,envelopes.
 Current quantitative models indicate (hat a critical core mass (Mog10M. ) is needed [or the onset of efficient accretion of the surrounding gas (Pollacketal.1996)., Current quantitative models indicate that a critical core mass $M_{\rm crit} \sim 10 M_\oplus$ ) is needed for the onset of efficient accretion of the surrounding gas \citep{Pollack1996}.
. This mass is determined by the heat transfer efficiency (Inaba&Ikoma2003) and the nebula boundary conditions (Bodenheimeretal.2000;Wuchterl2000:2006:Ralikov2006 ).," This mass is determined by the heat transfer efficiency \citep{Inaba2003} and the nebula boundary conditions \citep{Bodenheimer2000, Wuchterl2000, Papaloizou2006, Rafikov2006}."
. There are considerable uncertainties on (he magnitude of AZ44.," There are considerable uncertainties on the magnitude of $M_{\rm
crit}$."
 The first sets of quantitative models were constructed under the assumptions of spherical symmetry. hvdrostatie equilibrium. efficient convection. interstellaa-grain opacity. aud idealized planetesimal bombardment rate (Pollacketal.1996).," The first sets of quantitative models were constructed under the assumptions of spherical symmetry, hydrostatic equilibrium, efficient convection, interstellar-grain opacity, and idealized planetesimal bombardment rate \citep{Pollack1996}."
. These models indicate (hat uninterrupted planetesimal bombarcinents and a cooling barrier can delay the formation of Jupiter in a minimum mass nebula (MMN) by 10-20 Mvr., These models indicate that uninterrupted planetesimal bombardments and a cooling barrier can delay the formation of Jupiter in a minimum mass nebula (MMN) by 10-20 Myr.
" llowever. gas giants can only acquire their massive envelope inside gas-vich protostellar disks. their formation ime scale 7, must be smaller than (he (vpical gaseous disk depletion (nme scale τρίο2— 5Myr)."," However, gas giants can only acquire their massive envelope inside gas-rich protostellar disks, their formation time scale $\tau_m$ must be smaller than the typical gaseous disk depletion time scale $\tau_{\rm dep} (\sim 3-5 {\rm Myr}$ )."
 There have been several previous attempts to resolve this theoretical challenge., There have been several previous attempts to resolve this theoretical challenge.
" Alibert (2004) suggested that tvpe I migration of embryos (Ward 1997) may speed up the time scale needed [ον the onset of efficient eas accretion,", Alibert (2004) suggested that type I migration of Earth-mass embryos (Ward 1997) may speed up the time scale needed for the onset of efficient gas accretion.
 Although (his scenario may provide a solution for Saturn (because its core is relatively massive). it may not be appropriate for Jupiter il its core mass is limited (o a few Al," Although this scenario may provide a solution for Saturn (because its core is relatively massive), it may not be appropriate for Jupiter if its core mass is limited to a few $M_\oplus$."
 In an attempt to account for Jupiter's low-mass core. Inaba&Ikoma(2003);al.(2005). constructed models to show that the gas accretion rate increases with the heat iransport efficiency.," In an attempt to account for Jupiter's low-mass core, \citet{Inaba2003, 
Hubickyj2005} constructed models to show that the gas accretion rate increases with the heat transport efficiency."
 Since (here are radiative regions in proto gas giants! envelope. the critical mass for the onset of efficient gas accretion increases wilh the opacity of the inlalling envelope.," Since there are radiative regions in proto gas giants' envelope, the critical mass for the onset of efficient gas accretion increases with the opacity of the infalling envelope."
 The main sources of opacity in (hese regions are erains., The main sources of opacity in these regions are grains.
 Grain growth and formation of planetesimals can reduce the opacity of residual disk gas substantially (see relsec:envelo))., Grain growth and formation of planetesimals can reduce the opacity of residual disk gas substantially (see \\ref{sec:envelo}) ).
 It is also possible for dust to coagulate ancl sediment from the tenuous outer envelope of proto-planets (Ilelledetal.2008)., It is also possible for dust to coagulate and sediment from the tenuous outer envelope of proto-planets \citep{Helled2008}.
. In principle. these effects can suppress the barrier for the onset of gas accretion.," In principle, these effects can suppress the barrier for the onset of gas accretion."
" However. a rch population of super-Earths (with masses M,> a lew AL) has been discovered wilh raclial-velocity (Alavoretal.2009) and (transit (Quelozοἱal.2000). surveys."," However, a rich population of super-Earths (with masses $M_p >$ a few $M_\oplus$ ) has been discovered with radial-velocity \citep{Mayor2009} and transit \citep{Queloz2009}
 surveys."
 Some of these super-Earths have masses larger (han Jupiters estimated core mass (at least [or some nmocdels)., Some of these super-Earths have masses larger than Jupiter's estimated core mass (at least for some models).
" This discrepancy would introduce a paradox. if we assume these super Earth altained (heir present-day mass and became ~“lailed cores” in gas-rich protostellar disks because their mass M,«Mog."," This discrepancy would introduce a paradox, if we assume these super Earth attained their present-day mass and became “failed cores” in gas-rich protostellar disks because their mass $M_p < 
M_{\rm crit}$."
 It is possible that the onset of gas accretion onto these super-Eartlis may be delaved by planetesimal bombardment. albeit such events are likely {ο be suppressed by (he formation of a gap in the planetesimal disk (see," It is possible that the onset of gas accretion onto these super-Earths may be delayed by planetesimal bombardment, albeit such events are likely to be suppressed by the formation of a gap in the planetesimal disk (see"
range is still acceptable. with maximal deviations typically below,"range is still acceptable, with maximal deviations typically below."
" At the lower field strength shown in Figure 11 (B,=2<10 C). fr~0.35 which would inplv a radius larger than the pure blackbody radius by about a factor two."," At the lower field strength shown in Figure \ref{specdamp} $B_p=2\times
10^{13}$ G), $f_E\sim 0.35$ which would imply a radius larger than the pure blackbody radius by about a factor two."
 This is definitely larger than what is predicted by the cold electron gas iiodels with p=py. and may be euough to provide an acceptabe value of the stellar radius.," This is definitely larger than what is predicted by the cold electron gas models with $\rho=\rho_s$, and may be enough to provide an acceptable value of the stellar radius."
 However. at least for the uniform temperature distribution. for such values of the polar field the alsorption feature around wy300 eV is clearly present im the spectrum (see again Figure 11)).," However, at least for the uniform temperature distribution, for such values of the polar field the absorption feature around $\omega_0\sim 300$ eV is clearly present in the spectrum (see again Figure \ref{specdamp}) )."
 The feature is nof so pronounced at lareer fields but fr becomes higher (~0.15) making the radius a xoblenmi again.," The feature is not so pronounced at larger fields but $f_E$ becomes higher $\sim
0.45$ ) making the radius a problem again."
 One has also to bear in 1d that the spectra shown in Figure 14. have been computed for a fixed rejction threshold., One has also to bear in mind that the spectra shown in Figure \ref{specdamp} have been computed for a fixed rejection threshold.
 As Figure 12. VAshows. the choice of this parameter (even within a factor of a few) has a crucial influence on he shape of cluitted spectrum.," As Figure \ref{rejec} shows, the choice of this parameter (even within a factor of a few) has a crucial influence on the shape of emitted spectrum."
 Apart from the consicrable uncertainties in current modeling of the physics governing the plase transition (sec 82 and Lai2007 for a more detailed discussion). we reniud the reader that our spectra have been computed under a ΠΡΟ of simplifving asstuuptious," Apart from the considerable uncertainties in current modeling of the physics governing the phase transition (see \ref{bare} and \citealt{lai2001} for a more detailed discussion), we remind the reader that our spectra have been computed under a number of simplifying assumptions."
 A thorough discussion of the limitations of this kind of approach can be coud in (1950)., A thorough discussion of the limitations of this kind of approach can be found in \citet{bri80}.
. The greatest uncertainties arise because of the assuuption of a sharp transition from vac ο a smooth metallic surface. ucelecting the effects of the macroscopic surface structure.," The greatest uncertainties arise because of the assumption of a sharp transition from vacuum to a smooth metallic surface, neglecting the effects of the macroscopic surface structure."
 We assmuued the surface is made of pure iron. but differeu chemical compositions. or the presence of impurities in the iron surface. may change the results.," We assumed the surface is made of pure iron, but different chemical compositions, or the presence of impurities in the iron surface, may change the results."
 Inside the star woe neglect the role of bound clectrons aud further effects produced by the dissipation of those waves that are rapidly attenuated within a skin penetration depth., Inside the star we neglect the role of bound electrons and further effects produced by the dissipation of those waves that are rapidly attenuated within a skin penetration depth.
 Finally. from a differeut perspective aud regarding the possible application of the present work. we point out tha the calculation of the complex refractive indices below the plasma frequency prescutcc here may substantially coutribute to the determination of he photon thermal couductivities of 1tranunaenetized neutron stars.," Finally, from a different perspective and regarding the possible application of the present work, we point out that the calculation of the complex refractive indices below the plasma frequency presented here may substantially contribute to the determination of the photon thermal conductivities of ultramagnetized neutron stars."
 These are. in turn. miportaut for the accurate calculation of the thermal structure and cooling of these objects (see Potelshinctcl.2003) ).," These are, in turn, important for the accurate calculation of the thermal structure and cooling of these objects (see \citealt{pot03}) )."
bias in recovered lensed-light fraction. would lead to a bias in the optical depth as well.,bias in recovered lensed-light fraction would lead to a bias in the optical depth as well.
 The MACHO collaboration investigated the blending of their clump giant sample and decided to use the parameters [rom the unblended fits., The MACHO collaboration investigated the blending of their clump giant sample and decided to use the parameters from the unblended fits.
 They also used a subsample of events that were less likely to be blended to check for a bias due to blending and found no such bias., They also used a subsample of events that were less likely to be blended to check for a bias due to blending and found no such bias.
" To test for a systematic bias we generate 1000 lightcurves with Gaussian errors for each of three different values for the error on each point: g= 0.01, 0= 0.05. and a=0.15."," To test for a systematic bias we generate 1000 lightcurves with Gaussian errors for each of three different values for the error on each point: $\sigma = 0.01$ , $\sigma = 0.05$ , and $\sigma = 0.15$."
 The recovered lensed-light fractions for these events are shown in Figure 9.., The recovered lensed-light fractions for these events are shown in Figure \ref{fig:fllhists}.
" As the error on individual datum increases the distribution of /7, becomes increasingly skewed.", As the error on individual datum increases the distribution of $f_{ll}^\prime$ becomes increasingly skewed.
" We find that while the mean /7, may not decrease, the most probable value does decrease."," We find that while the mean $f_{ll}^\prime$ may not decrease, the most probable value does decrease."
" This reduction in the mode is at least partially compensated by the large tail of the distribution with /7,>1. but for the small number of events a microlensing experiment observes it is unlikely that many of the [ew events with /7,>>1 will be observed."," This reduction in the mode is at least partially compensated by the large tail of the distribution with $f_{ll}^\prime > 1$, but for the small number of events a microlensing experiment observes it is unlikely that many of the few events with $f_{ll}^\prime \gg 1$ will be observed."
" Even if one event with /7,>1 is observed it may be ignored as it is an unphysical value of the parameter, thus leading to an underesumate of the average value of. /;j."," Even if one event with $f_{ll}^\prime \gg 1$ is observed it may be ignored as it is an unphysical value of the parameter, thus leading to an underestimate of the average value of $f_{ll}$."
 Thus we find that as the errors in measurement increase blend fitting becomes more and more likely to return biased results., Thus we find that as the errors in measurement increase blend fitting becomes more and more likely to return biased results.
 The direction of the bias is more often toward small values of /7., The direction of the bias is more often toward small values of $f_{ll}$.
 Thus events that are in reality unblended become more and more likely toreturnfit values implying that they are heavily blended., Thus events that are in reality unblended become more and more likely toreturnfit values implying that they are heavily blended.
A main purpose of this study is to disentangle the effects of the initial turbulent density distribution on the formation of the pillars.,A main purpose of this study is to disentangle the effects of the initial turbulent density distribution on the formation of the pillars.
" Therefore, the level of turbulence is changed."," Therefore, the level of turbulence is changed."
 We take different turbulent setups: One has been evolved from a very high Mach number 20) to12., We take different turbulent setups: One has been evolved from a very high Mach number (Mach 20) to.
5.. The other four represent different (Machstages of the decay starting from our fiducial turbulent setup (G09b) at Mach 10., The other four represent different stages of the decay starting from our fiducial turbulent setup (G09b) at Mach 10.
" They are taken at7,,(G09b),, and 1.5, respectively."," They are taken at, and , respectively."
" When non-driven turbulence decays, most power is lost on the large scale modes."," When non-driven turbulence decays, most power is lost on the large scale modes."
 This can be seen in Fig. 2:, This can be seen in Fig. \ref{FIG_evol}:
" In ,((column 2) and (column 3) the surface density is clearly dominated by the large modes, which form the prominent fingers."," In (column 2) and (column 3) the surface density is clearly dominated by the large modes, which form the prominent fingers."
" In contrast, in (column 1) no significant pillars evolve, since the initial density distribution is already too smooth and the dominant mode has decayed to far."," In contrast, in (column 1) no significant pillars evolve, since the initial density distribution is already too smooth and the dominant mode has decayed to far."
" This trend can already be seen in (Fig. 3,,"," This trend can already be seen in (Fig. \ref{FIG_compare},"
" panel 4), where the structures are less distinct. "," panel 4), where the structures are less distinct. ("
4) is a much more violent case.,column 4) is a much more violent case.
" Since there is a lot of (columnpower on the largest density scale, structures are evolving."," Since there is a lot of power on the largest density scale, structures are evolving."
" However, these are already being torn apart at the same time, as discussed in 4.."," However, these are already being torn apart at the same time, as discussed in \ref{Globules}."
" Overall, the evolution is mainly dominated by the pressure differences between hot and cold gas."," Overall, the evolution is mainly dominated by the pressure differences between hot and cold gas."
 Compared to the increase in the pressure due to the ionization (three orders of magnitude) the differences from varying the Mach number are small., Compared to the increase in the pressure due to the ionization (three orders of magnitude) the differences from varying the Mach number are small.
" However, a small trend is visible in the average density of the assembled structure (see Table 2))."," However, a small trend is visible in the average density of the assembled structure (see Table \ref{TAB_compare}) )."
" The higher the Mach number, the the density of the formed structure."," The higher the Mach number, the higher the density of the formed structure."
" That can be higherdirectly related to the density of the initial turbulent filament,"," That can be directly related to the density of the initial turbulent filament,"
"The object Q2237[0305 comprises a source quasar at redshift 2=1.695 that is eravitationally lensecl by a foreground galaxy (2= 0.0394) producing 4 images with separations of ~1"".",The object Q2237+0305 comprises a source quasar at redshift $z=1.695$ that is gravitationally lensed by a foreground galaxy $z=0.0394$ ) producing 4 images with separations of $\sim 1''$.
 Each of the 4 images are observed through the bulge of the galaxy. which has an optical depth in stars that is of order unity (eg.," Each of the 4 images are observed through the bulge of the galaxy, which has an optical depth in stars that is of order unity (eg."
 Went Faleo 1988: Schneider et al., Kent Falco 1988; Schneider et al.
 LOSS: Schmidt. Webster Lewis 1998).," 1988; Schmidt, Webster Lewis 1998)."
 In addition. the proximity of the lensing galaxy. means that 10 projected transverse velocity at the source is an orcer of magnitude higher than for a typical lens configuration.," In addition, the proximity of the lensing galaxy means that the projected transverse velocity at the source is an order of magnitude higher than for a typical lens configuration."
 The combination of these considerations make Q2237|0305 16 ideal object from which to study microlensing., The combination of these considerations make Q2237+0305 the ideal object from which to study microlensing.
 Indeed. (Q2237|0305 is the only object in which cosmological microlensing has been confirmed (Irwin et al.," Indeed, Q2237+0305 is the only object in which cosmological microlensing has been confirmed (Irwin et al."
 1989: Corrigan etal., 1989; Corrigan et al.
 1991)., 1991).
 In. 1988 a high magnification event (LEME) was observed in image A. I had a measured. rise time of 26 days. and was followed by an event having a decline time of £z3 months.," In 1988 a high magnification event (HME) was observed in image A. It had a measured rise time of $\sim 26$ days, and was followed by an event having a decline time of $\la 3$ months."
 Phe resulting Leht-curve has been interpreted as a double peaked event. corresponding to the source having crossed. two fold caustics inside a cusp (Witt Mao 1994). implying that the peak was caused by a single caustic crossing.," The resulting light-curve has been interpreted as a double peaked event corresponding to the source having crossed two fold caustics inside a cusp (Witt Mao 1994), implying that the peak was caused by a single caustic crossing."
 “Phe observation thus provides an estimate of the event crossing time. and a lower limit to the event amplitude.," The observation thus provides an estimate of the event crossing time, and a lower limit to the event amplitude."
 Attempts have been made on both of these fronts to interpret the LALE in terms of the size of the magnified continuum region (eg., Attempts have been made on both of these fronts to interpret the HME in terms of the size of the magnified continuum region (eg.
 Wambsganss. Paczenski Schneider (1990): Rauch Dlandford 1991: Jaroszvnski. Wanmbsganss Paczvnski 1992: Webster et al.," Wambsganss, Paczynski Schneider (1990); Rauch Blandford 1991; Jaroszynski, Wambsganss Paczynski 1992; Webster et al."
 1991)., 1991).
 The amplitude of an LEMIS is a function of source size - smaller sources produce events of larger amplitude., The amplitude of an HME is a function of source size - smaller sources produce events of larger amplitude.
 Llowever. the event amplitude is also dependent on the width or strength of a caustic. a quantity that is the constant of proportionality in the near caustic approximation of Chang hnefsdal (1979).," However, the event amplitude is also dependent on the width or strength of a caustic, a quantity that is the constant of proportionality in the near caustic approximation of Chang Refsdal (1979)."
 Witt (1990) termed tis constant the [Lux factor and found that it takes on a range of values in the complex Caustic structures that are produced by high optical depth microlensing niocdels., Witt (1990) termed this constant the flux factor and found that it takes on a range of values in the complex caustic structures that are produced by high optical depth microlensing models.
 Phe mean value of the lux factor depends on the mass function., The mean value of the flux factor depends on the mass function.
 Thus the event. amplitudes have a distribution that is model dependent., Thus the event amplitudes have a distribution that is model dependent.
 Wambseanss. Paczvnski Schneider (1990). found that a microlensing model with a mean microlens mass of 225A. reproduces the observed. luminosity variation when the source has a," Wambsganss, Paczynski Schneider (1990) found that a microlensing model with a mean microlens mass of $M_{\odot}$ reproduces the observed luminosity variation when the source has a"
from magnetic fields. and ICAL temperature profiles.,"from magnetic fields, and ICM temperature profiles."
 Iudeed. analyses of some individual clusters provides binding masses derived from galaxy clyaiics which are siguificautly higher than those derived from livdrostatic equilibrimiun.," Indeed, analyses of some individual clusters provides binding masses derived from galaxy dynamics which are significantly higher than those derived from hydrostatic equilibrium."
 However. a systematic study by the CNOC collaboration of 14 intermediate redshift clusters fuds the ratio of galaxy ανασα to isothermal lvdrostatic lasses to be L.OL+#0.077°..," However, a systematic study by the CNOC collaboration of 14 intermediate redshift clusters finds the ratio of galaxy dynamical to isothermal hydrostatic masses to be $1.04\pm0.07$ \cite{lewis99}."
 Further studies using eravitatioual leusing aud the spatially resolved ICAL teiiperatures available from Chandra should provide much needed additional formation., Further studies using gravitational lensing and the spatially resolved ICM temperatures available from Chandra should provide much needed additional information.
 Takingthe svstematic from the uncertainty iu the PSPC effective area and the systematic uncertainty on the binding mass cstimates. we estimate a total systematic uncertainty ofLO%.," Taking the systematic from the uncertainty in the PSPC effective area and the systematic uncertainty on the binding mass estimates, we estimate a total systematic uncertainty of."
. This together with the observations outlined in the previous section leads to a confidence wpper liit of , This together with the observations outlined in the previous section leads to a confidence upper limit of $\Omega_{M}<0.44h^{-1/2}_{50}$ .
Studies of high redshitt SNe Ia profer cosmological models with ος>0 9," Studies of high redshift SNe Ia prefer cosmological models with $\Omega_{Q}>0$ \cite{schmidt98,perlmutter99}."
" Both cluster barvon fraction areuiueuts aud mass to light studies? favor low Qa, models.", Both cluster baryon fraction arguments and mass to light studies \cite{carlberg97} favor low $\Omega_{M}$ models.
 The mass to light ratio studies are more difficult to iuterpret. because the stellar populations of galaxies inside clusters differ siguificautlv from those outside clusters.," The mass to light ratio studies are more difficult to interpret, because the stellar populations of galaxies inside clusters differ significantly from those outside clusters."
 Nevertheless.these two approaches. subject to different systematics. indicate O3;<<1.," Nevertheless,these two approaches, subject to different systematics, indicate $\Omega_{M}<<1$."
 Together with coustraiuts ou CMD anisotropy... these clusters lead to the conclusion Oo>0. independent of the SNe Ia studies.," Together with constraints on CMB \cite{dodelson00}, these clusters lead to the conclusion $\Omega_{Q}>0$, independent of the SNe Ia studies."
 The relatively simple evolution (compared to galaxies) aud reeularity of galaxy clusters make them caudidate tracer particles to use im iieasurime the relation., The relatively simple evolution (compared to galaxies) and regularity of galaxy clusters make them candidate tracer particles to use in measuring the volume--redshift relation.
 This classical cosmological test? has been applied to ealaxies with limited success. due at least in part to the complex relation betwoeeu ealaxy brightucss aud mass aud the poorly uuderstood evolution of the galaxy abuudaice??((but see Newman Davis article for discussion of new approach being cousicered iu the DEEP survey).," This classical cosmological test \cite{tolman34} has been applied to galaxies with limited success, due at least in part to the complex relation between galaxy brightness and mass and the poorly understood evolution of the galaxy abundance \cite{loh86}( (but see Newman Davis article for discussion of new approach being considered in the DEEP survey)."
 Clusters are more amcuable to these studies. because our theoretical uuderstancding of their structure aud evolutio1 is ore complete.," Clusters are more amenable to these studies, because our theoretical understanding of their structure and evolution is more complete."
 We dout expect the abundance of clusters to remain constant with redshift. but we can calculate its evolution. enabling the volumeredshiftt relation test.," We don't expect the abundance of clusters to remain constant with redshift, but we can calculate its evolution, enabling the volume–redshift relation test."
 Moreover. the cosmological scusitivity of the abundance evolution itself provides additional leverage.," Moreover, the cosmological sensitivity of the abundance evolution itself provides additional leverage."
 Galaxy cluster surveys of the nearby universe are an old eudeavor 5: however. new technology and techniques are now making it possible to carry," Galaxy cluster surveys of the nearby universe are an old endeavor \cite{abell58}; ; however, new technology and techniques are now making it possible to carry"
Ay. but rather the inteerated albedo. weighted by the incident stellar spectra. known as the Doud albedo and denoted iu this paper as Ap.,"$A_{\lambda}$, but rather the integrated albedo, weighted by the incident stellar spectrum, known as the Bond albedo and denoted in this paper as $A_{B}$."
 The relation between Ay and the plauct’s Bond albedo is not trivial., The relation between $A_{\lambda}$ and the planet's Bond albedo is not trivial.
 If the albedo is dominated by erav clouds. then the albedo at a single wavelength can indeed be extrapolated to obtain cp.," If the albedo is dominated by gray clouds, then the albedo at a single wavelength can indeed be extrapolated to obtain $A_{B}$."
 For nou-erav reflectance spectra. however. it is critical to nieasure ly at the peak ciuitting waveleneth of the host star to obtain a good estimate of the plauct’s energy budget.," For non-gray reflectance spectra, however, it is critical to measure $A_{\lambda}$ at the peak emitting wavelength of the host star to obtain a good estimate of the planet's energy budget."
 For example. as pointed out in Alarleyetal. (1999).. planets with identical albedo spectra. Ay. may have radically different Ap depending on the spectral type of their host stars.," For example, as pointed out in \cite{Marley_1999}, planets with identical albedo spectra, $A_{\lambda}$, may have radically different $A_{B}$ depending on the spectral type of their host stars."
 The first few measurements of hot Jupiter phase varlatious showed sigus that these planets are not all cut from the same cloth., The first few measurements of hot Jupiter phase variations showed signs that these planets are not all cut from the same cloth.
 Warringtonetal.(2006) and Wuutsonctal.(2007a) quoted very different phase function amplitudes for —the © Andromeda aud IID 189733 systems., \cite{Harrington_2006} and \cite{Knutson_2007a} quoted very different phase function amplitudes for the $\upsilon$ Andromeda and HD 189733 systems.
 It was not clear whether the differences were intrinsic to the plaucts. however. because the data were taken with different iustruments. a different waveleneths. and with very differcut observation schemes (manycase.subsequentre-analysisoftheorig-inaldataanduewlyaquiredSprtcer observations of e Andromeda b paint a completely ciffercut picture of that2010).," It was not clear whether the differences were intrinsic to the planets, however, because the data were taken with different instruments, at different wavelengths, and with very different observation schemes \citep[in any case, subsequent re-analysis of the original data and newly aquired \emph{Spitzer} observations of $\upsilon$ Andromeda b paint a completely different picture of that."
 The uniform study presented in Cowanetal.(2007).. ou the other hand. showed that ΠΟ 179919b απ TID 209158b exhibit siguificautly different degrees of heat recirculation. confirnuneg suspicious.," The uniform study presented in \cite{Cowan_2007}, on the other hand, showed that HD 179949b and HD 209458b exhibit significantly different degrees of heat recirculation, confirming suspicions."
 But it was not clear whether hot exoplaucts were uuiauodal or bianodal m redistribution: are ΠΟ 179919 and WD 209158b eud-members of a single distribution. or prototypes for two fundamentally differeut sorts of exoplanets?," But it was not clear whether hot exoplanets were uni-modal or bi-modal in redistribution: are HD 179949b and HD 209458b end-members of a single distribution, or prototypes for two fundamentally different sorts of exoplanets?"
 The preseuce or lack of a stratospherie temperature inversion (IIubeuvyetal.2003:Fortuev2006:Bur- on the day-sides of exoplauets has been invoked to explain a purported bianuodalitv in recirculation efficiency on lot Jupiters (Fortuevctal. 2008)..," The presence or lack of a stratospheric temperature inversion \citep{Hubeny_2003, Fortney_2006b, Burrows_2007b, Burrows_2008, Zahnle_2009} on the day-sides of exoplanets has been invoked to explain a purported bi-modality in recirculation efficiency on hot Jupiters \citep{Fortney_2008}. ."
 The argument. simply put. is that optical absorbers hieh in the atmosphere of extremely hot Jupiters Cequilibrimm temperatures ercater than 1700 IN) would absorb incident photous where the radiative timescales areshort. making it difficult for these plauets to recirculate enerev.," The argument, simply put, is that optical absorbers high in the atmosphere of extremely hot Jupiters (equilibrium temperatures greater than $\sim 1700$ K) would absorb incident photons where the radiative timescales areshort, making it difficult for these planets to recirculate energy."
 The most robust detection of this tempcrature inversion ids for IID 209[55b (Ixuutsouetal.2008).. but this planet does not exhibit a large day-night brightness coutrast at 5 ju (Cowanetal.2007).," The most robust detection of this temperature inversion is for HD 209458b \citep{Knutson_2008}, but this planet does not exhibit a large day-night brightness contrast at 8 $\mu$ m \citep{Cowan_2007}."
. So while temperature inversons seen to exist in the majority of hot Jupiter atiuosplieres (I&nutsouetal.2010).. their connection to circulation efücienev if any d8 not clear.," So while temperature inversions seem to exist in the majority of hot Jupiter atmospheres \citep{Knutson_2010}, their connection to circulation efficiency —if any— is not clear."
 It has been sugeested (e.e..Tarringtonotal.2006:Cowanetal.2007) that observations of secondary eclipses and pliase variations cach coustrain a combination of a planet'* Doud albedo aud circulation eficiency.," It has been suggested \citep[e.g.,][]{Harrington_2006, Cowan_2007} that observations of secondary eclipses and phase variations each constrain a combination of a planet's Bond albedo and circulation efficiency."
 But observations —even phase variatious at a sinele wavebaud do little to constrain a planets οποιον budget., But observations —even phase variations--- at a single waveband do little to constrain a planet's energy budget.
 In this work we show how observations πι different wavebands and for different plauets cau be incaninefully combined to estimate these planetary parameters., In this work we show how observations in different wavebands and for different planets can be meaningfully combined to estimate these planetary parameters.
 In 2 we introduce a simple model to quautity the dav-side and night-side energv budget of a short-period planet. and show how a planet's Bond albedo. Ap. aud redistribution efiicicucy. ©. can be coustrained by observatious.," In 2 we introduce a simple model to quantify the day-side and night-side energy budget of a short-period planet, and show how a planet's Bond albedo, $A_{B}$, and redistribution efficiency, $\varepsilon$, can be constrained by observations."
 In 3 we use published observations of 21 transiting planets to estimate dav-xide aud where appropriate— uight-side effective temperatures., In 3 we use published observations of 24 transiting planets to estimate day-side and ---where appropriate— night-side effective temperatures.
 We construct a two-dimensional distribution function in Ap αμα τι Ll., We construct a two-dimensional distribution function in $A_{B}$ and $\varepsilon$ in 4.
 We state our conclusions in 5., We state our conclusions in 5.
 Short-period planets have a power budeet cutirely dictated bv the flux thev receive from their host. star. which chwarts tidal heating or remmant heat of formation.," Short-period planets have a power budget entirely dictated by the flux they receive from their host star, which dwarfs tidal heating or remnant heat of formation."
 Following Uansen(2008).. we define the equilibria temperature at the plauct’s sub-stellay poiut: Το)=ΤΠrt)1 where Tig and Π. are the star's effective temperature and radius. aud r(f) is the planetstar distance (for a circular orbit is simaply equal to the semu- axis. a).," Following \cite{Hansen_2008}, we define the equilibrium temperature at the planet's sub-stellar point: $T_{0}(t) = T_{\rm eff} (R_{*}/r(t))^{1/2}$ , where $T_{\rm eff}$ and $R_{*}$ are the star's effective temperature and radius, and $r(t)$ is the planet–star distance (for a circular orbit $r$ is simply equal to the semi-major axis, $a$ )."
 For shorthaud. we defiue the ecometrical factor a.=a/R... which is directly constrained by transit lightcurves (Seager&Mallén-Ornelas2003).," For shorthand, we define the geometrical factor $a_{*} = a/R_{*}$, which is directly constrained by transit lightcurves \citep{Seager_2003}."
. The incident faux on the planet is giveu bv Fine=SopT}. and it is significant that this quantity las some associated uucertaiuty.," The incident flux on the planet is given by $F_{\rm inc} = \frac{1}{2}\sigma_{B}T_{0}^{4}$ , and it is significant that this quantity has some associated uncertainty."
 For a plauct on a circular orbit. the πιο in Tj=Ἰωμήνας is related —to first order toτο theας uncertaiuties in the host stars effective temperature. aud the ecometrical factor: For a planet with non-zero eccentricity. Tj varies with time. but we are ouly concerned with its value at superior conjuuction: secondary eclipse occurs at superior conjunction. when we are secing the planct’s dav-side.," For a planet on a circular orbit, the uncertainty in $T_{0}=T_{\rm eff}/\sqrt{a_{*}}$ is related —to first order— to the uncertainties in the host star's effective temperature, and the geometrical factor: For a planet with non-zero eccentricity, $T_{0}$ varies with time, but we are only concerned with its value at superior conjunction: secondary eclipse occurs at superior conjunction, when we are seeing the planet's day-side."
 At that point in the orbit. the plauctstar distance is re=e(lc7)esinew). where e and ware the plauct’s orbital eccentricity aud argument of periastron. respectively.," At that point in the orbit, the planet–star distance is $r_{\rm sc} = a(1-e^{2})/(1-e\sin\omega)$, where $e$ and $\omega$ are the planet's orbital eccentricity and argument of periastron, respectively."
 For planets with non-zeroecceutricitv. the uncertainty in Ty is given by where co ANd σα are the observational unecrtaintics in the two components of the planet's c," For planets with non-zeroeccentricity, the uncertainty in $T_{0}$ is given by where $\sigma_{e\cos\omega}$ and $\sigma_{e\sin\omega}$ are the observational uncertainties in the two components of the planet's ."
"ontricityτς, At secondary eclipse. audiu the absence of albedo or cherey circulation. the equilibrium temperature of a reeion on the planet depends on the normalized projected"," At secondary eclipse, andin the absence of albedo or energy circulation, the equilibrium temperature of a region on the planet depends on the normalized projected"
Efforts to understaxd (he newly identified classes of neutron stars. in particular anomalous X-ray pulsars (ANDs - Mereghetti 1999) and soft gamma-ray repeaters (SGRs - Woods οἱ al.,"Efforts to understand the newly identified classes of neutron stars, in particular anomalous X-ray pulsars (AXPs - Mereghetti 1999) and soft gamma-ray repeaters (SGRs - Woods et al."
 1999) have followed (vo avenues., 1999) have followed two avenues.
" Magnetar models. involving neutron star dipole magnetic fields Bo~10!!—LOY G. above the quantum critical field B,=ο44xLol G. were advanced to explain the mechanism and energetics of soft gamuna-ray repeaters (Thompson Dunean 1995)."," Magnetar models, involving neutron star dipole magnetic fields $B \sim10^{14}-10^{15}$ G, above the quantum critical field $B_c=m^2c^3/e\hbar= 4.4 \times 10^{13}$ G, were advanced to explain the mechanism and energetics of soft gamma-ray repeaters (Thompson Duncan 1995)."
 Alternative models propose to explain the new classes of neutron stars in terms of conventional B—107 G fields., Alternative models propose to explain the new classes of neutron stars in terms of conventional $B\sim10^{12}$ G fields.
 These models involve accretion or propeller (Illarionov Sunvaev 1975) torques from an accretion disk surrounding the isolated neutron stars (Alpar 1999. 2001: Chatterjee. ILernquist Naravan 2000).," These models involve accretion or propeller (Illarionov Sunyaev 1975) torques from an accretion disk surrounding the isolated neutron stars (Alpar 1999, 2001; Chatterjee, Hernquist Narayan 2000)."
 Alpar (1999. 2001) argued (hat radio pulsars. dim thermal neutron stars (DTNs: Treves et al.," Alpar (1999, 2001) argued that radio pulsars, dim thermal neutron stars (DTNs; Treves et al."
 2000). AXPs and radio quiet neutron stars (RQNSs: Chakrabarty et al.," 2000), AXPs and radio quiet neutron stars (RQNSs; Chakrabarty et al."
 2001) and perhaps SCGRs represent alternative pathways of voung neutron stars. distinguished by the history of mass inflow (AL) from a fall-back accretion disk.," 2001) and perhaps SGRs represent alternative pathways of young neutron stars, distinguished by the history of mass inflow $\dot{M}$ ) from a fall-back accretion disk."
 This work classified voung neutron stars according to ranges, This work classified young neutron stars according to ranges
Barthetal.(1997). have reported the detection of eenission above the lanh of Gauvinede extending ucarly one Cauvinede radius (2631 km). which they attribute to a lvdrogen exosphere.,"\citet{bar97} have reported the detection of emission above the limb of Ganymede extending nearly one Ganymede radius (2634 km), which they attribute to a hydrogen exosphere."
" Such cussion should be detectable in our loue-slit spectral iniage but is masked by the strong ecocoronal ecluission that fills the eutire 2"" wide slit (see Figure 1)).", Such emission should be detectable in our long-slit spectral image but is masked by the strong geocoronal emission that fills the entire $2''$ wide slit (see Figure \ref{rawimage}) ).
" To remove the eeocoronal component. à ""füat field” alone the slit is needed."," To remove the geocoronal component, a “flat field” along the slit is needed."
 This is obtained roni our data in the following manner., This is obtained from our data in the following manner.
 The final three orbits contain separate spectral images with clistinctly different values of eeocoronal background. 15 kR for ιο first of cach pair. 3.5 kR for the second.," The final three orbits contain separate spectral images with distinctly different values of geocoronal background, 15 kR for the first of each pair, 3.5 kR for the second."
" The three ""hieh nuages aud the three ""low nuages are separatelv ombined (again uxing the flat-fielded counts files rather iui the flux calibrated fles). and spatial profiles along re slit (sunnüug 82 pixels in the dispersion direction) we obtained."," The three “high” images and the three “low” images are separately combined (again using the flat-fielded counts files rather than the flux calibrated files), and spatial profiles along the slit (summing 82 pixels in the dispersion direction) are obtained."
 These are shown in the top panel of Figure 6.., These are shown in the top panel of Figure \ref{lymana}.
 The profiles are normalized to the sliehtlv different cumulative exposure times and the difference is taken. which clininates the signal due to Ganmvinede. aud this is also shown (after median filtering) iu the figure.," The profiles are normalized to the slightly different cumulative exposure times and the difference is taken, which eliminates the signal due to Ganymede, and this is also shown (after median filtering) in the figure."
 The ecocoronal backerouncd is then uormalized to aud subtracted from the “low” image giviug the net SoApatial profile associated with Coumauede. as shown iu the lower panel of Figure 6.. where cussion above both —σαinibs is clearly detected.," The geocoronal background is then normalized to and subtracted from the “low” image giving the net spatial profile associated with Ganymede, as shown in the lower panel of Figure \ref{lymana}, where emission above both limbs is clearly detected."
 The radial model of Barthetal. (1997).. iutegrated across the width of the STIS slit. is also shown iu the fleure aud is found to fit our data very well.," The radial model of \citet{bar97}, integrated across the width of the STIS slit, is also shown in the figure and is found to fit our data very well."
 Objective erating images of Canvinede obtained with TSTΣΤΙΣ show clearly separated celuissions confriuus the result of Talletal.(1998) that the enissious are confined to polar regions (latitudes above 1[57))., Objective grating images of Ganymede obtained with HST/STIS show clearly separated emissions confirming the result of \citet{hal98} that the emissions are confined to polar regions (latitudes above ).
 The total fluxes are consistent with those reported by Halletal. but appear to vary iu time and in the relative iuteusities between northern aud southern hemispheres., The total fluxes are consistent with those reported by \citeauthor{hal98} but appear to vary in time and in the relative intensities between northern and southern hemispheres.
 The ]lull301 ratio is consistent with the primary excitation mechanism being electron impact on O». as postulated by Talletal. While the spatial distribution of the emissious is cousistent with current models of the maguetie Ποια of Gauvinede. expected longitudinal uniformity aud lub brightening are not observed.," The 1304 ratio is consistent with the primary excitation mechanism being electron impact on $_2$, as postulated by \citeauthor{hal98} While the spatial distribution of the emissions is consistent with current models of the magnetic field of Ganymede, expected longitudinal uniformity and limb brightening are not observed."
 Iu addition. Taub emission from a liydrogen exospliere is detected aud the measured brieltuess is found to be in good agreement with the Galileo UWS observations of Barth ((L997).," In addition, limb emission from a hydrogen exosphere is detected and the measured brightness is found to be in good agreement with the Galileo UVS observations of Barth (1997)."
 This work is based on observations with the National Acronauties aud Space Adiinistration Enropean Space Agency TST obtained at the Space Telescope Scieuce Iustitute. which is operated by the Association of Universities for Research in Astronomy. Iucorporated. under NASA contract NAS5S-26555.," This work is based on observations with the National Aeronautics and Space Administration – European Space Agency HST obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5-26555."
 We acknowledec partial support by NASA contract. NAS5S-30103 to the Johus IHopkius University., We acknowledge partial support by NASA contract NAS5-30403 to the Johns Hopkins University.
even if a uniform star-lormation rate is assumed.,even if a uniform star-formation rate is assumed.
 The theoretical models discussed here can be used to prediet mass or age distributious of objects as a function of spectral type., The theoretical models discussed here can be used to predict mass or age distributions of objects as a function of spectral type.
 Figure 6 shows illustrative results from our nominal model., Figure \ref{fig:spta} shows illustrative results from our nominal model.
 We show the predicted. probability density distributions (i.e.. the likelihood. per unit mass or age. an object has a certain mass or age) for spectral tvpes AIG. LO. L5. late-L. earlv-T. and late-T. The top panel of Figure 6 plots the age distributions aud the bottom panel (he mass distributions. and Table 2 lists the average age and mass of each spectral type.," We show the predicted probability density distributions (i.e., the likelihood, per unit mass or age, an object has a certain mass or age) for spectral types M6, L0, L5, late-L, early-T, and late-T. The top panel of Figure \ref{fig:spta} plots the age distributions and the bottom panel the mass distributions, and Table 2 lists the average age and mass of each spectral type."
 Given the uncertainties inherent in the models al verv voung ages. we have discarded all model results with ages less than 20 Mivrs of the sample for a constant star formation history).," Given the uncertainties inherent in the models at very young ages, we have discarded all model results with ages less than 20 Myrs of the sample for a constant star formation history)."
 We examine the features of these mass and age distributions to better understand je physical properties of the underlying substellar population., We examine the features of these mass and age distributions to better understand the physical properties of the underlying substellar population.
 The AIG age distribution is essentially flat., The M6 age distribution is essentially flat.
 This reflects the overwhelming predominance of hydrogen-burning stars., This reflects the overwhelming predominance of hydrogen-burning stars.
 In our baseline model. M6 dwarls form at a uniform rate over the LO Gyr spanned by the V.imulations and settle rapidly onto the main sequence with little subsequent evolution.," In our baseline model, M6 dwarfs form at a uniform rate over the 10 Gyr spanned by the simulations and settle rapidly onto the main sequence with little subsequent evolution."
 In contrast. the relative proportion of voung (<2 Gyr) dwarls increases. ancl (he average age decreases. as one progresses down the L and T. dwarf spectral sequence (see Table 2).," In contrast, the relative proportion of young $< 2$ Gyr) dwarfs increases, and the average age decreases, as one progresses down the L and T dwarf spectral sequence (see Table 2)."
 This behavior stems partly from the decreasing contribution of hvdrogen-burning stars and partly from rapid cooling of brown cwarls through (these temperature reeimes., This behavior stems partly from the decreasing contribution of hydrogen-burning stars and partly from rapid cooling of brown dwarfs through these temperature regimes.
 Late-tvpe T cdwals. however. exhibit a much flatter age distribution. albeit still decreasing with increasing age.," Late-type T dwarfs, however, exhibit a much flatter age distribution, albeit still decreasing with increasing age."
 The constant birthrate of new brown dwarls. coupled with the slower cooling rate at these temperatures (12901TOOK). as compared to L clwarls. vields an approximately constant density of late-T dwarfs as a function of age.," The constant birthrate of new brown dwarfs, coupled with the slower cooling rate at these temperatures $\sim$ 1250K–700K), as compared to L dwarfs, yields an approximately constant density of late-T dwarfs as a function of age."
 This is refleetecl in the average age of ~5 Gyr. comparable with that of stellaramass MÓ dwarts.," This is reflected in the average age of $\sim 5$ Gyr, comparable with that of stellar-mass M6 dwarfs."
 The mass distribution as a funcüon of spectral (wpe changes significantly as one crosses the stellar/substellar boundary., The mass distribution as a function of spectral type changes significantly as one crosses the stellar/substellar boundary.
 As can be seen in the bottom panel of Figure 6.. the mostly stellar M6 mass distribution has a well-defined mass range with a shallow tail.," As can be seen in the bottom panel of Figure \ref{fig:spta}, the mostly stellar M6 mass distribution has a well-defined mass range with a shallow tail."
 The LO and L5 mass distributions are strongly peaked al masses near the hvedrogen-burning limit. which reflects (he long main sequence liletimes of stellar L clwarls.," The L0 and L5 mass distributions are strongly peaked at masses near the hydrogen-burning limit, which reflects the long main sequence lifetimes of stellar L dwarfs."
 The distribution broadens for late-L and earlv-T clwarls. both of which include only substellar-mass objects.," The distribution broadens for late-L and early-T dwarfs, both of which include only substellar-mass objects."
 Nevertheless. hieher-inass brown dwarls. which spend long periods of time as L aud early-T dwarls. are the majority constituent in both cases.," Nevertheless, higher-mass brown dwarfs, which spend long periods of time as L and early-T dwarfs, are the majority constituent in both cases."
" The average mass is lower for earlv-T. clwarls. since the hiehest-mass brown clwarls (2520.055M. ) in Che Galactic disk have not had sufficient time to cool to temperatures below ~ 1300Ix. Much longer cooling times in the late-T temperature range lead to a verv broad mass distribution. although one should note that most of the lowest-niass brown dwarls have dropped below Tpyp,~ TOOK. the lower temperature limit for this bin."," The average mass is lower for early-T dwarfs, since the highest-mass brown dwarfs $m > 0.055~M_{\odot}$ ) in the Galactic disk have not had sufficient time to cool to temperatures below $\sim1300$ K. Much longer cooling times in the late-T temperature range lead to a very broad mass distribution, although one should note that most of the lowest-mass brown dwarfs have dropped below $_{eff} \sim 700$ K, the lower temperature limit for this bin."
resolution are the same as Figure 2a.,resolution are the same as Figure 2a.
Fic. 3., 3.—
" An image of the radio continuum emission from 12020725 at 1.4 GlIz made with the VLA at a resolution of 2.0""x1.5"". major axis position angle = -30°. and a=16 jiJy +."," An image of the radio continuum emission from 1202–0725 at 1.4 GHz made with the VLA at a resolution of $2.0'' \times 1.5''$, major axis position angle = $^o$ , and $\sigma = 16$ $\mu$ Jy $^{-1}$."
 The contour levels are a geometric progression in (he square root of (wo with the first level being 354/Jy ο.Fic., The contour levels are a geometric progression in the square root of two with the first level being $\mu$ Jy $^{-1}$.
 da., 4a.—
 The contours show the VLA image of CO(2-1) emission from 13350417 at 2=44074., The contours show the VLA image of CO(2-1) emission from 1335–0417 at $z = 4.4074$.
" The spatial resolution is 1.47x1.3"" with major axis PA = 39"". and a=0.11 mJy !."," The spatial resolution is $1.4'' \times
1.3''$ with major axis PA = $^o$, and $\sigma = 0.11$ mJy $^{-1}$."
 This frame shows the first IF at 42.635 611 and a bandwidth of 50 MIL., This frame shows the first IF at 42.635 GHz and a bandwidth of 50 MHz.
 The contour levels are: -0.24. -0.12. 0.12. 0.24. 0.36. 0.48. 0.50 mJy +.," The contour levels are: -0.24, -0.12, 0.12, 0.24, 0.36, 0.48, 0.50 mJy $^{-1}$."
 The crosses in (his and subsequent images. mark (he positions of the two peaks as seen in Figure te.," The crosses in this and subsequent images, mark the positions of the two peaks as seen in Figure 4c."
 4h. , 4b. —
The same as 4a but for the second IF at 42.835 GIIz., The same as 4a but for the second IF at 42.835 GHz.
 te. , 4c. —
"The same as 4a but using uniform weighting of the visibilities. leading to a spatial resolution of 1.4""x1.3” with major axis PA = 39"". and o=0.14 mJy !."," The same as 4a but using uniform weighting of the visibilities, leading to a spatial resolution of $1.4'' \times 1.3''$ with major axis PA = $^o$ , and $\sigma = 0.14$ mJy $^{-1}$."
 The contour levels are: -0.26. -0.13. 0.13. 0.26. 0.39. 0.52 mJv beam1. Fia.," The contour levels are: -0.26, -0.13, 0.13, 0.26, 0.39, 0.52 mJy $^{-1}$. ."
 5. , 5. —
"An image of the CO(2-1) emission from 13350417 ad a spatial resolution of 0.17"". and o=0.00 mJv +."," An image of the CO(2-1) emission from 1335–0417 at a spatial resolution of $0.17''$, and $\sigma = 0.09$ mJy $^{-1}$."
 This frame shows the first IF at 42.635 GlIz and a bandwidth of 50 MIIz., This frame shows the first IF at 42.635 GHz and a bandwidth of 50 MHz.
" The contour levels are: -0.28. -0.14. 0.14. 0.28. 0.42 mJy |,Fic."," The contour levels are: -0.28, -0.14, 0.14, 0.28, 0.42 mJy $^{-1}$."
 6. , 6. —
The CO ladder for the (vo high redshift QSOs in this paper and using data from Omont et al. (, The CO ladder for the two high redshift QSOs in this paper and using data from Omont et al. (
1996). Ohta et al. (,"1996), Ohta et al. ("
1996). and Guillotean et al. (,"1996), and Guilloteau et al. ("
1997) lor the other transitions.,1997) for the other transitions.
 The open squares are (he results lor BRI 12020725., The open squares are the results for BRI 1202–0725.
 The opentriangles are those for 13350417., The opentriangles are those for 1335–0417.
 The solid triangles are the data for the COladder forthe integrated, The solid triangles are the data for the COladder forthe integrated
mag.,mag.
 passbands (By. Vp)7; are very similar to the Johnson (B. V) passbands and relations already exist between these two systems (?)..," passbands $B_{T}$ , $V_{T}$ ) are very similar to the Johnson $B$, $V$ ) passbands and relations already exist between these two systems \citep{1997yCat.1239....0E}."
 Additional discussion of the passbands and their relationship with the Johnson system can be found in ?.., Additional discussion of the passbands and their relationship with the Johnson system can be found in \cite{2000PASP..112..961B}.
 A large community of scientists has agreed to produce state-of-the-art libraries of synthetic spectra. with a homogeneous and complete coverage of the astrophysical-parameters space at the two resolutions required to produce simulations: 0.1 nm for the low-dispersion (300-1100 nm) and 0.001 nm for the high resolution mode (840-890 nm).," A large community of scientists has agreed to produce state-of-the-art libraries of synthetic spectra, with a homogeneous and complete coverage of the astrophysical-parameters space at the two resolutions required to produce simulations: 0.1 nm for the low-dispersion (300–1100 nm) and 0.001 nm for the high resolution mode (840–890 nm)."
 The capability of reproducing real spectra is improving. and each code producing synthetic spectra is tuned for a given type of stars.," The capability of reproducing real spectra is improving, and each code producing synthetic spectra is tuned for a given type of stars."
 These libraries. summarized in Table 2.. span a large range in atmospheric parameters. from super-metal-rich to very metal-poor stars. from cool stars to hot stars. from dwarfs to giant stars. with small steps in all parameters. typically AT yp=2250 K (for cool stars). Alog g=0.5 dex. A|Fe/H|=0.5 dex.," These libraries, summarized in Table \ref{sinopt}, span a large range in atmospheric parameters, from super-metal-rich to very metal-poor stars, from cool stars to hot stars, from dwarfs to giant stars, with small steps in all parameters, typically $\Delta$ 250 K (for cool stars), $\Delta \log g$ =0.5 dex, $\Delta$ [Fe/H]=0.5 dex."
 Depending onTy. these libraries rely mostly on MARCS (F.G.K_ stars). PHOENIX (cool and € stars). KURUCZ ATLAS9 and TLUSTY (A. B. O stars) models.," Depending on, these libraries rely mostly on MARCS (F,G,K stars), PHOENIX (cool and C stars), KURUCZ ATLAS9 and TLUSTY (A, B, O stars) models."
 Those models are based on different. assumptions: KURUCZ are LTE plane-parallel models. MARCS implements also spherical symmetry. while PHOENIX and TLUSTY (hot stars) can caleulate NLTE models both in plane-parallel mode and spherical symmetry (forà1noredetaileddiscussionsee?)..," Those models are based on different assumptions: KURUCZ are LTE plane-parallel models, MARCS implements also spherical symmetry, while PHOENIX and TLUSTY (hot stars) can calculate NLTE models both in plane-parallel mode and spherical symmetry \citep[for a more detailed discussion see][]{Gust08}."
 MARCS spectra are also calculated including a global [a/Fe] enhancement (from -0.2 to 0.4 dex with a step of 0.2 dex)., MARCS spectra are also calculated including a global $\alpha$ /Fe] enhancement (from -0.2 to 0.4 dex with a step of 0.2 dex).
 Moreover. enhancements of individual « elements (O. Mg. Si. Ca) are considered.," Moreover, enhancements of individual $\alpha$ elements (O, Mg, Si, Ca) are considered."
 Hot-star spectra take into account the effects of magnetic fields. peculiar abundances. mass loss. and circumstellar envelopes (Be).," Hot-star spectra take into account the effects of magnetic fields, peculiar abundances, mass loss, and circumstellar envelopes (Be)."
 The impact of the underlying assumptions. of the different input physics 1.5. atomic and molecular line lists. convection treatment) or ofthe inclusion of NLTE effects can be seen when comparing the broadband colours (B-V. V-R. V-D of the different libraries.," The impact of the underlying assumptions, of the different input physics (i.e. atomic and molecular line lists, convection treatment) or ofthe inclusion of NLTE effects can be seen when comparing the broadband colours $B-V$, $V-R$, $V-I$ ) of the different libraries."
 As an example we show in Fig., As an example we show in Fig.
 8 the comparison between the colours derived for solar metallicities from the empirical calibration of ? and those derived from the libraries described in Table 2.., \ref{A_VR} the comparison between the colours derived for solar metallicities from the empirical calibration of \cite{Worthey06} and those derived from the libraries described in Table \ref{sinopt}.
 They show a similar behaviour and are a good reproduction of the empirical relations in the diagram ACV—R)-(V—7). where the residuals are <0.07 mag. except for very red colours. as expected.," They show a similar behaviour and are a good reproduction of the empirical relations in the diagram $\Delta(V-R)-(V-I)$, where the residuals are $< 0.07 $ mag, except for very red colours, as expected."
 The agreement is worse in the A(B—V)-(VJ) diagram. where the residuals are of the order of 40.1.," The agreement is worse in the $\Delta(B-V)-(V-I)$ diagram, where the residuals are of the order of $\pm 0.1$."
" The work of ? is based on that of ?. who presented the first hybrid library of synthetic stellar spectra. BaSeL. usingσι three original grids. of model atmospheres (?.. ο and 19, respectively) in order to cover the largest possible ranges in stellar parameters (Tj. log g. and [M/H])."," The work of \cite{Lejeune3} is based on that of \cite{Lejeune1} who presented the first hybrid library of synthetic stellar spectra, BaSeL, using three original grids of model atmospheres \cite{1992IAUS..149..225K}, \cite{Fluks} and \cite{Bessell1,Bessell2}, respectively) in order to cover the largest possible ranges in stellar parameters $T_{\mathrm{eff}}$, $\log g$ , and [M/H])."
 The important point in the BaSeL library ts that it includes correction functions that have been applied to a (theoretical) solar-abundance model flux spectrum i order to yield synthetic ILBVRIJHKL colours that match the (empirical) colour-temperature calibrations derived from observations., The important point in the BaSeL library is that it includes correction functions that have been applied to a (theoretical) solar-abundance model flux spectrum in order to yield synthetic $UBVRIJHKL$ colours that match the (empirical) colour-temperature calibrations derived from observations.
 Lt this way. the discontinuity in the flux level provided by the match of several libraries is taken into account.," In this way, the discontinuity in the flux level provided by the match of several libraries is taken into account."
 ? extended this library to M dwarfs by using the models of ? and to non-solar metallicities. down to [M/H]~- 5.0 dex (BaSeL2.2).," \cite{Lejeune2} extended this library to M dwarfs by using the models of \cite{1999ApJ...512..377H} and to non-solar metallicities, down to $\sim$ -5.0 dex (BaSeL2.2)."
 The version 3.1 of BaSeL (BaSeL3.1. ?)) differs from the preceding 2.2 library by the colour-calibration at all metallicities using Galactic globular cluster photometric data.," The version 3.1 of BaSeL (BaSeL3.1, \citealt{Lejeune3}) ) differs from the preceding 2.2 library by the colour-calibration at all metallicities using Galactic globular cluster photometric data."
 The BaSeL3.1 library was constructed to improve the calibration models. especially at low metallicities.," The BaSeL3.1 library was constructed to improve the calibration models, especially at low metallicities."
 The M-giants used in the BaSeL2.2 were replaced in the version 3.1 with? models., The M-giants used in the BaSeL2.2 were replaced in the version 3.1 with\cite{Scholz1997} models.
 Given the level of differences in Fig.8.. we decided to use the latest versionof the BaSeL library (BaSeL3.1. ?)) below.," Given the level of differences in \ref{A_VR}, , we decided to use the latest versionof the BaSeL library (BaSeL3.1, \citealt{Lejeune3}) ) below."
 The last row of Table 2. represents the grid coverage of the BaSeL library used in this work., The last row of Table \ref{sinopt} represents the grid coverage of the BaSeL library used in this work.
lis backerouud. which dominates over the CMD above 500 Cz.,"this background, which dominates over the CMB above 500 GHz."
 In summary. the CAIB | coutiuunuu emission is or the most part iucdistinenishable from the CMD alone. and so we use just the CMD for our background radiation ποια.," In summary, the CMB + continuum emission is for the most part indistinguishable from the CMB alone, and so we use just the CMB for our background radiation field."
" The input paramcters required for RADEN are dackbody temperature of the backeround radiation (for our purposes. Tearp2.73 IN}. kinetic tempcrature (Trin). molecular livdrogen uuuber density (assumed to o the ouly collision partuer. 0(£753). column densityof re mmolecule CN,,,;). and the width of the molecular ines."," The input parameters required for RADEX are blackbody temperature of the background radiation (for our purposes, $T_{CMB} = 2.73$ K), kinetic temperature $T_{kin}$ ), molecular hydrogen number density (assumed to be the only collision partner, $n(H_2)$ ), column densityof the molecule $N_{mol}$ ), and the width of the molecular lines."
 Our calculations are all computed per uuit inewidth because this is the plivsicallv rclevaut quautity iat determines the optical depth scale: we later scale us value bv the linewidth iu our likelihood. analysis., Our calculations are all computed per unit linewidth because this is the physically relevant quantity that determines the optical depth scale; we later scale this value by the linewidth in our likelihood analysis.
" Furtheiunore. RADEN assumes that the eiissiou region Gs the entire beam. but our likelihood analysis also oeitroduces a beam fillue factor $4, to account for chuupiness in the eas."," Furthermore, RADEX assumes that the emission region fills the entire beam, but our likelihood analysis also introduces a beam filling factor $\Phi_A$ to account for clumpiness in the gas."
" We used RADEXN to create a grid of line intensities for a rause of Tj;,. ville). aud ρω"," We used RADEX to create a grid of line intensities for a range of $T_{kin}$, $n(H_2)$, and $N_{mol}$."
 RADEX oulv treats one molecular species at a time. therefore in order to conduct a iultispecies analysis. we first created a RADEN erid for one species. the primary species (CS).," RADEX only treats one molecular species at a time, therefore in order to conduct a multi-species analysis, we first created a RADEX grid for one species, the primary species (CS)."
 We next created exids for all other (secondary) species. in which we also explore their relative abundances to the primary species.," We next created grids for all other (secondary) species, in which we also explore their relative abundances to the primary species."
 In calls to RADEN. the ουπα density was the product of the primary species column density aud the secondary species relative abundance.," In calls to RADEX, the column density was the product of the primary species' column density and the secondary species' relative abundance."
 Our analvsis used a relatively coarsely sampled but wide ranging erid. detailed in Table 2..," Our analysis used a relatively coarsely sampled but wide ranging grid, detailed in Table \ref{table:radex}."
 Though cach RADEN exid is created separately. the presence of niultiple species at once is siuultaueouslv considered im the likelihood analysis.," Though each RADEX grid is created separately, the presence of multiple species at once is simultaneously considered in the likelihood analysis."
 We next compare the calculated. line intensities o the measurements. detailed in Table 3..," We next compare the calculated line intensities to the measurements, detailed in Table \ref{table:likeflux}."
 We add calibration error to the measurements in quadrature with he line uncertainties. asuniüug indepeudent Cassia nucertaimtics: this assumption is discussed in §??..," We add calibration error to the measurements in quadrature with the line uncertainties, assuming independent Gaussian uncertainties; this assumption is discussed in \ref{sec:sys}."
 Given ἃ πο oof ilneasurements a and model xwanmeters p=(Neos.n(IEo).Tiu.balΑι Xes). the Bavesian likelihood. of the model parameters given the neasurenients is where P(p) is the prior probability of the model paralcters (see 8&4 Pia) normalizes. aud Pap) is the probability of obtaining the observed data set eiven that the source follows the model described by. p. which is the product of Gaussian distributions in cach observation. Above. o; is the staucdard deviation of the observational nieasurenmieut for trausition / aud J;(p) is the RADEX-predicted line intensity for that transition and model.," Given a set of measurements $\bm{x}$ and model parameters $\bm{p} = (N_{CS},n(H_2),T_{kin},\Phi_A, \bm{X}_{mol} / \bm{X}_{CS})$ , the Bayesian likelihood of the model parameters given the measurements is where $P(\bm{p})$ is the prior probability of the model parameters (see \ref{sec:prior}) ), $P(\bm{x})$ normalizes, and $P(\bm{x} | \bm{p})$ is the probability of obtaining the observed data set given that the source follows the model described by $\bm{p}$, which is the product of Gaussian distributions in each observation, Above, $\sigma_i$ is the standard deviation of the observational measurement for transition $i$ and $I_i({\bf p})$ is the RADEX-predicted line intensity for that transition and model."
 The product is carried out over all of the molecular species considered., The product is carried out over all of the molecular species considered.
 The prior probability allows us to include previously known information about NCC 1068 iu our likelihood analysis., The prior probability allows us to include previously known information about NGC 1068 in our likelihood analysis.
" We created a ""binary? prior du which all physical situations were assignedo Pip)=1. aud all ecometrically tuphlysical situations were assigucc Pip)=0"," We created a “binary"" prior in which all physical situations were assigned $P(\bm{p}) = 1$, and all geometrically unphysical situations were assigned $P(\bm{p}) = 0$."
 There were | criteria that each point in our model erid needed to satisfy iu order to be deemed physically plausable., There were 4 criteria that each point in our model grid needed to satisfy in order to be deemed physically plausable.
 At high optical depths. RADEN is unreliable because the cloud excitation teniperature eau become too dependent on optical depth with large column deusitics.," At high optical depths, RADEX is unreliable because the cloud excitation temperature can become too dependent on optical depth with large column densities."
 Therefore. we oulv include results with 7x100 as recommended bv the RADEN documentation.," Therefore, we only include results with $\tau \leq 100$ as recommended by the RADEX documentation."
 Most. of the erid points excluded by this prior are at very hieh cohuun deusitv: iu fact. the likelihood results are nearly ideutical with or without this prior condition.," Most of the grid points excluded by this prior are at very high column density; in fact, the likelihood results are nearly identical with or without this prior condition."
 The average optical depths for the cols that we find for our likelihood solutions are geucrally less than 10., The average optical depths for the columns that we find for our likelihood solutions are generally less than 10.
" The iiass iu the cussion region (M,uu;) should not exceed the dynamical mass of the galaxy. so we require that We are asstunineg the eniüssion region is 312 pe wide (see 82 7)). 80 cheegion 8 the corresponding area."," The mass in the emission region $M_{region}$ ) should not exceed the dynamical mass of the galaxy, so we require that We are assuming the emission region is 312 pc wide (see \ref{sec:intro}) ), so $A_{region}$ is the corresponding area."
" IN, is the beam-averaged cohuuu deusitv. 1245, is tle mass4 of the hvdrogen molecule. the factor of 1.5 accounts for helimm aud other heavy elements. and οί 1s the abundance of the molecule relative to hydrogen. Πιοον UserofH"," $N_{mol} \Phi_A$ is the beam-averaged column density, $m_{H_2}$ is the mass of the hydrogen molecule, the factor of 1.5 accounts for helium and other heavy elements, and $X_{mol}$ is the abundance of the molecule relative to hydrogen, $n_{mol}/n_{H_2}$."
etal(2001) conducted previous λα siauulatious to determine the velative chemical abundances of αμα of the molecules discussed here: they found Ver to be 2.0ς105 in the East kuot and 1.6\107? in the West knot., \citet{Usero:2004} conducted previous LVG simulations to determine the relative chemical abundances of many of the molecules discussed here; they found $X_{CS}$ to be $2.0 \times 10^{-8}$ in the East knot and $1.6 \times 10^{-8}$ in the West knot.
 These values were derived assuming σος8< 10%., These values were derived assuming $X_{CO} = 8 \times 10^{-5}$ .
 Our beam does not distinguish between thetwo regions. so as a conservative limit we use the higher value.," Our beam does not distinguish between thetwo regions, so as a conservative limit we use the higher value."
 For auv erid poiut of a eivoen colunn deusitv aud filling factor. using a higher," For any grid point of a given column density and filling factor, using a higher"
The transmission fictions derived bv (Moller&Jakobsen1990) (or ZIK97) are characterized by a staircase behavior. in which the opacity from cach plivsical process (either a Lyman series line or photoelectric absorption) towards shorter wavelengths. due to the strong evolutionary nature of the fforest. iu which the density of absorbers mnereases steeply with redshift.,"The transmission functions derived by \citep{moeller} (or ZK97) are characterized by a stair-case behavior, in which the opacity from each physical process (either a Lyman series line or photoelectric absorption) towards shorter wavelengths, due to the strong evolutionary nature of the forest, in which the density of absorbers increases steeply with redshift."
 Iu the case of the transmission resulting from equations (1)(3). the opacity (aloneC» a Ooeiven step of the staircase transnissiou curve) tends to either remain high or increase towards shorter waveleneths (but. of corse. oulv up to the threshok waveleugth of the absorption process involved).," In the case of the transmission resulting from equations (1)–(3), the opacity (along a given step of the staircase transmission curve) tends to either remain high or increase towards shorter wavelengths (but, of course, only up to the threshold wavelength of the absorption process involved)."
 The obvious reason for this marked difference is that the cdelistributious usec here are characterized bv a deusitv that increases towards siunaller redshifts :., The obvious reason for this marked difference is that the distributions used here are characterized by a density that increases towards smaller redshifts $z$.
 An inspection of Fie., An inspection of Fig.
 3. suggests that. rather than looking for a sharp absorption edge near Hu the quasar rest-frame. the imost obvious demarcation produced by daistiibutious Gvhich satisfyBH condition eofBH a “good Πε} is at the shorter waveleugth cud. in the 1070 oobserver-fraie region where rrather than ddominates the absorption.," \ref{fig3} suggests that, rather than looking for a sharp absorption edge near in the quasar rest-frame, the most obvious demarcation produced by distributions (which satisfy condition of a `good fit') is at the shorter wavelength end, in the 1190--1070 observer-frame region where rather than dominates the absorption."
 In order to detect such a discoutiuuitv near 1216 )). one requires detectors with a scusitivity. which extends to wavelengths shorter than the earlier IIST-FOS window. such as provided by FUSE or IIST-STIS.," In order to detect such a discontinuity near 1216 ), one requires detectors with a sensitivity, which extends to wavelengths shorter than the earlier HST-FOS window, such as provided by FUSE or HST-STIS."
 Iu order to test our absorption liavpothesis agalust individual quasar spectra observed by STIS or FUSE. we must first calibrate the depth of the expected discoutiuuitv (on the blue side of οσα] σα) as a function of for our different uodels.," In order to test our absorption hypothesis against individual quasar spectra observed by STIS or FUSE, we must first calibrate the depth of the expected discontinuity (on the blue side of local ) as a function of for our different models."
 Since the intrinsic far-UV spectral iudex.egy. is not precisely known andl. as suggestcc wv the substautial scatter found x TZU2. may even vary from quasar to quasar. it makes sense to measure the depth of he jump In a wav that oes not depend on an a priori snowledee of the intrinsic ISED.," Since the intrinsic far-UV spectral index, is not precisely known and, as suggested by the substantial scatter found by TZ02, may even vary from quasar to quasar, it makes sense to measure the depth of the jump in a way that does not depend on an a priori knowledge of the intrinsic ISED."
 The technique xoposed here is to evaluate the discoutinuitys depth at (Cons)) by comparing the flux there to the extrapolated value. from a power-law ft redwiud of ο). within the marrow windowAA.," The technique proposed here is to evaluate the discontinuity's depth at ) by comparing the flux there to the extrapolated value from a power-law fit redward of ), within the narrow window."
. This window is meant to exclude the Calactic aabsorptiou trough as well as the eeocoronalLya., This window is meant to exclude the Galactic absorption trough as well as the geocoronal.
". We define the quantity 7j1569=log.oc[E1299/Bee‘|, which can be shown to be iuseusifive to the power-law index of he tutrinsic ISED assiiuect."," We define the quantity $\tauv = {\rm log_e} \, [F^{1160}_{obs.}/F_{extr.}^{1160}]$, which can be shown to be insensitive to the power-law index of the intrinsic ISED assumed."
 Tn Fig. 3..," In Fig. \ref{fig3},"
 we illustrate the procedure by takine as example he trausinitted SED of a το=1.0 quasar and Model € (the calculation assunies an ideal detector without wavelength coverage lanitations)., we illustrate the procedure by taking as example the transmitted SED of a $z_Q=1.0$ quasar and Model C (the calculation assumes an ideal detector without wavelength coverage limitations).
 The two squares illustrate the position (albeit here in the quasar rest-frame). at which it is proposed to define754169.," The two squares illustrate the position (albeit here in the quasar rest-frame), at which it is proposed to define."
. For cach moclel discussed (AD). we list in Table 1. the value of eevaliated at to=I. while iu Fig.," For each model discussed (A–D), we list in Table \ref{tbl_1} the value of evaluated at $z_Q =1$ , while in Fig."
 { we plot the behavior of aas a fiction of τω., \ref{fig4} we plot the behavior of as a function of $z_Q$.
" As discussed in 83.1. concerning the ""nearby linc-of-3ieht problem”. it is uuplivsical to have the local density vary when the backeround quasar. for iustance. lies at redshift 2 rather than 3."," As discussed in \ref{sec:steep} concerning the “nearby line-of-sight problem”, it is unphysical to have the local density vary when the background quasar, for instance, lies at redshift 2 rather than 3."
 We can easily find ou when a distribution suffers frou this problem by checking whether or not lis constant at mocerate aud Ligh values of quasar redshift., We can easily find out when a distribution suffers from this problem by checking whether or not is constant at moderate and high values of quasar redshift.
 It is appareu in Fie., It is apparent in Fig.
 d. that Models A aud D suffer severely from the above-mentioned probleii.," \ref{fig4}
 that Models A and B suffer severely from the above-mentioned problem."
 Iu the case of Model €. however. lis fat. at least bevoud το20.6.," In the case of Model C, however, is flat, at least beyond $z_Q
\ga 0.6$."
 However. within a radius around us given bv the huge value of rp~NOUO Προς we nay reasonably expect to ho within the zone of iuflueuce of a (dominant) quasar.," However, within a radius around us given by the large value of $\rP \sim 800$ Mpc, we may reasonably expect to lie within the zone of influence of a (dominant) quasar."
 Iu this case. rather than the smoothly increasing function depicted in Fie. L.," In this case, rather than the smoothly increasing function depicted in Fig. \ref{fig4},"
 a sinele valueeae ofaf nna instead apbel ireflects the local ddeusity)., a single value of may instead apply reflects the local density).
 Its value would depend ou our clistance roni this donnant quasar., Its value would depend on our distance from this dominant quasar.
 Furthermore. wwould not necessarily be isotropic.," Furthermore, would not necessarily be isotropic."
 Iu conclusion. he sinooth initial rise of in Model € is at vost an idealization.," In conclusion, the smooth initial rise of in Model C is at best an idealization."
 Caven the ikclihood of beingo positione inside thecavity of a single quasar. the predicted. ccoustitutes an upper lint (amore probable value," Given the likelihood of being positioned inside thecavity of a single quasar, the predicted constitutes an upper limit (a more probable value"
average X-ray luminosity to the age of late F to early M dwarfs: with z;=2.03x107 L5.,average X-ray luminosity to the age of late F to early M dwarfs: with $\tau_i = 2.03\times 10^{20} L_{\rm bol}^{-0.65}$ .
" Lx and Ly, arein ss' and Tis the age in Gyr."," $L_{\rm X}$ and $L_{\rm bol}$ arein $^{-1}$, and $\tau$ is the age in Gyr."
 The relation was found with independer= age indicators and/or wide binary coeval companions to Xray sources., The relation was found with independent age indicators and/or wide binary coeval companions to X-ray sources.
 The r; parameter marks the typical change from saturation regime to an inverse proportionality between Lx/Ly4 and rotation period (e.g.Pizzolatoetal..2003)., The $\tau_i$ parameter marks the typical change from saturation regime to an inverse proportionality between $L_{\rm X}/L_{\rm bol}$ and rotation period \citep[e.g.][]{piz03}.
. The calculation is taken as a first approximation of the stellar age (Table 1)). considering also that there is an uncertainty of about an order of magnitude inthe Ly levels of stars of the same spectral type and age (Penzetal..2008:Penz&Micela.2008 ).," The calculation is taken as a first approximation of the stellar age (Table \ref{tabfluxes}) ), considering also that there is an uncertainty of about an order of magnitude inthe $L_{\rm X}$ levels of stars of the same spectral type and age \citep{pen08b,pen08a}. ."
. The accumulated X-ray flux at the planet orbit i$ shown in Fig. 2.., The accumulated X-ray flux at the planet orbit is shown in Fig. \ref{agemasses}.
 Subgiants are marked with different symbols since it is not known whether they follow the same relation., Subgiants are marked with different symbols since it is not known whether they follow the same relation.
" A hard limit of ~10777 ccm in 10 Gyr is found by combining the highest luminosity (Lo,=107?erg s!) and the shortest distance to the star (0.02 iu.)", A hard limit of $\sim 10^{22.14}$ $^{-2}$ in 10 Gyr is found by combining the highest luminosity $L_{\rm bol}=10^{34.5}~{\rm erg}~{\rm s}^{-1}$ ) and the shortest distance to the star (0.02 a.u.)
 of planets in the sample., of planets in the sample.
" No higher values are expected to be found in future observations of “hot Jupiters"".", No higher values are expected to be found in future observations of “hot Jupiters”.
 Our highest flux is 1077 cem™., Our highest flux is $10^{21.23}$ $^{-2}$.
 The effects of erosion in the long term are also expected to have an effect on the density of the population of close- planets., The effects of erosion in the long term are also expected to have an effect on the density of the population of close-in planets.
 The valuable information regarding the density ts provided in most cases by the transit technique. that favours detection of planets with short periods. hence short distances.," The valuable information regarding the density is provided in most cases by the transit technique, that favours detection of planets with short periods, hence short distances."
 Our sample only has four planets with known density (HD 209458 b. HD 189733 b. Gj 436 b. and 2M1207 b). but we can check the distribution of density with mass (Fig. 3)).," Our sample only has four planets with known density (HD 209458 b, HD 189733 b, Gj 436 b, and 2M1207 b), but we can check the distribution of density with mass (Fig. \ref{density}) )."
 This distribution is not representative of the whole population of exoplanets. and its results should only apply to close-in planets since erosion effects might be relevant.," This distribution is not representative of the whole population of exoplanets, and its results should only apply to close-in planets since erosion effects might be relevant."
 The observed sample seems to indicate an “erosion line? (Fig. 1) , The observed sample seems to indicate an “erosion line” (Fig. \ref{masses}) )
below which most planets are located., below which most planets are located.
 There are few planets above the erosion line. and they are probably at an early evolutionary stage and have spent less time exposed to high Fx.," There are few planets above the erosion line, and they are probably at an early evolutionary stage and have spent less time exposed to high $F_{\rm X}$."
 The long-term accumulation effects are clearer in Fig. 2..," The long-term accumulation effects are clearer in Fig. \ref{agemasses},"
" which shows that only 3 out of 34 planets above MM). have survived a flux of 10!° cem"". although the determination of this flux could be wrong for two of them (see below)."," which shows that only 3 out of 34 planets above $_{\rm J}$, have survived a flux of $10^{19}$ $^{-2}$, although the determination of this flux could be wrong for two of them (see below)."
 This plot partially removes the effect of age., This plot partially removes the effect of age.
 Following dissipation of the protoplanetary disk. planets exposed to high radiation should suffer heavy erosion. until the X-ray flux decreases as stellar rotation slows or the planet has become small enough for gravity or magnetospherie trapping to halt erosion.," Following dissipation of the protoplanetary disk, planets exposed to high radiation should suffer heavy erosion, until the X-ray flux decreases as stellar rotation slows or the planet has become small enough for gravity or magnetospheric trapping to halt erosion."
 The thermal losses (Eq., The thermal losses (Eq.
 2) indicate that Fx and density control the mass loss rate., 2) indicate that $F_{\rm X}$ and density control the mass loss rate.
 The dependence of the erosion line on mass. combined with the mass distribution observed in Fig. 2..," The dependence of the erosion line on mass, combined with the mass distribution observed in Fig. \ref{agemasses},"
 confirms that Fx is the main variable. with few massive planets surviving exposure to high radiation as discussed below.," confirms that $F_{\rm X}$ is the main variable, with few massive planets surviving exposure to high radiation as discussed below."
 The distribution of density with mass displayed in Fig., The distribution of density with mass displayed in Fig.
 3. is also consistent with the effects of erosion. since planets with higher densities would suffer less erosion. resulting in a population of massive planets in the long term that are denser than lower mass planets.," \ref{density}
 is also consistent with the effects of erosion, since planets with higher densities would suffer less erosion, resulting in a population of massive planets in the long term that are denser than lower mass planets."
 Gaseous planets should not substantially increase their density. while being eroded above jovian-like masses.," Gaseous planets should not substantially increase their density, while being eroded above jovian-like masses."
 Note also that Eq., Note also that Eq.
" 2 is only valid for gaseous planets. and rocky planets should suffer little erosion from XUV radiation,"," 2 is only valid for gaseous planets, and rocky planets should suffer little erosion from XUV radiation."
 In addition to thermal evaporation. non-thermal losses. such as ton pick up and sputtering processes. could also be important following tonization of the outer atmosphere by the coronal radiation or high-energy particles mediated. by any planetary magnetic field.," In addition to thermal evaporation, non-thermal losses, such as ion pick up and sputtering processes, could also be important following ionization of the outer atmosphere by the coronal radiation or high-energy particles mediated by any planetary magnetic field."
 Indeed. it is possible that the observations already reflect the relative weakness of magnetic fields in massive planets and the consequent inability to slow erosion.," Indeed, it is possible that the observations already reflect the relative weakness of magnetic fields in massive planets and the consequent inability to slow erosion."
 Low-mass planets. with a wide range of densities and distances in this sample. might have stronger fields that reduce erosion.," Low-mass planets, with a wide range of densities and distances in this sample, might have stronger fields that reduce erosion."
 The planets τ Boo b. HD 195019 b and GI 86 b. seem to challenge this interpretation (Fig. 2)).," The planets $\tau$ Boo b, HD 195019 b and Gl 86 b, seem to challenge this interpretation (Fig. \ref{agemasses}) ),"
 retaining high masses despite the high X-ray flux received., retaining high masses despite the high X-ray flux received.
 However. the fact that we see a young planet. r Boo b (age ~400 Myr. according to Eq.," However, the fact that we see a young planet, $\tau$ Boo b (age $\sim 400$ Myr, according to Eq."
" 3). still suffering heavy erosion (My MM, GGyr7! for p=l cem) reinforces our interpretation of the erosion line."," 3), still suffering heavy erosion $\dot M_{\rm X}$ $_{\rm J}$ $^{-1}$ for $\rho$ $^{-3}$ ) reinforces our interpretation of the erosion line."
 The age and accumulated X-ray flux determination of HD 195019. a G3IV-V star. could be inaccurate. although it would have to be much younger for the accumulated X-ray flux to be substantially reduced.," The age and accumulated X-ray flux determination of HD 195019, a G3IV-V star, could be inaccurate, although it would have to be much younger for the accumulated X-ray flux to be substantially reduced."
 This object falls below the erosion line though., This object falls below the erosion line though.
 The third case. GI 86. has a white dwarf at only 2]aa.u. (Elsetal..2001:Mugrauer&Neuhiuser. 2," The third case, Gl 86, has a white dwarf at only $\sim$a.u. \citep{els01,mug05}, ,"
005).. and although its contribution to the X-ray flux should not be important. we cannot discard that dynamical processes have changed the distance of the planetto the star over its lifetime (seealsoLagrangeetal.. 2006)..," and although its contribution to the X-ray flux should not be important, we cannot discard that dynamical processes have changed the distance of the planetto the star over its lifetime \citep[see also][]{lag06}. ."
 Finally. it is possible that these," Finally, it is possible that these"
"For our specific supernova model. (he shock breakout begins when the forward shock (Ry) reaches Ry. which occurs at ,=LOREEUM'PD days; where A45 is Rae in units of LOY em.","For our specific supernova model, the shock breakout begins when the forward shock $R_{fs}$ ) reaches $R_w$, which occurs at $t_w=16 R_{w15}^{1.25}E_{51}^{-0.5}M_{e1}^{0.25}D_*^{0.25}$ days, where $R_{w15}$ is $R_w$ in units of $10^{15}$ cm."
 The [ree expansion velocity at the reverse shock is ej—5.7x10RISbeALPPD?km which leads to a radiated energy of E44=0.65xLOUROBsMο eves.," The free expansion velocity at the reverse shock is $v_0=5.7\times 10^3 R_{w15}^{-0.25}E_{51}^{0.5}M_{e1}^{-0.25}D_*^{-0.25}\kms$, which leads to a radiated energy of $E_{rad}=0.65\times 10^{50} R_{w15}^{0.5}\linebreak[2] E_{51}M_{e1}^{-0.5}D_*^{0.5}$ ergs."
" The rise time for the light curve is /,—lle/Ry=4AUSREPROοϱ days. so that Lesο...—|&~xLOBSR1oBLOpeseresI"," The rise time for the light curve is $t_r=t_wR_w/R_d=41 k^{-0.8} R_{w15}^{2.25}E_{51}^{-0.9}\linebreak[2] M_{e1}^{0.45}D_*^{-0.35}$ days, so that $L\approx E_{rad}/t_r=1.8\times 10^{43}k^{0.8}R_{w15}^{-1.75}E_{51}^{1.9}M_{e1}^{-0.95}D_*^{0.85}\ergs$."
" The temperature in the shocked shell is like (hat given in the first part of equation (7))""n except that fy is replaced by i.", The temperature in the shocked shell is like that given in the first part of equation \ref{temp}) ) except that $t_d$ is replaced by $t_w$.
 The temperature is lowered in the escape out to the photosphere if there is sufficient photon production in this region (Nakar&Sari2010)., The temperature is lowered in the escape out to the photosphere if there is sufficient photon production in this region \citep{nakar10}.
". The radiated energy from SN 2006gv from the initial optical rise to around (he peak is ~1x10 eres (Oleketal.2007:Smith2007).. which makes it a good candidate for the physical situation described here (will wind optical deptli τι>¢/ey,)."," The radiated energy from SN 2006gy from the initial optical rise to around the peak is $\sim 1\times 10^{51}$ ergs \citep{ofek07,smith07}, which makes it a good candidate for the physical situation described here (with wind optical depth $\tau_w>c/v_{sh}$ )."
 In this case. the observed rise (ime gives an estimate of /4. the diffusion time.," In this case, the observed rise time gives an estimate of $t_d$, the diffusion time."
 The observations indicate a rise time of 60 davs., The observations indicate a rise time of 60 days.
" Using equation (1)). the indicated wind densitwv is D,zz10."," Using equation \ref{td}) ), the indicated wind density is $D_*\approx 10$."
 The observed peak luminosity has sensitivity to the supernova energv., The observed peak luminosity has sensitivity to the supernova energy.
" At maximum light the observed huninosity was 4x10!!ergs! (Smithetal. 2010).. which implies Es,23 lor the other standard parameters."," At maximum light the observed luminosity was $4\times 10^{44}\ergs$ \citep{smith10}, , which implies $E_{51}\approx 3$ for the other standard parameters."
" With these parameters. equation (3)) gives Ry=2.5xLOPAL.. cnm while the dense medium may extend to ~1xLOM em (Smithetal.2010)so that A,27FH."," With these parameters, equation \ref{rd}) ) gives $R_d=2.5\times
10^{15}M_{e1}^{-0.2}$ cm while the dense medium may extend to $\sim 1\times 10^{16}$ cm \citep{smith10}, so that $R_w>R_d$."
 We attribute the flattening of the observed light curve (Smithetal.2010) to the continuing interaction in the extended region., We attribute the flattening of the observed light curve \citep{smith10} to the continuing interaction in the extended region.
" With /2,.=LO!6 em the implied circiumstellar mass is e»30AL...", With $R_w= 10^{16}$ cm the implied circumstellar mass is $\sim 30\Msun$.
 These parameters are close to those found by Smith&MeCray(2007) ancl (2010).. which is expected because the basic physical picture is similar in (he two cases.," These parameters are close to those found by \cite{smithmccray07}
 and \cite{smith10}, which is expected because the basic physical picture is similar in the two cases."
 Depending on (he ejecta mass. the condition that ο<c; may be violated. but we do not expect the results to be strongly. afecte.," Depending on the ejecta mass, the condition that $v_t<v_{rs}$ may be violated, but we do not expect the results to be strongly affected."
" Ucnithetal.(2007.2010) estimated an explosion date of 20 August. 2006 for SN 20068: (his time is just before the beginning of a rise in optical huninosityv from 0.01L,,,, to Linge where {ρω Is the maximum optical Iuminositv."," \cite{smith07,smith10} estimated an explosion date of 20 August, 2006 for SN 2006gy; this time is just before the beginning of a rise in optical luminosity from $0.01L_{max}$ to $L_{max}$, where $L_{max}$ is the maximum optical luminosity."
" In the shock breakout view. the sharp rise of optical radiation occurs after a (me 2/04, during which (he shock is traveling in the oplically thick region (Fig."," In the shock breakout view, the sharp rise of optical radiation occurs after a time $R_d/v_{sh}$ during which the shock is traveling in the optically thick region (Fig."
 1)., 1).
 The explosion date is (hus ~60 davs earlier (han the estimate of Smithetal.(2007.2010).. and mean velocities of uniformly expanding ejecta are lower than the estimates of Smith et al.," The explosion date is thus $\sim 60$ days earlier than the estimate of \cite{smith07,smith10}, and mean velocities of uniformly expanding ejecta are lower than the estimates of Smith et al."
 Another aspect of the rise to maximum in shock breakoutis that the increasing temperature as the shock breaks out is an important component of the rising luminosity., Another aspect of the rise to maximum in shock breakoutis that the increasing temperature as the shock breaks out is an important component of the rising luminosity.
 In the case of, In the case of
"where 'To solve for the mass lost per encounter as a function of y, we consider a star within a cubic array, where the star contains ~3x10° cubic elements.","where To solve for the mass lost per encounter as a function of $\gamma$, we consider a star within a cubic array, where the star contains $\sim 3 \times 10^{6}$ cubic elements."
" As a function of γ we compare the kick velocity in each element to the escape velocity for that element, and consider the mass within the element to be lost to the star if the velocities satisfy the condition given 2.."," As a function of $\gamma$ we compare the kick velocity in each element to the escape velocity for that element, and consider the mass within the element to be lost to the star if the velocities satisfy the condition given \ref{sec:condition}."
" We note that by 10? elements, the results converge to within about 296, and we are therefore confident that ~3x10° provides adequate resolution."," We note that by $\sim 10^5$ elements, the results converge to within about $2\%$, and we are therefore confident that $\sim 3 \times 10^{6}$ provides adequate resolution."
" 'To calculate the amount of mass in each element, the density profile for the perturbed star must be specified."," To calculate the amount of mass in each element, the density profile for the perturbed star must be specified."
" As with several previous studies on mass loss due to stellar collisions (Benz&Hills1987,1992;Lai,Rasio,Shapiro1993;Rauch1999) we utilize polytropic stellar profiles."," As with several previous studies on mass loss due to stellar collisions \citep{benz:1987, benz:1992, lai:1993, rauch:1999} we utilize polytropic stellar profiles."
" Polytropic profiles are easy to calculate, and yield reliable results for stars of certain masses."," Polytropic profiles are easy to calculate, and yield reliable results for stars of certain masses."
" Polytropic profiles of polytropic index n=1.5 describe the density structure of fully convective stars, and therefore very well describe MS stars with M,<0.3Mo (nearly fully convective) and MS stars with M,210M (convective cores)."," Polytropic profiles of polytropic index $n=1.5$ describe the density structure of fully convective stars, and therefore very well describe MS stars with $M_{\star} \lesssim 0.3 \mathrm M_{\odot}$ (nearly fully convective) and MS stars with $M_{\star} \gtrsim 10\mathrm M_{\odot}$ (convective cores)."
" MS stars with M,Z1Mo have radiative envelopes, and are therefore well described by n=3."," MS stars with $M_{\star} \gtrsim 1\mathrm M_{\odot}$ have radiative envelopes, and are therefore well described by $n=3$."
" For n for stars with masses of 0.3—IM and5—10Mo, we linearly interpolate between n=1.5 and 3."," For $n$ for stars with masses of $0.3 - 1\mathrm M_{\odot}$ and$5 - 10\mathrm M_{\odot}$, we linearly interpolate between $n=1.5$ and 3."
 We discuss the uncertainties introduced by this approach in 4., We discuss the uncertainties introduced by this approach in \ref{sec:mass_loss_rates}.
" Note that this approach is biased towards zero-age main sequence stars, since as stars evolve, they are less adequately described by polytropic profiles."," Note that this approach is biased towards zero-age main sequence stars, since as stars evolve, they are less adequately described by polytropic profiles."
" We plot the fraction of mass lost from the perturbed star per event, A, as a function of y in Fig."," We plot the fraction of mass lost from the perturbed star per event, $\Delta$, as a function of $\gamma$ in Fig."
 1 for several polytropic indeces., \ref{fig:mass_loss} for several polytropic indeces.
" The lines are third order polynomial fits to our results, in the range of 0.98x«y<5."," The lines are third order polynomial fits to our results, in the range of $0.98 \leq \gamma \leq 5$."
 We list the coefficients of the polynomial fits in Table 1.., We list the coefficients of the polynomial fits in Table \ref{tab:coeffs}.
" For each density profile, no mass is lost up until 7 of about 0.98, and thereafter the mass loss increases monotonically."," For each density profile, no mass is lost up until $\gamma$ of about 0.98, and thereafter the mass loss increases monotonically."
 The increasing trend is due to the fact that larger perturber masses and smaller impact parameters result in an increased potential felt by the perturbed star., The increasing trend is due to the fact that larger perturber masses and smaller impact parameters result in an increased potential felt by the perturbed star.
" Smaller velocities also cause more mass to be lost, as this increases the “interaction time"" between the perturber and perturbed stars."," Smaller velocities also cause more mass to be lost, as this increases the “interaction time” between the perturber and perturbed stars."
" 'The location of the mass loss within the perturbed star for fixed  depends upon the polytropic index, since the escape velocity within the star is dependent upon the density profile, as indicated by equation. (2))."," The location of the mass loss within the perturbed star for fixed $\gamma$ depends upon the polytropic index, since the escape velocity within the star is dependent upon the density profile, as indicated by equation. \ref{eqn:v_esc}) )."
" In Fig. 2,,"," In Fig. \ref{fig:slices_mass_lost},"
 we illustrate where mass will be lost in the perturbed star by plotting contours of the kick velocity (Ao(?)) due to the encounter normalized to i74(7) for n=1.5 and n=3 (top and bottom row respectively)., we illustrate where mass will be lost in the perturbed star by plotting contours of the kick velocity $\Delta \tilde v (\tilde r)$ ) due to the encounter normalized to $\tilde v_{esc}^{pd} (\tilde r)$ for $n=1.5$ and $n=3$ (top and bottom row respectively).
" We show two different cases: a slightly perturbing encounter with y=1.2 in the first column, and a severely perturbing encounter with y=1.6 in the second column."," We show two different cases: a slightly perturbing encounter with $\gamma=1.2$ in the first column, and a severely perturbing encounter with $\gamma=1.6$ in the second column."
" The grey region underneath shows where mass is still left after the encounter, since Ao/072(5) within this region is «1."," The grey region underneath shows where mass is still left after the encounter, since $\Delta \tilde v/\tilde v_{esc}^{pd} (\tilde r)$ within this region is $< 1$."
" The y=1.6 encounter results in bigger kick velocities, and so we see that the mass loss penetrates farther into the star."," The $\gamma=1.6$ encounter results in bigger kick velocities, and so we see that the mass loss penetrates farther into the star."
 We note that the shape and magnitude of the contours for both polytropic indeces at fixed y converge at large radii., We note that the shape and magnitude of the contours for both polytropic indeces at fixed $\gamma$ converge at large radii.
" This is due to the fact that regardless of the polytropic index used, «24, converges to the same value at large radii when the second term in equation (2)) becomes negligible."," This is due to the fact that regardless of the polytropic index used, $\tilde v_{esc}^{pd}$ converges to the same value at large radii when the second term in equation \ref{eqn:v_esc}) ) becomes negligible."
" Even though the location of where mass is lost is similar for different polytropic stars at the same value of , the amount of the mass lost is substantially different (as shown in Fig. 1)),"," Even though the location of where mass is lost is similar for different polytropic stars at the same value of $\gamma$, the amount of the mass lost is substantially different (as shown in Fig. \ref{fig:mass_loss}) ),"
 due to the different density profiles., due to the different density profiles.
" 'The impulse approximation is valid provided that the time over which the encounter takes place, tenc, is much shorter than the time it takes to cross the perturbed system, lcross."," The impulse approximation is valid provided that the time over which the encounter takes place, $t_{enc}$, is much shorter than the time it takes to cross the perturbed system, $t_{cross}$."
" lo estimate when our calculations break down, we approximate tence as b/Ure1, and teross as ts, the time it takes for a sound wave to cross an object that is in hydrostatic equilibrium: ''hese approximations lead to the condition that Aguilar&White(1985) find that for a large range of collisions, the impulse approximations remains remarkably valid, even when tence is almost as long as teross."," To estimate when our calculations break down, we approximate $t_{enc}$ as $b/v_{rel}$, and $t_{cross}$ as $t_s$, the time it takes for a sound wave to cross an object that is in hydrostatic equilibrium: These approximations lead to the condition that \citet{aguilar:1985} find that for a large range of collisions, the impulse approximations remains remarkably valid, even when $t_{enc}$ is almost as long as $t_{cross}$ ."
 We therefore assume that the impulse approximation holds until the left, We therefore assume that the impulse approximation holds until the left
We have test-run the above algorithm on a small munber of data sets. thirteen. in order (ο assess ils success rate and (o fine-tune the various crilical parameters (e.g. cell size in both spatial and energy. dimensions. backeround determination. threshold lor NLEO candidate [Iageing. ete).,"We have test-run the above algorithm on a small number of data sets, thirteen, in order to assess its success rate and to fine-tune the various critical parameters (e.g. cell size in both spatial and energy dimensions, background determination, threshold for XLEO candidate flagging, etc.)."
 Onlv the Epic-pu data have been used., Only the Epic-pn data have been used.
 We have chosen (he test observations among those al high ealactic latitude. with an exposure time in the range [rom ~1.5x10! sto 4.5x10! s. Of the candidates found during the test-run. we present here (he three most significant ones. which are also characterized by (he highest continuum.," We have chosen the XMM-Newton test observations among those at high galactic latitude, with an exposure time in the range from $\sim
1.5\times 10^4$ s to $4.5\times 10^4$ s. Of the candidates found during the test-run, we present here the three most significant ones, which are also characterized by the highest continuum."
 The (three candidates were flagged because of the detection of 9 counts in the enerev bin 3.7—3.9 keV (1.4 counts expected). 7 counts in the bin 4.5—4.7 keV (0.7 counts expected) and LO counts in the bin 4.6—4.8 keV (1.2 counts expected) respectively (see insel in Figure 1a—c).," The three candidates were flagged because of the detection of 9 counts in the energy bin $-$ 3.9 keV (1.4 counts expected), 7 counts in the bin $-$ 4.7 keV (0.7 counts expected) and 10 counts in the bin $-$ 4.8 keV (1.2 counts expected) respectively (see inset in Figure $-$ c)."
 With respect to the statistical significance of the lines. we woukl like to stress the following.," With respect to the statistical significance of the lines, we would like to stress the following."
 In the energv bin where the line is detected. (he probability that the excess seen is a random noise fluctuation is 1.6x10/7. 8.9x10. and 5.8x10* for the three sources respectivelv.," In the energy bin where the line is detected, the probability that the excess seen is a random noise fluctuation is $1.6 \times 10^{-5}$, $8.9 \times
10^{-6}$ and $5.8 \times 10^{-7}$ for the three sources respectively."
 This is computed as the probability of observing 9. 7 aud 10 counts (or more) when 1.4. 0.7. and 1.2 counts are expected.," This is computed as the probability of observing 9, 7 and 10 counts (or more) when 1.4, 0.7, and 1.2 counts are expected."
 HLowever. one should also consider the number ol energv bins (14) and of the spatial cells searched.," However, one should also consider the number of energy bins (14) and of the spatial cells searched."
 Although we have raster-scanned the whole image (but have ignored cells affected by gaps ancl edges). in analvzing the preliminary results of our search we have conservatively considered here only those XNLEO candidates coincident with an X-ray source. unambiguously detected by other means (i.e. standard XMM Science Analvsis System).," Although we have raster-scanned the whole image (but have ignored cells affected by gaps and edges), in analyzing the preliminary results of our search we have conservatively considered here only those XLEO candidates coincident with an X-ray source, unambiguously detected by other means (i.e. standard XMM Science Analysis System)."
 Indeed. these three sources were independently found by the stancarcl detection algorithm used to produce (he INMM source catalog (NMM-Newton SSC. and are listed there.," Indeed these three sources were independently found by the standard detection algorithm used to produce the 1XMM source catalog (XMM-Newton SSC, and are listed there."
 Thus. given that there are ~600 sources in the set of images used at the brightness level considered. the number of trials is 14κ600 and the resulting total number of [alse detections expected is 0.1.," Thus, given that there are $\sim 600$ sources in the set of images used at the brightness level considered, the number of trials is $14 \times 600$ and the resulting total number of false detections expected is $\sim 0.1$."
 Furthermore. we can adopt the X-ray positions reported in the 1XMM catalog since they. are significantly better than those produced by our algorithm.," Furthermore, we can adopt the X-ray positions reported in the 1XMM catalog since they are significantly better than those produced by our algorithm."
 For all three sources. we did go back to the NMM-Newton data to extract the broad band spectrum. estimating the background from a nearby. source-Iree region.," For all three sources, we did go back to the XMM-Newton data to extract the broad band spectrum, estimating the background from a nearby, source-free region."
 Apertures of.. and radius were used to extract the source counts. and of (because of the closeness to an intra-ehip gap). and radius for the background counts.," Apertures of, and radius were used to extract the source counts, and of (because of the closeness to an intra-chip gap), and radius for the background counts."
 When possible. (XLEOJ153241—032906 and XLEO.J220425—015123) data [rom the MOS detectors were also used in order to maximize the available statistics and have contributed to the determination," When possible, $-$ 082906 and $-$ 015123) data from the MOS detectors were also used in order to maximize the available statistics and have contributed to the determination"
" 128.0. 1102 frac2),,:4/333 where 7;=7;/105K and j/=13.7 for a plasma with Xj»=Xig= 0.5."," = 10^2 where $T_{i,8}=T_i/10^8\ {\rm K}$ and $\mu_i=13.7$ for a plasma with $X_{12}=X_{16}=0.5$ ."
" The large prefactor demonstrates that degeneracy greatly enhances the small changes in ;;7, on the temperature discontinuity.", The large prefactor demonstrates that degeneracy greatly enhances the small changes in $\mu_e$ on the temperature discontinuity.
 This 1s because the ions provide only a small contribution to the pressure. so that a large temperature jump is needed to offset a small change in density.," This is because the ions provide only a small contribution to the pressure, so that a large temperature jump is needed to offset a small change in density."
" Using equation (19)). we find AM, =↑∣≏↧∟⋮∕∣∡∣⋅⋯⊃⊤∙↴∆≻↼≻↼ where 7.4=7./10°K."," Using equation \ref{eq:deltamc}) ), we find M_c = where $T_{c,8}=T_c/10^8\ {\rm K}$."
" It is interesting to note that although T; affects the absolute location of M, (see eq. [14]. AM,"," It is interesting to note that although $T_i$ affects the absolute location of $M_c$ (see eq. \ref{eq:mct}] ]),"
 is in factindependent of T;., $\Delta M_c$ is in fact of $T_i$.
 We next consider the temperature difference from changes in the composition of the nuclei., We next consider the temperature difference from changes in the composition of the nuclei.
" This is of relevance because evolution of the progenitor star during the helium burning stage enhances ""C versus '°O with larger radii (Stranieroal. 2003).", This is of relevance because evolution of the progenitor star during the helium burning stage enhances $^{12}$ C versus $^{16}$ O with larger radii \citep{str03}.
. First we present the effect of an increase of the mean molecular weight in the convection zone. Agr. using the equation of state given by equation (22)).," First we present the effect of an increase of the mean molecular weight in the convection zone, $\Delta\mu_i$, using the equation of state given by equation \ref{eq:eos}) )."
 Setting the density and pressure continuous across the convective boundary. As a concrete example. we consider the composition in Model 3 from Table 1.. which gives 2/5/45~0.06.," Setting the density and pressure continuous across the convective boundary, As a concrete example, we consider the composition in Model 3 from Table \ref{tab:models}, which gives $\Delta\mu_i/\mu_i\approx0.06$."
" This implies a change in convective mass of AM. 2-1.Sth frac2jj, which is negligible.", This implies a change in convective mass of M_c = ^2 which is negligible.
 However. compositional changes also alter the Coulomb contributions to the internal energy.," However, compositional changes also alter the Coulomb contributions to the internal energy."
 For a multi-component plasma. the strength of this effect is measured via the Coulomb parameter = (Schatzetal.1/3.1999) where « is the mean ton separation defined as παp/(rm)=1 and = We take the fitting function found by Chabrier&Potekhin in the limit P»| to model Coulomb effects. P-K," For a multi-component plasma, the strength of this effect is measured via the Coulomb parameter 		=, \citep{sch99} where $a$ is the mean ion separation defined as $4\pi a^3\rho/(3\mu_i m_p)=1$ and = _i We take the fitting function found by \citet{cp98} in the limit $\Gamma\gg1$ to model Coulomb effects, 	P ="
 For a multi-component plasma. the strength of this effect is measured via the Coulomb parameter = (Schatzetal.1/3.1999) where « is the mean ton separation defined as παp/(rm)=1 and = We take the fitting function found by Chabrier&Potekhin in the limit P»| to model Coulomb effects. P-K(," For a multi-component plasma, the strength of this effect is measured via the Coulomb parameter 		=, \citep{sch99} where $a$ is the mean ion separation defined as $4\pi a^3\rho/(3\mu_i m_p)=1$ and = _i We take the fitting function found by \citet{cp98} in the limit $\Gamma\gg1$ to model Coulomb effects, 	P ="
 For a multi-component plasma. the strength of this effect is measured via the Coulomb parameter = (Schatzetal.1/3.1999) where « is the mean ton separation defined as παp/(rm)=1 and = We take the fitting function found by Chabrier&Potekhin in the limit P»| to model Coulomb effects. P-K(A," For a multi-component plasma, the strength of this effect is measured via the Coulomb parameter 		=, \citep{sch99} where $a$ is the mean ion separation defined as $4\pi a^3\rho/(3\mu_i m_p)=1$ and = _i We take the fitting function found by \citet{cp98} in the limit $\Gamma\gg1$ to model Coulomb effects, 	P ="
 For a multi-component plasma. the strength of this effect is measured via the Coulomb parameter = (Schatzetal.1/3.1999) where « is the mean ton separation defined as παp/(rm)=1 and = We take the fitting function found by Chabrier&Potekhin in the limit P»| to model Coulomb effects. P-K(A0," For a multi-component plasma, the strength of this effect is measured via the Coulomb parameter 		=, \citep{sch99} where $a$ is the mean ion separation defined as $4\pi a^3\rho/(3\mu_i m_p)=1$ and = _i We take the fitting function found by \citet{cp98} in the limit $\Gamma\gg1$ to model Coulomb effects, 	P ="
 For a multi-component plasma. the strength of this effect is measured via the Coulomb parameter = (Schatzetal.1/3.1999) where « is the mean ton separation defined as παp/(rm)=1 and = We take the fitting function found by Chabrier&Potekhin in the limit P»| to model Coulomb effects. P-K(A0)," For a multi-component plasma, the strength of this effect is measured via the Coulomb parameter 		=, \citep{sch99} where $a$ is the mean ion separation defined as $4\pi a^3\rho/(3\mu_i m_p)=1$ and = _i We take the fitting function found by \citet{cp98} in the limit $\Gamma\gg1$ to model Coulomb effects, 	P ="
shifts by the introduction of metal cooling. consistently with the estimate by Hernquist&Springel(2003).,"shifts by the introduction of metal cooling, consistently with the estimate by \citet{Hernquist.Springel:03}."
. The N216LI0mv run has a lower SER at z9 and a higher SFR at 2S7 than the N216L10mc run., The N216L10mv run has a lower SFR at $z\gtrsim 9$ and a higher SFR at $z\lesssim 7$ than the N216L10mc run.
" This is because at high-z. the value of pi, is higher in the “mia run than in the me? run due to lower metallicity and mean molecular weight. leacing to a larger fraction of gas not being able to satisfv the SE criteria in the N2IGLIOmy run than in the N216L10mc."," This is because at $z$ , the value of $\rhoth$ is higher in the `mv' run than in the `mc' run due to lower metallicity and mean molecular weight, leading to a larger fraction of gas not being able to satisfy the SF criteria in the N216L10mv run than in the N216L10mc."
 The opposite is true at zZ3., The opposite is true at $z\lesssim 3$.
 Figure 2. also shows that the SER in the N216L10nw run is higher than other runs by an order of magnitucle., Figure \ref{fig:sfr_N216L10} also shows that the SFR in the N216L10nw run is higher than other runs by an order of magnitude.
 ‘This is because the gas can cool very efficiently. without being ejectecl by the galactic wind., This is because the gas can cool very efficiently without being ejected by the galactic wind.
 Although the current ealactic wind models in cosmological simulations are not well established. vet ancl need to be improved. both theoretical and. observational studies evidently suggest the important role of galactic wind feedback (Springcl&Llernquist2003a:Alartin2005.2006:Oppenheimer&Davé 2006).," Although the current galactic wind models in cosmological simulations are not well established yet and need to be improved, both theoretical and observational studies evidently suggest the important role of galactic wind feedback \citep{Springel.Hernquist:03,Martin:05,Martin:06, Oppenheimer.Dave:06}."
. As expected. the Nld4L10mec run has lower SER densities at 2c7 compared to the N216L10 series.," As expected, the N144L10mc run has lower SFR densities at $z\ge 7$ compared to the N216L10 series."
 This is because a lower resolution run is unable to resolve low-mass halos that would otherwise formis stars in them., This is because a lower resolution run is unable to resolve low-mass halos that would otherwise forms stars in them.
 When the star formation at high-z is underestimated. some of the gas remain unconverted into stars until lower redshift. resulting in a higher SEIt at z« din the N144L10mc run than in the :216LIO0mc run.," When the star formation at $z$ is underestimated, some of the gas remain unconverted into stars until lower redshift, resulting in a higher SFR at $z<4$ in the N144L10mc run than in the N216L10mc run."
 Figure 3. shows the cosmic SE history down to z=1 or the N288L34. series., Figure \ref{fig:sfr_N288L34} shows the cosmic SF history down to $z=1$ for the N288L34 series.
 Again. the SER. density in the ssL34me run is systematically higher than that in the 28SL34 run at alb redshifts.," Again, the SFR density in the N288L34mc run is systematically higher than that in the N288L34 run at all redshifts."
 Moreover. the dillerence in SER density. between the two runs increases at 23.," Moreover, the difference in SFR density between the two runs increases at $z\lesssim 3$."
 Dez3 the LGAL metallicity becomes high. enough. to noticeably increase the cooling rate. and the accretion of IGM onto galaxies becomes more efficient. which later fuels he star formation.," By $z \sim 3$ the IGM metallicity becomes high enough to noticeably increase the cooling rate, and the accretion of IGM onto galaxies becomes more efficient, which later fuels the star formation."
 Our results suggest that the cosmic SET density is enhanced by metal cooling at zZ3 by both of the ollowing two ellects: 1) more ellicient. LGAL aceretion onto ealaxies due to higher metallicity of LGAL and 2) increased SE elliciency due to higher cooling rate with the contribution rom metal cooling.," Our results suggest that the cosmic SFR density is enhanced by metal cooling at $z \lesssim 3$ by both of the following two effects: 1) more efficient IGM accretion onto galaxies due to higher metallicity of IGM, and 2) increased SF efficiency due to higher cooling rate with the contribution from metal cooling."
 In Figure 3 the analytic mocdel of Hernquist&Springel(2003.Iq.(2).hereafter.HI&S.model) is also shown in he ereen dot-dashed. line.," In Figure \ref{fig:sfr_N288L34} the analytic model of \citet[][Eq.\,(2), hereafter H\&S model]{Hernquist.Springel:03} is also shown in the green dot-dashed line."
 Phis model is a result of many cosmological SPLE simulations with increasing resolution. and the authors gave a theoretical interpretation to the empirical fitting formula for the cosmic SET density.," This model is a result of many cosmological SPH simulations with increasing resolution, and the authors gave a theoretical interpretation to the empirical fitting formula for the cosmic SFR density."
 Since our runs adopt a lower value of ax=0.85 than the original value used. to. derive the SS. model (as= 0.90). we mocdifv the H&SS model by rescaling the 7 parameter in heir (2) and (47).," Since our runs adopt a lower value of $\sigma_8=0.85$ than the original value used to derive the S model $\sigma_8=0.90$ ), we modify the S model by rescaling the $\beta$ parameter in their (2) and (47)."
 This reduces the SER. density ab zm5 by ~I0... but not much at z5.," This reduces the SFR density at $z\gtrsim 5$ by $\sim 10$, but not much at $z\lesssim 5$."
 Phe results of he N2SSL34 and N216L10moec runs agree well with the LISS model at 2«4 and z« 6. respectively.," The results of the N288L34 and N216L10mc runs agree well with the S model at $z<4$ and $z<6$ , respectively."
 This is expected. »ecause the N2SSL34 run adopts the same physical models as in the original simulations that were used to derive the SS model.," This is expected, because the N288L34 run adopts the same physical models as in the original simulations that were used to derive the S model."
 At high-z. both runs fall short compared to he LICSS moclel owing to insullicient resolution.," At $z$, both runs fall short compared to the S model owing to insufficient resolution."
 The metal enrichment and metal cooling also change the 1hase space1 distribution (pE7 diagram)g of cosmic &gas., The metal enrichment and metal cooling also change the phase space distribution $\rho - T$ diagram) of cosmic gas.
 ligure 4. shows the state of cosmic gas at 2=3 forhe N216L10 series., Figure \ref{fig:phase.N216L10} shows the state of cosmic gas at $z=3$ forthe N216L10 series.
" As shown in panel (a). the barvons in he Universe can be broadly. categorised into four cillerent ohases according to their overdensity. and. temperature: ""hot. warm-hot. ‘diffuse’. and ""condensed (Davectal.1909:Cen&Ostriker1999:Daveοἱal.2001)."," As shown in panel $a$ ), the baryons in the Universe can be broadly categorised into four different phases according to their overdensity and temperature: `hot', `warm-hot', `diffuse', and `condensed' \citep{Dave.etal:99, 
Cen.Ostriker:99, Dave.etal:01}."
. The first wo phases are mostly. the shock-heated gas. in. clusters and groups of galaxies., The first two phases are mostly the shock-heated gas in clusters and groups of galaxies.
 The ‘diffuse’ phase is mosth the xhotoionised. IGM. with lower temperature. which can be observed as the Ενα forest.," The `diffuse' phase is mostly the photoionised IGM with lower temperature, which can be observed as the $\alpha$ forest."
 Phe tight power-law relationship tween p and 7 ab p/p&3 and T«OXIX. is governed w the ionisation equilibrium (Hui&Cnedin1997).. where pis the mean density of barvons at z=0.," The tight power-law relationship between $\rho$ and $T$ at $\overd \lesssim 3$ and $T<10^4$ K is governed by the ionisation equilibrium \citep{Hui.Gnedin:97}, where $\bar{\rho}$ is the mean density of baryons at $z=0$."
" The ""condensed! phase is the high density. cold. gas in ealaxies."," The `condensed' phase is the high density, cold gas in galaxies."
 Because the primordial cooling curve has a sharp cutoll at Z2103 WIS. the temperature of condensed. phase decreases only down to this temperature in Figure 4taa.b. The characteristic lingor-like feature at p/p103 is due to the pressurisation of the star-forming gas by SN feedback in the multiphase LSAT model of Springel&Llernquist(2003a).," Because the primordial cooling curve has a sharp cutoff at $T\simeq 10^4$ K, the temperature of condensed phase decreases only down to this temperature in Figure \ref{fig:phase.N216L10}a a,b. The characteristic finger-like feature at $\overd \gtrsim 10^4$ is due to the pressurisation of the star-forming gas by SN feedback in the multiphase ISM model of \citet{Springel.Hernquist:03}."
. A fitting formula for this cllective equation. of state was derived by Robertsonetal.(2004)... which is shown by the blue dashed lines.," A fitting formula for this effective equation of state was derived by \citet{Robertson.etal:04}, which is shown by the blue dashed lines."
 Above the SE threshold density pi. the eas particles in the simulation eo into the multiphase mode ancl are allowed to forni stars.," Above the SF threshold density $\rhoth$, the gas particles in the simulation go into the multiphase mode and are allowed to form stars."
" The most noticeable and interesting change in the pT plot by the metal cooling is in the distribution of ""condensed! gas.", The most noticeable and interesting change in the $\rho - T$ plot by the metal cooling is in the distribution of `condensed' gas.
 Star formation and SN explosions occur in the multiphase star-forming gas. therefore the immediate ellect of metal cooling appears in the condensed: phase.," Star formation and SN explosions occur in the multiphase star-forming gas, therefore the immediate effect of metal cooling appears in the condensed phase."
 The presence of gas at Z7«103 IXKI& with metal cooling results from the effective temperature calculation for the multiphase medium. and not from the direct. gas cooling down to £<LO? IxIx. According to the multiphase scheme in Springel&Lernquist(2003a).. the star forming gas consists of two phases: hot gas (1 YW οκ LOS KE) and cold gas (E=10) Why).," The presence of gas at $T < 10^4$ K with metal cooling results from the effective temperature calculation for the multiphase medium, and not from the direct gas cooling down to $T < 10^4$ K. According to the multiphase scheme in \citet{Springel.Hernquist:03}, the star forming gas consists of two phases: hot gas $10^5$ K $< T <$ $10^8$ K) and cold gas $T = 10^3$ K)."
 The effective temperature for the multiphase gas is computed from the internal energy of hot ancl col eases. which are derived using the cold gas fraction.," The effective temperature for the multiphase gas is computed from the internal energy of hot and cold gases, which are derived using the cold gas fraction."
 The cold. gas fraction is computed from the cooling rate of ho eas and the eas density., The cold gas fraction is computed from the cooling rate of hot gas and the gas density.
 The original GADGET imposes the elfective temperature of 107 IXIx at the SE threshold density., The original GADGET imposes the effective temperature of $10^4$ K at the SF threshold density.
 In our metal cooling scheme. however. the cooling rate of ho eas increases. and the cold gas fraction increases.," In our metal cooling scheme, however, the cooling rate of hot gas increases, and the cold gas fraction increases."
 Therefore. the multiphase gas above the SE threshold. density. with higher metallicity could have lower ellective temperature of T«MO IXIN in our implementation.," Therefore, the multiphase gas above the SF threshold density with higher metallicity could have lower effective temperature of $T < 10^4$ K in our implementation."
" In the N216L10moc run. the value of pi, was kept fixe as the original value. which causes a sharp edge at p/p101 for the multiphase gas."," In the N216L10mc run, the value of $\rhoth$ was kept fixed as the original value, which causes a sharp edge at $\overd \simeq 10^4$ for the multiphase gas."
 In the N216LI10mv run. the value of fra was varied according to the change in mean molecular weight. therefore the condensed. gas has a spread. in both temperature and density near ppc107.," In the N216L10mv run, the value of $\rhoth$ was varied according to the change in mean molecular weight, therefore the condensed gas has a spread in both temperature and density near $\overd \simeq 10^4$."
 Galactic wind returns the metal-enriched. star-forming eas to the hot and low density IGM. as evidenced. in the p diagrams.," Galactic wind returns the metal-enriched, star-forming gas to the hot and low density IGM, as evidenced in the $\rho - Z$ diagrams."
 Ειςmetal-enriched. low-density (p/p 10) eas is absent in the N216L10nw run. which clearly. shows the necessity ofgalactie wind to explain the metallicity observed in Lye forest.," Thismetal-enriched, low-density $\overd \lesssim 10$ ) gas is absent in the N216L10nw run, which clearly shows the necessity ofgalactic wind to explain the metallicity observed in $\alpha$ forest."
 Ehe phase distribution of IGM in the N216L10. N216L10mc. and N216L10nw runs are very similar.," The phase distribution of IGM in the N216L10, N216L10mc, and N216L10mv runs are very similar."
 Εις is presumably because the effects. of metal cooling is not so significant vet in the IGM at z2 3., This is presumably because the effects of metal cooling is not so significant yet in the IGM at $z>3$ .
 As, As
applicable to stellar explosions with shock velocity larger than 0.5c. in which the breakout shell ends its acceleration during the planar phase. ie.. its final Lorentz factor <30 for (vpical stars.,"applicable to stellar explosions with shock velocity larger than 0.5c, in which the breakout shell ends its acceleration during the planar phase, i.e., its final Lorentz factor $\lesssim 30$ for typical stars."
 We consider only cases where the progenitor wind has no effect on the observed CUSSION., We consider only cases where the progenitor wind has no effect on the observed emission.
 A relativistic radiation mediated shock brings the gas to a roughly constant rest frame temperature. ~200 keV. and loads it with pairs (Ixatz.Dudnik&Waxmanal. 2010).," A relativistic radiation mediated shock brings the gas to a roughly constant rest frame temperature, $\sim 200$ keV, and loads it with pairs \citep{Katz10,Budnik10}."
. Photons remain confined to the post-shock expanding gas as long as pairs keep il optically thick., Photons remain confined to the post-shock expanding gas as long as pairs keep it optically thick.
 A significant number of photons are released towards the observer only [rom optically thin regions. which has a gas rest frame temperature <50 keV. (low pair load) and unloaded pair gas opacitv. 7. smaller (han unity.," A significant number of photons are released towards the observer only from optically thin regions, which has a gas rest frame temperature $\lesssim 50$ keV (low pair load) and unloaded pair gas opacity, $\tau$, smaller than unity."
 Our solution of the shock structure shows that the shock width is significantly smaller (han 7=1. implvine that the shock accelerates also shells with 7<I. which become transparent once their pairs annihilate.," Our solution of the shock structure shows that the shock width is significantly smaller than $\tau = 1$, implying that the shock accelerates also shells with $\tau \leq 1$, which become transparent once their pairs annihilate."
 Among these shells the one that carries most of the energy is the most massive one. Le.. 7&l. which we refer to as the shell.," Among these shells the one that carries most of the energy is the most massive one, i.e., $\tau \approx 1$, which we refer to as the shell."
 In the regime that we consider the shell becomes transparent during the planar phase (i.e. before its radius doubles) and alter it achieves ils final Lorentz [actor.," In the regime that we consider the shell becomes transparent during the planar phase (i.e., before its radius doubles) and after it achieves its final Lorentz factor."
 Light travel time and relativistic effects dictate that the emission of the shell. once it become transparent. dominates during the entire planar phase.," Light travel time and relativistic effects dictate that the emission of the shell, once it become transparent, dominates during the entire planar phase."
 Slower shells release (heir photons only during the spherical phase., Slower shells release their photons only during the spherical phase.
 The processes described above produce the main following (i) This flare is generated by the shell when it becomes The Energy. temperature and duration of the flare depend only on (wo parameters. ro and the breakout radius.," The processes described above produce the main following (i) This flare is generated by the shell when it becomes The Energy, temperature and duration of the flare depend only on two parameters, $\g_{f,0}$ and the breakout radius."
 Thus. in addition to providing the value of these two physical parameters. the three observables must satisfy (he relativistic breakout relation (equation 18)).," Thus, in addition to providing the value of these two physical parameters, the three observables must satisfy the relativistic breakout relation (equation \ref{eq tbo test}) )."
 This relation can be used to test if an observed flare may. have been produced by a quasi-spherical relativistic breakout., This relation can be used to test if an observed flare may have been produced by a quasi-spherical relativistic breakout.
 Note. (hat our calculation of the breakout flare energy. temperature and duration are independent of the exact profile of the pre-breakout density. as long as il is sleeply decreasing. à," Note, that our calculation of the breakout flare energy, temperature and duration are independent of the exact profile of the pre-breakout density, as long as it is steeply decreasing. ("
"i) Due to light travel tme effects. the breakout flare contains photons Irom faster ancl lighteroO shells. producinge a highex energve. power-law spectrum. p£,ixVvO71.","ii) Due to light travel time effects, the breakout flare contains photons from faster and lighter shells, producing a high energy power-law spectrum, $\nu F_\nu \propto \nu^{-0.74}$."
 It also contains photons emitted by the shell after it becomes (transparent aud cools adiabatically.," It also contains photons emitted by the shell after it becomes transparent and cools adiabatically,"
 Waneeltetal.(200L).. Evilsseretal.(200la) were deseribed bv οDwyer D)... and. Erikseietal.(2006.2007a).," \citet{jewell:2004} \citet{wandelt:2004}, \citet{eriksen:2004a} \citet{larson:2007}, were described by \citet{odwyer:2004}, and \citet{eriksen:2006,eriksen:2007a}."
. These papers mainly focused on the cosmological CMD signal. and adopted the foregrouad corrected data provided by the WMAP team.," These papers mainly focused on the cosmological CMB signal, and adopted the foreground corrected data provided by the WMAP team."
 Recently this algorithii was extended to include internal component scparation capabilities by Exikseiotal. (2007b)., Recently this algorithm was extended to include internal component separation capabilities by \citet{eriksen:2007b}.
. Using very general parauuceterizatious of the foreground. compoucuts. this method produces the full joint and exact foreground-CMD posterior. aud thereOre allows us both to estimate cach component separatelv through mareinalized statistics and to propagate the foreground uncertainties through to the final CAIB products.," Using very general parameterizations of the foreground components, this method produces the full joint and exact foreground-CMB posterior, and therefore allows us both to estimate each component separately through marginalized statistics and to propagate the foreground uncertainties through to the final CMB products."
" The implementation of this algorithia usec in this paper is called ""C'onuuauder aud is a direct desceudaur of the code preseuted bv. Exriksenet(200 1a)."," The implementation of this algorithm used in this paper is called “Commander”, and is a direct descendant of the code presented by \citet{eriksen:2004a}."
. Tn this Letter. we apply the method to the 3-vr WALAP temperature observations (Winshawetal.2007).," In this Letter, we apply the method to the 3-yr WMAP temperature observations \citep{hinshaw:2007}."
. This data set. with five frequency bands. allows ouly very lanited foreground models: however. the analysis provides a powerful demonstration of the capabilities of the method.," This data set, with five frequency bands, allows only very limited foreground models; however, the analysis provides a powerful demonstration of the capabilities of the method."
 For a comprehcusive analysis of a coutrolled simulation with ideutical properties to thisdata set. sce Eviksenetal. (2007))..," For a comprehensive analysis of a controlled simulation with identical properties to thisdata set, see \citet{eriksen:2007b}. ."
 We consider the vr WMAP teiiperature data.," We consider the 3-yr WMAP temperature data,"
The speed of propagation of gravity. which initially appeared in (he retarded potentials. is nowhere to be found in Chis final expression.,"The speed of propagation of gravity, which initially appeared in the retarded potentials, is nowhere to be found in this final expression."
 The only consequence of using an alternative theory of gravity is in the PPN parameters 5 and ¢=04/(2425)., The only consequence of using an alternative theory of gravity is in the PPN parameters $\gamma$ and $\zeta=\alpha_1/(2+2\gamma)$.
" The variable x,=x(o,)—x,(0) can be converted so that all times are referred to the moment of reception of the rav. using (he expressions x,, =x(o,)—Xx,(0,)and v, =v,(o,)."," The variable ${\bf \tilde x}_{ra} = {\bf x}(\sigma_r)-{\bf x}_a(0)$ can be converted so that all times are referred to the moment of reception of the ray, using the expressions where ${\bf x}_{ra}
\equiv {\bf x}(\sigma_r)-{\bf x}_a(\sigma_r)$ and ${\bf v}_a \equiv {\bf v}_a(\sigma_r)$."
Substituting into Eq. (32)), Substituting into Eq. \ref{semifinal}) )
 and rearranging. we find. to the necessaryorder. where In general relalivilv (5=1. ¢= 0) this agrees completely with results derived by ]xopeikinandSchaler(1999).. to 1.5PN order.," and rearranging, we find, to the necessaryorder, where In general relativity $\gamma=1$, $\zeta=0$ ) this agrees completely with results derived by \citet{KopSch99}, to 1.5PN order."
 We have shown that the speed of propagation of eravily has no direct influence on the time delay of light to 1.5PN order., We have shown that the speed of propagation of gravity has no direct influence on the time delay of light to 1.5PN order.
 The only effect comes from any modification of the PPN parameters that mieht arise in a theory. with a different propagation speed., The only effect comes from any modification of the PPN parameters that might arise in a theory with a different propagation speed.
 This contraclicts Claims made by Ixopeikin(2001.2002).," This contradicts claims made by \citet{Kop01,Kop02}."
". In addition. existing solar-svstem experiments already place sufficiently strong bounds on the PPN parameters > and ay, (hat even the potential difference [rom GR. in the 19208 correction represented by (he parameter ¢ in Eq. (34))"," In addition, existing solar-system experiments already place sufficiently strong bounds on the PPN parameters $\gamma$ and $\alpha_1$ that even the potential difference from GR in the 1.5PN correction represented by the parameter $\zeta$ in Eq. \ref{final}) )"
 must be small., must be small.
 The parameter > is known to be unity to a part in 1000 Irom standard time delay and light deflection measurements. while |o4|«2x10.+ from analyses of Lunar laser ranging 1996) and binary pulsar data (Belletal.1996).," The parameter $\gamma$ is known to be unity to a part in 1000 from standard time delay and light deflection measurements, while $|\alpha_1| < 2 \times 10^{-4}$ from analyses of Lunar laser ranging \citep{muller} and binary pulsar data \citep{bell}."
. The latter bounds assume Chat the solar svslem and (he relevant binary pulsar are moving with respect to the cosmic background radiation with known velociGes of order 300 km/s. and that. in anv theory of gravity. with αισε O. the rest frame of that radiation coincides with a cosmological preferred. frame.," The latter bounds assume that the solar system and the relevant binary pulsar are moving with respect to the cosmic background radiation with known velocities of order 300 km/s, and that, in any theory of gravity with $\alpha_1 \ne 0$ , the rest frame of that radiation coincides with a cosmological preferred frame."
 Such, Such
The study of elephant trunks. pillars and globules. found at the borders of H regions around massive stars. has received significant attention in recent vears. both from an observational perspective and in theoretical and computational models.,"The study of elephant trunks, pillars and globules, found at the borders of H regions around massive stars, has received significant attention in recent years, both from an observational perspective and in theoretical and computational models."
 The famous “Pillars of Creation in M16 were observed at optical wavelengths. with HST ©). in. the IR. (22).. and. in. sub- (e.g.22). showing that these are dynamic structures with ongoing star formation which may or may not have been triggered by the radiation which has shaped the pillars.," The famous `Pillars of Creation' in M16 were observed at optical wavelengths with HST \citep{HesScoSanEA96}, in the IR \citep{IndRobWhiEA07,SugWatTamEA07}, and in sub-mm/radio \citep[e.g.][]{Pou98,WhiNelHolEA99}, showing that these are dynamic structures with ongoing star formation which may or may not have been triggered by the radiation which has shaped the pillars."
 ? provide strong evidence that pillars in the Carina Nebula are signiticant sites of sequential star formation propagating away from the older star clusters in this region. building on previous observations of synchronised star formation around the periphery of the nebula by ?..," \citet{SmiPovWhiEA10} provide strong evidence that pillars in the Carina Nebula are significant sites of sequential star formation propagating away from the older star clusters in this region, building on previous observations of synchronised star formation around the periphery of the nebula by \citet{SmiBro07}."
 On smaller scales. studies of T-Tauri star ages in the Orion Nebula (22). show decreasing stellar ages moving away from massive stars and towards bright-rimmed clouds at the H region/molecular cloud interface. again strongly suggesting at least sequential and possibly triggered star formation.," On smaller scales, studies of T-Tauri star ages in the Orion Nebula \citep{LeeCheZhaEA05,LeeChe07} show decreasing stellar ages moving away from massive stars and towards bright-rimmed clouds at the H region/molecular cloud interface, again strongly suggesting at least sequential and possibly triggered star formation."
 The clear relationship between pillars/globules and second generation star formation around OB associations. and the question of the extent o which this star formation is triggered. provides strong motivation o understand the formation and evolution of these structures.," The clear relationship between pillars/globules and second generation star formation around OB associations, and the question of the extent to which this star formation is triggered, provides strong motivation to understand the formation and evolution of these structures."
 In a previous paper (2.hereafterMLIO) we investigated he formation and evolution of dense pillars of gas and dust — elephant trunks — on the boundaries of H regions using 3D hydrodynamical simulations including photoionising radiative ransfer (R-HD)., In a previous paper \citep[][hereafter ML10]{MacLim10} we investigated the formation and evolution of dense pillars of gas and dust – elephant trunks – on the boundaries of H regions using 3D hydrodynamical simulations including photoionising radiative transfer (R-HD).
 It was found that shadowing of ionising radiation by an inhomogeneous density field naturally forms elephant runks without the assistance of self-gravity. or of ionisation ront and cooling instabilities.," It was found that shadowing of ionising radiation by an inhomogeneous density field naturally forms elephant trunks without the assistance of self-gravity, or of ionisation front and cooling instabilities."
 A combination of radiation-driven implosion (RDI:?). and acceleration due to the rocket effect (2) produce elongated. structures: RDI compresses neutral gas unti oressure equilibrium with ionised gas is achieved: the rocket effec accelerates gas away from the radiation source producing dynamic elongated structures with lifetimes of a few hundred kyr (depending on clump masses/densities)., A combination of radiation-driven implosion \citep[RDI;][]{Ber89} and acceleration due to the rocket effect \citep{OorSpi55} produce elongated structures: RDI compresses neutral gas until pressure equilibrium with ionised gas is achieved; the rocket effect accelerates gas away from the radiation source producing dynamic elongated structures with lifetimes of a few hundred kyr (depending on clump masses/densities).
 Strong neutral gas cooling was found to enhance this formation mechanism. producing denser and longer lived pillar-like structures compared to models with weak cooling.," Strong neutral gas cooling was found to enhance this formation mechanism, producing denser and longer lived pillar-like structures compared to models with weak cooling."
 Models such as these for the formation of bright-rimmec clouds. globules and pillars have been considered for many years (e.g.2222): much of this work is summarised by ?..," Models such as these for the formation of bright-rimmed clouds, globules and pillars have been considered for many years \citep[e.g.][]{Pot58, Mar70, BodTenYor79, SanWhiKle82}; much of this work is summarised by \citet{Yor86}."
 The RDI of a photoionised clump and its subsequent acceleration and evolution was calculated analytically (22). and subsequently numerically by 2..," The RDI of a photoionised clump and its subsequent acceleration and evolution was calculated analytically \citep{Ber89,BerMcK90} and subsequently numerically by \citet{LeFLaz94}."
 ? considered a range of axisymmetric models showing that multiple scenarios could form long-lived pillar-like structures., \citet{WilWarWhi01} considered a range of axisymmetric models showing that multiple scenarios could form long-lived pillar-like structures.
 It has been shown (1919) that RDI of single clumps can," It has been shown \citep{KesBur03, MiaWhiNelEA06, PouKanRyuEA07, BisWhiWueEA10} that RDI of single clumps can"
"long term homogeneous survey of hot subdwarf stars (?),, in September and October 2004.","long term homogeneous survey of hot subdwarf stars \citep{GreenFontaine2008}, in September and October 2004."
" The spectrograph parameters, observational procedures, and reduction techniques were kept the same for all the observing nights."," The spectrograph parameters, observational procedures, and reduction techniques were kept the same for all the observing nights."
" The 400/mm grating, blazed at 4889A, gives a resolution of R = 560 over the wavelength region 3620—6895 A, when used with the 2.5 arcsec slit."," The 400/mm grating, blazed at $4889\,\rm\AA$, gives a resolution of R = 560 over the wavelength region $3620-6895\,\rm\AA$ , when used with the 2.5 arcsec slit."
 The spectra were taken during clear or mostly clear conditions with integration times between 1050 and 1200ss. Approximately 1000 bias and flat-field images were obtained for each run., The spectra were taken during clear or mostly clear conditions with integration times between 1050 and s. Approximately 1000 bias and flat-field images were obtained for each run.
" The data reductions were performed using standard IRAF tasks, and each night was flux-calibrated separately."," The data reductions were performed using standard IRAF tasks, and each night was flux-calibrated separately."
" The individual spectra were cross-correlated against a super-template to determine the relative velocity shifts, and then shifted and combined into a single spectrum."," The individual spectra were cross-correlated against a super-template to determine the relative velocity shifts, and then shifted and combined into a single spectrum."
" Although the resolution is rather low, the S/N is quite high: 221/pixel or 795/resolution element for the combined spectrum."," Although the resolution is rather low, the S/N is quite high: 221/pixel or 795/resolution element for the combined spectrum."
" The continuum fit to the combined flux-calibrated spectrum were done with great care to select regions devoid of any weak lines, including expected unresolved lines of heavier elements."," The continuum fit to the combined flux-calibrated spectrum were done with great care to select regions devoid of any weak lines, including expected unresolved lines of heavier elements."
" The final sspectrum was fitted using two separate grids of NLTE models designed for sdB stars, in order to derive the effective"," The final spectrum was fitted using two separate grids of NLTE models designed for sdB stars, in order to derive the effective"
There is growing evidence that Active Galactic Nuclei (AGN) behave like scalec-up versions of black hole. X-ray binaries (BINTBs). because of the similar X-ray variability characteristics and spectral-scaling properties in both types of svstem (e.g. Alerloni.Heinz&diMatteo2003:UttlevAlellardy 2005)).,"There is growing evidence that Active Galactic Nuclei (AGN) behave like scaled-up versions of black hole X-ray binaries (BHXRBs), because of the similar X-ray variability characteristics and spectral-scaling properties in both types of system (e.g. \citealt{Merloni,3227}) )."
 Le is therefore tempting to assume that AGN should be found in various accretion states. similar to the DIEXIUB high/soft and Iow/hard states and possibly also the transitional very high or intermediate states.," It is therefore tempting to assume that AGN should be found in various accretion states, similar to the BHXRB high/soft and low/hard states and possibly also the transitional very high or intermediate states."
 1 the longest. variability time-scales in these objects follow the linear scaling with black hole mass seen on shorter time-scales (e.g. Mellardyetal. 2005)). then the state transitions seen in. DIIXIUDs on time-scales of hours and longer would occur in ACN on time-scales of thousands to millions of vears.," If the longest variability time-scales in these objects follow the linear scaling with black hole mass seen on shorter time-scales (e.g. \citealt{McHardyMCG}) ), then the state transitions seen in BHXRBs on time-scales of hours and longer would occur in AGN on time-scales of thousands to millions of years."
 Therefore. we might expect to see dillerent states in different AGN. but changes in state in a single AGN are unlikely to be seen within a human lifetime.," Therefore, we might expect to see different states in different AGN, but changes in state in a single AGN are unlikely to be seen within a human lifetime."
 In BUNRBs. the cilferent states can be. identified w their distinct spectral and timing properties (e.g. AeClintock&Remillard 2005)).," In BHXRBs, the different states can be identified by their distinct spectral and timing properties (e.g. \citealt{McClintock}) )."
 ὃν measuring the X-ray variability power spectral density. (PSD). Mellardy (2004).. Alellardyetal.(2005) and Wttles&Acllarely(2005) have shown that the Sevlert galaxies NGC 4051. AICG6-30-15 and NGC 3227 resemble. BIIXIUDs in the ügh/soft state. while other AGN. such as NGC 3783 (Alarkowitzetal.2003). and NGC 4258 (Markowitz&Ut-ley2005). may correspond to BUNRBs in the low/harel state.," By measuring the X-ray variability power spectral density (PSD), \citet{McHardy4051}, \citet{McHardyMCG} and \citet{3227} have shown that the Seyfert galaxies NGC 4051, MCG–6-30-15 and NGC 3227 resemble BHXRBs in the high/soft state, while other AGN, such as NGC 3783 \citep{Markowitzark} and NGC 4258 \citep{4258} may correspond to BHXRBs in the low/hard state."
 lt has been argued that the Narrow Line Sevtert 1 rresembles BUNRBs in the rarer very high state due to its very high accretion rate (Papadakisetal.2002) and its doubly-broken PSD shape. where the separation of the breaks is too broad to reconcile this PSD with that of the BUARB €veg N-1 in the low/hard state (Papadakisetal.2002:Done&Cierlinski 2005).," It has been argued that the Narrow Line Seyfert 1 resembles BHXRBs in the rarer very high state due to its very high accretion rate \citep{Papadakis_ark} and its doubly-broken PSD shape, where the separation of the breaks is too broad to reconcile this PSD with that of the BHXRB Cyg X-1 in the low/hard state \citep{Papadakis_ark,doneger}."
. In this paper. we will use the cross spectrum (ie. time laes ancl coherence between different energy bands) to compare this AGN with BLINRBs in dilferent states.," In this paper, we will use the cross spectrum (i.e. time lags and coherence between different energy bands) to compare this AGN with BHXRBs in different states."
 iis a nearby. Xray bright. Narrow Line Sevlert 1. galaxy," is a nearby, X–ray bright, Narrow Line Seyfert 1 galaxy"
The most recent cosmological observations indicate that the present universe is flat. and. vacuum dominated. (IXomatsuetal. 2009).,The most recent cosmological observations indicate that the present universe is flat and vacuum dominated \citep{Komatsu2009}.
. In such a vacuum. dominated: space-time. the distance analysis requires computer intensive numerical calculations.," In such a vacuum dominated space-time, the distance analysis requires computer intensive numerical calculations."
 Even though. computers today are very fast. ellicient analytical calculation of distance scales would be very useful for various types of Monte Carlo simulations.," Even though, computers today are very fast, efficient analytical calculation of distance scales would be very useful for various types of Monte Carlo simulations."
" The most Fundamental distance scale in the universe is 10 luminosity clistance. defined by d;=VL(Axf). where f is the observed. Dux of an astronomical object and. {, is Ress luminosity."," The most fundamental distance scale in the universe is the luminosity distance, defined by $d_L = \sqrt{L/(4 \pi f)}$, where $f$ is the observed flux of an astronomical object and $L$ is its luminosity."
 Current astronomical observations indicate mt the present density. parameter of the universe satisfy OQ.|Oy—1 with Oy~0.7.," Current astronomical observations indicate that the present density parameter of the universe satisfy $\Omega_\Lambda
+ \Omega_M = 1$ with $\Omega_\Lambda \sim 0.7$."
 Here Oy is the contribution rom the vacuum and £33; is the contribution from all other iclels., Here $\Omega_\Lambda$ is the contribution from the vacuum and $\Omega_M$ is the contribution from all other fields.
" Phe distance calculations in such a vacuum dominated universe involve repeated numerical calculations ancl elliptic ""unctions (Eisenstein1997).", The distance calculations in such a vacuum dominated universe involve repeated numerical calculations and elliptic functions \citep{Eisenstein1997}.
. In order to simplify the numerical calculations. Pen(1999). (hereafter Pend9) has developed: quite an eLlicient analytical recipe.," In order to simplify the numerical calculations, \cite{Pen1999}
 (hereafter Pen99) has developed quite an efficient analytical recipe."
 In this paper. we show another analytical method. similar in many respect to that of Pen99. that can oe used: to calculate the distances in a vacuum dominated lat universe.," In this paper, we show another analytical method, similar in many respect to that of Pen99, that can be used to calculate the distances in a vacuum dominated flat universe."
 Our analytical calculation is shown to run faster than hat of Pen99 and has smaller error variations with respect o pedshift (2) and Ον., Our analytical calculation is shown to run faster than that of Pen99 and has smaller error variations with respect to redshift $z$ ) and $\Omega_\Lambda$.
 Our recipe for caleulating the luminosity distance is the following (fy is the present Hubble constant ancl e is the speed. of light): We first begin by analyzing how the scale factor. a(/) varies as a function of time / in a flat universe in which O4z0.," Our recipe for calculating the luminosity distance is the following $H_0$ is the present Hubble constant and $c$ is the speed of light): We first begin by analyzing how the scale factor, $a(t)$ varies as a function of time $t$ in a flat universe in which $\Omega_\Lambda
\neq 0$."
 1n this case. a(£) is given by (Weinberg2008) where ag is the present value of the scale factor.," In this case, $a(t)$ is given by \citep{Weinberg2008}
 where $a_0$ is the present value of the scale factor."
 The above equation is then immecdiately integrated intoThe scale factor is directly related to the z as. Let us define »=34fo£/y/ and indicate its present value by ary=or(0. O4).," The above equation is then immediately integrated intoThe scale factor is directly related to the $z$ as, Let us define $x = 3 H_{0} t \sqrt{\Omega_\Lambda}$ and indicate its present value by $x_0=x(0, \Omega_\Lambda)$ ."
 Then. equations3 6. and 7 give," Then, equations \ref{eq:no4} and \ref{eq:no4b} give"
ISO archive.,$\it{ISO}$ archive.
 We decided not to use the [RAC 3.6 sam baud intensities. which are attribuable to Ho ro-vibrational emissious.," We decided not to use the IRAC 3.6 $\mu$ m band intensities, which are attributable to $_{2}$ ro-vibrational emissions."
 The excitation of H» vibrational trausitious. unlike the pure roalional lines we cousiderect. is comiuatecd w collisions by atomic hydrogen even with a small ((H /n(Ha) ratio ~ 3% (NYOS).," The excitation of $_{2}$ vibrational transitions, unlike the pure rotational lines we considered, is dominated by collisions by atomic hydrogen even with a small $n$ $n$ $_{2}$ ) ratio $\sim$ $\%$ (NY08)."
 Sitice the coisional dissociatiou processes for molecular hydrogen a‘e lore efficient. within the hoter COMmpoOent of the shocked gas. the depeucence of the Ho vib‘alloual einission upou temperaure will be more complicated! than what our model describes.," Since the collisional dissociation processes for molecular hydrogen are more efficient within the hotter component of the shocked gas, the dependence of the $_{2}$ vibrational emission upon temperature will be more complicated than what our model describes."
 TUs. we exclude IRAC bat 1 (3.6 jun) in the fitting to avoid it allecting our estiiyate of the best fit temperature clistriblion and censity.," Thus, we exclude IRAC band 1 (3.6 $\mu$ m) in the fitting to avoid it affecting our estimate of the best fit temperature distribution and density."
 For the other traisitious mentioned alove. the excitation processes should be always domiated by collisions witi Ho given the concitious in molecular shocks.," For the other transitions mentioned above, the excitation processes should be always dominated by collisions with $_{2}$ given the conditions in molecular shocks."
 Iu our calcualiou. we take into account. collisiona excitation by H» αιd belitun.," In our calculation, we take into account collisional excitation by $_{2}$ and helium."
 A helitun abundance n(He)/n (H2) of 0.2 is assumed., A helium abundance $n$ $n$ $_{2}$ ) of 0.2 is assumed.
" Errors iutrodiced. by neglecting c«Alision with atomic hydrogen are larges for the CO lines aud those high-lyiig Ho transitions coitributing to IRAC bai 2, which are however still less than 15% given an average n(H)/n(Ha) ratio of 10%. which is the upper limit of the value for ICLI3C estimated by Burton et (01955) j3sed on the Br intensity."," Errors introduced by neglecting collision with atomic hydrogen are largest for the CO lines and those high-lying $_{2}$ transitions contributing to IRAC band 2, which are however still less than $\%$ given an average $n$ $n$ $_{2}$ ) ratio of $\%$, which is the upper limit of the value for IC443C estimated by Burton et (1988) based on the $\gamma$ intensity."
 As mentioned in Section D+) we used two ways to derive the best-fit yarameters.," As mentioned in Section 3, we used two ways to derive the best-fit parameters."
 In the first approach. ouly URS Ho lines were considered.," In the first approach, only IRS $_2$ lines were considered."
 In the second approach. all avallable molecular data were included iu the fittiue process.," In the second approach, all available molecular data were included in the fitting process."
 In the case of IC1ος and HHL. tjese data comprise he Hy HD ine intensities observed by HRS. the IRAC band 2 intensity. aud the CO line iutensities observed by ZSO/LWS.," In the case of IC443C and HH54, these data comprise the $_{2}$ HD line intensities observed by IRS, the IRAC band 2 intensity, and the CO line intensities observed by /LWS."
 For W2s. WIE and 30301. we itcluded the H» lires and SWS-measu'ed S(9)/5(3) ‘atios.," For W28, W44 and 3C391, we included the $_{2}$ lines and SWS-measured S(9)/S(3) ratios."
 For HHT. ouly tte IRS-observed Ho anc HD lines were use.," For HH7, only the IRS-observed $_{2}$ and HD lines were used."
" We found that the uncertaluties in the LAWS-meastrec CO line intensities for Wes, WIL 3€391 and HH7 are too large 1o provide useful information abott the physical couditious in the gas."," We found that the uncertainties in the LWS-measured CO line intensities for W28, W44, 3C391 and HH7 are too large to provide useful information about the physical conditions in the gas."
 To de'edden the ICLSC line fluxes. we originally tried the extinction correction with Aeqj 1.3 - 1.6 by Richter et ((1995 aud the Ry = 3.1 extinetion curves from Weilneartuer Draine (2001). which ended up with a S(3) intensity almost two times larger than expected given the other H» liue intensities.," To deredden the IC443C line fluxes, we originally tried the extinction correction with $A_{2.12\mu m}$ = 1.3 – 1.6 by Richter et (1995) and the $_{V}$ = 3.1 extinction curves from Weingartner Draine (2001), which ended up with a S(3) intensity almost two times larger than expected given the other $_2$ line intensities."
 Treatiig the extinction as a [ree parameter in our fit to the Ho liue intensities vielded an Ay close to zero., Treating the extinction as a free parameter in our fit to the $_2$ line intensities yielded an $_V$ close to zero.
 Thus. we applied uo extinction correction for ICE13C in the following caleilatious.," Thus, we applied no extinction correction for IC443C in the following calculations."
" For W28. we applied au extinction correction with Ey, y= 1 - 1.3 given by Loug et (1991) derived [roi1 the [S H] line ratios."," For W28, we applied an extinction correction with $_{B - V}$ = 1 – 1.3 given by Long et (1991) derived from the [S II] line ratios."
 This value is also consistent. with the estimate by Bohieas et ((198:3) who obtained Ej; y= 1.16., This value is also consistent with the estimate by Bohigas et (1983) who obtained $_{B - V}$ = 1.16.
 For WIL the absorbing coltumu density. along the liue-oC-sight to tlus 'egion is estimated to be ~2x107? cm? (Rho et 11991. corresponcli toaL Ay ~ 10.," For W44, the absorbing column density along the line-of-sight to this region is estimated to be $\sim 2\times10^{22}~$ $^{-2}$ (Rho et 1994), corresponding to an $_V$ $\sim$ 10."
 For 3C391. Reach et ((2009) suggested a visual extinction of Ay = 19 [or t IRS-observed region. Wwüch is deuser than other parts of the cloucd. based upou ai upper limit « the oreeround column density of (2—3.6)x107? ? infer'ed [rom a spectral analysis of t X-ray data (Rho & Petο 1996).," For 3C391, Reach et (2002) suggested a visual extinction of $_V$ = 19 for the IRS-observed region, which is denser than other parts of the cloud, based upon an upper limit on the foreground column density of $(2-3.6) \times 10^{22}$ $^{-2}$ inferred from a spectral analysis of the X-ray data (Rho $\&$ Petre 1996)."
 For HHT. we adopted Ey4 = 0.7. as estimated by Greclel (1996)," For HH7, we adopted $_{J -
K}$ = 0.7, as estimated by Gredel (1996)"
on stars by a short period giant planet.,on stars by a short period giant planet.
" The estimates of this efficiency are based on direct simulations of the dissipation of externally driven perturbations in a small, but still significantly stratified, piece of a convective zone."," The estimates of this efficiency are based on direct simulations of the dissipation of externally driven perturbations in a small, but still significantly stratified, piece of a convective zone."
" While due to numerical limitations we are unable to explore the entire range of the ratio of tidal frequency to local convective turnover time that occurs in the surface convective zones of low mass we show that the rate of dissipation of tidal energy stars,averaged over the entire convective zone is constrained to within a factor of ten."," While due to numerical limitations we are unable to explore the entire range of the ratio of tidal frequency to local convective turnover time that occurs in the surface convective zones of low mass stars, we show that the rate of dissipation of tidal energy averaged over the entire convective zone is constrained to within a factor of ten."
 This is a significant improvement over the current range of three to five orders that authors wishing to calculate the tidal magnitudeevolution of manyexoplanet orbits are forced to consider (e.g.??????)..," This is a significant improvement over the current range of three to five orders magnitude that many authors wishing to calculate the tidal evolution of exoplanet orbits are forced to consider \citep[e.g.][]{wasp18_nature, Jackson_et_al_09b, Barker_Ogilvie_09,
Levrard_et_al_09, Patzold_et_al_04, Adams_Laughlin_06}."
" Since the usual way to parametrize the dissipation of tides is using the stellar quality factor Q., we calculate effective values for this parameter as a function of the orbital frequency."," Since the usual way to parametrize the dissipation of tides is using the stellar quality factor $Q_*$, we calculate effective values for this parameter as a function of the orbital frequency."
" We find that our estimates lie towards the upper end (small dissipation) of the usually assumed range for this parameter — 10°<Q,10? — and are significantly larger than the value needed to explain the fact that the maximum period to which solar type binary stellar orbits are circularized increases noticeably over the main sequence lifetime of these systems.", We find that our estimates lie towards the upper end (small dissipation) of the usually assumed range for this parameter – $10^8<Q_*<10^9$ – and are significantly larger than the value needed to explain the fact that the maximum period to which solar type binary stellar orbits are circularized increases noticeably over the main sequence lifetime of these systems.
" We argue, however, that this is not necessarily a contradiction, since in tha case of binary stars synchronization of the stellar rotation to the orbit happens much faster than the circularization of the orbit."," We argue, however, that this is not necessarily a contradiction, since in tha case of binary stars synchronization of the stellar rotation to the orbit happens much faster than the circularization of the orbit."
" This means that the tidal is close to the rotation rate of the star, for most frequencyof the time circularization occurs."," This means that the tidal frequency is close to the rotation rate of the star, for most of the time circularization occurs."
" This opens the possibility that inertial waves are resonantly excited in the stars, which what is likely to occur in planet star systems, which typically have the star rotating much slower than the tides raised by the planet."," This opens the possibility that inertial waves are resonantly excited in the stars, which results in a much enhance dissipation \citep{Savonije_Papaloizou_97, Dintrans_Ouyed_01, Ogilvie_Lin_04,
Wu_05a, Wu_05b, Papaloizou_Ivanov_05, Ogilvie_Lin_07, Ivanov_Papaloizou_07,
Ogilvie_09}, over what is likely to occur in planet star systems, which typically have the star rotating much slower than the tides raised by the planet."
 This idea seems to be confirmed by a number of transiting extrasolar planets which are found to lie very close to their host star., This idea seems to be confirmed by a number of transiting extrasolar planets which are found to lie very close to their host star.
" So close in fact that were the value of Q. implied by main sequence binary stars applicable to star-planet systems, we would conclude that we caught several of those planets in the last less than of their lifetime e.g.),, which seems rather unlikely given the current(??, sample of about a hundred known transiting planets."," So close in fact that were the value of $Q_*$ implied by main sequence binary stars applicable to star-planet systems, we would conclude that we caught several of those planets in the last less than of their lifetime \citep[e.g.]{wasp18_nature, Hebb_et_al_10}, which seems rather unlikely given the current sample of about a hundred known transiting planets."
" We show that our much smaller dissipation results in future lifetimes for all the currently known planets comparable to their age (Fig. 3)), andtransi"," We show that our much smaller dissipation results in future lifetimes for all the currently known transiting planets comparable to their age (Fig. \ref{fig: lifetimes}) ),"
ting is hence consistent with those observations., and is hence consistent with those observations.
 We also calculate the inferred TTVs due to tidal decay of the orbit (Fig. 2)), We also calculate the inferred TTVs due to tidal decay of the orbit (Fig. \ref{fig: Pdot}) )
 and find values of < 1ms/yr for all currently know transiting planets., and find values of $\lesssim$ 1ms/yr for all currently know transiting planets.
" Much smaller than we can hope to observe from the ground in the near future, but perhaps within reach of an extended Kepler mission if a very short period massive planet happens to be among its targets, leaving the possibility to measure Q. directly."," Much smaller than we can hope to observe from the ground in the near future, but perhaps within reach of an extended Kepler mission if a very short period massive planet happens to be among its targets, leaving the possibility to measure $Q_*$ directly."
"that contains the disk center at (x,y,z)= (1203,334,334) AU, coincides with the x-axis for an inclination angle 0=0°.","that contains the disk center at $x$ $y$ $z$ )= (1203,334,334) AU, coincides with the $x$ -axis for an inclination angle $\theta=0^{\circ}$."
" For larger inclination angles, the disk axis rotates clockwise, with respect to the x-axis, as depicted in Figure 2.."," For larger inclination angles, the disk axis rotates clockwise, with respect to the $x$ -axis, as depicted in Figure \ref{f2}."
" The remaining volume of the computational domain is filled with an ionized environment of uniform density n,=500 cm?."," The remaining volume of the computational domain is filled with an ionized environment of uniform density $n_a =
500$ $^{-3}$."
" All models except M1a have an initial wind of vw = 100 km s! and density ny=500 cm, entering the computational domain through the x=0 boundary."," All models except M1a have an initial wind of $_\mathrm{w}$ = 100 km $^{-1}$ and density $_\mathrm{w} = 500$ $^{-3}$, entering the computational domain through the $x=0$ boundary."
" The ionizing/dissociating photon source is placed along the x-axis, outside the computational domain to the left."," The ionizing/dissociating photon source is placed along the $x$ -axis, outside the computational domain to the left."
" In Table | we present all the relevant parameters used in our models: the dissociating photon rate, Syy (in units of 1049 s-!; second column), the distance from the disk to the external star (in pc; third column), the inclination angle ϐ between the disk and the x axis (fourth column), the velocity of the wind from the external star (in km s!; fifth column) and the temperature of the PDR region (in K; sixth column)."," In Table \ref{tab1} we present all the relevant parameters used in our models: the dissociating photon rate, $S_{FUV}$ (in units of $10^{49}$ $^{-1}$ ; second column), the distance from the disk to the external star (in pc; third column), the inclination angle $\theta$ between the disk and the $x$ axis (fourth column), the velocity of the wind from the external star (in km $^{-1}$ ; fifth column) and the temperature of the PDR region (in K; sixth column)."
 All the models have an ionizing photon flux Sguy=7.2x1058 s-! (similar to the values used by Richling Yorke 2000) and rg=50 AU.," All the models have an ionizing photon flux $S_{EUV}=7.2\times
10^{48}$ $^{-1}$ (similar to the values used by Richling Yorke 2000) and $r_d = 50$ AU."
" The simulations have been computed in a 5-level, binary adaptive grid with a maximum resolution (along the three axes) of 5.2 AU for all models."," The simulations have been computed in a 5-level, binary adaptive grid with a maximum resolution (along the three axes) of 5.2 AU for all models."
" The computational domain has a size (Xmnax»Vmax»Zmax)7 337,668,668) AU."," The computational domain has a size $(x_{max},y_{max},z_{max})=$ $\,$ 337,668,668) AU."
" In Fig. 3,,"," In Fig. \ref{f3},"
 we show the xz-midplane density stratifications (left) and Ha maps (right) for model Mla (top) and model M1b (bottom) at t=2000 years.," we show the $xz$ -midplane density stratifications (left) and $\alpha$ maps (right) for model M1a (top) and model M1b (bottom) at $t=2\,000$ years."
 The models present only an EUV radiation field from the ionizing source (at a 0.1 pc distance from the disk)., The models present only an EUV radiation field from the ionizing source (at a 0.1 pc distance from the disk).
" The difference between the two models is the presence of a stellar wind in model M1b, as described in Table 1.."," The difference between the two models is the presence of a stellar wind in model M1b, as described in Table \ref{tab1}."
" The disk axis has no inclination with respect to the direction of the impinging photons (i. e., 0=0? see Figure 2 and also Table 1))."," The disk axis has no inclination with respect to the direction of the impinging photons (i. e., $\theta=0^{\circ}$ see Figure \ref{f2}
 and also Table \ref{tab1}) )."
" The Ha emission in model Mla, is restricted to a region near the disk surface (and facing the ionizing source), and the edge of the shadow on the non-illuminated side of the disk."," The $\alpha$ emission in model M1a, is restricted to a region near the disk surface (and facing the ionizing source), and the edge of the shadow on the non-illuminated side of the disk."
" For model M1b, we have Ha emission close to the disk (with morphology and intensity similar to those seen in model Mla), and also fainter emission regions distributed along the interaction region between the stellar wind and the photoevaporated flow."," For model M1b, we have $\alpha$ emission close to the disk (with morphology and intensity similar to those seen in model M1a), and also fainter emission regions distributed along the interaction region between the stellar wind and the photoevaporated flow."
" It is known that some proplyds in Orion show faint Ha arcs facing 6! Ori C (Ballyetal.,1998),, which correspond to the stellar wind/photoevaporated flow interaction emission found in our models."," It is known that some proplyds in Orion show faint $\alpha$ arcs facing $\theta^1$ Ori C \citep{bally..98}, which correspond to the stellar wind/photoevaporated flow interaction emission found in our models."
" In Figure 4 we show xz-midplane density maps for model Mlb at ¢= 60, 80, 100 and 120 yr, in order to illustrate the initial evolution of such an interaction."," In Figure \ref{f4} we show $xz$ -midplane density maps for model M1b at $t=$ 60, 80, 100 and 120 yr, in order to illustrate the initial evolution of such an interaction."
" At {=60 yr, the stellar wind and the photoevaporated flow start to interact at x~ 668 AU.At later times, theinteraction region moves towards the disk, and stabilizes around the position of the point of ram pressure balance between the stellar wind and"," At $t=60$ yr, the stellar wind and the photoevaporated flow start to interact at $x \simeq$ 668 AU.At later times, theinteraction region moves towards the disk, and stabilizes around the position of the point of ram pressure balance between the stellar wind and"
"are sampled every | s. We have also assumed that all the strands are strictly out of phase, 1.c. only one strand is switched on at any time.","are sampled every $1$ s. We have also assumed that all the strands are strictly out of phase, i.e. only one strand is switched on at any time."
 At time Ξ0 all strands are switched off., At time $t = 0$ all strands are switched off.
" Then the heat pulses gradually turn them on, one after the other."," Then the heat pulses gradually turn them on, one after the other."
 We have chosen to turn them on with constant cadence to have a smooth transition from no bright strands to maximum number of bright strands (Fig. 4))., We have chosen to turn them on with constant cadence to have a smooth transition from no bright strands to maximum number of bright strands (Fig. \ref{time_profile_T_med}) ).
" At a certain time, part of the strands will still be off, in a few the heat pulse will be on, the others will be cooling after the heat pulse has ended."," At a certain time, part of the strands will still be off, in a few the heat pulse will be on, the others will be cooling after the heat pulse has ended."
" Since all strands have the same evolution, at cach time each strand will be at a different phase of the same evolution."," Since all strands have the same evolution, at each time each strand will be at a different phase of the same evolution."
" A whole loop at à given time is therefore simulated as a set of otherwise identically evolving strands, but each with a different heating start, all glued together."," A whole loop at a given time is therefore simulated as a set of otherwise identically evolving strands, but each with a different heating start, all glued together."
 This approach is not completely new; outputs of the same loop simulation have been put together in the past to simulate multistrand nanoflaring loops (22???) but in all cases they wereaveraged to obtain the effective aspect and evolution of a loop as a whole.," This approach is not completely new; outputs of the same loop simulation have been put together in the past to simulate multistrand nanoflaring loops \citep{Peres_al_1993_inproc,Warren_al_2002,Warren_al_2003,Winebarger_al_2003_a,Winebarger_al_2003_b} but in all cases they were to obtain the effective aspect and evolution of a loop as a whole."
" The novelty of our approach is that we do not model each loop as whole, but we keep the information of its spatial longitudinal and transversal distribution."," The novelty of our approach is that we do not model each loop as whole, but we keep the information of its spatial longitudinal and transversal distribution."
 In our model one heat pulse is switched on every one second in one new strand., In our model one heat pulse is switched on every one second in one new strand.
 One loop consists of =60 strands and we put =30 loops one by the other., One loop consists of $\approx 60$ strands and we put $\approx 30$ loops one by the other.
 Every second there are 60 strands where the heat pulse is on out of a total of 2000., Every second there are $60$ strands where the heat pulse is on out of a total of $2000$.
 In the steady-state the loop heating per unit volume is therefore H=Hox60/20000.011 ere. em? s~!., In the steady-state the loop heating per unit volume is therefore $\overline{H} = {H_0} \times 60/2000 \approx 0.011$ erg $^{-3}$ $^{-1}$.
 According to scaling law (?).. this steady heating sustains a loop with an apex temperature of =3.8MK corresponding to an average temperature along the loop of about 3M K(Fig. 4)).," According to scaling law \citep{Rosner_1978}, , this steady heating sustains a loop with an apex temperature of $ \approx 3.8 ~ MK$ corresponding to an average temperature along the loop of about $3 ~ MK$ (Fig. \ref{time_profile_T_med}) )."
" When we put all strands side by side, we obtain a mesh 1024x2000 erid cells."," When we put all strands side by side, we obtain a mesh $1024 \times 2000$ grid cells."
 The transversal width of cach strand 1s constant along the loops., The transversal width of each strand is constant along the loops.
 Therefore it is only a multiplicative constant which determines the cross-section of the entire loop system., Therefore it is only a multiplicative constant which determines the cross-section of the entire loop system.
 From model results we synthesized the loop emissionin different spectral lines., From model results we synthesized the loop emissionin different spectral lines.
 We selected, We selected
The collapsar model links LGRBs to the evolution of single massive stars whose lifetimes are negligible on cosmological scales.,The collapsar model links LGRBs to the evolution of single massive stars whose lifetimes are negligible on cosmological scales.
 Π no other condition is required for producing a LGRB event. then the rate of LGRBs should be an unbiased tracer of he global star formation in the Universe (e.g.22222222222. therein).," If no other condition is required for producing a LGRB event, then the rate of LGRBs should be an unbiased tracer of the global star formation in the Universe \citep[e.g.][and
references therein]{Totani_1997,Wijers_etal_1998,mao98,Porciani_Madau_2001,bro02,fyn06,pri06,Savaglio_2006,tot06,pro07,li08a}."
 ? have recently suggested that GRB and Damped Lyman-Alpha samples. in contrast with magnitude imited samples. provide an almost complete census of 2~3 star-forming galaxies.," \cite{fyn08} have recently suggested that GRB and Damped Lyman-Alpha samples, in contrast with magnitude limited samples, provide an almost complete census of $z\sim3$ star-forming galaxies."
 We note. however. that the sample used in his study are biased against high-metallicity and dusty However. both observations and theoretical studies indicate hat the metallicity of the progenitor star plays an important role in setting the necessary conditions fora LGRB explosion.," We note, however, that the sample used in this study are biased against high-metallicity and dusty However, both observations and theoretical studies indicate that the metallicity of the progenitor star plays an important role in setting the necessary conditions for a LGRB explosion."
 In this case. he rate of LGRBs is expected to be a biased tracer of the cosmic star formation rate.," In this case, the rate of LGRBs is expected to be a biased tracer of the cosmic star formation rate."
 This is demonstrated explicitly in Fig. 2..," This is demonstrated explicitly in Fig. \ref{fig:sfr},"
 which compares the cosmie star formation rate obtained using all galaxies in the simulation box to that obtained for the three LGRB host samples detined in the Sec. 3.., which compares the cosmic star formation rate obtained using all galaxies in the simulation box to that obtained for the three LGRB host samples defined in the Sec. \ref{sec:method}.
 The sample with no threshold on metallicity (HOST|) traces exactly the global star formation rate (solid line in Fig. 29., The sample with no threshold on metallicity (HOST1) traces exactly the global star formation rate (solid line in Fig. \ref{fig:sfr}) ).
 This is not the case for the two samples with metallicity thresholds (ΠΟΡΤΟ - dot-dashed line and HOST3 - dashed line)., This is not the case for the two samples with metallicity thresholds (HOST2 - dot-dashed line and HOST3 - dashed line).
 For the HOST? and ΠΟΣΤΟ samples. the LGRB rate peaks at higher redshift than the cosmic star formation rate. as a consequence of the global decrease of metallicity with increasing redshift.," For the HOST2 and HOST3 samples, the LGRB rate peaks at higher redshift than the cosmic star formation rate, as a consequence of the global decrease of metallicity with increasing redshift."
 At higher redshift. the mean metallicity of the intergalactic medium is lower. which implies that a larger fraction of stars form below the metallicity thresholds adopted for HOST? and HOSTS.," At higher redshift, the mean metallicity of the intergalactic medium is lower, which implies that a larger fraction of stars form below the metallicity thresholds adopted for HOST2 and HOST3."
 Therefore the deviation of the LGRB rate from the star formation rate decreases with increasing redshift., Therefore the deviation of the LGRB rate from the star formation rate decreases with increasing redshift.
 At z~9. the HOST? sample measures about 99 per cent of the global star formation density.," At $z\sim 9$, the HOST2 sample measures about 99 per cent of the global star formation density."
 The fraction decreases to about 30 per cent at >~5 and to only about 10 per cent at present., The fraction decreases to about 30 per cent at $z\sim 5$ and to only about 10 per cent at present.
 For the HOSTS sample. the bias is even stronger because of the lower metallicity threshold: it traces only 30 per cent of the global star formation density at +~9. and less than [O per cent at 2«5.," For the HOST3 sample, the bias is even stronger because of the lower metallicity threshold: it traces only 30 per cent of the global star formation density at $z\sim 9$, and less than 10 per cent at $z<5$."
 The results shown in Fig., The results shown in Fig.
 2. are in qualitative agreement with recent observational estimates (2)... and with recent theoretical studies also based on the collapsar model (Q2. 2. 2).," \ref{fig:sfr} are in qualitative agreement with recent observational estimates \citep{Kistler_etal_2008}, , and with recent theoretical studies also based on the collapsar model \citealt*{Yoon_Langer_Norman_2006}, \citealt{Cen_Fang_2007}, \citealt{Nuza_etal_2007}, \citealt{Lapi_etal_2008}) )."
 Finally. Fig.," Finally, Fig."
 2. also shows that adopting a cosmological model compatible with third-year WMAP measurements (right panel). a delay is produced in the cosmic star formation rate. due to the delay in structure formation.," \ref{fig:sfr} also shows that adopting a cosmological model compatible with third-year WMAP measurements (right panel), a delay is produced in the cosmic star formation rate, due to the delay in structure formation."
 Except for this delay. the predicted trends are the same for the WMAP! and WMAP3 simulations.," Except for this delay, the predicted trends are the same for the WMAP1 and WMAP3 simulations."
 In the following. we will only show results obtained using the WMAP3 simulation as those obtained for the WMAPI simulation are very similar.," In the following, we will only show results obtained using the WMAP3 simulation as those obtained for the WMAP1 simulation are very similar."
 In addition. we will focus only on the two host samples with metallicity thresholds (HOST? and ΠΟΣΤΟ).," In addition, we will focus only on the two host samples with metallicity thresholds (HOST2 and HOST3)."
 We remind the reader that we consider as “hosts” all galaxies which can host at least one LGRB event between two simulation output., We remind the reader that we consider as `hosts' all galaxies which can host at least one LGRB event between two simulation output.
 Since galaxies at higher redshift have lower metallicities and form stars at higher rates. the rate of LGRBs per host galaxy increases rapidly with redshift.," Since galaxies at higher redshift have lower metallicities and form stars at higher rates, the rate of LGRBs per host galaxy increases rapidly with redshift."
 The left panel in Fig., The left panel in Fig.
 3. shows the redshift evolution of the number of LGRBs (solid line) and of host galaxies (HOSTS - dashed line).," \ref{fig:loggrb_myr}
 shows the redshift evolution of the number of LGRBs (solid line) and of host galaxies (HOST3 - dashed line)."
 The two vertical lines indicate the peaks of the distributions: the number of LGRBs peaks at +~5. while the number of host galaxies is maximum at 2~2.," The two vertical lines indicate the peaks of the distributions: the number of LGRBs peaks at $z\sim 5$, while the number of host galaxies is maximum at $z\sim 2$."
 The right panel of Fig., The right panel of Fig.
 3. shows the rate of LGRBs per galaxy and perMyr computed for the WMAP3 simulation and for the HOSTS sample., \ref{fig:loggrb_myr} shows the rate of LGRBs per galaxy and perMyr computed for the WMAP3 simulation and for the HOST3 sample.
 The predicted rate of LGRBs decreases from ~1000 at 2o Oto about 10Myr1ealaxy Sats~0. in agreement with calculations by ?..," The predicted rate of LGRBs decreases from $\sim 1000$ at $z \sim 9$ to about $10\,{\rm
Myr}^{-1}\,{\rm galaxy}^{-1}$ at $z \sim 0$, in agreement with calculations by \citet{Fryer_Woosley_Hartmann_1999}."
 Note that the LGRB rate computed above is not directly comparable to the observed rate because that would require us to take into account many unknown factors like the jet angle. and to include any possible observational bias (see??)..," Note that the LGRB rate computed above is not directly comparable to the observed rate because that would require us to take into account many unknown factors like the jet angle, and to include any possible observational bias \citep[see][]{Lapi_etal_2008,li08a}."
 A number of recent papers have studied the physical properties of LGRB host galaxies using deep observations covering a large wavelength range. both in imaging and in spectroscopy.," A number of recent papers have studied the physical properties of LGRB host galaxies using deep observations covering a large wavelength range, both in imaging and in spectroscopy."
 These studies have revealed that LGRB host galaxies are typically faint and star forming galaxies. dominated by young and metal-poor stellar populations (2222)..," These studies have revealed that LGRB host galaxies are typically faint and star forming galaxies, dominated by young and metal-poor stellar populations \citep{lef03,fru06,wai07,Savaglio_etal_2008}. ."
 In this section. we analyse the physical properties of our modelhost galaxies. and compare these with the," In this section, we analyse the physical properties of our modelhost galaxies, and compare these with the"
As discussed in Soriano et al. (2007)).,"As discussed in Soriano et al. \cite{soriano07}) ),"
 the asymptotic theory has been derived with some assumptions that are no longer valid in the cases we are studying., the asymptotic theory has been derived with some assumptions that are no longer valid in the cases we are studying.
" The most drastic of: these assumptions. is. related to integrals. that should be computed between the internal. turning. point. of the waves r, and stellar surface. they are replaced by integrations fromthe zero to R. This whereasmeans that the sound velocity at the turning point is assumed identical to that in the stellar centre."," The most drastic of these assumptions is related to integrals that should be computed between the internal turning point of the waves $r_t$ and the stellar surface, whereas they are replaced by integrations from zero to R. This means that the sound velocity at the turning point is assumed identical to that in the stellar centre."
 This assumption is completely wrong in stars with convective cores. and it becomes worse and worse às the helium-to-hydrogen ratio increases.," This assumption is completely wrong in stars with convective cores, and it becomes worse and worse as the helium-to-hydrogen ratio increases."
 A second important assumption is that the large separations for all frequencies and all modes are assumed identical to This isnot correct. as the £z0 modes do not travel down to the stellar centre.," A second important assumption is that the large separations for all frequencies and all modes are assumed identical to This isnot correct, as the $\ell \neq 0$ modes do not travel down to the stellar centre."
 They are trapped at the turning point /;. so that for each mode. integral (1)) should be computed from +; to R. not from 0 to R. Asaconsequence. the mean large separation for a mode £ is larger than Avo. due to the smaller integral.," They are trapped at the turning point $r_t$, so that for each mode, integral \ref{eqn1}) ) should be computed from $r_t$ to R, not from 0 to R. As a consequence, the mean large separation for a mode $\ell$ is larger than $\Delta\nu_0$, due to the smaller integral."
 This effect can be important if the sound velocity decreases strongly in the central regions., This effect can be important if the sound velocity decreases strongly in the central regions.
 Following Tassoul (1980)). but relaxing these assumptions. Soriano et al. (2007))," Following Tassoul \cite{tassoul80}) ), but relaxing these assumptions, Soriano et al. \cite{soriano07}) )"
 derived the following approximate expressions for the (= 0 - € = 2 and for the (= 1 - (= 3 small separations: where n 15 the radial order of the modes. « correspondspad to a surface phase shift. and Avo. Av). Avo. and Avs are the large separations computed respectively for the degrees (=0. I. 2. and 3.," derived the following approximate expressions for the $\ell$ = 0 - $\ell$ = 2 and for the $\ell$ = 1 - $\ell$ = 3 small separations: where $n$ is the radial order of the modes, $\alpha$ corresponds to a surface phase shift, and $\Delta\nu_0$, $\Delta\nu_1$, $\Delta\nu_2$, and $\Delta\nu_3$ are the large separations computed respectively for the degrees $\ell=0$, $1$, $2$, and $3$."
 From now on. we basically concentrate on the Ovis separations. which are the most relevant for our purpose.," From now on, we basically concentrate on the $\delta\nu_{02}$ separations, which are the most relevant for our purpose."
 We cun see that the integral. 767)=[RoyLeapde plays an important. role in. the computations. of the small separations., We can see that the integral $I(r)=\int_{r_t}^R \frac{1}{r}\frac{dc}{dr} dr$ plays an important role in the computations of the small separations.
". Using. the real boundary value +, instead of zero can lead to significant changes in the results.", Using the real boundary value $r_t$ instead of zero can lead to significant changes in the results.
 Also the difference between the large separations for the £=0 and the (=2 modes. which vanishes in the asymtotie theory. can be important. ever =: it is small.," Also the difference between the large separations for the $\ell=0$ and the $\ell=2$ modes, which vanishes in the asymtotic theory, can be important, even if it is small."
 Indeed this difference is multiplied by the radial order 7 which can be significant for the considered modes (of order 30)., Indeed this difference is multiplied by the radial order $n$ which can be significant for the considered modes (of order 30).
 We will see below that for some models. the integral Ir). which is generally negative. may become positive at the boundary of the core when the helium over hydrogen ratio is high enough.," We will see below that for some models, the integral $I(r)$ , which is generally negative, may become positive at the boundary of the core when the helium over hydrogen ratio is high enough."
 This is due to the resulting rapid variation of, This is due to the resulting rapid variation of
In Figure 1 we present the rest-frame UV J-diagram for a stellar mass-limited sample at0.,In Figure \ref{fig_UVJ_letter} we present the rest-frame $UVJ$ -diagram for a stellar mass-limited sample at.
9. 'The combination of these two colors allow one to break the degeneracy between age and reddening for red galaxies as discussed below., The combination of these two colors allow one to break the degeneracy between age and reddening for red galaxies as discussed below.
 Quiescent galaxies are delineated from SFGs using the boundary computed by Williamsetal.(2009)., Quiescent galaxies are delineated from SFGs using the boundary computed by \citet{williams2009}.
. We note that this boundary results in ~31% of galaxies with U—V>1.7 AB mag being classified as SFGs., We note that this boundary results in $\sim 31\%$ of galaxies with $U-V>1.7$ AB mag being classified as SFGs.
 This fraction does not vary significantly for different mass bins above our mass cut., This fraction does not vary significantly for different mass bins above our mass cut.
 Figure lbshowsagrayscalerepresentationo fthedensityof point #imAKY 208cbyi, Figure \ref{fig_UVJ_letter}$ $b$ shows a gray scale representation of the density of points in the $UVJ$ diagram.
oshidwetli dhafquAPS galuxiesisdisti , The concentration of quiescent galaxies is distinct from the broader distribution of $UVJ$ classified SFGs.
Model star formation histories (SFHs) reinforce the Williamsetal.(2009) division between quiescent and SFGs in the UVJ diagram., Model star formation histories (SFHs) reinforce the \citet{williams2009} division between quiescent and SFGs in the $UVJ$ diagram.
 The color evolution of a BCO03 solar metallicity single burst (SSP) and constant star formation rate model (CSF) are shown in Figure la., The color evolution of a BC03 solar metallicity single burst (SSP) and constant star formation rate model (CSF) are shown in Figure \ref{fig_UVJ_letter}$ $a$.
"After~3—5 Gyr, the SSP lies in the region of the UVJ diagram populated by quiescent galaxies."," After $\sim 3-5$ Gyr, the SSP lies in the region of the $UVJ$ diagram populated by quiescent galaxies."
" Meanwhile, after ~5 Gyr, the CSF lies in the star forming region of the UVJ diagram where no galaxies with mass ccan be found."," Meanwhile, after $\sim 5$ Gyr, the CSF lies in the star forming region of the $UVJ$ diagram where no galaxies with mass can be found."
" However, the reddening vector, computed assuming a Calzettietal.(2000) reddening law, suggests that the addition of varying amounts of extinction can explain a large range of colors for SFGs above our mass limit."," However, the reddening vector, computed assuming a \citet{calzetti2000} reddening law, suggests that the addition of varying amounts of extinction can explain a large range of colors for SFGs above our mass limit."
" Pateletal. show the color evolution of more complex SFHs in (2011)the UVJ diagram, including bursts and other composite SFHs."," \citet{patel2011} show the color evolution of more complex SFHs in the $UVJ$ diagram, including bursts and other composite SFHs."
 We reiterate their finding that the slightest amount of star formation (SF) on top of a dominant older stellar population can easily move galaxies from the quiescent region to the star forming region., We reiterate their finding that the slightest amount of star formation (SF) on top of a dominant older stellar population can easily move galaxies from the quiescent region to the star forming region.
 The SSP and CSF models shown here are intended to provide a simple overview of the kinds of SFHs that can produce colors consistent with UVJ classified quiescent and SFGs., The SSP and CSF models shown here are intended to provide a simple overview of the kinds of SFHs that can produce colors consistent with $UVJ$ classified quiescent and SFGs.
" \Rhtalgtaah..T A ddetections primarily trace the region of the UVJ diagram occupied by SFGs including those with the reddest colors (U—V>1.7 AB mag), therefore providing empirical support for the Williamsetal.(2009) boundary."," Finally, \citet{patel2011} showed that MIPS 24 detections primarily trace the region of the $UVJ$ diagram occupied by SFGs including those with the reddest colors $U-V>1.7$ AB mag), therefore providing empirical support for the \citet{williams2009} boundary."
" WithHST ACS imaging, we gain anew understanding for the kinds of galaxies that populate various regions of the UV diagram."," With ACS imaging, we gain anew understanding for the kinds of galaxies that populate various regions of the $UVJ$ diagram."
 These data provide perhaps the most informativeJ explanation as to why the UVJ selection works as well as it does., These data provide perhaps the most informative explanation as to why the $UVJ$ selection works as well as it does.
" In Figure 2,, for three different mass bins, we show the UVJ diagram populated with"," In Figure \ref{fig_UVJ_ACS_binmass}, , for three different mass bins, we show the $UVJ$ diagram populated with"
The mechanisms behind the pulsed radio emission of magnetars are poorly understood.,The mechanisms behind the pulsed radio emission of magnetars are poorly understood.
 It is not ruled out that their radio emission is related to the braking in a way similar to that of the ordinary radio pulsars. but the radio properties of the two magnetars detected so far in radio. XTEJII8I0-197 and IET1547.0-5408. are quite distinguishing: their flux is highly variable on daily timescales. their spectrum is very flat. and their average pulse profile changes with time. from minutes to days (2???).," It is not ruled out that their radio emission is related to the braking in a way similar to that of the ordinary radio pulsars, but the radio properties of the two magnetars detected so far in radio, J1810–197 and 1547.0–5408, are quite distinguishing: their flux is highly variable on daily timescales, their spectrum is very flat, and their average pulse profile changes with time, from minutes to days \citep{camilo06,camilo07,camilo08,kramer07}."
 ? (2. (2 ," \citet{camilo08atel1558} \citep{corbel99}, \citealt{camilo08atel1558} "
to the temperature of interest (ivpically 1000 Ix. for sub-stellar brown dwarls).,to the temperature of interest (typically 1000 K for sub-stellar brown dwarfs).
 For (his reason. (hese extrapolated spectra rarely match observations satisfactorily (see Figure 1)) due to the lack of hot bands ancl highly-exeited rotational transitions which contribute significantly to the SED in these temperature ranges.," For this reason, these extrapolated spectra rarely match observations satisfactorily (see Figure \ref{fig1}) ) due to the lack of hot bands and highly-excited rotational transitions which contribute significantly to the SED in these temperature ranges."
 Along with brown dwarls. it has only recently become possible to detect planets outside of the Solar System (exoplanets).," Along with brown dwarfs, it has only recently become possible to detect planets outside of the Solar System (exoplanets)."
 51 Pegasi b was the pioneering discovery by (1995) (hat paved the way for many more exoplauet detections. wilh over 500 discovered to date (http://exoplanet.eu/).," 51 Pegasi b was the pioneering discovery by \citet{mandq95} that paved the way for many more exoplanet detections, with over 500 discovered to date (http://exoplanet.eu/)."
 The vast majority of these exoplanets are large eas glants close to their parent star with high temperature gaseous atmospheres (wpically relerred (o as ‘hot Jupiters., The vast majority of these exoplanets are large gas giants close to their parent star with high temperature gaseous atmospheres typically referred to as `hot Jupiters'.
 The new technique of transit spectroscopy. (Charbonneauel2000) has been used to probe exoplanet atmospheres (Charbonneauetal.2002). and familiar molecules such as 40. CII;. CO and COs have all been shown to be present in exanples like the well studied ID 209458b (Swainetal.2009:Snellen2010).," The new technique of `transit spectroscopy' \citep{char00} has been used to probe exoplanet atmospheres \citep{char02} and familiar molecules such as $_{2}$ O, $_{4}$, CO and $_{2}$ have all been shown to be present in examples like the well studied HD 209458b \citep{swain09,snellen10}."
. The properües (composition. temperature/pressure profiles. etc.)," The properties (composition, temperature/pressure profiles, etc.)"
 of exoplanet abtmospheres retrieved [rom the emergent flux or from (ransil spectroscopy depend on the molecular opacities used to simulate the observed spectra., of exoplanet atmospheres retrieved from the emergent flux or from transit spectroscopy depend on the molecular opacities used to simulate the observed spectra.
 Spectroscopic studies of brown cdwarfs and exoplanet atmospheres therelore need improved line parameters for hot NIL; and CIL., Spectroscopic studies of brown dwarfs and exoplanet atmospheres therefore need improved line parameters for hot $_{3}$ and $_{4}$.
" Currently the best line list for NIL, is the LITRAN 2008 database. which is incomplete and has insufficient hot band information for the astronomical applications considered here."," Currently the best line list for $_{3}$ is the HITRAN 2008 database, which is incomplete and has insufficient hot band information for the astronomical applications considered here."
" Aloreover recent theoretical work has demonstrated that HETBRAN 2008 has many errors in «quantum number assignments of NIL, (huangetal.2011b:;Yurchenko 2009)..."," Moreover recent theoretical work has demonstrated that HITRAN 2008 has many errors in quantum number assignments of $_{3}$ \citep{huang11b, yurchenko09}. ."
 NIL; has already been shown to contribute significantly to the SED of brown dwarls al 2620 Ix (Delormeetal.2008)., $_{3}$ has already been shown to contribute significantly to the SED of brown dwarfs at $\sim$ 620 K \citep{delorme08}.
. Improved theoretical predictions for the vibration-rotation lines will help toassign the complicated spectra of NII4 (Zobovetal.2011) presented in (this paper., Improved theoretical predictions for the vibration-rotation lines will help toassign the complicated spectra of $_{3}$ \citep{zobov11} presented in this paper.
observed pattern complies with models including general (gravitational redshift and light bending) and special (Doppler boosting) relativistic effects.,observed pattern complies with models including general (gravitational redshift and light bending) and special (Doppler boosting) relativistic effects.
" We will describe the method, and discuss the probability of detecting such events in present and future observations."," We will describe the method, and discuss the probability of detecting such events in present and future observations."
" In particular, we will show that it is already possible to detect these effects today withXMM-Newton andSuzaku observations, if a complete, Compton-thick occultation occurs: this appears to be a rare event, but not an impossible one."," In particular, we will show that it is already possible to detect these effects today with and observations, if a complete, Compton-thick occultation occurs: this appears to be a rare event, but not an impossible one."
" We will then show that the proposed test may become almost routine with future large-area observatories, which will be able to detect the same effects during partial and/or Compton-thin eclipses: the statistics of black hole eclipses available today guarantees a high probability of success."," We will then show that the proposed test may become almost routine with future large-area observatories, which will be able to detect the same effects during partial and/or Compton-thin eclipses: the statistics of black hole eclipses available today guarantees a high probability of success."
 Here we review briefly the current evidence for occultations in AGNs., Here we review briefly the current evidence for occultations in AGNs.
 A comparison of column density measurements showed that cold absorption variability in obscured (Ng>1033 cm~?) AGNs is almost ubiquitous (Risaliti et al., A comparison of column density measurements showed that cold absorption variability in obscured $_H>10^{22}$ $^{-2}$ ) AGNs is almost ubiquitous (Risaliti et al.
 2002)., 2002).
" In the last few years, several cases have been discussed where such variations occur in times scales compatible with a single X-ray observation: the best studied case is NGC 1365 (Risaliti et al."," In the last few years, several cases have been discussed where such variations occur in times scales compatible with a single X-ray observation: the best studied case is NGC 1365 (Risaliti et al."
" 2005, 2007, 2009A, 2009B, Brenneman et al."," 2005, 2007, 2009A, 2009B, Brenneman et al."
" 2011, in prep.),"," 2011, in prep.),"
" where several occultations have been measured, both by Compton-thick (Ny 1034 επι3) and Compton-thin (Ng -1-5x10? cm clouds."," where several occultations have been measured, both by Compton-thick $_H>$ $^{24}$ $^{-2}$ ) and Compton-thin $_H\sim$ $\times$ $^{23}$ $^{-2}$ ) clouds."
" For this source, the high quality of the available?) data allowed a detailed analysis of the structure of the X-ray absorber."," For this source, the high quality of the available data allowed a detailed analysis of the structure of the X-ray absorber."
 The other well studied cases are NGC 4388 (Elvis et al., The other well studied cases are NGC 4388 (Elvis et al.
" 2004), NGC 4151 (Puccetti et al."," 2004), NGC 4151 (Puccetti et al."
" 2007), NGC 7582 (Bianchi et al."," 2007), NGC 7582 (Bianchi et al."
" 2009), Mrk 766 (Risaliti et al."," 2009), Mrk 766 (Risaliti et al."
" 2011), UGC 4203 (Risaliti et al."," 2011), UGC 4203 (Risaliti et al."
 2010)., 2010).
" A few more events have been found by our group in archival observations (NGC 4395, MCG-6-30-15), and will be discussed in forthcoming papers."," A few more events have been found by our group in archival observations (NGC 4395, MCG-6-30-15), and will be discussed in forthcoming papers."
 An updated summary of the measured g variations is reported in Risaliti (2009)., An updated summary of the measured $_H$ variations is reported in Risaliti (2009).
" A complete discussion of the consequences of these observations is beyond the purpose of this Letter, and will be presented elsewhere."," A complete discussion of the consequences of these observations is beyond the purpose of this Letter, and will be presented elsewhere."
 In the following we only point out the aspects relevant for the present 1) Eclipses on time scales of hours arecommon among AGNs., In the following we only point out the aspects relevant for the present 1) Eclipses on time scales of hours are among AGNs.
" The above-mentioned sources are among the 20-30 intrinsically brightest AGNs in X-ray (as found, for example, in the Swift-BAT Catalog, Cusumano et al."," The above-mentioned sources are among the 20-30 intrinsically brightest AGNs in X-ray (as found, for example, in the -BAT Catalog, Cusumano et al."
 2009)., 2009).
" Even if the sample is not yet suited for a quantitative analysis, it is large enough to conclude that eclipses are not rare events, in the sense that if several bright AGNs are observed for at least a few 10* s each, we have a high probability of finding a few eclipsing events."," Even if the sample is not yet suited for a quantitative analysis, it is large enough to conclude that eclipses are not rare events, in the sense that if several bright AGNs are observed for at least a few $^4$ s each, we have a high probability of finding a few eclipsing events."
" 2) The occultation times, from a few hours to a few days, and the measured column densities, put strong constraints on the size of the X-ray source and on the size and distance of the absorber."," 2) The occultation times, from a few hours to a few days, and the measured column densities, put strong constraints on the size of the X-ray source and on the size and distance of the absorber."
" While we refer to our papers on single eclipses for a more detailed treatment of this point, here we summarize the main argument: - the limits on the ionization state of the obscuring clouds, and the estimate of the ionizing luminosity from the intrinsic X-ray flux, provide a relation between the density of the cloud (i.e. its linear size, since the column density is measured) and its distance from the center. -"," While we refer to our papers on single eclipses for a more detailed treatment of this point, here we summarize the main argument: - the limits on the ionization state of the obscuring clouds, and the estimate of the ionizing luminosity from the intrinsic X-ray flux, provide a relation between the density of the cloud (i.e. its linear size, since the column density is measured) and its distance from the center. -"
" the assumption of Keplerian velocity, and the requirement that the size of the cloud is of the same"," the assumption of Keplerian velocity, and the requirement that the size of the cloud is of the same"
coordinate svstem are listed in Table 1 at epoch JD 2452274.0.,coordinate system are listed in Table 1 at epoch JD 2452274.0.
 The svstem shown in Table 1 was found to be stable in MeArthural... but it was also noted that the svstem is close to the stability boundary.," The system shown in Table 1 was found to be stable in McArthur, but it was also noted that the system is close to the stability boundary."
 Therefore we cannot exclude the possibility that other solutions may result in significantly different dvnamical behavior., Therefore we cannot exclude the possibility that other solutions may result in significantly different dynamical behavior.
 Here and below we assume that such a situation is not the case., Here and below we assume that such a situation is not the case.
 The orbits of planets c and d undergo mutual perturbations which cause periodic variations in orbital elements over thousands of orbits., The orbits of planets c and d undergo mutual perturbations which cause periodic variations in orbital elements over thousands of orbits.
 The long-term changes can be conveniently divided into two parts: the apsidal evolution (changes in eccentricitv ο and longitude of periastron zc) and (he nodal evolution (changes in inclination 7. longitude of ascending node O. and hence the mutual inclination V).," The long-term changes can be conveniently divided into two parts: the apsidal evolution (changes in eccentricity $e$ and longitude of periastron $\varpi$ ) and the nodal evolution (changes in inclination $i$, longitude of ascending node $\Omega$, and hence the mutual inclination $\Psi$ )."
 The variations. starting with the conditions in Table 1. are shown in Fig. 1..," The variations, starting with the conditions in Table 1, are shown in Fig. \ref{fig:secular}."
 In this figure. we chose a Jacobi coordinate svstem in order to minimize frequencies due to the reflex motion of the star.," In this figure, we chose a Jacobi coordinate system in order to minimize frequencies due to the reflex motion of the star."
 In Fig., In Fig.
 1 (he left panels show the apsidal behavior. and the right show the nodal behavior.," \ref{fig:secular} the left panels show the apsidal behavior, and the right show the nodal behavior."
 The lines of apse oscillate about zc=πι. anti-aligned major axes.," The lines of apse oscillate about $\Delta\varpi = \pi$, anti-aligned major axes."
 This revision once again changes the expected apsidal evolution., This revision once again changes the expected apsidal evolution.
 Initially Chiang Murray (2002) and Malhotra (2002) found the major axes oscillated about alignment., Initially Chiang Murray (2002) and Malhotra (2002) found the major axes oscillated about alignment.
 Then Ford (2005: see also Barnes Greenberg 20062.0) found the svstem was better described as “hear-separalvix.” meaning the apsides lie close to the boundary between libration and circulation.," Then Ford (2005; see also Barnes Greenberg 2006a,c) found the system was better described as “near-separatrix,” meaning the apsides lie close to the boundary between libration and circulation."
 Now we find that the svstem found by MeArthur (2010) librates in an anti-aligned sense!, Now we find that the system found by McArthur (2010) librates in an anti-aligned sense!
 Substantial research has examined the secular behavior of exoplanetary svstems. vet the story of Απ shows that predicting the dvnamical evolution of a planetary svstem based on minimum masses and poorly constrained eccentricilies is uncertain al best and foolhardy at worst.," Substantial research has examined the secular behavior of exoplanetary systems, yet the story of $\upsilon$ And shows that predicting the dynamical evolution of a planetary system based on minimum masses and poorly constrained eccentricities is uncertain at best and foolhardy at worst."
 Even now. without full three-dimensional information about planets b. and ο (a (trend seen in MeArthur TTable 2: Dynamical Properties of e and," Even now, without full three-dimensional information about planets b and e (a trend seen in McArthur Table 2: Dynamical Properties of c and"
emission and subimun flix of Ser A*.,emission and submm flux of Sgr A*.
 Exceptions to this trend are two data points at 7.8h UT during, Exceptions to this trend are two data points at 7.8h UT during
equilibrium is maintained over a few million years. as long as the disks are optically thick. aud is independent of the population or cuvironment studied.,"equilibrium is maintained over a few million years, as long as the disks are optically thick, and is independent of the population or environment studied."
 Iu this paper we present a comprehensive study of the mineralogical composition of disks around stars in voung star-forming regions (where most stars are stil surrounded by optically thick disks) aud older clusters Gvhere the majority of disks has already dissipated)., In this paper we present a comprehensive study of the mineralogical composition of disks around stars in young star-forming regions (where most stars are still surrounded by optically thick disks) and older clusters (where the majority of disks has already dissipated).
 Correlating the results on mean size aud composition of dust erains per region. obtained m a homogencous wav using the same methodology. with the properties of s2al )xdies in our own Solar System can put constraints ou some of the processes responsible for disk evolution iux auet formation.," Correlating the results on mean size and composition of dust grains per region, obtained in a homogeneous way using the same methodology, with the properties of small bodies in our own Solar System can put constraints on some of the processes responsible for disk evolution and planet formation."
 The Serpeus Molecular Cloud. whose complete ftux-Iiited YSO population has been observec w the IRS instrument (Oliveiractal.2010)... is use as a prototype of a voung star-forming region. together with Taurus. the best studied region to date.," The Serpens Molecular Cloud, whose complete flux-limited YSO population has been observed by the IRS instrument \citep{OL10}, is used as a prototype of a young star-forming region, together with Taurus, the best studied region to date."
 The sources hat have retained their protopluietary disks in the j Chamacleoutis aud Upper Scorpius clusters are used to xobe the mineralogv in the older bin of disk evolution., The sources that have retained their protoplanetary disks in the $\eta$ Chamaeleontis and Upper Scorpius clusters are used to probe the mineralogy in the older bin of disk evolution.
 Section 2. describes the YSO samples in the | regions nentioncd., Section \ref{sdata} describes the YSO samples in the 4 regions mentioned.
 TheSpitzer IRS observations aud reduction are explained., The IRS observations and reduction are explained.
 The spectral decomposition method B2C (Olofssonctal.2010) is brieflv iutroduced in 3. aud its results for individual and mean cluster eraiu sizes and composition are shown in Ll.," The spectral decomposition method B2C \citep{OF10} is briefly introduced in \ref{s_spdecomp}, and its results for individual and mean cluster grain sizes and composition are shown in \ref{sres}."
 In 5 the results are discussed in the context of time evolution., In \ref{sdis} the results are discussed in the context of time evolution.
 There we demonstrate that no evolution is secu in either mean eran sizes or crystallinity fractions as clusters evolve from 1 to 8 Myr., There we demonstrate that no evolution is seen in either mean grain sizes or crystallinity fractions as clusters evolve from $\sim$ 1 to 8 Myr.
 The iuplicatious for disk formation and dissipation. and plauet formation are discussed.," The implications for disk formation and dissipation, and planet formation are discussed."
 Iu 6 we preseut our conclusions., In \ref{scon} we present our conclusions.
 The four regious presented here were chosen due to the availability of complete sets of IRS spectra of their Ift-excess sources. while spauniug a wide range of stellar characteristics. environment. ican ages and disk fractious (the disk fraction of Serpens is still unknown. see Table 1)).," The four regions presented here were chosen due to the availability of complete sets of IRS spectra of their IR-excess sources, while spanning a wide range of stellar characteristics, environment, mean ages and disk fractions (the disk fraction of Serpens is still unknown, see Table \ref{t_overview}) )."
 The IRS spectra of a complete flux-liited sample of voung stellar objects (YSO) in the Serpeus. Molecular Cloud have Όσοι. presented dy Oliveiractal.(2010).. based on program ID #330223 (PL Poutoppidan).," The IRS spectra of a complete flux-limited sample of young stellar objects (YSO) in the Serpens Molecular Cloud have been presented by \citet{OL10}, based on program ID 30223 (PI: Pontoppidan)."
 As detailed there. the spectra were extracted from the basic calibration data (BCD) using the reduction pipeline frou the Spitzer Legacy. Program “Frou Molecular Cores to Plauct-Forming Disks” (c2d. Laluisetal. 2006)).," As detailed there, the spectra were extracted from the basic calibration data (BCD) using the reduction pipeline from the Spitzer Legacy Program “From Molecular Cores to Planet-Forming Disks” (c2d, \citealt{LH06}) )."
 A similarly large YSO sample in the Taurus star-forming region has been preseuted by Furlanetal.(2006)., A similarly large YSO sample in the Taurus star-forming region has been presented by \citet{FU06}.
. IRS spectra of all 18 members of the 7 Chamacleoutis cluster were first shown by Sicilia-Aeuilaretal.(2009).. while he spectra of 26 out of the 35 TR-excess sources in the Upper Scorpius OB association were shown bv Daluu&Carpenter(2009). (the remaining 9 objects were nof shown at the time the observations were proposed).," IRS spectra of all 18 members of the $\eta$ Chamaeleontis cluster were first shown by \citet{SI09}, while the spectra of 26 out of the 35 IR-excess sources in the Upper Scorpius OB association were shown by \citet{DC09} (the remaining 9 objects were not known at the time the observations were proposed)."
 For the latter 3 regious. the post-BCD data were downloaded from the SSC pipeline (version SLs. aud hen extracted with the Spitzer IRS Custom Extractionl) software (SPICE. version 2.3) using the batch ecueric eniplate for point sources.," For the latter 3 regions, the post-BCD data were downloaded from the SSC pipeline (version S18.4) and then extracted with the Spitzer IRS Custom Extraction software (SPICE, version 2.3) using the batch generic template for point sources."
 As a test. the IRS spectra of the YSOs in Serpeus were also reduced using SPICE o ensure that both pipelines produce uecarly ideutical results.," As a test, the IRS spectra of the YSOs in Serpens were also reduced using SPICE to ensure that both pipelines produce nearly identical results."
 Ou visual inspection. no discrepancies were found between the results from the two pipelines. all objects showed the exact same features in both spectra.," On visual inspection, no discrepancies were found between the results from the two pipelines, all objects showed the exact same features in both spectra."
" The sinularity iu outputs is such that the effects on the spectral decomposition results are within the cited error ars,", The similarity in outputs is such that the effects on the spectral decomposition results are within the cited error bars.
 Since the spectral decomposition method applied here alus to reproduce the silicate ciission from. dust yarticles im circumstellar disks. the sample has been nuited to spectra that show clear silicate features.," Since the spectral decomposition method applied here aims to reproduce the silicate emission from dust particles in circumstellar disks, the sample has been limited to spectra that show clear silicate features."
 The ‘ow sources with PAID cimission have been excluded roni the sample., The few sources with PAH emission have been excluded from the sample.
 PAID sources amount to less than in low-inass star-forming reeious (Geersetal.2006:Oliveiraetal.2010).," PAH sources amount to less than in low-mass star-forming regions \citep{GE06,OL10}."
. Furthermore. spectra with verv ow signal-to-noise ratios (S/N) are excluded. from the analysed sample in order to euarautee the quality of 1ο results.," Furthermore, spectra with very low signal-to-noise ratios (S/N) are excluded from the analysed sample in order to guarantee the quality of the results."
 Iu addition. for objects #1111 aud 137 oeu Serpeus. aud 0137012559 and V955Tau iu Taurus le Κα coniponent ft contributes to most of the spectrum. leaving very low fluxes to be fitted by the cold conrponeut.," In addition, for objects 114 and 137 in Serpens, and 04370+2559 and V955Tau in Taurus the warm component fit contributes to most of the spectrum, leaving very low fluxes to be fitted by the cold component."
 This produces large uncertainties iu the cold component fit. and they are therefore not further used iu the analvsis.," This produces large uncertainties in the cold component fit, and they are therefore not further used in the analysis."
 The low S/N objects rejected amount to less than 10% of cach of the Serpeus aud Taurus samples. so the statistical results derived here should not be affected by this removal.," The low S/N objects rejected amount to less than 10 of each of the Serpens and Taurus samples, so the statistical results derived here should not be affected by this removal."
 The final sample of 139 sources analysed is composed of 60 objects iu Serpeus. 66 in Taurus. 9 objects in Upper Scorpius. aud tiny Chamacleoutis.," The final sample of 139 sources analysed is composed of 60 objects in Serpens, 66 in Taurus, 9 objects in Upper Scorpius, and 4 in $\eta$ Chamaeleontis."
 The statistical uncertainties of the spectra were estimated as explained in Olofssonetal.(2009)., The statistical uncertainties of the spectra were estimated as explained in \citet{OF09}.
. The ercat majority of the objects studied here are mmass stars (spectral types I& aud M. see Table A5)).," The great majority of the objects studied here are low-mass stars (spectral types K and M, see Table \ref{t_comp}) )."
 The study of mineralogical evolution across stellar mass is not the focus of this paper., The study of mineralogical evolution across stellar mass is not the focus of this paper.
 Such a study would require a separate paper. in which the same techniques are used for low- and intermecdiate-ass stars.," Such a study would require a separate paper, in which the same techniques are used for low- and intermediate-mass stars."
 Thus. the statistical results derived in the following sections concern T Tauri stars. and not uccessarily apply to intermediate-uass Herbie Ac/Be stars.," Thus, the statistical results derived in the following sections concern T Tauri stars, and not necessarily apply to intermediate-mass Herbig Ae/Be stars."
 Tn order to reproduce the observed IRS spectra of these circumstellar disks the B2C decomposition method. explained in detail aud tested extensively in Olofssonetal. (2010).. is applied.," In order to reproduce the observed IRS spectra of these circumstellar disks the B2C decomposition method, explained in detail and tested extensively in \citet{OF10}, is applied."
" Two dust eram populations. or colmpoucuts, at different temperatures (varm and cold) are used in the method. iu addition to a continua clnission."," Two dust grain populations, or components, at different temperatures (warm and cold) are used in the method, in addition to a continuum emission."
 The wari component reproduces the 10 pau feature. while the cold compoucut reproduces the uou-ueeleible residuals at longer waveleneths. over the full spectral range (see Figure 1)).," The warm component reproduces the 10 $\mu$ m feature, while the cold component reproduces the non-negligible residuals at longer wavelengths, over the full spectral range (see Figure \ref{f_fit}) )."
 Each component. wari. and cold. is the combination of five different dust species and three erain sizes for amorphous silicates or two erain sizes for crystalline silicates.," Each component, warm and cold, is the combination of five different dust species and three grain sizes for amorphous silicates or two grain sizes for crystalline silicates."
" The three amorphous species are silicates of olivine stoichiometry (AIeFeSiO,). silicates of pyroxene stoichiometry (MgFeSiOG). and silica (SiO2)."," The three amorphous species are silicates of olivine stoichiometry $_4$ ), silicates of pyroxene stoichiometry $_6$ ), and silica $_2$ )."
" The two crystalline species are both Ale-rich eud μονος of the pyroxene and olivine groups. custatite (MeSiO5). and forsterite (Ale.SiO,)."," The two crystalline species are both Mg-rich end members of the pyroxene and olivine groups, enstatite $_3$ ) and forsterite $_2$ $_4$ )."
 As further explained in Olofssou (2010).. the theoretical opacities of the amorphous species are computed assuming homogeneous spheres (Mie theory). while those for the crystalline species use the distribution of hollow spheres (DIIS.," As further explained in \citet{OF10}, the theoretical opacities of the amorphous species are computed assuming homogeneous spheres (Mie theory), while those for the crystalline species use the distribution of hollow spheres (DHS,"
Our understanding of heating and cooling mechanisms operating 11 the hot Intra-Cluster Medium (ICM) in the cores of clusters of galaxies is not yet complete.,Our understanding of heating and cooling mechanisms operating in the hot Intra-Cluster Medium (ICM) in the cores of clusters of galaxies is not yet complete.
 The cooling times of the relatively dense X-ray emitting plasma in the central region are short compared to the Hubble time. which lead to the theory of cooling-flows (e.g.?)..," The cooling times of the relatively dense X-ray emitting plasma in the central region are short compared to the Hubble time, which lead to the theory of cooling-flows \citep[e.g.][]{fabian1994}."
 The first cluster observations with the high-resolution Reflection Grating Spectrometer (RGS.?) aboard XMM-Newton show. however. that the amount of cool gas in the centre of clusters is much smaller than expected (2???)..," The first cluster observations with the high-resolution Reflection Grating Spectrometer \citep[RGS,][]{herder2001} aboard XMM-Newton show, however, that the amount of cool gas in the centre of clusters is much smaller than expected \citep{peterson2001,tamura2001a,kaastra2001,peterson2003}."
 In recent years. it has been suggested that this lack of cool gas can be explained by feedback from the central Active Galactic. Nucleus (AGN).," In recent years, it has been suggested that this lack of cool gas can be explained by feedback from the central Active Galactic Nucleus (AGN)."
 The relativistic plasma in the jets originating from this accreting central super-massive black hole creates cavities in the hot X-ray emitting gas. which appear as dark regions in X-ray images of clusters.," The relativistic plasma in the jets originating from this accreting central super-massive black hole creates cavities in the hot X-ray emitting gas, which appear as dark regions in X-ray images of clusters."
 The energy enclosed in these plasma bubbles appears to be enough to balance the cooling flow (e.g.???)..," The energy enclosed in these plasma bubbles appears to be enough to balance the cooling flow \citep[e.g.][]{churazov2002,bruggen2002,birzan2004}."
 The mechanism responsible for gently transferring the energy from the bubbles to the X-ray gas is. however. still unclear.," The mechanism responsible for gently transferring the energy from the bubbles to the X-ray gas is, however, still unclear."
 The lowest temperatures detected in clusters through rays are about 0.5 keV.which appears to be a universal floor for clusters and groups.," The lowest temperatures detected in clusters through X-rays are about 0.5 keV,which appears to be a universal low-temperature floor for clusters and groups."
 However. these low-temperature regions are usually found in clusters which show AGN activity. like. for example. (?).. (?).. and (e.g.?)..," However, these low-temperature regions are usually found in clusters which show AGN activity, like, for example, \citep{mcnamara2000}, \citep{sanders2007}, and \citep[e.g.][]{werner2010}."
 This appears contradictory. because AGN are supposed to heat the gas.," This appears contradictory, because AGN are supposed to heat the gas."
 Studies of the volume filling fraction of this 0.5 keV component (e.g.??) show that the cool gas is actually distributed in clumps or filaments.," Studies of the volume filling fraction of this 0.5 keV component \citep[e.g.][]{sanders2002,sanders2004} show that the cool gas is actually distributed in clumps or filaments."
 This suggests that gas can cool locally to low temperatures despite the fact that it is embedded in hotter gas., This suggests that gas can cool locally to low temperatures despite the fact that it is embedded in hotter gas.
 In many clusters these cool regions are seen at the same position as bright Hcr regions and filaments detected in optical images of these clusters., In many clusters these cool regions are seen at the same position as bright $\alpha$ regions and filaments detected in optical images of these clusters.
 The connection between the 0.5 keV gas and He emission ts an important piece of the puzzle of understanding heating and cooling in cluster cores., The connection between the 0.5 keV gas and $\alpha$ emission is an important piece of the puzzle of understanding heating and cooling in cluster cores.
 On slightly larger scales. disturbances due to merger events cause the dark matter and subsequently the hot X-ray gas to oscillate in the deep gravitational potential well of a cluster.," On slightly larger scales, disturbances due to merger events cause the dark matter and subsequently the hot X-ray gas to oscillate in the deep gravitational potential well of a cluster."
 This sloshing of gas is usually recognised in X-ray images through asymmetries and jumps in the surface brightness of the hot gas., This sloshing of gas is usually recognised in X-ray images through asymmetries and jumps in the surface brightness of the hot gas.
 The underlying density discontinuity. also called a cold front. marks the boundary between relatively cool moving gas from the central part of the cluster and the hot gas in the outer regions (see?.forareview)..," The underlying density discontinuity, also called a cold front, marks the boundary between relatively cool moving gas from the central part of the cluster and the hot gas in the outer regions \citep[see][for a review]{markevitch2007}."
 The slow release of mechanical energy from the sloshing movements and the mixing of hot gas from the outer parts into the cooling core may both contribute to heat the inner parts of the cluster in concurrence with the AGN., The slow release of mechanical energy from the sloshing movements and the mixing of hot gas from the outer parts into the cooling core may both contribute to heat the inner parts of the cluster in concurrence with the AGN.
 Sloshing is probably also an important mechanism for transporting metals from the metal-rich core to the metal-poor outer parts (?).., Sloshing is probably also an important mechanism for transporting metals from the metal-rich core to the metal-poor outer parts \citep{simionescu2010}. .
 The cluster of galaxies ts also a bright cool-core cluster in X-rays showing AGN activity and Ha regions (?).., The cluster of galaxies is also a bright cool-core cluster in X-rays showing AGN activity and $\alpha$ regions \citep{blanton2001}.
 The cluster was detected and studied in the 1970's (22)..," The cluster was detected and studied in the 1970's \citep{giacconi1972,heinz1974}."
 is also extensively studied with the current generation of X-ray observatories., is also extensively studied with the current generation of X-ray observatories.
 It was member of several samples of clusters observed with ASCA (?) and XMM-Newton (e.g. ?2??)..," It was member of several samples of clusters observed with ASCA \citep{finoguenov2001} and XMM-Newton \citep[e.g.][]{kaastra2004,tamura2004,deplaa2007}."
 Chandra images (???) show evidence of AGN feedback by the central radio source (?)..," Chandra images \citep{blanton2001,blanton2003,blanton2009} show evidence of AGN feedback by the central radio source \citep{zhao1993}."
 In the inner core (< 1.0) of the cluster. the X-ray image shows bubbles which are associated with the radio lobes of317.," In the inner core $<$ $^{\prime}$ ) of the cluster, the X-ray image shows bubbles which are associated with the radio lobes of."
. The energy contained in the cavities ts thought to effectively heat the Intra-Cluster Medium (ICM)., The energy contained in the cavities is thought to effectively heat the Intra-Cluster Medium (ICM).
 In addition. density discontinuities. probably shocks have been detected by Chandra (?) just outside the region with the bubbles.," In addition, density discontinuities, probably shocks have been detected by Chandra \citep{blanton2009} just outside the region with the bubbles."
 We have obtained a long observation of Abell 2052 with XMM-Newton. which was performed in 2007.," We have obtained a long observation of Abell 2052 with XMM-Newton, which was performed in 2007."
 In this paper. we combine this new observation with an older AOT observation of ~ 40 ks and study the thermodynamies m and around the core.," In this paper, we combine this new observation with an older AO1 observation of $\sim$ 40 ks and study the thermodynamics in and around the core."
 We use the spatially resolved spectra from the European Photon Imaging Camera (EPIC) to make two-dimensional maps., We use the spatially resolved spectra from the European Photon Imaging Camera (EPIC) to make two-dimensional maps.
" In our analysis. we use Hp = 70 km s! Mpe!. ©, = 0.3. and Q4 = 0.7."," In our analysis, we use $_{0}$ = 70 km $^{-1}$ $^{-1}$, $\Omega_{\mathrm{m}}$ = 0.3, and $\Omega_{\Lambda}$ = 0.7."
 At the redshift of Abell 2052 (220.0348). an angular distance of I’ corresponds to 42 kpe.," At the redshift of Abell 2052 $z$ =0.0348), an angular distance of $^{\prime}$ corresponds to 42 kpc."
 The elemental abundances presented in this paper aregiven relative to the proto-solar abundances from ? .., The elemental abundances presented in this paper aregiven relative to the proto-solar abundances from \citet{lodders2003}. .
 Measurement errors are given at confidence level., Measurement errors are given at confidence level.
"Msg=-17.2 adopting distances of 4.5 and 9.5 Mpc, respectively).","$M_B=-17.2$ adopting distances of 4.5 and 9.5 Mpc, respectively)."
 Panel (b) of Fig., Panel (b) of Fig.
" 3 also suggests that the apparent positive abundance gradient obtained in the outer disc of NGC 4625 from the use of the upper branch of R23 could be due to small number statistics at large radius, since the scatter of the points is similar for the two galaxies, and M83 does not show a positive gradient in its outer parts."," \ref{fig:abund} also suggests that the apparent positive abundance gradient obtained in the outer disc of NGC 4625 from the use of the upper branch of $_{23}$ could be due to small number statistics at large radius, since the scatter of the points is similar for the two galaxies, and M83 does not show a positive gradient in its outer parts."
 This would imply that the Ros-inferred change of slope between inner and outer disc of NGC 4625 would be made roughly consistent with what is observed with the other diagnostics., This would imply that the $_{23}$ -inferred change of slope between inner and outer disc of NGC 4625 would be made roughly consistent with what is observed with the other diagnostics.
 Earlier on (Fig. 2)), Earlier on (Fig. \ref{fig:bpt}) )
" we showed the familiar BPT diagnostic diagrams for our sample in NGC 4625, concluding that all objects were indeed photoionized nebulae."," we showed the familiar BPT diagnostic diagrams for our sample in NGC 4625, concluding that all objects were indeed photoionized nebulae."
" However, these plots also revealed a subset of outer disc rregions which apparently lie off the main ionisation sequence defined by extragalactic giant rregions in the vvs. pplane, whilst apparently conforming to the less robust sequence formed in the vvs. pplane."," However, these plots also revealed a subset of outer disc regions which apparently lie off the main ionisation sequence defined by extragalactic giant regions in the vs. plane, whilst apparently conforming to the less robust sequence formed in the vs. plane."
" We have arbitrarily subdivided the outer disc rregions in NGC 4625 by making a cut at u1]//H=0.25, represented in Fig."," We have arbitrarily subdivided the outer disc regions in NGC 4625 by making a cut at $\beta = 0.25$, represented in Fig."
 2 with a horizontal dashed line., \ref{fig:bpt} with a horizontal dashed line.
" The outer rregions which lie on the tight, well defined ionisation sequence shown in the left panel of Fig."," The outer regions which lie on the tight, well defined ionisation sequence shown in the left panel of Fig."
 2 fall above our cut and are highlighted with central cyan dots., \ref{fig:bpt} fall above our cut and are highlighted with central cyan dots.
 Those which lie off the ionisation sequence and below our ccut were marked with red dots., Those which lie off the ionisation sequence and below our cut were marked with red dots.
 It is not obvious whether the latter deviate as a result of either a smaller oor a smaller eemission (or both) relative to the sequence defined by bright rregions., It is not obvious whether the latter deviate as a result of either a smaller or a smaller emission (or both) relative to the sequence defined by bright regions.
" We note that a few of the outer disc objects in M83, as well as a small number of nebulae in other galaxies, also lie below and to the left of the ionisation sequence."," We note that a few of the outer disc objects in M83, as well as a small number of nebulae in other galaxies, also lie below and to the left of the ionisation sequence."
" It is worth testing whether these apparently deviant rregions share any common attributes, such as ionising luminosity, spatial distribution, metallicity and so forth."," It is worth testing whether these apparently deviant regions share any common attributes, such as ionising luminosity, spatial distribution, metallicity and so forth."
 This is done in Fig. 4.., This is done in Fig. \ref{fig:hiicross}.
" The top-left panel shows the lline ratio, i.e. the N2 chemical abundance indicator, as a function of galactocentric radius."," The top-left panel shows the line ratio, i.e. the N2 chemical abundance indicator, as a function of galactocentric radius."
 No differential behaviour between the two groups of outer disc rregions (blue and red symbols) is evident., No differential behaviour between the two groups of outer disc regions (blue and red symbols) is evident.
" The two groups also appear to share similar ionising luminosities (upper right and lower left panels) and to be evenly distributed throughout the XUV disc of NGC 4625, without the presence of obvious separate sub-structures (lower right)."," The two groups also appear to share similar ionising luminosities (upper right and lower left panels) and to be evenly distributed throughout the XUV disc of NGC 4625, without the presence of obvious separate sub-structures (lower right)."
" There are slight indications that the deviant rregions have a systematically higher lline ratio than the other outer disc rregions, but this could easily be explained by the variance of the two distributions."," There are slight indications that the deviant regions have a systematically higher line ratio than the other outer disc regions, but this could easily be explained by the variance of the two distributions."
 In the following we consider what might affect the line fluxes in such a way as to produce the observed deviation of a small number of outer disc rregions from the main ionisation sequence in the BPT diagnostic diagram., In the following we consider what might affect the line fluxes in such a way as to produce the observed deviation of a small number of outer disc regions from the main ionisation sequence in the BPT diagnostic diagram.
" The direct observation of the ionising population of nebulae in outer galaxy discs are extremely difficult, thus the properties of the associated stellar clusters have so far been obtained from studies of their aand UV luminosities(???),, together with their IR emission(?)."," The direct observation of the ionising population of nebulae in outer galaxy discs are extremely difficult, thus the properties of the associated stellar clusters have so far been obtained from studies of their and UV luminosities, together with their IR emission."
". The total ionising photon flux of individual clusters can be easily estimated from the lluminosity, using the conversion given by?."," The total ionising photon flux of individual clusters can be easily estimated from the luminosity, using the conversion given by."
. In Fig., In Fig.
" 5 we show histograms of the hydrogen ionising photon flux for both the inner (orange) and outer (green) disc rregions, along with their median values."," \ref{fig:hiiionhist} we show histograms of the hydrogen ionising photon flux for both the inner (orange) and outer (green) disc regions, along with their median values."
" As a reference, we also show the hydrogen ionising fluxes of 09, O6 and O9 dwarf stars, taken from?."," As a reference, we also show the hydrogen ionising fluxes of O3, O6 and O9 dwarf stars, taken from."
". The luminosities that we measure do not account for slit losses, which are expected to be smaller for the outer disc rregions, given that a greater percentage of their flux will fall through the 1” slits compared to the brighter and larger"," The luminosities that we measure do not account for slit losses, which are expected to be smaller for the outer disc regions, given that a greater percentage of their flux will fall through the $''$ slits compared to the brighter and larger"
polvnonual fits to their cross-sections.,polynomial fits to their cross-sections.
 To enable backwarcd compatibility. with MM83 we have adopted (he same fitting Iunction and energv ranges., To enable backward compatibility with MM83 we have adopted the same fitting function and energy ranges.
 The X-ray. photoelectric cross-section per II nucleus. e(£E). is described by the piecewise polynomial fitting Dunction. wwhere E is the A-rav energyand eg. 04. and ο are the coefficients to be found.," The X-ray photoelectric cross-section per H nucleus, $\sigma(E)$, is described by the piecewise polynomial fitting function, where $E$ is the X-ray energyand $c_{0}$ , $c_{1}$, and $c_{2}$ are the coefficients to be found."
 We extend Equation 1. by decomposing the medium into a mixture of gas and dust 1974).., We extend Equation \ref{eq:fn_fitting} by decomposing the medium into a mixture of gas and dust \citep[e.g.][]{Fireman:1974ay}.
 Initially we might split the total cross-section into (wo contributions so that Gor=Tyas+0444 (units ceni per Hl nucleus)., Initially we might split the total cross-section into two contributions so that $\sxtot=\sxgas+\sxdust$ (units $^2$ per H nucleus).
 From the point of view of computing X-ray opacities. the relatively small dust erains in the diffuse ISM can be treated as (hough (heir constituent atoms are in (he gas phase (WOO).," From the point of view of computing X-ray opacities, the relatively small dust grains in the diffuse ISM can be treated as though their constituent atoms are in the gas phase (W00)."
 In this case the distinction between gas and dust can be suspended., In this case the distinction between gas and dust can be suspended.
 As discussed in Section 1. the dust in protoplanetary disks maa undergo both settling aud growth., As discussed in Section \ref{sec:intro} the dust in protoplanetary disks may undergo both settling and growth.
" To accommodate both these phenomena we introduce two quantities. e and f,(E). encapsulating dust settling (the physical removal of dust) and erain growth (sell-blanketing) respectively."," To accommodate both these phenomena we introduce two quantities, $\epsilon$ and $\fb$, encapsulating dust settling (the physical removal of dust) and grain growth (self-blanketing) respectively."
 These are erain-specilic parameters. and as such only alfeet the contribution due to dust.," These are grain-specific parameters, and as such only affect the contribution due to dust."
 Therefore we write the total cross-section as. This is also (rue for combining fitting coelficients. The elemental abundances we have adopted are given in Table 1. 2009)..," Therefore we write the total cross-section as, This is also true for combining fitting coefficients, The elemental abundances we have adopted are given in Table \ref{table_abundances} \citep[based on data from ][]{Asplund:2009jl}. ."
 Itis from these abundances that we make up our total gas-dust, Itis from these abundances that we make up our total gas-dust
"GCs are within 30—40"". bevond which the backeround contamination rises sharply (size measurements are unreliable al these faint magnitudes).","GCs are within $30-40\arcsec$, beyond which the background contamination rises sharply (size measurements are unreliable at these faint magnitudes)."
" Thus lor the dEs we selected only those GC's within 30"" of the center of the galaxy.", Thus for the dEs we selected only those GCs within $30\arcsec$ of the center of the galaxy.
 In the previous sections we used photometric and structural euts to reduce (he nunber of background galaxies ancl foreground stars interloping in our GC samples., In the previous sections we used photometric and structural cuts to reduce the number of background galaxies and foreground stars interloping in our GC samples.
 However. (hese same culs cannot be directly used to fit GCLFs. since these measurements become increasingly inaccurate for lunt GCs (which may then be incorrectly removed).," However, these same cuts cannot be directly used to fit GCLFs, since these measurements become increasingly inaccurate for faint GCs (which may then be incorrectly removed)."
 For example. applying onlv the color cut (0.5<g—z« 2.0) vs. the full selection criteria (ο AIST changes the number of GCs with z«223.5 by (1444 vs. 1210) and shifts the peak of the GCLFE by ~0.1 mag. which is «quite significant.," For example, applying only the color cut $0.5 < g-z < 2.0$ ) vs. the full selection criteria to M87 changes the number of GCs with $z < 23.5$ by (1444 vs. 1210) and shifts the peak of the GCLF by $\sim 0.4$ mag, which is quite significant."
" We directly fit /5 distributions to the three gE GCLFs using using the code of Secker Πανάς (1993). which uses maximunm-likelihood fitting and incorporates photometric errors and incompleteness (Gaussian fits gave similar results within the errors: note that 1.200,45)."," We directly fit $t_5$ distributions to the three gE GCLFs using using the code of Secker Harris (1993), which uses maximum-likelihood fitting and incorporates photometric errors and incompleteness (Gaussian fits gave similar results within the errors; note that $\sigma_{gauss} = 1.29 \, \sigma_{t5}$ )."
 These GCLFs only have a color eut applied: 0.5<g—2«2.0 lor M87 and NGC 4472 and 0.35<g—z«2.0 for NGC 4649 (since stir-Iormine reeions in the nearby spiral NGC! 4647 strongly contaminate the blue part of the CMD)., These GCLFs only have a color cut applied: $0.5 < g-z < 2.0$ for M87 and NGC 4472 and $0.85 < g-z < 2.0$ for NGC 4649 (since star-forming regions in the nearby spiral NGC 4647 strongly contaminate the blue part of the CMD).
 The results are given in Table 2., The results are given in Table 2.
 We fit both total populations and blue and red GC's separately. using the color cuts given in the table.," We fit both total populations and blue and red GCs separately, using the color cuts given in the table."
 Similar to what is commonly seen in V-band GCLFs (e.g.. Larsen 2001). the g turnovers ave ~0.3—0.4 mag brighter for the blue GCs (han the red GC's.," Similar to what is commonly seen in $V$ -band GCLFs (e.g., Larsen 2001), the $g$ turnovers are $\sim 0.3-0.4$ mag brighter for the blue GCs than the red GCs."
 This is predicted for equal-mnass/age turnovers separated by ~1 dex in metallicity (Ashman. Conti Zepl 1995).," This is predicted for equal-mass/age turnovers separated by $\sim 1$ dex in metallicity (Ashman, Conti Zepf 1995)."
 However. in z the blue GC's are only slightly brighter than the red GC's (the mean difference is negligible. but the blue GCs are brighter in M87 and NGC 4472 and fainter in NGC 4649. which may be biased slightly faint because of contamination).," However, in $z$ the blue GCs are only slightly brighter than the red GCs (the mean difference is negligible, but the blue GCs are brighter in M87 and NGC 4472 and fainter in NGC 4649, which may be biased slightly faint because of contamination)."
 This difference between g ancl 2 is qualitatively consistent with stellar population models: Maraston (2005) models predict. that equalamass 18 Gyr GCs with |M/II] = —1.35 and —0.33 will have Ag=0.6 and Az=0.2: the = difference is one-third of the g difference., This difference between $g$ and $z$ is qualitatively consistent with stellar population models: Maraston (2005) models predict that equal-mass 13 Gyr GCs with [M/H] = $-1.35$ and $-0.33$ will have $\Delta g = 0.6$ and $\Delta z = 0.2$; the $z$ difference is one-third of the $g$ difference.
 This ellect is probably due to the greater sensitivity of g to the (urnoll region and the larger nunmber of metal lines in (he blue., This effect is probably due to the greater sensitivity of $g$ to the turnoff region and the larger number of metal lines in the blue.
 The errors for (he blue GCLF parameters may be slightly larger (han formally stated. because of the presence of the Ἡ GCs discussed. previously.," The errors for the blue GCLF parameters may be slightly larger than formally stated because of the presence of the “H"" GCs discussed previously."
 Variations in this feature and in the blue tilt among galaxies could represent a [fundamental limitation (o the accuracy to using the blue GCLF turnover as a standard candle (see. e.g.. Ixissler-Patig 2000).," Variations in this feature and in the blue tilt among galaxies could represent a fundamental limitation to the accuracy to using the blue GCLF turnover as a standard candle (see, e.g., Kissler-Patig 2000)."
 However. the total peak locations themselves are quite constant. with a range of only 0.03 mag in g and 0.05 mag in z.," However, the total peak locations themselves are quite constant, with a range of only 0.03 mag in $g$ and 0.05 mag in $z$."
 At least for the well-populated old GC svstenis of eEs. the GCLF turnover appears (ο be an accurate distance indicator whose primary limitation is accurate photometry.," At least for the well-populated old GC systems of gEs, the GCLF turnover appears to be an accurate distance indicator whose primary limitation is accurate photometry."
 Unfortunately. we cannot directly [it (he composite dE GCLF as for the eEsit is far," Unfortunately, we cannot directly fit the composite dE GCLF as for the gEs—it is far"
abundances will simply be observed as a helium star — for example. studies such as that of Vanbeveren. Van Bever De Donder (1997) take this minimum mass to be 35M..,"abundances will simply be observed as a helium star – for example, studies such as that of Vanbeveren, Van Bever De Donder (1997) take this minimum mass to be $5\, \msun$."
 In the catalogue of van der Hucht (2001) the WR star listed as having the lowest determined mass is WR97. at 2.3M..," In the catalogue of van der Hucht (2001) the WR star listed as having the lowest determined mass is WR97, at $2.3\, \msun$."
 However the source paper for these values (Niemela. Cabanne Bassino 1995) quotes them as lower limits only. with the values corrected for inclination potentially being ten times greater.," However the source paper for these values (Niemela, Cabanne Bassino 1995) quotes them as lower limits only, with the values corrected for inclination potentially being ten times greater."
 The lowest contirmed WR mass is then 39M. for WR31I (Lamontagne et al.," The lowest confirmed WR mass is then $3.9\, \msun$ for WR31 (Lamontagne et al."
 1996)., 1996).
 The most evolved WC stars may also be shrouded by dust. appearing as faint red objects. although we do not consider that here since the lifetimes involved are short.," The most evolved WC stars may also be shrouded by dust, appearing as faint red objects, although we do not consider that here since the lifetimes involved are short."
 There are also a small number of stars in our models with WR-like abundances which become essentially cool He giants., There are also a small number of stars in our models with WR-like abundances which become essentially cool He giants.
 These will be unable to maintain a WR atmosphere., These will be unable to maintain a WR atmosphere.
 We therefore rerun our simulations with the assumption that stars with WR-like composition are not observable if they have masses below 3.9M.. or logTey below 4.0. and that massive stars younger than 10° years are obscured.," We therefore rerun our simulations with the assumption that stars with WR-like composition are not observable if they have masses below $ 3.9 \,\msun$ or ${\log \rm T_{eff}}$ below 4.0, and that massive stars younger than $10^{6}$ years are obscured."
 These are shown in Fig., These are shown in Fig.
 3: panela shows full evolutionary models with conservative mass transfer and these assumptions. and models with non-conservative mass transfer as above.," 3; panel shows full evolutionary models with conservative mass transfer and these assumptions, and models with non-conservative mass transfer as above."
 These changes have a relatively small but positive effect., These changes have a relatively small but positive effect.
 In the case that the runaway fraction amongst O stars is close to the Mason et al. (, In the case that the runaway fraction amongst O stars is close to the Mason et al. (
1998) value of 8 percent. the resulting O star runaway fraction is consistent with the conclusion of Hoogerwerf et al. (,"1998) value of 8 percent, the resulting O star runaway fraction is consistent with the conclusion of Hoogerwerf et al. ("
2000) that two-thirds of massive runaways are from the BSS and the remaining third from dynamical interaction.,2000) that two-thirds of massive runaways are from the BSS and the remaining third from dynamical interaction.
 The WR star runaway fraction is similarly consistent with that of Moffat et al. (, The WR star runaway fraction is similarly consistent with that of Moffat et al. (
1998) — in fact. an extra component from the DES is not needed at all in the case of conservative mass transfer.,"1998) – in fact, an extra component from the DES is not needed at all in the case of conservative mass transfer."
 Amongst the observed WR stars marked as runaways there is a higher incidence of non-compact companion stars than amongst runaway O stars. however. so it is likely that there is a signiticant DES component in the WR runaway population.," Amongst the observed WR stars marked as runaways there is a higher incidence of non-compact companion stars than amongst runaway O stars, however, so it is likely that there is a significant DES component in the WR runaway population."
 A further variable which has the potential to have a strong effect. as noted above. is metallicity.," A further variable which has the potential to have a strong effect, as noted above, is metallicity."
 Foellmi et al. (, Foellmi et al. (
2003) find that eight of their sample of 61 LMC WR stars have unusual radial velocities (Le. significantly different from the mean value).,2003) find that eight of their sample of 61 LMC WR stars have unusual radial velocities (i.e. significantly different from the mean value).
 This suggests a similar or slightly higher runaway fraction to the Milky Way., This suggests a similar or slightly higher runaway fraction to the Milky Way.
 However. whereas several of the MW runaway sample have OB companions. all the suspected LMC runaways appear to be single.," However, whereas several of the MW runaway sample have OB companions, all the suspected LMC runaways appear to be single."
 This could indicate a higher proportion of BSS runaways. but is most likely just a consequence of small number statistics.," This could indicate a higher proportion of BSS runaways, but is most likely just a consequence of small number statistics."
 Lower-metallieity stars of similar mass and evolutionary status usually have smaller radii than comparable solar-metallicity stars., Lower-metallicity stars of similar mass and evolutionary status usually have smaller radii than comparable solar-metallicity stars.
 This leads to fewer contact systems. fewer mergers and more systems surviving until the first SN: and wind mass-loss rates are lower. which raises the mass limit above which a single star will go through a WR phase.," This leads to fewer contact systems, fewer mergers and more systems surviving until the first SN; and wind mass-loss rates are lower, which raises the mass limit above which a single star will go through a WR phase."
 WR secondaries are less affected by the lower mass-loss rates if their effective metallicity is raised by accretion., WR secondaries are less affected by the lower mass-loss rates if their effective metallicity is raised by accretion.
 Lower mass loss in the wind of the primary also leads to a more massive primary at the time of explosion. which may result in a lower kick velocity.," Lower mass loss in the wind of the primary also leads to a more massive primary at the time of explosion, which may result in a lower kick velocity."
 Therefore theoretically one would expect WR stars to have a higher runaway fraction at lower metallicity if the secondary accretes signiticantly (i.e. the conservative models) but otherwise to be relatively similar., Therefore theoretically one would expect WR stars to have a higher runaway fraction at lower metallicity if the secondary accretes significantly (i.e. the conservative models) but otherwise to be relatively similar.
 Decreasing the metallicity also shifts the main sequence bluewards. increasing non-runaway O star lifetimes.," Decreasing the metallicity also shifts the main sequence bluewards, increasing non-runaway O star lifetimes."
 This is likely to reduce the fraction of the O star population which is runaway., This is likely to reduce the fraction of the O star population which is runaway.
 These speculations are contirmed in Fig., These speculations are confirmed in Fig.
 4. for which the same simulations as in Fig.," 4, for which the same simulations as in Fig."
 3 are carried out. but at Z = 0.01.," 3 are carried out, but at Z = $0.01$."
 These general trends also held true when we ran the same simulations at Z = 0.004., These general trends also held true when we ran the same simulations at Z = $0.004$.
 From the above analysis it seems likely that the systems which have the potential to produce BSS WR runaways are those which have initially the most massive primary stars. and that because these primaries are still relatively massive when they explode. the velocities imparted to their companions are. on average. smaller. so that observed WR runaways represent the higher-velocity end of this spectrum.," From the above analysis it seems likely that the systems which have the potential to produce BSS WR runaways are those which have initially the most massive primary stars, and that because these primaries are still relatively massive when they explode, the velocities imparted to their companions are, on average, smaller, so that observed WR runaways represent the higher-velocity end of this spectrum."
 This in turn increases the likelihood that such systems in fact remain bound and moving with relatively low velocity — ie. not enough to be registered as runaways., This in turn increases the likelihood that such systems in fact remain bound and moving with relatively low velocity – i.e. not enough to be registered as runaways.
" In the kick restriction scenarios above over fifty percent of secondaries which go on to become WR stars retain their companions, the vast majority of which do not attain runaway velocities."," In the kick restriction scenarios above over fifty percent of secondaries which go on to become WR stars retain their companions, the vast majority of which do not attain runaway velocities."
 Even without Kick restrictions. the fraction of the total observed WR population which might be expected to have a compact companion. assuming no further interaction after the first SN. is around 8 percent.," Even without kick restrictions, the fraction of the total observed WR population which might be expected to have a compact companion, assuming no further interaction after the first SN, is around 8 percent."
 The question which then arises is. where are the WR-BH and WR-NS post-explosion binaries which are predicted by this scenario?," The question which then arises is, where are the WR-BH and WR-NS post-explosion binaries which are predicted by this scenario?"
the asymptotic behaviour of the density profile at both small and large radii.,the asymptotic behaviour of the density profile at both small and large radii.
" An asymptotic analysis of the functions U; and U2 learns that both terms converge to a finite value at small radii, Assume that ourdensity profile p(r) behaves as a power law at small radii, with 0€Yo«3."," An asymptotic analysis of the functions $U_1$ and $U_2$ learns that both terms converge to a finite value at small radii, Assume that ourdensity profile $\rho(r)$ behaves as a power law at small radii, with $0\leq\gamma_0<3$."
" It is easy to check that the mean density f(r) has a similar slope, Combining the expressions (9)), (25)), (33)), (34)), (35)) and (36)), we find the asymptotic behaviour of pr(r,0) at small radii, This result demonstrates that the asymptotic behaviour of the original spherical model is preserved after the flattening: the slope of the density profile remains, only the zero point changes and becomes dependent of the polar angle 0."," It is easy to check that the mean density $\bar\rho(r)$ has a similar slope, Combining the expressions \ref{msmallr}) ), \ref{rhof2}) ), \ref{U1smallr}) ), \ref{U2smallr}) ), \ref{rhosmallr}) ) and \ref{barrhosmallr}) ), we find the asymptotic behaviour of $\rho_{\text{f}}(r,\theta)$ at small radii, This result demonstrates that the asymptotic behaviour of the original spherical model is preserved after the flattening: the slope of the density profile remains, only the zero point changes and becomes dependent of the polar angle $\theta$."
" In particular, along the major and minor axes we find the expansions Using these expressions, we easily find the expression for the flattening q, of the isodensity surfaces at small radii, For modest flattening (q< 1) we find a nearly linear relation, Apart from the well-known fact that the isodensity surfaces are generally more flattened than the isopotential surfaces, this equation illustrates that the flattening of the inner isodensity surfaces increases with increasing o."," In particular, along the major and minor axes we find the expansions Using these expressions, we easily find the expression for the flattening $q_\rho$ of the isodensity surfaces at small radii, For modest flattening $q\lesssim1$ ) we find a nearly linear relation, Apart from the well-known fact that the isodensity surfaces are generally more flattened than the isopotential surfaces, this equation illustrates that the flattening of the inner isodensity surfaces increases with increasing $\gamma_0$."
" As an application of the formalism we have described in the previous section, we construct in this section a set of flattened dark matter halo models."," As an application of the formalism we have described in the previous section, we construct in this section a set of flattened dark matter halo models."
 Our starting point is the general three-parameter family of generalized NFW models or Zhao models The density of this general model is characterized by a power law with (negative) slopes Yo and yoo at respectively small and large radii., Our starting point is the general three-parameter family of generalized NFW models or Zhao models The density of this general model is characterized by a power law with (negative) slopes $\gamma_0$ and $\gamma_\infty$ at respectively small and large radii.
" The third parameter, 5, is a measure of the width of the transition region between the two power-law zones."," The third parameter, $\delta$, is a measure of the width of the transition region between the two power-law zones."
" This three-parameter model, the general dynamical properties of which are described by Saha(1993) and Zhao(1996),, includes a large variety of well-known simple potential density pairs used extensively throughout the literature to describe dynamical systems ranging from galactic nuclei to dark matter haloes (e.g.Plummer1911;Jaffe1983;Hernquist1990;Dehnen1993;Tremaineetal.1994;Navarro,Frenk,&White1997).."," This three-parameter model, the general dynamical properties of which are described by \citet{1993MNRAS.262.1062S} and \citet{1996MNRAS.278..488Z}, includes a large variety of well-known simple potential density pairs used extensively throughout the literature to describe dynamical systems ranging from galactic nuclei to dark matter haloes \citep[e.g.][]{1911MNRAS..71..460P,
 1983MNRAS.202..995J, 1990ApJ...356..359H, 1993MNRAS.265..250D,
 1994AJ....107..634T, 1997ApJ...490..493N}."
" To demonstrate our recipe to construct oblate dark matter haloes, we focus on a particular, non-trivial subset of this general set of models presented by Dehnen&McLaughlin(2005).."," To demonstrate our recipe to construct oblate dark matter haloes, we focus on a particular, non-trivial subset of this general three-parameter set of models presented by \citet{2005MNRAS.363.1057D}."
 These authors used the Jeans equations to derived the density profile of a self-gravitating spherically symmetric dynamical system that satisfy two characteristics of dark haloes observed in cosmological simulations., These authors used the Jeans equations to derived the density profile of a self-gravitating spherically symmetric dynamical system that satisfy two characteristics of dark haloes observed in cosmological simulations.
" The first of these characteristics is the mysterious power-law behaviour of the so-called pseudo phase-space Q=p/c? with o(r) the velocity dispersion (Taylor&Navarro2001;Ascasibaretal.2004;Rasia,Tormen,Moscardini 2004).."," The first of these characteristics is the mysterious power-law behaviour of the so-called pseudo phase-space $Q = \rho/\sigma^3$ with $\sigma(r)$ the velocity dispersion \citep{2001ApJ...563..483T,
 2004MNRAS.352.1109A, 2004MNRAS.351..237R}. ."
" The second ingredient in their model is a linear relation between the logarithmic density slope and the anisotropy, observed in different haloes with radically different"," The second ingredient in their model is a linear relation between the logarithmic density slope and the anisotropy, observed in different haloes with radically different"
We thank D. J. Rickett for helpful discussions aud sugecstious. and F. IHoitsch for help in constructing aud analyzing power specra.,"We thank B. J. Rickett for helpful discussions and suggestions, and F. Heitsch for help in constructing and analyzing power spectra."
" The Westerbork Svuthesis Racio Telescope is operated |"" the Netherlands Foundation or Research in Astronomy (ASTRON) with financial support from the Netherlands Organization for Scicutific Research (NWO).", The Westerbork Synthesis Radio Telescope is operated by the Netherlands Foundation for Research in Astronomy (ASTRON) with financial support from the Netherlands Organization for Scientific Research (NWO).
 Computations presented here were rerformecd ou the SCI Origin 2000 iachine of the Rechenzeutrm Carchineg of the \lax-Planck-Cesellschatt., Computations presented here were performed on the SGI Origin 2000 machine of the Rechenzentrum Garching of the Max-Planck-Gesellschaft.
 MOT acknowledges the support from NWO erant 61151-, MH acknowledges the support from NWO grant 614-21-006.
Studying how galaxies form and evolve is a fundamental step to better understanding our place in the Universe.,Studying how galaxies form and evolve is a fundamental step to better understanding our place in the Universe.
" The Universe is believed to follow a ACDM cosmology (e.g. in which 7 is composed of dark SnerSy, while the remammg ~30% 70%is made of matter; subdivided into baryonie(~ 5%) and dark(~ 25%)."," The Universe is believed to follow a $\Lambda$ CDM cosmology \citep[e.g.][]{Blu84,
Fre01,Efs02, Pry02, Spe03} in which $\sim70\%$ is composed of dark energy, while the remaining $\sim$ is made of matter, subdivided into $\sim5\%$ ) and $\sim25\%$ )."
 This model appears with experimental measurements of the Cosmic consistentMicrowave Background (CMB) (e.g.Dunkleyetal.etal.2009) and large scale clustering (e.g.Sanchez," This model appears consistent with experimental measurements of the Cosmic Microwave Background (CMB) \citep[e.g.][]{Dun09,Mat09} and large scale clustering \citep[e.g.][]{San09}."
" - A key feature of the 18 à al.hierarchical2009) bottom-up formation ACDMparadigm, with cosmogonysmaller bodies accreting to form progressively larger ones1978)."," A key feature of the $\Lambda$ CDM cosmogony is a hierarchical bottom-up formation paradigm, with smaller bodies accreting to form progressively larger ones."
. Small dark matter halos form first and subsequently merge to form bigger halos (e.g.Peebles1982;Blumenthaletal.1984).," Small dark matter halos form first and subsequently merge to form bigger halos \citep[e.g.][]{Pee82, Blu84}."
. Baryonic (gas) inflow into the gravitational potential wells created by these halos builds the stellar mass and central black holes in the first galaxies (e.g.Renzini1977;Fall&Efstathiou1980;al. 2006).. (," Baryonic (gas) inflow into the gravitational potential wells created by these halos builds the stellar mass and central black holes in the first galaxies \citep[e.g.][]{Ren77, Fal80, Dal97, Mo98, Mac01, SHD03, Ven06}. ("
"and perhaps also in systems in their immediate vicinity, see Shabala et al.","and perhaps also in systems in their immediate vicinity, see Shabala et al."
 2011) which plausibly produces the observed correlation between the mass of the central black hole and the stellar mass contained in, 2011) which plausibly produces the observed correlation between the mass of the central black hole and the stellar mass contained in
the sensitivity is considerably lower than that calculated in the appendix to Verbiest ct al. (,the sensitivity is considerably lower than that calculated in the appendix to Verbiest et al. (
2009).,2009).
 We believe the estimated errors to be correct because they are calibrated by simulation. so we ask the question: Vo investigate this we have run a series of with GAVB signals of dillering amplitudes injected into the observations (?)..," We believe the estimated errors to be correct because they are calibrated by simulation, so we ask the question: To investigate this we have run a series of with GWB signals of differing amplitudes injected into the observations \citep{hjl+09}."
 The results are shown in Figure 5., The results are shown in Figure \ref{fig:AinVsAout}.
" The mean values of the derived 24° are plotted as solid. lines connecting error bars (which indicate the uncertainty in the mean) for two cases: (1) the algorithm including correction with the σε, calibration [actors (thick solid line): and (2) the algorithm with 5;;=1 (thin solid line)", The mean values of the derived $\hat{A^2}$ are plotted as solid lines connecting error bars (which indicate the uncertainty in the mean) for two cases: (1) the algorithm including correction with the $\gamma_{ij}$ calibration factors (thick solid line); and (2) the algorithm with $\gamma_{ij} \equiv 1$ (thin solid line).
 ‘These results show that our method returns a GWD amplitude estimate ουσnu such that. on average. Jo=2d.," These results show that our method returns a GWB amplitude estimate $\hat{A}_{\rm out}^2$ such that, on average, $\hat{A}_{\rm out}^2 = A_{\rm in}^2$."
 Fieure 6 shows that this GWD signal is at the correct level on average in every pulsar pair., Figure \ref{fig:HD2} shows that this GWB signal is at the correct level on average in every pulsar pair.
 The difference between the thick solid line and the thin solid line in Figure 5. indicates that the GAVB power is reduced by a [factor of 12 because of the pulsar parameter fitting., The difference between the thick solid line and the thin solid line in Figure \ref{fig:AinVsAout} indicates that the GWB power is reduced by a factor of $\sim$ 12 because of the pulsar parameter fitting.
 We can estimate the amount of GAVB signal lost. in estimation of dillerent timing parameters by calculating the weighted average calibration factor in the lowest. [requenevy channel of cach pulsar pair., We can estimate the amount of GWB signal lost in estimation of different timing parameters by calculating the weighted average calibration factor in the lowest frequency channel of each pulsar pair.
 While this will be at a different frequency for cach pair. it nevertheless. provides a straightforward figure of merit for comparing the cllect of fitting different timing model parameters.," While this will be at a different frequency for each pair, it nevertheless provides a straightforward figure of merit for comparing the effect of fitting different timing model parameters."
 For the full Lit acting on the Verbiest ct al. (, For the full fit acting on the Verbiest et al. (
2008. 2009) residuals. we [find 5:5(f—Γον)=0.0790X 0.0002. which represents an average loss of 0.0790.1=12.7 in GWD signal at f£.=1Ενω.,"2008, 2009) residuals, we find $\overline{\gamma_{ij}}(f=1/\tol) = 0.0790\pm0.0002$ , which represents an average loss of $0.0790^{-1}=12.7$ in GWB signal at $f=1/\tol$."
 Phi explains the large decrease in sensitivity of our method. compared. to that. presented in the appendix of 2.. which did not fully account for the effect. of pulsar parameter estimation on the GWD signal.," This explains the large decrease in sensitivity of our method compared to that presented in the appendix of \citet{vbc+09}, which did not fully account for the effect of pulsar parameter estimation on the GWB signal."
 In Table 3. we show the weighted average calibration factor ab fo=l/ffsesa when fitting for different parameters in he timing model., In Table \ref{tbl:fit} we show the weighted average calibration factor at $f = 1 / \tol$ when fitting for different parameters in the timing model.
 The estimation of the pulsar position and xwallax have little effect on 5:5;Cf=LA) since Zoos is a few times greater than 1vvr for most of our. pulsar airs. and so are not shown in Table 3..," The estimation of the pulsar position and parallax have little effect on $\overline{\gamma_{ij}}(f=1/\tol)$ since $\tol$ is a few times greater than yr for most of our pulsar pairs, and so are not shown in Table \ref{tbl:fit}."
 Phis table indicates hat one can almost determine the complete ellect of fitting on the GWD sensitivity by only. including fits for the spin pequenev. its derivative and the arbitrary phase olfsets retwween cdillerent observing svstems.," This table indicates that one can almost determine the complete effect of fitting on the GWB sensitivity by only including fits for the spin frequency, its derivative and the arbitrary phase offsets between different observing systems."
 Acdcditionallv. while the spin frequency derivative fit only significantly allects the »»wer in the lowest [requeney channel. the arbitrary phase olfsets alfect the power in the lowest few channels which can significantly alfect our estimate of 24>.," Additionally, while the spin frequency derivative fit only significantly affects the power in the lowest frequency channel, the arbitrary phase offsets affect the power in the lowest few channels which can significantly affect our estimate of $A^2$."
 The dashed lines in Figure 5. show that for GWD amplitudes| around 413—510.207. the average uncertainty: on cl? is double the average uncertainty when there is no input CGWD.," The dashed lines in Figure \ref{fig:AinVsAout} show that for GWB amplitudes around $A^2 = 5\e{-30}$, the average uncertainty on $\hat{A^2}$ is double the average uncertainty when there is no input GWB."
 This extra. contribution to the uncertainty comes from the effect of the GWs passing near the pulsar. which we refer toas the ~sell-noise” of the GWD.," This extra contribution to the uncertainty comes from the effect of the GWs passing near the pulsar, which we refer toas the “self-noise” of the GWB."
 For larger values of AP. the uncertainty on LÀ? is dominated. by. the CGWD sel(-noise as discussed in ?..," For larger values of $A^2$, the uncertainty on $\hat{A^2}$ is dominated by the GWB self-noise as discussed in \citet{jhlm05}."
 This provides a limitation on the confidence with which we can place an upper bound on the amplitude of the CWD., This provides a limitation on the confidence with which we can place an upper bound on the amplitude of the GWB.
 Because of the self-noise of the GWD. we can obtain at best an SO per cent confidence upper bound on the CWD amplitude: we can never obtain a 95 per cent confidence bound with our current time series and weighting scheme.," Because of the self-noise of the GWB, we can obtain at best an 80 per cent confidence upper bound on the GWB amplitude; we can never obtain a 95 per cent confidence bound with our current time series and weighting scheme."
 Furthermore. anv limit obtained thus would. be considerably. worse than one obtained through othermethods. such as direct power estimation. because of the huge variation in noise levels amongst our pulsars?..," Furthermore, any limit obtained thus would be considerably worse than one obtained through othermethods, such as direct power estimation, because of the huge variation in noise levels amongst our ."
clear mass seeregation between these substellar objects.,clear mass segregation between these substellar objects.
 Comparison with Monte Carlo simulations shows no evideuce of the presence of agerceation of brown cwarfs iu the cluster., Comparison with Monte Carlo simulations shows no evidence of the presence of aggregation of brown dwarfs in the cluster.
" Based ou near-intrared data frou: 2\TASS and UKIDSS and mid-infrared data fromSpitzer. we couclude that ~ and mid-infrared excesses at wavelengths longer than μα, respectively, probably related to the presence of disks."," Based on near-infrared data from 2MASS and UKIDSS and mid-infrared data from, we conclude that $\sim$ and mid-infrared excesses at wavelengths longer than $\mu$ m, respectively, probably related to the presence of disks."
 The majority of them beloug to the so called “transition disks”. where a process of cleariug out has occurred in their ΠΟ regions.," The majority of them belong to the so called “transition disks”, where a process of clearing out has occurred in their inner regions."
 We have estimated the substellar mass spectrum of the cluster. aud found that his is a rising function towards lower masses aud can )o represeuted by a potential function (LN/dii x1a7) with a exponent à between 0.1 aud 1.1in the mass rauge )eteen 0.11.0.013 AL...," We have estimated the substellar mass spectrum of the cluster, and found that this is a rising function towards lower masses and can be represented by a potential function $dN/dm$ $\propto$$^{-\alpha}$ ) with a exponent $\alpha$ between 0.4 and 1.1in the mass range between 0.11–0.013 $_{\odot}$."
 These results are consistent with he majority of other studies of voung open clusters and associations and indicates that. although we caunot sav that the substellay uiass function is universal. its chavior is rather general.," These results are consistent with the majority of other studies of young open clusters and associations and indicates that, although we cannot say that the substellar mass function is universal, its behavior is rather general."
 We thank J. Licaudro for his help im the acquisition of infrared. data at the Carlos Saunchez Telescope., We thank J. Licandro for his help in the acquisition of infrared data at the Carlos Sánnchez Telescope.
 We thank 1. Baraffe aud the Lyon eroup. F. D'Antona aud A. Burrows for sending us electronic versions of their models.," We thank I. Baraffe and the Lyon group, F. D'Antona and A. Burrows for sending us electronic versions of their models."
 This svork is based ou observations obtained at: the Carlos Sáunchez Telescope operated by the Iustituto de Astrofissica de Canarias at the Observatorio del Teide (Tenerite. Spain): the Isaac Newton Telescope operated oun the island of La Palma by the Isaac Newton Croup in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofissica de Canarias: and the GCerman-Spanish Astronomical Couter. Cali Alto. jointly operated by the Max-Plauck-Iustitut fürr Astronomie Heidelberg and the Tustituto de trofissica de Audaluciaa (CSIC).," This work is based on observations obtained at: the Carlos Sánnchez Telescope operated by the Instituto de sica de Canarias at the Observatorio del Teide (Tenerife, Spain); the Isaac Newton Telescope operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de sica de Canarias; and the German-Spanish Astronomical Center, Calar Alto, jointly operated by the Max-Planck-Institut fürr Astronomie Heidelberg and the Instituto de sica de a (CSIC)."
" The United Ninedom Iufired Telescope is operated by the Joint Astronomy, Centre on behalf of the Science and Technology Facilities Council of the U.IK.. This publication makes use of data products from the Two Micron All Sky Survey. which is a joiut project of the University of Massachusetts aud the Iufrared Processing and Analysis Center/Califormia Institute of Technology. fuuded by he National Acronautics and Space Administration and the National Science Foundation."," The United Kingdom Infrared Telescope is operated by the Joint Astronomy Centre on behalf of the Science and Technology Facilities Council of the U.K. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation."
 This research das nade use of the VizieR catalogue access tool arc he SIMBAD database. operated at CDS. Strasbourg. France. and IRAF. which is distributed lw Nationa Optical Astronomy Observatories. which is opcratec o» the Association of Universities for Research in Astronomy. luc. under contract with the Nationa Science. Foundation.," This research has made use of the VizieR catalogue access tool and the SIMBAD database, operated at CDS, Strasbourg, France, and IRAF, which is distributed by National Optical Astronomy Observatories, which is operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation."
 V. J. S. D. is partially supporte wo the Spanish Ramoun x Cajal program., V. J. S. B. is partially supported by the Spanish Ramónn y Cajal program.
 Partia financial support was provided by the Spanish Ministerio de Cienciaο Lunovacióun projects AYA2007-67Ls. AYA2010-20535. AYA2ZOL0-21038-C'03-01 and AYA2OL0-21038-C'03-02.," Partial financial support was provided by the Spanish Ministerio de Cienciae Innovaciónn projects AYA2007-67458, AYA2010-20535, AYA2010-21038-C03-01 and AYA2010-21038-C03-02."
 E. L. AL acknowledeecs support from Necks PI Data Analvsis grant awarded by the Michelson Science Center. (CAIN).. AVEO)... (Oieea-Prime).. (ALTACIC)..," E. L. M. acknowledges support from Keck PI Data Analysis grant awarded by the Michelson Science Center. , , , ."
In recent vears there has been an extensive debate over the origin of hot subdwarl stars. largely because they seem to provide the best explanation for the UV-upturn seen in elliptical galaxies Yi. Demarque Oemler 1997. 1998: Lan. Poclsiacllowski Lyvnas-Gray. 2007).,"In recent years there has been an extensive debate over the origin of hot subdwarf stars, largely because they seem to provide the best explanation for the UV-upturn seen in elliptical galaxies Yi, Demarque Oemler 1997, 1998; Han, Podsiadlowski Lynas-Gray 2007)."
 “Phe production of such stars in elobular clusters. where they are often relerrecl to as CELIB) stars. has been a long-standing mystery (sec. οσοι van den Bereh 1967: Sandage Wildev 1967: Soker LOOS: Han 2008).," The production of such stars in globular clusters, where they are often referred to as (EHB) stars, has been a long-standing mystery (see, e.g., van den Bergh 1967; Sandage Wildey 1967; Soker 1998; Han 2008)."
 Subelwarl D (sclB) stars ave believed to be helium-core-burning stars with masses 0.5M... posessing very small (<0.02 M.) bydrogen-rich envelopes. (Lleber 1986: Salfer et 11994).," Subdwarf B (sdB) stars are believed to be helium-core-burning stars with masses $\rm \sim 0.5~M_{\odot}$, posessing very small $\rm <
0.02~M_{\odot}$ ) hydrogen-rich envelopes (Heber 1986; Saffer et 1994)."
 Their. formation has been studied in sonyο detail by Han et ((2002 2003). who showed that binary evolution can account for the properties of the observed sdB stars.," Their formation has been studied in some detail by Han et (2002 2003), who showed that binary evolution can account for the properties of the observed sdB stars."
 Other authors have suggested. enhanced: mass-loss from single recd-giant stars in order to try to explain the formation of sdB stars YYi et 11997: see also Lan. Poclsiacdlowski Eeeleton 1994). or mixing driven by avery late helium Ilash (Sweigart 1907: Brown et 22001). or that interactions with planets can eject the envelopes of red giants (Soker 1998: Nelemans “Tauris 1998).," Other authors have suggested enhanced mass-loss from single red-giant stars in order to try to explain the formation of sdB stars Yi et 1997; see also Han, Podsiadlowski Eggleton 1994), or mixing driven by a very late helium flash (Sweigart 1997; Brown et 2001), or that interactions with planets can eject the envelopes of red giants (Soker 1998; Nelemans Tauris 1998)."
 Subelwarl ο (sdO) stars. are assumed. to be related o πα stars., Subdwarf O (sdO) stars are assumed to be related to sdB stars.
" Stroeer ct ((2007) have examined the ormation of sdO stars ancl concluded that the sdO stars with a subsolar photospheric helium abundance Cholium-deficient) have a different origin to the ""helium-enriched? (Lle-rich) sdO stars (which they define as having a super-solar helium abundance).", Stroeer et (2007) have examined the formation of sdO stars and concluded that the sdO stars with a subsolar photospheric helium abundance (`helium-deficient') have a different origin to the `helium-enriched' (He-rich) sdO stars (which they define as having a super-solar helium abundance).
 Specifically. Stroeer et ffound hat the helium-deficient. sclO stars are likely to be evolved sdD stars. but that the Lle-rich κο stars cannot be explained throug= ic canonical evolution of sd. Nroposed formation channels for those Le-rich sc stars include mergers of two helium white cwarls (Saigo Jelferv ) and the shot flasher scenario AlAlochler et 22007: Miller. Bertolami ct 22008).," Specifically, Stroeer et found that the helium-deficient sdO stars are likely to be evolved sdB stars, but that the He-rich sdO stars cannot be explained through the canonical evolution of sdB Proposed formation channels for those He-rich sdO stars include mergers of two helium white dwarfs (Saio Jeffery 2000) and the `hot flasher scenario' Moehler et 2007; Miller Bertolami et 2008)."
 Though neither of these models seems. entirely satisfactory. one piece of evidence which apparently favours the white-cwarl merger scenario is the very low binary fraction of the Le-rich scd stars (see. eg. Leber et al.," Though neither of these models seems entirely satisfactory, one piece of evidence which apparently favours the white-dwarf merger scenario is the very low binary fraction of the He-rich sdO stars (see, e.g., Heber et al."
 2006: Leber 2008)., 2006; Heber 2008).
 Hore. we, Here we
"i.c. to the inverse square of the noise contribution to the eror in 92,4,5.","i.e. to the inverse square of the noise contribution to the error in $\widehat{\sigma^{2}}_{{\rm lens},f}$."
 This weighting scheme is nearly optimal. and avoids including the lensing signal Tra} itself.," This weighting scheme is nearly optimal, and avoids including the lensing signal $\sigma^{2}_{{\rm
lens},f}$ itself."
" The average weights (eg) in several maguitude bins are shown in Figure 1,", The average weights $\langle w_{f} \rangle$ in several magnitude bins are shown in Figure 1.
 As expected. deeper fields have burger weights since they contain a larger number of galaxies and thus have a sinaller value of Ayoisct," As expected, deeper fields have larger weights since they contain a larger number of galaxies and thus have a smaller value of $\sigma_{\rm noise,f}$."
 To measure the shear variance on the field scale. we first average the shear within each field aud apply the same procedure.," To measure the shear variance on the field scale, we first average the shear within each field and apply the same procedure."
 This time. however. the cross-correlation term in Equation (3)) vanishes since cach field is iudepenudoeut.," This time, however, the cross-correlation term in Equation \ref{eq:sig2_sig2_lens}) ) vanishes since each field is independent."
 Sinuilulv. we cau cousider pairs of chips to measure the shear variance ou intermediate scales.," Similarly, we can consider pairs of chips to measure the shear variance on intermediate scales."
" 0,σαι Our measurement for the shear variance oj.(0) on different scales is shown iu Figure 2.", -0.3cm Our measurement for the shear variance $\sigma_{\rm lens}^2(\theta)$ on different scales is shown in Figure 2.
 The augular scale Mis the radius of an effective. circular cell whose mean pair separation equals that of the chip configuration considered (0~0.72/. 1.11/.. and 1.38’. for 1. 2 and 3 1.27! chips. respectively).," The angular scale $\theta$ is the radius of an effective circular cell whose mean pair separation equals that of the chip configuration considered $\theta \simeq
0.72', 1.11'$ , and $1.38'$, for 1, 2 and 3 $1.27'$ chips, respectively)."
 The outer 1o error bars include both statistical errors and cosmic variance (from Eq. 2/0).," The outer $1\sigma$ error bars include both statistical errors and cosmic variance (from Eq. \ref{eq:sig2_sig2_lens}] ]),"
 while the inner error bars oulv include statistical errors (i.c. by setting ma and a? to 0 on the rielit-haud. side of this Eq.)., while the inner error bars only include statistical errors (i.e. by setting $\sigma_{\rm lens}^2$ and $\sigma_{\times}^{2}$ to 0 on the right-hand side of this Eq.).
" For imstauce. ou the chip scale we obtain L2"")—(3.52z045214)«10.1, vielding a detection miusignificance (immer error) of 3.80 with this scale alone."," For instance, on the chip scale we obtain $\sigma_{\rm lens}^{2}(0.72')=(3.5\pm 0.9 \pm 1.1)\times 10^{-4}$, yielding a detection significance (inner error) of $3.8\sigma$ with this scale alone."
" As a check of svstematics. we analyzed our signal into £ ixl Baunodes using the aperture mass AL),(G7"") statistic o1 the chip scale (Schneider et al."," As a check of systematics, we analyzed our signal into $E$ and $B$ -modes using the aperture mass $M_{\rm ap}(0.67')$ statistic on the chip scale (Schneider et al."
 1998: van Waerbeke οἳ al., 1998; van Waerbeke et al.
 2001)., 2001).
 For L-modes. we find the upper lit OI)=(ιατὸς10! (le) which is consistent with the siena *xpected in a ACDAL mode GMTE)~0.6«10 Schucider et al.," For $E$ -modes, we find the upper limit $\langle M_{{\rm
ap},E}^{2} \rangle =(0.4\pm1.7) \times 10^{-4}$ $1\sigma$ ) which is consistent with the signal expected in a $\Lambda$ CDM model $\langle
M_{{\rm ap},E}^{2} \rangle \simeq 0.6 \times 10^{-4}$; Schneider et al."
 1998)., 1998).
 For the B-modes. we find ARa=(0.341.7).10 (lo). as expected in the absence of svstcluatics πάσα corresponds to Me—0).," For the $B$ -modes, we find $\langle M_{{\rm ap},B}^{2}
\rangle =(0.3\pm1.7) \times 10^{-4}$ $1\sigma$ ), as expected in the absence of systematics (which corresponds to $\langle M_{{\rm
ap},B}^{2} \rangle \equiv 0$ )."
 The measurements frou other groups are also plottec oe1 Figure 2. along with the predictions for a ACDM mode with og=1 aud D=0.21.," The measurements from other groups are also plotted in Figure 2, along with the predictions for a $\Lambda$ CDM model with $\sigma_{8}=1$ and $\Gamma=0.21$."
 The ceutral value for D is close to the recent measurement of this parameter frou ealaxy clustering (eg., The central value for $\Gamma$ is close to the recent measurement of this parameter from galaxy clustering (eg.
 Percival et al., Percival et al.
" 2001). while keeping the P=Q,,f relation valid for h=0.7."," 2001), while keeping the $\Gamma=\Omega_{m}h$ relation valid for $h=0.7$."
" The predictions are plotted for a range of galaxy redshifts ;,,=0.9+0.1. corresponding approximately to the uncertaintv aud dispersion of this pauneter in the different surveys."," The predictions are plotted for a range of galaxy redshifts $z_{m}=0.9\pm0.1$ , corresponding approximately to the uncertainty and dispersion of this parameter in the different surveys."
" Iu our case. the effective median Euagnuitude of our nieasuremoenut ig DL,=Napling3angm235. which corresponds to a ποια redshift of τρ=0.95+0.10 (see Eq. |1]|."," In our case, the effective median I-magnitude of our measurement is $I_{m}=\sum_{f}
w_f I_{m,f}/ \sum_{f} w_f \simeq 23.5$, which corresponds to a median redshift of $z_{m}=0.95\pm0.10$ (see Eq. \ref{eq:red_mag}] ])."
 The effective niaguitude aud corresponding redshift are plotted in Fieure 1., The effective magnitude and corresponding redshift are plotted in Figure 1.
 Given the range of median redshifts in the different survevs aud the correlation between augular bius for the variance. our results are in good agreement with these other measurements aud with the ACDM model.," Given the range of median redshifts in the different surveys and the correlation between angular bins for the variance, our results are in good agreement with these other measurements and with the $\Lambda$ CDM model."
 Our inueasurciunents can be used to constrain cosmological parameters., Our measurements can be used to constrain cosmological parameters.
 Because our nieasurenieuts— on different scales are not independent. we couservativelv ouly consider the shear variance ou the chip scale (0=0.72%).," Because our measurements on different scales are not independent, we conservatively only consider the shear variance on the chip scale $\theta =0.72'$ )."
 Within a ACDM model. it is predicted to be (see RRGI). within an excellent approximation. where σς is the amplitude of dass fluctuations ou SN A iMpe scales. and Ὁ is the imatter density parameter.," Within a $\Lambda$ CDM model, it is predicted to be (see RRGII), within an excellent approximation, where $\sigma_{8}$ is the amplitude of mass fluctuations on 8 $h^{-1}$ Mpc scales, and $\Omega_{m}$ is the matter density parameter."
" Tuverting this equation. we find that our measurement of Thane vields a,=(οιO.100.120,/0.3)H(D/021).&oes,(0.95) ""9. where the first error is statistical ο] and the second also includes cosluic variance."," Inverting this equation, we find that our measurement of $\sigma_{\rm lens}^{2}$ yields $\sigma_{8} = (0.94 \pm 0.10 \pm 0.12)
(\Omega_{m}/0.3)^{-0.44} (\Gamma/0.21)^{-0.15} (z_{m}/0.95)^{-0.70}$ , where the first error is statistical only and the second also includes cosmic variance."
" To this error must be added that arising from the uncertainty in the median effective redshift 0.95+ 0.10, ", To this error must be added that arising from the uncertainty in the median effective redshift $z_{m}=0.95 \pm 0.10$ .
After propagating this error. we obtain where the first error reflects statistical errors oly. aud the latter is the total error aud mceludes statistical errors. cosnule variance. and redshift muacertainty (all lo}.," After propagating this error, we obtain where the first error reflects statistical errors only, and the latter is the total error and includes statistical errors, cosmic variance, and redshift uncertainty (all $1\sigma$ )."
 Figure 3 shows the comparison of our 1rieasureimmentof σς (IIST/WFEC?2) with that from other weak lensing surveys and from other methods., Figure 3 shows the comparison of our measurementof $\sigma_{8}$ (HST/WFC2) with that from other weak lensing surveys and from other methods.
" A ACDAL model with Q,,=0.3 and P=0.21 was assumed (except for van Waerbeke et al.", A $\Lambda$ CDM model with $\Omega_{m}=0.3$ and $\Gamma=0.21$ was assumed (except for van Waerbeke et al.
 2001 who mareinalized over P)., 2001 who marginalized over $\Gamma$ ).
 Our oy value is cousisteut with the other recent cosmic shear measurements of Bacon, Our $\sigma_{8}$ value is consistent with the other recent cosmic shear measurements of Bacon
absence of the K-band data results in only a 0.04 dex overestimate of the stellar mass.,absence of the $K_{S}$ -band data results in only a $\sim 0.04$ dex overestimate of the stellar mass.
" The DEEP2 galaxies with K,-band data from the full sample are generally brighter and more massive than our selected galaxies, while the color distribution is consistent with our selected sample."," The DEEP2 galaxies with $K_{s}$ -band data from the full sample are generally brighter and more massive than our selected galaxies, while the color distribution is consistent with our selected sample."
" The K,-band data for our selected sample span the full range of mass, color and absolute B-band magnitude and the medians are 9.81, 0.68 and -20.7 respectively."," The $K_{s}$ -band data for our selected sample span the full range of mass, color and absolute B-band magnitude and the medians are 9.81, 0.68 and -20.7 respectively."
" To check for any systematic variations with galaxy properties we fit half of the data that is below the median in mass, color and magnitude respectively and find that the fits are all consistent within the errors."," To check for any systematic variations with galaxy properties we fit half of the data that is below the median in mass, color and magnitude respectively and find that the fits are all consistent within the errors."
" When K-band photometry is unavailable, we subtract 0.04 dex from the mass to correct for the systematic overestimate."," When $K_{s}$ -band photometry is unavailable, we subtract 0.04 dex from the mass to correct for the systematic overestimate."
" After applying this correction, there is a 0.12 dex dispersion between the one-to-one correspondence of the two mass estimates."," After applying this correction, there is a 0.12 dex dispersion between the one-to-one correspondence of the two mass estimates."
" We have redetermined the local MZ and LZ relations from ~21,000 galaxies in the SDSS data release 7 (see "," We have redetermined the local MZ and LZ relations from $\sim21,000$ galaxies in the SDSS data release 7 (see appendix)."
We compared our stellar mass determination using Le appendix).Phare with those determined by the MPA/JHU team from fitting the photometry and a Kroupa IMF (?).., We compared our stellar mass determination using Le Phare with those determined by the MPA/JHU team from fitting the photometry and a Kroupa IMF \citep{Kroupa2001}.
 Both methods use stellar population synthesis to fit the photometry and we expect the estimates to only vary by a constant offset., Both methods use stellar population synthesis to fit the photometry and we expect the estimates to only vary by a constant offset.
 The right panel of Figure 2 shows this comparison., The right panel of Figure \ref{fig:mass} shows this comparison.
 The dashed line is the one-to-one correspondence and the solid line is a bootstrap linear bisector fit to the data as described earlier., The dashed line is the one-to-one correspondence and the solid line is a bootstrap linear bisector fit to the data as described earlier.
 The linearfit is given by ΧΤΡ=Mrp—10 and Xspss=Mspss—10., The linearfit is given by where $X_{LP} = M_{LP} - 10$ and $X_{SDSS} = M_{SDSS} - 10$.
" Mryp whereand Mspss are the stellar masses determined using Le Phare and those provided by the MPA/JHU team, respectively."," $M_{LP}$ and $M_{SDSS}$ are the stellar masses determined using Le Phare and those provided by the MPA/JHU team, respectively."
" As before, to minimize the covariance of the slope and intercept, we zero point the data by subtracting 10 from the masses."," As before, to minimize the covariance of the slope and intercept, we zero point the data by subtracting 10 from the masses."
 The slope is near unity and to first order the estimates differ by only a constant offset of 0.198 dex (a factor of —1.6)., The slope is near unity and to first order the estimates differ by only a constant offset of 0.198 dex (a factor of $\sim1.6$ ).
" Taking into account this constant offset, there is a 0.14 dex dispersion in the one-to-one correspondence between the two mass estimates."," Taking into account this constant offset, there is a 0.14 dex dispersion in the one-to-one correspondence between the two mass estimates."
 For local galaxies it has been shown that the errors between photometric and dynamical mass are typically ~0.2 dex (?)., For local galaxies it has been shown that the errors between photometric and dynamical mass are typically $\sim\!0.2$ dex \citep{Drory2004}.
" In this study, we observe galaxies at z~0.8 and therefore expect even greater errors in the photometric determination of mass."," In this study, we observe galaxies at $z\sim0.8$ and therefore expect even greater errors in the photometric determination of mass."
" Moreover, ? have shown that additional uncertainties in estimates of physical parameters from stellar population synthesis modeling result from the choice of IMF, dust model and spectral libraries."," Moreover, \citet{Conroy2009} have shown that additional uncertainties in estimates of physical parameters from stellar population synthesis modeling result from the choice of IMF, dust model and spectral libraries."
" However, the full impact of these effects on the absolute calibration of the physical parameters are still not well understood."," However, the full impact of these effects on the absolute calibration of the physical parameters are still not well understood."
" Therefore, when investigating evolution of the MZ relation, we take care to have a consistent relative calibration of the physical parameters between the samples."," Therefore, when investigating evolution of the MZ relation, we take care to have a consistent relative calibration of the physical parameters between the samples."
 The absolute calibration remains uncertain., The absolute calibration remains uncertain.
 When measuring EWs it is necessary to make a correction for underlying stellar absorption in the Balmer lines., When measuring EWs it is necessary to make a correction for underlying stellar absorption in the Balmer lines.
 ? have estimated an average correction of 2A in the EW(Hf) for the underlying Balmer absorption using 22 galaxies from the spectroscopic galaxy atlas of ?.., \citet{Kobulnicky2003b} have estimated an average correction of $2\AA$ in the $EW(H\beta)$ for the underlying Balmer absorption using 22 galaxies from the spectroscopic galaxy atlas of \citet{Kennicutt1992}.
 The galaxies in the Kennicutt atlas have a spectral resolutions of 5-84., The galaxies in the Kennicutt atlas have a spectral resolutions of $\AA$.
 We expect the effects of Balmer absorption to be greater in galaxy spectra with lower resolution because the flux of the narrow emission line is spread over a broader region of the absorption trough., We expect the effects of Balmer absorption to be greater in galaxy spectra with lower resolution because the flux of the narrow emission line is spread over a broader region of the absorption trough.
" Presumably for this reason, ? find a correction of 1A by stacking spectra observed using onboard Keck with a spectral resolution of 3.5.4."," Presumably for this reason, \cite{Cowie2008} find a correction of $1\AA$ by stacking spectra observed using DEIMOS onboard Keck with a spectral resolution of $3.5\AA$ ."
 The DEIMOSDEEP2 data have also been obtained using DEIMOS but with a smaller spectral resolution of 1.44., The DEEP2 data have also been obtained using DEIMOS but with a smaller spectral resolution of $1.4\AA$ .
 Previous works onBBN,to happen in the first few seconds of the Universe.
 inthemirror sector [13]. have parameterized," The reaction rates of the processes \ref{reactions}) ) can be adapted from the standard relations present in e.g. Ref. \cite{Weinberg},"
 the abundance of Le’ in terms ofsome initial 77/7 value. withoutconsidering the effects ofphoton-mirror photon kinetic mixing. llerewe consile," in which we can neglect the Pauli blocking effect on neutrinos because $T_{\nu'} \ll T'$: where $G_{\rm wk} = 1.16637 \times 10^{-5} \ {\rm GeV^{-2}}$ is the weak coupling constant, $g_{\rm A} = 1.257$ is the axial vector coupling of beta decay, measured from the rate of neutron decay, and $\theta_{\rm C}$ is the Cabibbo angle."
"r (heimplications ofkinetic mirror producedinthelow7""MN<5 MeV region. oO mirrorweak interactions are too weak to significantly populate the/ νο.Thusto agood approximation "," For $n'+e'^+ \to p' + \bar \nu', \ E_{\nu'} - E_{e'} = Q$, while for $p' + e'^- \to n' + \nu', \ E_{e'} - E_{\nu'} = Q$ , where $Q \equiv m_n - m_p = 1.293$ MeV. The extremals of integrals in \ref{1}) ) are fixed considering that integrations are taken over all allowed positive values of $p_{e'}$."
the radiation content of (he mirror sector consistsjustofεἰand4’. From ourearlierpaper[14].. we obtained an approximate analytical expression for T'," The differential equation for the ratio $X_{n'}$ of mirror neutrons to nucleons is: Note that $Y_{He'} \simeq 2X_{n'}$ since, as mentioned earlier, we can neglect $n'$ decay, and thus all available mirror neutrons go into forming $He'$."
"/Twhich is validfor7""= 1 MeV. andfor T C100MeV. and isgiven by: T; x 2TC(3)n2? ewe SD (10) neelecting Pauli-blocking factors. ete.). Asstunine 7;>> 100 MeVthen E«q.(9))"," We have solved the above equations numerically, using the usual time-temperature relation for radiation dominated epoch where $g$ takes into account only the degrees of freedom of ordinary particles, since the contribution of mirror particles is negligible given the initial condition $T' \ll T$."
 reduces to: ~ (11) T — (T/MeV) FAI10 In this (he mirror sectorstarts with atemperature," We used the initial condition $X_{n'}(0)=0.5$ in \ref{eq:Xn}) ), and followed the evolution until $X_{n'}$ reaches the asymptotic value."
 much lower thanthe temperaturetheoryofthe ordinary sector. and later(he interactions induced by photon-mirror photonkinetic increasesonlv the temperatureof mirror el," Our results are shown in Figure \ref{fig:He-epsi}, where we plot the obtained mass fraction of mirror helium versus the strength of the photon-mirror photon kinetic mixing $\epsilon$ ), for the parameter range of interest for cosmology."
ectrons. positronsancl photons.since ," As expected, we obtain high values of the primordial $He'$ mass fraction, with $ Y_{He'} \gtrsim 0.8$ for $\epsilon \lesssim 3 \times 10^{-9}$."
"neutrinosmixing are We thus assume < 7"".where 7""T.~ T. whichis a reasonable approximationdecoupled."," For the preferred value emerging from the analysis of the DAMA signal, $\epsilon \simeq 10^{-9}$, we obtain $ Y_{He'}\simeq 0.9$, which means that the dark matter is largely mirror helium dominated."
"for maythe valuesof interest.Z,;Thus. reactions we need(ο consider", We can make a rough estimate of the primordial mass fraction of mirror elements of carbon mass and heavier.
to ο are only compute note —qpaesp and pte silt’.," These are produced essentially via three-body interactions, the most important of which is the triple alpha process in the mirror sector:"
The polarimetric properties of CILA-DC-FE7 were originally reported by Whittetetal.(1992). before being used in the previous NICMOS polarimetry studies of Ilines.Schiuidt&Lytle (1997).. Tlines (1998).. InlC5.σε]πιο&Schueider(2000) aud Ilines (2002)...,"The polarimetric properties of CHA-DC-F7 were originally reported by \citet{whit92} before being used in the previous NICMOS polarimetry studies of \citet{hsandl97}, , \citet{hines98}, , \citet{hsands00} and \citet{hines02}. ."
 Witetetal.(1992) report. from eround based 1ieasuremoents. DODira.η)HOSx at O.55yau with an lustreital polarization of 0.035. aud p(2.01)=1.19+0.01% at 0-—1267E[D which we use in this comparison.," \citet{whit92} report, from ground based measurements, $p(\lambda_{max})=5.98\%$ at $0.55\micron$ with an instrumental polarization of $0.03\%$, and $p(2.04)=1.19\%\pm0.01\%$ at $\theta=126\degr\pm4\degr$ which we use in this comparison."
" The NICALOS polarimetry studies (Hiues.Sclunidt&Sch1cl-der2000) report p(2.05)=0.97E0.2'4 at 0=119x67 and p(2.05)=1.00%E0.2' (a ()—119""4ti for the 1997 and 1998 epochs respectively,", The NICMOS polarimetry studies \citep{hsands00} report $p(2.05)=0.97\%\pm0.2\%$ at $\theta=119\degr\pm6\degr$ and $p(2.05)=1.00\%\pm0.2\%$ at $\theta=119\degr\pm6\degr$ for the 1997 and 1998 epochs respectively.
" Exposures of 13.95 seconds were made, : every epoch. hrough cach of the three »olariziug elements."," Exposures of 13.95 seconds were made, at every epoch, through each of the three polarizing elements."
 With he exception of the 1997 and July 1998 epochs all observations used a four point dither tteru. cach rane being offset ly yl27:33.," With the exception of the 1997 and July 1998 epochs all observations used a four point dither pattern, each frame being offset by 3."
 All data in this study are consistent with previous poirizafioni esHuates apart roni the April 1998 epoch., All data in this study are consistent with previous polarization estimates apart from the April 1998 epoch.
 We note that «Xf all the data or CILA-DC-FE7 these observations are closest (.0 ninut«css) to a Sout1i Atlantic Anomaly passage aud are he oiilv pre-NC'S observation to IC dihered., We note that of all the data for CHA-DC-F7 these observations are closest $\sim50$ minutes) to a South Atlantic Anomaly passage and are the only pre-NCS observation to be dithered.
" While he iimber of cosie rav hits does not appear to be Ισ] than in the other epochs. we have uoticed large differeices in the protometry from cüffereit parts of the ασαλ,"," While the number of cosmic ray hits does not appear to be higher than in the other epochs, we have noticed large differences in the photometry from different parts of the array."
 Figue 3 ¢cluoustrates the difference between photometry obtained frou the iuidivilual nou-destructive readouts fro the ditlicred and nou-lithered data., Figure \ref{fig:dither} demonstrates the difference between photometry obtained from the individual non-destructive readouts from the dithered and non-dithered data.
 It cau ο seen that there is a OYSOY spreac in the photomoetrv Yolu he dithered data. which in turn could lea to a greater amount of polarization due to the ereater flux differences betwee1 the polarizers.," It can be seen that there is a larger spread in the photometry from the dithered data, which in turn could lead to a greater amount of polarization due to the greater flux differences between the polarizers."
 This effect is1 rot present im post-NC'S observations and suggests that he pedestal effect Is nor-negligible in pre-NCS dithered o)larimetry., This effect is not present in post-NCS observations and suggests that the pedestal effect is non-negligible in pre-NCS dithered polarimetry.
 Tt is well known that the NCS prodiCOS uuch more stable temperatures for the array (Schultz.Rove&Sosey2003:Arvihasetal. 2005).. which is why he pedestal effects are much less dramatic than swleni NICMOS was cooled with nitrogen ice.," It is well known that the NCS produces much more stable temperatures for the array \citep{srands03,arr05}, which is why the pedestal effects are much less dramatic than when NICMOS was cooled with nitrogen ice."
 We also note that there are late variations frou linear (~10 seconds onward) in the photometric curves of growth., We also note that there are late variations from linear $\sim10$ seconds onward) in the photometric curves of growth.
 This max be indicative of saturation. or at least non-neantv. but we do not find auv evidence for this in the Data Quality (DQ) data exteusious.," This may be indicative of saturation, or at least non-linearity, but we do not find any evidence for this in the Data Quality (DQ) data extensions."
" DQ values. of 3072 are reported which correspond to ""Pixel coutainius source” (1021) aud ""Pixel has signal iu the Oth read"" (2018). not “Saturated pixel (61) or ""Poor or uncertain Lincarity correction” (2)°."," DQ values of 3072 are reported which correspond to “Pixel containing source” (1024) and “Pixel has signal in the 0th read” (2048), not “Saturated pixel” (64) or “Poor or uncertain Linearity correction” ."
. Following on from this we also do uot see anv nou-luearity carly in the curves of growth., Following on from this we also do not see any non-linearity early in the curves of growth.
 This indicates that persistence is insiguificaut., This indicates that persistence is insignificant.
" Schinidt.Elston&Lupie(1992) report C191B2B to be an unpolarized standard with p(0.55)=0.09%+0.05% and 0=157 from observations using the ""ποΠοια polarincter.", \citet{seandl92} report G191B2B to be an unpolarized standard with $p(0.55)=0.09\%\pm0.05\%$ and $\theta=157\degr$ from observations using the “Two-Holer” polarimeter.
 The iustruneutal polarization is estimated to be., The instrumental polarization is estimated to be.
. Each NICMOS observation has au exposure time of 23.978 aud has been dithered using a three poiut pattern., Each NICMOS observation has an exposure time of 23.97s and has been dithered using a three point pattern.
 Compared to the CIIA-DC-F7 observations the point spacings for these dithers are simall., Compared to the CHA-DC-F7 observations the point spacings for these dithers are small.
 In addition. the spread iu the photometric curves of erowth is less than those seen in Figure 3..," In addition, the spread in the photometric curves of growth is less than those seen in Figure \ref{fig:dither}."
 Nevertheless the results frou this study do show polarization at a level of where something much closer to zero is expected., Nevertheless the results from this study do show polarization at a level of where something much closer to zero is expected.
 IID61299 is listed as an unpolarized staudard (pl~0.55)=0.1554 0.03€) Dy Turnsheketal.(1990)., HD64299 is listed as an unpolarized standard $p(\sim~0.55)=0.15\%\pm0.03\%$ ) by \citet{turn90}.
. Agcorecs&Walsh(1999). also use this standardiu order to characterize the iustruuceutal polarization of the ADONIS polarimeter (pins(~2.0)z 1.5%)., \citet{aandw99} also use this standardin order to characterize the instrumental polarization of the ADONIS polarimeter $p_{ins}(\sim~2.0)\approx1.5\%$ ).
 No dithering was used dunues each of the11.96s exposures andthere isno evidence for persistence or, No dithering was used during each of the11.96s exposures andthere isno evidence for persistence or
The organization of this paper is as follows.,The organization of this paper is as follows.
 In 2. we describe the modeling οἱ reijonizalion and Gunn-Peterson absorption.," In 2, we describe the modeling of reionization and Gunn-Peterson absorption."
 In 3. we compare observations [rom both quasars and WMADP to model predictions in order to constrain cosmological parameters.," In 3, we compare observations from both quasars and WMAP to model predictions in order to constrain cosmological parameters."
 In 4. we discuss our results ancl discuss their implications.," In 4, we discuss our results and discuss their implications."
 We summarize and conclude in 5., We summarize and conclude in 5.
- The details of the semianalvtic model are described in ChiuancOstriker(2000):: the basic principles are summarized here., The details of the semianalytic model are described in \citet{Chiu00}; the basic principles are summarized here.
 Ht 15 based on a (wo-phase model of the universe in which a statistical filling [actor for ionized gas is sell-consistentlv. ealeulated., It is based on a two-phase model of the universe in which a statistical filling factor for ionized gas is self-consistently calculated.
 It is assumed that the cold. neutral phase has no sources. aud evolves passively with (he expansion of the universe.," It is assumed that the cold, neutral phase has no sources, and evolves passively with the expansion of the universe."
 The hot. ionized phase contains the ionizing sources and evolves in line with local particle ancl energv conservation averaged over the phase.," The hot, ionized phase contains the ionizing sources and evolves in line with local particle and energy conservation averaged over the phase."
 The temperature of each phase is calculated. using standard physics. with photoheating as the source of heat in the ionized phase and cooling via multiple mechanisms. including IH». atomic lines. aud Compton scaltering.," The temperature of each phase is calculated using standard physics, with photoheating as the source of heat in the ionized phase and cooling via multiple mechanisms, including $_2$, atomic lines, and Compton scattering."
 The Gime evolution is determined by particle and enerey conservation., The time evolution is determined by particle and energy conservation.
 In each case. we only consider the regions outside of collapsed gas halos. which. of course will rise to the virial temperature.," In each case, we only consider the regions outside of collapsed gas halos, which, of course will rise to the virial temperature."
 Such collapsed halos are calculated separately. ancl considered potential sources of ionizing radiation.," Such collapsed halos are calculated separately, and considered potential sources of ionizing radiation."
 The abundance aud properties of these potential ionizing sources are calculated. on the basis of the Press-Schechter formalism (PressandSchechter1974).. constrained by the Jeans criterion (which utilizes the calculated gas temperatures) and by a cooling criterion (the cooling time must be less than the dvnamical time).," The abundance and properties of these potential ionizing sources are calculated on the basis of the Press-Schechter formalism \citep{PS74}, constrained by the Jeans' criterion (which utilizes the calculated gas temperatures) and by a cooling criterion (the cooling time must be less than the dynamical time)."
 Cooling in the halos includes the important contributions from IH» cooling., Cooling in the halos includes the important contributions from $_2$ cooling.
 Halos that statisf[y the Jeans criterion and that can cool efficiently are sources of ionizing radiation., Halos that statisfy the Jeans criterion and that can cool efficiently are sources of ionizing radiation.
" We calculate the luminosity of each ionizing source using the Schiniclt law where /, is the fraction of barvons already turned into stars (a small correction). My is (he barvonic mass of a halo. eg is the escape fraction from the halo. €, is a resolution [actor (related to the fraction of gas Chat can form stars) determined through calibration (see ChiuanclOstriker(2000) equation (28). aud below). ἐν is the mass to UV efficiency (where we have absorbed the notation in ChiuandOstriker(2000) of enmery into a single"," We calculate the luminosity of each ionizing source using the Schmidt law where $f_\ast$ is the fraction of baryons already turned into stars (a small correction), $M_b$ is the baryonic mass of a halo, $\epsilon_{\rm esc}$ is the escape fraction from the halo, $\epsilon_{\ast}$ is a resolution factor (related to the fraction of gas that can form stars) determined through calibration (see \citet{Chiu00} equation (28), and below), $\epsilon_{\rm UV}$ is the mass to UV efficiency (where we have absorbed the notation in \citet{Chiu00} of $\epsilon_{\rm hm}\epsilon_{\rm UV}$ into a single"
found red quasars in the Sloan Digital Sky Survey (SDSS)(Yorketal.2000).. and Glikmanetal.(2004) found them in a combination of the 2-Micron All Sky Survey (2MLASS) (Skrutskieetal.2006). anc an Automatic Plate Measuring. C'AValogue (APAICAT) of POSS/UINST sky survey plates (Irwin.Maddox.&MeMahon1994).,"found red quasars in the Sloan Digital Sky Survey \citep{2000AJ....120.1579Y}, and \citet{2004ApJ...607...60G} found them in a combination of the 2-Micron All Sky Survey (2MASS) \citep{2006AJ....131.1163S} and an Automatic Plate Measuring CATalogue (APMCAT) of POSS/UKST sky survey plates \citep{APMCAT}."
. Despite confirming the existence of red quasars. current observations have not explained the mechanism or mechanisms responsible for their existence.," Despite confirming the existence of red quasars, current observations have not explained the mechanism or mechanisms responsible for their existence."
 Dust obscuration by dust at the quasar redshift. in either the host galaxy or the quasar accretion disk (Websteretal.1995).. was the first mechanism. proposed for. quasar reddening.," Dust obscuration by dust at the quasar redshift, in either the host galaxy or the quasar accretion disk \citep{1995Natur.375..469W}, was the first mechanism proposed for quasar reddening."
 Websteretal.(1995) proposed this mechanism as a correlation between 2A colour and. redshift was not observed., \citet{1995Natur.375..469W} proposed this mechanism as a correlation between $B - K$ colour and redshift was not observed.
 “Phe result. of reddening a composite optically selected quasar spectral energy distribution (SED) with dust at the quasar redshift. was found to be consistent with the dust mechanism. because the reddening resulted in the SED ofa red. PLLIFS quasar (Websteretal.1995).," The result of reddening a composite optically selected quasar spectral energy distribution (SED) with dust at the quasar redshift, was found to be consistent with the dust mechanism, because the reddening resulted in the SED of a red PHJFS quasar \citep{1995Natur.375..469W}."
. As an alternative. Dennetal.(1998). suggested. that the DAN spread in the Websteretal.(1995) sample is partly or entirely. caused by host galaxy starlight.," As an alternative, \citet{1998MNRAS.295..451B} suggested that the $B - K$ spread in the \citet{1995Natur.375..469W} sample is partly or entirely caused by host galaxy starlight."
 Quasars with Uat-raclio-spectra are typically hosted. by [ater galaxy types (Bennetal.1998)... ancl the old. stellar population of late ἵνρο galaxies is a stronger emitter in It than D. reddening quasars (Bennctal.1998)...," Quasars with flat-radio-spectra are typically hosted by later galaxy types \citep{1998MNRAS.295..451B}, and the old stellar population of late type galaxies is a stronger emitter in K than B, reddening quasars \citep{1998MNRAS.295..451B}."
 An analysis in Alasei.Webster.&Francis(1998) of the host galaxy contribution to the red B.A colours of the PLLJIES quasars in Websteretal.(1995). was inconclusive. but. suggested host galaxy contribution was insullicient to cause the red DN colours observed.," An analysis in \citet{1998MNRAS.301..975M} of the host galaxy contribution to the red $B - K$ colours of the PHJFS quasars in \citet{1995Natur.375..469W} was inconclusive, but suggested host galaxy contribution was insufficient to cause the red $B - K$ colours observed."
 Further work in Macdox&Llewett(2006) confirmed that host galaxy starlight can delinitely redden quasars. particularly low luminosity and low redshift resolved: quasars.," Further work in \citet{2006MNRAS.367..717M} confirmed that host galaxy starlight can definitely redden quasars, particularly low luminosity and low redshift resolved quasars."
 In. accordance with Maddox.&Llewett (2006).. in this paper we use the criteria that luminous unresolved. quasars. which are not located at low redshift. are unlikely to be reddened by host galaxy contribution.," In accordance with \citet{2006MNRAS.367..717M}, in this paper we use the criteria that luminous unresolved quasars, which are not located at low redshift, are unlikely to be reddened by host galaxy contribution."
" Alternatively, Serjeant&Rawlings(1996)— proposed that a svnchrotron component of quasar emission. created a Ix-band. excess. reddening quasars."," Alternatively, \citet{1996Natur.379..304S} proposed that a synchrotron component of quasar emission created a K-band excess, reddening quasars."
 An analysis of 157 PILIES quasars and 12 LBOS quasars found. the shape of the SEDs was consistent with both line-of-sight dust and synchrotron emission. mechanisms (Lrancis.Whiting.&Webster 2000)., An analysis of 157 PHJFS quasars and 12 LBQS quasars found the shape of the SEDs was consistent with both line-of-sight dust and synchrotron emission mechanisms \citep{2000PASA...17...56F}.
. In. Barkhouse&Πα(2001). 1t was suggested that because. any svnchrotron. component to quasar emission is weaker in racio-quict quasars than in racdio-loud quasars. anysvnachrotron emission will only contribute to a small fraction of any reddening.," In \citet{2001AJ....121.2843B} it was suggested that because any synchrotron component to quasar emission is weaker in radio-quiet quasars than in radio-loud quasars, anysynchrotron emission will only contribute to a small fraction of any reddening."
" Based on the quasar sample contained therein. Barkhouse&Llall(2001) suggested that any racio-quict quasar redder than b,fy 3.7 is too red to be the result of svnchrotron emission. and is most likely the result. of dust. obscuration."," Based on the quasar sample contained therein, \citet{2001AJ....121.2843B} suggested that any radio-quiet quasar redder than $b_J - K \geq$ 3.7 is too red to be the result of synchrotron emission, and is most likely the result of dust obscuration."
 Throughout this paper we use the criterion that any red quasar that is also racio-quiet. is unlikely to be reddened by svnchrotron emission.," Throughout this paper we use the criterion that any red quasar that is also radio-quiet, is unlikely to be reddened by synchrotron emission."
 Finally. Malhotra.Ithoads.&Turner(1907). suggested that à small subset of red quasars was caused by the lensing of a quasar by a dusty galaxy.," Finally, \citet{1997MNRAS.288..138M} suggested that a small subset of red quasars was caused by the lensing of a quasar by a dusty galaxy."
 Not only. does the dust in the lens redden the quasar but the clusty galaxy potentially magnifies the host galaxy starlight contribution (Ciregg 2002).., Not only does the dust in the lens redden the quasar but the dusty galaxy potentially magnifies the host galaxy starlight contribution \citep{2002ApJ...564..133G}.
" This last mechanism was proposed. after. Malhotra.Rhoads.&""Turner(1907). observed. a similar phenomenon to Websteretal.(1995):: with racdio-selected lenses having recdeler colours than optically selected lenses.", This last mechanism was proposed after \citet{1997MNRAS.288..138M} observed a similar phenomenon to \citet{1995Natur.375..469W}; with radio-selected lenses having redder colours than optically selected lenses.
 Whichever mechanism creates red quasars. they are possibly απ evolutionary stage.," Whichever mechanism creates red quasars, they are possibly an evolutionary stage."
 After observing. ionisation Broad Absorption Line (BAL) quasars. Lacyetal.(2002) suggested. a model of quasar evolution where a quasar occupies a thick dusty torus after forming. eventually the torus dissipates leaving behind. an optically. due quasar.," After observing low-ionisation Broad Absorption Line (BAL) quasars, \citet{2002AJ....123.2925L} suggested a model of quasar evolution where a quasar occupies a thick dusty torus after forming, eventually the torus dissipates leaving behind an optically blue quasar."
 Alternately. quasars may emerge from. dusty starburst galaxies. residing in the dust stirred up by mergers (Urrutiaetal.2005)..," Alternately, quasars may emerge from dusty starburst galaxies, residing in the dust stirred up by mergers \citep{2005AAS...20717401U}."
 Either evolutionary sequence would naturally create a situation where quasars are reddened by dust at the quasar redshift., Either evolutionary sequence would naturally create a situation where quasars are reddened by dust at the quasar redshift.
 third. evolutionary path has »en proposed. where red. quasars are an evolutionary [ink tween. Ultra-Luminous Infrared. Galaxies (ULIS) and optically selected quasars (Chenctal.2006)..., A third evolutionary path has been proposed where red quasars are an evolutionary link between Ultra-Luminous Infrared Galaxies (ULIRGs) and optically selected quasars \citep{2006Ap&SS.302...17C}.
 Determining he fraction of red quasars and any dependence on redshift. uminositv. racio Lux. ete.," Determining the fraction of red quasars and any dependence on redshift, luminosity, radio flux, etc."
 will indicate if red quasars are an evolutionary stage. and which evolutionary path rec quasars xlong to.," will indicate if red quasars are an evolutionary stage, and which evolutionary path red quasars belong to."
 Depending on the mechanism. το quasars might explain the quasar contribution to the A-Ray Background (NIB).," Depending on the mechanism, red quasars might explain the quasar contribution to the X-Ray Background (XRB)."
 Using a theoretical model. Aladau.Chisellini.&Fabian(1904) showed that a ratio of two to three times as many cust obscured to unobscured active galactic nuclei (AGN)AGN) ealgalaxies can adequately.lequatel accountut for tthe existence[ of the XD.," Using a theoretical model, \citet{1994MNRAS.270L..17M} showed that a ratio of two to three times as many dust obscured to unobscured active galactic nuclei (AGN) galaxies can adequately account for the existence of the XRB."
 The model also accounts for the observed spectrum. and the source counts in the soft ancl hard. X-rav bands., The model also accounts for the observed spectrum and the source counts in the soft and hard X-ray bands.
 Ehe latest theoretical models of the NRB require a smaller ratio. Iving somewhere between 0.6 to 1.5 (11.Comastri.&Hasinger 2007).," The latest theoretical models of the XRB require a smaller ratio, lying somewhere between 0.6 to 1.5 \citep{2007A&A...463...79G}."
. Lit can be shown that. red uasars are the result of cust obscuration. and that the red uasar [fraction is within to604.. then red. quasars we the most probable source of the quasar contribution to w ARB.," If it can be shown that red quasars are the result of dust obscuration, and that the red quasar fraction is within to, then red quasars are the most probable source of the quasar contribution to the XRB."
 The existence of red quasars has various implications. 10 main one is that it can no longer be assumed that existing quasar samples are representative of the entire uasar population.," The existence of red quasars has various implications, the main one is that it can no longer be assumed that existing quasar samples are representative of the entire quasar population."
 “Phe statistics of a sample rellects the sroperties of the sub-set of a population from which the sample is drawn. previous quasar samples. such as the LDOS. are biassed to the inclusion of blue quasars: therefore. he statistics of such samples predominantly: reflects. the due quasar population.," The statistics of a sample reflects the properties of the sub-set of a population from which the sample is drawn, previous quasar samples, such as the LBQS, are biassed to the inclusion of blue quasars; therefore, the statistics of such samples predominantly reflects the blue quasar population."
 Use of existing quasar datasets requiring a sample that is representative of the entire quasar »o»pulation is therefore subject to review., Use of existing quasar datasets requiring a sample that is representative of the entire quasar population is therefore subject to review.
 Direct. examples of this are that the luminosity function. of quasars and he change in number density with redshift need to be evaluated while including red quasars., Direct examples of this are that the luminosity function of quasars and the change in number density with redshift need to be re-evaluated while including red quasars.
 In order to learn more about red. quasars. swe need Oo spectroscopically observe quasars over their. entire colour range.," In order to learn more about red quasars, we need to spectroscopically observe quasars over their entire colour range."
 To achieve this. future surveys will have o select. quasar candidates for. spectroscopic. follow-up using a technique that is not biased. against either red or blue quasars.," To achieve this, future surveys will have to select quasar candidates for spectroscopic follow-up using a technique that is not biased against either red or blue quasars."
. One candidate for a suitable selection echnique is the KX method. developed in Warren.Llewett. (2000)..," One candidate for a suitable selection technique is the KX method, developed in \citet{2000MNRAS.312..827W}. ."
 The IXX. method utilises the power-law nature of quasar SEDs at long wavelengths combined. with morphological classification., The KX method utilises the power-law nature of quasar SEDs at long wavelengths combined with morphological classification.
 Stars experience a turnover in their. SED in L-band while quasars follow a power-law. allowing cliscrimination between stars anc quasars.," Stars experience a turnover in their SED in H-band while quasars follow a power-law, allowing discrimination between stars and quasars."
 The stellar morphology of quasars discriminates between quasars, The stellar morphology of quasars discriminates between quasars
rather (han (he minimum used in Equation (3)).,rather than the minimum used in Equation \ref{eqn:rc}) ).
" Despite this. we choose to keep the more physically motivated definition of 7, for reasons discussed in relsec:clata.."," Despite this, we choose to keep the more physically motivated definition of $r_c$ for reasons discussed in \\ref{sec:data}."
 To quantify the amount of relative structure galaxies. we calculated (he root mean squared (xis) of (he pixel-to-pixel variations of the galaxies. structure maps within 7.," To quantify the amount of relative structure galaxies, we calculated the root mean squared (rms) of the pixel-to-pixel variations of the galaxies' structure maps within $r_c$."
 The more cust structure or star formation in a galaxy. the higher the dust contrast in the structure map. and therelore the higher (he rms.," The more dust structure or star formation in a galaxy, the higher the dust contrast in the structure map, and therefore the higher the rms."
 We assign an uncertaintv to the rms by caleulating the standard deviation of 11 measurements of (he rms within a circular aperture ranging in radius from 0.957. to 1.05r. in increments on 0.01r.., We assign an uncertainty to the rms by calculating the standard deviation of 11 measurements of the rms within a circular aperture ranging in radius from $0.95r_c$ to $1.05r_c$ in increments on $0.01r_c$.
" We further define 6,4, (to be the average of these 11 measured rms values.", We further define $\sigma_{\mbox{\scriptsize sm}}$ to be the average of these 11 measured rms values.
" The variation on a, is found to be no more than [or anv object.", The variation on $\sigma_{\mbox{\scriptsize sm}}$ is found to be no more than for any object.
 The measured rms values and uncertainties for each galaxy are given in Table 1.., The measured rms values and uncertainties for each galaxy are given in Table \ref{tbl:data}.
 Because the structure map is sensitive (ο structures on the scale of (he PSF. rather than some plivsical scale. (here may be a strong distance-clepencent bias in ao...," Because the structure map is sensitive to structures on the scale of the PSF, rather than some physical scale, there may be a strong distance-dependent bias in $\sigma_{\mbox{\scriptsize sm}}$."
 We therefore tested how σι changes for a given galaxy upon chaneine the resolution using a test sample ol nime galaxies with high enough resolutions (ο meet our resolution ancl signal-to-noise cuts (see relfsec:data)) even after being convolved with a Gaussian with a standard. deviation of 2.6 pixels. which corresponds to more (han doubling their distance.," We therefore tested how $\sigma_{\mbox{\scriptsize sm}}$ changes for a given galaxy upon changing the resolution using a test sample of nine galaxies with high enough resolutions to meet our resolution and signal-to-noise cuts (see \\ref{sec:data}) ) even after being convolved with a Gaussian with a standard deviation of 2.6 pixels, which corresponds to more than doubling their distance."
 For each object. we convolved both the image and the PSF with a Gaussian will a standard deviation of 1.02.6 pixels (in Q.1 pixel increments). Grom which a set of 17 degraded structure maps were constructed.," For each object, we convolved both the image and the PSF with a Gaussian with a standard deviation of 1.0–2.6 pixels (in 0.1 pixel increments), from which a set of 17 degraded structure maps were constructed."
 An example of this degradation for NGC4321 is shown in Figure 3.., An example of this degradation for NGC4321 is shown in Figure \ref{fig:rmsdegrade}.
 We then calculated Toy (and uncertainty. as described above) for each of these degraded structure maps.," We then calculated $\sigma_{\mbox{\scriptsize sm}}$ (and uncertainty, as described above) for each of these degraded structure maps."
 While Toy Cid change for each object. the change was found to be comparable with the calculated uncertainties for anv given structure map.," While $\sigma_{\mbox{\scriptsize sm}}$ did change for each object, the change was found to be comparable with the calculated uncertainties for any given structure map."
 This implies (hat at these scales. the dust styucture is roughly scale-invariant. in agreement wilh the findings of Elmegreenetal.(2002) that the power spectra of dust structure becomes relatively shallow at small scales.," This implies that at these scales, the dust structure is roughly scale-invariant, in agreement with the findings of \citet{elmegreen02} that the power spectra of dust structure becomes relatively shallow at small scales."
" We thus conclude that a, does not contain a distance«dependent bias and employ it below to compare different subsamples of galaxies.", We thus conclude that $\sigma_{\mbox{\scriptsize sm}}$ does not contain a distance-dependent bias and employ it below to compare different subsamples of galaxies.
on-source integration time at each point.,on-source integration time at each point.
" To obtain a spatial resolution comparable to that of the other two lines, the map was convolved with a Gaussian beam of 20"" at the DR 21 central position."," To obtain a spatial resolution comparable to that of the other two lines, the map was convolved with a Gaussian beam of $''$ at the DR 21 central position."
 The HIFI spectra are displayed inFig., The HIFI spectra are displayed inFig.
" 1. with, for comparison, an IRAM-30m spectrum of HCO""((1-0) (Schneideretal. 2010)."," \ref{fig:data} with, for comparison, an IRAM-30m spectrum of (1-0) \citep{schneider}."
. The line profiles exhibit both complex emission and absorption because of the multiplicity of velocity components and gas physical conditions within the beam., The line profiles exhibit both complex emission and absorption because of the multiplicity of velocity components and gas physical conditions within the beam.
 The line integrated areas in emission and absorption are remarkably comparable., The line integrated areas in emission and absorption are remarkably comparable.
 This would lead to a weak or non-detection with low spectral resolution instruments., This would lead to a weak or non-detection with low spectral resolution instruments.
" The dashed lines in the aand sspectra, at about half the continuum level, reveal the broad velocity ranges across which the absorption lines are saturated."," The dashed lines in the and spectra, at about half the continuum level, reveal the broad velocity ranges across which the absorption lines are saturated."
" The CH*((1-0), aand sspectra, plotted after their continuum has been subtracted, are superimposed in Fig."," The (1-0), and spectra, plotted after their continuum has been subtracted, are superimposed in Fig."
 2 for the frequency of the line set to 835.137 GHz., \ref{fig:3spec} for the frequency of the line set to 835.137 GHz.
 We propose in Sect., We propose in Sect.
" 5 that the broad line emission originates from a shock associated with the outflow, and we show that the three species,CH*,,, and aare connected with each other in the shock chemistry."," 5 that the broad line emission originates from a shock associated with the outflow, and we show that the three species, and are connected with each other in the shock chemistry."
" The good agreement (within + 1 kms~')) between the blue wing of the emission line profiles of these three species allows us to adopt v=835137+3 MHz as the rest frequency of the |CH*((1-0) line, which is remarkably consistent with the experimental value measured by Amano (2010)."," The good agreement (within $\pm$ 1 ) between the blue wing of the emission line profiles of these three species allows us to adopt $\nu=835137 \pm 3$ MHz as the rest frequency of the (1-0) line, which is remarkably consistent with the experimental value measured by Amano (2010)."
 The CH* lline profile can be decomposed into a broad emission line and a series of absorption features., The $^+$ line profile can be decomposed into a broad emission line and a series of absorption features.
" We used information from the line profiles of CO and HCO* ((see Fig. 1)),"," We used information from the line profiles of CO and $^+$ (see Fig. \ref{fig:data}) ),"
" the spectra of atomic carbon Jakobetal.(2007),, and other HIFI spectra to constrain the velocity and linewidth of these components."," the spectra of atomic carbon \cite{jakob}, and other HIFI spectra to constrain the velocity and linewidth of these components."
" Since the Iline has not been observed, the actual eemission profile is unknown."," Since the line has not been observed, the actual emission profile is unknown."
 We had to rely on the symmetric shapes of the CO emission lines to model the broad emission wings with Gaussians adjusted on the blue wings of the lines (Table 1)., We had to rely on the symmetric shapes of the CO emission lines to model the broad emission wings with Gaussians adjusted on the blue wings of the lines (Table 1).
" Over the velocity range -5 to 17kms!,, not only the continuum level but also the coreline emission is absorbed by intervening gas."," Over the velocity range -5 to 17, not only the continuum level but also the coreline emission is absorbed by intervening gas."
" The broad emission lines (Av=20sl, see Table 1) correspond to the emission associated with the outflow shock (see Sect."," The broad emission lines $\Delta v=20$, see Table 1) correspond to the emission associated with the outflow shock (see Sect."
 5)., 5).
 A still broader component in the [CII] line has a width similar to that of the Ηόόα recombination lines Roelfsemaetal., A still broader component in the [CII] line has a width similar to that of the $\alpha$ recombination lines \cite{prr}.
"(1989).. Self-absorption features in the range ~—3 to 2kms!,, caused by the close environment of the DR21 core, are visible in CO, HCO*(4-3), and other dense gas tracers (e.g., NH3 inversion lines)."," Self-absorption features in the range $\sim -3$ to 2, caused by the close environment of the DR21 core, are visible in CO, $^+$ (4-3), and other dense gas tracers (e.g., $_3$ inversion lines)."
" The absorption dip at this velocity is more prominent in the H2O(1;.; —00,0) profile as expected from the high critical density of this transition."," The absorption dip at this velocity is more prominent in the $_2$ $1_{1,1}-0_{0,0}$ ) profile as expected from the high critical density of this transition."
 We disregarded this velocity range in our analysis because of the unknown line intensity of the dense core emission., We disregarded this velocity range in our analysis because of the unknown line intensity of the dense core emission.
" In contrast, the absorption at v>7 ccorresponds to the gas that is most likely to be associated with the W75N cloud in the Cygnus X complex."," In contrast, the absorption at $v> 7 $ corresponds to the gas that is most likely to be associated with the W75N cloud in the Cygnus X complex."
 Its velocity coverage is very similar in the aand sspectra., Its velocity coverage is very similar in the and spectra.
" We fitted three components in this velocity range, guided by the absorption features of the HCO* aand H50 profiles at vrsg=7.5,11, and 13.7 !shown in Fig."," We fitted three components in this velocity range, guided by the absorption features of the $^+$ and $_2$ O profiles at $v_{LSR} = 7.5, 11$, and 13.7 shown in Fig."
" 1, the resulting profiles being in red."," 1, the resulting profiles being in red."
 The ccolumn density of the emission line was determined by assuming that it is optically thin., The column density of the emission line was determined by assuming that it is optically thin.
 This is consistent with the CH*((1-0) line not being detected in emission towards galactic massive star-forming regions (FalgaroneFalgaroneetal. 2005).," This is consistent with the (1-0) line not being detected in emission towards galactic massive star-forming regions \cite[Falgarone et al. in prep., ][]{falgarone05}."
. The total ccolumn density was therefore assumed to scale with the line integrated area (in Kkms~!)) with a coefficient that depends on the excitation temperature., The total column density was therefore assumed to scale with the line integrated area (in ) with a coefficient that depends on the excitation temperature.
" For 40 K«Τι«100 K, the range of Τεν that minimizes N(CH*), a lower limit N4,(CH*)=7x10!!cm?fT(v)dv was obtained, using the spontaneous decay rate Ajo=5.9x10? s! inferred from the dipole moment, 4—1.62 D Kobayashietal. (1993)."," For 40 $<T_{ex}<100$ K, the range of $T_{ex}$ that minimizes $N(\CHp)$, a lower limit $N_{em}(\CHp)=7 \times 10^{11} \pscm\ \int T(v) dv$ was obtained, using the spontaneous decay rate $A_{10}=5.9 \times 10^{-3}$ $^{-1}$ inferred from the dipole moment, $\mu=1.62$ D \cite{kobayashi93}. ."
". In absorption, we inferred the column density from the integral of the optical depth (in s~!)) to be Naps(CH*)=3.3x10?cm?f 104v."," In absorption, we inferred the column density from the integral of the optical depth (in ) to be $N_{abs}(\CHp)= 3.3 \times 10^{12} \pscm\ \int \tau(v) dv$ ."
" It is almost independent of T,, as long as Τε<<hv/k= 39K,"," It is almost independent of $T_{ex}$ as long as $T_{ex}<<h\nu/k=39$ K,"
can infer a lower limit recurrence time for a given svstem to be ~10!—10° vr.,can infer a lower limit recurrence time for a given system to be $\sim10^4-10^5$ yr.
 Thus the recurrence time is verv short compared to the lifetime ofa CV so that CVs will experience many classical nova outbursts in their lifetimes., Thus the recurrence time is very short compared to the lifetime of a CV so that CVs will experience many classical nova outbursts in their lifetimes.
 The old novae and recurrent novae are the only CVs that have recorded evidence of having undergone nova explosions., The old novae and recurrent novae are the only CVs that have recorded evidence of having undergone nova explosions.
 Among the old novae. DI Lac (Mover et al.," Among the old novae, DI Lac (Moyer et al."
 2003) and V841 Ophiuchi are the only such svslems (hat have optical aud UV spectra resembling the UX UMa-tvpe nova-like variables (Warner 1995 and relerences therein)., 2003) and V841 Ophiuchi are the only such systems that have optical and UV spectra resembling the UX UMa-type nova-like variables (Warner 1995 and references therein).
 Emission line widths are very narrow. indicating a low inclination. as first noted by Ίντα (1964) and later confirmed by other studies.," Emission line widths are very narrow, indicating a low inclination, as first noted by Kraft (1964) and later confirmed by other studies."
 A low inclination could explain why these (wo old novae have the highest optical to N-rav. [lux ratios., A low inclination could explain why these two old novae have the highest optical to X-ray flux ratios.
 We note however. that their optical spectra are «quite different. (loard et al.," We note however, that their optical spectra are quite different (Hoard et al."
 2000)., 2000).
 The optical spectra of DI Lac reveal broad. shallow Balmer aid helium absorption lines with superimposed weak emission lines. whereas V841 Oph reveals strong; single-peaked Balmer. Ile and He emission features.," The optical spectra of DI Lac reveal broad, shallow Balmer and helium absorption lines with superimposed weak emission lines, whereas V841 Oph reveals strong single-peaked Balmer, He and He emission features."
 The impetus for this work arises [rom the paucity of knowledge about the white dwarfs and accretion disks in old novae., The impetus for this work arises from the paucity of knowledge about the white dwarfs and accretion disks in old novae.
 Low high are (heir accretion rates in (he post-nova state?, How high are their accretion rates in the post-nova state?
 Is there a correlation between (he (me since the nova and (he accretion rate in the old nova svstem?, Is there a correlation between the time since the nova and the accretion rate in the old nova system?
 How quickly is an accretion disk established following a nova explosion?, How quickly is an accretion disk established following a nova explosion?
 Llow hot is the post-nova white dwarf and how was it affected bv the explosion?, How hot is the post-nova white dwarf and how was it affected by the explosion?
 These basic «questions lack definitive answers and underscore the need for advancing our knowledge of these svstems., These basic questions lack definitive answers and underscore the need for advancing our knowledge of these systems.
 This is especially true in the FUV range as shown in the recent analvsis of the HIST STIS spectrum of DI Lac (Mover et al., This is especially true in the FUV range as shown in the recent analysis of the HST STIS spectrum of DI Lac (Moyer et al.
 2003)., 2003).
 V841 Oph was discovered at the time of its outburst in 1848. as Nova Oph 1348 and the early literature classified it as à fast nova.," V841 Oph was discovered at the time of its outburst in 1848, as Nova Oph 1848 and the early literature classified it as a fast nova."
 However. the true maximum was very likely missed and hence the correct {η value remains uncertain.," However, the true maximum was very likely missed and hence the correct $t_{3}$ value remains uncertain."
 This uncertainty in {η and its impact on the speed class and distance estimates of V841 Oph is discussed in section 3.1 below., This uncertainty in $t_{3}$ and its impact on the speed class and distance estimates of V841 Oph is discussed in section 3.1 below.
 Its orbital period is 0.601442:0.00056 (Ritter and Ixolb 1993)., Its orbital period is $\pm$ 0.00056 (Ritter and Kolb 1998).
 The observed or estimated physical and orbital parameters published for V841 Oph are listed in Table 1., The observed or estimated physical and orbital parameters published for V841 Oph are listed in Table 1.
" Warner (1995) derives absolute magnitudes of CV subtypes and assigned M, = +3.9 as al average for old novae as a class which. if due to accretion. implies an accretion rate of 5 M, /vr."," Warner (1995) derives absolute magnitudes of CV subtypes and assigned $_V$ = +3.9 as an average for old novae as a class which, if due to accretion, implies an accretion rate of $^{-8}$ $_{\sun}$ /yr."
 Warner found a strong correlation between emission line equivalent widths and the inclinations of the CV svstems. as well as a strong correlation between the imelination angle and the absolute magnitude.," Warner found a strong correlation between emission line equivalent widths and the inclinations of the CV systems, as well as a strong correlation between the inclination angle and the absolute magnitude."
 The svstems having higher inclination angles also had lower M values than those that had smaller inclination angles., The systems having higher inclination angles also had lower $_V$ values than those that had smaller inclination angles.
 Moreover. the svstems that were nearly pole-on. like DI Lac and V841 Oph. were found to have the highest M values.," Moreover, the systems that were nearly pole-on, like DI Lac and V841 Oph, were found to have the highest $_V$ values."
Raj and A. are much larger than unity.,${\cal R}_{\rm B}$ and ${\cal R}_{\rm e}$ are much larger than unity.
 In the wind. case. with proper Ry and Ro. the RS emission may be dominant in the soft X-ray band. too.," In the wind case, with proper ${\cal R}_{\rm B}$ and ${\cal R}_{\rm e}$, the RS emission may be dominant in the soft X-ray band, too."
 But there is no flare expected since both the FS and RS emission components. decrease continually even at very carly time (see also Zou. Wu Dai 2005).," But there is no flare expected since both the FS and RS emission components decrease continually even at very early time (see also Zou, Wu Dai 2005)."
 So the FS-RS scenario is unable to account for the X- Hare detected in GRB 011121., So the FS-RS scenario is unable to account for the X-ray flare detected in GRB 011121.
 Moreover. in the general framework of accounting for X-ray Hares in GIU afterglows. the PS-RS model is further cdisfavored for the fact that. even in an ISA scenario with parameters suitable for a RS Hare arising above the FS emission. the predicted temporal decay is too shallow compared to the steep decay of X-rayDares observed so far (see Fig. 1)).," Moreover, in the general framework of accounting for X-ray flares in GRB afterglows, the FS-RS model is further disfavored for the fact that, even in an ISM scenario with parameters suitable for a RS flare arising above the FS emission, the predicted temporal decay is too shallow compared to the steep decay of X-rayflares observed so far (see Fig. \ref{fig:FRX}) )."
 In the standard fireball model of CRBs. the = rav emission is powered by internal shocks. whose duration depends on the active time of the central engine.," In the standard fireball model of GRBs, the $\gamma-$ ray emission is powered by internal shocks, whose duration depends on the active time of the central engine."
 Llowever. the variability ol some GIU afterglows implies that the activity of the GRB central engine may last much longer than the duration of the prompt emission recorded by ο ray monitors (e.g.. Dai Lu 1998: Granot. Nakar Piran 2003: loka. Ixobavashi Zhang 2005).," However, the variability of some GRB afterglows implies that the activity of the GRB central engine may last much longer than the duration of the prompt emission recorded by $\gamma-$ ray monitors (e.g., Dai Lu 1998; Granot, Nakar Piran 2003; Ioka, Kobayashi Zhang 2005)."
 In addition. it has been proposed that the Fe line observed in some GRB X-ray. alterelows could. be attributed to a prolonged activity of the central engine (Recs Alésszarros 2000: Gao Wei 2005).," In addition, it has been proposed that the Fe line observed in some GRB X-ray afterglows could be attributed to a prolonged activity of the central engine (Rees Mésszárros 2000; Gao Wei 2005)."
 A possible mechanism for the re-activity of the central engine could be as follows., A possible mechanism for the re-activity of the central engine could be as follows.
 During the accretion phase which powers the prompt 5. ray emission. a fraction of the material constituting the massive progenitor could possibly be pulled out: the central engine could thus be restarted at late times by the fall back of part of this material onto the central collapsar remnant (Ixing et al.," During the accretion phase which powers the prompt $\gamma-$ ray emission, a fraction of the material constituting the massive progenitor could possibly be pulled out; the central engine could thus be restarted at late times by the fall back of part of this material onto the central collapsar remnant (King et al."
 2005)., 2005).
 llere we assume that the central engine restarts a [ew minutes after the prompt 5. ray emission. powering a new unsteady relativistic outflow.," Here we assume that the central engine restarts a few minutes after the prompt $\gamma-$ ray emission, powering a new unsteady relativistic outflow."
 We suppose that the Lorentz actor of the ejected material can be highly variable. setting D.— 10 and E;~ 100. as the typical Lorentz factors. of he slow and fast shells. respectively.," We suppose that the Lorentz factor of the ejected material can be highly variable, setting $\Gamma_{\rm
s}\sim $ 10 and $\Gamma_{\rm f}\sim $ 100, as the typical Lorentz factors of the slow and fast shells, respectively."
 Lhe masses of the slow and fast shells are taken as mícm..., The masses of the slow and fast shells are taken as $m_{\rm f}\simeq m_{\rm s}$.
 When an inner ast shell catches up with an outer slow shell at à radius ονf(1E2) (where δε is the observed typical variability imescale of the X-ray Hares). internal shocks are generated.," When an inner fast shell catches up with an outer slow shell at a radius $\sim 2\Gamma_{\rm s}^2 c \delta t_\oplus/(1+z)$ (where $\delta t_\oplus$ is the observed typical variability timescale of the X-ray flares), internal shocks are generated."
 The Lorentz factor of the merged shell is EsVIE. (e.g. iran 1999). and the Lorentz factor of the internal shocks can be estimated by EazmlL.|D0/2.," The Lorentz factor of the merged shell is $\Gamma \approx \sqrt{\Gamma_{\rm f}
\Gamma_{\rm s}}$ (e.g., Piran 1999), and the Lorentz factor of the internal shocks can be estimated by $\Gamma_{\rm sh}\approx
(\sqrt{\Gamma_{\rm f}/\Gamma_{\rm s}}+\sqrt{\Gamma_{\rm
s}/\Gamma_{\rm f}})/2$."
 We call this re-generated internal (Γιshocks as theVT. “late internal shocks”.," We call this re-generated internal shocks as the “late internal shocks""."
 The internal shock model has been discussed. by many authors (ο... Paezvisski Xu 1994: Rees Alésszarros 1994: Daigne Alochkoviteh 1998. 2000: Piran 1999: Dai Lu 2002).," The internal shock model has been discussed by many authors (e.g., Paczyńsski Xu 1994; Rees Mésszárros 1994; Daigne Mochkovitch 1998, 2000; Piran 1999; Dai Lu 2002)."
 Generally speaking. to caleulate the synchrotron emission of internal shocks. the following parameters. are involved: the outflow Luminosity £4. af). E. Ey. and of course the shock parameters e; anc ep.," Generally speaking, to calculate the synchrotron emission of internal shocks, the following parameters are involved: the outflow luminosity $L_{\rm m}$ , $\delta t_\oplus$, $\Gamma$, $\Gamma_{\rm sh}$, and of course the shock parameters $\epsilon_{\rm e}$ and $\epsilon_{\rm B}$."
 For typical GRBs. (Lu.of).V.Va.6. ep) are taken to he 0.1). respectively (e... Dai Lu 2002).," For typical GRBs, $L_{\rm m}, ~\delta t_\oplus,~\Gamma,~\Gamma_{\rm sh},~\epsilon_{\rm e},~\epsilon_{\rm B}$ ) are taken to be $\sim (10^{52}~{\rm ergs~s^{-1}}, ~0.001-0.01~{\rm s},~100-1000,~{\rm a~few},~0.5,~0.01-0.1)$ , respectively (e.g., Dai Lu 2002)."
 The time averaged: isotropic luminosity (2-100. keV) of the X-ray re-bursting of CRB 011121 is Ly~610eress (P05)., The time averaged isotropic luminosity (2-700 keV) of the X-ray re-bursting of GRB 011121 is $ L_{\rm x}\sim 6 \times 10^{48}{\rm ergs~s^{-1}}$ (P05).
 So we normalize our expression by taking Lu~5ΠΠ”...CresSNL. where c is. the elliciency factor of the X-ray flare.," So we normalize our expression by taking $L_{\rm m}\sim 5\times 10^{49}~L_{\rm x,49}(\epsilon/0.2)^{-1}~
{\rm ergs ~ s^{-1}}$, where $\epsilon$ is the efficiency factor of the X-ray flare."
 We take €~0.2. as found in typical GRBs/XREs (Llovd-Itonning Zhang 2004).," We take $\epsilon \sim 0.2$, as found in typical GRBs/XRFs (Lloyd-Ronning Zhang 2004)."
" Such small Lu, (comparing with the GRB case) implies that the fallback aceretion rate is just 0.0010.01 times that of the prompt accretion. if the cllicicney factor of converting je accretion energv into the kinetic cnerey of the outllow is nearly a constant (Macbadyen. Woosley Leger 200"," Such small $L_{\rm m}$ (comparing with the GRB case) implies that the fallback accretion rate is just $\sim 0.001-0.01$ times that of the prompt accretion, if the efficiency factor of converting the accretion energy into the kinetic energy of the outflow is nearly a constant (MacFadyen, Woosley Heger 2001)."
" The 9/4, measured in X-ray [lares is significantly longer iun that measured in the intrinsic hard burst (Burrows et al.", The $\delta t_\oplus$ measured in X-ray flares is significantly longer than that measured in the intrinsic hard burst (Burrows et al.
 2005)., 2005).
 In this Letter. we take δὲ~ 10 s. The spectra of the N-rav [lares detected so far are all nonthermal.," In this Letter, we take $\delta t_\oplus\sim $ 10 s. The spectra of the X-ray flares detected so far are all nonthermal."
 The optical thin condition implies a lower limit. on the bulk Lorentz Factor of the merged shell (e.g. Rees Mésszárros 1904) 1l The typical radius of the late internalshock is eià l," The optical thin condition implies a lower limit on the bulk Lorentz factor of the merged shell (e.g., Rees Mésszárros 1994) > 11 , The typical radius of the late internalshock is $R_{\rm int} \approx 2 \Gamma^2 c \delta t_\oplus/(1+z)>5\times 10^{13}~{\rm cm}~L_{\rm m,49.7}^{2/5}[1.36/(1+z)]^{3/5}\delta t_{\oplus,1}^{3/5}$ ."
could still be consistent with cuspy halo models.,could still be consistent with cuspy halo models.
" The systematic effects that were investigated fall into two categories,", The systematic effects that were investigated fall into two categories.
 These effects are difficult to recognize in long-slit. one-dimensional Ha data without additional information.," These effects are difficult to recognize in long-slit, one-dimensional $\alpha$ data without additional information."
 Many authors therefore. apart from modeling these effects. also emphasized the need for high-resolution. two-dimensional velocity fields.," Many authors therefore, apart from modeling these effects, also emphasized the need for high-resolution, two-dimensional velocity fields."
 These make pointing problems irrelevant. while non-circular motions can be directly measured.," These make pointing problems irrelevant, while non-circular motions can be directly measured."
 Fortunately. these velocity fields are now available (see 33.6). largely superseding the results derived from the Ha rotation curves.," Fortunately, these velocity fields are now available (see 3.6), largely superseding the results derived from the $\alpha$ rotation curves."
 Nevertheless. for completeness. the further analysis of the Ha curves ts briefly discussed here.," Nevertheless, for completeness, the further analysis of the $\alpha$ curves is briefly discussed here."
 In ? afirst attempt was made at modeling the observational systematic effects., In \citet{deBlok:2003p11} a first attempt was made at modeling the observational systematic effects.
 Their main conclusion was that NFW halos can be made to resemble dark matter cores only if. either systematic non-circular motions with an amplitude of ~20 km s exist in all disks. or systematic telescope pointing offsets of ~3-4” exist for all observations. or if the dynamical and photometric centers are systematically offset in all galaxies by ~0.5—1 kpe.," Their main conclusion was that NFW halos can be made to resemble dark matter cores only if, either systematic non-circular motions with an amplitude of $\sim 20$ km $^{-1}$ exist in all disks, or systematic telescope pointing offsets of $\sim 3-4''$ exist for all observations, or if the dynamical and photometric centers are systematically offset in all galaxies by $\sim 0.5-1$ kpc."
 ? and ? compare independent sets of observations of the same galaxies. obtained at different telescopes. by independent groups. using independent data sets. and find no evidence for telescope pointing errors.," \citet{Marchesini:2002p78} and \citet{deBlok:2002p47} compare independent sets of observations of the same galaxies, obtained at different telescopes, by independent groups, using independent data sets, and find no evidence for telescope pointing errors."
 In general. galaxies can be acquired and positioned on the slit with a repeatability accuracy of 0.3” or so.," In general, galaxies can be acquired and positioned on the slit with a repeatability accuracy of $''$ or so."
 Using further modeling. ?— find that a halo model with a mildly cuspy slope à2—0.240.2 gives the best description of the data in the presence of realistic observational effects.," Using further modeling, \citet{deBlok:2003p11} find that a halo model with a mildly cuspy slope $\alpha = -0.2 \pm 0.2$ gives the best description of the data in the presence of realistic observational effects."
 It is interesting to note that this best-fitting slope had already been derived by ? on the basis of the ? data., It is interesting to note that this best-fitting slope had already been derived by \citet{Kravtsov:1998p159} on the basis of the \citet{deBlok:1996p5} data.
 An analysis by ?.— of longsht Ho rotation curves of 165 low-mass galaxies comes to the same conclusion: depending on how they select their sample. they find best-fitting slopes of an2—0.22t:0.08 to a2—0.280.06.," An analysis by \citet{Spekkens:2005p36} of longslit $\alpha$ rotation curves of 165 low-mass galaxies comes to the same conclusion: depending on how they select their sample, they find best-fitting slopes of $\alpha = -0.22 \pm 0.08$ to $\alpha = -0.28 \pm 0.06$."
 They also model pointing and slit offsets. but come to the conclusion that. after correction. their data are consistent with cuspy haloes.," They also model pointing and slit offsets, but come to the conclusion that, after correction, their data are consistent with cuspy haloes."
 ? also present extensive modeling of high-resolution long-slit Ha rotation curves. and show that while their data are consistent with «=0 cores. steeper slopes cannot be ruled out.," \citet{Swaters:2003p49} also present extensive modeling of high-resolution long-slit $\alpha$ rotation curves, and show that while their data are consistent with $\alpha = 0$ cores, steeper slopes cannot be ruled out."
 Given the difference in interpretation of otherwise similar samples. a double-blind analysis of the modeling performed by the various groups would have been interesting.," Given the difference in interpretation of otherwise similar samples, a double-blind analysis of the modeling performed by the various groups would have been interesting."
 However. with the availability of high-resolution velocity fields. this is now a moot Issue.," However, with the availability of high-resolution velocity fields, this is now a moot issue."
 ? attempt to model many of the observational effects using numerical simulations., \citet{Rhee:2004p43} attempt to model many of the observational effects using numerical simulations.
 Most of their conclusions apply to long-slit observations., Most of their conclusions apply to long-slit observations.
" The systematic effects they investigate (dealing with inclination effects. non-circular motions and profile shapes) have now been directly tested on high-resolution velocity fields and do not critically affect the data (eσ 2222229),"," The systematic effects they investigate (dealing with inclination effects, non-circular motions and profile shapes) have now been directly tested on high-resolution velocity fields and do not critically affect the data (e.g., \citealt{Gentile:2005p89, Zackrisson:2006p1246,
 Trachternach:2008p152, Oh:2008p153, deBlok:2008p155,
 KuzioDeNaray:2008p50,KuzioDeNaray:2009p67}) )."
 As noted. high-resolution two-dimensional velocity fields provide the context which long-slit observations are missing.," As noted, high-resolution two-dimensional velocity fields provide the context which long-slit observations are missing."
 With these velocity fields the pointing problem becomes irrelevant. offsets between kinematical and dynamical centers can be directly measured. as can non-circular motions.," With these velocity fields the pointing problem becomes irrelevant, offsets between kinematical and dynamical centers can be directly measured, as can non-circular motions."
 Following is a brief overview of the various observational studies that have presented and analysed these velocity fields within the context of the core/cusp debate., Following is a brief overview of the various observational studies that have presented and analysed these velocity fields within the context of the core/cusp debate.
 Some of the first high-resolution optical velocity fields of late-type dwarf and LSB galaxies were presented by ?.., Some of the first high-resolution optical velocity fields of late-type dwarf and LSB galaxies were presented by \citet{BlaisOuellette:2001p1259}.
 They analyse Hea Fabry-Perot data of IC 2574 and NGC 3109. two nearby dwarf galaxies. and derive slowly rising rotation curves. consistent with a core.," They analyse $\alpha$ Fabry-Perot data of IC 2574 and NGC 3109, two nearby dwarf galaxies, and derive slowly rising rotation curves, consistent with a core."
 This work was later expanded in 2.. and led to the work presented in ?.. where optical velocity fields of 36 galaxies of different morphological types are presented.," This work was later expanded in \citet{BlaisOuellette:2004p51}, and led to the work presented in \citet{Spano:2008p143}, where optical velocity fields of 36 galaxies of different morphological types are presented."
 All three studies find that the PI model generally provided better fits than NFW models., All three studies find that the PI model generally provided better fits than NFW models.
 If NFW models give fits of comparable quality. then this is usually at the cost of an unrealistically low Y. value and non-cosmological (c.Vso5) values.," If NFW models give fits of comparable quality, then this is usually at the cost of an unrealistically low $\Upsilon_{\star}$ value and non-cosmological $(c,V_{200})$ values."
 A similarly large collection of Hai velocity fields is presented in ?.., A similarly large collection of $\alpha$ velocity fields is presented in \citet{Dicaire:2008p827}. .
 They do not explicitly address the core/cusp issue. but show that when bars are present. their influence on the velocity fields is very noticable.," They do not explicitly address the core/cusp issue, but show that when bars are present, their influence on the velocity fields is very noticable."
 ?? present DensePak velocity fields of LSB galaxies. many of them taken from the ? sample.," \citet{KuzioDeNaray:2008p50,KuzioDeNaray:2009p67} present DensePak velocity fields of LSB galaxies, many of them taken from the \citet{deBlok:1997p22} sample."
 Their conclusions are that NFW models provide a worse fit than PI models. for all values of Y..," Their conclusions are that NFW models provide a worse fit than PI models, for all values of $\Upsilon_{\star}$."
 Where an NFW model could be fit. the c-values generally again do not match the cosmological CDM (c.ορ) relation.," Where an NFW model could be fit, the $c$ -values generally again do not match the cosmological CDM $(c,V_{200})$ relation."
 They introduce a “cusp mass excess”: when the predicted (c.Vigo) relation is assumed. and the Vsoo velocities are matched with those in the outermost observed velocities. the inner parts require about ~2 times more dark matter mass than is implied by the observed rotation curves.," They introduce a “cusp mass excess”: when the predicted $(c,V_{200})$ relation is assumed, and the $V_{200}$ velocities are matched with those in the outermost observed velocities, the inner parts require about $\sim 2$ times more dark matter mass than is implied by the observed rotation curves."
 ?? also explore non-cireular motions: they find that random velocities with an amplitude of ~20 km s are needed to bring the observed curves in agreement with the CDM predictions.," \citet{KuzioDeNaray:2008p50,KuzioDeNaray:2009p67} also explore non-circular motions: they find that random velocities with an amplitude of $\sim 20$ km $^{-1}$ are needed to bring the observed curves in agreement with the CDM predictions."
 A comparison of simulated long-slit observations (extracted from the velocity fields) with the original long-slit data from ? and? shows good agreement., A comparison of simulated long-slit observations (extracted from the velocity fields) with the original long-slit data from \citet{McGaugh:2001p48} and \citet{deBlok:2002p47} shows good agreement.
 ? present a DensePak velocity field of the late-type dwarf galaxy DDO 39., \citet{Swaters:2003p79} present a DensePak velocity field of the late-type dwarf galaxy DDO 39.
 They derive a rotation curve. and show that its slope is steeper than implied by lower resolution HI data. and also different from earlier long-slit data from ?..," They derive a rotation curve, and show that its slope is steeper than implied by lower resolution HI data, and also different from earlier long-slit data from \citet{deBlok:2002p47}."
 They indicate that measurable non-circular motions are present. but do not explicitly quantify them.," They indicate that measurable non-circular motions are present, but do not explicitly quantify them."
 They show fit results for NFW halos. but do not show the corresponding results for a core model. so further comparisons are difficult to make.," They show fit results for NFW halos, but do not show the corresponding results for a core model, so further comparisons are difficult to make."
 ? present the HI velocity field of NGC 6822. a nearby Local Group dwarf galaxy.," \citet{Weldrake:2003p187} present the HI velocity field of NGC 6822, a nearby Local Group dwarf galaxy."
 Their data has a linear resolution of about 20 pe. so beam smearing ts definitely not a problem.," Their data has a linear resolution of about $20$ pc, so beam smearing is definitely not a problem."
 The rotation curve shows a strong preference for a core-like model. but they do not quantify possible non-circular motions.," The rotation curve shows a strong preference for a core-like model, but they do not quantify possible non-circular motions."
 ? present similarly high-resolution HI data (including VLA B array) of the dwarf galaxy DDO 47., \citet{Salucci:2003p33} present similarly high-resolution HI data (including VLA B array) of the dwarf galaxy DDO 47.
 Their analysis shows the dynamies are not consistent with à cusp., Their analysis shows the dynamics are not consistent with a cusp.
 Similar results are derived in? for à number of spiral galaxies., Similar results are derived in \citet{Gentile:2004p7} for a number of spiral galaxies.
 ? present results from CO and He velocity fields of 5 low-massdark-matter-dominated galaxies (see also? and ?))., \citet{Simon:2005p68} present results from CO and $\alpha$ velocity fields of 5 low-massdark-matter-dominated galaxies (see also \citealt{Simon:2003p52} and \citealt{Bolatto:2002p39}) ).
 They derive a range of slopes. from core-like (a=0.01 ," They derive a range of slopes, from core-like $\alpha = 0.01$ "
monitoring that led to an accurate measurement of their the maximum intensities.,monitoring that led to an accurate measurement of their the maximum intensities.
" The black hole candidates have been observed more sparsely, so that the maximum reported intensity is in most cases likely to be below the actual maximum intensity that the sources reached)."," The black hole candidates have been observed more sparsely, so that the maximum reported intensity is in most cases likely to be below the actual maximum intensity that the sources reached)."
 This further supports the idea that the black hole candidates lie in the far two-thirds of the Galaxy., This further supports the idea that the black hole candidates lie in the far two-thirds of the Galaxy.
" We, therefore, conclude that there is no room within the 32 black-hole candidates to hide any sizable population of sources that are fainter because they are intrinsically less massive."," We, therefore, conclude that there is no room within the 32 black-hole candidates to hide any sizable population of sources that are fainter because they are intrinsically less massive."
" The fact that our sample of secure black-holes is flux limited does not imply that it is luminosity limited, and, therefore, does not introduce any selection bias against the detection of low-mass black holes."," The fact that our sample of secure black-holes is flux limited does not imply that it is luminosity limited, and, therefore, does not introduce any selection bias against the detection of low-mass black holes."
 The sample of 16 sources that we used to infer the mass distribution of stellar black holes has been drawn from transient low-mass X-raybinaries?., The sample of 16 sources that we used to infer the mass distribution of stellar black holes has been drawn from transient low-mass X-ray.
". Here, we consider the possibility that low-mass black holes exist, but not in transient low-mass X-ray binaries."," Here, we consider the possibility that low-mass black holes exist, but not in transient low-mass X-ray binaries."
" In turn, we will consider the possibility that low-mass black holes are primarily in persistent binaries or that they are not members of binary systems at all."," In turn, we will consider the possibility that low-mass black holes are primarily in persistent binaries or that they are not members of binary systems at all."
" Most known neutron-star low-mass X-ray binaries are persistent sources, whereas the majority of black hole binaries are transient systems. "," Most known neutron-star low-mass X-ray binaries are persistent sources, whereas the majority of black hole binaries are transient systems. ("
latter statement is primarily a consequence of the fact that the transient behavior has so far been required in (Theestablishing the black hole nature of a compact object in a majority of the sources).,The latter statement is primarily a consequence of the fact that the transient behavior has so far been required in establishing the black hole nature of a compact object in a majority of the sources).
 Is it possible that low-mass black holes behave more like neutron stars than their more massive counterparts?, Is it possible that low-mass black holes behave more like neutron stars than their more massive counterparts?
" The most prominent explanation of the transient behavior of X-ray binaries is the irradiated disk instability model Paradijs 1996; King, Kolb, Burderi 1996; Dubus et "," The most prominent explanation of the transient behavior of X-ray binaries is the irradiated disk instability model (van Paradijs 1996; King, Kolb, Burderi 1996; Dubus et 1999)."
"In this model, whether an X-ray binary is a transient(van depends only weakly on the nature of the primary but is 11999).mainly determined by the orbital period of the system, the mass of the primary, and the evolutionary state of the companion star (King et 11996)."," In this model, whether an X-ray binary is a transient depends only weakly on the nature of the primary but is mainly determined by the orbital period of the system, the mass of the primary, and the evolutionary state of the companion star (King et 1996)."
" Thus, the expectation is that a 4 Mo black hole binary should behave like one containing a 6 Mo black hole if they have comparable orbital periods."," Thus, the expectation is that a 4 $M_\odot$ black hole binary should behave like one containing a 6 $M_\odot$ black hole if they have comparable orbital periods."
" Furthermore, our sample of 16 transient black hole sources includes both short-period and long-period systems, indicating that the transient behavior is seen over a range of orbital periods."," Furthermore, our sample of 16 transient black hole sources includes both short-period and long-period systems, indicating that the transient behavior is seen over a range of orbital periods."
" We, therefore, find it unlikely, albeit still possible, that low-mass black holes would preferentially exist in persistent binaries if the distribution of their orbital periods is similar to that of the confirmed black holes."," We, therefore, find it unlikely, albeit still possible, that low-mass black holes would preferentially exist in persistent binaries if the distribution of their orbital periods is similar to that of the confirmed black holes."
" We, nevertheless, explore whether the known number of persistent X-ray sources in the Galaxy is large enough to"," We, nevertheless, explore whether the known number of persistent X-ray sources in the Galaxy is large enough to"
ambient nebula. or supersonically through the environment. like PLIERS (last.low-ionizationemissional.1993) or BRETs (bipolar.rotating.etal. 1995)..,"ambient nebula, or supersonically through the environment, like FLIERs \citep[fast, 
low-ionization emission regions,][]{b05} or BRETs \citep[bipolar, rotating, 
episodic jets;][]{b028}."
 For over ten vears. the strong Iline emission from LISs has been attributed to a significant local overabundance of nitrogen (Balick ct al.," For over ten years, the strong line emission from LISs has been attributed to a significant local overabundance of nitrogen (Balick et al."
 1993. 1994. 1998: ancl references therein).," 1993, 1994, 1998; and references therein)."
 Balicketal.(1993) interpreted the N-cnrichment in PLIERS as evidence of their origins in recent. high-velocity ejections of the PN central star., \citet{b05} interpreted the N-enrichment in FLIERs as evidence of their origins in recent high-velocity ejections of the PN central star.
 The above work and successively Balicketal.(1994).. which included. the derivation of the ionic ancl elemental abundances of LISs. poinοἳ out. “an apparent enhancement of nitrogen relative to hydrogen by factors of 2-57 in FLIES.," The above work and successively \citet{b06}, which included the derivation of the ionic and elemental abundances of LISs, pointed out “an apparent enhancement of nitrogen relative to hydrogen by factors of 2-5"" in FLIERs."
 lHlowever. since then. further work casted. doubts over the latter statement (Llajianctal.1997:Alexander&Balick1997:Goncalvesetal.2003:Perinottoct 2004a).," However, since then, further work casted doubts over the latter statement \citep{b021,b01,b017,b033}."
. Abundances in PNe can be derived. from the analysis of collisionally excited line (CEL) or optical recombination line (ORL) spectra using empirical methods or tailorec photoionisation mocels (c.g.Stasiiska2004) OP à combination of the two., Abundances in PNe can be derived from the analysis of collisionally excited line (CEL) or optical recombination line (ORL) spectra using empirical methods or tailored photoionisation models \citep[e.g.][]{b040} or a combination of the two.
 For some elements (e.g. He) and ions (e.g. if only the optical spectrum is available) the use of ORL is mandatory. whilst for others the use of CIELs may be unavoidable.," For some elements (e.g. He) and ions (e.g. $^{++}$ if only the optical spectrum is available) the use of ORL is mandatory, whilst for others the use of CELs may be unavoidable."
 But. when both CEL and ORL determinations are available. the former have been commonly preferrec because they are generally. stronger and easier to detec than ORLs.," But, when both CEL and ORL determinations are available, the former have been commonly preferred because they are generally stronger and easier to detect than ORLs."
 Moreover. there is a well known cliscrepancy between CEL- and OltL-abundances. as well as electron temperature determinations (Liuetal.1995).," Moreover, there is a well known discrepancy between CEL- and ORL-abundances, as well as electron temperature determinations \citep{b027}."
.. LEmpirica abundance analysis rely on ionization correction factors (iefs) to account for the unseen ions (c.g. Ixingsburgh Barlow. 1994).," Empirical abundance analysis rely on ionization correction factors s) to account for the unseen ions (e.g. Kingsburgh Barlow, 1994)."
 Results obtained with thezef method can be somewhat uncertain in some cases. particularly when they are applied to spatially resolved long-slit spectra CXlexancer&Dalick 1997).. as has been the case for the work of Παjianetal.(1997). and Goncalves 1)..," Results obtained with the method can be somewhat uncertain in some cases, particularly when they are applied to spatially resolved long-slit spectra \citep{b01}, as has been the case for the work of \citet{b06,b021} and \citet[][hereafter \pi]{b017}."
 In fact. the abundances derived in aand shown here in Table 1. from optical long-slit: spectra of NGC 7009. using thezcef scheme of(1994).. showed only a marginal evidence for overabundance of ΔΕΗ in the outer. knots of the nebula (he ansac). reinforcing the doubts over previous results (Dalickοἱ1994) where the N/II enhancement of a factor of 2-5 in the ansae were reported.," In fact, the abundances derived in and shown here in Table 1, from optical long-slit spectra of NGC 7009, using the scheme of, showed only a marginal evidence for overabundance of N/H in the outer knots of the nebula (the ansae), reinforcing the doubts over previous results \citep{b06} where the N/H enhancement of a factor of 2-5 in the ansae were reported."
 One of the major shortcomings of empiricallv-determined. chemical. abundances lies in the fact that a number of assumptions on the ionization structure of the eas need to be made in order to obtain the 1ο. A preferrec alternative would be the construction of a tailored photoinisation model for a given object. aiming to fit the emission line spectrum and. in the case of spatially resolved objects. projected maps in a number of emission lines.," One of the major shortcomings of empirically-determined chemical abundances lies in the fact that a number of assumptions on the ionization structure of the gas need to be made in order to obtain the s. A preferred alternative would be the construction of a tailored photoinisation model for a given object, aiming to fit the emission line spectrum and, in the case of spatially resolved objects, projected maps in a number of emission lines."
 NGC 7009. the “Saturn Nebula”. is a PN comprising a bright elliptical rim.," NGC 7009, the “Saturn Nebula”, is a PN comprising a bright elliptical rim."
 Lis small-scale structures include a pair of jets ancl two pairs of low-ionization knots., Its small-scale structures include a pair of jets and two pairs of low-ionization knots.
 On a larger scale. it is known that NGC 7009 possessa tenuous halo with a ciameter of more than 4 arcmin (Morenoοἱal. 1998).. whose inner regions displav a system of concentric rings (Corradictal.2004). like those observed. in NGC 6543 and other few PNe (Balicketal2001).," On a larger scale, it is known that NGC 7009 possessa tenuous halo with a diameter of more than 4 arcmin \citep{b0032}, whose inner regions display a system of concentric rings \citep{b009} like those observed in NGC 6543 and other few PNe \citep{b07}."
. LHigh-exceitation ines dominate the inner regions along the minor axis. while emission from. low-ionization species is enhanced at the extremities of the major axis.," High-excitation lines dominate the inner regions along the minor axis, while emission from low-ionization species is enhanced at the extremities of the major axis."
 The ionization structure is urther enriched by the fact that the low-excitation regions resent strong variations in excitation level and clumpiness., The ionization structure is further enriched by the fact that the low-excitation regions present strong variations in excitation level and clumpiness.
 ας T0090 was classified as an oxveen-rich PN (lHlvung&Aller 1995a).. with an O/C ratio exceeding 1. and anomalous «OQ. and €abundances (Baker1983:Balickοἱal.," NGC 7009 was classified as an oxygen-rich PN \citep{b022}, with an O/C ratio exceeding 1, and anomalous N, O, and Cabundances \citep{b02,b06,b022}."
1994:Ilvung&Aller 1995a).. Its central star is an H-rich. O-tvpe star. with ellective temperature of S20000 Ix. (Méndezetal.1992:Winesbureh&Barlow 1992)..," Its central star is an H-rich O-type star, with effective temperature of 000 K \citep{b032,b024}."
 The kinematics of NGC τους was stucied first by Reavy&Atherton(1985) and Balicketal.(LOST). who showed that the ansae are expanding near the plane of the sky at highly. supersonic velocities.," The kinematics of NGC 7009 was studied first by \citet{b037} and \citet{b04}, who showed that the ansae are expanding near the plane of the sky at highly supersonic velocities."
 The derived: inclination of the inner (caps) and outer (ansae) knots. with respect to the line of sight. are P2:5|]? ands= δε. respectively (Reavy&Atherton 1985).," The derived inclination of the inner (caps) and outer (ansae) knots, with respect to the line of sight, are $i\cong 51^{\circ}$ and $i\cong 84^{\circ}$ , respectively \citep{b037}. ."
. More recently. Fernándezetal.(2004) have measured the proper motion and kinematics of the ansae in NGC 7009. assuming that they are equal and opposite from the central," More recently, \citet{b014} have measured the proper motion and kinematics of the ansae in NGC 7009, assuming that they are equal and opposite from the central"
Aladau 2012) of the star formation rate density. pai(2).,"Madau 2012) of the star formation rate density, $\dot{\rho}_{\rm SFR}(z)$."
 Figure 7 compares the effects of two choices of model atmosphleres. wilh a fixed SFR history from Trentietal. (2010).," Figure 7 compares the effects of two choices of model atmospheres, with a fixed SFR history from Trenti (2010)."
 The on-line caleulator provides ionization fractions. μμ) and Ques). together with CAIB optical depth. z.(:).," The on-line calculator provides ionization fractions, $Q_{\rm HII}(z)$ and $Q_{\rm HeIII}(z)$, together with CMB optical depth, $\tau_e(z)$."
 In the sinnuator. users can select other IGAL parameters and. SFR. histories.," In the simulator, users can select other IGM parameters and SFR histories."
 The main clilference between (he (wo SFR models lies in the assumptions al 2>8., The main difference between the two SFR models lies in the assumptions at $z>8$.
 Εαν! & Macau (2012) rely on an empirical extrapolation of the star lormation rate as a function of redshift. while Trentietal. (2010) adopt a plwsically motivated model based on the evolution of the dark-matter halo mass function.," Haardt & Madau (2012) rely on an empirical extrapolation of the star formation rate as a function of redshift, while Trenti (2010) adopt a physically motivated model based on the evolution of the dark-matter halo mass function."
 The two approaches are similar al 255. but differ signilicantly al higher redshift. where an empirical extrapolation does not capture the sharp drop in the number density of galaxies observed al 2~10 (see Figure 8 in Oeschelal. 2011).," The two approaches are similar at $z \lsim 8$, but differ significantly at higher redshift, where an empirical extrapolation does not capture the sharp drop in the number density of galaxies observed at $z \sim 10$ (see Figure 8 in Oesch 2011)."
 As a consequence. the reionization history [from the Haarclt & Maca (2012) nodel is more extended al hieh z. especially when the efficiency. of reionization is increased because of evolving clumping [actor ancl escape fraction (our preferred models. green and nagenta curves in Fig.," As a consequence, the reionization history from the Haardt & Madau (2012) model is more extended at high $z$, especially when the efficiency of reionization is increased because of evolving clumping factor and escape fraction (our preferred models, green and magenta curves in Fig."
 5)., 5).
 The two models vield quite different predictions for the duration of reionization. defined as the redshift interval. Xz. over which Qi) evolves [rom 20% to 80% ionized.," The two models yield quite different predictions for the duration of reionization, defined as the redshift interval, $\Delta z$, over which $Q_{\rm HII}$ evolves from 20% to 80% ionized."
 Our prelerred SFR models (green and magenta lines in Fig., Our preferred SFR models (green and magenta lines in Fig.
 5) have Azz3 (from zαὖ10.5 do 2z 7.5). whereas the Haardt-\ladan SER. histories exhibit a more extencled interval. Az26 (from z13 to zez 7).," 5) have $\Delta z \approx 3$ (from $z \approx 10.5$ to $z \approx 7.5$ ), whereas the Haardt-Madau SFR histories exhibit a more extended interval, $\Delta z \approx 6$ (from $z \approx 13$ to $z \approx 7$ )."
 This difference in Az could be tested by upcoming 2]-cm experiments: see Bowman & Rodgers (2010) lor an initial constraint. Az>0.06.," This difference in $\Delta z$ could be tested by upcoming 21-cm experiments; see Bowman & Rodgers (2010) for an initial constraint, $\Delta z > 0.06$."
 Figure 8 illustrates a third constraint on thereionization epoch (Pritchardetal. 2010: Lidzetal. 2011) comparing SFR. histories with estimates of the ionizing background al 2—5540.5 (Fan etal. 2006: Bolton & Ilaehnelt 2007: Πάσα & /Madaui: 2012)., Figure 8 illustrates a third constraint on thereionization epoch (Pritchard 2010; Lidz 2011) comparing SFR histories with estimates of the ionizing background at $z = 5.5 \pm 0.5$ (Fan 2006; Bolton & Haehnelt 2007; Haardt & Madau 2012).
 The LyC co-moving emissivity (in photons + 7). defined as Pico=PufeQuc: can be related to the ionizing background at 2=5—6. using recent estimates of the hydrogen pholoionization rate. Ες). from IHaardt & Madaui (2012) and the LvC mean free path. Ay from Songaila & Cowie (2010).," The LyC co-moving emissivity (in photons $^{-1}$ $^{-3}$ ), defined as $\dot{n}_{\rm LyC} = \dot{\rho}_{\rm SFR} f_{\rm esc} Q_{\rm LyC}$, can be related to the ionizing background at $z = 5-6$, using recent estimates of the hydrogen photoionization rate, $\Gamma_{\rm HI}(z)$, from Haardt & Madau (2012) and the LyC mean free path, $\lambda_{\rm HI}$, from Songaila & Cowie (2010)."
 The LyC enssivily is proportional to the star formation rate density. computed [rom our halo mass funcüon model (Trentietal. 2010). integrated down to absolutemagnitudes Map=—18 (Bouwensetal. 2011a) or to Map=—10. the [aint limit suggested bv Trentietal. (2010).," The LyC emissivity is proportional to the star formation rate density, computed from our halo mass function model (Trenti 2010), integrated down to absolutemagnitudes $M_{\rm AB} = -18$ (Bouwens 2011a) or to $M_{\rm AB} = -10$, the faint limit suggested by Trenti (2010)."
 We adopt a fiducial LvC production parameter Que=0.004. corresponding to tx10ο LvC photons produced per M. of star formation. and we use (wo different models for LvC escape fraction. f (constant al 20% and varving with redshift).," We adopt a fiducial LyC production parameter $Q_{\rm LyC} = 0.004$, corresponding to $4\times10^{60}$ LyC photons produced per $M_{\odot}$ of star formation, and we use two different models for LyC escape fraction, $f_{\rm esc}$ (constant at 20% and varying with redshift)."
" For quantitative values. we assume an ionizing backeround with specific intensity. Jy=αμίνη)"" (n unils erg 7s Far ! 1) with power-law index az2 al energiesabove hi4=1 rvd."," For quantitative values, we assume an ionizing background with specific intensity, $J_{\nu} = J_0 (\nu / \nu_0)^{-\alpha}$ (in units erg $^{-2}$ $^{-1}$ $^{-1}$ $^{-1}$ ) with power-law index $\alpha \approx 2$ at energiesabove $h \nu_0 = 1$ ryd."
" The hydrogen photoionization rate is Py=HxJuoo/h(α43)| for a hwvdrogen photoionization cross section c,&σημμη)"" wilh oy=6.3x10( ‘env’.", The hydrogen photoionization rate is $\Gamma_{\rm HI} = [4 \pi J_0 \sigma_0/ h (\alpha + 3)]$ for a hydrogen photoionization cross section $\sigma_{\nu} \approx \sigma_0 (\nu / \nu_0)^{-3}$ with $\sigma_0 = 6.3\times10^{-18}$ $^2$ .
" For (his spectrum.the frequencs-inteerated ionizing intensity is J44=Joro/(o— 1). aud the LvC photon flux (photons 7s +) integratedE over all solid anglesS is Pj,í0=(4xJ/ha )."," For this spectrum,the frequency-integrated ionizing intensity is $J_{\rm tot} = J_0 \nu_0 / (\alpha-1)$ , and the LyC photon flux (photons $^{-2}$ $^{-1}$ ) integrated over all solid angles is $\Phi_{\rm LyC} = (4 \pi J_0/h \alpha)$ ."
 In late 1995 the Magellanie Clouds Newsletter (MICNews) was fouuded by You-Hua Clu’s Magellanic Clouds Working Group at the University of Hlinois iu Vrbana-Champaten (UIUC).,t} In late 1995 the Magellanic Clouds Newsletter (MCNews) was founded by You-Hua Chu's Magellanic Clouds Working Group at the University of Illinois in Urbana-Champaign (UIUC).
" Two years earlier a joint. ""Ciraduiertenkolleg"" (graduate school) lor Magellanic Clouds research had been created by the Universities of Bonn aud Bochum.", Two years earlier a joint “Graduiertenkolleg” (graduate school) for Magellanic Clouds research had been created by the Universities of Bonn and Bochum.
 Several inembers of the Ciraduiertenkolles went to UIUC as exchange visitors. aud the University of Boun became the European mirror site lor MCNews.," Several members of the Graduiertenkolleg went to UIUC as exchange visitors, and the University of Bonn became the European mirror site for MCNews."
 The Craduiertenkolleg is now reaching the end of its funding period. aud. we use this opportunity to analyze the topical and demographical evolution of Magellanic Clouds researeli worldwide over the past five years as reflected in MICNews.," The Graduiertenkolleg is now reaching the end of its funding period, and we use this opportunity to analyze the topical and demographical evolution of Magellanic Clouds research worldwide over the past five years as reflected in MCNews."
 MCNews covers all areas of Magellanic Clouds research αμα publishes abstracts of submitted aud accepted refereed papers. PhD theses. conference proceedings. aud job aud conference announcements.," MCNews covers all areas of Magellanic Clouds research and publishes abstracts of submitted and accepted refereed papers, PhD theses, conference proceedings, and job and conference announcements."
 lis editors are Eva Crebel (NMIPLA) and You-Hua Chu (UIUC)., Its editors are Eva Grebel (MPIA) and You-Hua Chu (UIUC).
 Since September 1097 MCNews appears monthly aud is currently sent out electronically in [lornmat to [10 subscribers in 31 countries., Since September 1997 MCNews appears monthly and is currently sent out electronically in format to $\sim 440$ subscribers in 31 countries.
 Filty [ive issues have appeared as of May 2001. comprising a total of 532 abstracts of refereed papers (an estimated of the refereed publications iu this area). so we estimate that we are reaching ~80 of the researchers active iu this field.," Fifty five issues have appeared as of May 2001, comprising a total of 532 abstracts of refereed papers (an estimated of the refereed publications in this area), so we estimate that we are reaching $\sim 80$ of the researchers active in this field."
 Assuming that MCNews subscribers are approximately representative of Magellanic Clouds researchers. then Europe )) and North America )) have the highest concentration of Magellanic Clouds researchers.," Assuming that MCNews subscribers are approximately representative of Magellanic Clouds researchers, then Europe ) and North America ) have the highest concentration of Magellanic Clouds researchers."
" For the top eight countries the following fractional distribution of subscribers results: USA:32%... Germany:16%.. Australia:S96... France:756... Ul:οσο. Italy:οσοι, Chile:IY. Canacla:3%."," For the top eight countries the following fractional distribution of subscribers results: USA:, Germany:, Australia:, France:, UK:, Italy:, Chile:, Canada:."
. Between (Asia) and (South America) are women (i.e.. on average).," Between (Asia) and (South America) are women (i.e., on average)."
We seethat (henear-extremal Bekenstein-Lawking entropy [f,The auxiliary field $D$ may be determined by the constraint on the nonlinear multiplet \ref{nl}) ): This means that we must make the above substitution also for $D$ appearing in the hatted fields \ref{hatted}) ) in the Lagrangian \ref{lag}) ).
ormula hasthe same, We assume where the later equation is the $V$ -gauge \ref{gauge}) ).
structure Let, The equation of motion for $V_a$ must be shown to be satisfied.
"us introducethe dual field strength: e yj) n Ga = =FF + FEN,"," The equations of motion for $M_{ij}$ and $\Phi^i_{\phantom{i}\alpha}$ are trivially satisfied by the above assumption, where for the latter we assume a vanishing $SU(2)$ connection as we shall consider later."
" +FyEy, - (33) Gon,= IG, (34) The field strengths FEmay be extrac"," We therefore remain with the constraint: The area of the horizon $A$, the Weyl tensor $C_{0101}$, and the Ricci scalar $R$ are all calculated from the metric."
ted from (he fol," It remains to find solutions for the metric, the moduli $X^I(z)$, and the auxiliary field $T_{01}^-$ ."
"lowing equations: Be, A m ο = Gay Fy) + sha(Fy + Ej,NT 64FQC D)) (35) wher"," In addition, for solving the equations of motion, we will need solutions for the $U(1)$ connection $A_a$ and the $SU(2)$ connection $\mathcal{V}_{a\phantom{i}j}^{\phantom{a}i}$, which in the supersymmetric case could be taken as zero."
ewe used spherical svinmetryand (14)). The magnetic ," We will make an ansatz for the solution on the horizon, which is an extension of both the extremal case with $R^2$ -terms (see \cite{mohauptreview}) ) and the non-extremal case without $R^2$ -terms."
parts of the field strengths are obtained fromBianchi identities. which l," One may consider the ansatz of the non-extremal case for the metric \ref{metric}) ), \ref{ukansatz}) ), \ref{nonext}) ), the modified stabilization equations \ref{modified}) ) which give the moduli, and the auxiliary field \ref{aux}) ), with the $R^2$ prepotential \ref{r2prep}) )."
"ora static spherically svimietric metric give: Fy, opiscy"," However this proves to beinsufficient, and since we will consider a near-extremal solution, we introduce linear $\mu$ -corrections to the fields."
"position ο along the line of sight. and which is proportional to Q,,.","position $x$ along the line of sight, and which is proportional to $\Omega_m$."
 Consequently. measurements. of statistics for. the convergence are able to provide cosmological constraints. and comparisons of the power spectrum of the convergence with theoretical predictions and numerical values serve to validate our theoretical ancl numerical models (sce. e.g. AMoessner Jain. 1998. and Jain. 2002).," Consequently, measurements of statistics for the convergence are able to provide cosmological constraints, and comparisons of the power spectrum of the convergence with theoretical predictions and numerical values serve to validate our theoretical and numerical models (see, e.g., Moessner Jain, 1998, and Jain, 2002)."
 Of particular importance for interpreting weak lensing statistics is the fact that the scales of interest. lie largely in the non-linear regime (see. e. Jain. Seljak White. 2000).," Of particular importance for interpreting weak lensing statistics is the fact that the scales of interest lie largely in the non-linear regime (see, e.g., Jain, Seljak White, 2000)."
 On these scales. the non-linear gravitational evolution introcluces non-Gaussianity to the convergence distribution. and this signature becomes apparent in. higher-order moments. such as the skewness.," On these scales, the non-linear gravitational evolution introduces non-Gaussianity to the convergence distribution, and this signature becomes apparent in higher-order moments, such as the skewness."
 In addition. the magnitude of the skewness values is very sensitive to the cosmology. so that measurements of higher-order statistics in the convergence may be used as discriminators of cosmology.," In addition, the magnitude of the skewness values is very sensitive to the cosmology, so that measurements of higher-order statistics in the convergence may be used as discriminators of cosmology."
 In this work. we have obtained weak lensing statistics from cosmological N’-bocly simulations using an algorithm described by Couchman. Barber Thomas (1999) which computes the three-dimensional shear in the simulations.," In this work, we have obtained weak lensing statistics from cosmological $N$ -body simulations using an algorithm described by Couchman, Barber Thomas (1999) which computes the three-dimensional shear in the simulations."
" The code has been applied to cosmological simulations with Q,,=0.3 and Qy=0.7: cosmologies of this tvpe will be referred. to as LODAL cosmologies.", The code has been applied to cosmological simulations with $\Omega_m = 0.3$ and $\Omega_V = 0.7$; cosmologies of this type will be referred to as LCDM cosmologies.
 To obtain the required statistics on cdillerent angular scales. the computed shear values have been combined. (using the appropriate angular diameter distance factors ancl accounting [or multiple dellections) along lines of sight arranged racially from the observer's position at redshift z=0.," To obtain the required statistics on different angular scales, the computed shear values have been combined (using the appropriate angular diameter distance factors and accounting for multiple deflections) along lines of sight arranged radially from the observer's position at redshift $z =
0$."
" Detailed results are presented. for background. sources at. 1H. cdillerent: redshifts (2,=0.1 to 3.6) and angular scales [rom 1 to 32'.", Detailed results are presented for background sources at 14 different redshifts $z_s = 0.1$ to 3.6) and angular scales from $1'$ to $32'$.
 As a test of the accuracy of non-linear. fits to the convergence power we compare the numerically generated convergence power spectra with our own theoretically predicted: convergence spectra based on a Llalo Model fit to numerical simulations (Smith ct al.," As a test of the accuracy of non-linear fits to the convergence power we compare the numerically generated convergence power spectra with our own theoretically predicted convergence spectra based on a Halo Model fit to numerical simulations (Smith et al.,"
 2002)., 2002).
 We also investigate the statistical properties of the magnification power spectrum and test. predictions of the weak lensing regime., We also investigate the statistical properties of the magnification power spectrum and test predictions of the weak lensing regime.
 We also report on the expected. redshift’ and. scale dependence for higher-order statistics in the convergence., We also report on the expected redshift and scale dependence for higher-order statistics in the convergence.
 A brief outline of this paper is as follows., A brief outline of this paper is as follows.
 In Section 2. we define the shear. reduced. shear. convergence. and magnification in weak gravitational lensing and outline iow the magnification and convergence values are obtained in practice [rom observational data.," In Section 2, we define the shear, reduced shear, convergence and magnification in weak gravitational lensing and outline how the magnification and convergence values are obtained in practice from observational data."
 In Section 3 we describe the relationships between the power spectra [or he convergence. shear ancl magnification fluctuations. and row the power spectrum [or the convergence relates to he matter power spectrum.," In Section 3 we describe the relationships between the power spectra for the convergence, shear and magnification fluctuations, and how the power spectrum for the convergence relates to the matter power spectrum."
 We also describe our methods or computing the convergence power in the non-linear regime., We also describe our methods for computing the convergence power in the non-linear regime.
 Also in this Section. the higher-order moments of he non-linear convergence field are defined.," Also in this Section, the higher-order moments of the non-linear convergence field are defined."
 Phe numerical oocedure we use to generate the shear. convergence and magnification fields from the simulations are presented. in Section 4. while in Section 5 we present our results for the numerical and theoretical comparison of the convergence power spectra. the power in the magnification Luctuations. and the higher-order moments. particularly the 55 statistic.," The numerical procedure we use to generate the shear, convergence and magnification fields from the simulations are presented in Section 4, while in Section 5 we present our results for the numerical and theoretical comparison of the convergence power spectra, the power in the magnification fluctuations, and the higher-order moments, particularly the $S_3$ statistic."
 Finally we discuss the results and. present our conclusions in Section 6., Finally we discuss the results and present our conclusions in Section 6.
 Ellipticity measurements of observed galaxy images can be used to estimate the lensing shear signal., Ellipticity measurements of observed galaxy images can be used to estimate the lensing shear signal.
 One definition [or the cllipticity (see. e.g.. Blandford et ab.," One definition for the ellipticity (see, e.g., Blandford et al.,"
 1991. and Bartelmann Schneider. 2001) is the complex ellipticity. in which Qi; is the tensor of second brightness nioments [or a fixed isophotal contour.," 1991, and Bartelmann Schneider, 2001) is the complex ellipticity, in which $Q_{ij}$ is the tensor of second brightness moments for a fixed isophotal contour."
" ‘The ""reduced shear.” q- for a ealaxy"," The “reduced shear,” $g$, for a galaxy image at angular position $\mbox{\boldmath$ $}$, is defined by where $\gamma$ is the complex shear and $\kappa$ is the lensing convergence."
 image al a, Both $\gamma$ and $\kappa$ are obtained as projections from the values of the second derivatives of the lensing potential along the light path.
ngular ," Their detailed definitions and their relationships to the lensing potential are given by Schneider, Ehlers Falco (1992) and summarised by Barber (2002)."
position 9.," The transformation between the source ellipticities, $\epsilon^{(s)}$, and the image ellipticities, $\epsilon$, is given by for $\mid g \mid \leq 1$."
 is., The asterisk in equation \ref{source_ell}) ) denotes the complex conjugate.
 defined⋅ ," In the case of weak lensing, for which $\kappa$, and are much less than unity, the transformation reduces to + g for low intrinsic source ellipticites."
byg," The intrinsic ellipticities of given galaxies are not known, but averaging over the binned galaxy distribution, and assuming random ellipticities, yields a net lens shear: This equality suggests that for weak lensing the variances in both the shear and the reduced shear for a given angular scale are expected to be similar."
(@) The lens," However, from numerical simulations, Barber (2002) has given explicit expressions for both as functions of redshift and angular scale, which show the expected differences."
ing magnifica," It is also possible to reconstruct the convergence from the shape information alone, up to an arbitrary constant, using methods such as those described by Kaiser Squires (1993) and Seitz Schneider (1996) for the two-dimensional reconstruction of cluster masses."
tion., Kaiser (1995) generalised the method for applications beyond the linear regime.
 sr.," Drawbacks to the reconstruction method arise from contamination by intrinsic galaxy alignments (Pen, Lee Seljak, 2000, Brown et al.,"
 ," 2002a, Crittenden et al.,"
can be com," 2001, Catelan, Kamionkowski Blandford, 2001, Mackey, White Kamionkowski, 2002, Heavens, Refregier Heymans, 2000, and Croft Metzler, 2001), although these can be statistically removed if redshift information is available ( Heyman Heavens, 2002, and King Schneider, 2002)."
puted c," In addition, map-making of the convergence field over a finite area suffers from non-local effects due to missing information beyond the survey area (Bacon Taylor, 2002)."
ireeth, For these reasons it is useful to have an alternative method for estimating the convergence.
y from where να is the two-dimensional Jacobian matrix which describes the mapping of a source onto its image.," The lensing magnification, $\mu$, can be computed directly from where $\cal{A}$ is the two-dimensional Jacobian matrix which describes the mapping of a source onto its image."
 The elect of magnification on galaxy source counts results in a decrease due to the increase in the lensed image area. and an increase in counts due to the brightening of galaxies allowing their inclusion in a llux-limited. catalogue.," The effect of magnification on galaxy source counts results in a decrease due to the increase in the lensed image area, and an increase in counts due to the brightening of galaxies allowing their inclusion in a flux-limited catalogue."
 For a power-law [ux clistribution. the ellect of lensing is (Broadhurst. Tavlor Peacock. 1995. and Bartelmann Schneider. 2001): where n(>Sos) and nol5.2) are the lensed and unlensecl number of galaxy images per unit solid angle with lux greater than S and with redshift within dz of z. and à is he power-law exponent of S.," For a power-law flux distribution, the effect of lensing is (Broadhurst, Taylor Peacock, 1995, and Bartelmann Schneider, 2001): n_0(>S,z) n(>S,z), where $n(>S,z)$ and $n_0(>S,z)$ are the lensed and unlensed number of galaxy images per unit solid angle with flux greater than $S$ and with redshift within $z$ of $z$, and $\alpha$ is the power-law exponent of $S$."
 Hence with calibration of the ancerlving number count amplitude and slope it is possible o estimate the magnification averaged over recshift., Hence with calibration of the underlying number count amplitude and slope it is possible to estimate the magnification averaged over redshift.
" Alternatively, magnification values may be obtained rom the change in image sizes at [ixed surface brightness."," Alternatively, magnification values may be obtained from the change in image sizes at fixed surface brightness."
 This method. is described. in. detail by Bartelmann aad suravan (1995) and summarised. concisely by Bartclmann and Schneider (2001)., This method is described in detail by Bartelmann and Narayan (1995) and summarised concisely by Bartelmann and Schneider (2001).
 See also Jain (2002) for a recent cdiscussion., See also Jain (2002) for a recent discussion.
 Estimates of the lensing magnification based on number counts suller [rom noise arising [rom the intrinsic clustering of the source galaxies. i£ redshift information is not available (e.8.. Droadhurst. Taylor Peacock. 1995. and Bartelmann Schneider. 2001).," Estimates of the lensing magnification based on number counts suffer from noise arising from the intrinsic clustering of the source galaxies, if redshift information is not available (e.g., Broadhurst, Taylor Peacock, 1995, and Bartelmann Schneider, 2001)."
 With redshift information one should either select. galaxies at dillerent. redshifts to remove the intrinsic. clustering signal. or use the brightening cllect behind structure (Dye et al..," With redshift information one should either select galaxies at different redshifts to remove the intrinsic clustering signal, or use the brightening effect behind structure (Dye et al.,"
. 2001)., 2001).
 Size distortions may also be allectecd if size is correlated. with the environment., Size distortions may also be affected if size is correlated with the environment.
ages and metallicities.,ages and metallicities.
 When degenerate SSPs are included. estimates can be highly variable.," When degenerate SSPs are included, estimates can be highly variable."
 Vhis is shown in the first paueb in Fig., This is shown in the first panel in Fig.
 19 and in the ΕΛΟΤ) code. itself. which in the presence of degeneracy. tends to converge to different solutions due to the random. walk taken through the parameter space by the Metropolis. algorithm.," \ref{sdss:tZ} and in the STARLIGHT code itself, which in the presence of degeneracy tends to converge to different solutions due to the random walk taken through the parameter space by the Metropolis algorithm."
 “Phe diffusion A'-means algorithm. on the other hand. includes only the mean spectrum and mean parameters of cach set of degenerate spectra.," The diffusion $K$ -means algorithm, on the other hand, includes only the mean spectrum and mean parameters of each set of degenerate spectra."
 This choice minimizes the statistical risk of the final solution by decreasing the variance ancl bias of the estimates (our measure of statistical risk is the AISE. which is the sum of the variance and squared. bias of an estimate). as seen in simulations (Figs.," This choice minimizes the statistical risk of the final solution by decreasing the variance and bias of the estimates (our measure of statistical risk is the MSE, which is the sum of the variance and squared bias of an estimate), as seen in simulations (Figs."
 5-9)., 5-9).
 Our SELL estimates for SDSS spectra are significantly less variable in the direction of the age-Z degeneracy. as seen in Fig. 10..," Our SFH estimates for SDSS spectra are significantly less variable in the direction of the age-Z degeneracy, as seen in Fig. \ref{sdss:tZ},"
 while the relative amount of bias is impossible to quantify without knowledge of the true SELL of cach galaxy., while the relative amount of bias is impossible to quantify without knowledge of the true SFH of each galaxy.
 1n the [ace of degeneracies and with no other outside information available. our proposed. method (of picking the mean of several degenerate solutions) is the best one can do in terms of minimizing the statistical risk of the estimates.," In the face of degeneracies and with no other outside information available, our proposed method (of picking the mean of several degenerate solutions) is the best one can do in terms of minimizing the statistical risk of the estimates."
 Llowever. with more information about what features in the SSP spectra ave most strongly related to their ages and metallicities. we could. potentially iniprove our estimates by incorporating such information in the construction of the similarity measure s(b;.b;) in 3).," However, with more information about what features in the SSP spectra are most strongly related to their ages and metallicities, we could potentially improve our estimates by incorporating such information in the construction of the similarity measure $s(\mathbf{b}_i,\mathbf{b}_j)$ in (3)."
 The weight matrix produced. by an expert-procluced similarity. measure. nav produce a more complete coverage of the parameter space in our SSP prototypes and help to remove degeneracies in the parameter estimates., The weight matrix produced by an expert-produced similarity measure may produce a more complete coverage of the parameter space in our SSP prototypes and help to remove degeneracies in the parameter estimates.
 Further study is required in. this direction., Further study is required in this direction.
 The ultimate goal of this project is to be able to quickly and accurately estimate physical property and SELL parameters for a large data base of galaxies., The ultimate goal of this project is to be able to quickly and accurately estimate physical property and SFH parameters for a large data base of galaxies.
 As an extension of this work. we plan to study how to quickly and elfectively extend estimates found for à small set of galaxies using the computationally intensive STABRULIGIUE routine to a large database of galaxies.," As an extension of this work, we plan to study how to quickly and effectively extend estimates found for a small set of galaxies using the computationally intensive STARLIGHT routine to a large database of galaxies."
 To achieve this goal. we must exploit the low-cimensional structure of these data.," To achieve this goal, we must exploit the low-dimensional structure of these data."
 This approach was taken by Richardsctal.(2009). in galaxy recishift estimation., This approach was taken by \citet{Rich2009} in galaxy redshift estimation.
 These methods must. be further developed. and refined to reliably estimate SELL parameters., These methods must be further developed and refined to reliably estimate SFH parameters.
 The methods presented in this paper are applicable in a wide range of problems in astrophysical cata analysis., The methods presented in this paper are applicable in a wide range of problems in astrophysical data analysis.
 Dilfusion map is a powerful tool to uncover simple structure in complicated. high-dimensional data. whether they be spectra. photometric colours. two-dimensional images. data cubes. etc;," Diffusion map is a powerful tool to uncover simple structure in complicated, high-dimensional data, whether they be spectra, photometric colours, two-dimensional images, data cubes, etc."
 Specifically. cilfusion map is both more flexible and more widely applicable than PCX. which relies on the linear correlation structure of the data ancl assumes that the data reside on a low-dimensional. Linear manifold.," Specifically, diffusion map is both more flexible and more widely applicable than PCA, which relies on the linear correlation structure of the data and assumes that the data reside on a low-dimensional, linear manifold."
 “Phe dilfusion. A-means method. can be usec in a variety of problems often encountered in astrophysics where a large set of observed or model data are described with a few prototype examples., The diffusion $K$ -means method can be used in a variety of problems often encountered in astrophysics where a large set of observed or model data are described with a few prototype examples.
 Future work will attempt to more concretely define criteria. for the performance of algorithms that define A prototypes [rom JN. data points and to theoretically. justify the use of dilfusion. A-means., Future work will attempt to more concretely define criteria for the performance of algorithms that define $K$ prototypes from $N$ data points and to theoretically justify the use of diffusion $K$ -means.
. We plan to explore more deeply the relationship between the A-means. methods introduced. here and to compare the methocls introduced in this paper to other methods of basis selection. such as Jasis Pursuit and Matching Pursuit.," We plan to explore more deeply the relationship between the $K$ -means methods introduced here and to compare the methods introduced in this paper to other methods of basis selection, such as Basis Pursuit and Matching Pursuit."
 We also will investigate how meaningful standard errors can be attached to our parameter estimates using anv choice of basis., We also will investigate how meaningful standard errors can be attached to our parameter estimates using any choice of basis.
 We thank the reviewer for their helpful comments., We thank the reviewer for their helpful comments.
 This work was supported by NSE grants CCT-0625879 and DMS-0707059 and ON]. grant. NOO014-08-1-0673., This work was supported by NSF grants CCF-0625879 and DMS-0707059 and ONR grant N00014-08-1-0673.
 Funding for the SDSS and SDSS-LE has been provided bv the Alfred P. Sloan. Foundation. the Participating Institutions. the National Science. Foundation. the U.S. Department of Energy. the National Acronautics and Space Administration. the Japanese Monbukagakusho. the Max Planck Society. and. the |Higher. Exlucation Funding Council for England.," Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England."
 The SDSS Web site. ds htt/www.sdss.org/. Lhe SDSS is managed by the Astrophysicalp:/ Research Consortium for the Participating Institutions., The SDSS Web site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions.
 The Participating Lnstitutions are the American Museum of Natural Llistory. Astrophysical Institute Potsdam. University of Bascl. Cambridge University. Case Western. Reserve University. University of Chicago. Drexel University. Fermilab. the Institute for Advanced. Study. the Japan Participation Croup. Johns Hopkins University. the Joint. Institute for Nuclear Astrophysics. the Ixavli Institute for Particle Astrophysics and Cosmology. the Korean Scientist. Group. the Chinese Academy of Sciences (LAALOST). Los Alamos National Laboratory. the Alas-Planek-lnstitute for Astronomy (MPLA). the Alas-Planek-Lnstitute for Astrophysics (MIA). New Mexico State University. Ohio. State University. University of Pittsburgh. University of Portsmouth. Princeton University. the United States Naval Observatory. and the University of Washington.," The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, Cambridge University, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington."
 The STARLIGLIE project is supported by the Brazilian agencies CNPq. CAPES and. FAPIESP ancl by the CAPES/Colccub program.," The STARLIGHT project is supported by the Brazilian agencies CNPq, CAPES and FAPESP and by the France-Brazil CAPES/Cofecub program."
up near 3500 seconds in this plot if beating is present.,up near 3500 seconds in this plot if beating is present.
 But our best guess is that the phase did not experience that large a change., But our best guess is that the phase did not experience that large a change.
 It is notable that the slow variation in the amplitude of fic is reflected in the large residual peak near 200/;Hz in the bottom panel of Fig.10.., It is notable that the slow variation in the amplitude of $f_{16}$ is reflected in the large residual peak near $\mu$ Hz in the bottom panel of \ref{ft_10553698}.
 Clearly. a longer observing run on this star should aid in determining the true nature of these periodicities.," Clearly, a longer observing run on this star should aid in determining the true nature of these periodicities."
 Theoretical consideration of the HHer class (Fontaineetal.2003) showed that the pulsation modes detected in these stars correspond to high order g-modes., Theoretical consideration of the Her class \citep{fontaine03} showed that the pulsation modes detected in these stars correspond to high order $g$ -modes.
 As such. we could invoke asymptotic limit for no>/ in which consecutive overtones should be evenly spaced in period.," As such, we could invoke asymptotic limit for $n\gg l$ in which consecutive overtones should be evenly spaced in period."
 This behavior has been observed in oulsating. white dwarfs (Kawaler&Bradley1994)., This behavior has been observed in pulsating white dwarfs \citep{kawaler94}.
. Because of he low-amplitude signal that is characteristic of these stars. and he logistical challenges of observing these frequencies from a single ground-based observing site. this asymptotic behaviour had not been seen in HHer stars until space-based observations became available.," Because of the low–amplitude signal that is characteristic of these stars, and the logistical challenges of observing these frequencies from a single ground–based observing site, this asymptotic behaviour had not been seen in Her stars until space–based observations became available."
 The first set ofKepler HHer stars were ‘ound to show clear evidence of equal period spacings. with values of approximately 145 and 2505s reported in Paper III and in a later work (Paper VHT).," The first set of Her stars were found to show clear evidence of equal period spacings, with values of approximately 145 and s reported in Paper III and in a later work (Paper VIII)."
 The five new detected HHer class also show evidence of evenly-spaced periods., The five new detected Her class also show evidence of evenly–spaced periods.
 For all stars we found average spacing in 250—270ss range., For all stars we found average spacing in s range.
 According to the Paper III. all of the peaks matehing this spacing are likely to be /==11 modes.," According to the Paper III, all of the peaks matching this spacing are likely to be $l$ 1 modes."
 There is also evidence of a second series of peaks with spacings in the IH40-150ss range. consistent with them being /—-22 modes.," There is also evidence of a second series of peaks with spacings in the s range, consistent with them being $l$ 2 modes."
 This simple relation between consecutive overtones provides a determination of the degree / of the modes. which will be crucial for interior modeling efforts.," This simple relation between consecutive overtones provides a determination of the degree $l$ of the modes, which will be crucial for interior modeling efforts."
 Detailed analysis of period spacing on five stars presented here and stars already published in previous papers of our series is a subject of Paper VIII., Detailed analysis of period spacing on five stars presented here and stars already published in previous papers of our series is a subject of Paper VIII.
 We found five new long-period pulsating sdB HHer) stars using theKepler photometer., We found five new long-period pulsating sdB Her) stars using the photometer.
 The oscillations are mostly in the 100—400 region. although we also found some single peaks at higher frequencies.," The oscillations are mostly in the $\mu$ Hz region, although we also found some single peaks at higher frequencies."
Hz The nature of those higher-frequency peaks. which are at low amplitude. remain uncertain. and we canno rule out contamination from variable contaminating sources. or unknown spacecraft artefacts.," The nature of those higher-frequency peaks, which are at low amplitude, remain uncertain, and we cannot rule out contamination from variable contaminating sources, or unknown spacecraft artefacts."
" On the other hand. assuming tha peaks at high frequencies are indeed p-modes. the stars match the previously known T,4r - pulsation type correlation."," On the other hand, assuming that peaks at high frequencies are indeed $p$ -modes, the stars match the previously known $_{\rm eff}$ - pulsation type correlation."
 We believe tha more data should confirm or disprove our hypothesis anc detinitively answer the quesion about the origin of the peaks., We believe that more data should confirm or disprove our hypothesis and definitively answer the question about the origin of the peaks.
 The amplitudes of detected peaks in the low frequency region are abou or less which is in similar to other known HHer star:s., The amplitudes of detected peaks in the low frequency region are about or less which is in similar to other known Her stars.
 As we have not founc any signatures of binarity we caim that these are single stars., As we have not found any signatures of binarity we claim that these are single stars.
 The pulsation spectra show only limited evidence of rotational splitting. but these occur with OW-amplitude periodicities and therefore require continued observation to improve the signal-to-noise and look for other similar spacings in the same stars.," The pulsation spectra show only limited evidence of rotational splitting, but these occur with low-amplitude periodicities and therefore require continued observation to improve the signal-to-noise and look for other similar spacings in the same stars."
 While many of the observed oscillations are coherent. several modes show the signature of possible stochastic amplitude and phase modulation.," While many of the observed oscillations are coherent, several modes show the signature of possible stochastic amplitude and phase modulation."
 This paper completes our initial analysis of the survey phase data on compact stars byKepler., This paper completes our initial analysis of the survey phase data on compact stars by.
 In total we found 12 new members of the HHer class (5 in this paper. 2 in Paper V. and 5 in Paper IN). one HHer star (Paper IT) and one hybrid star (Ostensenetal.2010c).," In total we found 12 new members of the Her class (5 in this paper, 2 in Paper V, and 5 in Paper III), one Her star (Paper II) and one hybrid star \citep{ostensen10c}."
. Among the former two groups. many showing additional peaks in the opposite side of the amplitude spectrum.," Among the former two groups, many showing additional peaks in the opposite side of the amplitude spectrum."
Blind surveys allow us to explore a variety of objects.,Blind surveys allow us to explore a variety of objects.
 The EffelshergBoun Survey (CEBIITS) covers not ouly the \ilky Way but also the local universe out to a redshift of 0.07., The Effelsberg–Bonn Survey (EBHIS) covers not only the Milky Way but also the local universe out to a redshift of 0.07.
 Accordingly. EBUIS will serve as a major database for many scientific questions. addressing. c.e.. the structure aud quass distribution of the Milkv Way. the size distribution of halo clouds. or the structure formation of the local universe.," Accordingly, EBHIS will serve as a major database for many scientific questions, addressing, e.g., the structure and mass distribution of the Milky Way, the size distribution of halo clouds, or the structure formation of the local universe."
 A complete description of the scientific aims will be given ina forthcoming paper., A complete description of the scientific aims will be given in a forthcoming paper.
 Here. the technical setup aud the data reduction software as used for the survey are presented.," Here, the technical setup and the data reduction software as used for the survey are presented."
 Today. the most comprehensive database for ealactic scieuce is the Leiden/ArecutineBonn stavey (LAB:?). the first allsky survey corrected for stray radiation.," Today, the most comprehensive database for galactic science is the Leiden/Argentine/Bonn survey \citep[LAB;][]{kalberla05} the first all-sky survey corrected for stray radiation."
 Toward high ealactic latitudes. the faint Millay Wav emission from the direction of interest can be severcly degraded by radiation of the Alilsy Way disk cutering the receiver system via the near and far side lobes.," Toward high galactic latitudes, the faint Milky Way emission from the direction of interest can be severely degraded by radiation of the Milky Way disk entering the receiver system via the near and far side lobes."
 SR correction is crucial for quantitative analyses of most of the galactie sky. using couveutional single dish optics., SR correction is crucial for quantitative analyses of most of the galactic sky using conventional single dish optics.
 The Parkes and. Arecibo telescopes perform multiple consecutive surveys to observe the ealactic and extragalactic sky., The Parkes and Arecibo telescopes perform multiple consecutive surveys to observe the galactic and extragalactic sky.
 The data acquisition of the Parkes Calactic All Sky Survey (CASS:2?) ds already: completed aud the final data products are released (?)..," The data acquisition of the Parkes Galactic All Sky Survey \citep[GASS;][]{mcclure06,mcclure09} is already completed and the final data products are released \citep{kalberla10}."
 The Galactic ALFA (GALFA:??) is still in progress.," The Galactic ALFA \citep[GALFA;][]{goldsmith04,heiles04} is still in progress."
 Iu the extragalactic regime the Parkes All Sky Survey (IIIPASS:??)— inapped. the complete southern hemisphere detecting more than 5000) ealaxics providing a valuable database to infer the properties of galaxies in the local universe.," In the extragalactic regime the Parkes All Sky Survey \citep[HIPASS;][]{barnes01,meyer04} mapped the complete southern hemisphere detecting more than 5000 galaxies providing a valuable database to infer the properties of galaxies in the local universe."
 The Arecibo Legacy Fast ALFA survey (ALFALFA:?) is ongoing aud will result iu deeper data at higher aneular resolution though it is limited to a smaller, The Arecibo Legacy Fast ALFA survey \citep[ALFALFA;][]{giovanelli05p} is ongoing and will result in deeper data at higher angular resolution though it is limited to a smaller
fits are subtracted from the observed radial velocity variations of both the binaries and the single stars with significant periodic radial velocity variations.,fits are subtracted from the observed radial velocity variations of both the binaries and the single stars with significant periodic radial velocity variations.
" The half peak-to-peak values of these residuals are plotted as a function of surface gravity in Fig. 4,,"," The half peak-to-peak values of these residuals are plotted as a function of surface gravity in Fig. \ref{kloggres},"
" also showing the linear fit through the non-periodic stars, and the amplitudes of the subtracted periodic signals."," also showing the linear fit through the non-periodic stars, and the amplitudes of the subtracted periodic signals."
 There are several interesting points to make about this graph., There are several interesting points to make about this graph.
" Firstly, almost all periodic stars show larger radial velocity variations than predicted by the relation found for non-periodic stars, but when the periodicities are removed, their residual radial velocity variations follow the same relation as found for the non-periodic stars."," Firstly, almost all periodic stars show larger radial velocity variations than predicted by the relation found for non-periodic stars, but when the periodicities are removed, their residual radial velocity variations follow the same relation as found for the non-periodic stars."
 This could be interpreted as evidence for both intrinsic (non-periodic radial velocity variation) and extrinsic (periodic variations) mechanisms playing a role in these stars., This could be interpreted as evidence for both intrinsic (non-periodic radial velocity variation) and extrinsic (periodic variations) mechanisms playing a role in these stars.
" Secondly, there is no correlation between the amplitude of the subtracted periodic signal and logg, which provides additional evidence for the presence of companions."," Secondly, there is no correlation between the amplitude of the subtracted periodic signal and $\log g$, which provides additional evidence for the presence of companions."
" Thirdly, almost all (8 out of 9) stars with logg<1.6 exhibit periodic variations."," Thirdly, almost all (8 out of 9) stars with $\log g \leq 1.6$ exhibit periodic variations."
" If these indeed have an extrinsic mechanism, it would mean that ~90% of these stars have sub-stellar companions."," If these indeed have an extrinsic mechanism, it would mean that $\sim 90\%$ of these stars have sub-stellar companions."
" However, from an astrophysical point of view, stars with such low surface gravities are already very high on the giant branch or even on the asymptotic giant branch."," However, from an astrophysical point of view, stars with such low surface gravities are already very high on the giant branch or even on the asymptotic giant branch."
" At these low gravities, stars cannot be constant anymore, as the outer layers are so diluted that instabilities occur easily, either periodic or random."," At these low gravities, stars cannot be constant anymore, as the outer layers are so diluted that instabilities occur easily, either periodic or random."
" Stated differently, these stars are"," Stated differently, these stars are"
applving the technique).,applying the technique).
 Even outside of this radius. it is unclear whether the contrast is entirelv applicable to blind searches. since a certain fraction of their flux would still be lost in the particular version of the SD technique upon which hat result is based.," Even outside of this radius, it is unclear whether the contrast is entirely applicable to blind searches, since a certain fraction of their flux would still be lost in the particular version of the SD technique upon which that result is based."
 Of importance for high-coutrast imagine purposes is not only the instrunuental contrast that can be achieved. bu also the spectral enerev. distribution of the possible companion.," Of importance for high-contrast imaging purposes is not only the instrumental contrast that can be achieved, but also the spectral energy distribution of the possible companion."
 Tere. the SDI techuique has a strong advantage over the SD techuique for cool conipauions such απ low-iass brown dwarfs and exoplaucts.," Here, the SDI technique has a strong advantage over the SD technique for cool companions such as low-mass brown dwarfs and exoplanets."
 Such objects exhibit strouegly increasing absorption iu the II- and K-bands with decreasing temperature., Such objects exhibit strongly increasing absorption in the H- and K-bands with decreasing temperature.
 According O0. e.g. the spectral models of Burrows et al. (," According to, e.g., the spectral models of Burrows et al. ("
2003). for voung planets. the flux is strongly concentrated directly shortwards of the methane feature at 1.6 sau in the U- and practically uo flux is present iu he IK-baud.,"2003), for young planets, the flux is strongly concentrated directly shortwards of the methane feature at 1.6 $\mu$ m in the H-band, and practically no flux is present in the K-band."
 This favors the SDI techuique. since the offancthane filters are located precisely at the peak of the planctary flux.," This favors the SDI technique, since the off-methane filters are located precisely at the peak of the planetary flux."
 At the same time. it cisfavors the SD technique. since it iuchides a huge spectral range that practically contains only noise from he primary aud uo signal frou he companion.," At the same time, it disfavors the SD technique, since it includes a large spectral range that practically contains only noise from the primary and no signal from the companion."
 To give a practical example of this. we use the Baraffe et al. (," To give a practical example of this, we use the Baraffe et al. ("
2003) and. Burrows et al. (,2003) and Burrows et al. (
"2003) heoretical models to model the actual plivsical coutrast hat the SDI and SD methods will face. respectively. iu he case of a 2 Mi, companion to a (0.3 A; star at an age of 100 Myr.","2003) theoretical models to model the actual physical contrast that the SDI and SD methods will face, respectively, in the case of a 2 $M_{\rm jup}$ companion to a 0.3 $M_{\sun}$ star at an age of 100 Myr."
 The same method is used iu. ce. Janson et al. (," The same method is used in, e.g., Janson et al. ("
2007) aud Apai et al. (,2007) and Apai et al. (
2007).,2007).
 The physical contrast is subtracted from the instrmucutal (achieved contrast). and the results are shown iu Fie. 6..," The physical contrast is subtracted from the instrumental (achieved contrast), and the results are shown in Fig. \ref{sdi_phys_err}."
 It is clear hat SD is considerably less well :yplicable than SDI for such cool objects. at least iu its present form.," It is clear that SD is considerably less well applicable than SDI for such cool objects, at least in its present form."
 Obviously. lis difference is less problematic for hotter objects.," Obviously, this difference is less problematic for hotter objects."
 Still. Hel-contrast searches in general primarily ain to detect cool objects. and the SDI method is clearly preferable or such an objective.," Still, high-contrast searches in general primarily aim to detect cool objects, and the SDI method is clearly preferable for such an objective."
 Since NACO-SDI performs better han SINFONT in this regard. this speaks in favor of the ornier for blind companion searches.," Since NACO-SDI performs better than SINFONI in this regard, this speaks in favor of the former for blind companion searches."
 In any case. for the SD technique to reach its full otential. if 18 necessary," In any case, for the SD technique to reach its full potential, it is necessary"
 (<1 (~12 AbüunobQueraltóetal.(2008)—," $< 1$ $\sim 1-2$ \citep[e.g.,][]{Trager00b,SB06b}."
 presented a detailed study. of the CO baud at 2.3. pan as a function of the basic stellar atmospheric parameters (effective temperature. surface eravity and ictallicitv) musing aa new spectral library of stars in the EK baud.," \citet{libCO} presented a detailed study of the CO band at 2.3 $\mu$ m as a function of the basic stellar atmospheric parameters (effective temperature, surface gravity and metallicity) using a a new spectral library of stars in the K band."
 This work confirmed that this CO absorption band is sensitive to metallicity aud it also shows good. evidence for increased CO absorption strength in ACB stars colmpared to non-AGD stars (see Fiewe 11 in MQOS and Figure d. iu this letter)., This work confirmed that this CO absorption band is sensitive to metallicity and it also shows good evidence for increased CO absorption strength in AGB stars compared to non-AGB stars (see Figure 14 in MQ08 and Figure \ref{fig1} in this letter).
 These results confi the suitabilitv of the CO index for stellar population studies., These results confirm the suitability of the CO index for stellar population studies.
 Furthemore. in this spectral ranee there is à proniünoeut absorption feature at 2.2 ju mainly due to sodimm and scanclimm (Wallace&Iiukle1996).," Furthemore, in this spectral range there is a prominent absorption feature at 2.2 $\mu$ m mainly due to sodium and scandium \citep{WH96}."
. This feature is very sensitive to effective temperature of the stars;, This feature is very sensitive to effective temperature of the stars.
 Ouce hat parameter is fixed. ACB and RGB stars show very simular values (sce Figure 1)).," Once that parameter is fixed, AGB and RGB stars show very similar values (see Figure \ref{fig1}) )."
 The study of galaxies in different environneuts ds a xwverfull tool to uuderstaud their evolution aud star ormatiou history (c.g... SAnuchez-Blazzquez et al.," The study of galaxies in different environments is a powerfull tool to understand their evolution and star formation history \citep[e.g.,
S{\'a}n nchez-Blázzquez et al."
 2003 icreafer 2006)., 2003 --hereafer .
 Iu this letter. we investigate possible differences imn heir stellar populations comparing the more prominent absorption features in the IK&-baud.," In this letter, we investigate possible differences in their stellar populations comparing the more prominent absorption features in the K-band."
 Ouly a few detailed studies have been preseuted in this spectral range after he pioneering photometric work bv Frogeletal.(1978) and Aaronsonctal.(1978) in early-type ealaxies., Only a few detailed studies have been presented in this spectral range after the pioneering photometric work by \citet{Frogel78} and \citet{Aaronson78} in early-type galaxies.
 The first detailed spectroscopic analysis in the IK-baud of these ealaxies depending ou their euvironinnet was presented by Mobasher&James(1996).. who usec the strength of the first CO baud at 2.3 422 as au indicator of the presence of ACB stars and. therefore. of au intermediate-age population iu elliptical galaxies.," The first detailed spectroscopic analysis in the K-band of these galaxies depending on their environmnet was presented by \citet{Mobasher96}, who used the strength of the first CO band at 2.3 $\mu$ m as an indicator of the presence of AGB stars and, therefore, of an intermediate-age population in elliptical galaxies."
 They explored the influence of cuviromment fiudiug. initially. a systematic difference between field and cluster galaxies that was later coutradicted in," They explored the influence of environment finding, initially, a systematic difference between field and cluster galaxies that was later contradicted in"
Since DSA operates on relativistic particles of the same rigidity (R=pe/Ze) in the same wav. both electrons and protons are expected to be accelerated at shocks.,"Since DSA operates on relativistic particles of the same rigidity $R=pc/Ze$ ) in the same way, both electrons and protons are expected to be accelerated at shocks."
 However. electrons lose energy. mainlv by synchrotron emission aud Inverse Compton (IC) scattering. ancl the injection of postshock thermal electrons is believed (to be much less efficient. compared to protons.," However, electrons lose energy, mainly by synchrotron emission and Inverse Compton (IC) scattering, and the injection of postshock thermal electrons is believed to be much less efficient, compared to protons."
 The maximum energy of CR electrons accelerated at shocks can be estimated by the condition that the momentum gain per evele by DSA is equal to the svnehrotron/IC loss per evele. CNp)psa+ CMp)ga0 (seeWebbetal.1984:Zirakashvili&Aharonian2007).," The maximum energy of CR electrons accelerated at shocks can be estimated by the condition that the momentum gain per cycle by DSA is equal to the synchrotron/IC loss per cycle, $\langle \Delta p \rangle_{\rm DSA}+\langle \Delta p \rangle_{\rm rad}$ =0 \citep[see][]{wdb84,za07}."
. With the assumed Dohm-ivpe diffusion coefficient. the electron spectrum has a cutoff at where By=(B?+Dé)? with Begg=324x10/5 G is the effective magnetic field strength for svnchrotron and IC coolings upstream and downstream of shock. ancl 6=0 was assumed.," With the assumed Bohm-type diffusion coefficient, the electron spectrum has a cutoff at where $B_{\rm eff}=(B^2 + B_{\rm CMB}^2)^{1/2}$ with $B_{\rm CMB}=3.24\times
10^{-6}$ G is the effective magnetic field strength for synchrotron and IC coolings upstream and downstream of shock, and $\delta=0$ was assumed."
 Note that the electron cutoff energy is a time-asvinplolic quantity that depends only on the shock speed and the magnetic field strength. independent of the shock age.," Note that the electron cutoff energy is a time-asymptotic quantity that depends only on the shock speed and the magnetic field strength, independent of the shock age."
For a Mach 3 shock and By=1iG. for example. the shock jump condition gives q=3. (q=4.5 (with à= 0) and D»= 3jG (assuming Dx p). resulting in the eutoff Lorentz factor. See=Deafe85.6x10*(wu./1000kmsB,"For a Mach 3 shock and $B_0 = 1\muG$, for example, the shock jump condition gives $\sigma = 3$, $q=4.5$ (with $\delta=0$ ) and $B_2 = 3\mu$ G (assuming $B \propto \rho$ ), resulting in the cutoff Lorentz factor, $\gamma_{\rm e,cut} = p_{\rm cut}/m_e c
\approx 5.6 \times 10^7\ (u_s/1000\kms)$."
" Thus. we may model the downstream electron spectrum as where fj,5(p) is the downstream proton spectrum (Zirakashvili&Aharonian2007)."," Thus, we may model the downstream electron spectrum as where $f_{p,2}(p)$ is the downstream proton spectrum \citep{za07}."
". The elecPUN mnunber ratio. A,;,. is nol vet constrainedprecisely by --sics 2008).. ll"," The electron-to-proton number ratio, $K_{e/p}$, is not yet constrained precisely by plasma physics \citep[see, e.g.,][]{reynolds08}."
"aAlthough A;~107 is inferred. for the Galactic CRs 2002).. a much value. A,Z10| is preferred for young supernova remnants (Morlinoetal. 2009)."," Although $K_{e/p}\sim 10^{-2}$ is inferred for the Galactic CRs \citep{schl02}, a much smaller value, $ K_{e/p} \la 10^{-4}$, is preferred for young supernova remnants \citep{mab09}."
". However. A, lor the pre-exisüng population in ICMs and cluster outskirts could be quite different [rom these estimates."," However, $K_{e/p}$ for the pre-existing population in ICMs and cluster outskirts could be quite different from these estimates."
wieht secu most straightforward to use the leneth aud nuc-seales of the cucrey-conserving phase (ie. Sedov phase) to control where aud when to turn cooling off. but hese turn out to be too snall and too short (a few 10! vears) to make a significant difference. as acknowledecd wo previous studies (?7)..,"might seem most straightforward to use the length and time-scales of the energy-conserving phase (i.e. Sedov phase) to control where and when to turn cooling off, but these turn out to be too small and too short (a few $10^4$ years) to make a significant difference, as acknowledged by previous studies \citep{Stinson:2006p1023}."
 Instead. the method emplovs he radius aud time at the eud of the momentiuu-conserving phase under the assumption that during his phase. much of the euergy is couserved iu kinetic notion (and hot. diffuse gas). which the code caunot nodel. aud would otherwise dissipate.," Instead, the method employs the radius and time at the end of the momentum-conserving phase under the assumption that during this phase, much of the energy is conserved in kinetic motion (and hot, diffuse gas), which the code cannot model, and would otherwise dissipate."
 The larger leugth and timescales of the suowplow phase used are further justified as the combined forces of multiple superuovae in the star particle: however. although these superunovae nay mteract m a complex wav. it is wulikely their effects will simply add coustructively.," The larger length and timescales of the snowplow phase used are further justified as the combined forces of multiple supernovae in the star particle; however, although these supernovae may interact in a complex way, it is unlikely their effects will simply add constructively."
 This prescription for cooling suppression feedback has generally been used in SPILT codes. but receutlv some AMR codes have also adopted this techuique (27)...," This prescription for cooling suppression feedback has generally been used in SPH codes, but recently some AMR codes have also adopted this technique \citep{Agertz:2010p461, Colin:2010p1053}."
 The conimion prescription is to suppress cooling for a period of time (30.50 Mi) in the eas innediatelv. around a star-formation event. regardless of where the star goes afterwards.," The common prescription is to suppress cooling for a period of time $30-50$ Myr) in the gas immediately around a star-formation event, regardless of where the star goes afterwards."
 Iu our implementation. we suppress cooling of the eas in the sinele cell iun which the star particle resides.," In our implementation, we suppress cooling of the gas in the single cell in which the star particle resides."
 This is done for 50 Myr after the star particle is first created., This is done for 50 Myr after the star particle is first created.
 Since both of these leugth aud time scales correspond closely to those over which energy from the star particle is injected i the simulation (the feedback follows Eq. 2..," Since both of these length and time scales correspond closely to those over which energy from the star particle is injected in the simulation (the feedback follows Eq. \ref{eq:feedback},"
 above). this acts to suppress cooling in newly heated sas.," above), this acts to suppress cooling in newly heated gas."
 Caven our chosen cell size (125 comoving pe iu most runs). these leugth aud timescales are simular to the region and duration of influcuce adopted by other researchers (2?)..," Given our chosen cell size (425 comoving pc in most runs), these length and timescales are similar to the region and duration of influence adopted by other researchers \citep{Stinson:2006p1023, Colin:2010p1053}."
" For this work. we use the WALAP 5-voar results as our cosniological parzuueters (7).. iu particular we use: Ομ=0.258. Oy=0,712. On=OOLL σς=0.796. IL, =71.9lus +."," For this work, we use the WMAP 5-year results as our cosmological parameters \citep{Komatsu:2009p1070}, , in particular we use: $\Omega_{0} = 0.258$, $\Omega_{\Lambda} = 0.742$, $\Omega_{\rm baryon} = 0.044$, $\sigma_8 = 0.796$, $H_{\rm o}$ = 71.9 km $^{-1}$."
 We generate our initial couditious usingmits. a program included in the suite.," We generate our initial conditions using, a program included in the suite."
 sets up a 128? particleaucsh grid. aud modifies the velocity aud position of the dark matter particles in cach eid cell as specified by linear perturbations with the required power spectrum at 2=99.," sets up a $128^3$ particle-mesh grid, and modifies the velocity and position of the dark matter particles in each grid cell as specified by linear perturbations with the required power spectrum at $z = 99$."
 The initial conditions are generated for a cubic volume of £L=20h* comoving Mpc ona side with periodic boundary conditions., The initial conditions are generated for a cubic volume of $L = 20 h^{-1}$ comoving Mpc on a side with periodic boundary conditions.
" First. the simulation is populated with oulv dark matter particles at resolution (Mp,=3.2ς105 ML.) aud run to += 0, where candidate \Tillkw-Wav-like halos are ideutified."," First, the simulation is populated with only dark matter particles at low-resolution $M_{\rm DM} = 3.2 \times 10^8$ ) and run to $z = 0$ , where candidate Milky-Way-like halos are identified."
 Talos are chosen based on their final mass and accretion history. preferentially selecting halos with final masses Adfogy~Lot?AL... and those which have not undergone niajor mergers after 2~ (ALoyy is the mass cuclosed within a radius correspouding to a mean density of 200 times the critical density).," Halos are chosen based on their final mass and accretion history, preferentially selecting halos with final masses $M_{200} \sim 10^{12}$, and those which have not undergone major mergers after $z \sim 2$ $M_{200}$ is the mass enclosed within a radius corresponding to a mean density of 200 times the critical density)."
 Five such halos are ideutified. rauging in mass from Moog=Ls«lot to 1.2«1077AL...," Five such halos are identified, ranging in mass from $M_{200} = 4.8 \times 10^{11}$ to $ 1.2 \times 10^{12}$."
 For each halo. the component dark matter particles are traced back to their positious in the initial conditions at 2=99.," For each halo, the component dark matter particles are traced back to their positions in the initial conditions at $z = 99$."
 This Laeraneian volume is further refined with two additional levels of refinement., This Lagrangian volume is further refined with two additional levels of refinement.
 It is here that the initial conditions are regenerated. and iu these nested boxes. we additionally refine the dark matter particle masses bv a factor of 8 for each region.," It is here that the initial conditions are regenerated, and in these nested boxes, we additionally refine the dark matter particle masses by a factor of 8 for each region."
 The resulting hnieh-resolutiou dark matter particle mass within the vicinity of cach halo is Mp=L9<10°ML., The resulting high-resolution dark matter particle mass within the vicinity of each halo is $M_{\rm DM} = 4.9 \times 10^6$.
.. A series of new simulations are performed using these new initial conditions: cach one focuses on a differeut halo., A series of new simulations are performed using these new initial conditions; each one focuses on a different halo.
 Barvous are included in these runs., Baryons are included in these runs.
 The hiseh-resolutiou regions are further refined dynamically with adaptively-placed evids. using the refinement scheme described earlier.," The high-resolution regions are further refined dynamically with adaptively-placed grids, using the refinement scheme described earlier."
 We conducted. five canonical simulatious using identical simulation parameters and the initial conditions deserihed above., We conducted five canonical simulations using identical simulation parameters and the initial conditions described above.
 These simulatious are referred to as: TI26SPAL TB0SPAL. T37SPAM. ITITSPM. and II5ISPM.," These simulations are referred to as: H26SPM, H30SPM, H37SPM, H47SPM and H54SPM."
 Additionally. several different runs were performed ou the initial conditions for halo 26 (II26SPM). which svstenaaticalle varied simulation auc physical parameterso to investigate the effects of each ou galactic evolution.," Additionally, several different runs were performed on the initial conditions for halo 26 (H26SPM), which systematically varied simulation and physical parameters to investigate the effects of each on galactic evolution."
 The paraicters togeled (aud their respective siuulations) include: (3) excluding nünnunuun pressure support (i) changing the maximum spatial resolution|I26S]: DSII26SPM. M]: (ii) using a constaut[D7II268PM. plivsical resolution insteadDIOIT26SP of a coustaut comoving resolution |l26SPMRB.. H268PMECR]: Gv) including thermal feedback. (v) lowering the star-formatiou|II26SPME. cfficieucyII268PMECTI: |H26SPMI]: and (wi) suppressing cooling iu star formune reelous [TI26SPAIC. H26SPMFEC. II268PMECT].," The parameters toggled (and their respective simulations) include: (i) excluding minimum pressure support [H26S]; (ii) changing the maximum spatial resolution [D7H26SPM, D8H26SPM, D10H26SPM]; (iii) using a constant physical resolution instead of a constant comoving resolution [H26SPMR, H26SPMFCR]; (iv) including thermal feedback [H26SPMF, H26SPMFCR]; (v) lowering the star-formation efficiency [H26SPML]; and (vi) suppressing cooling in star forming regions [H26SPMC, H26SPMFC, H26SPMFCR]."
 The details of the various simulations and the resulting galaxies are shown in Table 1.., The details of the various simulations and the resulting galaxies are shown in Table \ref{tab:halos}.
 Tn this section. we present the results of our galaxy formation simulations. first describing the five canonical runs. which all contain identical physical prescriptious but track different galactic halos.," In this section, we present the results of our galaxy formation simulations, first describing the five canonical runs, which all contain identical physical prescriptions but track different galactic halos."
 Then. we explore variatious in resolution as well as the αποΊσα] parameters we use to describe the gas aud star formation.," Then, we explore variations in resolution as well as the numerical parameters we use to describe the gas and star formation."
 The mass accretion history for a galaxy including the different anodes of its accretion is thought to plav a crucial role in determining its final dynamical state (6.8. 7).., The mass accretion history for a galaxy including the different modes of its accretion is thought to play a crucial role in determining its final dynamical state \citep[e.g.][]{Keres:2005p1111}.
 In order to analyze the simulation in hieh time resolution. we record outputs frou the simulation every 10 Myr.," In order to analyze the simulation in high time resolution, we record outputs from the simulation every 10 Myr."
 For cach output we run the TWOP aleorithin (7) ou the dark matter particles iu order to ideutify halos., For each output we run the HOP algorithm \citep{Eisenstein:1998p1073} on the dark matter particles in order to identify halos.
 Given the particles in cach of our five halos at 2=0. we identify aud track these halos back to early times.," Given the particles in each of our five halos at $z=0$, we identify and track these halos back to early times."
 Each halo is tracked backwards in time by ideutifving the local progenitor which shares the largest ummber of tielth-bound dark matter particles., Each halo is tracked backwards in time by identifying the local progenitor which shares the largest number of tightly-bound dark matter particles.
 The resulting mass-accretion history for cach halo is shown in Figure 2.., The resulting mass-accretion history for each halo is shown in Figure \ref{fig:canonical_mass}.
 The halo masses are computed inside of rogo. the radius within which the mean density is 200 times the critical density of the universe at that redshift.," The halo masses are computed inside of $r_{200}$, the radius within which the mean density is 200 times the critical density of the universe at that redshift."
 At cach time. we determine the center of the halo using an iterated ceuter-ofinass techuique. which starts with the center of lnass Within rogy. aud then successively recomputes the center of mass in snaller spherical volumes. decreasing the radius byou each iteration and using the ceuter of mass of the previous volume.," At each time, we determine the center of the halo using an iterated center-of-mass technique, which starts with the center of mass within $r_{200}$, and then successively recomputes the center of mass in smaller spherical volumes, decreasing the radius byon each iteration and using the center of mass of the previous volume."
 This is necessary in order to make an accurate determination of the halo ceuter (wo fouud that simply choosing either the densest poit, This is necessary in order to make an accurate determination of the halo center (we found that simply choosing either the densest point
re-accelerate} the relativistic particles responsible for the radio eniission.,re-accelerate) the relativistic particles responsible for the radio emission.
 Most of the clusters studied by BT96 do not possess radio halos or relies., Most of the clusters studied by BT96 do not possess radio halos or relics.
" If we consider the brightest ~30 clusters for which the sample of BT96 is more than complete (N-rav selected) inost of the clusters without radio halos or relics have P,/D,X107 placing them in the lower left portion of Fieure 1.", If we consider the brightest $\sim 30$ clusters for which the sample of BT96 is more than complete (X-ray selected) most of the clusters without radio halos or relics have $P_1/P_0\la 10^{-5}$ placing them in the lower left portion of Figure \ref{fig.radio}.
 These clusters are therefore approximately relaxed systems aud. iji accordance with the formation scenario discussecl previously. do not have powerful radio halos or relics.," These clusters are therefore approximately relaxed systems and, in accordance with the formation scenario discussed previously, do not have powerful radio halos or relics."
" However. three bright clusters (Ατοι. A3266, Cveuus-À) exist that are lighly morphologically disturbed (Py,/Py=LO 4) yet have no (or only weakly) detected euissiou from a radio halo at 1.1 CdIz."," However, three bright clusters (A754, A3266, Cygnus-A) exist that are highly morphologically disturbed $P_1/P_0 \ge 10^{-4}$ ) yet have no (or only weakly) detected emission from a radio halo at 1.4 GHz."
" Thus cach would lie iu the bottom right portion of Figure as sienificant outlicrs in the Po,PED, correlation."," Thus each would lie in the bottom right portion of Figure \ref{fig.radio}
 as significant outliers in the $P_{1.4}-P_1/P_0$ correlation."
 It is possible that powerful radio halos for these systems have not been detected at 1. CGIIz owing to their steep spectra: c.e.. after our paper was xubnütted we became aware of a paper by Nassimetal.(2001) which preseuts evidence for a very powerfu radio halo iu À7T51 at 330 MIIz.," It is possible that powerful radio halos for these systems have not been detected at 1.4 GHz owing to their steep spectra; e.g., after our paper was submitted we became aware of a paper by \citet{kassim} which presents evidence for a very powerful radio halo in A754 at 330 MHz."
 Whether halos in these or other clusters are detected at other radio frequencies 1s al iuportant subject for future studies., Whether halos in these or other clusters are detected at other radio frequencies is an important subject for future studies.
 For the remainder of his paper we confine our discussion to studies at 1.1 GIIz., For the remainder of this paper we confine our discussion to studies at 1.4 GHz.
 These clusters do have strong radio euission frou either a central source (Cyvenus-A) or collectively from severa yoint sources (Ατομα A3266) which could be relate o their current dyvnuauucal state., These clusters do have strong radio emission from either a central source (Cygnus-A) or collectively from several point sources (A754 and A3266) which could be related to their current dynamical state.
 These clisters have simular structure iu their N-vayv temperature distribution where relatively cool gas exists within the central few iundred kpe and hotter gas. cousisteunt with shock-ieating. is located at larecr radi (c.g... Henry Bricl 1995: Teuriksen Alarkevitch 1996: Markeviteh ct al.," These clusters have similar structure in their X-ray temperature distribution where relatively cool gas exists within the central few hundred kpc and hotter gas, consistent with shock-heating, is located at larger radii (e.g., Henry Briel 1995; Henriksen Markevitch 1996; Markevitch et al."
 1999.2001: Tleurissen ct al.," 1999,2001; Henriksen et al."
 2000: Sarazin 2000)., 2000; Sarazin 2000).
 The teiiperature maps of these svstenmis nuplv mergers that have not disrupted the cores. aud detailed bydrodvuamical models coufirin that the mergers in these svstems are offaxis and must be in the very earliest stages (c.g.. Rocttiger et al.," The temperature maps of these systems imply mergers that have not disrupted the cores, and detailed hydrodynamical models confirm that the mergers in these systems are off-axis and must be in the very earliest stages (e.g., Roettiger et al."
 1998: Flores et al., 1998; Flores et al.
 2000: Rocttiger Flores 2000)., 2000; Roettiger Flores 2000).
 The temperature structure of these deviant clusters is similar to that of A3667 (e.g. Vikhlinin et al.," The temperature structure of these deviant clusters is similar to that of A3667 (e.g, Vikhlinin et al."
 2000) which also has no detected radio halo., 2000) which also has no detected radio halo.
" As cliscussed previously, this svstem has a large-scale ανασα. disturbance with a large value of P)/P)z10+ within the 1. Mpe aperture simular to those clusters with the most powerful halos."," As discussed previously, this system has a large-scale dynamical disturbance with a large value of $P_1/P_0\approx 10^{-4}$ within the 1 Mpc aperture similar to those clusters with the most powerful halos."
 Iu contrast. A2256. the most deviant cluster in Figure 1 when cousicdering only the cussion from radio halos. does have a measured weal radio halo.," In contrast, A2256, the most deviant cluster in Figure \ref{fig.radio} when considering only the emission from radio halos, does have a measured weak radio halo."
 Uulike the other clusters deseribed in this section. the N-vay temperature map of A2256 (e.e.. Sun ct al.," Unlike the other clusters described in this section, the X-ray temperature map of A2256 (e.g., Sun et al."
 2001) indicates a more advanced merger that has begun to disrupt the core., 2001) indicates a more advanced merger that has begun to disrupt the core.
" The formation of halos and relies also appears to be related since the relic sources (most notably A2256) are consistent with the Py,xP4/P, trend when both halo and relic cussion are included.", The formation of halos and relics also appears to be related since the relic sources (most notably A2256) are consistent with the $P_{1.4}\propto P_1/P_0$ trend when both halo and relic emission are included.
 Further study is needed to establish the existence of a direct link between lhialos and relies; especially to ascertain if peripheral relics are formed prefercutially at carly tines duiug mergers.," Further study is needed to establish the existence of a direct link between halos and relics, especially to ascertain if peripheral relics are formed preferentially at early times during mergers."
 Finally. the faimtest cluster studied by D'T96. ASL1. has the largest power ratios but docs uot possess a radio halo.," Finally, the faintest cluster studied by BT96, A514, has the largest power ratios but does not possess a radio halo."
 This cluster consists of several sumall clumaps eiibedded im a diffuse halo of X-ray eiission (6.g.. Figure 5 iu Duote Tsai 1995).," This cluster consists of several small clumps embedded in a diffuse halo of X-ray emission (e.g., Figure 5 in Buote Tsai 1995)."
 The lack of a radio halo could arise because ADLL is apparently in the earliest formation stages aud perhaps has not had enouch time to eenerate a reservolr of relativistie particles for re-acceleratiou., The lack of a radio halo could arise because A514 is apparently in the earliest formation stages and perhaps has not had enough time to generate a reservoir of relativistic particles for re-acceleration.
 Altcruatively.," Alternatively,"
(Rees&Gunn1974:KennelCoroniti1954a:;deJageretal.2009:Venterc,"\citep{rg74, kc84a, det09, vd06}."
le Rees&Gunn(1974). considered that the magnetic field evolution is determined by the number of turns of the central pulsar., \citet{rg74} considered that the magnetic field evolution is determined by the number of turns of the central pulsar.
 They considered that the magnetic field in the PWN was built up by the winding of field lines because of the pulsar spin., They considered that the magnetic field in the PWN was built up by the winding of field lines because of the pulsar spin.
 The total number of the (turns of (he magnetic field line is given bv This number is proportional to the magnetic flux. which means For />7). we obtain. BU)ox(7/0! so that BO)x(I? for n=3 and BUI)x19 for n=2.5.," The total number of the turns of the magnetic field line is given by This number is proportional to the magnetic flux, which means For $t > \tau_0$, we obtain $B(t) \propto t^{n / (1-n)}$ so that $B(t) \propto t^{-1.5}$ for $n = 3$ and $B(t) \propto t^{-5 / 3}$ for $n = 2.5$."
 Our choice of the magnetic field evolution is not so different., Our choice of the magnetic field evolution is not so different.
" ]xennel&Coroniti(1984a) considered (he steady. state spatial structure of PWN,", \citet{kc84a} considered the steady state spatial structure of PWN.
 In the IXC model. the magnetic field increases with the distance from the pulsar till the magnetic pressure dominates over the particle pressure.," In the KC model, the magnetic field increases with the distance from the pulsar till the magnetic pressure dominates over the particle pressure."
 Although the assumption of the steady state PWN makes it diffieult to compare wilh our model. it seems to be natural to regard (hat (he magnetic energy is a constant fraction of the total energy (~ the particle energv). which means where we include the adiabatie cooling of the total energy. so that BU)x/7 for [Ty ," Although the assumption of the steady state PWN makes it difficult to compare with our model, it seems to be natural to regard that the magnetic energy is a constant fraction of the total energy $\sim$ the particle energy), which means where we include the adiabatic cooling of the total energy, so that $B(t) \propto t^{-2}$ for $t > \tau_0$."
Equation (11)) is allernatively interpreted as (he magnetic flux conservation., Equation \ref{eq11}) ) is alternatively interpreted as the magnetic flux conservation.
 The inagnelic [ield decreases more rapidly (han our model. but it is still close to our model.," The magnetic field decreases more rapidly than our model, but it is still close to our model."
 In deJageretal. (2009).. they mentioned that the spatially averaged magnetic field strength of the PWN decreases as BU)x!tin their caleulation of non-relativistic MIID," In \citet{det09}, , they mentioned that the spatially averaged magnetic field strength of the PWN decreases as $B(t) \propto t^{-1.3}$in their calculation of non-relativistic MHD"
To determine the contribution of these objects to the GRB one should make direct observations in the οταν band of nearby LRAS sources known bright starburst galaxies.,To determine the contribution of these objects to the GRB one should make direct observations in the $\gamma$ -ray band of nearby IRAS sources – known bright starburst galaxies.
 prospects for the detection of these galaxies in the 5-ray rangeUnfortunately. with the present day instruments are ," Unfortunately, prospects for the detection of these galaxies in the $\gamma$ -ray range with the present day instruments are discouraging."
This is because in the present model a substantial fraction ofdiscouraging. the GRB is produced by a large number of relatively weak 5-ravy sources., This is because in the present model a substantial fraction of the GRB is produced by a large number of relatively weak $\gamma$ -ray sources.
 EGIT observations show that some AGNs reach Iuminosities of 10710 eres! (von Montigny et al., EGRET observations show that some AGNs reach luminosities of $10^{47}-10^{49}$ $^{-1}$ (von Montigny et al.
 1995). while in our mocel Local 5- luminosities dueto the IC cover the range of 107—107 ra," 1995), while in our model local $\gamma$ -ray luminosities dueto the IC process cover the range of $10^{36}-10^{39}$ $^{-1}$."
yThe total 5-ray luminosities ofprocess PLR galaxies are most probably eres larger because of the but still are several orderssubstantial of uce below blazar luminosities.," The total $\gamma$ -ray luminosities of FIR galaxies are most probably substantialy larger because of the Bremsstrahlung, but still are several orders of magnitude below blazar luminosities."
Bremsstrahlung. However. it is likely that the relativelymagnit high density of ELI galaxies makes them dominant contributors to the spat," However, it is likely that the relatively high spatial density of FIR galaxies makes them dominant contributors to the GRB."
ialGRB. = 12pt p03C00910. = 12pt, \bsk = 12pt \ssk = 12pt
of a selberavitating gas of CDM particles in thermodynamic equilibrium take cifferent values when computed in different statistical ensembles because (he long-range nature of the eravitational potential renders (he svstem inseparable [rom its environment (Pachuanabhan1990:Ispolatov&Cohen2001:deVegaSanchez 2002).,"of a self-gravitating gas of CDM particles in thermodynamic equilibrium take different values when computed in different statistical ensembles because the long-range nature of the gravitational potential renders the system inseparable from its environment \citep{pad90,ispolcohen01,vegasan02}."
. In this paper. we follow previous studies by considering the sell-gravitating gas in the microcanonical ensemble (AICE). whose features are constant energy. volume and particle number.," In this paper, we follow previous studies by considering the self-gravitating gas in the microcanonical ensemble (MCE), whose features are constant energy, volume and particle number."
 Particles do not evaporate from the svstem over lime and (he walls of the container are perfectly reflecting., Particles do not evaporate from the system over time and the walls of the container are perfectly reflecting.
 The AICE is more appropriate (han (he canonical ensemble (CE) lor three reasons: (i) it is unclear how to construct an external heat bath (equired by the CE) lor a long-range potential. because (he svstem interferes with the environment (IIuang1987): (i1) states wilh negative specific heat are inaccessible in (he CE (Pacdinanabhan1990):: and (iii) the equilibrium density prolile in (he violently relaxed (Simoluchowski) limit is (he singular isothermal sphere in the CI. contrary to observations (Sire&Chavanis2002 )..," The MCE is more appropriate than the canonical ensemble (CE) for three reasons: (i) it is unclear how to construct an external heat bath (required by the CE) for a long-range potential, because the system interferes with the environment \citep{huang87}; (ii) states with negative specific heat are inaccessible in the CE \citep{pad90}; and (iii) the equilibrium density profile in the violently relaxed (Smoluchowski) limit is the singular isothermal sphere in the CE, contrary to observations \citep{sire02}. ."
 The density of states. gi). is the volume ofthe (6.4— 1)-dimensional surface of constant enerev FL in phase space (Xj....X«.pj. ...p.). where (x;.p;) are the co-ordinates. and momenta of the ;-th particle.," The density of states, $g(E)$ , is the volume ofthe $N-$ 1)-dimensional surface of constant energy $E$ in phase space ${\bf{x}}_1,...,{\bf{x}}_N,{\bf{p}}_1,...,{\bf{p}}_N$ ), where ${\bf{x}}_i,{\bf{p}}_i$ ) are the co-ordinates and momenta of the $i$ -th particle."
 At any one moment. the svstem occupies one point in the 6.N -dimensional phase space.," At any one moment, the system occupies one point in the $N$ -dimensional phase space."
 For particles of equal mass m. one has the first aud second sums give the kinetic ancl potential energy. and (he integral is over phase space volume.," For particles of equal mass $m$, one has where the first and second sums give the kinetic and potential energy, and the integral is over phase space volume."
 The gravitational potential. V. is given bv V =—Gniz[x;-x;|!or. if the potential is artificially softened over a characteristic length ¢. by V gg ," The gravitational potential, $V$, is given by $V=-Gm^2|{\bf{x}}_i-{\bf{x}}_j|^{-1}$ or, if the potential is artificially softened over a characteristic length $\zeta$, by $V=-Gm^2[({\bf{x}}_i-{\bf{x}}_j)^2+\zeta^2]^{-1/2}$ ."
The thermodynamic entropy 5 (up to a constant) and the temperature Z of the svstem are defined in terms of g(E): These quantities are hard (to interpret when assigned to à system far from equilibrium., The thermodynamic entropy $S$ (up to a constant) and the temperature $T$ of the system are defined in terms of $g(E)$: These quantities are hard to interpret when assigned to a system far from equilibrium.
 Note that gi) diverges for ¢=0 andNo72: any (wo particles can be brought arbitrarily close together. liberating an infinite amount of potential energy. so that the co-ordinate space," Note that $g(E)$ diverges for $\zeta=0$ and$N>2$; any two particles can be brought arbitrarily close together, liberating an infinite amount of potential energy, so that the co-ordinate space"
"connected with kinetic effects, that can be caused by non-equilibrium of the particles energy distribution function (mainly, anomalous Doppler effect in the region of cyclotron resonance); two-stream instability (Kazbegi, Machabeli Melikidze 1991); the instability connected with the nonstationarity of plasma particle production in the region of its generation (Lyubarskii 1996).","connected with kinetic effects, that can be caused by non-equilibrium of the particles energy distribution function (mainly, anomalous Doppler effect in the region of cyclotron resonance); two-stream instability (Kazbegi, Machabeli Melikidze 1991); the instability connected with the nonstationarity of plasma particle production in the region of its generation (Lyubarskii 1996)."
" 'The saturation mechanism, whose investigation requires involving the effects of a nonlinear wave interaction, is the most complex from the theoretical point of view."," The saturation mechanism, whose investigation requires involving the effects of a nonlinear wave interaction, is the most complex from the theoretical point of view."
" Therefore, it is not surprising that only a few researchers have managed to consider this question consistently (see, e.g., Istomin 1988)."," Therefore, it is not surprising that only a few researchers have managed to consider this question consistently (see, e.g., Istomin 1988)."
" Finally, the processes of the wave propagation in pulsar magnetosphere have not yet been investigated with sufficient detail either, although the part of theory that includes the propagation processes can be constructed using the standard linear methods of plasma physics."," Finally, the processes of the wave propagation in pulsar magnetosphere have not yet been investigated with sufficient detail either, although the part of theory that includes the propagation processes can be constructed using the standard linear methods of plasma physics."
" 'There are four assumptions in the hollow cone model: first, the emission is generated in the inner magnetospheric regions (where the magnetic field may be considered as a dipole); second, the emission propagates along the straight line; third, the cyclotron absorption may be neglected; and fourth, the polarization is determined at the emission point."," There are four assumptions in the hollow cone model: first, the emission is generated in the inner magnetospheric regions (where the magnetic field may be considered as a dipole); second, the emission propagates along the straight line; third, the cyclotron absorption may be neglected; and fourth, the polarization is determined at the emission point."
" Such basic characteristics of the received radio emission allow to determine the change of the position angle (p.a.) of the linear polarization along the mean profile (Radhakrishnan Cocke 1969) Here is the inclination angle of the magnetic dipole to the rotationa axis, ¢ is the angle between the rotation axis and the observer’s direction, and ¢ is the pulse phase."," Such basic characteristics of the received radio emission allow to determine the change of the position angle $p.a.$ ) of the linear polarization along the mean profile (Radhakrishnan Cocke 1969) Here $\alpha$ is the inclination angle of the magnetic dipole to the rotation axis, $\zeta$ is the angle between the rotation axis and the observer's direction, and $\phi$ is the pulse phase."
" As a result, the radiation beam width W, itself and its statistical dependence on the period P can be qualitatively explained under these assumptions (Rankin 1983, 1990)."," As a result, the radiation beam width $W_{\rm r}$ itself and its statistical dependence on the period $P$ can be qualitatively explained under these assumptions (Rankin 1983, 1990)."
 It is not surprising that the hollow cone model in its simplest realization is currently widely used for quantitative determination of the parameters of neutron stars., It is not surprising that the hollow cone model in its simplest realization is currently widely used for quantitative determination of the parameters of neutron stars.
" At the same time, it is well known that, in general, three main assumptions are incorrect."," At the same time, it is well known that, in general, three main assumptions are incorrect."
" First of all, after the paper by Barnard Arons (1986), it became clear that the ordinary wave does not propagate in a straight line, but deflects away from the magnetic axis."," First of all, after the paper by Barnard Arons (1986), it became clear that the ordinary wave does not propagate in a straight line, but deflects away from the magnetic axis."
" Subsequently, this effect was studied in detail by Petrova Lyubarskii (1998, 2000), it was an important element in the BGI theory."," Subsequently, this effect was studied in detail by Petrova Lyubarskii (1998, 2000), it was an important element in the BGI theory."
 The correction to relation (1)) connected with the aberration was determined by Blaskiewicz et al. (, The correction to relation \ref{p.a.}) ) connected with the aberration was determined by Blaskiewicz et al. (
"1991), but it wasrarely used in analysis of the observational data as well.","1991), but it was used in analysis of the observational data as well."
" Further, the cyclotron absorption that must take place near the light cylinder (Mikhailovsky et al."," Further, the cyclotron absorption that must take place near the light cylinder (Mikhailovsky et al."
" 1982) turns out to be so large that it will not allow the radio emission to escape the pulsar's magnetosphere (see, e.g., Fussel et al."," 1982) turns out to be so large that it will not allow the radio emission to escape the pulsar's magnetosphere (see, e.g., Fussel et al."
 2003)., 2003).
" Finally, the limiting polarization effect had not been discussed seriously over many years, although it was qualitatively clear that this effect must be decisive for explaining of high degree of circular polarization, typically 5-20%."," Finally, the limiting polarization effect had not been discussed seriously over many years, although it was qualitatively clear that this effect must be decisive for explaining of high degree of circular polarization, typically $5$ $20$."
". Indeed, in the region of the radio emission generation located at 10-100 neutron star radii (these values result from the hollow cone model), the magnetic field is still strong enough so the polarization of the two orthogonal modes is indistinguishable from a linear one.Nevertheless,"," Indeed, in the region of the radio emission generation located at $10$ $100$ neutron star radii (these values result from the hollow cone model), the magnetic field is still strong enough so the polarization of the two orthogonal modes is indistinguishable from a linear one.,"
" in an overwhelming majority of the papers, Eqn. (1))"," in an overwhelming majority of the papers, Eqn. \ref{p.a.}) )"
 is used to investigate the polarization., is used to investigate the polarization.
" Recall that the limiting polarization effect is related to the escape of radio emission from a region of dense plasma, where the propagation is well described in the geometrical optics approximation (in this case, the polarization ellipse is defined by the orientation of the external magnetic field in the picture plane), into the region of rarefied plasma, where the emission polarization becomes almost constant along the ray."," Recall that the limiting polarization effect is related to the escape of radio emission from a region of dense plasma, where the propagation is well described in the geometrical optics approximation (in this case, the polarization ellipse is defined by the orientation of the external magnetic field in the picture plane), into the region of rarefied plasma, where the emission polarization becomes almost constant along the ray."
" This process was well studied (Zheleznyakov 1977; Kravtsov Orlov 1990) and was used successfully for numerous objects, for example, in connection with the problems of solar radio emission (Zheleznyakov 1964)."," This process was well studied (Zheleznyakov 1977; Kravtsov Orlov 1990) and was used successfully for numerous objects, for example, in connection with the problems of solar radio emission (Zheleznyakov 1964)."
" However, in the theory of pulsar radio emission, such problem has not been solved."," However, in the theory of pulsar radio emission, such problem has not been solved."
" Above the papers where the level r=re at which the transition from the geometrical optics approximation to the vacuum occurs, was only estimated (see, e.g., Cheng Ruderman 1979; Barnard 1986), one can note only a few paper by Petrova Lyubarskii (2000) (these authors considered the problem in the infinite magnetic field), by Petrova (2001, 2003, 2006), as well as the recent papers by Wang, Lai Han (2010, 2011)."," Above the papers where the level $r = r_{\rm esc}$ at which the transition from the geometrical optics approximation to the vacuum occurs, was only estimated (see, e.g., Cheng Ruderman 1979; Barnard 1986), one can note only a few paper by Petrova Lyubarskii (2000) (these authors considered the problem in the infinite magnetic field), by Petrova (2001, 2003, 2006), as well as the recent papers by Wang, Lai Han (2010, 2011)."
" The goal of our paper is to consider all three main effects (i.e., refraction, cyclotron absorption, and limiting polarization) simultaneously in a consistent manner for realistic case."," The goal of our paper is to consider all three main effects (i.e., refraction, cyclotron absorption, and limiting polarization) simultaneously in a consistent manner for realistic case."
 Not only the plasma density but also the magnetic field decreases with increasing distance from the neutron star will be included into consideration., Not only the plasma density but also the magnetic field decreases with increasing distance from the neutron star will be included into consideration.
" Also, the non-dipole magnetic field, the drift motion of plasma particles, and realistic distribution function of outgoing plasma will be taken into account."," Also, the non-dipole magnetic field, the drift motion of plasma particles, and realistic distribution function of outgoing plasma will be taken into account."
 In section 2 both ordinary and extraordinary waves propagation in the pulsar magnetosphere is briefly, In section 2 both ordinary and extraordinary waves propagation in the pulsar magnetosphere is briefly
when large amplitude circular polarisation variations were detected with a period of 90 min.,when large amplitude circular polarisation variations were detected with a period of 90 min.
 Based on a typical polar A-ray spectrum in the high aceretion state. V347 Pay was brighter during the observations compared to Alarch 1993 but not as bright as in July 1994 (Ramsay et al 1996).," Based on a typical polar X-ray spectrum in the high accretion state, V347 Pav was brighter during the observations compared to March 1993 but not as bright as in July 1994 (Ramsay et al 1996)."
 It was therefore in a high accretion state., It was therefore in a high accretion state.
 GG. Leo was also discovered: as part of theROSAL all sky. survey. on this occasion using the X-ray ‘Telescope.," GG Leo was also discovered as part of the all sky survey, on this occasion using the X-ray Telescope."
 Followup observations by Burwitz et al (1998) identified the optical counterpart as a V=1617 mag polar with an orbital period close to 90 min., Followup observations by Burwitz et al (1998) identified the optical counterpart as a $V=16-17$ mag polar with an orbital period close to 90 min.
 Durwitz et al (1998) reported X-rav data taken from 3 epochs: it was bright on each occasion and showed a narrow dip which was taken to be the accretion stream obscuring the accretion region., Burwitz et al (1998) reported X-ray data taken from 3 epochs: it was bright on each occasion and showed a narrow dip which was taken to be the accretion stream obscuring the accretion region.
 Comparing the count rates we find that GC Leo was at a similar X- brightness during these observations as in May. 1994. so that it was also in a high accretion state.," Comparing the count rates we find that GG Leo was at a similar X-ray brightness during these observations as in May 1994, so that it was also in a high accretion state."
 IU UMa was discovered: using theAT. extreme UV WEC survey and identified with a V—17 mag CY by Alittag et al (1992)., EU UMa was discovered using the extreme UV WFC survey and identified with a $V$ =17 mag CV by Mittaz et al (1992).
 Observations usingEUVE by Howell et al (1995) found that the orbital period. was likely to be 90 mins., Observations using by Howell et al (1995) found that the orbital period was likely to be 90 mins.
 X-ray observations using data (Ramsay οἱ al 1994. Ramsay 1995) showed it had a peak count rate of 75 etfs. We estimate that it was fainter bv a factor of 3 in these observations. although it is still likely to have been in a relatively high accretion state.," X-ray observations using data (Ramsay et al 1994, Ramsay 1995) showed it had a peak count rate of $\sim$ 5 ct/s. We estimate that it was fainter by a factor of 3 in these observations, although it is still likely to have been in a relatively high accretion state."
 V347 Pav is relatively bright in soft and hard. X-ravs. peaking at over 1 οἐν (in the EPIC pn detector) in both soft and. hard. X-ray. bands.," V347 Pav is relatively bright in soft and hard X-rays, peaking at over 1 ct/s (in the EPIC pn detector) in both soft and hard X-ray bands."
 Le shows a distinct faint and bright phase lasting nearly 0.5 eveles each. (Figure 1))., It shows a distinct faint and bright phase lasting nearly 0.5 cycles each (Figure \ref{lightv347}) ).
 The count rate in the faint phase is significant at. 0.037-E0.007 ct/s. The intensity shows à rapid rise at. o—0.0 when the bright accretion region comes into view over the limb ofthe white chvarl, The count rate in the faint phase is significant at $\pm$ 0.007 ct/s. The intensity shows a rapid rise at $\phi$ =0.0 when the bright accretion region comes into view over the limb of the white dwarf.
 As seen from the hardness ratio curve (Figure 1). the hard. X-ray light curve rises more rapidly than the soft. N-ravs.," As seen from the hardness ratio curve (Figure \ref{lightv347}) ), the hard X-ray light curve rises more rapidly than the soft X-rays."
 This is expected since in the standard. models (eg Lamb Masters 1979. Wine Lasota 1979) hare X-ravs are optically thin whereas the soft X-rays are optically thick.," This is expected since in the standard models (eg Lamb Masters 1979, King Lasota 1979) hard X-rays are optically thin whereas the soft X-rays are optically thick."
 The rapid but not instantaneous rise in the hard X-rav [lux indicates that the shock has a significant vertical height above the photosphere of the white dwarf and/or the accretion region is extended., The rapid but not instantaneous rise in the hard X-ray flux indicates that the shock has a significant vertical height above the photosphere of the white dwarf and/or the accretion region is extended.
 Based on our emission. mocel described in 84.1 we predict that for a white dwarl mass ofLOAL... a specific accretion rate of | stem 7? and a magnetic field strength of POALG (Potter. Cropper Hakala 2000). the shock height would be ο. 2.7.," Based on our emission model described in \ref{model} we predict that for a white dwarf mass of, a specific accretion rate of 1 $^{-1}$ $^{-1}$ $^{-2}$ and a magnetic field strength of 20MG (Potter, Cropper Hakala 2000), the shock height would be $\sim$ 0.1 $R_{wd}$."
 This is hieh enough to cause the observed. difference in the rise time in the hard. X-ray. light. curve., This is high enough to cause the observed difference in the rise time in the hard X-ray light curve.
 From the hardness ratio plot. the light curve is ⊓⋅⊀⊀⊀harder near the center of the bright⋅⇁ phase (ὁ ~0.35) indicating that some absorption⊀ alleet maybe present at these phases.," From the hardness ratio plot, the light curve is harder near the center of the bright phase $\phi\sim$ 0.35) indicating that some absorption affect maybe present at these phases."
 The V band data show a rise in Hux at the same phase as the onset of the bright phase., The $V$ band data show a rise in flux at the same phase as the onset of the bright phase.
 Phase zero on the optical ephemeris of Ramsay et al (1996) was definedas the start of the rapid rise [rom the faint hase., Phase zero on the optical ephemeris of Ramsay et al (1996) was defined as the start of the rapid rise from the faint phase.
 Ehe accumulated error in that ephemoeris is 020.02., The accumulated error in that ephemeris is $\phi$ =0.02.
 μαφίας our data on that ephemeris shows the bright phase starting at a much earlier phase (60—0.8)., Phasing our data on that ephemeris shows the bright phase starting at a much earlier phase $\phi$ =0.8).
 We revisited the optical data ancl included. the timing of the start. of the wight phase reported by Bailey et al (1995)., We revisited the optical data and included the timing of the start of the bright phase reported by Bailey et al (1995).
 We find that he period of Ramsay et al (1996) was actually a one day alias of the true orbital period., We find that the period of Ramsay et al (1996) was actually a one day alias of the true orbital period.
 The best fit ephemeris is: We have therefore used the above ephemeris to phase our data., The best fit ephemeris is: We have therefore used the above ephemeris to phase our data.
 We also re-analysed theROSAT data shown by Ramsay et al (1996)., We also re-analysed the data shown by Ramsay et al (1996).
 We find that all those data are consistent with the main accretion region being the prime source of N-ravs., We find that all those data are consistent with the main accretion region being the prime source of X-rays.
 The fact that Ramsay et al (1996) found the phase of the bright X-ray region to vary is phase was therefore due to the use of an incorrect ephemeris., The fact that Ramsay et al (1996) found the phase of the bright X-ray region to vary is phase was therefore due to the use of an incorrect ephemeris.
 Like V347 Pav. GG Leo shows a relatively high count rate in both X-ray. bands (~1 ct/s in the EPIC pn detector).," Like V347 Pav, GG Leo shows a relatively high count rate in both X-ray bands $\sim$ 1 ct/s in the EPIC pn detector)."
Fig.,Fig.
 10 of L07 (Fig., 10 of L07 (Fig.
 10 in this paper)., \ref{Figw} in this paper).
" In the simulations of that paper, the core continuum was sampled with a set of densely and regularly-placed Alfven modes by slicing the field into finite-width flux shells."," In the simulations of that paper, the core continuum was sampled with a set of densely and regularly-placed Alfven modes by slicing the field into finite-width flux shells."
 The spacing dw between the modes was not constant but a function of the Alfven frequency w., The spacing $\delta\omega$ between the modes was not constant but a function of the Alfven frequency $\omega$.
" In that case, the QPO drifts with the QPO frequency w(t) given by the inverse relation With this relation we are able to fit all of L07 drifting QPOs, as shown in Fig."," In that case, the QPO drifts with the QPO frequency $\omega(t)$ given by the inverse relation With this relation we are able to fit all of L07 drifting QPOs, as shown in Fig."
 10 and 11.., \ref{Figw} and \ref{Figz}.
 Note that multiple QPOs correspond to different branches of the Alfven continuum., Note that multiple QPOs correspond to different branches of the Alfven continuum.
" As expected, the drifting QPOs amplified near the crustal frequencies, since there the response of the crust to the core modes’ pull is the strongest."," As expected, the drifting QPOs amplified near the crustal frequencies, since there the response of the crust to the core modes' pull is the strongest."
 In this section we extend the constant magnetic field and constant-density magnetar model from L07 to include more realistic pressure and density profiles and more general (but still axisymmetric) magnetic field configurations., In this section we extend the constant magnetic field and constant-density magnetar model from L07 to include more realistic pressure and density profiles and more general (but still axisymmetric) magnetic field configurations.
" Our aim is to use this model to: 1) calculate numerically Alfven eigenmodes and their eigenfrequencies on different flux surfaces inside the star, in order to determine the continuous spectrum of the fluid core, and 2) use these modes to simulate the dynamics of a realistic magnetar."," Our aim is to use this model to: 1) calculate numerically Alfven eigenmodes and their eigenfrequencies on different flux surfaces inside the star, in order to determine the continuous spectrum of the fluid core, and 2) use these modes to simulate the dynamics of a realistic magnetar."
 In order to calculate the Alfven eigenmodes and eigenfrequencies for a realistic magnetar, In order to calculate the Alfven eigenmodes and eigenfrequencies for a realistic magnetar
with the largest forces are located in a region of strong; positive magnetic flix a degree or so West of the sunspot.,with the largest forces are located in a region of strong positive magnetic flux a degree or so West of the sunspot.
 The field changes themselves. at about 270 G. are significantly weaker than the strongest changes curing the flare. of about 450 G. that are to be found in the region above (he left part of the red line in Figure Hr)5.. but their force estimates are larger because they occur in a much stronger field.," The field changes themselves, at about 270 G, are significantly weaker than the strongest changes during the flare, of about 450 G, that are to be found in the region above the left part of the red line in Figure \ref{mosaic}, but their force estimates are larger because they occur in a much stronger field."
 Shown in Figure 10 is a simultaneous L0-minute-averaged GONG continuum-intensitv image. remapped {ο (he same local Cartesian coordinates with the same forces plotted as in Figure 15..," Shown in Figure \ref{forcesint} is a simultaneous 10-minute-averaged GONG continuum-intensity image, remapped to the same local Cartesian coordinates with the same forces plotted as in Figure \ref{forcesbala}."
 This intensity image shows the sunspot structure., This intensity image shows the sunspot structure.
 Most of the field and force changes appear to fall within the South-Western quadrant of (he sunspot penumbra., Most of the field and force changes appear to fall within the South-Western quadrant of the sunspot penumbra.
 The Inner penunmbra has a mixture of field increases and decreases. including (he strongest field changes observed during this flare (see Figure 5)).," The inner penumbra has a mixture of field increases and decreases, including the strongest field changes observed during this flare (see Figure \ref{mosaic}) )."
 The very large contiguous region of field decreases to (he South-West follows the outer penumbra. including a relatively intense outer penumbral structure due East of the sunspot where the largest force changes occur.," The very large contiguous region of field decreases to the South-West follows the outer penumbra, including a relatively intense outer penumbral structure due East of the sunspot where the largest force changes occur."
 The 2006 December 6 X6.5 [lare exemplifies many of the features characteristic of our data set., The 2006 December 6 X6.5 flare exemplifies many of the features characteristic of our data set.
 The majority of the pixels show longitudinal field decreases while the strongest changes. (hose nearest the sunspot. are a mixture of longitudinal field increases and decreases.," The majority of the pixels show longitudinal field decreases while the strongest changes, those nearest the sunspot, are a mixture of longitudinal field increases and decreases."
 The largest [orces are associated. with longitudinal field decreases. suggesting a downward collapse.," The largest forces are associated with longitudinal field decreases, suggesting a downward collapse."
 These features are (vpical for flares both near disk-center and. as in this case. near ihe limb.," These features are typical for flares both near disk-center and, as in this case, near the limb."
 The temporal distribution of the inferred longitudinal Lorentz force changes peaked between 1540 and 1845 UT. around the time of the last acceleration phase of the associated CME (Balasubramaniam et al.," The temporal distribution of the inferred longitudinal Lorentz force changes peaked between 1840 and 1845 UT, around the time of the fast acceleration phase of the associated CME (Balasubramaniam et al."
 2010)., 2010).
 Fletcher IIudson (2008) give a physical argument relating flare Alfvénn waves with permanent photospheric field changes., Fletcher Hudson (2008) give a physical argument relating flare Alfvénn waves with permanent photospheric field changes.
 To our knowledge. no analogous argument for à CME bow shock has been given. but Fisher et al. (," To our knowledge, no analogous argument for a CME bow shock has been given, but Fisher et al. ("
2010) argue from Newton's third law that a change in the photospheric field to a more horizontal direction implies an inward impulse towards the solar interior accompanied by an equal ancl opposite outward force on the solar atmosphere.,2010) argue from Newton's third law that a change in the photospheric field to a more horizontal direction implies an inward impulse towards the solar interior accompanied by an equal and opposite outward force on the solar atmosphere.
 We have been unable to determine whether or not a seismic wave also occurred during (he flare because of the low quality of Doppler images so [ar from cisk-center., We have been unable to determine whether or not a seismic wave also occurred during the flare because of the low quality of Doppler images so far from disk-center.
 The observations presented in (his paper provide information only on the component ol the magnetic field along the observers line of sight., The observations presented in this paper provide information only on the component of the magnetic field along the observer's line of sight.
 The measured net longitudinal fIux generally changes during a flare at a great rate (zz107 Mx/s) and so it seems most likely that, The measured net longitudinal flux generally changes during a flare at a great rate $\approx 10^{18}$ Mx/s) and so it seems most likely that
seen for an isolated mass.,seen for an isolated mass.
 The details of these are described in several recent reviews and will not be reproduced. here (c.g. Wambsganss 2001)., The details of these are described in several recent reviews and will not be reproduced here (e.g. Wambsganss 2001).
 At such high optical depths. the observed macroinmage is actually composed of an unresolved myriad of microimages.," At such high optical depths, the observed macroimage is actually composed of an unresolved myriad of microimages."
 The relative. brightnesses of these images change as the microlensing stars change their position in front of the source., The relative brightnesses of these images change as the microlensing stars change their position in front of the source.
 ltecentlv. Lewis Ibata (1998). examined. the astrometric shift. in the macroimage as a result of the changing microimage configuration. finding appreciable shifts of miilliareseconds: such shifts will be reacily observable with the next generation of space-based interferometers.," Recently, Lewis Ibata (1998) examined the astrometric shift in the macroimage as a result of the changing microimage configuration, finding appreciable shifts of milliarcseconds; such shifts will be readily observable with the next generation of space-based interferometers."
 The numerical approach of Lewis Ibata (1998) was to image the quasar source as it shines through an ensemble of microlensing masses: from this the brightness weighted macroimage centroid can be simply calculated., The numerical approach of Lewis Ibata (1998) was to image the quasar source as it shines through an ensemble of microlensing masses; from this the brightness weighted macroimage centroid can be simply calculated.
 It is. however. quite straightforward to extend this approach to consider the inlluence of a distribution of observing material amongst the lensing masses: such an approach was adopted here.," It is, however, quite straightforward to extend this approach to consider the influence of a distribution of observing material amongst the lensing masses; such an approach was adopted here."
 In summary. the numerical routine was based on the rav tracing procedure which has been the work horse in the study of gravitational microlensing (c.g. Ixavser. Iefscal Stabell 1986). in which a large. number of ravs are fired through a population of lensing masses.," In summary, the numerical routine was based on the ray tracing procedure which has been the work horse in the study of gravitational microlensing (e.g. Kayser, Refsdal Stabell 1986), in which a large number of rays are fired through a population of lensing masses."
 Considering where each rav intercepts the source plane. a microlensing magnification map can be derived ancl the statistics. of microlensing induced: variability inferred (e.g. Wambsganss 1992).," Considering where each ray intercepts the source plane, a microlensing magnification map can be derived and the statistics of microlensing induced variability inferred (e.g. Wambsganss 1992)."
 For the purposes of this study. absorbing material is added between the microlensing misses. attenuating the ravs as they pass through the lensing galaxy.," For the purposes of this study, absorbing material is added between the microlensing masses, attenuating the rays as they pass through the lensing galaxy."
 “Phe presence of absorbing material will intluence the form of the magnification map. as regions will receive less ravs than they would without it.," The presence of absorbing material will influence the form of the magnification map, as regions will receive less rays than they would without it."
" Hence. a comparison between the ""raw! magnification map. with no absorbing material. and that in the presence of the attenuating screen. gives the relative strength. of the absorption line to the continuum."," Hence, a comparison between the `raw' magnification map, with no absorbing material, and that in the presence of the attenuating screen, gives the relative strength of the absorption line to the continuum."
 It is assumed that the clouds are ellectively massless. not contributing to any additional gravitational microlensing convergence (Wambsganss 1992: Lewis Irwin 1995: Schechter Wambsganss 2002).," It is assumed that the clouds are effectively massless, not contributing to any additional gravitational microlensing convergence (Wambsganss 1992; Lewis Irwin 1995; Schechter Wambsganss 2002)."
 The complex patterns seen in gravitational microlensing magnification maps depend strongly on the surface density of microlensing objects (the optical depth e) and the large scale shear over the star field (he shears)., The complex patterns seen in gravitational microlensing magnification maps depend strongly on the surface density of microlensing objects (the optical depth $\sigma$ ) and the large scale shear over the star field (the shear $\gamma$ ).
 Furthermore. for a particular macrolens and source. where the physical scales are fixed. varving the mass function of the microlensing masses also changes the patterns of the magniication maps (Ixavser. Refsdal Stabell 1986: Wambseanss 1992).," Furthermore, for a particular macrolens and source, where the physical scales are fixed, varying the mass function of the microlensing masses also changes the patterns of the magnfication maps (Kayser, Refsdal Stabell 1986; Wambsganss 1992)."
 llence. the potential parameter space available for study is considerable.," Hence, the potential parameter space available for study is considerable."
 For this study. a fiducial microlensing parameters of @=0.5 and 5=0.0 were emploved. considering a source region which is 20 Einstein radii in extent.," For this study, a fiducial microlensing parameters of $\sigma=0.5$ and $\gamma=0.0$ were employed, considering a source region which is 20 Einstein radii in extent."
 Phe corresponding star field is scattered over a region of radius ~70 Einstein radii in the lens plane., The corresponding star field is scattered over a region of radius $\sim70$ Einstein radii in the lens plane.
 Absorption clouds can be distributed in a multitude of wavs. with varving shapes and sizes and absorption owofiles ete.," Absorption clouds can be distributed in a multitude of ways, with varying shapes and sizes and absorption profiles etc."
 and hence the potential parameter space to »' explored is immense., and hence the potential parameter space to be explored is immense.
 Such an exploration is bevond his current. contribution. and. so. for the purposes of this study. the absorption clouds are. simply represented: as xing circular with uniform absorption.," Such an exploration is beyond this current contribution, and so, for the purposes of this study, the absorption clouds are simply represented as being circular with uniform absorption."
 Two fiducial cloud sizes were considered. the larger. possessing a radius of δ Einstein radii (El). the smaller clouds being ~1 Einstein," Two fiducial cloud sizes were considered, the larger possessing a radius of 8 Einstein radii (ER), the smaller clouds being $\sim1$ Einstein"
A number of studies have analysed absorption line-strength indices of cluster galaxies. and claimed the detection. of variation of galaxy properties as a function of eluster-centric radius.,"A number of studies have analysed absorption line-strength indices of cluster galaxies, and claimed the detection of variation of galaxy properties as a function of cluster-centric radius."
 Guzmánetal.(1992). reported. a positive olfset of the zero-point of the relationship between Meg». index and galaxy velocity dispersion for massive elliptical galaxies between the core and the outskirts of the Coma cluster., \citet{guzman92} reported a positive offset of the zero-point of the relationship between $_2$ index and galaxy velocity dispersion for massive elliptical galaxies between the core and the outskirts of the Coma cluster.
 At a fixed. velocity dispersion. the Ales line strength is weaker at larger cluster-centric radius.," At a fixed velocity dispersion, the $_2$ line strength is weaker at larger cluster-centric radius."
 Carteretal.(2002). have used. a sample of Coma cluster galaxies extending oul to the virial radius. without morphological or colour selection and cüstributed over a luminosity range similar to galaxies in our sample. to report a significant racial decrease in the Mg» index. and an increase of the index.," \citet{carter02} have used a sample of Coma cluster galaxies extending out to the virial radius, without morphological or colour selection and distributed over a luminosity range similar to galaxies in our sample, to report a significant radial decrease in the $_2$ index, and an increase of the $\beta$ index."
 Carter et al., Carter et al.
 have attributed. the observed. radial trends to change in meta abundance at fixed. stellar mass between the core ancl the outskirts of the cluster. Smithetal.(2008).," have attributed the observed radial trends to change in metal abundance at fixed stellar mass between the core and the outskirts of the cluster. \citet{smith08},"
.. ina study of 75 reda-sequence dart ealaxies in the Coma cluster. find that the variations in line strength indices are driven by variations in age and in iron abundance. with a-clement abundances being independen of radius.," in a study of 75 red-sequence dwarf galaxies in the Coma cluster, find that the variations in line strength indices are driven by variations in age and in iron abundance, with $\alpha$ -element abundances being independent of radius."
 Dwarf galaxies in the outer regions of the Coma cluster are on average vounger and more iron-enriched than those in the core. at a given Luminosity.," Dwarf galaxies in the outer regions of the Coma cluster are on average younger and more iron-enriched than those in the core, at a given luminosity."
 Phese results mus be treated with caution however. as both of the Coma stuclies discussed above observed the same. possibly atypical. outer region of the cluster to the southern-west of the core.," These results must be treated with caution however, as both of the Coma studies discussed above observed the same, possibly atypical, outer region of the cluster to the southern-west of the core."
" Using a sample of ~3000 red sequence galaxics clominatec by £L, galaxies in ~90 nearby clusters. Smithetal.(2006). founcl strong evidence for stronger Balmer lines and weaker lieht-clement features. at fixed. mass. but no radial dependence for iron-dominated. indices over a range from the cluster centre to the virial radius."," Using a sample of $\sim3000$ red sequence galaxies dominated by $L_{*}$ galaxies in $\sim90$ nearby clusters, \citet{smith06} found strong evidence for stronger Balmer lines and weaker light-element features, at fixed mass, but no radial dependence for iron-dominated indices over a range from the cluster centre to the virial radius."
 The radial gradients detected for the synthetic cluster. formed bv stacking galaxies in all clusters in their sample. are significantly shallower than those found for the Coma cluster. with cillerent relative patterns for dilferent spectral indices.," The radial gradients detected for the synthetic cluster formed by stacking galaxies in all clusters in their sample, are significantly shallower than those found for the Coma cluster, with different relative patterns for different spectral indices."
 Smithetal.(2006) have argued that the observed cluster-centric radial gradients are. better. explained by a change in the mean age of the dominant stellar populations rather than in metallicitv between galaxies in the cores and the outskirts of clusters., \citet{smith06} have argued that the observed cluster-centric radial gradients are better explained by a change in the mean age of the dominant stellar populations rather than in metallicity between galaxies in the cores and the outskirts of clusters.
 Recl sequence galaxies at the virial radius have on average vounger ages than galaxies of the same velocity dispersion. situated near the cluster centres., Red sequence galaxies at the virial radius have on average younger ages than galaxies of the same velocity dispersion situated near the cluster centres.
 More recently. Rokasetal.(2007). estimated. the cluster-centric radial metallicity gradients for a sample of passive. red. galaxies in Abell 1185 cluster.," More recently, \citet{rakos07} estimated the cluster-centric radial metallicity gradients for a sample of passive, red galaxies in Abell 1185 cluster."
 They have found a signilicant cluster-centric metallicity eradient. with mean metallicities decreasing hy ~0.2 dex within 40 per cent of the Abell radius of the cluster.," They have found a significant cluster-centric metallicity gradient, with mean metallicities decreasing by $\sim0.2$ dex within 40 per cent of the Abell radius of the cluster."
 Our analysis shows that the average luminosity-weighted properties of Abell 1367 red sequence galaxies clo not show a significant change. at fixed stellar mass. with the location within the cluster over a radial distance ranging from the cluster centre to a radius of approximately half the cluster Abell radius.," Our analysis shows that the average luminosity-weighted properties of Abell 1367 red sequence galaxies do not show a significant change, at fixed stellar mass, with the location within the cluster over a radial distance ranging from the cluster centre to a radius of approximately half the cluster Abell radius."
 Phe complex structure and dynamics of Abell 1367 could lead however to concerns about the extent to which the region covered by our survey is representative of the entire galaxy population of the cluster., The complex structure and dynamics of Abell 1367 could lead however to concerns about the extent to which the region covered by our survey is representative of the entire galaxy population of the cluster.
 In contrast with Smithetal.(2006).. the red sequence ellipticals in the core of Abell 1367 appear to be of similar average Iuminosity-weighted ages than those in the outer regions of the cluster.," In contrast with \citet{smith06}, the red sequence ellipticals in the core of Abell 1367 appear to be of similar average luminosity-weighted ages than those in the outer regions of the cluster."
 To account for the observed gradients in star formation rate measured. for the CNOC cluster sample. Baloghetal.(2000) have proposed a model in which star-forming ealaxies fall into rich clusters ancl their star formation is eraclually quenchecl by rani pressure and. tidal. stripping. removing their eas over a lew Cyr.," To account for the observed gradients in star formation rate measured for the CNOC cluster sample, \citet{balogh00} have proposed a model in which star-forming galaxies fall into rich clusters and their star formation is gradually quenched by ram pressure and tidal stripping, removing their gas over a few Gyr."
 This mechanism would be expected to lead to a radial age gradient., This mechanism would be expected to lead to a radial age gradient.
 In the semi-analytical models of DeLuciaetal.(2006).. the mean luminositv-weighted age ol bulee-dominated &alaxies [alls from 12 GGvr at the cluster centres to ~10.5 GGwvr at the virial (ασας.," In the semi-analytical models of \citet{delucia06}, the mean luminosity-weighted age of bulge-dominated galaxies falls from $\sim12$ Gyr at the cluster centres to $\sim10.5$ Gyr at the virial radius."
 Some of this ellect is due to mass segregation however. as more massive galaxies are preferentially located at the core of the cluster.," Some of this effect is due to mass segregation however, as more massive galaxies are preferentially located at the core of the cluster."
 The restricted. range of cluster-centric radial cdistance covered by our survey. Le. oul to approximately 40 per cent of the virial radius of the eluster. combined with the low sensitivity of broad-band colours to age variation for old stellar populations. projection effects. and the size of the sample means we cannot rule out. the presence of a radial age gradient.," The restricted range of cluster-centric radial distance covered by our survey, i.e., out to approximately 40 per cent of the virial radius of the cluster, combined with the low sensitivity of broad-band colours to age variation for old stellar populations, projection effects, and the size of the sample means we cannot rule out the presence of a radial age gradient."
 A comprehensive answer to these concerns should result. (rom an extension of our survey out to the cluster infall region to test if galaxies in other parts of Abell 1367 display similar racial trends., A comprehensive answer to these concerns should result from an extension of our survey out to the cluster infall region to test if galaxies in other parts of Abell 1367 display similar radial trends.
 Using deep optical/near-L broad-band and narrow-band imagine data. we investigate the stellar population properties for a sample of Abell 1367. galaxies with spectroscopically determined memberships and visual morphological classifications.," Using deep optical/near-IR broad-band and narrow-band imaging data, we investigate the stellar population properties for a sample of Abell 1367 galaxies with spectroscopically determined memberships and visual morphological classifications."
 Our survey samples. galaxics with integrated stellar masses ranging from a few 107 MM. , Our survey samples galaxies with integrated stellar masses ranging from a few $10^{8}$ $_{\odot}$ 
that Euclid will be able to extract the growth characteristic thus allowing. potentially. a strong cosmological test of our eravitational framework.,"that Euclid will be able to extract the growth characteristic thus allowing, potentially, a strong cosmological test of our gravitational framework."
 Indeed. it will be able to constrain the fiducial =0.55 (LCDAM) to within an error of 0.0446 at lo with A445=500 which is further tightened to 0.038 with lax=10000.," Indeed, it will be able to constrain the fiducial $\gamma =0.55$ (LCDM) to within an error of 0.0446 at $1\sigma$ with $l_{\mathrm{max}} = 500$ which is further tightened to 0.038 with $l_{\mathrm{max}} = 10000$."
 The other 7 cosmological parameters (/. σε. Ow. nyc toss ns and Xo) have been varied and marginalised over.," The other 7 cosmological parameters $h$ , $\sigma_{8}$, $\Omega_{\mathrm{b}}$, $w_{0}$, $w_{a}$, $n_{s}$ and $\Sigma_{0}$ ) have been varied and marginalised over."
 Again this forecast is in contrast to Figure δ where even the combined probes of lensing. BAOs and Supernovae were incapable of constraining the growth.," Again this forecast is in contrast to Figure \ref{fig:combinedprobes} where even the combined probes of lensing, BAOs and Supernovae were incapable of constraining the growth."
 Finally. we include in Figure 10. à marginalised contour for * against Xo which further highlights how mocified &ravitv or verv generic dark energv signatures can be constrained. consistently. with weak lensing.," Finally, we include in Figure \ref{fig:modified} a marginalised contour for $\gamma$ against $\Sigma_{0}$ which further highlights how modified gravity or very generic dark energy signatures can be constrained, consistently, with weak lensing."
 We find. that with fas=500 (red contours) this survey could. constrain alterations in the powerspectrum with an error in Xo of 0.25 at lo., We find that with $l_{\mathrm{max}} = 500$ (red contours) this survey could constrain alterations in the powerspectrum with an error in $\Sigma_{0}$ of 0.25 at $1\sigma$.
" This parameter is more sensitive to the range of scales used than 5. however. with fis=10000 (black contours) confining Xo to within 0.069 of the fiducial value X,= 0."," This parameter is more sensitive to the range of scales used than $\gamma$, however, with $l_{\mathrm{max}} = 10000$ (black contours) confining $\Sigma_{0}$ to within 0.069 of the fiducial value $\Sigma_{0} = 0$ ."
 We should emphasise that the spectroscopic element of Euclid (2) will also be able to constrain growth via redshift space distortions (? ancl ?))., We should emphasise that the spectroscopic element of Euclid \citep{Cimatti08} will also be able to constrain growth via redshift space distortions \citet{Peacock02} and \citet{Guzzo08}) ).
 To summarise. we have noted that the surprising. but well confirmed. late-time acceleration of the universe be the result of a modification to gravity.," To summarise, we have noted that the surprising, but well confirmed, late-time acceleration of the universe be the result of a modification to gravity."
 We then. in Section 2.. reviewed. the concept of modified: gravity. detailing in the process a model that is motivated and acts το paranmeterise a large extra dimension. (mDGDP).," We then, in Section \ref{sec:modifiedgravity}, reviewed the concept of modified gravity detailing in the process a model that is motivated and acts to parameterise a large extra dimension (mDGP)."
 Interpolating. between LCDAI (a= 0) and DOP (a= 1) it can be tested. as a model in its own right and/or used as an example to demonstrate the rich set. of observational signatures. that are likely to arise for a modified gravity model in cosmology., Interpolating between LCDM $\alpha=0$ ) and DGP $\alpha=1$ ) it can be tested as a model in its own right and/or used as an example to demonstrate the rich set of observational signatures that are likely to arise for a modified gravity model in cosmology.
 These signatures include the expansion history. and rather interestinglv. the growth: of structure ancl a mocification to the relationship between the potential power spectrum and the matter power spectrum.," These signatures include the expansion history, and rather interestingly, the growth of structure and a modification to the relationship between the potential power spectrum and the matter power spectrum."
 With these characteristics in mind we then discussed attempts in the literature to parameterise modified gravity in this way., With these characteristics in mind we then discussed attempts in the literature to parameterise modified gravity in this way.
 This included a erowth parameter 5 and a power speetrum parameter MX., This included a growth parameter $\gamma$ and a power spectrum parameter $\Sigma$.
 In Section 4. we introduced: weak lensing ancl related its attributes to mocified gravity given that it is sensitive to the expansion history. the growth of structure ancl the power spectrum.," In Section \ref{sec:weaklensingasacosmologicalprobe} we introduced weak lensing and related its attributes to modified gravity given that it is sensitive to the expansion history, the growth of structure and the power spectrum."
 We noted. a severe caveat in the use of non-linear scales and therefore. in Section 4.1.. described the approapriate choice of survey (CELEELS-wide) and data (0>30 arcminutes) used in the cosmological analyses.," We noted a severe caveat in the use of non-linear scales and therefore, in Section \ref{sec:CFHTLS}, described the approapriate choice of survey (CFHTLS-wide) and data $\theta > 30$ arcminutes) used in the cosmological analyses."
 The subsequent lensing only constraints were given in Section 5.1. where we showed that one could not vet constrain meaningful values of a or 5 with the current data., The subsequent lensing only constraints were given in Section \ref{sec:lensing} where we showed that one could not yet constrain meaningful values of $\alpha$ or $\gamma$ with the current data.
 We then. bv adding it to Barvon Acoustic Oscillation and Supernovae data. demonstrated that weak lensing was hishlv beneficial in aiding the constraint of mDCGD? in combination.," We then, by adding it to Baryon Acoustic Oscillation and Supernovae data, demonstrated that weak lensing was highly beneficial in aiding the constraint of mDGP in combination."
 For without the inclusion of the lensing data the expansion-only probes were incapable of constraining a=]., For without the inclusion of the lensing data the expansion-only probes were incapable of constraining $\alpha=1$.
 We found however that the combined. probes dislavoured the DGP miocdel with over a 95% confidence level where specifically a<0.58 at lo and a<0.91 at 2a., We found however that the combined probes disfavoured the DGP model with over a $95\%$ confidence level where specifically $\alpha < 0.58$ at $1\sigma$ and $\alpha < 0.91$ at $2\sigma$ .
 We then showed that a constraint on the subtle. vet. potentially important. growth signature is bevond the current weak lensing. BAO and. Supernovac data.," We then showed that a constraint on the subtle, yet potentially important, growth signature is beyond the current weak lensing, BAO and Supernovae data."
 We allowed: almost total cosmological freedom in all these analyses. varving parameters: δω fo as. Qn. e. b and e for both models. in addition to à for mDGP and. wy and 5 for the growth model.," We allowed almost total cosmological freedom in all these analyses, varying parameters: $\Omega_{m}$, $h$, $\sigma_{8}$, $\Omega_{\mathrm{b}}$, $a$, $b$ and $c$ for both models, in addition to $\alpha$ for mDGP and $w_{0}$ and $\gamma$ for the growth model."
 Furthermore. we used the £g two point statistic while analytically marginalising over the residual offset c.," Furthermore, we used the $\xi_{E}$ two point statistic while analytically marginalising over the residual offset $c'$."
 We also demonstrated in Section 5.3. that our results are insensitive to a potential over or underestimation of the shear at high redshift., We also demonstrated in Section \ref{sec:systematics} that our results are insensitive to a potential over or underestimation of the shear at high redshift.
 Finally in Section 6 we looked towards the future space based weak lensing survey. [uclid. ancl discovered that it will have significant ability to distinguish between mocified gravity and LOCDAM.," Finally in Section \ref{sec:Euclid} we looked towards the future space based weak lensing survey, Euclid, and discovered that it will have significant ability to distinguish between modified gravity and LCDM."
 We included a forecast for the mDCGJP model finding that even for a lensing only analysis LEuclicl could restrict à to within 0.104 of the fiducial a=0 ab lo. even when the deeply non-lincar regime has been removed. (is=500).," We included a forecast for the mDGP model finding that even for a lensing only analysis Euclid could restrict $\alpha$ to within $0.104$ of the fiducial $\alpha = 0$ at $1\sigma$, even when the deeply non-linear regime has been removed $l_{\mathrm{max}} = 500$ )."
" In adcdition. we included a complete and consistent forecast. for. g&eneralised. modified. gravity demonstrating that deviations from a fiducial X,=0 of 0.25 at the 68% confidence level will be possible with fais.=500."," In addition, we included a complete and consistent forecast for generalised modified gravity demonstrating that deviations from a fiducial $\Sigma_{0} = 0$ of $0.25$ at the $68\%$ confidence level will be possible with $l_{\mathrm{max}} = 500$."
" With /Z,44;=10000 this gets restricted to ANY=0.069.", With $l_{\mathrm{max}} = 10000$ this gets restricted to $\Delta \Sigma_{0} = 0.069$.
 Lt will also confine 5 to within 0.045 (fas=500) ancl 0.038 (as= 10000) o£ the Gducial =0.55 at lo. where a full 9 cosmological parameters were varied.," It will also confine $\gamma$ to within $0.045$ $l_{\mathrm{max}} = 500$ ) and $0.038$ $l_{\mathrm{max}} = 10000$ ) of the fiducial $\gamma = 0.55$ at $1\sigma$, where a full 9 cosmological parameters were varied."
 In our analyses with data we have. except as an example case. actively removed. angular scales. less. than 30 arcminutes.," In our analyses with data we have, except as an example case, actively removed angular scales less than 30 arcminutes."
 This was to remove the contribution from the unknown non-linear regime from the constraints., This was to remove the contribution from the unknown non-linear regime from the constraints.
 ας constitutes removing vast quantities of attainable data., This constitutes removing vast quantities of attainable data.
 Not only is this clearly not maximising the available information but it could be that non-linear physics acts to emphasise anv dillerence in gravitational theory., Not only is this clearly not maximising the available information but it could be that non-linear physics acts to emphasise any difference in gravitational theory.
 Pherefore it would naturally be highly beneficial to understand. the evolution of these density perturbations within this regime., Therefore it would naturally be highly beneficial to understand the evolution of these density perturbations within this regime.
 In order to do this there needs to be continuing attempts in the community to study N-body simulations with varving eravitational frameworks., In order to do this there needs to be continuing attempts in the community to study N-body simulations with varying gravitational frameworks.
 Even though we have detailed the advantages of weak lensing in a moclilied eravity study. and even though Euclid in particular will be deeply insightful it seems. however. a collected: ancl coordinated assault on our gravitational framework would prove even more advantageous.," Even though we have detailed the advantages of weak lensing in a modified gravity study, and even though Euclid in particular will be deeply insightful it seems, however, a collected and coordinated assault on our gravitational framework would prove even more advantageous."
 This might exist in the form of a combination of probes as. for example. discussed in ?.. where ideally the four perturbation variables 6. 0. 9 and @ are independently targeted.," This might exist in the form of a combination of probes as, for example, discussed in \citet{Jain07}, where ideally the four perturbation variables $\phi$, $\psi$, $\delta$ and $\theta$ are independently targeted."
 This in principle would. allow us unpreciclentecl experimental scrutiny on the structure of our gravitational theory over large scales., This in principle would allow us unprecidented experimental scrutiny on the structure of our gravitational theory over large scales.
 However. to conclude. it is clear that to actually. solve the tantalising problem that. erips cosmology there needs to be a paradigm shift analogous to those that have revealed the great problems of the past.," However, to conclude, it is clear that to actually solve the tantalising problem that grips cosmology there needs to be a paradigm shift analogous to those that have revealed the great problems of the past."
 Acknowledgements: Ho is a pleasure. to thank the CEILS team for their. kind. distribution of the lensingdata., Acknowledgements: It is a pleasure to thank the CFHTLS team for their kind distribution of the lensingdata.
 Particular thanks &o to Martin. Wilbinger ancl also Liping Fu for answering and discussing some of the more technical aspects of the data and potential svstematies., Particular thanks go to Martin Kilbinger and also Liping Fu for answering and discussing some of the more technical aspects of the data and potential systematics.
 We wouldalso like to thank the Iuclid internal referee for careful reacing of this script., We wouldalso like to thank the Euclid internal referee for careful reading of this script.
 ST would like to thank Adam Amara for thorough and detailed weak lensing ancl fisher matrix code comparisons., ST would like to thank Adam Amara for thorough and detailed weak lensing and fisher matrix code comparisons.
 In addition. ST would like to thankSarah," In addition, ST would like to thankSarah"
objects are galaxies blended with stars where obviously the aperture photometry is unreliable.,objects are galaxies blended with stars where obviously the aperture photometry is unreliable.
 Note that ouly the ο/ ον diagram reveals these bleuds casily., Note that only the $g'-r'$ vs $r'-i'$ diagram reveals these blends easily.
 Using the published respouse of the CFITT. Aleeaprime and AIEGACAAL we lave computed svuthetic colours of the stars as a functiou of temperature. eravity aud metallicity.," Using the published response of the CFHT, Megaprime and MEGACAM we have computed synthetic colours of the stars as a function of temperature, gravity and metallicity."
 To do this we have used two sets of stellar atmosphere models: Basel 3.1 and NextGen., To do this we have used two sets of stellar atmosphere models: Basel 3.1 and NextGen.
 The Bascl3.1 library is a seni-enirieal library based on preceding eeneration o: nmiodels. Basel 2.2 (Lejeune et al. 1997)).," The Basel3.1 library is a semi-empirical library based on preceding generation of models, Basel 2.2 (Lejeune et al. \cite{Lejeune97}) ),"
 extended to non-xolar iactallicities by Westera ct al. (2002))., extended to non-solar metallicities by Westera et al. \cite{Westera}) ).
 The I&urucz theoretical spectra (1979)) have been modified to fi broad baud photometry using the aleoritlan by Cuisiuier et al. (, The Kurucz theoretical spectra \cite{Kurucz79}) ) have been modified to fit broad band photometry using the algorithm by Cuisinier et al. (
see I&urucz 1992)).,see Kurucz \cite{Buser92}) ).
 The corrected spectra are used for integrating the flux in the desired bauds., The corrected spectra are used for integrating the flux in the desired bands.
 NextGe is the 1997 version of atinosphere models from Allard ct al. (1997))., NextGen is the 1997 version of atmosphere models from Allard et al. \cite{Allard97}) ).
 These models use a direct opacity sampling including over 500 million lines of atomic aud molecular species., These models use a direct opacity sampling including over 500 million lines of atomic and molecular species.
 They give a more realistic description of the M dwarf population., They give a more realistic description of the M dwarf population.
 Figure 3 shows the CPUTLS colour-colour diagrams of the D1 field superimposed with the svuthetic colours of dwarf stars uxing the Basel3.1 stellay library. for solar iietallicitv. [Fo/TI]|2.—1.0 and |Fe/TI]|2.—2.0 (right panel) and the NextGen library for |[Fe/II|20.0 aud |Fe/TI|2.—1.0 (left panel).," Figure \ref{Figure1} shows the CFHTLS colour-colour diagrams of the D1 field superimposed with the synthetic colours of dwarf stars using the Basel3.1 stellar library for solar metallicity, $=-1.0$ and $=-2.0$ (right panel) and the NextGen library for [Fe/H]=0.0 and $=-1.0$ (left panel)."
" For a better definition of the stellar OCIS, WC use here only stellar objects which have a plotometric error estimate smaller than πας in cach filter."," For a better definition of the stellar locus, we use here only stellar objects which have a photometric error estimate smaller than mag in each filter."
 We noted that the /colour las a slielit offset of πας compared to the mocel which comes from nucertaintics on the photometric calibration., We noted that the $i'-z'$ colour has a slight offset of mag compared to the model which comes from uncertainties on the photometric calibration.
 For the D2 and D3 field we noted a shift of nuuae aud 1uinag og Z7 respectively., For the D2 and D3 field we noted a shift of mag and mag in $r'-i'$ respectively.
 These offsets have beeu applied., These offsets have been applied.
 Figure 3 illustrates the scusitivity of the colours in the CFIITLS svstem to metallicity aud he differences iu the stellar libraries., Figure 3 illustrates the sensitivity of the colours in the CFHTLS system to metallicity and the differences in the stellar libraries.
 For temperatures below INI. which correspond to IK/M stars. he Dasel3.1 library does not eive realistic colours for coo dwarts. but gives a etter fit to the data than NexCen models do for hotter stars.," For temperatures below K, which correspond to K/M stars, the Basel3.1 library does not give realistic colours for cool dwarfs, but gives a better fit to the data than NexGen models do for hotter stars."
 Tn the temperature range 7000 to IKIx. the most sensitive colour is gor. whereas for cooler stars this colour index saturates and ri )conmies better.," In the temperature range 7000 to K, the most sensitive colour is $g'-r'$, whereas for cooler stars this colour index saturates and $r'-i'$ becomes better."
" The POi colour secius to be redundant with 7, but eoine to very cool stars we expect it to be a very good iudicator for selecting brown dwarts (sec sect.7.2)."," The $i'-z'$ colour seems to be redundant with $r'-i'$, but going to very cool stars we expect it to be a very good indicator for selecting brown dwarfs (see sect.7.2)."
" Both atmosphere models show a strong imetallicity effect for cool dwarfs ing’r audi’ 2"".", Both atmosphere models show a strong metallicity effect for cool dwarfs in $g'-r'$ and $i'-z'$.
 It appears that at yoo’/cld this index is no longer seusitive to teniperature but to metallicity., It appears that at $g'-r'> 1$ this index is no longer sensitive to temperature but to metallicity.
 If the photometric calibration of the survey ds accurate and the model atmospheres reliable. we will be able to constrai- the metallicity. distribution of these cool stars. at least y.statistically.," If the photometric calibration of the survey is accurate and the model atmospheres reliable, we will be able to constrain the metallicity distribution of these cool stars, at least statistically."
 This will periit us to determine the metallicity range. aud probably the thin disc to thick dise density ratio. as we expect a cifferenee of metallicity of about 0.5 dex hetween these two populations. corresponding to about 0.15 magnitude ing? rat a temperature of 1000 Ix. The Besangoon Calaxy inodel is a simulation tool aimed at testing ealaxy evolution sccnari by comparing stellar distributions predicted bv these scenari with observations. such as photometric star counts and kinematics.," This will permit us to determine the metallicity range, and probably the thin disc to thick disc density ratio, as we expect a difference of metallicity of about 0.5 dex between these two populations, corresponding to about 0.15 magnitude in $g'-r'$ at a temperature of 4000 K. The Besançoon Galaxy model is a simulation tool aimed at testing galaxy evolution scenarii by comparing stellar distributions predicted by these scenarii with observations, such as photometric star counts and kinematics."
 A complete description of the model ineredicuts cau be found iu Robin et al. (2003))., A complete description of the model ingredients can be found in Robin et al. \cite{Robin2003}) ).
 We sunuuarise here the model's principal features., We summarise here the model's principal features.
 The model assumes that stars are created from gas following a star formation history and au initial mass function: stellar evolution follows evolutionary tracks., The model assumes that stars are created from gas following a star formation history and an initial mass function; stellar evolution follows evolutionary tracks.
 To reproduce the overall galaxy. formation aud evolution we, To reproduce the overall galaxy formation and evolution we
of NGC 253. it is difficult to explain the data point at IO GeV. even if we take into account the secondary +- populations.,"of NGC 253, it is difficult to explain the data point at 10 GeV, even if we take into account the secondary $\gamma$ -ray populations."
 Since the absorption is effective above 10 TeV and the seed photon density has à peak around 0.01 eV. the typical energy of the secondary 5-ray. E.. is E.—/27.cy.«0.01eV.~ ITeV.," Since the absorption is effective above 10 TeV and the seed photon density has a peak around 0.01 eV, the typical energy of the secondary $\gamma$ -ray, $E_c$, is $E_c\sim(10 {\rm TeV}/2m_ec^2)^2\times0.01 {\rm eV}\sim1 {\rm TeV}$ ."
 Thus. cascade emissior do notV contribute at ~10 GeV. rather. closer to around ~| TeV. By including cascade emissions. the total 5-ray flux above | TeV becomes and greater than the absorbec flux for M82 and NGC 253. respectively.," Thus, cascade emission do not contribute at $\sim$ 10 GeV, rather, closer to around $\sim 1$ TeV. By including cascade emissions, the total $\gamma$ -ray flux above 1 TeV becomes and greater than the absorbed flux for M82 and NGC 253, respectively."
 Fig., Fig.
" 4 also shows the expected >-ray spectra of these two starburst galaxies but changing the intrinsic. spectral index of proton. P. the highest proton kinetic energy. 7,may. and interstellar radiation field SED models for comparison."," \ref{fig:f_index_max} also shows the expected $\gamma$ -ray spectra of these two starburst galaxies but changing the intrinsic spectral index of proton, $\Gamma$, the highest proton kinetic energy, $T_{p, \rm max}$, and interstellar radiation field SED models for comparison."
 In the case of M82. the total x-ray flux above | TeV becomes 48 and 22 greater than the absorbed flux with (D.Ταν)=(2.3.512TeV) and (2.4.45.3TeV) model. respectively.," In the case of M82, the total $\gamma$ -ray flux above 1 TeV becomes 48 and 22 greater than the absorbed flux with $\Gamma, T_{p, \rm max}) = (2.3, 512\ {\rm TeV})$ and $(2.4, 45.3 \ {\rm TeV})$ model, respectively."
 When we use the dCdP09 interstellar radiation field SED model with the standard parameters. the total flux above 1 TeV is 47 greater than the absorbed flux.," When we use the dCdP09 interstellar radiation field SED model with the standard parameters, the total flux above 1 TeV is 47 greater than the absorbed flux."
" In the case of NGC 253. the total -ray flux above | TeV becomes 52 and 14 greater than the absorbed flux with (D.75,44)=(2.2.512TeV) and (2.3.45.3TeV) model. respectively."," In the case of NGC 253, the total $\gamma$ -ray flux above 1 TeV becomes 52 and 14 greater than the absorbed flux with $\Gamma, T_{p, \rm max}) = (2.2, 512\ {\rm TeV})$ and $(2.3, 45.3 \ {\rm TeV})$ model, respectively."
 When we use the DSTOS SED model with the standard parameters. the total flux above | TeV is 37 greater than the absorbed flux.," When we use the DST05 SED model with the standard parameters, the total flux above 1 TeV is 37 greater than the absorbed flux."
 Therefore. even if we use other interstellar radiation field model which do not fit to the near infrared observed data. the effect of the cascade emission would not be changed significantly.," Therefore, even if we use other interstellar radiation field model which do not fit to the near infrared observed data, the effect of the cascade emission would not be changed significantly."
 This ts because the near infrared photon density is not high enough to absorb VHE ~-rays effectively., This is because the near infrared photon density is not high enough to absorb VHE $\gamma$ -rays effectively.
 It would be difficult to explain the data by the standard parameters. but (D.7)ynay)=(2.2.4.0TeV) model would be able to explain the data.," It would be difficult to explain the data by the standard parameters, but $\Gamma, T_{p, \rm max}) = (2.2, 4.0\ {\rm TeV})$ model would be able to explain the data."
 We should note. however. note that. in this case. cascade emissions for this model would not contribute to the VHE spectrum since 7TeV emission is weak.," We should note, however, note that, in this case, cascade emissions for this model would not contribute to the VHE spectrum since $>$ TeV emission is weak."
 However. Ίρμαν=4.0 TeV model for M82 is inconsistent. with the data.," However, $T_{p, \rm max}=4.0$ TeV model for M82 is inconsistent with the data."
 We will need to wait for much longer time integration data fromFermi and future TeV 5-ray observatories to discuss this point in greater detail., We will need to wait for much longer time integration data from and future TeV $\gamma$ -ray observatories to discuss this point in greater detail.
 To see the feature of the cascade emission. it will be important to detect these two nearby starburst galaxies with a high signal-to-noise ratio with future VHE observations.," To see the feature of the cascade emission, it will be important to detect these two nearby starburst galaxies with a high signal-to-noise ratio with future VHE observations."
 The Cherenkov Telescope Array (CTA) is planned for the next generation imaging atmospheric Cherenkov telescope (TACT), The Cherenkov Telescope Array (CTA) is planned for the next generation imaging atmospheric Cherenkov telescope (IACT).
 The sensitivity and energy range of CTA will be improved by one order of magnitude compared to current IACTs such as H.E.S.S. MAGIC. and VERITAS.," The sensitivity and energy range of CTA will be improved by one order of magnitude compared to current IACTs such as H.E.S.S, MAGIC, and VERITAS."
 Here we investigate the required observational time to see the absorption and cascade signature with high significance by future CTA observations following the argument in $3 and $4 in Inoueetal.(2010)., Here we investigate the required observational time to see the absorption and cascade signature with high significance by future CTA observations following the argument in 3 and 4 in \citet{ino10}.
 First. the required observational time to detect the integral ~-ray flux above | TeV with 5 ¢ is 1.3 hrs for M82 and 1.0 hr for NGC 253. respectively.," First, the required observational time to detect the integral $\gamma$ -ray flux above 1 TeV with 5 $\sigma$ is 1.3 hrs for M82 and 1.0 hr for NGC 253, respectively."
 Next. to see the cascade features," Next, to see the cascade features"
ΝΗ 15D is a bilary system composed of ~0.5 ML. pre-inaln sequence stars ina highly eccentric fe22 0.6) orbit with a period of 18.37 days (Jolinsouetal.2001:Hamilton2001. 2006).,"KH 15D is a binary system composed of $\sim$ 0.5 $_\odot$ pre-main sequence stars in a highly eccentric $e \approx 0.6$ ) orbit with a period of 48.37 days \citep{j04,Ham05,w04,w06}."
. The o'bital plaue is iuclined to an opaque circumbinary disk or rine that precesses ou €a time scale of ~1(JOO vears (Chiane&Murray-Clay2001) aud has been progressively occulting the orbits of the sars since about 1960. (Johuson&Winn2001)., The orbital plane is inclined to an opaque circumbinary disk or ring that precesses on a time scale of $\sim$ 1000 years \citep{CM04} and has been progressively occulting the orbits of the stars since about 1960 \citep{J04}.
. This has produced clramatic otometric variability hat lias evolved steadily aid been vieilautly monitored siuce its re-discovery the mid-1990s (searis&Herbst1998:etal.2002:Hamilton2005).," This has produced dramatic photometric variability that has evolved steadily and been vigilantly monitored since its re-discovery in the mid-1990's \citep{KH98,Her02,Ham05}."
". Here we report in tlie last [ive vear ""ol his evolution during which time the disk edge has proceeded to completely cover the orbit auc LpmzXosphere of star A. Star B was last seen in 1995. so the system bas now tered a state of dinii[unished optical brightuess in which light from te illumiuating binary reaches is only though scattering [roin ciretuustellar or cir""umbiuary matter."," Here we report on the last five years of this evolution during which time the disk edge has proceeded to completely cover the orbit and photosphere of star A. Star B was last seen in 1995, so the system has now entered a state of diminished optical brightness in which light from the illuminating binary reaches us only though scattering from circumstellar or circumbinary matter."
 It is uncertain how long this ate will persist. perhaps [or centuries or perlaps or onlv a brief tiJe.," It is uncertain how long this state will persist, perhaps for centuries or perhaps for only a brief time."
 Tje las [ew vears of he progression of tle occultiug edge have yrovided us with information lat hiep οςonstraln p'operties of the disk. the binay orbit. star Aa dits inunediate environment.," The last few years of the progression of the occulting edge have provided us with information that helps constrain properties of the disk, the binary orbit, star A and its immediate environment."
 I1 particular. we Call suds the vertical distrilouticoÀÀ1 of the obscuri[n]oO matter that composes the [1lisk. its optical properties. aud the cletails of its p'OgresslOon across he orbit.," In particular, we can study the vertical distribution of the obscuring matter that composes the disk, its optical properties, and the details of its progression across the orbit."
 Because the edge is so sharj) — a stnall raction of a stellar radius (see below) — we ca also seek coustraints ou the (inhomogeneous) st(Tacee [[lux ane| tem»erature cisributiou across sar A and on the elements of 1he biary orbit., Because the edge is so sharp – a small fraction of a stellar radius (see below) – we can also seek constraints on the (inhomogeneous) surface flux and temperature distribution across star A and on the elements of the binary orbit.
 Th Sln‘ination is la'gely of a sot that cannot be obtained for any other star or |)nary system. pre-yall sedqueuce or otherwise.," This information is largely of a sort that cannot be obtained for any other star or binary system, pre-main sequence or otherwise."
 Heice. WH 15D plays a unique aud importaut role iu studies of pre-uiüu sequeuce stars. as well as disk evolution.," Hence, KH 15D plays a unique and important role in studies of pre-main sequence stars, as well as disk evolution."
 We emphasize iat there is Πο reason to expect that the stars or disk in IXH 15D are in any way luiisual for T Tauri stars., We emphasize that there is no reason to expect that the stars or disk in KH 15D are in any way unusual for T Tauri stars.
 What is unusual is the current aligniuent of the disk with respect to our, What is unusual is the current alignment of the disk with respect to our
Astronnony. Aladingley Road. Cambridge CBI OLLA The most extreme continuum variability in CIN is usually seen in the X-ray spectral band.,"nomy, Madingley Road, Cambridge CB3 0HA The most extreme continuum variability in AGN is usually seen in the X-ray spectral band."
 Phe X-ray variability power spectrum reveals that. low-amplitude fast. lickering is an almost permanent. feature. but major changes. such as à [lare with a [large change in luminosity (like doubling) occur much less frequently.," The X-ray variability power spectrum reveals that low-amplitude fast flickering is an almost permanent feature, but major changes, such as a flare with a large change in luminosity (like doubling) occur much less frequently."
 Ehe duration of such Lares may bv of the order of a few thousand. seconds (e.g. see figures in Mellardy (1989))., The duration of such flares may by of the order of a few thousand seconds (e.g. see figures in McHardy (1989)).
. Reeent spectroscopic observations suggest that such X-ray Εαν variations can be accompanied bv Fe We line variability which occurs on a similar time scale (lwasawa et al. (, Recent spectroscopic observations suggest that such X-ray flux variations can be accompanied by Fe $\alpha$ line variability which occurs on a similar time scale (Iwasawa et al. (
1996)).,1996)).
 This might indicate that the size of the X-ray continuum emitting region is small in comparison with other sources contributing to the overal continuum and that the iron line is produced in a compac region close to the continuum source and ids correlate with the X-ray outburst., This might indicate that the size of the X-ray continuum emitting region is small in comparison with other sources contributing to the overall continuum and that the iron line is produced in a compact region close to the continuum source and is correlated with the X-ray outburst.
 The. X-ray emission. is though to originate from the innermost part of the aceretion disc., The X-ray emission is thought to originate from the innermost part of the accretion disc.
 This region is subject to a number of instabilities which may produce Uare-like activity., This region is subject to a number of instabilities which may produce flare-like activity.
 Phere is a large body of observational ancl theoretical work which supports this view., There is a large body of observational and theoretical work which supports this view.
 Among the proposed. scenarios invoked. to explain such a phenomenon are: the amplification of magnetic fielcdls in the dise by convection and. dillerential rotation leading to the emergence of magnetic fields. carrving hot plasma (Galeeyv. Rosner Vaiana. 1979). hot magnetic arces due to the Parker instability (Chagelishvili. Leminadze ltogava (1989)). magnetic [lares due to explosive. release of stored. magnetic energv in the accretion disc (Vries Ixuijpers (1992)) ancl vortices (Abramowiez et al. (," Among the proposed scenarios invoked to explain such a phenomenon are: the amplification of magnetic fields in the disc by convection and differential rotation leading to the emergence of magnetic fields carrying hot plasma (Galeev, Rosner Vaiana, 1979), hot magnetic arcs due to the Parker instability (Chagelishvili, Leminadze Rogava (1989)), magnetic flares due to explosive release of stored magnetic energy in the accretion disc (Vries Kuijpers (1992)) and vortices (Abramowicz et al. ("
1992)).,1992)).
 The Buorescent iron line emission. may be. produced: by irracliation of the disc material by such Lares located above the accretion disc (Lightman White (LOSS). George Fabian (1991). Matt. Perola Piro. (1991)).," The fluorescent iron line emission may be produced by irradiation of the disc material by such flares located above the accretion disc (Lightman White (1988), George Fabian (1991), Matt, Perola Piro, (1991))."
 As a result. the observed time-averagecl spectra have distinctive. skewed. clouble-peaked profiles which rellect the Doppler ancl gravitational shifts in a stronglv curved. spacetime (Fabian ct al.," As a result, the observed time-averaged spectra have distinctive, skewed, double-peaked profiles which reflect the Doppler and gravitational shifts in a strongly curved spacetime (Fabian et al."
 1989. Laor 1991. Mushotzkyv. et al. (," 1989, Laor 1991, Mushotzky et al. ("
1995). ‘Tanaka et al. (,"1995), Tanaka et al. ("
1995). Nandra et al. (,"1995), Nandra et al. ("
1997)).,1997)).
. Apart. [from the line emission. the disc material should also reflect a part of the X-ray continuum.," Apart from the line emission, the disc material should also reflect a part of the X-ray continuum."
 Evidence for this clleet was found. by Pounds. et al. (, Evidence for this effect was found by Pounds et al. (
1990) for a number of Sevfert galaxies.,1990) for a number of Seyfert galaxies.
 Since the spectral properties of the Fe Ixo line are, Since the spectral properties of the Fe $\alpha$ line are
archive. reduced with the Spitzer pipeline version S14.0. and investigated the images.,"archive, reduced with the Spitzer pipeline version S14.0, and investigated the images."
 The diffuse nebulosities of TMR-1 are well detected in the IRAC 3.6mie and 4.5mic images. which we show in Figure 2.. and they are very similar in appearance as in our ISAAC 2.2mic image. despite at much lower spatial resolution.," The diffuse nebulosities of TMR-1 are well detected in the IRAC 3.6mic and 4.5mic images, which we show in Figure \ref{irac3_6and4_5}, and they are very similar in appearance as in our ISAAC 2.2mic image, despite at much lower spatial resolution."
 The IRAC channel 1 has a central wavelength close to the ISAAC L’ filter. but due to its much larger pixels IRAC is more sensitive to extended emission than ISAAC.," The IRAC channel 1 has a central wavelength close to the ISAAC $^{\prime}$ filter, but due to its much larger pixels IRAC is more sensitive to extended emission than ISAAC."
 At IRAC channel 3 and 4 (5.8mie and 8.0mic) only the main source TMR-1AB is seen., At IRAC channel 3 and 4 (5.8mic and 8.0mic) only the main source TMR-1AB is seen.
 On none of the mosaiced IRAC images TMR-1C ts detected., On none of the mosaiced IRAC images TMR-1C is detected.
 This may partly be due to the closeness of TMR-1C to the very bright main source TMR-1AB. which has a flux of - mmly at 3.6mic. and ~ mmly at 4.5mic. but may also be related to an intrinsic faintness of TMR-IC in this wavelength range.," This may partly be due to the closeness of TMR-1C to the very bright main source TMR-1AB, which has a flux of $\sim$ mJy at 3.6mic, and $\sim$ mJy at 4.5mic, but may also be related to an intrinsic faintness of TMR-1C in this wavelength range."
 Given the local background and the Poisson noise measurement at the expected position of TMR-IC. we estimate upper 307 flux detection limits of 0.15mJy (3.6um) and O.51mJy (4.5jm).," Given the local background and the Poisson noise measurement at the expected position of TMR-1C, we estimate upper $\sigma$ flux detection limits of 0.15mJy $\mu$ m) and 0.51mJy $\mu$ m)."
 Concerning the 5.8um and 8.04 Images. the PSF wings of the extremely bright source TMR-1AB prevent any meaningful determination of an upper flux limit.," Concerning the $\mu$ m and $\mu$ m images, the PSF wings of the extremely bright source TMR-1AB prevent any meaningful determination of an upper flux limit."
 The upper flux limits extracted from the Spitzer data are listed together with the ISAAC photometry in Table 1.., The upper flux limits extracted from the Spitzer data are listed together with the ISAAC photometry in Table \ref{phot}.
 K-band low-resolution (R=450) long-slit spectroscopy of TMR-1C. and of the filament was performed with ISAAC during the night Dee 04-05. 1998.," K-band low-resolution (R=450) long-slit spectroscopy of TMR-1C, and of the filament was performed with ISAAC during the night Dec 04-05, 1998."
 In Figure 3. we show the slit positioning on TMR-1C and the filament., In Figure \ref{slitpos} we show the slit positioning on TMR-1C and the filament.
" The width of the slit was and spectra were obtained by observing the object alternately at two positions along the slit. bby nodding along the slit with a nodthrow size of40""."," The width of the slit was and spectra were obtained by observing the object alternately at two positions along the slit, by nodding along the slit with a nodthrow size of."
. An exposure time of I20sseconds per individual frame was used and the resulting effective exposure time of the final co-added spectrum is sseconds., An exposure time of seconds per individual frame was used and the resulting effective exposure time of the final co-added spectrum is seconds.
 Since the slit was positioned in a way to include TMR-1C and most of the filament. the binary TMR-IAB was correspondingly slightly out of the slit and only light from its PSF wings and from the immediate circumbinary environment entered the slit.," Since the slit was positioned in a way to include TMR-1C and most of the filament, the binary TMR-1AB was correspondingly slightly out of the slit and only light from its PSF wings and from the immediate circumbinary environment entered the slit."
 The spectral images were sky-subtracted in pairs using the respectively nodded companion image for subtraction. cleaned of pixels affected by cosmic rays and non-linear response. and then combined to a single spectral image of TMR-1. which ts shown in Cuby et ((2000).," The spectral images were sky-subtracted in pairs using the respectively nodded companion image for subtraction, cleaned of pixels affected by cosmic rays and non-linear response, and then combined to a single spectral image of TMR-1, which is shown in Cuby et (2000)."
 Four different apertures have been extracted from this 2D-spectrum at positions that are shown in Figure 3.., Four different apertures have been extracted from this 2D-spectrum at positions that are shown in Figure \ref{slitpos}.
 The largest aperture (H» knot 1) actually includes two separate peaks of molecular hydrogen emission (cf., The largest aperture $_2$ knot 1) actually includes two separate peaks of molecular hydrogen emission (cf.
 Figure 8))., Figure \ref{h2exc}) ).
 Both knots appeared to be very similar on the 2D spectral image and a single aperture was therefore used to extract the spectrum. improving the signal to noise ratio.," Both knots appeared to be very similar on the 2D spectral image and a single aperture was therefore used to extract the spectrum, improving the signal to noise ratio."
 In order to correct for telluric absorption. as well as to attempt flux-calibration. the spectrum of a B6IV standard star (BS3672) was observed directly after TMR-1. with the same instrumental setting and in the same manner (nodding along the slit) as the science spectra.," In order to correct for telluric absorption, as well as to attempt flux-calibration, the spectrum of a B6IV standard star (BS3672) was observed directly after TMR-1, with the same instrumental setting and in the same manner (nodding along the slit) as the science spectra."
 After the basic reduction the standard star spectrum was divided by a black body spectrum corresponding to the spectral type of the star from what the absolute spectroscopic response was derived., After the basic reduction the standard star spectrum was divided by a black body spectrum corresponding to the spectral type of the star from what the absolute spectroscopic response was derived.
 The extracted TMR-1 spectra were then divided by the spectroscopic response function., The extracted TMR-1 spectra were then divided by the spectroscopic response function.
 Absolute flux calibration based on the spectroscopic observations of the standard star had shown to be difficult. because it relied on the assumption that all flux from the standard star was inside the slit.," Absolute flux calibration based on the spectroscopic observations of the standard star had shown to be difficult, because it relied on the assumption that all flux from the standard star was inside the slit."
 Moreover. the seeing worsened by a factor of ~1.5 from the time of observation of TMR-1 to the standard star observation.," Moreover, the seeing worsened by a factor of $\sim 1.5$ from the time of observation of TMR-1 to the standard star observation."
 Consequently. the," Consequently, the"
1n the currently standard: cosmological model CXCDAD). a lat universe with a cosmological constant contains collisionless cold. dark matter as its dominant matter component. perturbecl by primordial Ciaussian-random-noise density [luctuations.,"In the currently standard cosmological model $\Lambda$ CDM), a flat universe with a cosmological constant contains collisionless cold dark matter as its dominant matter component, perturbed by primordial Gaussian-random-noise density fluctuations."
 This model has been highly successful at explaining. observations of the background universe and large-scale structure., This model has been highly successful at explaining observations of the background universe and large-scale structure.
 On small scales. however. the distribution of dark matter in coordinate and. velocity space is not fully understood.," On small scales, however, the distribution of dark matter in coordinate and velocity space is not fully understood."
 N-body simulations show that the density profiles of the virialized regions (“halocs’) that form in this collisionless dark matter are cuspy. such as the 2.NEW profile. in which poo»r toward. the centre.," $N$ -body simulations show that the density profiles of the virialized regions (`haloes') that form in this collisionless dark matter are cuspy, such as the \citet*[][NFW]{1997ApJ...490..493N} profile, in which $\rho \rightarrow r^{-1}$ toward the centre."
 Reecent high-resolution simulations show that the inner profile is not exactly a power law (?2???7).. but it diverges nevertheless.," Recent high-resolution simulations show that the inner profile is not exactly a power law \citep{2004MNRAS.355..794H, 2005MNRAS.364..665D,
 2006AJ....132.2685M, 2008MNRAS.387..536G, 2009MNRAS.398L..21S,
 2010MNRAS.402...21N}, but it diverges nevertheless."
 On the other hand. a cored. profile (a profile which Ilattens in the centre) such as a pseudo-isothermal profile. is favored by observations of dwarf and low surface brightness (LSB) galaxies (22722?77?).. D," On the other hand, a cored profile (a profile which flattens in the centre) such as a pseudo-isothermal profile, is favored by observations of dwarf and low surface brightness (LSB) galaxies \citep{2003MNRAS.340..657D,
 2004MNRAS.351..903G, 2006ApJS..165..461K,2006A&A...452..857Z,
 2007A&A...467..925G, 2008ApJ...676..920K, 2008AJ....136.2648D,
 2010arXiv1011.0899O, 2010AdAst2010E...5D}."
warl spiral and LSB galaxies are dark-matter dominated., Dwarf spiral and LSB galaxies are dark-matter dominated.
 As such. it was originally thought. their mass distribution should rellect the dark matter dvnamies alone. ancl be relatively," As such, it was originally thought, their mass distribution should reflect the dark matter dynamics alone, and be relatively"
02290 SSO id DO 0—u 9J- v QJ(36G) Siraightforward caleulations show that. in the second order in 6!. 0J= for 0—0. z/2.5. and 32/2 of (he critical curve in eq.(3.1.2)).,"0 = _-J = _- z J + _- z J 0 = u_- J + v_- J Straightforward calculations show that, in the second order in $\ell^{-1}$ $\partial_-J=0$ for $\theta = 0$, $\pi/2$, $\pi$, and $3\pi/2$ of the critical curve in \ref{eqCriticalCurveOne}) )."
 Therefore they are precusps in the second order approximation., Therefore they are precusps in the second order approximation.
" Sel 2=re"" and ὁ—w-εί,", Set $z = r e^{i\theta}$ and $\zeta =\omega - \epsilon/\ell$.
 The lens equation for the shifted source position is given by C= x(37)TERMES where £ and 5 ave functions of r. u, The lens equation for the shifted source position is given by = + where $\xi$ and $\eta$ are functions of $r$ .
"u i—r—""E"" n= ir ς105) If we let ὁ=+ies. Qi =te )))tela: Gale Wisin "," = r -; = (r - ) If we let $\zeta = \zeta_1 + i \zeta_2$, _1 = + ); _2 = - ) ,and an equation for $r$ is obained. )"
"theta,",^2 + )^2= 1
the LW range. 11.213.6 eV see eq. (τὸ).,"the LW range, $11.2-13.6$ eV – see eq. \ref{rad_rates}) ),"
 in the next Sect., in the next Sect.
 77 shielded according to ?.., \ref{Sect:chemistry} – shielded according to \cite{DraineBertoldi1996}.
 To couple radiation. with chemistry. we include non-equilibrium: reactions for Il. He ancl molecule evolution (whose ionization and dissociation energies are quoted. in ‘Tab. 1)).," To couple radiation with chemistry, we include non-equilibrium reactions for H, He and molecule evolution (whose ionization and dissociation energies are quoted in Tab. \ref{tab:Eion}) ),"
 by following a chemical network (see Tab. 2)), by following a chemical network (see Tab. \ref{tab:reactions}) )
 of several species: . H1. 11. . Hoe. Ho2 He. He. LL. D. . IID.," of several species: $^-$, H, $^+$ , $^-$, He, $^+$, $^{++}$, $_2$, $_2^+$, D, $^+$, HD, $^+$."
 οσον some updates in the rates and in he reaction network. the implementation used is the same asthe one in ? ancl? (andbasedon??7?)..," Besides some updates in the rates and in the reaction network, the implementation used is the same asthe one in \cite{Maio2007} and \cite{Maio2010}
 \cite[and based on][]{Abel_et_al1997,GP98,Yoshida2003}."
 Since the main coolants at carly times are He-derived molecules. LH» (e.g.?) and LED (e.g.?).. the inclusion ofàlarge network is crucial to correctly resolve the hydrodynamies aid the fragmentation processes of hieh-recshift eas. as well demonstrated by e.g. T2 TT. 5τν ?1..," Since the main coolants at early times are H-derived molecules, $_2$ \cite[e.g.][]{SaZi1967} and HD \cite[e.g.][]{LeppShull1984}, the inclusion of alarge network is crucial to correctly resolve the hydrodynamics and the fragmentation processes of high-redshift gas, as well demonstrated by e.g. \cite{Abel_et_al1997}, \cite{Yoshida2003,Yoshida2006}, \cite{Maio2006,Maio2007,Maio2009,Maio2010, Maio2011a}, \cite{Maio2011b,MaioIannuzzi2011}."
 lo take into account chemical evolution. at each timestep ancl for each species ἐςthe time variation of its number censityv a; is computed. for collisional and photoionization/photodissociation events. via where Ay. is the rate of creation of the species i from species p ancl q. Ay; is the destruction rate of the species 7 [romcollisions with species /. and &-; is the photoionization or photocdissociation rate of species i due to radiation (see ‘Tab. 1)).," To take into account chemical evolution, at each timestep and for each species $i$ ,the time variation of its number density $n_i$ is computed, for collisional and photoionization/photodissociation events, via where $k_{pq,i}$ is the rate of creation of the species $i$ from species $p$ and $q$, $k_{li}$ is the destruction rate of the species $i$ fromcollisions with species $l$, and $k_{\gamma i}$ is the photoionization or photodissociation rate of species $i$ due to radiation (see Tab. \ref{tab:Eion}) )."
 The collisional rates are given by (and the analogous for 4j). with & relative velocity of particles p and q. mmn) interaction cross-section. and f(r) AMaxwellian. velocity. clüstribution function.," The collisional rates are given by (and the analogous for $k_{li}$ ), with $u$ relative velocity of particles $p$ and $q$, $\sigma_{pq,i}(u)$ interaction cross-section, and $f(u)$ Maxwellian velocity distribution function."
 More precisely. we do not compute the integrals on the fly. but. insteac we interpolate. pre-computed. tables (whose references. are listed in Tab. 2))," More precisely, we do not compute the integrals on the fly, but instead we interpolate pre-computed tables (whose references are listed in Tab. \ref{tab:reactions}) )"
 in order to speed-up the code., in order to speed-up the code.
 These rates are temperature dependent and are. expressed. in units of volume per time. Le. em?s] in the egs system.," These rates are temperature dependent and are expressed in units of volume per time, i.e. $\rm [cm^3\, s^{-1}]$ in the cgs system."
 As in the Ioft-hand. side. the first ancl second term in the right-haux side of equation (5)) have dimensions of a number density per unit time. ems !]in the ces system.," As in the left-hand side, the first and second term in the right-hand side of equation \ref{noneq_eq}) ) have dimensions of a number density per unit time, $\rm [cm^{-3}\,s^{-1}]$ in the cgs system."
 Consistently with Sect. 2?..," Consistently with Sect. \ref{Sect:radtrans},"
" when the species 7 interacts with radiation (45) — see Table 2 and gets photo-ionized (like for HI. D. HE... He. } or photo-clissociated (like for Ilo. HD. ). the corresponding radiative rate Ae; can be HL,written. as where the dz stands for isotropic radiation. /(5) is the source intensity. as a function of frequency. p. a;(47) is the cross-section for the given. process. ην is the Planck constant. e the speed of light. and Ες(7) the photon number density per frequency."," when the species $i$ interacts with radiation $\gamma$ ) – see Table \ref{tab:reactions} – and gets photo-ionized (like for H, D, $^-$, He, $^+$ ) or photo-dissociated (like for $_2$, $_2^+$,HD, $^+$ ), the corresponding radiative rate $k_{\gamma i}$ can be written as where the $4\pi$ stands for isotropic radiation, $I(\nu)$ is the source intensity as a function of frequency $\nu$, $\sigma_{\gamma i}(\nu)$ is the cross-section for the given process, $h_p$ is the Planck constant, $c$ the speed of light, and $n_\gamma (\nu)$ the photon number density per frequency."
 In. the final equality we mace use of eq. (4)).," In the final equality we made use of eq. \ref{n_gamma1}) ),"
 to formally get the rate expression similar to eq. (6))., to formally get the rate expression similar to eq. \ref{collisional_rates}) ).
 Phe radiative rates are probabilities per unit time. and are given in. s+] in the ces system.," The radiative rates are probabilities per unit time, and are given in $\rm [s^{-1}]$ in the cgs system."
 So. the number of radiative interactions per unit time and volume between photons and m; particles is &Á-;nm;.," So, the number of radiative interactions per unit time and volume between photons and $n_i$ particles is $k_{\gamma i} n_i$."
 The latter quantity is acded on the right-hand side of equation (5)) when photon interactions are taken in consideration. ancl Consistently with the other terms in the equation. this is also given in units of number density per time. Le. emHs] in the cgs system.," The latter quantity is added on the right-hand side of equation \ref{noneq_eq}) ) when photon interactions are taken in consideration, and consistently with the other terms in the equation, this is also given in units of number density per time, i.e. $\rm [cm^{-3}\,
 s^{-1}]$ in the cgs system."
 When talking about radiative interactions. one has to consider that. while ionization energies (see Tab. 1))," When talking about radiative interactions, one has to consider that, while ionization energies (see Tab. \ref{tab:Eion}) )"
 are uniquely defined. molecular dissociation. energies might depend on the particular radiative process considered. and hus all the various channels must be taken into account.," are uniquely defined, molecular dissociation energies might depend on the particular radiative process considered, and thus all the various channels must be taken into account."
 For cxample (see Tab. 2)).," For example (see Tab. \ref{tab:reactions}) ),"
" LW radiation above the energy hreshold of 11.2 eV. can dissociate Ho in PIL. but. harder xhotons with energies larger than 15.42 eV. would simply ionize the residual Ls into Ll, | 6."," LW radiation above the energy threshold of 11.2 eV can dissociate $_2$ in 2H, but harder photons with energies larger than 15.42 eV would simply ionize the residual $_2$ into $_2^+$ + $e^-$."
" Also lor LL, there are wo possible branches: one above an energy threshold of 2.65 eV and below 21 eV (11,15.HE.| HD). and à second one between 30 eV and 70 eV (11,15.REE |e)."," Also for $_2^+$ there are two possible branches: one above an energy threshold of 2.65 eV and below 21 eV $\rm H_2^+ + \gamma \rightarrow H^+ + H$ ), and a second one between 30 eV and 70 eV $\rm H_2^+ + \gamma \rightarrow 2 H^+ + e^-$ )."
 For he radiative interaction considered in our. network he energv threshold is about 1.7 eV. The set of dillerential equation (5)) is integrated via simple lincarization. so. given the timestep Af. at each time f the temporal variation of the numberfraction of species i can be written as where we have introduced. the creationcoellicicnt for the species 7 in cmὃν+). and the destruction coellicient in s +}.," For the $^+$ radiative interaction considered in our network the energy threshold is about 1.7 eV. The set of differential equation \ref{noneq_eq}) ) is integrated via simple linearization, so, given the timestep $\Delta t$, at each time $t$ the temporal variation of the numberfraction of species $i$ can be written as where we have introduced the creationcoefficient for the species $i$ in $\rm [cm^{-3} s^{-1}]$ and the destruction coefficient in $\rm [s^{-1}]$ ."
" ""Phe contribution from photoionization or photodissociation is accounted for by adding. in equation (10)). the &; rates."," The contribution from photoionization or photodissociation is accounted for by adding, in equation \ref{D}) ), the $k_{\gamma i}$ rates."
" The number density is updated [rom equation (8)): We apply this treatment to all the chemical species included. with the cocllicients for cach reaction in the network quoted in ""Table 2.."," The number density is updated from equation \ref{discrete}) ): We apply this treatment to all the chemical species included, with the coefficients for each reaction in the network quoted in Table \ref{tab:reactions}. ."
 Gas cooling or heating is computed from LE and. Le collisional excitations (?7).. ionizations. (7).. recombinations (7).. Hl». anc Hs ," Gas cooling or heating is computed from H and He collisional excitations \cite[][]{Black1981,Cen1992}, , ionizations \cite[][]{Abel_et_al1997}, , recombinations \cite[][]{HG1997}, , $_2$ and $_2^+$ "
where Q is the solid angle of the DIRBE beam and £j is the flux of the j star.,where $\Omega$ is the solid angle of the DIRBE beam and $F_j$ is the flux of the $j^{th}$ star.
 We also ueed to know the variauce of the intensity in the pixel due to the random orientations aud raudom placements of observatious withniu the pixel boundaries., We also need to know the variance of the intensity in the pixel due to the random orientations and random placements of observations within the pixel boundaries.
 Tus cau be obtained from the expected value of H? within a pixel. but since H?=A we find that tle variance of pj; is given by ρε.pij).," This can be obtained from the expected value of $H^2$ within a pixel, but since $H^2
= H$ we find that the variance of $p_{ij}$ is given by $p_{ij}(1-p_{ij})$."
 Thus stars at the edge of the beam (p~0.5) make the greatest contribution to the variance. a phenomenou known as “flicker noise”.," Thus stars at the edge of the beam $p \simeq 0.5$ ) make the greatest contribution to the variance, a phenomenon known as “flicker noise”."
 We then get where e is an uncertainty in cross-calibrating the DIRBE aud grouud-based data for iudividual stars which also includes au allowauce for variability Hu the stars., We then get where $\epsilon$ is an uncertainty in cross-calibrating the DIRBE and ground-based data for individual stars which also includes an allowance for variability in the stars.
 We- use e>=Q.14 inH thisH work., We use $\epsilon^2 = 0.1$ in this work.
 Many IR bright stars are long period. variables aud wil uot have the same flux during the DIRBE observations as they have uine years later curing our ground-based survey. so a fairly large value of € EPis appropriate.," Many IR bright stars are long period variables and will not have the same flux during the DIRBE observations as they have nine years later during our ground-based survey, so a fairly large value of $\epsilon^2$ is appropriate."
". Note- that the variance. stun is. domina""ed by the brightest stars. aud is minimized in the ""dark spot""."," Note that the variance sum is dominated by the brightest stars, and is minimized in the “dark spot”."
 We have evaluated the bright star contribution for all stars with A«9 mag or L«9 mag in the dark spot., We have evaluated the bright star contribution for all stars with $K < 9$ mag or $L < 9$ mag in the dark spot.
 Note that the cutoff iuagnitude does uot come from LIRC2 so as to avoid any additional error being iutroduced because of LIRC2's dhotometric inaccuracy in the final resu|., Note that the cutoff magnitude does not come from LIRC2 so as to avoid any additional error being introduced because of LIRC2's photometric inaccuracy in the final result.
 Stars were detected below these limits with accurate shotometry but were uot used. with tlle conservative cut-off being at 9th. maguitude.," Stars were detected below these limits with accurate photometry but were not used, with the conservative cut-off being at 9th magnitude."
 There are ouly 17 DIRBE pixels whose respouse a Uniform illumination pattern is at least due to adiatiou from within the dark spot. ai these 17 pixels form our DIRBE sample.," There are only 17 DIRBE pixels whose response to a uniform illumination pattern is at least due to radiation from within the dark spot, and these 17 pixels form our DIRBE sample."
 Given the DIRBE data D; aud the bright star inteusi Bj. we can estimate the cosmic infrared backgrouud usile C;—-D;—B;F-—Z. where F is te contribution from faint stars evaluated from star couut 1iocdlels. ancl Z is the zodiacal contributiol.," Given the DIRBE data $D_i$ and the bright star intensity $B_i$, we can estimate the cosmic infrared background using $C_i = D_i-B_i-F-Z$, where $F$ is the contribution from faint stars evaluated from star count models, and $Z$ is the zodiacal contribution."
 Both F and Z are esseutially coustaut over our spot aid thus are not subscripted by pixel., Both $F$ and $Z$ are essentially constant over our spot and thus are not subscripted by pixel.
 We combine the several estimates of the cosmic infrared bacseground usiug a weighted mediau: we fia the value C' that minimizes The uncertainty in C is fotud sine the Παπαρ] method (Babu&Feigelson1996): maiM7 loute Carlo runs were performed each with a raidoinly. chosen half of the pixels. aud the scatter in these determinations gives ! le|lice‘tainty in C.," We combine the several estimates of the cosmic infrared background using a weighted median: we find the value $\hat{C}$ that minimizes The uncertainty in $\hat{C}$ is found using the half-sample method \citep{BF96}: many Monte Carlo runs were performed each with a randomly chosen half of the pixels, and the scatter in these determinations gives the uncertainty in $\hat{C}$."
" The result for the CIRB plus the faint sta""s (C4 F) at IS is 28.27+0.90kysr1 .and at Lis 17.8140.75.Κανsr.|."," The result for the CIRB plus the faint stars $\hat{C}+F$ ) at K is $28.27 \pm 0.90\;\kJysr$, and at L is $17.81 \pm 0.75 \; \kJysr$."
 These uncertainties a'e owed ouly on the statistical pixel 1o jixel scatter within the “dark spot. but they do inclue he fluctuations in the faint star c)itrilnition.," These uncertainties are based only on the statistical pixel to pixel scatter within the “dark spot”, but they do include the fluctuations in the faint star contribution."
 Figure L shows the zodi-subtracted DIRBE 3.5 4i intensity. D;—Z. plotted agaius the brielit star inteusity j»redicted from the Lick L band data.," Figure \ref{fig:LSQ-cold-spot-L} shows the zodi-subtracted DIRBE 3.5 $\mu$ m intensity, $D_i-Z$, plotted against the bright star intensity predicted from the Lick L band data."
 TI slope of a liue fitted to these poiES Is οuly 0.1. but this does not mean that the DIRBE calibratioli differs by a factor of 0.E from the ground-based calibration.," The slope of a line fitted to these points is only 0.4, but this does not mean that the DIRBE calibration differs by a factor of 0.4 from the ground-based calibration."
 Rather it shows that the variance of ttT stellar contribution is not comated by the bright stars i this “dark spot”. aud thus the predicted," Rather it shows that the variance of the stellar contribution is not dominated by the bright stars in this “dark spot”, and thus the predicted"
where the solutions are Here ταςb.e) is the confiucut hypergeoimetzrie fiction aud £8(0) is the generalized Laguerre polvuouial.,"where the solutions are Here $U(a,b,c)$ is the confluent hypergeometric function and $L_n^a(x)$ is the generalized Laguerre polynomial."
 We ueed to take both Cyz0 and Cyz0 to satisfy (0.7)=0.," We need to take both $C_{1}\neq 0$ and $C_{2}\neq 0$ to satisfy $\Psi(0,t)=0$ ."
 For flat space time (4= 0). stiff matter (@=1). aud standard Chaplveiu gas (a=1) equation (L1) reduces to with the solutious as Tere again. we have Cy#0 aud C>z0 in order to satisfy the first boundary condition (28}). Iu labe," For flat space time $k=0$ ), stiff matter $w=1$ ), and standard Chaplygin gas $\alpha=1$ ), equation \ref{sle2-b}) ) reduces to with the solutions as Here again, we have $C_{1}\neq 0$ and $C_{2}\neq 0$ in order to satisfy the first boundary condition \ref{boundary}) )."
lsecthis| work we have nünisuperspace ΕΠΑΝ quantum cosmological models with and fluid as the matter investigatedcontent m early and late times., In this work we have investigated minisuperspace FRW quantum cosmological models with Chaplygin gas and perfect fluid as the matter content in early and late times.
 The use of Schutz’s formalismChaplveiu for the easChaplvein eas pertectallowed us to obtain SWD equations with the perfect fuid’s effective potential., The use of Schutz's formalism for the Chaplygin gas allowed us to obtain SWD equations with the perfect fluid's effective potential.
 We have obtained eieenfuuctious aud therefore acceptable wave packets were constructed: by appropriate linear combination of these cigeuftuictions., We have obtained eigenfunctions and therefore acceptable wave packets were constructed by appropriate linear combination of these eigenfunctions.
 The time evolution of the expectation value of the scale factor has been determined iu the spirit of the mauv-worlds interpretation of quautuni cosmology., The time evolution of the expectation value of the scale factor has been determined in the spirit of the many-worlds interpretation of quantum cosmology.
 We have showed that contrary to the classical case. the value of the scale factor avoids singuluitv at the quantum level.," We have showed that contrary to the classical case, the expectation value of the scale factor avoids singularity at the quantum level."
 Moreover. this model predictsan expectationaccelerated Universe for late times.," Moreover, this model predictsan accelerated Universe for late times."
"and perpendicular, decreases with the pattern speed of the bar (Table 1, column 7).","and perpendicular, decreases with the pattern speed of the bar (Table 1, column 7)."
" Thus the lower the pattern speed of the inner bar, the more eccentric that bar is and the more it pulsates."," Thus the lower the pattern speed of the inner bar, the more eccentric that bar is and the more it pulsates."
" In Figure 7 we plot the average ratio of eccentricities of the loops between the moments when the two bars are parallel and perpendicular, as well as between the moments when the two bars are parallel and at45°."," In Figure 7 we plot the average ratio of eccentricities of the loops between the moments when the two bars are parallel and perpendicular, as well as between the moments when the two bars are parallel and at."
. It can be seen that the average eccentricity of the loops when the bars are perpendicular increases from its value when they are parallel by about twice as much as it increases when the angle between the two bars is45°., It can be seen that the average eccentricity of the loops when the bars are perpendicular increases from its value when they are parallel by about twice as much as it increases when the angle between the two bars is.
". It is worth pointing out that the inner bar pulsates even when it is very round: the largest axial ratio of the loops supporting the inner bar in model 05E is only 1.5 when the bars are parallel, but it still increases by to 1.78 when the bars are perpendicular."," It is worth pointing out that the inner bar pulsates even when it is very round: the largest axial ratio of the loops supporting the inner bar in model 05E is only 1.5 when the bars are parallel, but it still increases by to 1.78 when the bars are perpendicular."
" For the models with the highest inner bar pattern speeds (models 01, 05 and 05E), the loops pulsate only slightly and in a coherent way (see Figure 4)."," For the models with the highest inner bar pattern speeds (models 01, 05 and 05E), the loops pulsate only slightly and in a coherent way (see Figure 4)."
" For models with lower pattern speeds of the inner bar, and model 02 in particular, the average pulsation is more extreme and there is more variation in the pulsation of individual loops (Figure 7)."," For models with lower pattern speeds of the inner bar, and model 02 in particular, the average pulsation is more extreme and there is more variation in the pulsation of individual loops (Figure 7)."
 Thus a slowly rotating inner bar does not pulsate coherently: when the eccentricity of its outermost loops increases by a mere the eccentricity of its inner loops can increase by factors larger than six., Thus a slowly rotating inner bar does not pulsate coherently: when the eccentricity of its outermost loops increases by a mere the eccentricity of its inner loops can increase by factors larger than six.
" As predicted from the orbital structure of double bars (MS00) and confirmed by numerical models (Debattista Shen the inner bar in a doubly barred galaxy does not 2007),rotate uniformly, but its angular velocity is highest when the bars are aligned and lowest when the bars are perpendicular."," As predicted from the orbital structure of double bars (MS00) and confirmed by numerical models (Debattista Shen 2007), the inner bar in a doubly barred galaxy does not rotate uniformly, but its angular velocity is highest when the bars are aligned and lowest when the bars are perpendicular."
" The same is implied by the orbital models presented here: the loops supporting the inner bar align with the uniformly rotating major axis of the bar in the assumed gravitational potential when this bar is parallel or perpendicular to the outer bar, but they lead this axis when the inner bar departs from the alignment with the outer one, and trail it on the way back to the alignment (see Figure 3, left-hand panels)."," The same is implied by the orbital models presented here: the loops supporting the inner bar align with the uniformly rotating major axis of the bar in the assumed gravitational potential when this bar is parallel or perpendicular to the outer bar, but they lead this axis when the inner bar departs from the alignment with the outer one, and trail it on the way back to the alignment (see Figure 3, left-hand panels)."
" In particular, when in the assumed gravitational potential the angle between the major axes of the two bars is45°,, the PA of the major axis of the loops supporting the inner bar is offset from this angle to a larger value."," In particular, when in the assumed gravitational potential the angle between the major axes of the two bars is, the PA of the major axis of the loops supporting the inner bar is offset from this angle to a larger value."
 This offset is listed in the last column of Table 1., This offset is listed in the last column of Table 1.
 It indicates the amplitude of the variation of the pattern speed of the inner bar., It indicates the amplitude of the variation of the pattern speed of the inner bar.
" If for simplicity one assumes that this variation is sinusoidal, then the actual pattern speed of the inner bar, relates to the assumed constant pattern speed, Qs, Q%(t),by Q(t)=Qg(1+2€cos[2Qgt]), where e in radians is the PA offset listed in Table 1."," If for simplicity one assumes that this variation is sinusoidal, then the actual pattern speed of the inner bar, $\Omega_S^v(t)$, relates to the assumed constant pattern speed, $\Omega_S$ , by $\Omega_S^v(t) = \Omega_S (1+2\epsilon\cos[2\Omega_S t])$, where $\epsilon$ in radians is the PA offset listed in Table 1."
" In Figure 8, we plot the PA offset when the angle between the inner and the outer bar is aand135°."," In Figure 8, we plot the PA offset when the angle between the inner and the outer bar is and."
". In addition to the average PA offset, we plot its maximum and minimum among the loops supporting the inner bar in each model, represented by error bars."," In addition to the average PA offset, we plot its maximum and minimum among the loops supporting the inner bar in each model, represented by error bars."
" The offset for aand llooks the same, because time is reversible in the equation of motion."," The offset for and looks the same, because time is reversible in the equation of motion."
" Small range between the minimum and maximum offset indicates that the loops remain aligned, and therefore the non-uniform rotation of the bar remains coherent."," Small range between the minimum and maximum offset indicates that the loops remain aligned, and therefore the non-uniform rotation of the bar remains coherent."
" Thus fast inner bars (models 04, 01, 05 and 05E) rotate coherently."," Thus fast inner bars (models 04, 01, 05 and 05E) rotate coherently."
" When the angle between the bars in the assumed potential is45?,, they lead the inner bar in the assumed potential by5°—7°,, which implies that the pattern speed of the inner bar varies by around its nominal value."," When the angle between the bars in the assumed potential is, they lead the inner bar in the assumed potential by, which implies that the pattern speed of the inner bar varies by around its nominal value."
" Also in 1896—Figure 24968 it can be seen that slowly rotating inner bars (models 02 and 03) have the PA offset on average larger, and the range between its minimum and maximum increases as the pattern speed of the inner bar is lowered."," Also in Figure 8 it can be seen that slowly rotating inner bars (models 02 and 03) have the PA offset on average larger, and the range between its minimum and maximum increases as the pattern speed of the inner bar is lowered."
" This means that the slower the inner bar rotates, the less uniform and less coherent its rotation is."," This means that the slower the inner bar rotates, the less uniform and less coherent its rotation is."
" On average, the pattern speed of the inner bar is predicted to vary around its nominal value by in model 03 and by in model 02."," On average, the pattern speed of the inner bar is predicted to vary around its nominal value by in model 03 and by in model 02."
" However, as can be seen in the left-hand panels of Figure 3, in both models the PA offset increases towards the centre, hence the rotation is least uniform in the central parts of the inner bar."," However, as can be seen in the left-hand panels of Figure 3, in both models the PA offset increases towards the centre, hence the rotation is least uniform in the central parts of the inner bar."
" Inner loops in model 02 have the PA offset above25?,, which means that their pattern speed varies by factor of a few no longer adequate sinusoidal approximationa gives the (theamplitude of 90%))."," Inner loops in model 02 have the PA offset above, which means that their pattern speed varies by a factor of a few (the no longer adequate sinusoidal approximation gives the amplitude of )."
" On the other hand, rotation in the outer parts of the slowly rotating inner bars is as uniform as in the fast bars."," On the other hand, rotation in the outer parts of the slowly rotating inner bars is as uniform as in the fast bars."
" In Figure 9, we show the PA offset (averaged between the moments when the angle between the bars in the assumed gravitational potential is aand 135?)) for individual loops in all the models."," In Figure 9, we show the PA offset (averaged between the moments when the angle between the bars in the assumed gravitational potential is and ) for individual loops in all the models."
" Its value at the ends of the inner bar in models 02 and 03 (1.3 and 1.12 kpc, respectively) is as low as the lowest value for models 05 and 05E — just about4°."," Its value at the ends of the inner bar in models 02 and 03 (1.3 and 1.12 kpc, respectively) is as low as the lowest value for models 05 and 05E – just about."
. It corresponds to the variation of inner bar's pattern speed by just14%., It corresponds to the variation of inner bar's pattern speed by just.
". Interestingly, in Figure 9 can also be seen that the minimal PA offset in each model is bound within a very small range:3.5?—4.2?,, indicated by the two dashed lines in that figure."," Interestingly, in Figure 9 can also be seen that the minimal PA offset in each model is bound within a very small range:, indicated by the two dashed lines in that figure."
" Given the analysis above, the rotation of the inner bar should be most coherent in models 05 and 05E. However, in Figure 8 the range of the PA offset inthese"," Given the analysis above, the rotation of the inner bar should be most coherent in models 05 and 05E. However, in Figure 8 the range of the PA offset inthese"
we can study the effect of the medium on quarkonia or on jets.,we can study the effect of the medium on quarkonia or on jets.
 Both will interact stronely in a deconfined medium aud less or not at all with haclronic matter: thus thev can provide inlormation on the temperature and/or density of the QGP., Both will interact strongly in a deconfined medium and less or not at all with hadronic matter; thus they can provide information on the temperature and/or density of the QGP.
" Quarkonia are bound states of heavy quark-antiquark pairs (σσ,bb)."," Quarkonia are bound states of heavy quark-antiquark pairs $c\bar c, b \bar b$ )."
" Thev are much smaller than ""light hadrones (rà<rjc1 Bn) and much more tightly bound. with binding energies up (o 0.5 to 1.0 GeV. Therelore (hev can survive in a QGP up (o temperature above the deconfinement point and “melt” only when the color screening radius has dropped to quarkonium size [20].."," They are much smaller than “light” hadroncs $r_Q \ll r_h \sim 1$ fm) and much more tightly bound, with binding energies up to 0.5 to 1.0 GeV. Therefore they can survive in a QGP up to temperature above the deconfinement point and “melt” only when the color screening radius has dropped to quarkonium size \cite{MS}."
" Since the different. quarkonium states have clifferent sizes and binding energies. since will lead (o a ""sequential? suppression of quarkonia: first. the larger and more loosely bound excited states are dissolved. finally the small and lightly bound ground states."," Since the different quarkonium states have different sizes and binding energies, since will lead to a “sequential” suppression of quarkonia: first, the larger and more loosely bound excited states are dissolved, finally the small and tightly bound ground states."
 For charmonia. this is illustrated in 77. with and melting followed eventually by (hat of theώ," For charmonia, this is illustrated in 7, with and melting followed eventually by that of the."
"ν, Such patterns can provide a spectral analysis of the QGP. similar to that obtained for the sun by solar spectra [21].."," Such patterns can provide a spectral analysis of the QGP, similar to that obtained for the sun by solar spectra \cite{KS}."
 Jets are fast partons (quarks or gluons) passing trough the medium., Jets are fast partons (quarks or gluons) passing through the medium.
 They are colored aud hence interact stronger with a QGP than with eolor-neutral hadronic matter., They are colored and hence interact stronger with a QGP than with color-neutral hadronic matter.
" A substantial altenuation (""quenching"") of jets thus indicates the presence ofa dense deconfined medium "," A substantial attenuation (“quenching”) of jets thus indicates the presence of a dense deconfined medium \cite{Bj,Schiff}."
"We had called quarkonia and jets ""external probes.", We had called quarkonia and jets “external” probes.
 It is clear. however. (hat thev have to be produced in the same collision which leads to the QGP candidate to be probed.," It is clear, however, that they have to be produced in the same collision which leads to the QGP candidate to be probed."
 Thex are. however. produced (through very early bared interactions. which take place before the QGP is lormed.," They are, however, produced through very early hard interactions, which take place before the QGP is formed."
 We can then study the subsequent effect of the QGP on their behavior., We can then study the subsequent effect of the QGP on their behavior.
 Moreover. their initial production is to a large extent calculable by perturbative QCD. ancl it can be gauged in the study of pp ancl pel collisions. which presumably do not produce a QGP.," Moreover, their initial production is to a large extent calculable by perturbative QCD, and it can be gauged in the study of $pp$ and $pA$ collisions, which presumably do not produce a QGP."
 The QGP predicted by statistical QCD is the ultimate state of matter to be studied in hieh energv nuclear collisions., The QGP predicted by statistical QCD is the ultimate state of matter to be studied in high energy nuclear collisions.
 This is a speculative endeavor. since il is not clear to what extent such collisions can produce something to be called matter.," This is a speculative endeavor, since it is not clear to what extent such collisions can produce something to be called matter."
 We therefore close our survev with three questions to (he next generation of experiments which might help us in finding an answer to this Iundamental enigma., We therefore close our survey with three questions to the next generation of experiments which might help us in finding an answer to this fundamental enigma.
 If an increase of collision energv indeed leads to (he production of a hotter bubble of deconlined. primordial matter. then (his must expand more in order (o reach the," If an increase of collision energy indeed leads to the production of a hotter bubble of deconfined primordial matter, then this must expand more in order to reach the"
"the input rotation, but the exact shape of the rotation curve is different from the expected (e.g., cross-correlation 16), but in most cases the rotation shows much less latitudinal variation than expected based on the input rotation.","the input rotation, but the exact shape of the rotation curve is different from the expected (e.g., cross-correlation 16), but in most cases the rotation shows much less latitudinal variation than expected based on the input rotation."
" The surface DR measurements for model L1, shown in Fig. 5,,"," The surface DR measurements for model L1, shown in Fig. \ref{CC_solar},"
" cover slightly more than one activity cycle, which also includes a flip-flop event."," cover slightly more than one activity cycle, which also includes a flip-flop event."
 Similar phase in the cycle as in the map | is reached in the map 28., Similar phase in the cycle as in the map 1 is reached in the map 28.
 Clear evolution in the surface rotation patterns are seen throughout the cycle., Clear evolution in the surface rotation patterns are seen throughout the cycle.
 In general the shape of the surface rotation pattern over the latitude can be divided into four parts., In general the shape of the surface rotation pattern over the latitude can be divided into four parts.
" Closest to the equator the surface rotation follows the internal rotation law, and in most maps three abrupt changes in the surface rotation occur at higher latitudes."," Closest to the equator the surface rotation follows the internal rotation law, and in most maps three abrupt changes in the surface rotation occur at higher latitudes."
 Clear evolution in the latitude at which the breaks occur is seen over the activity cycle., Clear evolution in the latitude at which the breaks occur is seen over the activity cycle.
 When the cycle advances the breaks drift towards the higher latitudes., When the cycle advances the breaks drift towards the higher latitudes.
" Even at the point that the spots move to lower latitude, the breaks continue drifting towards the polar regions."," Even at the point that the spots move to lower latitude, the breaks continue drifting towards the polar regions."
 The highest latitudes for the breaks are obtained just before the time when the second spot starts to appear in the flip-flop event., The highest latitudes for the breaks are obtained just before the time when the second spot starts to appear in the flip-flop event.
" When the breaks abruptly move towards the equator again, the rotation measurements for the lower latitudes become less ordered and appear chaotic."," When the breaks abruptly move towards the equator again, the rotation measurements for the lower latitudes become less ordered and appear chaotic."
 In this model the axisymmetric dynamo wave is not only a poleward migration as indicated in Fig. 2.., In this model the axisymmetric dynamo wave is not only a poleward migration as indicated in Fig. \ref{sketch}.
 It starts at the bottom of the convection zone at 30° latitude and expands outwards in radius and latitude., It starts at the bottom of the convection zone at $30\degr$ latitude and expands outwards in radius and latitude.
 For lower latitudes the expansion along the non-axisymmetric spiral gives now a counter clockwise acceleration., For lower latitudes the expansion along the non-axisymmetric spiral gives now a counter clockwise acceleration.
 This leads to the qualitative agreement with the stellar rotation law near the equator., This leads to the qualitative agreement with the stellar rotation law near the equator.
 The effect depends on the expansion speed and the pitch angle of the underlying non-axisymmetric field., The effect depends on the expansion speed and the pitch angle of the underlying non-axisymmetric field.
 For the rotation law dependent small pitch angle near the equator this is a huge effect., For the rotation law dependent small pitch angle near the equator this is a huge effect.
 At higher latitudes the spot motion is determined by the field geometry and the migration speed of the poleward moving dynamo wave and therefore the rotation is reduced by the clockwise motion of the spot along the spiral., At higher latitudes the spot motion is determined by the field geometry and the migration speed of the poleward moving dynamo wave and therefore the rotation is reduced by the clockwise motion of the spot along the spiral.
 At the very polar region the wave moves slower and the rotation appears again faster., At the very polar region the wave moves slower and the rotation appears again faster.
 This behaviour depends on the phase of the cycle., This behaviour depends on the phase of the cycle.
" If the field reversal between two cycles lies at mid latitudes (50°) we see the rotation of the non-axisymmetric field, which coincides here with the stellar rotation (cf."," If the field reversal between two cycles lies at mid latitudes $50\degr$ ) we see the rotation of the non-axisymmetric field, which coincides here with the stellar rotation (cf."
 Cross-correlation | to 5 and 26 to 30)., Cross-correlation 1 to 5 and 26 to 30).
ejecta-CSM contribution before maximum light.,ejecta-CSM contribution before maximum light.
" In each figure, the “[exp] ejecta-CSM fit w/o gap"" line shows how the SN ejecta-CSM interaction would continue if the density profile remained the same."," In each figure, the “[exp] ejecta-CSM fit w/o gap” line shows how the SN ejecta-CSM interaction would continue if the density profile remained the same."
 Both lines significantly disagree with the earliest light curve point., Both lines significantly disagree with the earliest light curve point.
 This is consistent with our earlier conclusion that the light curve is dominated by the SN until near maximum light., This is consistent with our earlier conclusion that the light curve is dominated by the SN until near maximum light.
 The massive CSM and spatial extent inferred for SN 2002ic are surprisingly similar to certain PPNe and the atmospheres of very late red giant stars evolving to PPNe., The massive CSM and spatial extent inferred for SN 2002ic are surprisingly similar to certain PPNe and the atmospheres of very late red giant stars evolving to PPNe.
 Such structures are normally short-lived (less than or on the order of 1000 years)., Such structures are normally short-lived (less than or on the order of $1000$ years).
 The polarization seen by suggests the presence of a disk-like structure surrounding SN 2002ic., The polarization seen by \citet{wang04} suggests the presence of a disk-like structure surrounding SN 2002ic.
" Furthermore, the Ha luminosity and mass and size estimates suggest a clumpy medium."," Furthermore, the $\alpha$ luminosity and mass and size estimates suggest a clumpy medium."
" Combined with the evidence presented here for a possible transition region between a slow and fast wind, we are left with an object very similar to observed PPNe."," Combined with the evidence presented here for a possible transition region between a slow and fast wind, we are left with an object very similar to observed PPNe."
 We encourage more detailed radiative hydrodynamic modeling of SNe Ia in a surrounding medium as our data provide valuable constraints on this important early-time phase., We encourage more detailed radiative hydrodynamic modeling of SNe Ia in a surrounding medium as our data provide valuable constraints on this important early-time phase.
 Of particular interest are bi-polar PPNe where a WD companion emits a fast wind that shapes the AGB star wind while simultaneously accreting (Soker&Rappaport2000) mass from the AGB star., Of particular interest are bi-polar PPNe where a WD companion emits a fast wind that shapes the AGB star wind while simultaneously accreting \citep{soker00} mass from the AGB star.
" Typical thermonuclear supernovae are believed to have accretion time scales of 10’ years, yet several SNe Ia (SN 2002ic and possibly SN 1988Z, SN 1997cy, and SN 1999E) out of several hundred have been observed to show evidence for significant CSM."," Typical thermonuclear supernovae are believed to have accretion time scales of $10^{7}$ years, yet several SNe Ia (SN 2002ic and possibly SN 1988Z, SN 1997cy, and SN 1999E) out of several hundred have been observed to show evidence for significant CSM."
" If the presence of a detectable CSM is taken as evidence that these SNe exploded within a particular ~1000 year-period in their respective evolution, such as the PPN phase, this coincidence would imply a factor of ~100 enhancement (107 years /1000 years /100) in the supernova explosion rate during this period."," If the presence of a detectable CSM is taken as evidence that these SNe exploded within a particular $\sim1000$ year-period in their respective evolution, such as the PPN phase, this coincidence would imply a factor of $\sim100$ enhancement $10^7$ years $ /
1000$ years $/100$ ) in the supernova explosion rate during this period."
 Thus we suggest that it is not a coincidence that the supernova explosion is triggered during this phase., Thus we suggest that it is not a coincidence that the supernova explosion is triggered during this phase.
 The supernova 2002ic exhibits the light curve behavior and hydrogen emission of a Type IIn supernova after maximum but was spectroscopically identified as a Type Ia supernova near maximum light., The supernova 2002ic exhibits the light curve behavior and hydrogen emission of a Type IIn supernova after maximum but was spectroscopically identified as a Type Ia supernova near maximum light.
 The additional emission is attributed to a contribution from surrounding CSM., The additional emission is attributed to a contribution from surrounding CSM.
 This emission remains quite significant ~11 months after the explosion., This emission remains quite significant $\sim$ 11 months after the explosion.
 The discovery of dense CSM surrounding a Type Ia supernova strongly favors the binary nature of Type Ia progenitor systems to explain the simultaneous presence of at least one degenerate object and substantial material presumably ejected, The discovery of dense CSM surrounding a Type Ia supernova strongly favors the binary nature of Type Ia progenitor systems to explain the simultaneous presence of at least one degenerate object and substantial material presumably ejected
wilh the rest where we do not show the dependence on / in the integrals.,with the rest where we do not show the dependence on $t$ in the integrals.
 We remark in particular that this rest is formally equal to zero if 42=I. To guarantee (he existence of continuous solutions when z=0. we will assume later (112) which guarantees the non-negativitv on the second term of the left hand side of inequality (3.17)). Coming back (o a rigorous statement. we will prove the following result.," We remark in particular that this rest is formally equal to zero if $\varphi\equiv
1$ To guarantee the existence of continuous solutions when $\e=0$, we will assume later $(H2)$ which guarantees the non-negativity on the second term of the left hand side of inequality \ref{EM:eq:entropie}) Coming back to a rigorous statement, we will prove the following result."
 For the proof of Proposition 3.1.. we need the following technical lemma:," For the proof of Proposition \ref{EM:lemme:entro}, we need the following technical lemma:"
fiber would cover a distance of 6 kpc at the median redshift of the AGES sample (z= 0.26) and the fiber would be placed at the center of the target galaxy.,fiber would cover a distance of 6 kpc at the median redshift of the AGES sample $z = 0.26$ ) and the fiber would be placed at the center of the target galaxy.
 Thus our BPT classification would be sensitive to the nuclear flux from the AGN but could miss the emission lines contributions from star-forming regions outside the fiber., Thus our BPT classification would be sensitive to the nuclear flux from the AGN but could miss the emission lines contributions from star-forming regions outside the fiber.
" In the case that star formation dominates the global optical emission but an AGN dominates the emission within the fiber, the global 24 wm flux could in fact be dominated by the emission from star-forming activity and excluding such objects would lead to an underestimation of the star formation rate."," In the case that star formation dominates the global optical emission but an AGN dominates the emission within the fiber, the global 24 $\micron$ flux could in fact be dominated by the emission from star-forming activity and excluding such objects would lead to an underestimation of the star formation rate."
 We therefore investigate the origin of mid-IR emissions from the optically selected AGN by studying the IRAC colors of these AGN., We therefore investigate the origin of mid-IR emissions from the optically selected AGN by studying the IRAC colors of these AGN.
" Using IRAC photometry from the IRAC Shallow Survey (6” aperture, Section ?7)), we study the [3.6 wm] — [4.5 um] versus [5.8 pm] — [8.0 um] color-color diagram (hereafter, [3.6]—[4.5] and [5.8]— [8.0], for optically selected AGN 3,, left). The respec"," Using IRAC photometry from the IRAC Shallow Survey $^{\prime\prime}$ aperture, Section \ref{sec:data}) ), we study the [3.6 $\micron$ ] $-$ [4.5 $\micron$ ] versus [5.8 $\micron$ ] $-$ [8.0 $\micron$ ] color-color diagram (hereafter, $-$ [4.5] and $-$ [8.0], respectively) for optically selected AGN (Figure \ref{AGN_diagplot_IRAC}, left)."
"tively)color-color diagram can be used to (Figureidentify MIR aromatic emission characteristic of star formation activity (Smithetal.2007;Shi2007),, because the strongest aromatic features at 6.2, 7.7, and 8.6 jm fall into the 8.0 jum band (channel 4; ~ 6.2 — 10 pm) at redshifts 0.0€z<0.5."," The color-color diagram can be used to identify MIR aromatic emission characteristic of star formation activity \citep{JDSmith07, Shi07}, because the strongest aromatic features at 6.2, 7.7, and 8.6 $\micron$ fall into the 8.0 $\micron$ band (channel 4; $\simeq$ 6.2 $-$ 10 $\micron$ ) at redshifts $0.0 \leq z \leq 0.5$."
" This behavior results in a redder [5.8]—[8.0] color for objects with MIR aromatic emission, which also implies that the MIR emission of these objects is dominated by star formation."," This behavior results in a redder $-$ [8.0] color for objects with MIR aromatic emission, which also implies that the MIR emission of these objects is dominated by star formation."
 The empirical color boundary that separates the aromatic and non-aromatic region is — ~1 (Brandetal.2009)., The empirical color boundary that separates the aromatic and non-aromatic region is $-$ [8.0] $\simeq 1$ \citep{Brand09}.
. We found optically selected [5.8][8.0]AGN distributed across the full range of [5.8]—[8.0] color., We found optically selected AGN distributed across the full range of $-$ [8.0] color.
" However, if we further separate optically selected AGN into those detected at 24 wm and those that are not, they"," However, if we further separate optically selected AGN into those detected at 24 $\micron$ and those that are not, they"
First of all. we mention that. since we are not solving the radiative transfer problem. our results have to be considered as complementary informations to the models taking into account radiative transfer without collisions and realistic multilevel models.,"First of all, we mention that, since we are not solving the radiative transfer problem, our results have to be considered as complementary informations to the models taking into account radiative transfer without collisions and realistic multilevel models."
 We introduce the collisional effect together with radiative rates and we determine the emergent fractional polarization in the limit of tangential observation in a plane-parallel atmosphere where the cosine of the heliocentric angle Hx., We introduce the collisional effect together with radiative rates and we determine the emergent fractional polarization in the limit of tangential observation in a plane-parallel atmosphere where the cosine of the heliocentric angle $\mu$ $\simeq$ 0.
 If we calculate the polarization in the framework of the 5 levels-5 lines model as a function of the neutral hydrogen density ny (see Fig. 3).," If we calculate the polarization in the framework of the 5 levels-5 lines model as a function of the neutral hydrogen density $_\textrm{\scriptsize{H}}$ (see Fig. \ref{PoverPmax}) ),"
 one could remark that collisions start to play a notable role for my~3x10? em., one could remark that collisions start to play a notable role for $n_{\textrm {\scriptsize H}} \sim 3 \times 10^{13}$ $^{-3}$.
 The alignment of the metastable levels Dis and ος. start to diminish due to collisions and thus the polarization of the line at 44554 decreases., The alignment of the metastable levels $^2D_{3/2}$ and $^2D_{5/2}$ start to diminish due to collisions and thus the polarization of the line at ${\lambda}4554$ decreases.
 Indeed. for ny~3x10? em. the ratio of the polarization degree p divided by the polarization Όρων Is ~ 0.9 Ce. a collisional depolarization of ~ 10%)).," Indeed, for $n_{\textrm {\scriptsize H}} \sim 3 \times 10^{13}$ $^{-3}$ , the ratio of the polarization degree $p$ divided by the zero-collisions polarization $p_{max}$ is $\sim$ 0.9 (i.e. a collisional depolarization of $\sim$ )."
 However. in the framework of the simplified model (Fig. 1)).," However, in the framework of the simplified model (Fig. \ref{figure1}) ),"
 a collisional depolarization of ~ of the 4554 line is attempted only where ng~3x10? cmos (ie. ~ 100 times larger)., a collisional depolarization of $\sim$ of the ${\lambda}4554$ line is attempted only where $n_{\textrm {\scriptsize H}} \sim 3 \times 10^{15}$ $^{-3}$ (i.e. $\sim$ 100 times larger).
 This is because the upper level P; of the 44554 line start to be affected by collisions solely for densities ny>10? em (see Fig. 3))., This is because the upper level $^2P_{3/2}$ of the ${\lambda}4554$ line start to be affected by collisions solely for densities $_\textrm{\scriptsize{H}}> 10^{15}$ $^{-3}$ (see Fig. \ref{PoverPmax}) ).
 An estimate height of formation of the 24554 line is /7~800 km which corresponds to a neutral hydrogen density ny~2x10! em7* and a temperature of theformation of the lines T~ 5350K (e.g. model C of Vernazza et al., An estimate height of formation of the ${\lambda}4554$ line is $h \sim 800$ km which corresponds to a neutral hydrogen density $n_{\textrm {\scriptsize H}} \sim 2 \times 10^{14}$ $^{-3}$ and a temperature of theformation of the lines $T \sim$ 5350K (e.g. model C of Vernazza et al.
 1981)., 1981).
 In these typical conditions of formation of, In these typical conditions of formation of
Iu the ast few vears. a burst of new information on cosmic abundances. provided by high-resolution spectra of very netalOOF stars In the halo jas hada considerable iupact Ou our understanding of bohi stellar uucleosvuthesis aud he chemical eurichiueut of the primordia interstellar nediuu (ISM).,"In the last few years, a burst of new information on cosmic abundances, provided by high-resolution spectra of very metal-poor stars in the halo has had a considerable impact on our understanding of both stellar nucleosynthesis and the chemical enrichment of the primordial interstellar medium (ISM)."
 Iu. particuar. it is in the halo of the Alilky Wav that the oldest aud most metal-voor stars dn he Universe are observable. born at times («y equivaleu redshiTs) still οιt of reaci of the deepes suvevs of omnordial galaxies.," In particular, it is in the halo of the Milky Way that the oldest and most metal-poor stars in the Universe are observable, born at times (or equivalent redshifts) still out of reach of the deepest surveys of primordial galaxies."
 Several tCalls (0.0.TT) have studied the ολοσα conpositiou of liao lnetal-poor stars (stars with less than B00 down to 1710000 the solar iron abuudauce).," Several teams \citep[e.g.][]{cayrel04,cohen07,bark05,aok07} have studied the chemical composition of halo metal-poor stars (stars with less than 1/300 down to 1/10000 the solar iron abundance)."
 These ow-lnass stars have lifetimes comparable to the age of he Universe. an they retain in thei atmospheres the eleiieutal abundances of the eas at the time of their irth.," These low-mass stars have lifetimes comparable to the age of the Universe, and they retain in their atmospheres the elemental abundances of the gas at the time of their birth."
 Hence. these stars contain a mecuorv of the unique incleosvuthesis contribution of the first stellar generations o the eurichinent of the ISM. offeriug a local beuchinark. or cosmologv.," Hence, these stars contain a memory of the unique nucleosynthesis contribution of the first stellar generations to the enrichment of the ISM, offering a local benchmark for cosmology."
 These massive stars are ong dead but there are hopes of observing them directly in very lieh-+vedshitt ealaxies., These massive stars are long dead but there are hopes of observing them directly in very high-redshift galaxies.
 The current way to constraii the properties of he first ecucratiois of stars and check whether the very different priuordial environment has produced noticeable effects conccnius their properties is to searci for their Hupriuts ou he okest extremely meal-poor stars (EAIPs) in our ealacic hak), The current way to constrain the properties of the first generations of stars and check whether the very different primordial environment has produced noticeable effects concerning their properties is to search for their imprints on the oldest extremely metal-poor stars (EMPs) in our galactic halo.
 Receutly ἃ saldde of EMP ([Fe/TI|= 3) halo stars has become avallable., Recently a sample of EMP $\leq -3$ ) halo stars has become available.
" Using UVES on he VLT. ? provided abundance Leasclucuts of maprececented accuracy for several elements 1 ra fairly large sample of uctal-poor stays (to¢istinguishfrou.tιοC-richEXIPstars.see δν,"," Using UVES on the VLT, \citet{cayrel04} provided abundance measurements of unprecedented accuracy for several elements in a fairly large sample of metal-poor stars \citep[to distinguish from the C-rich EMP stars, see][]{beers05}."
 Their data have revealed a striking homogeneity in the chemical properties of halo stars., Their data have revealed a striking homogeneity in the chemical properties of halo stars.
 In particular. a very low scatter for the [a/Fe| ratios was fouud.," In particular, a very low scatter for the $\alpha$ /Fe] ratios was found."
 Iu a subsequent paper. the authors (7T.2hereafterS05) again report some unexpected results. namely: these same metal-poor stars show a high N/O ratio sugeestingOO high evels of prodiction of primary nitrogen iu massive stars (see below).," In a subsequent paper, the authors \citep[, hereafter S05]{spite05} again report some unexpected results, namely: these same metal-poor stars show a high N/O ratio suggesting high levels of production of primary nitrogen in massive stars (see below)."
 Furthermore. a larec scatter in their N/O ratios (iuuch arecr than their quoted error bars) was oud.," Furthermore, a large scatter in their N/O ratios (much larger than their quoted error bars) was found."
 S05 al«» report a slight incruse in the C/O of the sue stars wit1 decreasing uetallicity., S05 also report a slight increase in the C/O of the same stars with decreasing metallicity.
 As discussed in 77?7.. the data of S05 happen to ο in a very interesting ictalicitvorange: at such low netallicities. t101 Observer stars are probably made of ouly massive star ejecta diluted ba* the prinunordial ISM.," As discussed in \citet{chiap05,chiap06a,chiap06b}, the data of S05 happen to be in a very interesting metallicity range: at such low metallicities, their observed stars are probably made of only massive star ejecta diluted by the primordial ISM."
 Iudeed. chemical evoution modes (CEA) of he halo (77?) show that an& AL: star dies at |Fe/UJ~ 3.5.," Indeed, chemical evolution models (CEM) of the halo \citep{chiap06a,pran03} show that an 8 $M_{\sun}$ star dies at [Fe/H] $\sim -3.5$."
 This means tat. below this metalliciv. he ISAL is enriched exclusively DV lnassive stius.," This means that, below this metallicity, the ISM is enriched exclusively by massive stars."
" AMore«JVOY. according to these models t1ο contribution of AGB stars is negligible below [Fe/T| 2,5,"," Moreover, according to these models the contribution of AGB stars is negligible below [Fe/H] $\sim -2.5$."
 More imptaut. these theoretical predictions ποσα to be confiiied by VOYV recent observalous.," More important, these theoretical predictions seem to be confirmed by very recent observations."
" 7 have show1 tiat the ο... 2 ""Me ratios in halo dwarts are low and that AGB stars woul Lhave plaved a minor role below [Fe/T]] ~35.40."," \citet{mel07} have shown that the $^{25,26}$ $^{24}$ Mg ratios in halo dwarfs are low and that AGB stars would have played a minor role below [Fe/H] $\sim -2.0$."
 If AGB indeed had not had enough time to coutribte to the ISM euricliment at such low metallicities aud laassive stAUS are LO producers of primary nitrogen (asprecicted1ostandardstellarnocdels.e.g..?).. one woud expect to obscrve a decline in the N/O or N/Fe ratios towards low Z. coutrary to wiat has been fouud by S05.," If AGB indeed had not had enough time to contribute to the ISM enrichment at such low metallicities and massive stars are not producers of primary nitrogen \citep[as predicted by standard stellar models, e.g.,][]{whw02}, one would expect to observe a decline in the N/O or N/Fe ratios towards low $Z$, contrary to what has been found by S05."
" Ieicc. t1e high leve sof N/O observed i halo stars have to be a result of t1ο nucleosvuthesis taking place in the metal)OOr Massive stars. osieoosting a revision of standard niocels for the uncleosvutLOIS dmn lnassive stars,"," Hence, the high levels of N/O observed in halo stars have to be a result of the nucleosynthesis taking place in the metal-poor massive stars, suggesting a revision of standard models for the nucleosynthesis in massive stars."
 The effecS of stellar axial rotation aro nunierotis and at low netallicity iav lead to a clastic revision of current wisdom (sec??)..," The effects of stellar axial rotation are numerous and at low metallicity may lead to a drastic revision of current wisdom \citep[see][]{mem06,hir07}."
 The stellar models of he Geneva erou» includiug rotation (77).. have proved to be successful iu explaining some observations that could uot be explained by noncotatius models. namely. he observed imuuber ratio of Wolf Ravet stars to O-tvpo stars," The stellar models of the Geneva group, including rotation \citep{mm00,mm01}, have proved to be successful in explaining some observations that could not be explained by non-rotating models, namely, the observed number ratio of Wolf Rayet stars to O-type stars"
Space Research Institute. 117997. Prolsovuznava st.,"Space Research Institute, 117997, Profsoyuznaya st."
 84/32. Moscow. (doraumx.ikiassi.) We propose a general physical mechanism which could contribute to the formation of fast. line-driven outflows at the vicinity of strong gravitational fielcl sources.," 84/32, Moscow, (doramx.iki.rssi.ru) We propose a general physical mechanism which could contribute to the formation of fast line-driven outflows at the vicinity of strong gravitational field sources."
 We argue that the gradient of the gravitational potential plavs (he same role as the velocity gradient plavs in Sobolev approximation., We argue that the gradient of the gravitational potential plays the same role as the velocity gradient plays in Sobolev approximation.
 Both Doppler effect and gravitational redshifting are taken into account in Sobolev approximation., Both Doppler effect and gravitational redshifting are taken into account in Sobolev approximation.
 The radiation force becomes a function of the local velocity eracdient and the gradient of the gravitational potential., The radiation force becomes a function of the local velocity gradient and the gradient of the gravitational potential.
 The derived equation ol motion has a critical point that is different from (that of CAIx., The derived equation of motion has a critical point that is different from that of CAK.
 A solution that is continuous through the singular point obtained! numerically., A solution that is continuous through the singular point obtained numerically.
 A comparison with CAK theory is presented., A comparison with CAK theory is presented.
 It is shown that the developed theory predicts terminal velocities which are greater than those obtained [from the CAI theory., It is shown that the developed theory predicts terminal velocities which are greater than those obtained from the CAK theory.
 hvdrodynamies - quasars: general - radiation mechanisis Acceleration of matter due to radiation pressure in lines plavs an important role in formation of outflows from hot stars and possibly from active galactic, hydrodynamics - quasars: general - radiation mechanisms Acceleration of matter due to radiation pressure in lines plays an important role in formation of outflows from hot stars and possibly from active galactic
"the trend that objects where AL, estimates exceed Maya have relaxation times shorter than the Hubble time.",the trend that objects where $M_{*}$ estimates exceed $M_{\mathrm{dyn}}$ have relaxation times shorter than the Hubble time.
 This trend is similar to that presented. in Fig 12 of ?.. but in our case the dynamical mass-to-light ratios are normalised bv the stellar ones.," This trend is similar to that presented in Fig 12 of \citet{Mieske+08}, but in our case the dynamical mass-to-light ratios are normalised by the stellar ones."
 Ht suggests that [or some of the least massive UCDs dynamical evolution is sulliciently advanced to have experienced. preferential loss of low mass stars and a corresponding Hattening of the low-mass stellar mass function. such that we overestimate stellar masses assuming -- to have the WKroupa IME. shape.," It suggests that for some of the least massive UCDs dynamical evolution is sufficiently advanced to have experienced preferential loss of low mass stars and a corresponding flattening of the low-mass stellar mass function, such that we overestimate stellar masses assuming it to have the Kroupa IMF shape."
 We notice that at the same time very little. if any. dark mass bevond a canonical Kroupa EME is required to explain 10 dyvnamical AJ/L ratios of the more massive UCDs investigated here.," We notice that at the same time very little, if any, dark mass beyond a canonical Kroupa IMF is required to explain the dynamical $M/L$ ratios of the more massive UCDs investigated here."
 Since the massive UCDs described in this μαμον are dynamically un-evolved. the mass segregation and »ossible tidal stripping of low-mass stars should not alfect vm.," Since the massive UCDs described in this study are dynamically un-evolved, the mass segregation and possible tidal stripping of low-mass stars should not affect them."
" Therefore. we can rule out very bottom heavy λος ike in ον, whieh would. correspond to 50 per cent. larger stellar masses and hence imply negative dark matter fraction or all investigated sources."," Therefore, we can rule out very bottom heavy IMFs like in \citet{Salpeter55}, which would correspond to 50 per cent larger stellar masses and hence imply negative dark matter fraction for all investigated sources."
 There have been various claims in the recent literature regarding a possible variation or invariance of the IME ab cosmological clistances., There have been various claims in the recent literature regarding a possible variation or invariance of the IMF at cosmological distances.
 While 2? argue against a Àtom heavy Salpeter type IME at veh redshift. other gravitational lens results do favour a bottom-heavy Salpeter IME (222).," While \citet{Cappellari+06,FSB08} argue against a bottom heavy Salpeter type IMF at high redshift, other gravitational lens results do favour a bottom-heavy Salpeter IMF \citep{Treu+10,Auger+10,GG10}."
 Our result for the investigated Fornax UCDs is rence in line with the former studies., Our result for the investigated Fornax UCDs is hence in line with the former studies.
 A caveat is that the ALL ratios of UCDs appear to vary svstematically amongst cilferent environments (?).., A caveat is that the M/L ratios of UCDs appear to vary systematically amongst different environments \citep{Mieske+08}.
 Phe case may indeed be dillerent or Virgo UCDs which show on average some 40 per cent ugher M/L at comparable metallicity and age. ancl which rence appear good candidates for an IME that deviates from he Ixroupa form (7 )..," The case may indeed be different for Virgo UCDs which show on average some 40 per cent higher M/L at comparable metallicity and age, and which hence appear good candidates for an IMF that deviates from the Kroupa form \citep{DHK08}. ."
 Three objects in our sample. £-1 (UCD 2). £-19 (UCD 3). and £-24(UCD 4). have published measurements of internal," Three objects in our sample, $F$ -1 (UCD 2), $F$ -19 (UCD 3), and $F$ -24(UCD 4), have published measurements of internal"
evenis wilh pulse height invariant channel (PI) equal to 0. 1. or 1024 were removed as they represent unphysical signals: hot CCD columns ancl pixels were removed using (he stundaxd table provided by the Chandra X-ray Center (CAC).,"events with pulse height invariant channel (PI) equal to 0, 1, or 1024 were removed as they represent unphysical signals; hot CCD columns and pixels were removed using the standard table provided by the Chandra X-ray Center (CXC)."
 Short term (ransients due to cosnic ravs Which produced events in (ree or more consecutive frames (hat could mimic a point source (van Spevbroeck 2000. private communication) also were removed.," Short term transients due to cosmic rays which produced events in three or more consecutive frames that could mimic a point source (van Speybroeck 2000, private communication) also were removed."
 Cen A was observed twice. on December 5. 1999 and May. 17. 2000. with the ACIS-I instrument.," Cen A was observed twice, on December 5, 1999 and May 17, 2000, with the ACIS-I instrument."
 The exposure times for the (wo observations (ODSIDs 00316 and 00962) were 35856 s and 36510 s. The data were examined for periods of high background or problems wilh (he aspect solution. but none were found.," The exposure times for the two observations (OBSIDs 00316 and 00962) were 35856 s and 36510 s. The data were examined for periods of high background or problems with the aspect solution, but none were found."
" The aspect solution lor observations is generally good to 2"" or better CAlderofte£al2000).. but we have independently verified the aspect solution of both data sets by comparing the positions of X-ray point sources al the edge of the field of view with stellar positions tabulated in the USNO A2.0 catalog 1993).. and estimate that our absolute astrometrv is accurate (ο within e0.5"" 2001)."," The aspect solution for observations is generally good to $2''$ or better \citep{ald00}, but we have independently verified the aspect solution of both data sets by comparing the positions of X-ray point sources at the edge of the field of view with stellar positions tabulated in the USNO A2.0 catalog \citep{mon98}, and estimate that our absolute astrometry is accurate to within $\sim0.5''$ \citep{kra01}."
. The FOV for each of the observations ancl the position of best locus is shown in Figure 1. superimposed on an optical DSs image., The FOV for each of the observations and the position of best focus is shown in Figure \ref{fov} superimposed on an optical DSS image.
" The raw. co-added X-ray image in the 0.4-5 keV bandpass binned at 2"" per pixel is shown in Figure 2.."," The raw, co-added X-ray image in the 0.4-5 keV bandpass binned at $2''$ per pixel is shown in Figure \ref{xraw}."
 The nucleus is clearly. visible. along with the X-ray. jet extending to the NE. many point sources. emission [from the hot ISM. and emission coincident with the SW racio lobe.," The nucleus is clearly visible, along with the X-ray jet extending to the NE, many point sources, emission from the hot ISM, and emission coincident with the SW radio lobe."
 This image has not been exposure corrected., This image has not been exposure corrected.
 The radial stripes pointing from the nucleus are (he result of removing the frame transfer streak caused by. oul of time events., The radial stripes pointing from the nucleus are the result of removing the frame transfer streak caused by out of time events.
 The other linear features around the image are gaps between (he various CCDs in one or the other of the exposures., The other linear features around the image are gaps between the various CCDs in one or the other of the exposures.
 An adaptively smoothed. co-added. exposure-corrected. X-ray image of Cen A in the 1-3 keV band is shown in Figure 3..," An adaptively smoothed, co-added, exposure-corrected X-ray image of Cen A in the 1-3 keV band is shown in Figure \ref{cena}."
 We also use radio observations of Cen A made at 3.4 GlIIz between October 1990 and November 1991 with the NRAO Verv Large Array(VLA)!.. consisting of approximately two hours on-source integration time in each of the A. DB. C and DnC arrays.," We also use radio observations of Cen A made at 8.4 GHz between October 1990 and November 1991 with the NRAO Very Large Array, consisting of approximately two hours on-source integration time in each of the A, B, C and DnC arrays."
" The data were reduced in the standard manner using AIPS and then combined (after correcting for variations in (he flux density of the core) to produce a single ue dataset. sensitive to structure with a largest scale of ~100"" and with a maximal resolution of 0.9""x0.2""."," The data were reduced in the standard manner using AIPS and then combined (after correcting for variations in the flux density of the core) to produce a single $uv$ dataset, sensitive to structure with a largest scale of $\sim 100''$ and with a maximal resolution of $0.9'' \times 0.2''$."
 The radio maps presented in (his paper are all made from (his fill dataset with appropriate tapering and weiehting of the «e plane., The radio maps presented in this paper are all made from this full dataset with appropriate tapering and weighting of the $uv$ plane.
 The nominal dnanmic range of the maps (peak to offl-source r.m.s., The nominal dynamic range of the maps (peak to off-source r.m.s.
 noise) is about 107. but their fidelity is limited by residual phase and amplitude artifacts about the 7 Jv core.," noise) is about $^4$, but their fidelity is limited by residual phase and amplitude artifacts about the 7 Jy core."
 We compared the position of the radio core in (his data set with its, We compared the position of the radio core in this data set with its
The area of background sky within which a galaxy would be detectable in cach cluster was determined. from a map of the magnification in the source plane. derived using the LENSTOOL models.,"The area of background sky within which a galaxy would be detectable in each cluster was determined from a map of the magnification in the source plane, derived using the LENSTOOL models."
 This quautitv is also a weak. function of redshift for οκ21., This quantity is also a weak function of redshift for $z_s \gs 1$.
" The area of the source plane behind each cluster that lies within the SCUBA field of view andl is maenified by a factor ereater than p. id. is shown in Ll. as an example for +,=2."," The area of the source plane behind each cluster that lies within the SCUBA field of view and is magnified by a factor greater than $\mu$, $A_>$, is shown in 1, as an example for $z_s=2$."
 Due to the maenification. AL. is sinaller than the SCUBA field of view.," Due to the magnification, $A_>$ is smaller than the SCUBA field of view."
" A ealaxy with a flux density S in the source plane will appear in the nage plane of a particular cluster above a detection threshold S$,,4, 1£ it is magnified bv a actor ercater than jp=Suan/S.", A galaxy with a flux density $S$ in the source plane will appear in the image plane of a particular cluster above a detection threshold $S_{\rm min}$ if it is magnified by a factor greater than $\mu = S_{\rm min}/S$.
 The area in the source aue within which such a galaxy would be detected in that cluster is thus el.(Siyin/S. 2).," The area in the source plane within which such a galaxy would be detected in that cluster is thus $A_>(S_{\rm min}/S, z)$ ."
 The flux density hreshold σι aud the form of 4A are different for cach cluster., The flux density threshold $S_{\rm min}$ and the form of $A_>$ are different for each cluster.
 By dividing the ummber of detected galaxies IN o» the suu of the areas Aw(Synιτ). for all seven clusters. the cwunuulative count IN(Sit)NWS.MNALσµµμο.2) is found.," By dividing the number of detected galaxies $N_{\rm raw}$ by the sum of the areas $A_>(S_{\rm min}/S, z)$ for all seven clusters, the cumulative count $N(>S, z) \simeq N_{\rm raw}(>S, z) / \sum A_>(S_{\rm min}/S, z)$ is found."
 The count of identified oreeround field galaxies is then calculated iu the nonual way ancl added to the result., The count of identified foreground field galaxies is then calculated in the normal way and added to the result.
 The count was calculated indepeudently using this uecthod for redshifts :;=1. 2. 3 aud. L," The count was calculated independently using this method for redshifts $z_s=1$, 2, 3 and, 4."
 The spread in the results between these four cases as a function of Hux deusitv threshold is shown in Figure22., The spread in the results between these four cases as a function of flux density threshold is shown in 2.
 The results obtained from both the and samples at cach redshift are compared with the mean count iu cach sample., The results obtained from both the and samples at each redshift are compared with the mean count in each sample.
 The counts are remarkably consistent. reflecting partly hat the value of the power-law iudex 5 iu the count NosS)xSo isscL. indicating a small but positive naenification bias.," The counts are remarkably consistent, reflecting partly that the value of the power-law index $\gamma$ in the count $N(> S) \propto S^\gamma$ is $\gamma \ls -1$, indicating a small but positive magnification bias."
 The redshitt-dependent scatter within he results obtained using both the aud samples is never more than 30%., The redshift-dependent scatter within the results obtained using both the and samples is never more than .
. Averaged over the range of flux densities from 0.5 to 8SnuuJw. the mean scatter is12%.," Averaged over the range of flux densities from 0.5 to mJy, the mean scatter is."
.. Providing that :;21 for backeround galaxies. as suggestedCoco by the initial spectroscopic results (Barecr et 1999). the systematic uncertaiuty iu the results due to the redshift distribution of the detected background.ο galaxies is expected to be smaller than the absolute calibration uncertainties in the SCUBA images.," Providing that $z_s \gs 1$ for background galaxies, as suggested by the initial spectroscopic results (Barger et 1999), the systematic uncertainty in the results due to the redshift distribution of the detected background galaxies is expected to be smaller than the absolute calibration uncertainties in the SCUBA images."
 These systematic uncertainties are inchided iu the reported errors., These systematic uncertainties are included in the reported errors.
 To reinforce this poiut. if the galaxies that are identified in the foreerouud of the clusters are assumed to be 12iidentified. and are actually background galaxies. then the counts at 5< 2uundy are expected to increase by about 0.50 with the brighter counts remaining the same.," To reinforce this point, if the galaxies that are identified in the foreground of the clusters are assumed to be mis-identified, and are actually background galaxies, then the counts at $S<2$ mJy are expected to increase by about $\sigma$ with the brighter counts remaining the same."
" If all the backerouud galaxies are assed to be at τν=L then the count at fux densities less than aud ereater than 21uuJy is expected to be reduced. aud increased by about 0.26. respectively,"," If all the background galaxies are assumed to be at $z_s=4$, then the count at flux densities less than and greater than mJy is expected to be reduced and increased by about $\sigma$, respectively."
 21un To confi the reliabilitv of the results from the direct Inversion we performed Monte Carlo simulations of our observations using a parametric model for the background ealaxy counts. and thus derived the best-fit paramcters by comparison with the observations.," 2mm To confirm the reliability of the results from the direct inversion we performed Monte Carlo simulations of our observations using a parametric model for the background galaxy counts, and thus derived the best-fit parameters by comparison with the observations."
 This technique has the advantage that we can explicitly include the incompleteness of our maps at faint flux densities aud so derive the counts separately for both the and sunples., This technique has the advantage that we can explicitly include the incompleteness of our maps at faint flux densities and so derive the counts separately for both the and samples.
 Calaxies were drawn from a population with a count described by a power-law model: Αιο).= AK(S/54)'., Galaxies were drawn from a population with a count described by a power-law model: $N(>S) = K (S/S_0)^\alpha$ .
 For each realization. we selected a value. of A and a and populated the source planes of the seven clusters at random for each of the four values of redshift used above., For each realization we selected a value of $K$ and $\alpha$ and populated the source planes of the seven clusters at random for each of the four values of redshift used above.
 The source planes were then mapped outo the image planes using the LENSTOOL models., The source planes were then mapped onto the image planes using the LENSTOOL models.
 The source catalogs derived from the areas of the image planes for each cluster covered by our SCUBA observations were them convolved with the appropriate incompleteness function determined by Sul et ((1998) to determine the uuuber of galaxies that would be detected in cach cluster in the aud samples., The source catalogs derived from the areas of the image planes for each cluster covered by our SCUBA observations were then convolved with the appropriate incompleteness function determined by Smail et (1998) to determine the number of galaxies that would be detected in each cluster in the and samples.
 One thousand realizations of this process were executed for cach set of model parameters να to derive a Monte Carlo estimate of the count of backerouud galaxies., One thousand realizations of this process were executed for each set of model parameters $K$ $\alpha$ ] to derive a Monte Carlo estimate of the count of background galaxies.
 As for the direct method. counts were calculated assuming 2.=1. 2. 3. aud Ll for the backerouud ealaxies.," As for the direct method, counts were calculated assuming $z_s = 1$, 2, 3, and 4 for the background galaxies."
" The predicted couuts from each cluster aud value of z, were then added and compared with the observed counts for all seven clusters. assume Poisson statistics. and the probability that the observed counts could beproduced from cach [A.6]| pairwas determined."," The predicted counts from each cluster and value of $z_s$ were then added and compared with the observed counts for all seven clusters, assuming Poisson statistics, and the probability that the observed counts could beproduced from each $K$ $\alpha$ ] pairwas determined."
 The most probable values of Jv aud à were determined at fux densities Sy 1. 2. aud παν.," The most probable values of $K$ and $\alpha$ were determined at flux densities $S_0=1$ , 2, and mJy."
 ΜΗ, 2mm
Fig.,Fig.
 l is 2.8. between the observations on M.JD-50000—3015 to 4234. while the SALARTS D band data produce a ratio of 3.14 between days 3950 and 4240.," \ref{lcs} is 2.8, between the observations on MJD-50000=3915 to 4234, while the SMARTS B band data produce a ratio of 3.14 between days 3950 and 4240."
 An even larger Lux ratio is shown on the period covered by the Wise Observatory data. when the B band Uux drops by a factor of 4 between 3571 and 3950.," An even larger flux ratio is shown on the period covered by the Wise Observatory data, when the B band flux drops by a factor of 4 between 3571 and 3950."
 Figure 6 shows the B band flux as a function of its nearest (less than 2 days apart) X-ray measurement. each normalised by the corresponding mean Εαν of the complete light curve.," Figure \ref{fluxflux_X_B} shows the B band flux as a function of its nearest (less than 2 days apart) X-ray measurement, each normalised by the corresponding mean flux of the complete light curve."
 The dots correspond to the long term. ~2-week sampled campaign covering 900 clavs. Wise Observatory data: the squares represent a shorter. 4-day sampling light curve covering 500 days. and the crosses represent the intensive monitoring data. sampled claily for 90 days.," The dots correspond to the long term, $\sim$ 2-week sampled campaign covering 900 days, Wise Observatory data; the squares represent a shorter, 4-day sampling light curve covering 500 days, and the crosses represent the intensive monitoring data, sampled daily for 90 days."
 The rest fitting linear relation for cach data set gets Latter for shorter time-scales probed: BY=LOTNYN O.1L for the ong term light curve (solid lines) B/B=O.TGON/N|0.24 for he intermediate (dashed lino) and 2/2=O.B9NYN|0.62 or the daily sampled. 90 day lone light curve (dotted line).," The best fitting linear relation for each data set gets flatter for shorter time-scales probed: $B/\bar B=1.07X/\bar X-0.11$ for the long term light curve (solid lines) $B/\bar B=0.76X/\bar X+0.24$ for the intermediate (dashed line) and $B/\bar B=0.39X/\bar X+0.62$ for the daily sampled, 90 day long light curve (dotted line)."
 This change in slope shows how the D and X-ray light curves. although always correlated. have dillerent time-scale »haviour. with rapid fluctuations being much stronger in he X-ray band and long term trends being stronger in the D band.," This change in slope shows how the B and X-ray light curves, although always correlated, have different time-scale behaviour, with rapid fluctuations being much stronger in the X-ray band and long term trends being stronger in the B band."
 The optical B and. V. band light curves from SNLATICES are almost identical in shape and only differ inthe amplitude of the Dluctuations., The optical B and V band light curves from SMARTS are almost identical in shape and only differ inthe amplitude of the fluctuations.
 Figure 7 shows the V [lux as a function of B flux for the same epoch. for the evenly 4-day sampled data and for the intensive monitoring sample. separately.," Figure \ref{fluxflux} shows the V flux as a function of B flux for the same epoch, for the evenly 4-day sampled data and for the intensive monitoring sample, separately."
 The flux-Hlux. plots are almost linear. following a relation V—(0.39820.005).|(1.0020.03)10 GA?=137 for τὸ cof) lor the non-intensive segments and =(03750.01)|(L3120.00)-10.Perg GA?=93.4 for 73 dof) for the intensive sampling data.," The flux-flux plots are almost linear, following a relation $V=(0.398\pm{0.005}) B+(1.09\pm
0.03)\times 10^{-12}$ $\chi^2=137$ for 79 dof) for the non-intensive segments and $V=(0.375\pm0.01) B+(1.31\pm 0.09)\times
10^{-12}$ $\chi^2=93.4$ for 73 dof) for the intensive sampling data."
 Notice that the short term light curve has a slightly Latter Ilux-Iux relation., Notice that the short term light curve has a slightly flatter flux-flux relation.
 Normalising each light curve to its mean before computing the Eux-ILux relation produces the relative changes of [lux in cach band: V/V=οτοῦ| 0.027.," Normalising each light curve to its mean before computing the flux-flux relation produces the relative changes of flux in each band: $V/\bar V= 0.75B/\bar B +0.027$ ,"
a transitional stage between CNO-dominated biydroseu-free WN stars. and a-burning dominated WC stars (?)..,"a transitional stage between CNO-dominated hydrogen-free WN stars, and $\alpha$ -burning dominated WC stars \citep*{Crowther1995a}."
 A confirination of culauced neon abundance in one of the transition objects would support this interpretation. but uufortunatelv anv neon in WRILS must be present asἘν ἂν expected from the strong Cluission the star exhibits.," A confirmation of enhanced neon abundance in one of the transition objects would support this interpretation, but unfortunately any neon in WR145 must be present as, as expected from the strong emission the star exhibits."
 As pointed out bv ?.. the use of neon abundauices as derived iu the previous section to coustrain true core-evolution nuclear processes ijs colplicated by the different enmüttiug reguues of the elements in question.," As pointed out by \citet{Dessart2000}, the use of neon abundances as derived in the previous section to constrain true core-evolution nuclear processes is complicated by the different emitting regimes of the elements in question."
 Because of their comparatively πια. radiative A cocficicnts. the fine structure lines originate further out in the wind than the heliun ciission. at densities near LPcn7.," Because of their comparatively small radiative $A$ coefficients, the fine structure lines originate further out in the wind than the helium emission, at densities near $10^5\,\mathrm{cm}^{-3}$."
 A dependence on precise mass loss rates aud (less problematic) terminal velocities also reduces the accuracy of direct. abundance measuremeuts. especially eiven the tendency of chuuping to modifv the measured AL by factors of 25.," A dependence on precise mass loss rates and (less problematic) terminal velocities also reduces the accuracy of direct abundance measurements, especially given the tendency of clumping to modify the measured $\dot{M}$ by factors of 2–5."
" A imnethod which overcomes these difficulties is available iu the παπιαποσο,", A method which overcomes these difficulties is available in the abundance.
 Since both aaud ooriginate[Ne 11]in roughly the same region of the wind. the abundance ratio derived from them should he independent of details of the wind structure. and remove any attendant svsteiiatie errors in estimating the mass loss rate. distance. and bulk parameters of the star.," Since both and originate in roughly the same region of the wind, the abundance ratio derived from them should be independent of details of the wind structure, and remove any attendant systematic errors in estimating the mass loss rate, distance, and bulk parameters of the star."
 The aad lines blended with anre known bv wind ionization models to coutribute ouly very weakly to this line in +? Velorum (<15%. 7).," The and lines blended with are known by wind ionization models to contribute only very weakly to this line in $\gamma^2$ Velorum \citep[$<$15\%,][]{DeMarco2000}."
 Due to the bleud of neutral and iomzed helium and hvdrosen lines at this location. this contamination fraction 1s expected to remain nearly constant with WR subtype.," Due to the blend of neutral and ionized helium and hydrogen lines at this location, this contamination fraction is expected to remain nearly constant with WR subtype."
 We have therefore reduced the measured Huput flux in Table 1. by this amount., We have therefore reduced the measured input flux in Table \ref{tab:abund} by this amount.
 The aalbundanuce found for the WN9 star 1105 is in good agreement with the cosnic value of S/Ile=7.5«10 and if S! constitutes about one-third of tle sulfur. as in WRILIG (2).. the total sulfur abundance comes quite close to cosmic.," The abundance found for the WN9 star 105 is in good agreement with the cosmic value of $\she=7.5\times 10^{-5}$, and if $^{++}$ constitutes about one-third of the sulfur, as in 146 \citep{Willis1997}, the total sulfur abundance comes quite close to cosmic."
 The neon to sulfur ratio we find is No!/S?!=15.7. somewhat larger than the cosinie value of the full abundance ratio NefS=7.," The neon to sulfur ratio we find is $\nepsppp=15.7$, somewhat larger than the cosmic value of the full abundance ratio $\nes=7$."
 If as expected. sulfur is less completely accounted for by S?! than neon is by Ne!. the total sulfur abundance would be increase by a larger factor than would που (around a factor of 2). and the final implied οσα approach the expected cosmic value. as expected im this less-evolved WN star.," If, as expected, sulfur is less completely accounted for by $^{3+}$ than neon is by $^+$, the total sulfur abundance would be increase by a larger factor than would neon (around a factor of 2), and the final implied can approach the expected cosmic value, as expected in this less-evolved WN star."
 We lave computed neon abundances for 3 WN aud 1 WC star from erouud-based spectra of the eenisson line., We have computed neon abundances for 3 WN and 1 WC star from ground-based spectra of the emission line.
 1121. the WC star. shows elevated aabundance. with an estimated total neon Ll... the cosmic value. close to the expected 17.8. merease predicted by WR core evolution models.," 121, the WC star, shows elevated abundance, with an estimated total neon $\times$ the cosmic value, close to the expected $\times$ increase predicted by WR core evolution models."
 À siguificaut population of eiutting nucon ious iu the ionization level. or realistic cChuuping £ll factors 0 would cach revise this value upwards by up to a factor of 2. but distance and mass-Ioss rate uncertainties also coutribute.," A significant population of emitting neon ions in the ionization level, or realistic clumping fill factors $\delta$ would each revise this value upwards by up to a factor of 2, but distance and mass-loss rate uncertainties also contribute."
" ""Though elevated neon abundances have been fouud iu several other WC stars. this is the least-evolved star for which such cuhancement has been demonstrated."," Though elevated neon abundances have been found in several other WC stars, this is the least-evolved star for which such enhancement has been demonstrated."
 The AWN stars were found to have abundauces close to cosuic. consistent with no nuclear neon eulhaucemieut.," The WN stars were found to have abundances close to cosmic, consistent with no nuclear neon enhancement."
 For the suele WN star for which neon aud sulfur were both observed. the irafio. Which is iuseusitive to uncertainties in the stars bulk paraincters. was found to be consistent with cosmic values. despite larger uncertainties in the total sulfur abundance.," For the single WN star for which neon and sulfur were both observed, the ratio, which is insensitive to uncertainties in the star's bulk parameters, was found to be consistent with cosmic values, despite larger uncertainties in the total sulfur abundance."
 We are grateful for the assistance and conunenuts provided by Audre Maeder. Luc Dessart. Pat Morris. aud Cooetz Craefener.," We are grateful for the assistance and comments provided by Andre Maeder, Luc Dessart, Pat Morris, and Goetz Graefener."
 We thauk Johu Iiüllier for his helpful discussion of neon ionization structure., We thank John Hillier for his helpful discussion of neon ionization structure.
 We also thank the staff of Palomar Observatory for their dedicated support., We also thank the staff of Palomar Observatory for their dedicated support.
 JDTS acknowledges support from NASA through JPL contract 1221769., JDTS acknowledges support from NASA through JPL contract 1224769.
The key results emerging from these (and other similar) studies are as follows (see et al.,The key results emerging from these (and other similar) studies are as follows (see Dodds-Eden et al.
" 2009 for a more comprehensive compilation): (1) IR/NIR flares occur more frequently than X-ray flares, typically ~4 times per day, compared with roughly 1 per day for the latter; (2) consequently, every X-ray flare appears to be associated with an NIR flare, but not every NIR event is correlated with an X-ray flare; additionally, (3) though X-ray and NIR flares occur simultaneously, with no significant delay, the former are typically shorter in (4) polarimetric measurements in the NIR show that the source is significantly polarized (by as much as 25%; see Eckart et al."," 2009 for a more comprehensive compilation): (1) IR/NIR flares occur more frequently than X-ray flares, typically $\sim 4$ times per day, compared with roughly 1 per day for the latter; (2) consequently, every X-ray flare appears to be associated with an NIR flare, but not every NIR event is correlated with an X-ray flare; additionally, (3) though X-ray and NIR flares occur simultaneously, with no significant delay, the former are typically shorter in (4) polarimetric measurements in the NIR show that the source is significantly polarized (by as much as $\sim 12\%-25\%$ ; see Eckart et al."
" 2006, Nishiyama et al."," 2006, Nishiyama et al."
" 2009; (5) the brightest flares have a constant spectral index a~0.6 between 3.8 and 1.6 um, where the flux is given as F,«v (see, e.g., Hornstein et al."," 2009; (5) the brightest flares have a constant spectral index $\alpha\sim 0.6$ between 3.8 and 1.6 $\mu$ m, where the flux is given as $F_\nu\propto \nu^{-\alpha}$ (see, e.g., Hornstein et al."
 2007)., 2007).
" At lower intensities, there may also be a possible trend of spectral index with flux, though this is still in dispute."," At lower intensities, there may also be a possible trend of spectral index with flux, though this is still in dispute."
" Additional results emerge when we include observations at longer wavelengths, but our focus in thisLetter will be on the NIR and X-ray emission, so we will defer the more complete discussion to a subsequent paper."," Additional results emerge when we include observations at longer wavelengths, but our focus in this will be on the NIR and X-ray emission, so we will defer the more complete discussion to a subsequent paper."
" As we shall see, three of the critical questions that must be resolved for a complete understanding of the flare phenomenon in Sgr A* (at least in the NIR/X-ray) are (1) how are the X-rays produced? ("," As we shall see, three of the critical questions that must be resolved for a complete understanding of the flare phenomenon in Sgr A* (at least in the NIR/X-ray) are (1) how are the X-rays produced? ("
2) how do we understand Sgr A*'s polarized NIR flare emission?,2) how do we understand Sgr A*'s polarized NIR flare emission?
" and (3) can we predict the associated polarization fraction and position angle for the variable X-ray component, in anticipation of future polarimetric measurements at ~ keV energies?"," and (3) can we predict the associated polarization fraction and position angle for the variable X-ray component, in anticipation of future polarimetric measurements at $\sim$ keV energies?"
" Based on preliminary work (some of it by our group), we now suspect that the NIR/X-ray flares originate close to Sgr A*’s event horizon."," Based on preliminary work (some of it by our group), we now suspect that the NIR/X-ray flares originate close to Sgr A*'s event horizon."
" As such, it will not be possible to carry out a meaningful simulation of the emission and polarization profiles without a general relativistic (GR) approach."," As such, it will not be possible to carry out a meaningful simulation of the emission and polarization profiles without a general relativistic (GR) approach."
 Addressing these (and related) questions within the context of GR is therefore the principal goal of thisLetter., Addressing these (and related) questions within the context of GR is therefore the principal goal of this.
" Sgr A*'s transient X-ray emission has variously been attributed to thermal processes or invese Compton scattering—of either seed mm/sub-mm photons (by the relativistic particles producing the IR/NIR synchrotron emission; see, e.g., Yusef-Zadeh et al."," Sgr A*'s transient X-ray emission has variously been attributed to thermal processes or invese Compton scattering—of either seed mm/sub-mm photons (by the relativistic particles producing the IR/NIR synchrotron emission; see, e.g., Yusef-Zadeh et al."
 2006) or of the IR/NIR photons, 2006) or of the IR/NIR photons
"response to the perturbation. $,,,,. aud py=ρῇ|συ","response to the perturbation, $\Phi_{resp}$, and $\rho_1=\rho_1^{p}+\rho_1^{resp}$."
 The coupled Boltzimanu-Poissou equations lead to an iutegrodiffereutial equation for the poteutial., The coupled Boltzmann-Poisson equations lead to an integrodifferential equation for the potential.
 This can be solved bv performing a Fourier transform in the angle variables. a Laplace transform iu the time variable and expanding the perturbed quantities iu ternis of spherical harmonics aud of a bi-orthogonal censity-poteutial basis functions for the augular aud the radial parts respectively.," This can be solved by performing a Fourier transform in the angle variables, a Laplace transform in the time variable and expanding the perturbed quantities in terms of spherical harmonics and of a bi-orthogonal density-potential basis functions for the angular and the radial parts respectively."
 The iutegrodifferential equation is then reduced to au algebraic equation for the vector of coefficients of the expansion ofthe response poteutial aud deusity.a. b).," The integrodifferential equation is then reduced to an algebraic equation for the vector of coefficients of the expansion of the response potential and density, ) ."
 The inatrzis5R contains the time dependence of the perturbation and the equilibrium properties of the perturbed svstemi aud is the vector of the cocficicuts of the expansion of the external perturbing potential., The matrix contains the time dependence of the perturbation and the equilibrium properties of the perturbed system and is the vector of the coefficients of the expansion of the external perturbing potential.
 It is clear from equation (3)) that the selfcousisteut response of the perturbed system is determined both by he perturbation applied bv the external perturber aud x the reaction of the system to its own response to this erturbation., It is clear from equation \ref{mateq}) ) that the self-consistent response of the perturbed system is determined both by the perturbation applied by the external perturber and by the reaction of the system to its own response to this perturbation.
 Iu general. an additional contribution to he total response cones from excitation of the discrete damped modes of the primary system besides the effects of he perturber aud the sclf-eravity of the distorted primary.," In general, an additional contribution to the total response comes from excitation of the discrete damped modes of the primary system besides the effects of the perturber and the self-gravity of the distorted primary."
 The differences in the mathematical structure of these wo contributions are illustrated in the Appendix., The differences in the mathematical structure of these two contributions are illustrated in the Appendix.
 The ransicnt response due to the discrete damped modes can iive a strong effect ou the amplitude of the response (cf., The transient response due to the discrete damped modes can have a strong effect on the amplitude of the response (cf.
 8323) and it is particularly miportaut when the moces are weakly damped with camping timescales longer than the Hv-bv timescale., 3) and it is particularly important when the modes are weakly damped with damping timescales longer than the fly-by timescale.
 In this case. the discrete damped modes xoduce loug-lived features which completely determine he amplitude and the structure of the response long after the pericenter passage of the perturber.," In this case, the discrete damped modes produce long-lived features which completely determine the amplitude and the structure of the response long after the pericenter passage of the perturber."
" Ouce the above algebraic equation has been solved. the caleulation of response potential aud density is straightforward where d; aud s; are the br-orthogoual deusity-poteutial basis function and Y15,,(0.0) are the spherical harmonics."," Once the above algebraic equation has been solved, the calculation of response potential and density is straightforward where $d_i$ and $u_i$ are the bi-orthogonal density-potential basis function and $Y_{lm}(\theta,\phi)$ are the spherical harmonics."
 Features excited in the halo can give rise to visible distortions in an οπουσα disk even though dark halo perturbations are not directly observable., Features excited in the halo can give rise to visible distortions in an embedded disk even though dark halo perturbations are not directly observable.
 While several other processes could be responsible for the observed distorted morphologies of stellar disks (see e.g. Sellwood Merritt 1991. Levine Sparke 1998. Bertin Miuk 1980. Nelsou Tremaine 1995). the role plaved by a distorted ealactic dark halo in exciting peculiar features in disks has becu advanced for the case of an interaction of a ealaxy with a satellite companion by Weinberg (01995.19008b) arc applied to the case of the Milky Way-Aagelanic Clo system.," While several other processes could be responsible for the observed distorted morphologies of stellar disks (see e.g. Sellwood Merritt 1994, Levine Sparke 1998, Bertin Mark 1980, Nelson Tremaine 1995), the role played by a distorted galactic dark halo in exciting peculiar features in disks has been advanced for the case of an interaction of a galaxy with a satellite companion by Weinberg (1995,1998b) and applied to the case of the Milky Way-Magellanic Cloud system."
 Halo deformations leading to morphological aix kinematical lopsidednuess has been invoked by Swaters et al. (, Halo deformations leading to morphological and kinematical lopsidedness has been invoked by Swaters et al. (
1998) in anu analysis of two kinematically lopside« spiral galaxies (DDO 9. NGC 1395).,"1998) in an analysis of two kinematically lopsided spiral galaxies (DDO 9, NGC 4395)."
 The ubiquity of Magellanic-class dwart compauious of normal spirals (6.8. Zaritsky White 1991 aud Zaritsky ct al., The ubiquity of Magellanic-class dwarf companions of normal spirals (e.g. Zaritsky White 1994 and Zaritsky et al.
" 1997) suggests that such interactions may be important sources of structure,", 1997) suggests that such interactions may be important sources of structure.
 Unbound eucouuters can have similar effect as we will illustrate here., Unbound encounters can have similar effect as we will illustrate here.
 Our standard dark halo model is an isotropic Nine model with a dimensionless central potential Wy=3.0 (concentration e=0.67) a total mass Af=ος10HAF. aud a total radius Ry=200 kpc.," Our standard dark halo model is an isotropic King model with a dimensionless central potential $W_0=3.0$ (concentration $c=0.67$ ) a total mass $M=6 \times 
10^{11} M_{\odot}$ and a total radius $R_t=200$ kpc."
 These values are appropriate for the Galactic halo (see e.g. Iochanck 1996) and together with a standard exponential disk results iu a fair ft to the observed rotation curve., These values are appropriate for the Galactic halo (see e.g. Kochanek 1996) and together with a standard exponential disk results in a fair fit to the observed rotation curve.
 Given the primary model. the perturber's velocity V aud oricenter p determine the structure of the response to the serturbation.," Given the primary model, the perturber's velocity $V$ and pericenter $p$ determine the structure of the response to the perturbation."
 The amplitude of the response scales with he mass of the perturber., The amplitude of the response scales with the mass of the perturber.
 Table 1 sunuuarizes the values of V aud p explored here along with the corresponding values of the ratio of the ieeuter to the halfanass radius of the primary svsteni. píB. aud the ratio of the characteristic frequency of the notion of the perturber to the circular frequency at the edee of the primary svstem. Q=V.pyRiGAL.," Table 1 summarizes the values of $V$ and $p$ explored here along with the corresponding values of the ratio of the pericenter to the half-mass radius of the primary system, $p/R_h$, and the ratio of the characteristic frequency of the motion of the perturber to the circular frequency at the edge of the primary system, $\Omega \equiv
V/p \sqrt{R_{t}^3/ GM}$."
 All the cases considered here correspond to flv-bys in which part of he orbit passes through the halo: external encounters are ikelv to produce weaker distortions aud will be considered ater in 83.3., All the cases considered here correspond to fly-bys in which part of the orbit passes through the halo; external encounters are likely to produce weaker distortions and will be considered later in 3.3.
 The values of W considered are chosen to cover a typical range of relative encounter velocitics in he field. groups aud clusters.," The values of $V$ considered are chosen to cover a typical range of relative encounter velocities in the field, groups and clusters."
 In order to clearly assess he importance of weakly damped modes. we consider the evolution. of the respouse both with and without their effect for all the cases listed in Table 1.," In order to clearly assess the importance of weakly damped modes, we consider the evolution of the response both with and without their effect for all the cases listed in Table 1."
 For cases that iuclude the weakly damped modes. we must first deteriune thei natural frequencies.," For cases that include the weakly damped modes, we must first determine their natural frequencies."
 We used the method adopted in Weinberg (199D): the deteriminnaut of the dispersion matrix D(5) (see Appendix for its definition) is evaluated on a grid of values of s in the, We used the method adopted in Weinberg (1994): the determinant of the dispersion matrix ${\bf D}(s)$ (see Appendix for its definition) is evaluated on a grid of values of $s$ in the
to the line-of-sight. then for P=10 s (appropriate for the AXPs). the fraction of pulsars which would be beamed towards us ts estimated to be citebig90b:: )).,"to the line-of-sight, then for $P=10$ s (appropriate for the AXPs), the fraction of pulsars which would be beamed towards us is estimated to be \\cite{big90b}; \cite{tm98}) )."
 Thus even if all the AXPs are radio pulsars. 1t is likely that none of them are beamed in our direction.," Thus even if all the AXPs are radio pulsars, it is likely that none of them are beamed in our direction."
 Of the four (possibly five) SGRs identified to date. in all cases associations have been claimed with nearby SNRs ()).," Of the four (possibly five) SGRs identified to date, in all cases associations have been claimed with nearby SNRs \cite{hur00b}) )."
 Below we review recent results on each system. and use similar criteria as for the AXPs to assess the validity of the proposed SNR associations.," Below we review recent results on each system, and use similar criteria as for the AXPs to assess the validity of the proposed SNR associations."
 SGR 0526-66 was discovered as a result of its intense >- activity on 5 Mar 1979. data which also contained an second periodicity (5: ))," SGR 0526–66 was discovered as a result of its intense $\gamma$ -ray activity on 5 Mar 1979, data which also contained an 8-second periodicity \cite{bch+79}; ; \cite{tekl80}) )."
 This >-ray emission was localized to à small 0.1 aremin? region of the Large Magellanic Cloud (LMC) which overlaps the SNR N49 ())., This $\gamma$ -ray emission was localized to a small 0.1 $^2$ region of the Large Magellanic Cloud (LMC) which overlaps the SNR N49 \cite{cdt+82}) ).
 The X-ray point source RX JO5260.3-660433 falls within this error box and lies on the rim of the SNR (€: )): this source is presumed to be the X-ray counterpart to the SGR., The X-ray point source RX J05260.3–660433 falls within this error box and lies on the rim of the SNR \cite{rkl94}; \cite{mrlp96}) ); this source is presumed to be the X-ray counterpart to the SGR.
 The probability of à chance alignment between SGR and SNR N49 was estimated by Felten (1982)) to be ~1077., The probability of a chance alignment between SGR 0526--66 and SNR N49 was estimated by Felten \nocite{fel82}) ) to be $\sim10^{-3}$.
 There have been many new results on SNRs in the LMC since this estimate was made., There have been many new results on SNRs in the LMC since this estimate was made.
 We consequently here make a revised calculation as to the probability of coincidence between the SNR and SGR., We consequently here make a revised calculation as to the probability of coincidence between the SNR and SGR.
" The most recent catalog of LMC SNRs ts that of Williams ((1999)), who list 37 confirmed SNRs."," The most recent catalog of LMC SNRs is that of Williams \nocite{wcd+99}) ), who list 37 confirmed SNRs."
 The total solid angle subtended by these SNRs is ~180 aremin-., The total solid angle subtended by these SNRs is $\sim180$ $^2$.
 If we assume the LMC to be delineated by a circle of radius 3° and that SNRs are randomly distributed throughout this region. then using the same approach as in Section 4.1 above the probability of the SGR falling on the rim of an unrelated SNR is0.2%.. double the estimate of Felten (1982)).," If we assume the LMC to be delineated by a circle of radius $3^\circ$ and that SNRs are randomly distributed throughout this region, then using the same approach as in Section \ref{sec_axps_rxj}
 above the probability of the SGR falling on the rim of an unrelated SNR is, double the estimate of Felten \nocite{fel82}) )."
 However. because both SNRs and SGRs are believed to be formed in supernova explosions. their distributions should be similar to those of massive stars and star-forming regions within the LMC. neither of which are uniformly distributed throughout the entire galaxy.," However, because both SNRs and SGRs are believed to be formed in supernova explosions, their distributions should be similar to those of massive stars and star-forming regions within the LMC, neither of which are uniformly distributed throughout the entire galaxy."
 The above calculation therefore considers too large a possible area for these objects. and is an underestimate of the probability of a spurious association.," The above calculation therefore considers too large a possible area for these objects, and is an underestimate of the probability of a spurious association."
 In Figure ??. we show an 660 μπι image of the LMC. on which the positions of SNRs from the catalog of Williams ((1999)) are marked.," In Figure \ref{fig_lmc} we show an 60 $\mu$ m image of the LMC, on which the positions of SNRs from the catalog of Williams \nocite{wcd+99}) ) are marked."
 It is clear that the distribution of SNRs within the LMC is indeed far from uniform. and follows the multi-armed spiral pattern traced in the infra-red.," It is clear that the distribution of SNRs within the LMC is indeed far from uniform, and follows the multi-armed spiral pattern traced in the infra-red."
" If we only consider those parts of the LMC in which there is bright infrared emission (Soja,>10 MIy si! ). the total area under consideration is then ~7 deg. and the probability of a chance coincidence between SGR 0526-66 and a SNR rises to0."," If we only consider those parts of the LMC in which there is bright infrared emission $\Sigma_{60\, {\rm \mu m}} >
10$ MJy $^{-1}$ ), the total area under consideration is then $\sim7$ $^2$, and the probability of a chance coincidence between SGR 0526–66 and a SNR rises to."
7%.. Alternatively. the scale length for the distribution of OB stars in the LMC is 1.6 kpe (). corresponding to an area of —10 deg? (for a distance of 50 kpe) and thus a probability of random alignment of0.," Alternatively, the scale length for the distribution of OB stars in the LMC is 1.6 kpc \cite{wn01}) ), corresponding to an area of $\sim10$ $^2$ (for a distance of 50 kpc) and thus a probability of random alignment of."
55c.. There are certainly many LMC SNRs still to be discovered. especially given the difficulty in identifying SNRs in complex star-forming regions ()).," There are certainly many LMC SNRs still to be discovered, especially given the difficulty in identifying SNRs in complex star-forming regions \cite{ck88}) )."
 The above calculations are thus likely to be underestimates. and the true probability of coincidental alignment may be as large as several percent.," The above calculations are thus likely to be underestimates, and the true probability of coincidental alignment may be as large as several percent."
 Furthermore. as we have discussed above for the case of300910.. a low probability of chance alignment does not imply that the SGR and SNR were formed in the same supernova explosion. but possibly that two separate supernovae occurred near each other.," Furthermore, as we have discussed above for the case of, a low probability of chance alignment does not imply that the SGR and SNR were formed in the same supernova explosion, but possibly that two separate supernovae occurred near each other."
 The many examples of closely-grouped SNRs in the LMC indeed demonstrate the clustered nature of their progenitors (2: :: ))., The many examples of closely-grouped SNRs in the LMC indeed demonstrate the clustered nature of their progenitors \cite{clg+93}; \cite{scm+94}; \cite{wcd+97}) ).
 These considerations suggest that the claimed association between SGR 0526-66 and N49. while by far the most likely of the SGR/SNR associations (see further discussion below). is considerably less convincing than the cases for AXPs in SNRs considered above.," These considerations suggest that the claimed association between SGR 0526–66 and N49, while by far the most likely of the SGR/SNR associations (see further discussion below), is considerably less convincing than the cases for AXPs in SNRs considered above."
 Doubt has also recently been cast on this association by Kaplan ((2001)). who infer an age for the SGR of ~1000 yr on the basis of its energetics and broad-band spectrum.," Doubt has also recently been cast on this association by Kaplan \nocite{kkv+01}) ), who infer an age for the SGR of $\sim$ 1000 yr on the basis of its energetics and broad-band spectrum."
 This ts clearly inconsistent with the age of 5-16 kyr estimated for the SNR (:: )., This is clearly inconsistent with the age of 5–16 kyr estimated for the SNR \cite{shu83}; \cite{vblr92}) ).
 SGR 1806-20 was originally localized to a small region centered on the unusual SNR G10.0-0.3 (:: )., SGR 1806–20 was originally localized to a small region centered on the unusual SNR G10.0–0.3 \cite{abh+87}; \cite{mtk+94}) ).
" However. a re- of x-ray data for SGR 1806-20 demonstrates its most likely position to be offset by 15"" from the center of G10.0-0.3 ()."," However, a re-analysis of $\gamma$ -ray data for SGR 1806–20 demonstrates its most likely position to be offset by $15''$ from the center of G10.0–0.3 \cite{hkc+99}) )."
 Recent observations of the region using the hhave confirmed this refined position ())., Recent observations of the region using the have confirmed this refined position \cite{kap01}) ).
 Meanwhile. VLA observations of G10.0-0.3 have shown a centrally-condensed. changing morphology and an unusually steep spectrum. with no evidence for a blast-wave and/or a supernova explosion (:; :: )).," Meanwhile, VLA observations of G10.0–0.3 have shown a centrally-condensed, changing morphology and an unusually steep spectrum, with no evidence for a blast-wave and/or a supernova explosion \cite{kfk+94}; \cite{vfk95}; \cite{fvk97}) )."
 The classification of G10.0-0.3 as a SNR therefore seems to have been erroneous: it rather seems to be powered by some central object unrelated to SGR 20. possibly the massive star identified by van Kerkwijk ((1995)).," The classification of G10.0–0.3 as a SNR therefore seems to have been erroneous; it rather seems to be powered by some central object unrelated to SGR 1806--20, possibly the massive star identified by van Kerkwijk \nocite{vkmn95}) )."
 We thus conclude that there is no SNR associated with SGR 1806-20., We thus conclude that there is no SNR associated with SGR 1806–20.
 SGR 1900-14 has been identified with an unresolved X-ray source located 5 outside the rim of the SNR G42.8+0.6 (QJ., SGR 1900+14 has been identified with an unresolved X-ray source located $5'$ outside the rim of the SNR G42.8+0.6 \cite{hlk+99}) ).
 As is the case forJ170849—400910.. this source falls in a complicated region in the inner Galaxy.," As is the case for, this source falls in a complicated region in the inner Galaxy."
 Considering the region 35°</<<45°. |b|<1°. we find by the same approach as used earlier that there is a ~4% probability that the proximity to a SNR ts simply by chance.," Considering the region $35^\circ < l < 45^\circ$, $|b| < 1^\circ$, we find by the same approach as used earlier that there is a $\sim$ probability that the proximity to a SNR is simply by chance."
 As discussed above. this low probability may simply represent the natural spatial clustering of supernova explosions rather than any specific association between the SGR and SNR.," As discussed above, this low probability may simply represent the natural spatial clustering of supernova explosions rather than any specific association between the SGR and SNR."
 Furthermore. a radio pulsar. PSR J1907+0918. has recently been identified just 2’ from SGR 1900-14. and has a characteristicage of only 38 kyr ()).," Furthermore, a radio pulsar, PSR J1907+0918, has recently been identified just $2'$ from SGR 1900+14, and has a characteristicage of only 38 kyr \cite{lx00}) )."
 The case for an association between the radio pulsar and SNR G32.8+0.6 1s far from compelling. but is just as plausible as the SGR/SNR association. further weakening the argument for the latter.," The case for an association between the radio pulsar and SNR G32.8+0.6 is far from compelling, but is just as plausible as the SGR/SNR association, further weakening the argument for the latter."
 Finally. we note that Vrba ((2000)) have discovered a cluster of massive stars separated from SGR 1900414 by just a few aresec.," Finally, we note that Vrba \nocite{vhl+00}) ) have discovered a cluster of massive stars separated from SGR 1900+14 by just a few arcsec."
 They propose an, They propose an
It is important to compare the IR properties of the galaxies with clilferent strengths of interaction (aud thus. with different projected separation d»).,"It is important to compare the IR properties of the galaxies with different strengths of interaction (and thus, with different projected separation $d_P$ )."
" To allow significan results to emerge in spite of (he bias introduced by projection effects. we considered [our interaction classes: (1) mergers (5 Sanders objects + mergers from DIRG). (2) strongly interacting svstenis (galaxies with companion closer than 30 Άρο (logd,< 1.5. where d, is in Ixpc). 5 Sanders objects + BIRG). (2) weakly interacting svstems (galaxies wilh a companion bevond 30 Ixpe (logd,> 1.5)). and (4) isolated objects (objects without a companion within our search radius of 250 Ixpc)."," To allow significant results to emerge in spite of the bias introduced by projection effects, we considered four interaction classes: (1) mergers (5 Sanders objects + mergers from BIRG), (2) strongly interacting systems (galaxies with companion closer than 30 Kpc $\log d_p <$ 1.5, where $d_p$ is in Kpc), 5 Sanders objects + BIRG), (3) weakly interacting systems (galaxies with a companion beyond 30 Kpc $\log d_p >$ 1.5)), and (4) isolated objects (objects without a companion within our search radius of 250 Kpc)."
 The objects were split between BIRG aud control sample of clilerent interaction classes., The objects were split between BIRG and control sample of different interaction classes.
 Fig., Fig.
 7 shows the F(60;an)/F(LO00jan) vs. F(12 pam) /F(25 jm) color-color diagram for the four interaction classes., \ref{fig05} shows the $\mu$ $\mu$ m) vs. F(12 $\mu$ m)/F(25 $\mu$ m) color-color diagram for the four interaction classes.
 Mergers and strongly interacting svstems show higher values of F(60jm)/ F(I00jym) and lower values of F(12 jm)/F(25 jun) while isolated objects show lower values of F(60jm)/F(100j0n) and higher values of F(12. jim)/F(25 jm)., Mergers and strongly interacting systems show higher values of $\mu$ m)/ $\mu$ m) and lower values of F(12 $\mu$ m)/F(25 $\mu$ m) while isolated objects show lower values of $\mu$ $\mu$ m) and higher values of F(12 $\mu$ m)/F(25 $\mu$ m).
 Fig., Fig.
 7 is divided in three regions., \ref{fig05} is divided in three regions.
 In the first one (F(60jm)/F(100ja). & 0.75 and 2 0.65). almost all objects are mergers and strongly interacting.," In the first one $\mu$ $\mu$ m) $\simgt$ 0.75 and $\simlt$ 0.65), almost all objects are mergers and strongly interacting."
 In the second region (F(60j) 10050) A 0.75 and F(12 jam)/F(25 jm) & 0.65). there is an agglomeration of objects of all interaction classes.," In the second region $\mu$ $\mu$ $\simlt$ 0.75 and F(12 $\mu$ m)/F(25 $\mu$ $\simlt$ 0.65), there is an agglomeration of objects of all interaction classes."
 However (he 3 mergers in this region are near the border to the first region. and their IR colors are verv close to the values of the first region mergers.," However the 3 mergers in this region are near the border to the first region, and their IR colors are very close to the values of the first region mergers."
 The third region (F(6O;an)/FCLOO;an) & 0.75 and F(12 yom)/F(25 jum) & 0.65) shows only objects with a companion bevond 30 Ixpe. and isolated galaxies.," The third region $\mu$ $\mu$ $\simlt$ 0.75 and F(12 $\mu$ m)/F(25 $\mu$ $\simgt$ 0.65) shows only objects with a companion beyond 30 Kpc, and isolated galaxies."
 Table 2 reports average and sample standard deviation values of the parameters considered in our analvsis (Column 1). for different interaction strenet classes.," Table 2 reports average and sample standard deviation values of the parameters considered in our analysis (Column 1), for different interaction strength classes."
 Columns 25 report sample average and sample standard deviation for CS and BIRG isolated ealaxies (dpZ250 IXpe)., Columns 2–5 report sample average and sample standard deviation for CS and BIRG isolated galaxies $d_P \simgt 250$ Kpc).
 Columns 69 report. values for BIRG and CS weekly interacting ealaxies with dpZ30 pc., Columns 6–9 report values for BIRG and CS weekly interacting galaxies with $d_P \simgt 30$ Kpc.
 The next columns list the sample average and standard deviation for the DIRG sample for the remaining5 (wo interaction classes: stronglySt interacting.5 and mergers (there are no C'S galaxies will dp&30 IXpe nor mergers).," The next columns list the sample average and standard deviation for the BIRG sample for the remaining two interaction classes: strongly interacting, and mergers (there are no CS galaxies with $d_P \simlt
30$ Kpc nor mergers)."
" The last lour rows provide standard estimates of star-formation-related parameters: (1) the Star Formation Rate (SER). which was computed from uusing the standard relationship SFR224.5x10HEpbbeege: LAL. ! (Kennicutt1998): (2) hydrogen molecular mass (collected [rom various sources in literature and available or 41 objects): (3) the ratio Mj,2: (4) the depletion time in vr simply defined as the ivdrogen molecular gas nass assumed over the SFR. ty,= // SER."," The last four rows provide standard estimates of star-formation-related parameters: (1) the Star Formation Rate (SFR), which was computed from using the standard relationship $SFR \approx 4.5\times 10^{-44}L_{FIR, ergs s^{-1} }$ $_{\odot}$ $^{-1}$ \citep{k98}; (2) hydrogen molecular mass (collected from various sources in literature and available for 41 objects); (3) the ratio 2; (4) the depletion time in yr simply defined as the hydrogen molecular gas mass assumed over the SFR, $\tau_{H_2} = $ / SFR."
 There is a clear continuity on FIR properties aud SFR from isolated objects to mergers (except Lor (he 3 isolated BIBGs. but see below).," There is a clear continuity on FIR properties and SFR from isolated objects to mergers (except for the 3 isolated BIRGs, but see below)."
strong synelirotron radiative Osses tu the iniermost reeious.,strong synchrotron radiative losses in the innermost regions.
 Addiional acceleration outside the intra-jnary shock (e.g..Se. via 1uagnetic reconnectloiin the spiral-lise tall) may provide a way to circuiivent this limitation.," Additional acceleration outside the intra-binary shock (e.g., via magnetic reconnection in the spiral-like tail) may provide a way to circumvent this limitation."
" Aernativelv. coild be somewhat lowe""M the inagnetic field is 1eher than estinated above. which is possible if the |ull low speed if somewhat higher than the terla O-star wind speed."," Alternatively,$\gamma$ could be somewhat lower if the magnetic field is higher than estimated above, which is possible if the bulk flow speed if somewhat higher than the terminal O-star wind speed."
 Lucleect. Ud (o a certain cliSla'e. the fast. pulsar wind could providesonie to the O-star d until both copolents become well mixed.," Indeed, up to a certain distance, the fast pulsar wind could providesome re-acceleration to the O-star wind until both components become well mixed."
 However. the cdeallec inocdeine of this complex |‘action is bevouc the scope of this payer.," However, the detailed modeling of this complex interaction is beyond the scope of this paper."
 The observed softeriug of the exterded emission wit e cdistance from the volt source could be attributed to syucliOlFOL coolitο which canbesubst:ial at αZVif B10 pC or somewhat larger., The observed softening of the extended emission with the distance from the point source could be attributed to synchrotron cooling which canbesubstantial at $\alpha\gtrsim1'$ if $B\sim 10$ $\mu$ G or somewhat larger.
 Iiverse Compton (IC iabatic expansion cooling compete with svuchrotrou coolit& alu Cal even dominate. ceper i the distancefrom the particle acceleration 'eelon (the shock).," Inverse Compton (IC) and adiabatic expansion cooling compete with synchrotron cooling and can even dominate, depending on the distancefrom the particle acceleration region (the intra-binary shock)."
" Although at listances of interest here. the O-star radiatior energy. Crag—38x10πια]26 1oE cm?. +>6x10! ?)). TG920(E/5keV)!*(B/10pC).ία] gs E—SkkeVsin B—I0 pO. altat οδη;"">~TE/SkeV)L?(B/10pe)“kyr. Tv ((28) ?)). ? νὰ +~20. ? 2x107. . ? (0.1—)S)x10 ! "," Although at the distances of interest here, the O-star radiation energy $\epsilon_{\rm rad}=3.8\times10^{-10}(\alpha/1')^{-2}$ $^{-3}$ $\epsilon_{\rm B}=4.0\times10^{-12}(B/10~\mu{\rm
 G})^2$ $^{-3}$ $\gamma\gtrsim6\times10^4$ \citealt{1970RvMP...42..237B}) $\tau_{\rm IC}\sim 20 (E/5~{\rm keV })^{1/2}(B/10\,\mu{\rm
 G})^{-1/2} (\alpha/1')^{2}$ $E=5$ $B=10$ $\mu$ $\tau_{\rm IC,CMB}\simeq 7 (E/5~{\rm keV })^{-1/2}(B/10\,\mu{\rm
 G})^{1/2}$ $\tau_{\rm syn}$ \citealt{2006A&A...456..801D}) \citet{2010MNRAS.403.1873Z} $\gamma\sim 20$ $\gamma$ $2\times10^4$ $\gamma$ \citet{2011MNRAS.411..193S} $\dot{E}=(0.1$$38)\times10^{36}$ $^{-1}$ "
all stars. a common envelope efficiency o.=3.0. and zero initial orbital eccentricity. were found by Hurley et al. (,"all stars, a common envelope efficiency $\alpha=3.0$, and zero initial orbital eccentricity, were found by Hurley et al. ("
2000) to best reproduce the observed numbers of double degenerate. symbiotic. cataclysmic variable and other binary star populations in the Galaxy.,"2000) to best reproduce the observed numbers of double degenerate, symbiotic, cataclysmic variable and other binary star populations in the Galaxy."
 Here. we evolve pairs in which both stars have masses between 0.1 and 20 ... and the initial semi-major axis distribution extends from 2 to 10° ZAMS stellar diameters.," Here, we evolve pairs in which both stars have masses between 0.1 and 20 $_{\odot}$, and the initial semi-major axis distribution extends from 2 to $10^5$ ZAMS stellar diameters."
 Note that the code uses the Nauenberg (1972) mass-radius relation for WDs., Note that the code uses the Nauenberg (1972) mass-radius relation for WDs.
 We distribute this population according to a double exponential disk model. with scale length 2.75 kpe.," We distribute this population according to a double exponential disk model, with scale length 2.75 kpc."
 The scale height / is chosen to vary according to stellar age ¢. with hxEU7. set equal to 100 pe for stars born today and to 300 pe for the oldest stars in the disk.," The scale height $h$ is chosen to vary according to stellar age $t$, with $h \propto t^{1/2}$, set equal to 100 pc for stars born today and to 300 pc for the oldest stars in the disk."
 We use the extinction corrections of Baheall&Soneira(1980)... and thus model the stars in theKepler field of view within the magnitude limits of the survey.," We use the extinction corrections of \citet{bah80}, and thus model the stars in the field of view within the magnitude limits of the survey."
 We normalize to the number of dwarf stars counted in this field (~136.000 with 9<<V<I4. from webpage: results can be re-scaled if this number is later revised).," We normalize to the number of dwarf stars counted in this field $\sim 136,000$ with $9<V<14$, from webpage; results can be re-scaled if this number is later revised)."
 We estimate that the total number of WD-MS systems within this sample of stars is ~15.000. while the sample should contain ~ 35.000 WD-MS systems.," We estimate that the total number of WD–MS systems within this sample of stars is $\sim 15,000$, while the sample should contain $\sim$ 35,000 WD–MS systems."
 The resulting orbital period distribution of target WD-MS systems is plotted in Figure l.. and is seen to display the double-peaked structure expected from 3.1.. with a relative dearth ofsystems with periods from months to years.," The resulting orbital period distribution of target WD–MS systems is plotted in Figure \ref{fig:period}, and is seen to display the double-peaked structure expected from \ref{sec:evol}, with a relative dearth ofsystems with periods from months to years."
 A similar distribution was predicted by deKool&Ritter(1993)., A similar distribution was predicted by \citet{dek93}.
 The detectability depends on the signal-to-noise ratio of all transits combined in the time series for a given system., The detectability depends on the signal-to-noise ratio of all transits combined in the time series for a given system.
" We require that the transit duration be at least | hour (fourKepler time-samples) for detection,", We require that the transit duration be at least 1 hour (four time-samples) for detection.
 We assume photon counting statistics typically dominate the noise. but also add in a fractional instrumental noise of 107.," We assume photon counting statistics typically dominate the noise, but also add in a fractional instrumental noise of $10^{-5}$."
 For simplicity. we neglect limb-darkening.," For simplicity, we neglect limb-darkening."
 Shorter period systems are doubly favored. since the time spent in transit and. the probability of a transit in a system with random orientation both scale as P-?.," Shorter period systems are doubly favored, since the time spent in transit and the probability of a transit in a system with random orientation both scale as $P^{-2/3}$."
 For this reason. Kepler's sensitivity — designed to detect the longer-period terrestrial systems — is easily good enough to detect a large fraction of the transiting WD-MS systems within the magnitude limits at good signal to noise.," For this reason, 's sensitivity --- designed to detect the longer-period terrestrial systems — is easily good enough to detect a large fraction of the transiting WD–MS systems within the magnitude limits at good signal to noise."
 The same is not true ofEddington.. with its deeper magnitude limits. which restrict most detectable transits to lower-mass MS primaries.," The same is not true of, with its deeper magnitude limits, which restrict most detectable transits to lower-mass MS primaries."
 The properties of the detectable systems. assuming an80 detection threshold. and the parent population from which they are drawn. are illustrated in Figures 1..2.. and 3 forKepler.," The properties of the detectable systems, assuming an$8 \sigma$ detection threshold, and the parent population from which they are drawn, are illustrated in Figures \ref{fig:period}, \ref{fig:mass}, and \ref{fig:dm} for."
 The total numbers of WD-MS systems detectable are summarised for bothKepler and in Table 1., The total numbers of WD–MS systems detectable are summarised for both and in Table 1.
 We split the transits into the three modes of detection described in 2.., We split the transits into the three modes of detection described in \ref{sec:wdvar}.
 Note that many systems have both detectable primary and secondary transits., Note that many systems have both detectable primary and secondary transits.
 For a blind search. a number of transits (Z73) would need to be seen for detection as a periodic signal amongst the noise. but if radial velocity information were additionally available. it is possible that an identification could be made based on fewer transits.," For a blind search, a number of transits $\ga 3$ ) would need to be seen for detection as a periodic signal amongst the noise, but if radial velocity information were additionally available, it is possible that an identification could be made based on fewer transits."
 For this reason. systems at all periods are included as detectable (weighted by their transit probabilities and appropriate signal-to-noise ratios): 1 no such additional information ts available. the curves in Figure | should be cut off at about P~1.3 years. though it can be seen that this makes little difference to the overall number of detectable systems. as a result of the underlying WD-MS period distribution.," For this reason, systems at all periods are included as detectable (weighted by their transit probabilities and appropriate signal-to-noise ratios); if no such additional information is available, the curves in Figure 1 should be cut off at about $P \sim 1.3$ years, though it can be seen that this makes little difference to the overall number of detectable systems, as a result of the underlying WD–MS period distribution."
 We see from Table | that several hundred transiting WD-MS systems are in principle detectable with each mission., We see from Table 1 that several hundred transiting WD–MS systems are in principle detectable with each mission.
 However. the most serious (and least well-defined) limitation i5 still to be added: that of stellar variability noise. which is discussed in the following section.," However, the most serious (and least well-defined) limitation is still to be added: that of stellar variability noise, which is discussed in the following section."
 The issue of stellar microvariability is of concern in terrestrial planet transit surveys (e.g. Jenkins 2002.. Batalhaet 2002.. Aigrainetal. 2002)).," The issue of stellar microvariability is of concern in terrestrial planet transit surveys (e.g. \citealt{jen02}, , \citealt{bat02}, , \citealt{aig02}) )."
 Variability levels are higher.," Variability levels are higher,"
1974).. the source has been regularly monitored at many. observable frequencies. although less regularly at radio frequencies (Alleretal.1992:Takalo 1996). ,", the source has been regularly monitored at many observable frequencies, although less regularly at radio frequencies \citep{aller1992, takalo1996}. ."
Fan&Lin(1999.2000) have studied the long-term optical and UR variability of the source and. reported a variation of 1.5 mag at time scales of —1 week to several vears at those two frequencies.," \citet{fan1999, fan2000} have studied the long-term optical and IR variability of the source and reported a variation of $\leq$ 1.5 mag at time scales of $\sim$ 1 week to several years at those two frequencies."
 Bottcheretal.(2005). reported a large microvariability of —0.2 mag within 6 hours: they also reported several major outbursts in the source separated by —D50 days and argued that the outbursts seem to have a quasi-periodic behaviour., \citet{bottcher2005} reported a large microvariability of $\sim$ 0.2 mag within 6 hours; they also reported several major outbursts in the source separated by $\sim$ 50 days and argued that the outbursts seem to have a quasi-periodic behaviour.
 At the end of 2007 the source was found to be in an optically active phase. which triggered a new Optical-Llt-Radio Whole Earth Blazar Telescope (WIZDT) campaign on the source (Bottcherctal.2009).," At the end of 2007 the source was found to be in an optically active phase, which triggered a new Optical-IR-Radio Whole Earth Blazar Telescope (WEBT) campaign on the source \citep{bottcher2009}."
. Our optical LOW observations of the source ὃς GGA comprise a total of seven LCs. spanning a time perioc between October 2008 and January 2009.," Our optical IDV observations of the source 3C 66A comprise a total of seven LCs, spanning a time period between October 2008 and January 2009."
 During this perio a change of —1 magnitude in brightness of the source is seen (Ranictal.2010b)., During this period a change of $\sim$ 1 magnitude in brightness of the source is seen \citep{rani2010b}.
. The source showed significan microvariability only on October 22 and 26. 2008 11).," The source showed significant microvariability only on October 22 and 26, 2008 1)."
 There is à continuous fading trend of 0.05 and. ~0.06 magnitude. respectively on those two nights.," There is a continuous fading trend of $\sim$ 0.08 and $\sim$ 0.06 magnitude, respectively on those two nights."
 The SE ane DCE analvsis of the LCs revealed. that any timescale of variability in this source at those epochs is greater than the engths of our observations., The SF and DCF analysis of the LCs revealed that any timescale of variability in this source at those epochs is greater than the lengths of our observations.
 The blazar .NO 0235]164 at 2=0.94 (Nilssonetal.1996) was classified as a BL Lac object by Spinrad&Smith(1975)., The blazar AO 0235+164 at $z = 0.94$ \citep{nilsson1996} was classified as a BL Lac object by \citet{spinrad1975}.
. Over the past lew decades this Xazar has been seen to be highly variable over all timescales and at all frequencies (Chosh&Soundararajaperumal1995:Heidt&Wagner1996:Raiterietal.2001) ancl à very igh fractional polarization of ~40% has been reported. in he source both at visible and LH frequencies (Lmipeyetal. 1982).," Over the past few decades this blazar has been seen to be highly variable over all timescales and at all frequencies \citep{ghosh1995, heidt1996, raiteri2001} and a very high fractional polarization of $\sim$ $\%$ has been reported in the source both at visible and IR frequencies \citep{impey1982}."
. By analysing 25 vears 2000) of optical and radio data. Raiterietal.(2001) argued that the source seemed to have an optical outburst. period of ~5.70 vears but the expected: outburst in. 2004 was not detected. by a 20032005 multiwavelength WEBT observing campaign (Raiterictal.2006a).," By analysing 25 years $-$ 2000) of optical and radio data, \citet{raiteri2001} argued that the source seemed to have an optical outburst period of $\sim$ 5.70 years but the expected outburst in 2004 was not detected by a 2003–2005 multiwavelength WEBT observing campaign \citep{raiteri2006a}."
. A more detailed long term optical data analvsis suggested a possible out period. of ~s vears in this source (Raiterietal.90000) and burst.this period was supported by subsequent observations Guptaetal.(2008c)., A more detailed long term optical data analysis suggested a possible outburst period of $\sim$ 8 years in this source \citep{raiteri2006b} and this period was supported by subsequent observations \citet{gupta2008c}.
. Strong LDV tus variations of 9.54. and 13.7% during two nights were observed by Guptactal.(2008€)., Strong IDV flux variations of $\%$ and $\%$ during two nights were observed by \citet{gupta2008c}.
.. Recently. tanietal.(2009). reported the possible presence of nearly »eriodic Ductuations. with a timescale of ~17 clays. ina 12.7 vear long. X-ray light curve of AO | 164 obtained by he All Sky Monitor (ASAI) instrument on the Rossi X-ray ‘Timing Explorer (RXTE) satellite.," Recently, \citet{rani2009} reported the possible presence of nearly periodic fluctuations, with a timescale of $\sim$ 17 days, in a 12.7 year long X-ray light curve of AO $+$ 164 obtained by the All Sky Monitor (ASM) instrument on the Rossi X-ray Timing Explorer (RXTE) satellite."
 We observed three LOY LCs of the source AO 0235|164 oetween October 2008 and January 2009., We observed three IDV LCs of the source AO 0235+164 between October 2008 and January 2009.
 The brightness of he source decayed by —2.2 magnitude during this period (Ranietal.2010b)., The brightness of the source decayed by $\sim$ 2.2 magnitude during this period \citep{rani2010b}.
. We found a significant [lux variation in two out of three LCs., We found a significant flux variation in two out of three LCs.
 A continuous fading trend. of —0.13 magnitude and both brightening anc decaving of 70.04 magnitude were observed on October 20 11) and October 23. 2008 22). respectively.," A continuous fading trend of $\sim$ 0.13 magnitude and both brightening and decaying of $\sim$ 0.04 magnitude were observed on October 20 1) and October 23, 2008 2), respectively."
 A possible timescale ol variability is 75.2 hr (from the SE analysis) for the LC observed on 20 October. while any such timescale exceeds the length of our observation on 23 October.," A possible timescale of variability is $\sim$ 5.2 hr (from the SF analysis) for the LC observed on 20 October, while any such timescale exceeds the length of our observation on 23 October."
 However this putative timescale is not supported by the DCE analysis., However this putative timescale is not supported by the DCF analysis.
 The blazar PIs 014 is classified as a FSRQ and has a redshift of 0.915., The blazar PKS $-$ 014 is classified as a FSRQ and has a redshift of 0.915.
 It has been observed in optical bands since 1969., It has been observed in optical bands since 1969.
 Several papers have reported multiple opticallyactive and. bright phases of the source ancl perhaps regular major Daring eveles (c.g.Villatactal.therein). Webbctal.(1998).," Several papers have reported multiple opticallyactive and bright phases of the source and perhaps regular major flaring cycles \citep[e.g.,][and references therein]{villata1997, webb1998, 
raiteri1998}."
 reported. that. there were increases of ~ 3 magnitudes during the active phases of this blazar during their observations that stretched fron December 1969 to January 1986., \citet{webb1998} reported that there were increases of $\sim$ $-$ 3 magnitudes during the active phases of this blazar during their observations that stretched from December 1969 to January 1986.
 Clementsetal.(1995) have reported. variations of z mag Te 2.8 mag with a time scale of ~22 vears., \citet{clements1995} have reported variations of $\Delta$ mag $\cong$ 2.8 mag with a time scale of $\sim$ 22 years.
 We found a variation of 70.1 magnitude within 2 hrs in the brief optical LCs of the source on both of the clays of observation in October and December 2008., We found a variation of $>$ 0.1 magnitude within 2 hrs in the brief optical LCs of the source on both of the days of observation in October and December 2008.
 During this »eriod the source brightened by a factor of —0.7 magnitude (Ranietal.2010b)., During this period the source brightened by a factor of $\sim$ 0.7 magnitude \citep{rani2010b}.
. The nominal timescale of variability (from the peak of the SE) is 0.12 hrs for the LC observed on December 26 and multiple dips might indicate à possible »eriodicity around 0.18 hrs. which is weakly supported. by he DCE curve.," The nominal timescale of variability (from the peak of the SF) is 0.12 hrs for the LC observed on December 26 and multiple dips might indicate a possible periodicity around 0.18 hrs, which is weakly supported by the DCF curve."
 The other LC is irregular ancl shows no hint of a timescale 22)., The other LC is irregular and shows no hint of a timescale 2).
 The blazar S5 0716] 714 is classified as a BL Lac object., The blazar S5 $+$ 714 is classified as a BL Lac object.
 Nilssonetal.(2008) mace a recent. claim of redshift determination of the source to be 2=0.31+0.08., \citet{nilsson2008} made a recent claim of redshift determination of the source to be $z = 0.31\pm0.08$.
 This source has been extensively studied at all observable wavelengths [rom radio to 5-ravs on diverse time scales (Magneretal.1990:οσα&Wagner1996:Villatactetal.2006:OstoreroctGupta 2008a.c).," This source has been extensively studied at all observable wavelengths from radio to $\gamma$ -rays on diverse time scales \citep{wagner1990, heidt1996, villata2000, raiteri2003, montagni2006, foschini2006, ostorero2006, 
gupta2008a, gupta2008c}."
. This source is one of the brightest BL Lacs in optical bands with an LOW duty evele of nearly 1., This source is one of the brightest BL Lacs in optical bands with an IDV duty cycle of nearly 1.
 Unsurprisingly. it has been the subject of several optical monitoring campaigns on LDV timescales (Lleidt&Wagner1996:Montagnietal.2006:Guptaetal. 2008c).," Unsurprisingly, it has been the subject of several optical monitoring campaigns on IDV timescales \citep{heidt1996, montagni2006, gupta2008c}."
. This source has shown [ive major optical outhursts (Ciuptactal.2008€). at intervals of ~3.0£0.3 vears., This source has shown five major optical outbursts \citep{gupta2008c} at intervals of $\sim$ $\pm$ 0.3 years.
 High optical polarizations of ~ 20% - 20% has also been observed in the source (Lakaloetal.1994:Fanetal. 1997).," High optical polarizations of $\sim$ $\%$ - $\%$ has also been observed in the source \citep{takalo1994, 
fan1997}."
.. Guptaetal.(2009). reported: good evidence [or nearly periodic oscillations in a few of the intraclay optical light curves of the source observed by Montagni (2006)., \citet{gupta2009} reported good evidence for nearly periodic oscillations in a few of the intraday optical light curves of the source observed by \citet{montagni2006}.
. Good evidence of presence ofa 715 minute periodic oscillation at optical frequencies has been reported by Ranietal.(20102 )., Good evidence of presence of a $\sim$ 15 minute periodic oscillation at optical frequencies has been reported by \citet{rani2010a}.
. Our optical IDV observations of 55 0716] 714 spans a time period from October 2008 to January 2009., Our optical IDV observations of S5 $+$ 714 spans a time period from October 2008 to January 2009.
 The source brightened by a factor of ~2 magnitude during this period (Ranietal.2010b)., The source brightened by a factor of $\sim$ 2 magnitude during this period \citep{rani2010b}.
. We found significant. microvariability of —0.1 magnitude in three out of four LCs of the source., We found significant microvariability of $\sim$ 0.1 magnitude in three out of four LCs of the source.
 The LCs observed on December 24. 2008 and January 03. 2009 show continuous [fading trends trend of the order of 7.1 magnitude. though the former is abrupt while the latter is eracual.," The LCs observed on December 24, 2008 and January 03, 2009 show continuous fading trends trend of the order of $\sim$ 0.1 magnitude, though the former is abrupt while the latter is gradual."
 Both fading ancl brightening and fading trends of 70.05 magnitude were observed over just a Low minutes on December 23. 2008.," Both fading and brightening and fading trends of $\sim$ 0.05 magnitude were observed over just a few minutes on December 23, 2008."
 The caleulated possible variability timescales are listed in Table 4. but the lack of agreement between the SE and. DCL possibilities leads us to discount their reality.," The calculated possible variability timescales are listed in Table 4, but the lack of agreement between the SF and DCF possibilities leads us to discount their reality."
 Vheblazar PAS 0735] 718 has been classified as à BL Lac object (Carswelletal. 1974).., Theblazar PKS $+$ 718 has been classified as a BL Lac object \citep{carswell1974}. .
 Papers concerning its redshift determination (Carswelletal.1974: had. set a lower limit of s>0.4 and z=0.424 was reported for the source using a LIST," Papers concerning its redshift determination \citep{carswell1974, falomo2000} had set a lower limit of $z > 0.4$ and $z = 0.424$ was reported for the source using a HST"
The existence of near-infrarecl period-Iuminosity. relations in LAIC Asymptotic Giant Braneh (AGB) stars is now well-known.,The existence of near-infrared period-luminosity relations in LMC Asymptotic Giant Branch (AGB) stars is now well-known.
 They have also been found in the 66522 Daade's Window of the inner Bulge by Glass Schultheis (2003) and have since been extenced to globular clusters and other members of the Local Group., They have also been found in the 6522 Baade's Window of the inner Bulge by Glass Schultheis (2003) and have since been extended to globular clusters and other members of the Local Group.
 The LMC and the 66522 fields clifler markedly in metallicity but contain large numbers of stars at approximately uniform distances. making them highly suitable places for studying population dillerences.," The LMC and the 6522 fields differ markedly in metallicity but contain large numbers of stars at approximately uniform distances, making them highly suitable places for studying population differences."
 Among the AGB stars. many of the semi-regular variables have small amplitudes so that. in contrast to the AMiras. they can reveal useful distance information from single-cpoch observations if their periods are otherwise known.," Among the AGB stars, many of the semi-regular variables have small amplitudes so that, in contrast to the Miras, they can reveal useful distance information from single-epoch observations if their periods are otherwise known."
 Infrared studies have the additional advantage that the effects of interstellar absorption are minimized: εν in the mid-LII. can be as low as «di0.04 mag., Infrared studies have the additional advantage that the effects of interstellar absorption are minimized; $A_{\lambda}$ in the mid-IR can be as low as $\sim A_V \times 0.04$ mag.
 Examination of the period-Iuminosity relations of ACD stars olfers the possibility. of gaining insight into the physics of their outer atmospheres., Examination of the period-luminosity relations of AGB stars offers the possibility of gaining insight into the physics of their outer atmospheres.
 Many of the. semi-regulars exhibit multiple periodicities., Many of the semi-regulars exhibit multiple periodicities.
 The principal peaks in their periodograms lie in the range 10-200 clavs. usually accompanied by other peaks within a factor of two in period and sometimes with additional periods about 10 times as long as the principal ones.," The principal peaks in their periodograms lie in the range 10-200 days, usually accompanied by other peaks within a factor of two in period and sometimes with additional periods about 10 times as long as the principal ones."
 The origin of the long periods is not vet understood., The origin of the long periods is not yet understood.
 At least one case is known in which a variation of this kind starts as a momentary decrease in amplitude ancl develops in width over subsequent eveles (Blanco 26: see Glass Schultheis. 2002).," At least one case is known in which a variation of this kind starts as a momentary decrease in amplitude and develops in width over subsequent cycles (Blanco 26; see Glass Schultheis, 2002)."
 One of the most important. aspects of the Iong-period variables is their high mass-loss rates., One of the most important aspects of the long-period variables is their high mass-loss rates.
 Though Mira variables are major contributors of matter to the interstellar medium. the ISOGAL survey in the galactic plane (Omont ct al 2003). which made use of the ISO infrared satellite. showed that many other Iate-type giants also shed large quantities of dust.," Though Mira variables are major contributors of matter to the interstellar medium, the ISOGAL survey in the galactic plane (Omont et al 2003), which made use of the ISO infrared satellite, showed that many other late-type giants also shed large quantities of dust."
" The 7] - 15] vs 15] colour-magnitude diagrams that resulted from ISOCGAL show a continuous distribution of mass-losing stars from the λαο end of the colour range to the ""red! (Class et 11999).", The [7] - [15] vs [15] colour-magnitude diagrams that resulted from ISOGAL show a continuous distribution of mass-losing stars from the `blue' end of the colour range to the `red' (Glass et 1999).
 Jocause these stars are comparatively numerous they rival the Miras in their total dust output., Because these stars are comparatively numerous they rival the Miras in their total dust output.
 Using an objective prism. survey of the 66522 field. by Blanco (1986). it was possible to show that the mass-losinge stars are all giants of [ater spectral type than about ALS (Class Schultheis 2002)., Using an objective prism survey of the 6522 field by Blanco (1986) it was possible to show that the mass-losing stars are all giants of later spectral type than about M5 (Glass Schultheis 2002).
 Moreover. thanks to variability data generated as à product of the NLACIIO. OGLE ancl similar gravitational-lensing experiments. it is also known that they are nearly," Moreover, thanks to variability data generated as a by-product of the MACHO, OGLE and similar gravitational-lensing experiments, it is also known that they are nearly"
first VELTI/ MIDI observations of V1647 Ori whose eruptive behavior suggests that il is either an FUOR or an EX Lupi (EXor) type object.,first VLTI/ MIDI observations of V1647 Ori whose eruptive behavior suggests that it is either an FUOR or an EX Lupi (EXor) type object.
 In this case it was possible to fit both. the SED and the observed MIR. visibility with a simple disk model with moderate disk flaring.," In this case it was possible to fit both, the SED and the observed MIR visibility with a simple disk model with moderate disk flaring."
 For FU Ori itself it was Malbetetal.(2005) who analvzed a wealth of NIR interferometric data., For FU Ori itself it was \citet{malbet} who analyzed a wealth of NIR interferometric data.
 Thev showed that the NIR visibilities and the SED could be fitted with two models: One consisting simplv of an optically (hick ancl geometrically (hin accretion disk ancl a second one consisting of an accretion disk and an embedded “hot spot”.," They showed that the NIR visibilities and the SED could be fitted with two models: One consisting simply of an optically thick and geometrically thin accretion disk and a second one consisting of an accretion disk and an embedded ""hot spot""."
 From (heir error statistics these authors concluded that the latter model was more likely., From their error statistics these authors concluded that the latter model was more likely.
 In summary il becomes clear that up to now no coherent picture can be derived [rom the interferometric observations of FUORSs and the group of objects seems to be rather inhomogeneous., In summary it becomes clear that up to now no coherent picture can be derived from the interferometric observations of FUORs and the group of objects seems to be rather inhomogeneous.
 In this paper we present the first MUR interferometric measurements of FU Orionis., In this paper we present the first MIR interferometric measurements of FU Orionis.
 The data are (hus complementary to (he NIB. observations of Malbet et al. (, The data are thus complementary to the NIR observations of Malbet et al. (
2005).,2005).
 In section 2 we briefly describe the observations and the data reduction process., In section 2 we briefly describe the observations and the data reduction process.
 In section 3 we discuss the findings derived from the N-band acquisition images., In section 3 we discuss the findings derived from the N-band acquisition images.
 The 8-13/mi spectrum of FU Ori is anialvzed in section 4., The $\mu$ m spectrum of FU Ori is analyzed in section 4.
 In sections 5 and 6 we discuss the results from the interferometric measurements. Le. the visibilities and the correlated Παν spectra. respectively.," In sections 5 and 6 we discuss the results from the interferometric measurements, i.e. the visibilities and the correlated flux spectra, respectively."
 A simple analviical disk model and its fit to the SED and the visibilities is presented in section 7., A simple analytical disk model and its fit to the SED and the visibilities is presented in section 7.
 Finally. we summarize our conclusions and mention some future prospects in section 8.," Finally, we summarize our conclusions and mention some future prospects in section 8."
 The observations were carried out between October 31°! and November 4 2004 with the Mid-Infrared Interferometrie Instrument (MIDI) at ESOs Very Large Telescope Iiterferometer (VLTI) on Paranal/Chile., The observations were carried out between October $^{st}$ and November $^{th}$ 2004 with the Mid-Infrared Interferometric Instrument (MIDI) at ESO's Very Large Telescope Interferometer (VLTI) on Paranal/Chile.
 Together with the heck Interferometer Nuller that recently started to produce first scientific results (Mennessonetal.2005).. MIDI is currently. worldwide the onlv instrument able to conduct spectrally resolved interferometric observations in (he infrared (Leinertetal.2004)..," Together with the Keck Interferometer Nuller that recently started to produce first scientific results \citep{mennesson}, MIDI is currently worldwide the only instrument able to conduct spectrally resolved interferometric observations in the mid-infrared \citep{leinert}."
 For the observations MIDI was used in high-sens mode using the δα. prism as clispersive element vielding a spectral resolution of 30., For the observations MIDI was used in high-sens mode using the NaCl prism as dispersive element yielding a spectral resolution of 30.
 The maximum projected baseline was 56.25m and the minimum projected baseline 44.561 leading (o an angular resolution at 10jan of 0.7029 and 0.7056. respectively.," The maximum projected baseline was 86.25m and the minimum projected baseline 44.56m leading to an angular resolution at $\mu$ m of $''$ 029 and $''$ 056, respectively."
 For an assumed distance of 450 pe these values correspond to 13.1 AU and 25.2 AU., For an assumed distance of 450 pc these values correspond to 13.1 AU and 25.2 AU.
 A journal of the observations including projected baselines. position angles and calibrator stars is given in Table 1..," A journal of the observations including projected baselines, position angles and calibrator stars is given in Table \ref{journal}."
 For completeness we also mention the observations from: December 2004 although thev are cisregardecl in the following sections., For completeness we also mention the observations from December 2004 although they are disregarded in the following sections.
 These observations had almost exactly the same baseline ancl position angle as the October observations but showed in general a lower level of total and correlated, These observations had almost exactly the same baseline and position angle as the October observations but showed in general a lower level of total and correlated
where 7' is the temperature of the electron laver. which can be taken as a constant. since we assunie the electrons ave in (thermodynamic equilibrium with the constant temperature quark matter.,"where $T$ is the temperature of the electron layer, which can be taken as a constant, since we assume the electrons are in thermodynamic equilibrium with the constant temperature quark matter."
 In Eqs. (4))-(5)).," In Eqs. \ref{p2}) \ref{3}) ),"
 2 is the space coordinate measuring height above the quark surface. a is the fine structure constant and is the quark charge density inside the quark matter.," $z$ is the space coordinate measuring height above the quark surface, $\alpha $ is the fine structure constant and }$ is the quark charge density inside the quark matter."
 The boundary conditions for Eqs. (4))-(5)), The boundary conditions for Eqs. \ref{p2}) \ref{3}) )
" are V—V, as 2——o€ and V—0 for 2— oc."," are $V\rightarrow V_{q}$ as $z\rightarrow -\infty $ and $V\rightarrow
0$ for $z\rightarrow \infty $ ."
" In the case of the zero temperature electron distribution at the boundary 200 we have the condition V(0)=(3/4)V, (Alcocketal.1986).", In the case of the zero temperature electron distribution at the boundary $z=0$ we have the condition $V(0)=(3/4)V_{q}$ \citep{Al86}.
. The general solution of Eq. (5)), The general solution of Eq. \ref{3}) )
 is given bv (ChengandIarko2003) where zy is a constant of integration.," is given by \citep{ChHa03}
 where $z_{0}$ is a constant of integration."
" Its value can be obtained [rom the condition of the continuity of the potential across the stars surface. requiring V,(0).7)=V(0.T). where V,(z.D) is the value of the electrostatic potential in the region 2<0. described by Eq. (4))."," Its value can be obtained from the condition of the continuity of the potential across the star's surface, requiring $V_{q}(0,T)=V\left(
0,T\right) $, where $V_{q}\left( z,T\right) $ is the value of the electrostatic potential in the region $z\leq 0$ , described by Eq. \ref{p2}) )."
" Therelore The number censity distribution », of the electrons at the quark star surface can be obtained from n.(2.0)=V/3z?+VT?/3 Uxetinerοἱal.1995:ChengandIHarko2003) and is given by In the limit of zero temperature. 77—0 we obtain V(z)=ag/(z+6). where and bis an integration5 constant."," Therefore The number density distribution $n_{e}$ of the electrons at the quark star surface can be obtained from $n_{e}\left( z,T\right)
=V^{3}/3\pi ^{2}+VT^{2}/3$ \citep{Ke95,ChHa03} and is given by In the limit of zero temperature, $T\rightarrow 0$ we obtain $V(z)=a_0/(z+b)$, where $a_0=\sqrt{3\pi /2\alpha }$ and $b$ is an integration constant."
" ὁ can be determined [rom the boundary condition V(0)=(3/4)V,. which gives b=(4a0/3V,)."," $b$ can be determined from the boundary condition $V(0)=(3/4)V_{q}$, which gives $b=\left(
4a_0/3V_{q}\right) $."
" Therefore. in this case we find for the electron particle number distribution the expression: n,(2)=(1/327)a5/2(z+Qob)."," Therefore, in this case we find for the electron particle number distribution the expression: $n_{e}(z)=(1/3\pi ^{2})a^{3}_{0}/ \left(z+b\right) ^{3}$."
 In the absence of a crust of the quark star.the electron laver can extend (o several thousands fermis outside the stars surface.," In the absence of a crust of the quark star,the electron layer can extend to several thousands fermis outside the star's surface."
 The strength of the electric field £ outside the quark starsurface is given by, The strength of the electric field $E$ outside the quark starsurface is given by
Given the similarity of SN 19988 and SN 1979€ photometric and spectral properties (Liu et al.,Given the similarity of SN 1998S and SN 1979C photometric and spectral properties (Liu et al.
 2000). the light curve of SN 19985 is likely of the same nature as that of SN 1979€. 1n line with the hverodvnamical model of the SN. 1979€ (Blinnikov Bartunoy 1993) we suggest that the light curve OL SN 19988 is the result of an explosion of a red supergiant with an extended envelope. £2—(110)101H.. and a moderate mass of ejecta ~5M...," 2000), the light curve of SN 1998S is likely of the same nature as that of SN 1979C. In line with the hydrodynamical model of the SN 1979C (Blinnikov Bartunov 1993) we suggest that the light curve of SN 1998S is the result of an explosion of a red supergiant with an extended envelope, $R\sim (1-10)\times 10^3~R_{\odot}$, and a moderate mass of ejecta $\sim 5~M_{\odot}$."
 The radioactivity as well as the ejecta-wind interaction are likely responsible for the late-time SN 19988 luminosity., The radioactivity as well as the ejecta-wind interaction are likely responsible for the late-time SN 1998S luminosity.
 One cannot rule out that the ejecta-wind interaction may contribute to the initial phase ofthe light curve as well., One cannot rule out that the ejecta-wind interaction may contribute to the initial phase of the light curve as well.
 The bolometric light curve will be simulated. using a incar Composition of the analytical bolometric light curve of ‘hare’ without wind) SN LE CArnett 1980. 1982) and the ight curve powered by the ejecta-wind interaction (Chugai 1992).," The bolometric light curve will be simulated using a linear composition of the analytical bolometric light curve of 'bare' without wind) SN II (Arnett 1980, 1982) and the light curve powered by the ejecta-wind interaction (Chugai 1992)."
 Phe latter model computes the optical luminosity. ooduced as a result. of reprocessing of the X-ray. radiation rom the outer and inner shocks.," The latter model computes the optical luminosity, produced as a result of reprocessing of the X-ray radiation from the outer and inner shocks."
 This model is upgraded rere to include the Compton cooling of the postshock eas (EFransson 1982) and the reprocessing of the X-ray radiation »w the wind material as well., This model is upgraded here to include the Compton cooling of the postshock gas (Fransson 1982) and the reprocessing of the X-ray radiation by the wind material as well.
 Phe dynamics of the cjecta deceleration in a thin shell approximation (Chevalier. 1982) is solved: numerically. which vields the thin shell radius I) and its velocity eff).," The dynamics of the ejecta deceleration in a thin shell approximation (Chevalier 1982) is solved numerically, which yields the thin shell radius $R_{\rm s}(t)$ and its velocity $v(t)$."
 The light curve computed in an approximation of the instant radiation escape from the C'S shell. is corrected for the diffusion delay in the CS medium using Sobolev (1980) analvtical formula for the escaping luminosity.," The light curve computed in an approximation of the instant radiation escape from the CS shell, is corrected for the diffusion delay in the CS medium using Sobolev (1980) analytical formula for the escaping luminosity."
 The density. profile of a freely. expanding SN envelope (esr/f) used for the calculations of the thin shell dvnamies is a plateau with an outer power law tale where po and ey are defined by the SN mass CA) and kinetic energy. (do): fo is an arbitrary relference moment., The density profile of a freely expanding SN envelope $v=r/t$ ) used for the calculations of the thin shell dynamics is a plateau with an outer power law tale where $\rho_0$ and $v_0$ are defined by the SN mass $M$ ) and kinetic energy $E$ ); $t_0$ is an arbitrary refference moment.
 We adopt a steep density gradient. ὦ=16. to take into account the effect of sweeping up the material of the extended envelope into a dense shell during shock wave breakout phase (Cirasberg et al.," We adopt a steep density gradient, $\omega=16$, to take into account the effect of sweeping up the material of the extended envelope into a dense shell during shock wave breakout phase (Grasberg et al."
 1971: Falk Arnett 1977)., 1971; Falk Arnett 1977).
 Phe template CS density distribution (Fig., The template CS density distribution (Fig.
 1) is used., 1) is used.
" The ""Ni with the mass o£ 0.15AL. (Fassia et al.", The $^{56}$ Ni with the mass of $0.15~M_{\odot}$ (Fassia et al.
 2000) is assumed to be mixed within inner half of the SN mass., 2000) is assumed to be mixed within inner half of the SN mass.
 The average SN ejecta opacity &=0.2 eng + is adopted for the Arnett’s model., The average SN ejecta opacity $k=0.2$ $^2$ $^{-1}$ is adopted for the Arnett's model.
 The list of the essential. parameters of the light curve model. includes the cjecta mass Af. kinetic energy ££. presupernova radius £5. the wind parameters ey and. wes assuming the fixed shape of the density. distribution of the SN cjccta and the CS eas.," The list of the essential parameters of the light curve model includes the ejecta mass $M$, kinetic energy $E$, presupernova radius $R_0$, the wind parameters $w_1$ and $w_2$ assuming the fixed shape of the density distribution of the SN ejecta and the CS gas."
" Exploring the parameter space Lec us to the optimal choice of the SN parameters: M—5M... E—Ll.10% erg and A,=2410H cm."," Exploring the parameter space led us to the optimal choice of the SN parameters: $M=5~M_{\odot}$, $E=1.1\times10^{51}$ erg and $R_0=2.4\times10^{14}$ cm."
 Le shouk be stressed. that these values may be in some error given a simplicity of our model.," It should be stressed, that these values may be in some error given a simplicity of our model."
 The density in the inner CS shell (ep) affects the very carly phase <30 d of the ligh curve. although. we are not able to derive wy reliably from the light curve analysis. since the Arnett’s analytical mode underestimates the early luminosity (Arnett 1980).," The density in the inner CS shell $w_1$ ) affects the very early phase $<30$ d of the light curve, although, we are not able to derive $w_1$ reliably from the light curve analysis, since the Arnett's analytical model underestimates the early luminosity (Arnett 1980)."
 The lieh curve is insensitive to the outer wind density unless we substantially exceeds 2.LOH ο +., The light curve is insensitive to the outer wind density unless $w_2$ substantially exceeds $2\times 10^{16}$ g $^{-1}$.
 1n Fig., In Fig.
 2 two models of the light curve are shown or input parameters given in Table 1 and assuming that he explosion occured on. 1998. February 24.7 UT. the day after the last pre-discovery observation.," 2 two models of the light curve are shown for input parameters given in Table 1 and assuming that the explosion occured on 1998 February 24.7 UT, the day after the last pre-discovery observation."
 This choice is consistent with the evolution of the photospherie radius (Vig., This choice is consistent with the evolution of the photospheric radius (Fig.
 2)., 2).
 The template CS density. distribution (Fig., The template CS density distribution (Fig.
" 1) is used for the model A. while the model B dillers bv. the slightlv higher eutolf. radius. 2,4."," 1) is used for the model A, while the model B differs by the slightly higher cutoff radius $R_{\rm c,1}$."
 Phe parameter ay is ouncl from the modeling of the light curve. photospheric radius. CDS velocity and the line broadening cllect (section 3) using an itterative procedure.," The parameter $w_1$ is found from the modeling of the light curve, photospheric radius, CDS velocity and the line broadening effect (section 3) using an itterative procedure."
 Derivecl values shown in ‘Table 1 include the moment ἐν. when the optical depth of the CDS in the Paschen continuum at Hà. wavelength τοομαι}=1. the time fo. when the outer shock becomes adiabatic. and three important values on March. 6: the padius of the thin shell (2.0). which coincides with the CDS. cllective temperature (Z5). and. Thomson optical depth (rp) of the wind.," Derived values shown in Table 1 include the moment $t_1$, when the optical depth of the CDS in the Paschen continuum at $\alpha$ wavelength $\tau(0.65\mu{\rm m})=1$, the time $t_{\rm c}$, when the outer shock becomes adiabatic, and three important values on March 6: the radius of the thin shell $R_{\rm s}$ ), which coincides with the CDS, effective temperature $T_{\rm eff}$ ), and Thomson optical depth $\tau_{\rm T}$ ) of the wind."
 The optical depth of the CDS in the Paschen continuum is caleulated assuming LTE for To=Tap and the number density of the CDS defined. by the isobaric condition. with the thermal pressure equal to the cynanmical pressure pe. where p is the preshock wind density and oe is the thin shell velocity.," The optical depth of the CDS in the Paschen continuum is calculated assuming LTE for $T=T_{\rm eff}$ and the number density of the CDS defined by the isobaric condition, with the thermal pressure equal to the dynamical pressure $\rho v^2$, where $\rho$ is the preshock wind density and $v$ is the thin shell velocity."
 Models. A and D produce similar results being consistent with the empirical light curve. photospheric radii and CDS velocity.," Models A and B produce similar results being consistent with the empirical light curve, photospheric radii and CDS velocity."
 Some luminosity deficit before clay 30 might be related to the mentioned fact that in the analytical light curve the initial luminosity peak is uncdeproduced (Arnett 1980)., Some luminosity deficit before day 30 might be related to the mentioned fact that in the analytical light curve the initial luminosity peak is undeproduced (Arnett 1980).
 Yet. eiven large uncertainties of data. the dillerence between the model and the empirical light curve is not dramatic.," Yet, given large uncertainties of data, the difference between the model and the empirical light curve is not dramatic."
 Note. the factor of two increase in the Luminosity corresponds to higher value of Z;4r.," Note, the factor of two increase in the luminosity corresponds to higher value of $T_{\rm eff}$."
 The CDS is opaque during initial =47 davs in agreement with the previous estimates (section 2)., The CDS is opaque during initial $\approx 47$ days in agreement with the previous estimates (section 2).
 Taking into account the six davs lag between the explosion aud the discovery we conclude that the opaque CDS gets transparent ab zz40 d after the discovery., Taking into account the six days lag between the explosion and the discovery we conclude that the opaque CDS gets transparent at $\approx 40$ d after the discovery.
 This is consistent with the observational [act that strong broad emission and absorption, This is consistent with the observational fact that strong broad emission and absorption
(n= (1) movine toward higher frequencies.,$\alpha = -0.1$ ) moving toward higher frequencies.
 By 30 GIIz (the Ίνα baud). the SED of such a galaxy would contain roughly equal parts thermal aud non-thermal cnussion with flatter à than at 5.95 GIIz.," By $\sim 30$ GHz (the Ka band), the SED of such a galaxy would contain roughly equal parts thermal and non-thermal emission with flatter $\alpha$ than at $5.95$ GHz."
 Figure 2 shows hat this simple expectation docs not hold for our data., Figure \ref{fig:seds} shows that this simple expectation does not hold for our data.
 Qur I&a-baud flux densities texd to lie below the simple nodel: the model predicts a typical C-to-ka ratio z 2.1. while our miceiui ratio is z3.15 with lo scatter 0.75.," Our Ka-band flux densities tend to lie below the simple model: the model predicts a typical C-to-Ka ratio $\approx 2.4$ , while our median ratio is $\approx 3.15$ with $1\sigma$ scatter $0.75$."
 The radio spectim is significaitly steeper than expected noving to higjer frequencies., The radio spectrum is significantly steeper than expected moving to higher frequencies.
 A steep SED at hieh frequencies has been previously served in U/LIRGs by Clemensetal.(2008).. aud re dwarf starburst NGC 1569 (Liseufeldetal.200L).," A steep SED at high frequencies has been previously observed in U/LIRGs by \citet{CLEMENS08}, and the dwarf starburst NGC 1569 \citep{LISENFELD04}."
. If there is a significant thermal coutribution at ÓÉ) GIIz. and there must be based on the high level of star formation in these svstenis. then the svuchrotrou spectral index must be steepeuiug.," If there is a significant thermal contribution at $\nu \sim 30$ GHz, and there must be based on the high level of star formation in these systems, then the synchrotron spectral index must be steepening."
 Clemenset discuss possible imechanisius for this and etal.(2010). revisit the topic. while Liseufeldctal.(2001) discuss possible explanations for a similar observation in the starburst NGC 1569.," \citet{CLEMENS08} discuss possible mechanisms for this and \citet{CLEMENS10} revisit the topic, while \citet{LISENFELD04}
 discuss possible explanations for a similar observation in the starburst NGC 1569."
 Allowiug that the thermal cmission should be present. the svuchrotron enission must be depressed at high frequency.," Allowing that the thermal emission should be present, the synchrotron emission must be depressed at high frequency."
 Depressed svuchrotrou chussion could result from svuchrotron aud inverse Compton losses in aging starbursts or reelous with high maeuetic fields., Depressed synchrotron emission could result from synchrotron and inverse Compton losses in aging starbursts or regions with high magnetic fields.
 However. there is no evidence that we observe all of these galaxies at a preferential time aud these explanations appear inadequate to match the maguitude of the effect.," However, there is no evidence that we observe all of these galaxies at a preferential time and these explanations appear inadequate to match the magnitude of the effect."
 Alternatively. the injection spectruii of electron energies could differ from those iu norlal galaxies.," Alternatively, the injection spectrum of electron energies could differ from those in normal galaxies."
 This is possible for an ACN. but less plausible for radio contiuuuu enuüssiou originating frou star formation.," This is possible for an AGN, but less plausible for radio continuum emission originating from star formation."
 We suspect that a modified iujection spectrin leads to a deficit of high frequency svuchrotron cluission and dives the ligh-frequency flux deficit., We suspect that a modified injection spectrum leads to a deficit of high frequency synchrotron emission and drives the high-frequency flux deficit.
 This is a topic that we will investigate further with our full hieh resolutiou data., This is a topic that we will investigate further with our full high resolution data.
 Depressed svuchrotron at high frequencies may be a way to distiuguisli systems where the radio is dominated by AGN., Depressed synchrotron at high frequencies may be a way to distinguish systems where the radio is dominated by AGN.
" We expect a ΙΙ level of thermal cussion in systems with radio cuuission due inostlv το star formation. so ACN likely provide most of the radio enission iu the steepest-spectruni sources,"," We expect a minimum level of thermal emission in systems with radio emission due mostly to star formation, so AGN likely provide most of the radio emission in the steepest-spectrum sources."
 Despite the surprises iu the radio SED. the radio and infrared fiuxes still track one another well.," Despite the surprises in the radio SED, the radio and infrared fluxes still track one another well."
" We calculate the far-infrared-to-radio ratio defined by Ποιοιetal.(1985) as qo,=logyy(Frin/S$.) with Fri; the £u- in units of 3.75«1042 W in? and 5, in Wan 7 +."," We calculate the far-infrared-to-radio ratio defined by \citet{HELOU85} as $q_{\rm \nu} = \log_{10}
\left(F_{\rm FIR} / S_{\rm \nu}\right)$ with $F_{\rm FIR}$ the far-IR in units of $3.75 \times
10^{12}$ W $^{-2}$ and $S_{\nu}$ in W $^{-2}$ $^{-1}$."
 The median «σος=2.8 with a scatter of dex., The median $q_{5.95} = 2.8$ with a scatter of $\approx 0.16$ dex.
 The Ίνα baud shows comparable scatter., The Ka band shows comparable scatter.
 The band qus has ~50% more scatter. ~0.25 dex.," The L-band $q_{1.5}$ has $\sim 50\%$ more scatter, $\sim 0.25$ dex."
 Yunetal.(2001) observed 0.26 dex scatter iu the Z-band radio-IBR correlation aud 0.33 dex scatter for LIRGs and ULIRGs., \citet{YUN01} observed 0.26 dex scatter in the $L$ -band radio-IR correlation and 0.33 dex scatter for LIRGs and ULIRGs.
 The sinaller overall scatter iu our sample may simply be a result of small τήν statistics., The smaller overall scatter in our sample may simply be a result of small number statistics.
 We interpret the lower scatter at high frequencies iu our sample as a manifestation of the same phenomenon that leads to lieher scatter in 4i; at high luminosities., We interpret the lower scatter at high frequencies in our sample as a manifestation of the same phenomenon that leads to higher scatter in $q_{\rm 1.5}$ at high luminosities.
 The curved SED at low frequeucies in luminous IB salaxies adds scatter to the radio-IR. correlation as plivsieal processes otherthan just star formation become important., The curved SED at low frequencies in luminous IR galaxies adds scatter to the radio-IR correlation as physical processes otherthan just star formation become important.
 At lieher frequencies and in lower huuinositv galaxies the effects are less iniportant., At higher frequencies and in lower luminosity galaxies the effects are less important.
 The correlation among the radio bands is stronger than +16 correlation with the IR. with the strongest correlation," The correlation among the radio bands is stronger than the correlation with the IR, with the strongest correlation"
as shown in Section 3.1.,as shown in Section 3.1.
 We attempt to bracket (he range of possible spectra by first analvzine a sample of blazars whose power law spectral inclices are normally distributed: around. a mean of -2.15 with standard deviation 0.04. representing a situation where there is a range of spectral indices but no intrinsic rolloff in this energy range.," We attempt to bracket the range of possible spectra by first analyzing a sample of blazars whose power law spectral indices are normally distributed around a mean of -2.15 with standard deviation 0.04, representing a situation where there is a range of spectral indices but no intrinsic rolloff in this energy range."
 To model intrinsic rolloffs. we (hen repeat the analysis with a sample of blazars whose unredshifted spectra have a broken power law with mean index -2.15 below 50Hr GeV and -3.15 above. again with a standard deviation of 0.04 in each case.," To model intrinsic rolloffs, we then repeat the analysis with a sample of blazars whose unredshifted spectra have a broken power law with mean index -2.15 below 50 GeV and -3.15 above, again with a standard deviation of 0.04 in each case."
 The Gamma-ray Large. Area Space Telescope (GLAST) is under development with a planned launch in 2006 (Michelson 2001)., The Gamma-ray Large Area Space Telescope (GLAST) is under development with a planned launch in 2006 (Michelson 2001).
 The Large Area Telescope (LAT) of GLAST will observe gamma ravs with energies [rom 20 MeV to >300 GeV. GLAST will have a much larger effective area than EGRET. especially at higher energies (peak effective area >SOOO cm? al >1 GeV). a larger field of view. and sub-arcmünute scale source localization.," The Large Area Telescope (LAT) of GLAST will observe gamma rays with energies from 20 MeV to $>300$ GeV. GLAST will have a much larger effective area than EGRET, especially at higher energies (peak effective area $>8000$ $^{2}$ at $>1$ GeV), a larger field of view, and sub-arcminute scale source localization."
 GLAST should be able to reach a 56 point source fIux sensitivity of less than 1.5x10? photons ? ! for E>100 MeV within live νου»., GLAST should be able to reach a $5\sigma$ point source flux sensitivity of less than $1.5\times10^{-9}$ photons $^{-2}$ $^{-1}$ for $E>100$ MeV within five years.
 As noted above. using the distribution of blazars observed by EGRET aud extrapolating to lower fluxes. it is estimated that GLAST will detect thousands of blazars.," As noted above, using the distribution of blazars observed by EGRET and extrapolating to lower fluxes, it is estimated that GLAST will detect thousands of blazars."
 Improved. angular resolution should allow a high percentage of optical idenüfications ancl redshift measurements. depending on the available ground-based resources.," Improved angular resolution should allow a high percentage of optical identifications and redshift measurements, depending on the available ground-based resources."
 Inproved high-enerey performance should vield accurate flux determinations above 10 GeV [or many of these sources., Improved high-energy performance should yield accurate flux determinations above 10 GeV for many of these sources.
 Note that our modeling is based on (he generic parameters outlined in the GLAST Science Requirements Document (Michelson 2001): the performance of the flight instrument may be substantially better., Note that our modeling is based on the generic parameters outlined in the GLAST Science Requirements Document (Michelson 2001); the performance of the flight instrument may be substantially better.
 Tosimulate the gamma-ray sources observable bv GLAST. we need a reasonable extrapolation ol the EGRET source distribution to the GLAST flix limit.," To simulate the gamma-ray sources observable by GLAST, we need a reasonable extrapolation of the EGRET source distribution to the GLAST flux limit."
 We used the two Iuminosity functions described in section 2.2.1. for this purpose. but our main conclusions do not depend significantly on (his choice.," We used the two luminosity functions described in section \ref{sec-2.2.1}
 for this purpose, but our main conclusions do not depend significantly on this choice."
 We note that any predictions made now will be supplanted by ihe data GLAST itself provides., We note that any predictions made now will be supplanted by the data GLAST itself provides.
 Belore any observational selection. according to the luminosity [unction by Salamon S(ecker (1996). ~12.000 blazars in principle will have fluxes in the range detectable by GLAST.," Before any observational selection, according to the luminosity function by Salamon Stecker (1996), $\sim12,000$ blazars in principle will have fluxes in the range detectable by GLAST."
 Each one was assigned a random huminositv and redshift according to this model., Each one was assigned a random luminosity and redshift according to this model.
"Using this in the last line of equation (28)) we find where wSw,=we.",Using this in the last line of equation \ref{eq:mom1exp}) ) we find where $\omega\equiv\omega_1=\omega_2$.
" In deriving the second equality. we note that the bombardment must occur between £ and /|7 and use the shiftκ. properties. of⋅ the Fourier∖⋠ transform⋅ to writeMM (b(uo,Join(us)&y=eoe)b""(uo)us) where the transform. b(u) denotes the transform of an event centred about the temporal origin."," In deriving the second equality, we note that the bombardment must occur between $t$ and $t+\tau$ and use the shift properties of the Fourier transform to write $\left\langle b^{lm}_r (\omega_1) b^{\ast lm}_s (\omega_2)
\right\rangle = e^{-2\omega t} \left\langle {\bar b}^{lm}_r (\omega_1)
 {\bar b}^{\ast lm}_s (\omega_2) \right\rangle$ where the transform ${\bar b}(\omega)$ denotes the transform of an event centred about the temporal origin."
" Inthe limit τ+0. this expression becomes 4z0(u,—we)."," In the limit $\tau\rightarrow0$, this expression becomes $4\pi\delta(\omega_1-\omega_2)\tau$."
 Substituting. this back intoequation (28)) we can perform one of the w integrals straight away.," Substituting, this back intoequation \ref{eq:mom1exp}) ) we can perform one of the $\omega$ integrals straight away."
" After rearranging we have The expression for GAL;|rAd,(f7); follows by analogy with the equations (28)) and (39)) in refsecipointmass.."," After rearranging we have The expression for $\left\langle \Delta I_j(t+\tau) \Delta I_k(t+\tau)
\right\rangle$ follows by analogy with the equations \ref{eq:mom1exp}) ) and \ref{eq:mom2exp}) ) in \\ref{sec:pointmass}."
 Symmetry suggests the choice of perturbing orbits on the equatorial plane should not ellect the final results., Symmetry suggests the choice of perturbing orbits on the equatorial plane should not effect the final results.
 This can be explicitly demonstrated. explicitly. using the rotational properties of the spherical harmonies., This can be explicitly demonstrated explicitly using the rotational properties of the spherical harmonics.
" Let A5,(0.3.5) be the rotation matrix with the Euler angles a.3.5."," Let ${\cal
 R}^l_{mm^\prime}(\alpha,\beta,\gamma)$ be the rotation matrix with the Euler angles $\alpha,\beta,\gamma$."
 Then. because where the primed coordinates refer to the rotated coordinate system. we have For an isotropic spherical s ) is independent of n.," Then, because where the primed coordinates refer to the rotated coordinate system, we have For an isotropic spherical system ${\cal M}^{lm}_{\mu r}(\omega)$ is independent of $m$ ."
" We can exploit this and the rotational properties of f""(4) to simplify the computation ""n(hf?(obe(aes)."," We can exploit this and the rotational properties of $b^{lm}_r (\omega)$ to simplify the computation of $ \left\langle
 b^{lm}_r (\omega_1) b^{\ast lm}_s (\omega_2) \right\rangle$."
" We may express p""ζω} in any convenient coordinate svstem and. use the rotation matrices to rotate this to any orientation: Summing over all values m for à given / we have having used the orthogonality of rotation matrices.", We may express $b^{lm}_r (\omega)$ in any convenient coordinate system and use the rotation matrices to rotate this to any orientation: Summing over all values $m$ for a given $l$ we have having used the orthogonality of rotation matrices.
 Finally. we assume that the ensemble average includes random events from alldirections and therefore only the same event will be correlated in the computation of¢(uim(as)(wea).," Finally, we assume that the ensemble average includes random events from all directions and therefore only the same event will be correlated in the computation of $\left\langle b^{lm}_r (\omega_1) b^{\ast lm}_s
 (\omega_2) \right\rangle$."
 This paper presents a general equation for noise-driven evolution which incorporates the full self-gravitating response of a stochastic process in the perturbation limit., This paper presents a general equation for noise-driven evolution which incorporates the full self-gravitating response of a stochastic process in the perturbation limit.
 Phe motivating question is same as that of violent relaxation: what is the response of a stellar svstem to a lluetuating potential?, The motivating question is same as that of violent relaxation: what is the long-term response of a stellar system to a fluctuating potential?
 By working in the perturbation limit. the linearity &uarantees that the process is Markovian and. therefore the response of the stellar system to repeated stochastic events is naturally treated using the matrix-methoc and the statistic methods for handling general stochastic cilferential equations.," By working in the perturbation limit, the linearity guarantees that the process is Markovian and therefore the response of the stellar system to repeated stochastic events is naturally treated using the matrix-method and the statistic methods for handling general stochastic differential equations."
 In general. expansions of integral equations for stochastic processes vield an infinite number of terms.," In general, expansions of integral equations for stochastic processes yield an infinite number of terms."
 A general theorem demonstrates that the truncation at quadratic order is consistent for a Markov. process and the resulting evolution equation takes the Pokker-Planck form’., A general theorem demonstrates that the truncation at quadratic order is consistent for a Markov process and the resulting evolution equation takes the Fokker-Planck .
.. Evaluation of the Fokker-Planck cocllicicnts requires the specifvingthe response of stellar system individual events in the stochastic process., Evaluation of the Fokker-Planck coefficients requires the specifyingthe response of stellar system individual events in the stochastic process.
wav through the thermally pulsing ΑΟ and amass loss phases.,way through the thermally pulsing AGB and mass loss phases.
 Because of the full caleulation of the evolution of progenitor stars. the white dxecarf sequences incorporates realistic and consistent carbon-oxvecn profiles of relevance for an accurate computation of the energv released by carbon-oxvgeu pliase separation.," Because of the full calculation of the evolution of progenitor stars, the white dwarf sequences incorporates realistic and consistent carbon-oxygen profiles — of relevance for an accurate computation of the energy released by carbon-oxygen phase separation."
 Iu addition. detailed nou-erav model atmospheres are used to derive the outer boundary condition for the evolving sequences.," In addition, detailed non-gray model atmospheres are used to derive the outer boundary condition for the evolving sequences."
 At the low huuiuosities where the process of ??Ne sedimentation becomes relevant. the outer boundary conditions influence the cooling tines.," At the low luminosities where the process of $^{22}$ Ne sedimentation becomes relevant, the outer boundary conditions influence the cooling times."
 We find that 7?Ne sedimentation las notable consequences for the cooling times of cool white dwarfs characterized by a high metal couteut iu their iuteriors., We find that $^{22}$ Ne sedimentation has notable consequences for the cooling times of cool white dwarfs characterized by a high metal content in their interiors.
 The related energy release strouely delays their cooling., The related energy release strongly delays their cooling.
 The precise value of the delavs depends on the mass of the white dur. its Inninositv aud ou the metal content.," The precise value of the delays depends on the mass of the white dwarf, its luminosity and on the metal content."
 For instance. because of their larger eravities. the impact of ??Ne sedimentation starts earlier in more massive white dwarts.," For instance, because of their larger gravities, the impact of $^{22}$ Ne sedimentation starts earlier in more massive white dwarfs."
 Di particular. appreciable delays in the cooling rates start to manifest themselves at Iuninosities oflos(L/L.)2z3.5 to L2.," In particular, appreciable delays in the cooling rates start to manifest themselves at luminosities of $\log(L/L_{\sun}) \approx -3.5$ to $-4.2$."
 In ecneral. the magnitude of the delays iu the cooling rates resulting. from 7?Ne sedimentation 1s comparable (Cor even larger iu the case of Z— 0.06) to the delays induced by carbon-oxveen pliase separation.," In general, the magnitude of the delays in the cooling rates resulting from $^{22}$ Ne sedimentation is comparable (or even larger in the case of $Z=0.06$ ) to the delays induced by carbon-oxygen phase separation."
 At the approximate location of the faint peal in the white dxvarf luuinesity fuuctiou of NCC 6791. delavs between Land 1.5 Cr are expected as a result of 22No sedimentation oulv.," At the approximate location of the faint peak in the white dwarf luminosity function of NGC 6791, delays between 1 and 1.5 Gyr are expected as a result of $^{22}$ Ne sedimentation only."
 As receutly shown in GarcíaaBerro ct al (2010). the occurrence of this process in the interior of cool white dwarfs is a kev factor in solving the onegstanding age discrepancy of NCC 6791.," As recently shown in Garc\'iaa--Berro et al (2010), the occurrence of this process in the interior of cool white dwarfs is a key factor in solving the longstanding age discrepancy of NGC 6791."
 lu sununary. we find that the evolution of cool white dwarts stemming frou progenitor stars with super-solar uetallicitv. is strouely modified bv the energy released youn ??Ne sedimentation.," In summary, we find that the evolution of cool white dwarfs stemming from progenitor stars with super-solar metallicity, is strongly modified by the energy released from $^{22}$ Ne sedimentation."
 The resulting delays in cooling ines of such white dwarts are inportaut and have to be aken into account in age determünations of metal-rich clusters from the cooling sequence of their white dwarts., The resulting delays in cooling times of such white dwarfs are important and have to be taken into account in age determinations of metal-rich clusters from the cooling sequence of their white dwarfs.
 The erid of evolutionary sequences we have prescuted rere ds the first one iutented for such a purpose. and incorporates the effects carbon-oxvecu phase separation and ??Ne sedimentation in the evolution of these stars.," The grid of evolutionary sequences we have presented here is the first one intented for such a purpose, and incorporates the effects carbon-oxygen phase separation and $^{22}$ Ne sedimentation in the evolution of these stars."
 We acknowledge the conuueuts aud sugecstious of our referee. which help us to mnuprove the original version of this paper.," We acknowledge the comments and suggestions of our referee, which help us to improve the original version of this paper."
 This research was supported bv AGAUR. by MCINN evauts AYA200801211.C0201 and AYAOS-I839/ESDP. by the European Union FEDER nds. dy ACGENCTA: Programa de Modernizaciduu Tecnoldgeica BID 1728/OC-AR. and by PIP 2008-009LO yon CONICET.," This research was supported by AGAUR, by MCINN grants AYA2008–04211–C02–01 and AYA08-1839/ESP, by the European Union FEDER funds, by AGENCIA: Programa de Modernizaciónn Tecnológgica BID 1728/OC-AR, and by PIP 2008-00940 from CONICET."
 LGA also acknowledges a PIV eraut of 1ο AGAUR of the Generalitat de Cataluuva., LGA also acknowledges a PIV grant of the AGAUR of the Generalitat de Catalunya.
catalog. aud peakss with ügher significance might also be rejected Gf they al to have ο pixels all above the 30 thresold).,"catalog, and peaks with higher significance might also be rejected (if they fail to have $N_{min}$ pixels all above the $\sigma$ threshold)."
 Trerefore otos properties of the noise eelcraed peaks were use to Lait the detection when a lower thresιο is used., Therefore other properties of the noise generated peaks were used to limit the detection when a lower threshold is used.
 Fie., Fig.
" 1 shows the distribution of tle most relevant of these oxoperties as derived using the SExtractor paraneters Nunlr, ando gua2.0.", \ref{fig:noise_properties} shows the distribution of the most relevant of these properties as derived using the SExtractor parameters $N_{min}=1r_c$ and $\sigma_{det} = 2.0$.
 The yequency of detected peaks (scaled to a one square deeree projected area) is plotted as a function of the detection sienific:uice. of the umber of filter redshifts where the detecjon took place. and of the interred cluster richness A.," The frequency of detected peaks (scaled to a one square degree projected area) is plotted as a function of the detection significance, of the number of filter redshifts where the detection took place, and of the inferred cluster richness $\Lambda_{cl}$."
 From the fleure it is seen that iu addition to the detection significance. the uunber of filter redshifts at whici the peak appears is a valuable tool for discriminating the noise peaks.," From the figure it is seen that in addition to the detection significance, the number of filter redshifts at which the peak appears is a valuable tool for discriminating the noise peaks."
 Typically noise peaks appear at only a few filter redshifts. while clusters are detected at5 to 1! redslüfts.," Typically noise peaks appear at only a few filter redshifts, while clusters are detected at 5 to 10 redshifts."
 Therefore oue further nolse-rejection criterion that was enforced is the requirement hat a peak shoud be detected over at least 3 dittereut filter redshifts. f«| be included. ia a cluster candidates catalog.," Therefore one further noise-rejection criterion that was enforced is the requirement that a peak should be detected over at least 3 different filter redshifts, to be included in a cluster candidates catalog."
 The lower pancl of Fig., The lower panel of Fig.
 1 shows another useful rose discriminant. namely the iuferred richness. which or the noise pe:uss is rarely above 50.," \ref{fig:noise_properties} shows another useful noise discriminant, namely the inferred richness, which for the noise peaks is rarely above 50."
" Therefore the requirement that he inferred richuess slowd be z>50 has cor, used as atird criterion for the clister cauclicate selection.", Therefore the requirement that the inferred richness should be $\geq 50$ has been used as a third criterion for the cluster candidate selection.
 Iu Table the results«)btaiued. applying cüffereut detection strateeies to the backeround-oulv si.ations aro snnuuarized., In Table \ref{tab:detection_parameters} the results obtained applying different detection strategies to the background-only simulations are summarized.
 The uumber of detections that were found im the simutations. scaled to a common reference area of one square degree. are reported as a funcion of different SExtractor detection thresholds. of the adopted persisteucv cnterion. aud of the Iack or presence of further restrictive criterd von the richness or the sijenificauce associated wit ithe detection.," The number of detections that were found in the simulations, scaled to a common reference area of one square degree, are reported as a function of different SExtractor detection thresholds, of the adopted persistency criterion, and of the lack or presence of further restrictive criteria on the richness or the significance associated with the detection."
" As discussed aove. While a eood nolse το]ection can be obtaired with IN,lr, σε3 and η.»2, this is too restrictive a setting to be used iu the cluster detectiOl procecaure."," As discussed above, while a good noise rejection can be obtained with $N_{min} \sim 1 r_c$, $\sigma_{det} >
3$ and $n_z > 2$, this is too restrictive a setting to be used in the cluster detection procedure."
" At he sale time a too low detection twesholad (0,54 5) results iu too Waly bleuded detections.", At the same time a too low detection threshold $\sigma_{det} = 1.5$ ) results in too many blended detections.
 Because the automatic SExtractor de-llending procedure cau override the specified Αι4 Criterion. it was decided not to use it. and use instead a detection threshold which does iot produce a significant nunuber of bleuds.," Because the automatic SExtractor de-blending procedure can override the specified $N_{min}$ criterion, it was decided not to use it, and use instead a detection threshold which does not produce a significant number of blends."
" Trerefore he detection threshold of σι,=2 was chosen.", Therefore the detection threshold of $\sigma_{det} = 2$ was chosen.
 The acopted selection criteria are therefore Ninin~dre 0442 2.0. ihe Ew50. detection," The adopted selection criteria are therefore $N_{min} \sim 1 r_c$, $\sigma_{det} > 2.0$ , $n_z > 2$, $\Lambda_{cl} > 50$."
sThis produces an expected frecWeonev of spurious iu the cluster candidate catalogs deseribed in Sect., This produces an expected frequency of spurious detections in the cluster candidate catalogs described in Sect.
 5 of 0.2+0.1 if a restrictive criterion im the detection siguificance {3 Lo) is nuposed. ancl of L.940.2  for a detection significance =360.," \ref{sec:results} of $0.2 \pm 0.1$ $^{-2}$, if a restrictive criterion in the detection significance $\geq 4\sigma$ ) is imposed, and of $1.9 \pm 0.2$ $^{-2}$ for a detection significance $\geq
3\sigma$."
" For coluparison. tlie ¢sxpected frequency of spurious detections in the PDCS is L8d D when peaks with. significance.[p lo ire considπου, and L2B D when peaks with- sjenificauce =Do are taken iuto consideration."," For comparison, the expected frequency of spurious detections in the PDCS is 0.8 $^{-2}$ when peaks with significance $\geq 4\sigma$ are considered, and 4.2 $^{-2}$ when peaks with significance $\geq 3\sigma$ are taken into consideration."
 The cluster-fiudiug procedure described im the previous section was applied to Patch A even aud odd. single-frame catalogs., The cluster-finding procedure described in the previous section was applied to Patch A even and odd single-frame catalogs.
 To facilitate a comparison between the derived cluster candidates. the search was restricted to the region of overlap between the odd/eveu galaxy catalogs.," To facilitate a comparison between the derived cluster candidates, the search was restricted to the region of overlap between the odd/even galaxy catalogs."
 Furtheriuore. a region at the north-east corner of the patch was discarded. because of severe mceonipleteuess Paper D.," Furthermore, a region at the north-east corner of the patch was discarded, because of severe incompleteness Paper I)."
 Tιο effective area searclied is deΠιοτος iu Fie.B. 2le," The effective area searched is delineated in Fig. \ref{fig:proj_distr},"
 coverme 2.5 dee., covering 2.5 $^2$ .
 Using the c1ster model described iu Sect., Using the cluster model described in Sect.
 1.2 aud the selection crieria described iu the previots section. two cluster cat:ηςyes were constructed.," \ref{sec:cluster_pipeline}
 and the selection criteria described in the previous section, two cluster catalogs were constructed."
 Ouc COsisting of detected candiates witi Nguificauc lo. in at least one catalog (Ta ud the other of detectios having significances beween 3a and 1o (Tahe 3)).," One consisting of detected candidates with significance $\geq 4\sigma$ , in at least one catalog (Table \ref{tab:good_clusters}) ), and the other of detections having significances between $3\sigma$ and $4\sigma$ (Table \ref{tab:so_so_clusters}) )."
 In both cases the adcaitioual ¢yiterla of detection re(urne s.>2 aud Αι>50 are nayosed., In both cases the additional criteria of detection requiring $n_z>2 $ and $\Lambda_{cl} \ge 50$ are imposed.
. The results shov- that there are 15 lo detections 1i the even and LS in 16 odd catalog., The results show that there are 15 $4\sigma$ detections in the even and 18 in the odd catalog.
 As shown below. most of tlose represent paired deections.," As shown below, most of these represent paired detections."
 For lower siguificances. oue finds 13 deectious in the even and 9 in the odd catalog. respectively.," For lower significances, one finds 13 detections in the even and 9 in the odd catalog, respectively."
 For each cluster. Tables 2 alc 3 eive: in coltun (1) the cluster ID: iun cols (2) ancl BJ tie J200 λοςuatorial coordinates: in column 1) the estinated recIsüft usi18o a Ix-coirecttion. obtained assumiis no evolitio ioft 1ο stellar population: iu cohuuus {5) and (6) the richness estimates Ay aud ANHC in cohunIs (T) axb (8) the sjeuificauce for the detection iu tlic NOron aud «xdld catalog. M avalable: aud in coliuun (9) noος based on the vistal specion of the images of cach cilida," For each cluster, Tables \ref{tab:good_clusters} and \ref{tab:so_so_clusters} give: in column (1) the cluster ID; in columns (2) and (3) the J2000 equatorial coordinates; in column (4) the estimated redshift using a tion obtained assuming no evolution of the stellar population; in columns (5) and (6) the richness estimates $\Lambda_{cl}$ and $N_R$; in columns (7) and (8) the significance for the detection in the even and odd catalog, if available; and in column (9) notes based on the visual inspection of the images of each candidate."
 «These notCR aro intended to SOTVC as al acdàtiona ede of t1e most likevy candidates., These notes are intended to serve as an additional guide of the most likely candidates.
 For iustae. a brigito star cal lead to tie duclusion of spurious Ojects in the galaxy catalogys. Which might lead to a s]W1OUS ¢etection.," For instance, a bright star can lead to the inclusion of spurious objects in the galaxy catalogs, which might lead to a spurious detection."
 When a candidatte clusteris detected iu )oth the even aud odd catalogs. he redshift aud richuess estimaes presented iu the tables are the ones derived from the catalog where the highest likelihood. value was measured.," When a candidate cluster is detected in both the even and odd catalogs, the redshift and richness estimates presented in the tables are the ones derived from the catalog where the highest likelihood value was measured."
 Iu total lo candiates are reported. giving a density of S.L per square deeree.," In total 21 $4\sigma$ candidates are reported, giving a density of 8.4 per square degree."
" For comparison. the density of lo Lbaud candidates in the PDCS is 6.3 per square cleeree,"," For comparison, the density of $4\sigma$ I-band candidates in the PDCS is 6.3 per square degree."
 Thisslightly higher detection rate is probably duc toa fainter Iuuitiugmagnitude of the EIS catalogs (Paper Ij., Thisslightly higher detection rate is probably due toa fainter limitingmagnitude of the EIS catalogs (Paper I).
in different observed types of SNe and/or GRBs.,in different observed types of SNe and/or GRBs.
 Neutrino-driven explosions generates spherical si-relativistic outflows. while GRB explosion results in a jetted relativistic component.," Neutrino-driven explosions generates quasi-spherical sub-relativistic outflows, while GRB explosion results in a jetted relativistic component."
 Classical SNe are all neutrino driven. where GRB engine is negligible.," Classical SNe are all neutrino driven, where GRB engine is negligible."
 As the relative streneth of the GRB οιeiue increases. this leads to phenomena of sub-euergetic aud regular GRBs.," As the relative strength of the GRB engine increases, this leads to phenomena of sub-energetic and regular GRBs."
 The relative contribution of the neutriuo-driven aud CRB energies are cleiuitely not independent of each other: one expects that in case of a success] ueutriuo-driven SN. the amount of material accreted ou the central source is sinall. resulting ini weak or uo relativistic co-—yonent aud a weak GRB: recall that all SN-associated GRBs are subluimiOlls.," The relative contribution of the neutrino-driven and GRB energies are definitely not independent of each other: one expects that in case of a successful neutrino-driven SN, the amount of material accreted on the central source is small, resulting in weak or no relativistic component and a weak GRB: recall that all SN-associated GRBs are subluminous."
 Thus. a SN explosion cau be viewed as a two-paraimeer phenomenon. the two parameters beiug the power of tlie neutriuo-drisren aud GRB-cdriven ottflows.," Thus, a SN explosion can be viewed as a two-parameter phenomenon, the two parameters being the power of the neutrino-driven and GRB-driven outflows."
 Most supernova are neutrino- quasi-spherical outflows. whe' the GRB-driven component is weak or non-existeut.," Most supernova are neutrino-driven quasi-spherical outflows, where the GRB-driven component is weak or non-existent."
 The recent discovery of the relativistic tyye [he supernova withot a detected GRB signal requires both two euergy sources: one to generate the relativistic outflow. another to expel the SN envelope.," The recent discovery of the relativistic type Ibc supernova without a detected GRB signal \citep[SN 2009bb][]{2010Natur.463..513S} requires both two energy sources: one to generate the relativistic outflow, another to expel the SN envelope."
 In addition. some of the well studied supernova remnants. like Cas A. o show jet-like features.," In addition, some of the well studied supernova remnants, like Cas A, do show jet-like features."
 7. indeed suggestedMOD that Cas A could have been a failed CB. generating a jet with a typical euergy order of inaguitude smaller than a typical loug; CRB.," \cite{LamingCasAGRB} indeed suggested that Cas A could have been a failed GRB, generating a jet with a typical energy order of magnitude smaller than a typical long GRB."
 As the power of the nettrino-driven outflow decrease. the fall-back material may power the GRB-like central engine.," As the power of the neutrino-driven outflow decrease, the fall-back material may power the GRB-like central engine."
 Thiis. the SN aud (48 explosious are two related. but dillerent events: SN shock expels or nearly ex»els the envelope. while the CUB outflow is concentrated in a narrow solid angle. presumably. alor& the axis of rotation ofthe central object.," Thus, the SN and GRB explosions are two related, but different events: SN shock expels or nearly expels the envelope, while the GRB outflow is concentrated in a narrow solid angle, presumably along the axis of rotation of the central object."
 Iu this picture. the GRB engine does need (but still iiv) to contribute to overall dvnuanmies of the envelope: most of the heavy lifting (unbiudiug the euvelope) is clone by the neutrinos.," In this picture, the GRB engine does need (but still may) to contribute to overall dynamics of the envelope: most of the heavy lifting (unbinding the envelope) is done by the neutrinos."
 For the purpose of this Japel. we accep us paradigm. that both GRBs auc some non-GRB SNe have two cdriviug mecharius with the relative energies «X the two outflows varying over a large ange.," For the purpose of this paper, we accept this paradigm, that both GRBs and some non-GRB SNe have two driving mechanisms with the relative energies of the two outflows varying over a large range."
 We assume that GRB shock follows the ol the SN. but not by much. so that the couliniug anm pressure of the ejecta is unportaut for propagating of tlje secondary. CRB shock.," We assume that GRB shock follows that of the SN, but not by much, so that the confining ram pressure of the ejecta is important for propagating of the secondary GRB shock."
 Iu passing we note that a two stage model of SN explosious have already been advocated by ? oug before the discovery of jet-like features in SNe., In passing we note that a two stage model of SN explosions have already been advocated by \cite{Grasberg} long before the discovery of jet-like features in SNe.
 This was based ou mocleling of liue emission. iu yarticular of remarkably narrow eumission aud absorption lines.," This was based on modeling of line emission, in particular of remarkably narrow emission and absorption lines."
 They suggestMOD that weak explosion sroceecdecd the SN shock. though.," They suggest that weak explosion proceeded the SN shock, though."
 Also. a supranova model of 2 postulates a two-staged explosion.," Also, a supranova model of \cite{2002astro.ph.11300D} postulates a two-staged explosion."
 How is the CRB jet collimated?, How is the GRB jet collimated?
 Most models of jet formation iu a collapsing star employ a highly anisotropic driving. elther through meutrino-incdtuced heating ? or magnetic collimation (2??)).," Most models of jet formation in a collapsing star employ a highly anisotropic driving, either through neutrino-induced heating \cite{1999ApJ...524..262M} or magnetic collimation \cite{lb03,KomissarovGRBSN,BuciantGRB}) )."
 In this paper we investigate au alternative mechanisin that produces a highly. anisotropic outflow. while been driveu by a anisotropic central source.," In this paper we investigate an alternative mechanism that produces a highly anisotropic outflow, while been driven by a anisotropic central source."
 The collimation mechanism relies on the ram pressure of the external mecdiums aud large scale Raleigh-Taylor (RT) instability of, The collimation mechanism relies on the ram pressure of the external mediums and large scale Raleigh-Taylor (RT) instability of
these candidates has. of course. ifs pros aud cons. which were discussed im the same literature: see in partictlar the extensive aud uubiased discussion by Posch et al. (2001...,"these candidates has, of course, its pros and cons, which were discussed in the same literature; see in particular the extensive and unbiased discussion by Posch et al. \cite{pos}."
 However. TiC attracted special attention m view of the exccllent agreement. in position axd width. of the published laboratory feature with the PPN feature.," However, TiC attracted special attention in view of the excellent agreement, in position and width, of the published laboratory feature with the PPN feature."
 For the same reason. several authors looked further iuto this candidate.," For the same reason, several authors looked further into this candidate."
 Henning auxAfutschke (2001). showed that the feature is not present iu the reflection spectui of bulk TiC. aud deduced from their measurements that it could not be exhibited by ια] TiC particles of various shapes.," Henning andMutschke \cite{hen} showed that the feature is not present in the reflection spectrum of bulk TiC, and deduced from their measurements that it could not be exhibited by small TiC particles of various shapes."
 Li (2003) ruled out the TiC model based on the excessive amounts of TiC required by Nraimers-Krocuig relaions between total dust mass aud integrated extinction cross-section., Li \cite{li} ruled out the TiC model based on the excessive amounts of TiC required by Kramers-Kroenig relations between total dust mass and integrated extinction cross-section.
 Tie samme conclusion Was arrived at by Chieai et al. (2003).., The same conclusion was arrived at by Chigai et al. \cite{chi}. .
 Zhanue et al., Zhang et al.
 (2010) also critically analyzed several of the piiblishied proposals., \cite{zhak} also critically analyzed several of the published proposals.
 Thiotrea was already proposed as a carrier of the 21-42 feature by Sourisseau et al. (1992).., Thiourea was already proposed as a carrier of the $\mu$ m feature by Sourisseau et al. \cite{sou}.
 It is a coumon molecule ou earth aud in the industry. aud Was «escribed in detail o» Stewart (1957).. Nutzelnigeao aud Meck (1961).. Lin-Vion (2009) and Alia et al. (1999)..," It is a common molecule on earth and in the industry, and was described in detail by Stewart \cite{ste}, Kutzelnigg and Meck \cite{kut}, Lin-Vien \cite{lin} and Alia et al. \cite{ali},"
 and in Ulhman’s Encyclopedia. of ludusral Chemistry (20]0) anong others (see further relevant bibliograply iu Sotrissea et al. (1992 )))., and in Ullman's Encyclopedia of Industrial Chemistry \cite{ull} among others (see further relevant bibliography in Sourisseau et al. \cite{sou}) ).
 Its chemical formula is SCONITDo)o.., Its chemical formula is $_{2})_{2}$.
 As an asice. Miffers from urea ouly xw the presence of sulphur. S. iustead of oxvgen. O. Its cliaracteristic subegroip. CS. was observed. along several sightlines in the Ciaανν (e.e. Turner (1987 ))).," As an aside, it differs from urea only by the presence of sulphur, S, instead of oxygen, O. Its characteristic subgroup, CS, was observed along several sightlines in the Galaxy (e.g. Turner \cite{tur87b}) )."
 Also note that the cosmic abundance of sulphur Insightly eher than that of Silicon. which is kuown to associate readily wihi CATyon. both being chemicaly active.," Also note that the cosmic abundance of sulphur is slightly higher than that of Silicon, which is known to associate readily with carbon, both being chemically active."
 Sulphur associated with silicon was also detected i ithe form of SiS uolecules (e.g. Turner (1987)))., Sulphur associated with silicon was also detected in the form of SiS molecules (e.g. Turner \cite{tur87a}) ).
 According to Stewar (1957).. thiourea exhibi san absorption baud which is reproluced in Fie.1: it peass at 20.1 gan. but is distinctly wider than the PPNe feature. aud uuch wider than moleclar features. for that matter.," According to Stewart \cite{ste}, thiourea exhibits an absorption band which is reproduced in Fig.1; it peaks at 20.4 $\mu$ m, but is distinctly wider than the PPNe feature, and much wider than molecular features, for that matter."
 The tliourea molecile. ]scing made of 8 atoms. has 18 vibrational modes: theorc5ical analysis iudicates that oulv 3 of them ave notably IR-active between LO ix LO pau. and he stroneest falls iude at [86 3 (20.6 jan).," The thiourea molecule, being made of 8 atoms, has 18 vibrational modes; theoretical analysis indicates that only 3 of them are notably IR-active between 10 and 40 $\mu$ m, and the strongest falls indeed at 486 $^{-1}$ (20.6 $\mu$ m)."
 But this alone canrot be respousible for the baud width in Fig.l., But this alone cannot be responsible for the band width in Fig.1.
 Obviously. this Is mainly due to its preparation. as solid. stae nücroeraius. enuibedded in a Nujol uull (wwuch is expected to add a snall. uniform absorbance).," Obviously, this is mainly due to its preparation, as solid state micrograins, embedded in a Nujol mull (which is expected to add a small, uniform absorbance)."
 If is well known that the spectrum of small eraius is cifferent from that of the same mnaterial iu buk. aud that article size aud shape have au enormous influence ou the position. shape aud width of spectral lines (see Suuth (199933) ," It is well known that the spectrum of small grains is different from that of the same material in bulk, and that particle size and shape have an enormous influence on the position, shape and width of spectral lines (see Smith \cite{smi}) ) ."
A popular example.of course. is SiC. which lias a very discrete mid-IR spectrum," A popular example,of course, is SiC, which has a very discrete mid-IR spectrum"
quasi-circular orbits (condition 9). corresponds to the point where disk is fat.,"quasi-circular orbits (condition 9), corresponds to the point where disk is fat."
 Writing M in astrophysical units as: we see that for values ἱνρίσα of what is observationally inferred for the stellar mass and position and temperature of accretion disk walls in E Tauri protoplanetary disks. those indicated in the above equation (e.g. D'Xlessio et αἱ.," Writing ${\mathcal M}$ in astrophysical units as: we see that for values typical of what is observationally inferred for the stellar mass and position and temperature of accretion disk walls in T Tauri protoplanetary disks, those indicated in the above equation (e.g. D'Alessio et al."
 2005. Espaillat et al.," 2005, Espaillat et al."
 2007. Llughes et al 2009). one should expec the breakdown of the thin disk approximation (A421. e.g. Pringle 1981). and consequently. the transition to raclia How.," 2007, Hughes et al 2009), one should expect the breakdown of the thin disk approximation ${\mathcal M} >>1$, e.g. Pringle 1981), and consequently, the transition to radial flow."
 Taking typical inferred. values for fff at the wall of 5 (e.g. D’Alessio et al., Taking typical inferred values for $R/H$ at the wall of $\sim 5$ (e.g. D'Alessio et al.
 2005. Espaillat ct al.," 2005, Espaillat et al."
 2007. Llughes et al 2009). we can now write the condition for the transition to radial Dow. locally at the wall. as: We see that for à standard value of n~1 the above equation implies a reasonable value of a~1 at the thick wall. significantly higher than the values of ~0.01 and lower. which apply for the body of the thin accretion disk bevond this racius.," 2007, Hughes et al 2009), we can now write the condition for the transition to radial flow, locally at the wall, as: We see that for a standard value of $n\sim1$ the above equation implies a reasonable value of $\alpha \sim 1$ at the thick wall, significantly higher than the values of $\sim 0.01$ and lower, which apply for the body of the thin accretion disk beyond this radius."
 A substantial increase of à as 2/44 decreases is expected in any turbulence driven: viscosity model. for accretion disks. e.g. Firmani. Hernandez Gallagher (1996). in the context of galactic disks.," A substantial increase of $\alpha$ as $R/H$ decreases is expected in any turbulence driven viscosity model for accretion disks, e.g. Firmani, Hernandez Gallagher (1996), in the context of galactic disks."
 In terms of the debate surrounding the inference of inner holes in observed aceretion disks. many solutions have been proposed in terms of disk clearing mechanisms: erain erowth (es. Strom et al.," In terms of the debate surrounding the inference of inner holes in observed accretion disks, many solutions have been proposed in terms of disk clearing mechanisms; grain growth (e.g. Strom et al."
 1989. Dullemond Dominik 2005). photoevaporation (e.g. Clarke ct al.," 1989, Dullemond Dominik 2005), photoevaporation (e.g. Clarke et al."
 2001). magnetorotational instability inside-out clearing (e.g. Chiang Alurray-Clayv 2007. Dutrey et al.," 2001), magnetorotational instability inside-out clearing (e.g. Chiang Murray-Clay 2007, Dutrey et al."
 2008). binarity (e.g. Ireland Kraus 2008) and planet-cisk interactions (e.g. Rice et al.," 2008), binarity (e.g. Ireland Kraus 2008) and planet-disk interactions (e.g. Rice et al."
 2003)., 2003).
 None of the above is entirely satisfactory. as noted by Hughes et al. (," None of the above is entirely satisfactory, as noted by Hughes et al. ("
2009). mostly. due to their incompatibility with a steady state solution.,"2009), mostly due to their incompatibility with a steady state solution."
 An alternative solution under the proposed. scenario. is that. there is no actual disk material clearing. only a transition to racial Dow at the thick wall. and consequently a shear-free How interior to this point.," An alternative solution under the proposed scenario, is that there is no actual disk material clearing, only a transition to radial flow at the thick wall, and consequently a shear-free flow interior to this point."
 Once the disk heating mechanism is removed. as one should expect from. the analysis presented. in this section. the inner disk disappears from sight.," Once the disk heating mechanism is removed, as one should expect from the analysis presented in this section, the inner disk disappears from sight."
 We shall now model the physical situation resulting fron the scenario described. above as an axially symmetrical distribution of cold matter in free fall towards a central star of mass Al., We shall now model the physical situation resulting from the scenario described above as an axially symmetrical distribution of cold matter in free fall towards a central star of mass $M$.
 Taking a spherical coordinate svstem with 6 the angle between the positive vertical direction and the position vector F we have: [or the continuity equation. ancl the radial ancl angular components of Euler's equation.," Taking a spherical coordinate system with $\theta$ the angle between the positive vertical direction and the position vector $\vec{r}$ we have: for the continuity equation, and the radial and angular components of Euler's equation."
 In the above. V. C. p and {3 eive the radial velocity. angular velocity. matter density. and pressure. respectively.," In the above, $V$, $U$, $\rho$ and $P$ give the radial velocity, angular velocity, matter density and pressure, respectively."
 We have neglected temporal derivatives. as we are interested. at this. point. in the characteristics of steady state solutions.," We have neglected temporal derivatives, as we are interested at this point, in the characteristics of steady state solutions."
" We take as a background state a [ree-lalline axially svnimetrical distribution of cold gas. described bv ἕωςΛΙ. Gy=0 andl VP,=(. a consistent solution to cqs.(15) and (16)."," We take as a background state a free-falling axially symmetrical distribution of cold gas, described by $V_{0}=-(2GM/r)^{1/2}$, $U_{0}=0$ and $\nabla \vec{P_{0}}=0$, a consistent solution to eqs.(15) and (16)."
 Having ignored the inclusion of the radius at. which the transition to radial Low takes place in the choice of Vo limits the validity of the analysis to radial scales along the plane of the disk much smaller than Zr., Having ignored the inclusion of the radius at which the transition to radial flow takes place in the choice of $V_{0}$ limits the validity of the analysis to radial scales along the plane of the disk much smaller than $R_{T}$.
 FEhis is justified by the fact that jets appear as phenomena extremely. localised towards £2.20., This is justified by the fact that jets appear as phenomena extremely localised towards $R \rightarrow 0$.
 We now take a density profile given by: were fr) is a dimensionless function of r and g(9) describes the polar angle dependence of the infalling material. for example. one can ask for g(@=z/2)po. diminishing svnunetrically towards the poles.," We now take a density profile given by: were $f(r)$ is a dimensionless function of $r$ and $g(\theta)$ describes the polar angle dependence of the infalling material, for example, one can ask for $g(\theta=\pi/2)=\bar{\rho}_{0}$, diminishing symmetrically towards the poles."
 The choice of this last function will determine the details of the problem. and can be thought of as something of the type with po a normalisation constant and. 6 a formi constant describing the Uattening of the disk of infalling material.," The choice of this last function will determine the details of the problem, and can be thought of as something of the type with $\bar{\rho}_{0}$ a normalisation constant and $\theta_{0}$ a form constant describing the flattening of the disk of infalling material."
 However. we shall mostly leave results inclicated in terms of g(9).," However, we shall mostly leave results indicated in terms of $g(\theta)$ ."
 VFhe continuity equation (14) now fixes f(r) through: and hence [i?=fe. which completes the description of the background state through: with ra constant which determines the point at which iv2) = opu=qu.," The continuity equation (14) now fixes $f(r)$ through: and hence $f(r) r^{3/2} =cte.$, which completes the description of the background state through: with $\bar{r}$ a constant which determines the point at which $g(\theta=\pi/2)$ $\Rightarrow$ $\rho_{0}=\bar{\rho}_{0}$."
 We shall now analyse the behaviour of a. fraction of somewhat hotter material. through a first order perturbation analysis of the above solution.," We shall now analyse the behaviour of a fraction of somewhat hotter material, through a first order perturbation analysis of the above solution."
 This small fraction could represent the last of the material to fully cool. or result. from the irradiation of the central star onto the upper and lower surfaces of the raclially infalling disk. as described by e.g. Hollenbach et al. (," This small fraction could represent the last of the material to fully cool, or result from the irradiation of the central star onto the upper and lower surfaces of the radially infalling disk, as described by e.g. Hollenbach et al. ("
1994) or Alexander et al. (,1994) or Alexander et al. (
2006) for the standard case of Keplerian accretion disks. in connection with the problem of disk photoevaporation.,"2006) for the standard case of Keplerian accretion disks, in connection with the problem of disk photoevaporation."
 La the above it is shown that ionizing radiation [rom the star generically creates an ionized laver on the surface of the disk., In the above it is shown that ionizing radiation from the star generically creates an ionized layer on the surface of the disk.
 Regarding the evolution of this component. we shall also be interested interested in a steady state solution given bv: where quantities with subscript (1) denote the perturbation on the background solution.," Regarding the evolution of this component, we shall also be interested interested in a steady state solution given by: where quantities with subscript (1) denote the perturbation on the background solution."
 Writing eqs.(14). (15) and (16) to first order in the perturbation one obtains afterrearranging ternis:," Writing eqs.(14), (15) and (16) to first order in the perturbation one obtains afterrearranging terms:"
"also adopt their melting value. Uy,=173.","also adopt their melting value, $\Gamma_M = 173$."
 The crust reactions reduce Z and beat the crust: both ol these effects decrease E. as shown in Figure 13. for inodels panel)) aud panel)). with each model accretiig at dts fiducial rate.," The crust reactions reduce $Z$ and heat the crust; both of these effects decrease $\Gamma$, as shown in Figure \ref{fig:Gamma} for models ) and ), with each model accreting at its fiducial rate."
 In both cases. the core superfluidity is as clescribed in Table 2..," In both cases, the core superfluidity is as described in Table \ref{t:superfluid}."
 For a low theral couductivity lines)). the crust melts in a series . layers.," For a low thermal conductivity ), the crust melts in a series of layers."
 The jaggeduessMD of D is because of the pyenonuclear reactious., The jaggedness of $\Gamma$ is because of the pycnonuclear reactions.
" Each oue doubles Z and halves ma. so that P increases by 2°)"" ad the crust refreezes."," Each one doubles $Z$ and halves $n_N$, so that $\Gamma$ increases by $2^{5/3}$ and the crust refreezes."
 Electron captures then decrease Z xl E until the crust melts again., Electron captures then decrease $Z$ and $\Gamma$ until the crust melts again.
 As a cousequence of this melting ad freezing. the crust resembles a layer cake at clensities ereater than ueutron drip.," As a consequence of this melting and freezing, the crust resembles a layer cake at densities greater than neutron drip."
 Figure LL slows the nuclear cliarge Za; line)). below which the ious are liquid. aloug with the Z of the nuclei preseut. lines)) according to (1990a).," Figure \ref{fig:Z-melt} shows the nuclear charge $Z_M$ ), below which the ions are liquid, along with the $Z$ of the nuclei present ) according to \citet{haensel90b}."
. The thermal structure is the same as plotted in Figure 13.. top panel. dotted line.," The thermal structure is the same as plotted in Figure \ref{fig:Gamma}, top panel, dotted line."
" P increases with density (or equivalently. Za, decreases). aud so the naive expectation is a sharp transition from au ionic ocean to a crust."," $\Gamma$ increases with density (or equivalently, $Z_M$ decreases), and so the naive expectation is a sharp transition from an ionic ocean to a crust."
 The Fermi energy. also increases with density. liowever.," The Fermi energy also increases with density, however,"
(Av=1710P For Abi=34.10 °) suggests that the pulsar's effective moment of inertia was reduced during the elitch by 8 per cent.,"$\Delta
 \dot{\nu}=-17\times10^{-15}$ $^{-2}$ or $\Delta \dot{\nu}/\dot{\nu}=34\times10^{-3}$ ) suggests that the pulsar's effective moment of inertia was reduced during the glitch by 3 per cent."
 Vhis reduction is transitory: after ~300 days. 7 approximates its pre-elitch value.," This reduction is transitory; after $\sim$ 300 days, $\dot{\nu}$ approximates its pre-glitch value."
 ‘This is the first observation of such an extreme elitch event., This is the first observation of such an extreme glitch event.
 Although such [arge events must be rare. the great number of pulsars now known due to the highly successful Parkes multibeam: survey increases the chance of studying such events in detail.," Although such large events must be rare, the great number of pulsars now known due to the highly successful Parkes multibeam survey increases the chance of studying such events in detail."
 Information obtained in these studies will provide unique constraints on theories of the internal structure of neutron stars and the mechanism which reduces a surprisingly large fraction. of the effective. moment. of inertia of these massive cosmic IDy-wheels., Information obtained in these studies will provide unique constraints on theories of the internal structure of neutron stars and the mechanism which reduces a surprisingly large fraction of the effective moment of inertia of these massive cosmic fly-wheels.
)) and total cosmic-ray energy density.,) and total cosmic-ray energy density.
 The parameters that we vary. and the range over which those parameters are varied. are summarized in Table ??..," The parameters that we vary, and the range over which those parameters are varied, are summarized in Table \ref{variationsInParameters}."
 First. do changes to any of these parameters modify the fiducial-model result that cosmic rays do not couple to gas in the clouds?," First, do changes to any of these parameters modify the fiducial-model result that cosmic rays do not couple to gas in the clouds?"
 No., No.
 In all of our calculations. we see this transition in the boundary of the cool cloud.," In all of our calculations, we see this transition in the boundary of the cool cloud."
 In all of our models. the streaming instability fails at the cloud boundary (due either to ion-neutral damping or a severe drop in cosmic-ray pressure). and cosmic rays do not transfer energy and momentum to the gas within the clouds.," In all of our models, the cosmic-ray streaming instability fails at the cloud boundary (due either to ion-neutral damping or a severe drop in cosmic-ray pressure), and cosmic rays do not transfer energy and momentum to the gas within the clouds."
" We do find changes in the cosmic-ray pressure on the cloud boundary. before the transition from the hydrodynamic limit to the kinetic limit (we refer to the last cosmic-ray hydrodynamic pressure within the wave-locked zone as the ""minimum cosmic-ray pressure force"")."," We do find changes in the cosmic-ray pressure on the cloud boundary, before the transition from the hydrodynamic limit to the kinetic limit (we refer to the last cosmic-ray hydrodynamic pressure within the wave-locked zone as the “minimum cosmic-ray pressure force”)."
 None of the models show an increase in the cosmic-ray pressure in the cloud., None of the models show an increase in the cosmic-ray pressure in the cloud.
 The cosmic-ray pressure decreases slightly on the cloud boundary in the fiducial case. so one might expect that as we increase the penetration of wave-locked cosmic rays into the cloud. a larger drop in cosmic-ray pressure on the cloud boundary would be seen.," The cosmic-ray pressure decreases slightly on the cloud boundary in the fiducial case, so one might expect that as we increase the penetration of wave-locked cosmic rays into the cloud, a larger drop in cosmic-ray pressure on the cloud boundary would be seen."
 This is true. although we always see a quick transition to the kinetic regime.," This is true, although we always see a quick transition to the kinetic regime."
 We find that the parameters that significantly affect the cosmic-ray pressure on the boundary of the cloud are the minimum cloud ionization fraction. the magnetic-field strength. and the initial cosmic-ray pressure.," We find that the parameters that significantly affect the cosmic-ray pressure on the boundary of the cloud are the minimum cloud ionization fraction, the magnetic-field strength, and the initial cosmic-ray pressure."
 In the case of the minimum cloud ionization fraction. as the cool cloud’s minimum ionization level increases (from an ionization fraction of 107 to about 0.1-0.2). the onset of ion-neutral damping is delayed. and the cosmic-ray pressure decreases further. as waves penetrate further into the cloud. before ion-neutral damping takes over.," In the case of the minimum cloud ionization fraction, as the cool cloud's minimum ionization level increases (from an ionization fraction of $^{-3}$ to about 0.1-0.2), the onset of ion-neutral damping is delayed, and the cosmic-ray pressure decreases further, as waves penetrate further into the cloud, before ion-neutral damping takes over."
 Also. for increased magnetic field strengths (~5—10 µία). the advective cosmic-ray flux is higher than in the fiducial case (because of a higher speed). and so the cosmic-ray generated waves dominate farther into the cloud than in the fiducial case before ion-neutral damping destroys the waves altogether.," Also, for increased magnetic field strengths $\sim 5-10$ ), the advective cosmic-ray flux is higher than in the fiducial case (because of a higher speed), and so the cosmic-ray generated waves dominate farther into the cloud than in the fiducial case before ion-neutral damping destroys the waves altogether."
 For B710 G.. dPafας ἰ so strongly negative that [ων drops to zero.," For $B > 10$ , $dP_{\rm cr}/dz$ is so strongly negative that $P_{\rm cr}$ drops to zero."
 The changes in the minimum cosmic-ray pressure are shown in Figures 5 and 6..," The changes in the minimum cosmic-ray pressure are shown in Figures \ref{minPcrVsMinIonization}
 and \ref{magneticFieldChangePcr}."
 In a similar way. increasing the initial cosmic-ray pressure also gives a stronger cosmic-ray flux at the surface of the cloud. which penetrates further into the cloud before ton-neutral damping takes over. and yields a change in the cosmic-ray pressure at the cloud interface (see Fig. 7)).," In a similar way, increasing the initial cosmic-ray pressure also gives a stronger cosmic-ray flux at the surface of the cloud, which penetrates further into the cloud before ion-neutral damping takes over, and yields a change in the cosmic-ray pressure at the cloud interface (see Fig. \ref{pcInitChangePcrRatio}) )."
 As shown in Section ??.. conductive heating overall strongly dominates the heating from cosmic-ray generated waves. although in very limited regimes. wave damping can compete with conductive heating (see Fig. 4)).," As shown in Section \ref{impactOfWaves}, conductive heating overall strongly dominates the heating from cosmic-ray generated waves, although in very limited regimes, wave damping can compete with conductive heating (see Fig. \ref{conductiveHeatingComparison}) )."
 As we vary the parameters in Table ??.. the heating at the cloud boundary changes. but in most cases and in most places on the cloud boundary. those changes yield heating rates that are orders of magnitude lower than that of thermal conduction.," As we vary the parameters in Table \ref{variationsInParameters}, the heating at the cloud boundary changes, but in most cases and in most places on the cloud boundary, those changes yield heating rates that are orders of magnitude lower than that of thermal conduction."
 However. we have found that. as we increase the magnetic-field strength and the initial cosmic-ray pressure. there are small regions of the cloud boundary that can become dominated by wave heating.," However, we have found that, as we increase the magnetic-field strength and the initial cosmic-ray pressure, there are small regions of the cloud boundary that can become dominated by wave heating."
 We present these results in Figures 8 and 9.. which show the factors by which conductive heating dominates the wave heatingwhen we change the magnetic-field strength and the initial cosmic-ray pressure.," We present these results in Figures \ref{magneticFieldChangeHOverC} and \ref{pcInitChangeHOverC}, which show the factors by which conductive heating dominates the wave heatingwhen we change the magnetic-field strength and the initial cosmic-ray pressure,"
Modes supported by the internal buovancy (i.e. modes) propagate in the stellar interior. where 47<.N? and w?<57.,"Modes supported by the internal buoyancy (i.e. g-modes) propagate in the stellar interior, where $\omega^2<N^2$ and $\omega^2<S_\ell^2$."
" As evident from Figure 3.. these inequalities are strong for frequencies ~Vyas.max: Vieldingof, A22((£4-1.N2/7247."," As evident from Figure \ref{fig:brunt}, these inequalities are strong for frequencies $\sim \nu_{\rm max}$, yielding $k_r^2\approx \ell(\ell+1)N^2/r^2\omega^2$ ."
" The highhg radial order (77,PS3»1) then g-modes have nz =(((2-1)?fNdlnr/e.vielding vy !—n,ND,with AP, being the period spacing."," The high radial order $n_g\gg 1$ ) g-modes then have $n_g\pi=(\ell(\ell+1))^{1/2}\int N d\ln r/\omega$, yielding $\nu^{-1}=n_g\Delta P_g$, with $\Delta P_g$ being the period spacing."
 For £ =1.this is 91/222 Mase ny F2lusMD)>100.safely in the WIXB limit.," For $\ell=1$, this is At $\nu_{\rm max}$, $n_g\approx 1/(\nu_{\rm max}\Delta P_g)>100$, safely in the WKB limit."
 The integral f Vdlnrextends over the region− where 4&7⋅↽≻↙<N==D and 47><2ο$;., The integral $\int N d \ln r$ extends over the region where $\omega^2<N^2$ and $\omega^2<S_\ell^2$.
" Now consider how AJ’, and Av evolve during the core flash phase.", Now consider how $\Delta P_g$ and $\Delta \nu$ evolve during the core flash phase.
 The KI contraction aller the initiating lash triggers a rapid decrease to RoxIli. and the increase of Av evident in (he second panel of Figure 4...," The KH contraction after the initiating flash triggers a rapid decrease to $R\approx 11R_\odot$, and the increase of $\Delta
\nu$ evident in the second panel of Figure \ref{fig:seismo}."
 Thereafter. the value of Av simply responds to the mild radius changes during subsequent subllashes.," Thereafter, the value of $\Delta \nu$ simply responds to the mild radius changes during subsequent subflashes."
 The Ile core radius expansion aud outer envelope contraction triggered by (he initiating Ie flash leads to an outer envelope structure during the /;222 Myr that is nearly the same as that on the red clump., The He core radius expansion and outer envelope contraction triggered by the initiating He flash leads to an outer envelope structure during the $t_f\approx 2$ Myr that is nearly the same as that on the red clump.
 Indeed. the profiles of N? and S$? in Figure 3. for the bottom three panels (all after the initiating flash) are nearly identical [or r>0.04...," Indeed, the profiles of $N^2$ and $S_\ell^2$ in Figure \ref{fig:brunt} for the bottom three panels (all after the initiating flash) are nearly identical for $r>0.04R_\odot$."
 The prime property that is changing over (he 2 Myr is the He core. as it undergoes additional subflashes (hat lift the degeneracy of the deep interior.," The prime property that is changing over the 2 Myr is the He core, as it undergoes additional subflashes that lift the degeneracy of the deep interior."
" The (=1 e-mode period spacings for the models in Figure 3. are AP,=61.2 s for the RGB. AP,=13 s for the core flash phase model between subllashes (second panel). and AP,=255 s for the red clamp."," The $\ell=1$ g-mode period spacings for the models in Figure \ref{fig:brunt} are $\Delta P_g=61.2$ s for the RGB, $\Delta
P_g=73$ s for the core flash phase model between subflashes (second panel), and $\Delta P_g=255$ s for the red clump."
 During the convective He burning shell subflashes (less than of the Ile core flash phase. so <2xLO? vears). an intervening evanescent zone appears in the core (see (hired panel in Figure 3)).," During the convective He burning shell subflashes (less than of the He core flash phase, so $< 2\times 10^5$ years), an intervening evanescent zone appears in the core (see third panel in Figure \ref{fig:brunt}) )."
" Though coupling through this zone is possible (see below). we calculated the period spacing assuming that only the outer ganode cavity is relevant. eiving AP,©250—270 s during each sub-flash."," Though coupling through this zone is possible (see below), we calculated the period spacing assuming that only the outer g-mode cavity is relevant, giving $\Delta P_g\approx 250-270$ s during each sub-flash."
" As evident in the third panel of Figure 4.. the existence of adegenerate core with V7>0 during the most of the core flash period keeps AP,< 1005. The fully convective He burning core of the red clamp is what causes the increase to AP,=255 s (Christensen-Dalsgaard201la) at the end of Figure 4.."," As evident in the third panel of Figure \ref{fig:seismo}, , the existence of adegenerate core with $N^2>0$ during the most of the core flash period keeps $\Delta P_g<100$ s. The fully convective He burning core of the red clump is what causes the increase to $\Delta P_g=255$ s \citep{christen11} at the end of Figure \ref{fig:seismo}."
 The (=1 mixed modes are more likely to be detected when the coupling through the outer evanescent region. (the region. .in the star where «79>V=? and «72<5;m so that ;2«5 0) is strong., The $\ell=1$ mixed modes are more likely to be detected when the coupling through the outer evanescent region (the region in the star where $\omega^2>N^2$ and $\omega^2<S_\ell^2$ so that $k_r^2<0$ ) is strong.
 In (he WINB limit.the ratio of the mode amplitudes (and also location of the mocle energv) between the (wo turning. points.. the inner one at r4 (where 4&75«I7 PEfirst occurs) and the outer one at rs (where w?>S?( first occurs) is lareelySUL determined by £=[7Pn και. but," In the WKB limit,the ratio of the mode amplitudes (and also location of the mode energy) between the two turning points, the inner one at $r_1$ (where $\omega^2<N^2$ first occurs) and the outer one at $r_2$ (where $\omega^2>S_\ell^2$ first occurs) is largely determined by $I=\int_{r_1}^{r_2} k_r dr$ , but"
Observatious of the speca of distant quasars aud galaxies have revealed tle absence of a trough. implying tlH ithe interealactic medium (IGM) was highly ionized by redshifts of about 5.,"Observations of the spectra of distant quasars and galaxies have revealed the absence of aGunn-Peterson trough, implying that the intergalactic medium (IGM) was highly ionized by redshifts of about 5."
 Since the universe 'ecombiued. at 'edshifts. z ~ 1100. the IGM is expected to remain ueutral until it is reionizect tl‘ough the activity of tie first luminous sources.," Since the universe recombined at redshifts, $z$ $\sim$ 1100, the IGM is expected to remain neutral until it is reionized through the activity of the first luminous sources."
 At present. it appears that the reionzationof Lyd‘open occurred »e[ore zoD (SchneikleretSpiuradeta. 1998).. while tat of doubly io izedelium is thought to have occurred before ~AG3 (Hoganetal.1997:Reimersal.1997).," At present, it appears that the reionizationof hydrogen occurred before $z \sim 5$ \citep{ssgunn, hugal, spinrad}, while that of doubly ionized helium is thought to have occurred before $z \sim
3$ \citep{hog97,reim97}."
. The iouZing sources res»onusible for reioUzatio Lean be a variety of astrophiysical objects. aud muuch work ias been clone ou retonization by the ist stars (Hatiman&Loeb1997:Fukugita]xawasaki199 [).. the first qiasars (Haiman&Loeb1998a:ValageasSilk 1999).. proto-galaxies (Cen&Ost‘iker1903:Ciuecin2000:GirouxShapiro1996:Ciarcietal.Miralcla-Escucle 1999).. and related phenomena such as supernova-driven winds," The ionizing sources responsible for reionization can be a variety of astrophysical objects, and much work has been done on reionization by the first stars \citep{hl97,fuka}, the first quasars \citep{hl98,valsilk}, , proto-galaxies \citep{cenost93,
gn99,gs96,ciardi,mirees99,madrees99}, , and related phenomena such as supernova-driven winds"
Gas giant planet formation depends upon the gas content of the circumstellar disk from which they form.,Gas giant planet formation depends upon the gas content of the circumstellar disk from which they form.
 Primordial inner disks traced by hot dust disappear after about 3 Myr with a range of 1—10 Myral., Primordial inner disks traced by hot dust disappear after about 3 Myr with a range of $1-10$ Myr.
"||2007).. If gas content and dust content in disks dissipate through similar mechanisms, then we would expect gas to disappear on these same timescales."," If gas content and dust content in disks dissipate through similar mechanisms, then we would expect gas to disappear on these same timescales."
" To understand the timescales of planet formation, we must understand how long a gas disk persists around its parent star."," To understand the timescales of planet formation, we must understand how long a gas disk persists around its parent star."
 Accretion rates (higher in CTTSs than WTTSs) also trace the time evolution of gas content as gas must be present to accrete., Accretion rates (higher in CTTSs than WTTSs) also trace the time evolution of gas content as gas must be present to accrete.
" suggest that gravitational instabilities in gas disks could account for their rapid («3 Myr) dissipation, locking up mass in planets."," suggest that gravitational instabilities in gas disks could account for their rapid $<3$ Myr) dissipation, locking up mass in planets."
" In contrast, simulations of the evolution of gas disk surface density for a 1 Meo star due to photo-evaporation indicate that gas disks disappear in about 6 Myral."," In contrast, simulations of the evolution of gas disk surface density for a 1 $_\sun$ star due to photo-evaporation indicate that gas disks disappear in about 6 Myr."
"|2007).. Because there are various theoretical results for the gas dispersal mechanisms and associated timescales, we might expect to observe diverse properties for gas disks around T Tauri stars."," Because there are various theoretical results for the gas dispersal mechanisms and associated timescales, we might expect to observe diverse properties for gas disks around T Tauri stars."
" Ideally, sub-millimeter interferometric images of T Tauri stars would yield the most information about circumstellar disks, including their orientation, geometry, and gas content."," Ideally, sub-millimeter interferometric images of T Tauri stars would yield the most information about circumstellar disks, including their orientation, geometry, and gas content."
 Yet observations of this sort have only been published for a few nearby stars2004)., Yet observations of this sort have only been published for a few nearby stars.
". Infrared photometric campaigns withSpitzer, such the Cores to Disks and the Formation and Evolution of Planetary SystemsSpitzer Legacy projects, provide knowledge of the dust circumstellar disks based upon IR excesses at many wavelengths including 24m, which trace dust within a few AU of the parent star, and at 70m, which trace cooler dust at larger radii."," Infrared photometric campaigns with, such the Cores to Disks and the Formation and Evolution of Planetary Systems Legacy projects, provide knowledge of the dust circumstellar disks based upon IR excesses at many wavelengths including $24\micron$, which trace dust within a few AU of the parent star, and at $70\micron$, which trace cooler dust at larger radii."
 surveyed 74 stars with ages between 3-30 Myr finding no stars with mid-IR excess that were not gas rich accreting T Tauri stars., surveyed 74 stars with ages between 3-30 Myr finding no stars with mid–IR excess that were not gas rich accreting T Tauri stars.
 however identified a handful of WTTS (lacking signatures of accretion) with evidence for mid— and far-IR excess emission., however identified a handful of WTTS (lacking signatures of accretion) with evidence for mid– and far–IR excess emission.
" Photometric IR observations do not, however, constrain the total gas content in circumstellar disks because of a potentially highly variable gas-to-dust ratio."," Photometric IR observations do not, however, constrain the total gas content in circumstellar disks because of a potentially highly variable gas-to-dust ratio."
" Observing the rotational energy transitions of !?CO, a proxy for molecular hydrogen (H3), and assuming the ISM abundance ratio [H2/CO]z10* enables one to trace the majority of cold gas in disks out to radii many times larger."," Observing the rotational energy transitions of $^{12}$ CO, a proxy for molecular hydrogen $_2$ ), and assuming the ISM abundance ratio $\left[\mathrm{H}_2/\mathrm{CO}\right]\approx10^4$ enables one to trace the majority of cold gas in disks out to radii many times larger."
 Is the timescale for gas dissipation similar to the timescale for dust dissipation around T Tauri stars?, Is the timescale for gas dissipation similar to the timescale for dust dissipation around T Tauri stars?
 This is the central question we address with our new observations., This is the central question we address with our new observations.
" Expanding on previous works2007),, we search for 1300 J=2—1 emission for two “evolved” T Tauri stars in Taurus to place constraints on their gas circumstellar disk masses."," Expanding on previous works, we search for $^{12}$ CO $J=2-1$ emission for two “evolved"" T Tauri stars in Taurus to place constraints on their gas circumstellar disk masses."
" St 34 is evolved in the sense that it is 8+3 Myr old, whereas RX J0432.8+1735 is evolved in the sense that—although it is much"," St 34 is evolved in the sense that it is $8\pm3$ Myr old, whereas RX J0432.8+1735 is evolved in the sense that—although it is much"
"The red beam fed the filter (SOUP,Titleetal,1986) to obtain Ha (46562.8 A)) and narrow-band images at 6302A.","The red beam fed the filter \citep[SOUP,][]{title1986} to obtain $\alpha$ $\lambda 6562.8$ ) and narrow-band images at $6302$."
. Single images were taken at a rate of 35 frames s! with CCDs of 1024x square pixels and an image-scale of 0.065 arcsec/pix., Single images were taken at a rate of 35 frames $^{-1}$ with CCDs of $1024 \times 1024$ square pixels and an image-scale of 0.065 arcsec/pix.
 A beam splitter in front of the SOUP deflected a fraction of light to obtain simultaneous broad-band Phase Diversity image-pairs in the continuum near 46302À., A beam splitter in front of the SOUP deflected a fraction of light to obtain simultaneous broad-band Phase Diversity image-pairs in the continuum near $\lambda6302$.
". These images made up an additional for the (MOMFBD,VanNoort,RouppevanderVoort&Lófdahl, algorithm to jointly restore both, the broad-band and the narrow-band images."," These images made up an additional for the \citep[MOMFBD,][]{MOMFBD} algorithm to jointly restore both, the broad-band and the narrow-band images."
" From the restored narrow-band images, we computed longitudinal magnetograms and Due to periods of bad seeing in which the quality did not reach the desired top level, some of the images were discarded and we kept only the best and longest consecutive sequence of images."," From the restored narrow-band images, we computed longitudinal magnetograms and Due to periods of bad seeing in which the quality did not reach the desired top level, some of the images were discarded and we kept only the best and longest consecutive sequence of images."
 The very final product were two G-band time series with the characteristics listed in Table 1.., The very final product were two G-band time series with the characteristics listed in Table \ref{poroseries}.
 The time gap of about 5 min between the two consecutive series for each wavelength resulted from a telescope tracking interruption., The time gap of about 5 min between the two consecutive series for each wavelength resulted from a telescope tracking interruption.
 That is also the reason why the FOV is slightly different in the time series., That is also the reason why the FOV is slightly different in the time series.
 Most images forming the time series show details near the diffraction limit of the The procedure followed for image restoration is extensively detailed in VargasDo, Most images forming the time series show details near the diffraction limit of the The procedure followed for image restoration is extensively detailed in \cite{vargasthesis}.
mínguez(2008).. Figure 1 shows one of the co-temporal sets of images of the emerging active region after restorations., Figure \ref{images_red} shows one of the co-temporal sets of images of the emerging active region after restorations.
" The upper left panel shows the FOV covered by the observations displaying the pores under analysis and the other panels useful information to characterize the region as derived from the red channel simultaneous After its launch on 22 September 2006, Solar Physics research."," The upper left panel shows the FOV covered by the observations displaying the pores under analysis and the other panels useful information to characterize the region as derived from the red channel simultaneous After its launch on 22 September 2006, Solar Physics research."
 It has managed to observe many high-detailed solar features by avoiding the blurring and distortion effects produced by the Earth's atmosphere., It has managed to observe many high-detailed solar features by avoiding the blurring and distortion effects produced by the Earth's atmosphere.
 The public archive of is an organized data base where all observations can be found out and easily downloaded., The public archive of is an organized data base where all observations can be found out and easily downloaded.
" We were interested in observations of solar pores taken with the Solar Optical Telescope (SOT,Tsunetaetal, 2008), in order to pursue our study of photospheric horizontal flows."," We were interested in observations of solar pores taken with the Solar Optical Telescope \citep[SOT,][]{tsuneta2008}, in order to pursue our study of photospheric horizontal flows."
 The next two sections describe the data we analyze in this paper., The next two sections describe the data we analyze in this paper.
 These data extend the sample of cases under study in the present work and moreover give us the possibility to compare with the results stemming from ground-based, These data extend the sample of cases under study in the present work and moreover give us the possibility to compare with the results stemming from ground-based
kept in mind: including information from &zO.1h/Alpe would. increase the resolution requirements. and high resolution plavs a Κον role in cleanly selecting the galaxy populations. aavoiding line confusion in emission line galaxies.,"kept in mind: including information from $k>0.1\,h$ /Mpc would increase the resolution requirements, and high resolution plays a key role in cleanly selecting the galaxy populations, avoiding line confusion in emission line galaxies."
 We can examine how a better understanding. of the transition to the non-linear part of the power spectrum could Iead to an improvement in determining σσ)., We can examine how a better understanding of the transition to the non-linear part of the power spectrum could lead to an improvement in determining $\sigma(\gamma)$.
 Instead of truncating the integral in Eq. (11)), Instead of truncating the integral in Eq. \ref{Fish}) )
 entering the Fisher matrix at A we can choose to implement a streaming mocel representing Fingers of God ellects (see for example Peebles (1980))).where we integrate over all & but multiply the power spectrum by a damping Factor. either Lorentzian or Gaussian.," entering the Fisher matrix at $k_+$, we can choose to implement a streaming model representing Fingers of God effects (see for example \citet{peeb}) ),where we integrate over all $k$ but multiply the power spectrum by a damping factor, either Lorentzian or Gaussian."
 This is supposed to model an exponential or Gaussian probability. distribution function for the peculiar velocities of galaxies., This is supposed to model an exponential or Gaussian probability distribution function for the peculiar velocities of galaxies.
 We investigate the three forms of the small-scale velocity clamping factors: PPh. p)= OK (hg) = PP(h.1) = where © is the Leaviside function., We investigate the three forms of the small-scale velocity damping factors: ) = (k_+ - ) = ) = where $\Theta$ is the Heaviside function.
 |yWe use fo /Mpe for all cases.," We use $k_+ = 0.1\,h$ /Mpc for all cases."
 Table 10 shows the ellects on the determination of the gravitational growth index., Table \ref{nonlinea} shows the effects on the determination of the gravitational growth index.
 We see that the statistical uncertainty on 5 is largest if we simply cut out all translincar information. by about a factor 2.," We see that the statistical uncertainty on $\gamma$ is largest if we simply cut out all translinear information, by about a factor 2."
 Thus we have adopted the most conservative method to predict o(5): the information might not. be completely lost on translinear scales. but only attenuated by Finger-of-Cod ellects.," Thus we have adopted the most conservative method to predict $\sigma(\gamma)$; the information might not be completely lost on translinear scales, but only attenuated by Finger-of-God effects."
 Aclopting a Gaussian or Lorentzian damping mocel allows extraction of some information. with the choice of model allecting the results at the ~25% level.," Adopting a Gaussian or Lorentzian damping model allows extraction of some information, with the choice of model affecting the results at the $\sim25\%$ level."
 However. an exponential or Gaussian probability distribution function for the streaming model is still not completely accurate. and along with the reduced statistical uncertainty on 5 could come a systematic bias.," However, an exponential or Gaussian probability distribution function for the streaming model is still not completely accurate, and along with the reduced statistical uncertainty on $\gamma$ could come a systematic bias."
 Thus we retain the conservative. eutolf method.," Thus we retain the conservative, cutoff method."
 Taking into account a halo model. for example Tinker.(2007).. could. allow a more detailed investigation of the proper treatment of the translinear regime.," Taking into account a halo model, for example \citet{halo}, could allow a more detailed investigation of the proper treatment of the translinear regime."
 Issues of nonlinear bias could also arise bevond the &=0.15 /Mpc adopted in this paper.," Issues of nonlinear bias could also arise beyond the $k_+=0.1\,h$ /Mpc adopted in this paper."
 While the survey volume due to the solid angle Og simply scales the parameter estimation as 0(5)xI/y/O in the statistical treatment without priors. the inlluence of redshift range is more complex and interesting.," While the survey volume due to the solid angle $\Omega_{\rm sky}$ simply scales the parameter estimation as $\sigma(\gamma) \propto 1 / 
\sqrt{\Omega_{\rm sky}}$ in the statistical treatment without priors, the influence of redshift range is more complex and interesting."
 Since the galaxy population used also depends on redshift we sipultaneously investigate the inlluence of the galaxy bias values., Since the galaxy population used also depends on redshift we simultaneously investigate the influence of the galaxy bias values.
 Table 11. shows the results for considering the populations. and their associated. redshift ranges. one at à time and also in combination with ciflerent values (0.8. 11.2) for the emission line galaxy population bias.," Table \ref{pop} shows the results for considering the populations, and their associated redshift ranges, one at a time and also in combination with different values (0.8 1.2) for the emission line galaxy population bias."
 As [found in Linder(2008).. most of the constraint on  comes from the redshift range zl. which mostly. corresponds to the LRG population.," As found in \citet{linder-gamma}, most of the constraint on $\gamma$ comes from the redshift range $z\lesssim1$, which mostly corresponds to the LRG population."
" The reason is simple: the cosmological information on , enters the power spectrum through the factor O,,(2). so at higher redshifts where £,,Cz2) is closer to 1. the sensitivity to 5. decreases."," The reason is simple: the cosmological information on $\gamma$ enters the power spectrum through the factor $\Omega_m(z)^\gamma$, so at higher redshifts where $\Omega_m(z)$ is closer to $1$, the sensitivity to $\gamma$ decreases."
 The value of the EL bias adopted does not have a significant ellect. especially when in combination with the low redshift. LRG sample.," The value of the EL bias adopted does not have a significant effect, especially when in combination with the low redshift, LRG sample."
 Furthermore. note that the EL only case for JDIZM-PS. which includes all the information from PS itself ancl none of the data to be provided by BOSS. only determines σσ)=0.2. even though the sample extends down to z=0.7.," Furthermore, note that the EL only case for JDEM-PS, which includes all the information from JDEM-PS itself and none of the data to be provided by BOSS, only determines $\sigma(\gamma)\approx0.2$, even though the sample extends down to $z=0.7$."
 For JDIZM-PS. the BOSS data enable an improvement of almost a factor 4 in the growth index parameter determination.," For JDEM-PS, the BOSS data enable an improvement of almost a factor 4 in the growth index parameter determination."
 These consequences of redshift range raise an important question: what is the science reach of the BigBOSS survey if the EL sample is shifted from 221. 2102207.1.77, These consequences of redshift range raise an important question: what is the science reach of the BigBOSS survey if the EL sample is shifted from $z=1-2$ to $z=0.7-1.7$?
 This not only changes the redshift range of the LL sample information but creates an overlap between LAG ancl [EL information., This not only changes the redshift range of the EL sample information but creates an overlap between LRG and EL information.
 The generalization. of Eq. (11)), The generalization of Eq. \ref{Fish}) )
 to multiple galaxy populations (AleDonaldetal.2009) reads: Bus DEου.Cy(27) where X. and Y are indices describing pairs of galaxy populations. and Ciyy is the covariance matrix of the power spectra.," to multiple galaxy populations \citep{urossamp,white} reads: = d^3 k, where X and Y are indices describing pairs of galaxy populations, and $C_{XY}$ is the covariance matrix of the power spectra."
" Adapting the BigBOSS specifications [rom Table 1 by shifting the EL sample to z—0.7.1.7 retains the science leverage and in fact delivers a mild improvement of AEgDOSSsop,—0LT τσ)—0.040 Moreover. a redshift maximum of 1.7 reduces the technical complexity of the data acquisition ancl analysis. ereathy ameliorating issues of line confusion and. reduced signal-to-noise that occur over 2=L3 2. ("," Adapting the BigBOSS specifications from Table \ref{spec} by shifting the EL sample to $z=0.7-1.7$ retains the science leverage and in fact delivers a mild improvement of : : )=0.043 =0.7-1.7 : )=0.040 Moreover, a redshift maximum of 1.7 reduces the technical complexity of the data acquisition and analysis, greatly ameliorating issues of line confusion and reduced signal-to-noise that occur over $z=1.7-2$ . ("
Note that,Note that
(1993).,.
. The errors in the Asin? are entirely dominated by errors in ¢sin/., The errors in the $R\sin i$ are entirely dominated by errors in $v\sin i$.
 Although the statistical sample (12) may seem small. we are helped by the fact that the probability density distribution for the projection factor sin’ of a random orientation favors close to edge-on geometries (see. e.g.. Appendix A in Drandekerοἱal.(2006))): Assuming a single age and the evolutionary models by Baralleοἱal.(1998)... equation (1)) can be used to find a maximum-likelihood estimate for the age.," Although the statistical sample (12) may seem small, we are helped by the fact that the probability density distribution for the projection factor $\sin i$ of a random orientation favors close to edge-on geometries (see, e.g., Appendix A in \citet{2006astro.ph..8352B}) ): Assuming a single age and the evolutionary models by \citet{1998A&A...337..403B}, equation \ref{e:sini}) ) can be used to find a maximum-likelihood estimate for the age."
 To take into account the estimated measurement error o. and to mitigate the singularity at sin?=l1. we assume ihe measured. sin? to be an outcome of a stochastic variable Ro€BU.Lig)+E. where )2sin/ is the projection [actor distributed according to equation (1)). E is normally distributed with zero mean and variance 67. and Bua.Zi) is the model radius for a star of age / and effective temperature Zig.," To take into account the estimated measurement error $\sigma$ , and to mitigate the singularity at $\sin i = 1$, we assume the measured $R\sin i$ to be an outcome of a stochastic variable $\mathcal{R} \in R_{\mathrm{mod}}(t,T_{\mathrm{eff}}) Y + E$ , where $Y = \sin i$ is the projection factor distributed according to equation \ref{e:sini}) ), $E$ is normally distributed with zero mean and variance $\sigma^2$ , and $R_{\mathrm{mod}}(t,T_{\mathrm{eff}})$ is the model radius for a star of age $t$ and effective temperature $T_{\mathrm{eff}}$."
 The probability distribution of R is obtained by numerical integration. ≀↧↴∐≼⇂⊔∐↲∐↓≀↧↴⇀↸↕∐∐∐⊔↥∐↘↽≼↲∐∐∪⋯⇂∣↽≻⋡∖⇁⇂∎↓∐≼∐∐≸≟⊔∐↲∐↓≀↕↴⇀↸↕∐∐∐∐∪↓≯⊔∐↲↥∐↘↽≼↲∐∐∪⋯⇂↓⋟∏∐≺∢∐∪∐ To estimate conservative confidence intervals for (Bis estimate. we integrate (he probability density function fr to get the cumulative probability function Fg.," The probability distribution of $\mathcal{R}$ is obtained by numerical integration, and the maximum likelihood by finding the maximum of the likelihood function To estimate conservative confidence intervals for this estimate, we integrate the probability density function $f_{\mathcal{R}}$ to get the cumulative probability function $F_{\mathcal{R}}$."
 We (hen find the agelimits fg and /4 such that the probabilitieswhere a is the sienilicance and (he probabilityfiuction is, We then find the agelimits $t_0$ and $t_1$ such that the probabilitieswhere $\alpha$ is the significance and the probabilityfunction is
The X-ray emission from young stellar objects (YSOs) at CCD-resolution is usually modelled as thermal emission from a hot plasma in coronal equilibrium. with higher characteristic temperatures than observed in older and less active stars.,"The X-ray emission from young stellar objects (YSOs) at CCD-resolution is usually modelled as thermal emission from a hot plasma in coronal equilibrium, with higher characteristic temperatures than observed in older and less active stars."
 An interesting deviation from a pure thermal X-ray spectrum ts the presence of fluorescent emission from neutral (or weakly ionised) Fe as shown by the presence of the 6.4 keV line., An interesting deviation from a pure thermal X-ray spectrum is the presence of fluorescent emission from neutral (or weakly ionised) Fe as shown by the presence of the 6.4 keV line.
 This was first detected by Imanishietal.(2001) in the ray emission of the YSO YLWI6A in p-Oph. during a large flare: in addition to the complex at 6.7 keV. a 6.4 keV emission line was clearly visibe.," This was first detected by \citet{ikt01} in the X-ray emission of the YSO YLW16A in $\rho$ -Oph, during a large flare: in addition to the complex at 6.7 keV, a 6.4 keV emission line was clearly visibe."
 Such fluorescence line is produced when energetic X-rays phototontse cold material close to the X-ray source. and it is therefore a useful diagnostic tool of the geometry of the X-ray emitting source and its surroundings.," Such fluorescence line is produced when energetic X-rays photoionise cold material close to the X-ray source, and it is therefore a useful diagnostic tool of the geometry of the X-ray emitting source and its surroundings."
 Since 2001. detections of the Fe K fluorescent emissior line at 6.4-keV in the spectra of YSOs have been reported by a number of authors.," Since 2001, detections of the Fe K fluorescent emission line at 6.4-keV in the spectra of YSOs have been reported by a number of authors."
 Tsujimotoetal.(2005) has identified seven sources with an excess emission at 6.4 keV among 127 observations of YSOs within the COUP observation of Orion: Favataetal.(2005b) report 6.4 keV fluorescent emission Ἡ Elias 29 in p-Oph both during quiescent and flaring emission. unlike all other reported detection of Fe fluorescent emissio1 in YSOs that were made during intense flaring: Giardinoetal.(2007) have detected Fe 6.4 keV emission from a low-mass young star in Serpens. during an intense. long-duration flare.," \citet{tfg+05} has identified seven sources with an excess emission at 6.4 keV among 127 observations of YSOs within the COUP observation of Orion; \citet{fms+05} report 6.4 keV fluorescent emission in Elias 29 in $\rho$ -Oph both during quiescent and flaring emission, unlike all other reported detection of Fe fluorescent emission in YSOs that were made during intense flaring; \citet{gfm+07} have detected Fe 6.4 keV emission from a low-mass young star in Serpens, during an intense, long-duration flare."
 Recently. Czesla&Schmitt(2007) have reported intense Fe fluorescent emission in the spectrum of V 1486 Ori during a strong flare. when the plasma reached a temperature in excess of 10 keV. The 6.4 keV fluorescent line has been detected in different classes of X-ray emitters: X-ray binaries. active galactic nuclei (AGNS). massive stars. supernova remnants. and the Sun itself during flares.," Recently, \cite{sc2007} have reported intense Fe fluorescent emission in the spectrum of V 1486 Ori during a strong flare, when the plasma reached a temperature in excess of 10 keV. The 6.4 keV fluorescent line has been detected in different classes of X-ray emitters: X-ray binaries, active galactic nuclei (AGNs), massive stars, supernova remnants, and the Sun itself during flares."
 In the case of the Sun. the fluorescing material is the solar photosphere. in the YSOs. however. indications are that the material in the circumstellar disk and its related accretion structures could be responsible for the fluorescence.," In the case of the Sun, the fluorescing material is the solar photosphere, in the YSOs, however, indications are that the material in the circumstellar disk and its related accretion structures could be responsible for the fluorescence."
 The typical equivalent width of the 6.4 keV emission line in the studies mentioned above is of the order of 150 eV and is too large to be explained with fluorescent emission in the stellar photosphere or in diffuse circumstellar material (e.g. Tsujimotoetal.. 2005:: Favataetal.. 2005b))., The typical equivalent width of the 6.4 keV emission line in the studies mentioned above is of the order of 150 eV and is too large to be explained with fluorescent emission in the stellar photosphere or in diffuse circumstellar material (e.g. \citealp{tfg+05}; \citealp{fms+05}) ).
" This scenario implies that the disk is ""bathed"" in high-energy X-rays emitted by the star. with significant astrophysical implications: for instance. X-rays. in addition to cosmic rays. would play an important role in phototonising the circumstellar material around young star and thus in coupling the gas to the ambient magnetic field (as suggested by e.g. Glassgoldetal.. 2000))."," This scenario implies that the disk is “bathed” in high-energy X-rays emitted by the star, with significant astrophysical implications; for instance, X-rays, in addition to cosmic rays, would play an important role in photoionising the circumstellar material around young star and thus in coupling the gas to the ambient magnetic field (as suggested by e.g. \citealp{gfm00}) )."
" Ceccarelltetal.(2002) suggest that the ""hot component they observe in the disk. in the infrared. is heated by the stellar high-energy emission."," \citet{cbt+02} suggest that the “hot” component they observe in the disk, in the infrared, is heated by the stellar high-energy emission."
 Observations of the time variability of the Fe 6.4 keV emission in. YSOs would provide useful constraints on the geometry and sizes of the star-accretion disk system and of other circumstellar structures such as funnel flows. Jets. or wind columns.," Observations of the time variability of the Fe 6.4 keV emission in YSOs would provide useful constraints on the geometry and sizes of the star-accretion disk system and of other circumstellar structures such as funnel flows, jets, or wind columns."
 We present here the results of a time-resolved spectral study of the X-ray emission of Elias 29. during ~9 days of nearly continuous observation by ΠΠ the context of the ultra-deep observation of p-Oph. named (from Deep Rho-Oph X-ray observation — Pillittertetal.. 2007)).," We present here the results of a time-resolved spectral study of the X-ray emission of Elias 29, during $\sim 9$ days of nearly continuous observation by in the context of the ultra-deep observation of $\rho$ -Oph, named (from Deep Rho-Oph X-ray observation – \citealp{psf+07}) )."
 We investigated the presence of variations in its strong Fe 6.4 keV emission over the 9-day time scale covered by the observations., We investigated the presence of variations in its strong Fe 6.4 keV emission over the 9-day time scale covered by the observations.
 This paper ts structured as follows., This paper is structured as follows.
 After a summary. below. of the properties of Elias 29. the observations and data analysis are briefly presented in refsec:obs..," After a summary, below, of the properties of Elias 29, the observations and data analysis are briefly presented in \\ref{sec:obs}."
 Results are summarised in refsec:res;; the simulations carried out to assess the reliability of the line detections and the significance of its variability are described in refsec:sim.., Results are summarised in \\ref{sec:res}; the simulations carried out to assess the reliability of the line detections and the significance of its variability are described in \\ref{sec:sim}. .
 The results are discussed in refsec:disc.., The results are discussed in \\ref{sec:disc}. .
interaction with the halo gasτ,interaction with the halo gas.
"ι, At any time. the angular momentum cdisplaved in he figure is normalized to the total angular momentum injecπου by the SN LE up to that time."," At any time, the angular momentum displayed in the figure is normalized to the total angular momentum injected by the SN II up to that time."
 The middle panel illustrwes the fraction of the SN 11 ejecta located at. dillerent. heigus. while the bottom panel shows 10 fraction of ejecta moving outside of the boundary. of 1ο active area and testifies that the amount of gas moving να is larger than that moving inward.," The middle panel illustrates the fraction of the SN II ejecta located at different heights, while the bottom panel shows the fraction of ejecta moving outside of the boundary of the active area and testifies that the amount of gas moving outward is larger than that moving inward."
 The latter starts ο increase after 70 Myr. when a substantial amount of 1e lifted. gas starts to fall back (see section 3.43)): having lost xut of its angular momentum. this gas tends to return at (Galacocentrie radius smaller than that at which it started --s JOULNOY.," The latter starts to increase after $\sim 70$ Myr, when a substantial amount of the lifted gas starts to fall back (see section \ref{subsec:feedback}) ); having lost part of its angular momentum, this gas tends to return at a Galacocentric radius smaller than that at which it started its journey."
 ]t is interesting to compare Fig., It is interesting to compare Fig.
 5 with the analogous, \ref{fig:angmo} with the analogous
"motion (i,=iij 0) and the core is initially in slow solid-body rotation ΞΩρ=5*1078Hz).",motion $\vec{u}_r = \vec{u}_\theta = 0$ ) and the core is initially in slow solid-body rotation $\left(|\vec{u}_\phi| / R = \Omega_0 = 5*10^{-13} \mbox{ Hz}\right)$.
 The total mass Meore in the computational(\ii|/R domain is chosen to be 50 or 100 Mo., The total mass $M_\mathrm{core}$ in the computational domain is chosen to be 50 or 100 $\mbox{M}_\odot$.
" to the influence of the different radiation transport methods described in the last sections, we check the dependence of the stability of the radiation pressure dominated cavity on the initial density slope of the pre-stellar core."," to the influence of the different radiation transport methods described in the last sections, we check the dependence of the stability of the radiation pressure dominated cavity on the initial density slope of the pre-stellar core."
 We chose the initial density slope to be either pccr7!? or pcr?., We chose the initial density slope to be either $\rho \propto r^{-1.5}$ or $\rho \propto r^{-2}$.
 An overview of the runs is given in Table 1.., An overview of the runs is given in Table \ref{tab:runs}.
" For a more comprehensive parameter scan of the initial conditions of this pre-stellar core collapse model, we refer to ? and ?.."," For a more comprehensive parameter scan of the initial conditions of this pre-stellar core collapse model, we refer to \citet{Kuiper:2010p17191} and \citet{Kuiper:2011p17433}."
" We summarize the qualitative outcome, and the overall morphology of the radiation pressure dominated cavities, depending on the different initial conditions and the radiation transfer method."," We summarize the qualitative outcome, and the overall morphology of the radiation pressure dominated cavities, depending on the different initial conditions and the radiation transfer method."
" In the six simulations, the radiation pressure is generally high enough to launch an outflow and form a cleared polar cavity."," In the six simulations, the radiation pressure is generally high enough to launch an outflow and form a cleared polar cavity."
" In the case of the RT+FLD radiation transport method, these outflow cavities, once launched, rapidly grow in their extent up to the outer computational domain at 0.1 pc away from the central star."," In the case of the RT+FLD radiation transport method, these outflow cavities, once launched, rapidly grow in their extent up to the outer computational domain at 0.1 pc away from the central star."
" In contrast to this monotonic growth, the outflow cavities in the FLD radiation transport scheme stop their increase along the polar axis at an extent of the order of several 100 to 1400 AU depending on the initial conditions."," In contrast to this monotonic growth, the outflow cavities in the FLD radiation transport scheme stop their increase along the polar axis at an extent of the order of several 100 to 1400 AU depending on the initial conditions."
" This stopping of their growth is followed by a penetration of the gas mass on top of the outflow cavity formed so far, i.e. the outflow cavity collapses."," This stopping of their growth is followed by a penetration of the gas mass on top of the outflow cavity formed so far, i.e. the outflow cavity collapses."
" During a follow-up second and third epoch of outflow launching, the resulting cavities grow in their extent, but on much longer timescales than in the RT+FLD case."," During a follow-up second and third epoch of outflow launching, the resulting cavities grow in their extent, but on much longer timescales than in the RT+FLD case."
" The epochs of frozen cavity growth in the FLD-only simulations suggest that (parts of) the top layer of the outflow cavity are in marginal Eddington equilibrium, i.e. the radiation pressure force is in equilibrium with the stellar gravity."," The epochs of frozen cavity growth in the FLD-only simulations suggest that (parts of) the top layer of the outflow cavity are in marginal Eddington equilibrium, i.e. the radiation pressure force is in equilibrium with the stellar gravity."
" The qualitative outcome of the simulations (depending on whether an extended epoch of marginal Eddington equilibrium occurs) is summarized in Table 1,, column 5."," The qualitative outcome of the simulations (depending on whether an extended epoch of marginal Eddington equilibrium occurs) is summarized in Table \ref{tab:runs}, column 5."
" In addition to the different growth rates, the radiation-pressure-driven outflow cavities also develop pronounced differences in their morphology depending on the applied radiation transport method."," In addition to the different growth rates, the radiation-pressure-driven outflow cavities also develop pronounced differences in their morphology depending on the applied radiation transport method."
" As an example, the different morphologies produced by the different radiation transport methods are visualized in three snapshots in time during the onset of the outflow launching in Fig. 3.."," As an example, the different morphologies produced by the different radiation transport methods are visualized in three snapshots in time during the onset of the outflow launching in Fig. \ref{fig:Snapshots}."
" In the case of FLD, the outflow is easily stopped by the infalling matter along the polar axis, while in the RT+FLD case the outflow cavity time."," In the case of FLD, the outflow is easily stopped by the infalling matter along the polar axis, while in the RT+FLD case the outflow cavity time."
" In the FLD approximation, the radiative flux tends to follow a path that minimizes the optical depth and hence avoids the swept-up mass on top of the cavity."," In the FLD approximation, the radiative flux tends to follow a path that minimizes the optical depth and hence avoids the swept-up mass on top of the cavity."
" This avoidance is alleviated by the centrifugal forces, which diminish the gravitational attraction in regions slightly above the disk."," This avoidance is alleviated by the centrifugal forces, which diminish the gravitational attraction in regions slightly above the disk."
" In the ray-tracing method, the isotropic stellar irradiation flux directly impinges onto the swept-up mass on top of the polar cavity and pushes the mass to larger radii."," In the ray-tracing method, the isotropic stellar irradiation flux directly impinges onto the swept-up mass on top of the polar cavity and pushes the mass to larger radii."
 The resulting large-scale morphology of the cavity is far more isotropic., The resulting large-scale morphology of the cavity is far more isotropic.
 The opening angle of the cavity is determined by the inner disk structure., The opening angle of the cavity is determined by the inner disk structure.
 In the following Sects., In the following Sects.
" 5 and 6,, we analyze quantitatively the outcome of the simulations presented here."," \ref{sect:QuantitativeResults1} and \ref{sect:QuantitativeResults2}, we analyze quantitatively the outcome of the simulations presented here."
" We check our hypothesis of epochs of marginal Eddington equilibrium in the FLD-only runs and determine via analytical estimates (Sect. 7)),"," We check our hypothesis of epochs of marginal Eddington equilibrium in the FLD-only runs and determine via analytical estimates (Sect. \ref{sect:Analytic}) ),"
 why the cavity shells in the RT+FLD case do not undergo these epochs and therefore remain stable with respect to the radiative Rayleigh-Taylor instability., why the cavity shells in the RT+FLD case do not undergo these epochs and therefore remain stable with respect to the radiative Rayleigh-Taylor instability.
 We analyze quantitatively the time-dependent extent of the outflow cavity., We analyze quantitatively the time-dependent extent of the outflow cavity.
" The radial extent Reayity of the outflow cavities above the central star is determined as the extent of the cleared cavity along the polar axis, as visualized in Fig. 3.."," The radial extent $R_\mathrm{cavity}$ of the outflow cavities above the central star is determined as the extent of the cleared cavity along the polar axis, as visualized in Fig. \ref{fig:Snapshots}."
 The resulting cavity radii as a function of time are shown for the three different initial conditions as well as the different radiation transport methods in Fig. 4.., The resulting cavity radii as a function of time are shown for the three different initial conditions as well as the different radiation transport methods in Fig. \ref{fig:OutflowRadiusvsTime}.
" For all initial conditions, the extent of the radiation pressure dominated cavities increases far more rapidly, if the stellar source of radiation is treated via a ray-tracing scheme (labeled “RT+FLD”) than simply included in the flux-limited diffusion solver (labeled “FLD”)."," For all initial conditions, the extent of the radiation pressure dominated cavities increases far more rapidly, if the stellar source of radiation is treated via a ray-tracing scheme (labeled “RT+FLD”) than simply included in the flux-limited diffusion solver (labeled “FLD”)."
" If using the FLD approximation, the outflow is launched a little bit earlier in time and after its initial growth phase undergoes an epoch of marginal stability, in which the radiation pressure force along the polar axis seems to be balanced by gravity; thecavity growth along the polar axis is first stopped and then reversed."," If using the FLD approximation, the outflow is launched a little bit earlier in time and after its initial growth phase undergoes an epoch of marginal stability, in which the radiation pressure force along the polar axis seems to be balanced by gravity; thecavity growth along the polar axis is first stopped and then reversed."
" Under these conditions of marginal Eddington equilibrium (Trad€ferav) with FLD, the cavity shell region has been proposed to be subject to the radiative Rayleigh-Taylor instability (?).."," Under these conditions of marginal Eddington equilibrium $\left(f_\mathrm{rad} \lesssim f_\mathrm{grav}\right)$ with FLD, the cavity shell region has been proposed to be subject to the radiative Rayleigh-Taylor instability \citep{Jacquet:2011p18452}. ."
" As a consequence, subsequent growth phases of the outflows in the FLD runs"," As a consequence, subsequent growth phases of the outflows in the FLD runs"
transform as where w = exp(2/7/3) is (he generator of Z4.,transform as where $\omega$ = $2i \pi/3$ ) is the generator of $Z_3$.
 These assigned (vanslormations generate (he diagonale chargede lepton mass matrix M., These assigned transformations generate the diagonal charged lepton mass matrix $M_l$ .
" The bilinears D,vy,1 and pg1jvp,τι relevant for Mp and AJ, transform as Assuming a complex scalar singlet \ that transforms under Zas V— «X. the [orm ol My becomes"," The bilinears $\overline{D}_{L_j}\nu_{R_k}$ and $\nu_{R_j}\nu_{R_k}$ relevant for $M_D$ and $M_R$ transform asSince, the SM Higgs doublet transforms trivially under $Z_3$, the form of $M_D$ becomes Assuming a complex scalar singlet $\chi$ that transforms under $Z_3$as $\chi \rightarrow \omega^2 \chi$ , the form of $M_R$ becomes"
mass niocdoels.,mass models.
" Iu practice. the values of the free parameters e aad 2 that result from fitting the URC to the svuthetic curves Vi, select the actual model."," In practice, the values of the free parameters $a$ and $\beta$ that result from fitting the URC to the synthetic curves $V_{syn}$ select the actual model."
 Adopting §~0.72|πο... and e&πο.d (see PSS) or. equivalently the correspondiug that we have plotted in Fig. (," Adopting $\beta ~\simeq 0.72 +~ 0.44\, log ({L_I \over L_*})$ and $a \simeq 1.5 ( {L_I \over L_*} )^{1/5}$ (see PSS) or, equivalently the corresponding that we have plotted in Fig. ("
2). the URC mass models reproduce the svuthetic curves Wy) within their yeun.s. (,"2), the URC mass models reproduce the synthetic curves $V_{syn}(r)$ within their r.m.s. ("
sce Fig. (,see Fig. (
1)).,1)).
 More in detail. atany Iuniuosity aud radius. IVeseVau: (and the le fitting uncertainties on (e and are about (PSS).," More in detail, atany luminosity and radius, $|V_{URC}-V_{syn}| < 
 2\%$ and the $1\sigma$ fitting uncertainties on $a$ and $\beta$ are about (PSS)."
 We then compare the dark halo velocities obtained with eq. (, We then compare the dark halo velocities obtained with eq. (
"7) and (9). with the Burkert velocities 1,07) of eqs. (","7) and (9), with the Burkert velocities $V_b(r)$ of eqs. ("
2)-CI).,2)-(4).
 We leave py and ry as free parameters. b.e. we do not impose the relationship of eq. (," We leave $\rho_0$ and $r_0$ as free parameters, i. e. we do not impose the relationship of eq. ("
5).,5).
 The results are shown in Fig (3): at anv Iuninositv. out to the outermost radii (~ 6424). iudistinguishable from Veer).," The results are shown in Fig (3): at any luminosity, out to the outermost radii $\sim 6 R_d$ ), $V_b(r)$ is indistinguishable from $V_{h,URC}(r)$."
 More specifically. by setting Vorge(r)= Ventre). we are able to reproduce the svuthetic rotation curves Viy4G]) at the level of their ranis.," More specifically, by setting $V_{h, URC}(r)\equiv V_{b}(r)$ , we are able to reproduce the synthetic rotation curves $V_{syn}(r)$ at the level of their r.m.s."
 For r>> 6Rp. ie. bevoud the region described by the URC. the two velocity profiles progressively differ.," For $r>>6 R_D$ , i.e. beyond the region described by the URC, the two velocity profiles progressively differ."
 The values obtained for ry aud py for the URC agrees with the extrapolation at high masses of the scaling law pry77 (Burkert. 1995) established for objects with core radii ry ten times smaller (see Fie [).," The values obtained for $r_0$ and $\rho_0$ for the URC agrees with the extrapolation at high masses of the scaling law $\rho \propto r_0^{-2/3} $ (Burkert, 1995) established for objects with core radii $r_0$ ten times smaller (see Fig 4)."
 Let us notice that the core radii ave very large: ry2Ry so that an everrising halo RC cannot be excluded by the data., Let us notice that the core radii are very large: $r_0>>R_d$ so that an ever-rising halo RC cannot be excluded by the data.
 Moreover. the diskanass vs. ceutral halo density relationship pyκMur. ound in dwarf galaxies (Durkert.1995). where the deusest alos harbor the least massive disks. holds also for disk systems of stellar mass up to 104AZ.. (see Fie 1).," Moreover, the disk-mass vs. central halo density relationship $\rho_0 \propto M_d^{-1/3}$ , found in dwarf galaxies (Burkert,1995), where the densest halos harbor the least massive disks, holds also for disk systems of stellar mass up to $10^{11} M_\odot$ (see Fig 4)."
" The above relationship show a curvature at the lighest lüasses/lowest deusilos that can be related to the existence of an upper liit in the dark halo mass Moog which is evident by the sudden decline of the barvonic function. of disk galaxies at ALP""=2«4108A, (Salucci aud Persic. 19998). that implies a maxima halo lass of where Oy aud Ον~0.03 (e.g. Burles aud Tytler. 1998) are the matter aud barvonic densities of the Universe in units of critical deusitv."," The above relationship show a curvature at the highest masses/lowest densities that can be related to the existence of an upper limit in the dark halo mass $M_{200}$ which is evident by the sudden decline of the baryonic function of disk galaxies at $M_{d}^{max}= 2\times 10^{11}M_\odot $ (Salucci and Persic, 1999a), that implies a maximum halo mass of where $\Omega_0$ and $\Omega_{b}\simeq 0.03$ (e.g. Burles and Tytler, 1998) are the matter and baryonic densities of the Universe in units of critical density."
 From the definition of Afoyy. bv means of eq. (," From the definition of $M_{200}$, by means of eq. ("
2) and (3). we can write Moog iun terms of the “observable” quantity Mo: Magy=Mo.,"2) and (3), we can write $M_{200}$ in terms of the ""observable"" quantity $M_{0}$ : $M_{200} = \eta M_0$."
 For (Qu.2)(0.3.3). 4στ 12: notice that there is a mild depeudences of yon τ aud Qy which is irrelevant for the present study.," For $(\Omega_0, z)=(0.3,3)$ , $\eta \simeq 12$ ; notice that there is a mild dependences of $\eta$ on $z$ and $\Omega_0$ which is irrelevant for the present study."
 Combining eq. (, Combining eq. (
3) aud (10) we obtain au upper limit for the central density. pj1«10ερνο)Oyfenr?. which implies a lack of objects with py>E&102gem? and ry>30kpe. as is evideut in Fieure 3.,"3) and (10) we obtain an upper limit for the central density, $\rho_0 <1\times 10^{-20}
(r_0/kpc)^{-3} g /cm^{3}$, which implies a lack of objects with $\rho_0> 4\times
10^{-25}g/cm^{3}$ and $r_0>30 kpc$, as is evident in Figure 3."
" Turning the areuneut aronud. the deficit of objects with M~ALP"" and py>Lx.anoslo7?gfem?. suggests that. at this mass scale. the total-to- barvonic mass fraction may approache the cosmological value οον~10."," Turning the argument around, the deficit of objects with $M_d \sim M_d^{max} $ and $\rho_0> 4\times 10^{-25}~g/cm^{3}$, suggests that, at this mass scale, the total-to- baryonic mass fraction may approache the cosmological value $\Omega/\Omega_{b}\simeq 10$."
 Out to two optical radii the Burkert density profile reproduces. for the whole spiral hwuninositv sequence. the DM halos mass distribution.," Out to two optical radii, the Burkert density profile reproduces, for the whole spiral luminosity sequence, the DM halos mass distribution."
 This density profile. though at very large radii coincides with the NEW profile. approaches a coustaut. finite deusity value at the center. imn away consistent with an isothermal distribution.," This density profile, though at very large radii coincides with the NFW profile, approaches a constant, finite density value at the center, in a way consistent with an isothermal distribution."
 This is iu contradiction to cosmological models (c.g. Fukushiee aud Makino 1997) which predict that the velocity dispersion σ of the dark matter particles decreases towards the center toreach o> Oforr»0., This is in contradiction to cosmological models (e.g. Fukushige and Makino 1997) which predict that the velocity dispersion $\sigma$ of the dark matter particles decreases towards the center to reach $\sigma \rightarrow 0$ for $r \rightarrow 0$.
 After the result of this study. the dark halo iuncr reeious. therefore. cannot be cousidered as kinematically cold but rather as “warm” reeious with size ryXpy1) The struc," After the result of this study, the dark halo inner regions, therefore, cannot be considered as kinematically cold structures but rather as ""warm"" regions with size $ r_0 \propto \rho_0^{-1.5}$."
tureshalo core sizes are very large: ro~Lo πι , The halo core sizes are very large: $r_0 \sim 4-7 R_d$ .
Then. the boundary of the core region is well bevoud theregionwhere the stars are located aud. as in Corbelli aud Salueci (2000). even at the outermost observed radiusthereis not the slightest evidence that dark halos converse toa porf.? (or à steepor) reeime.," Then, the boundary of the core region is well beyond theregionwhere the stars are located and, as in Corbelli and Salucci (2000), even at the outermost observed radiusthereis not the slightest evidence that dark halos converge to a $\rho \sim r^{-2}$ (or a steeper) regime."
It has been shown (Derezhko&Ellison1999:AmatoBlasi2006) that a good approximation to the solution of Eq.,"It has been shown \citep{be99, amato2} that a good approximation to the solution of Eq."
 48. is where P(r) is the plasma pressure as calewlated taking into account only acliabatic compression in the precursor. Eq. 15..," \ref{consen} is where $P(x)$ is the plasma pressure as calculated taking into account only adiabatic compression in the precursor, Eq. \ref{pgas}."
 This expression. which serves as an equation of state for the gas in the presence of effective Alfvénn heating. reduces to the standard Eq.," This expression, which serves as an equation of state for the gas in the presence of effective Alfvénn heating, reduces to the standard Eq."
 50 of Derezhko&Ellison(1999) for ¢=1. while. for ¢<1 the damping of the waves is mitigated and an effective amplification of the magnetic field is allowed.," 50 of \cite{be99} for $\zeta=1$, while, for $\zeta<1$ the damping of the waves is mitigated and an effective amplification of the magnetic field is allowed."
 The change in (he equation of state of the gas also manifests itself in the shock dynamics., The change in the equation of state of the gas also manifests itself in the shock dynamics.
"The new relation between the compression ratios /2,,5 ancl {τοι reads where we have introduced wilh a notation which allows a direct comparison between the effects of magnetic feedback and Allvénn heating.",The new relation between the compression ratios $\Rs$ and $\Rt$ reads where we have introduced with a notation which allows a direct comparison between the effects of magnetic feedback and Alfvénn heating.
 It is widely known that the inclusion of Alfvénn heating has an important impact on the total compression ratio. changing its scaling with the Mach number from MS qo M (seee.g.Derezhko&Ellison1999).," It is widely known that the inclusion of Alfvénn heating has an important impact on the total compression ratio, changing its scaling with the Mach number from $M_0^{3/4}$ to $M_A^{3/8}$ \citep[see e.g.][]{be99}."
. ILowever the situation is very different when the correct maenetized jump conditions are taken into account., However the situation is very different when the correct magnetized jump conditions are taken into account.
 In Tab. 4..," In Tab. \ref{tab:TH},"
 we report. for different values of ¢=0.0.5.0.5.0.99. the solutions of the problem including the full treatinent. of growth and damping of Alfvénn waves according to the approximate analvtical solution of Eq.," we report, for different values of $\zeta=0,0.5,0.8,0.99$, the solutions of the problem including the full treatment of growth and damping of Alfvénn waves according to the approximate analytical solution of Eq."
 38 along with the prescription of Eq. 47..," \ref{transw0k} along with the prescription of Eq. \ref{zeta},"
 namely It is clear Chat the increasing relevance of Alfvénn heating (¢ approaching 1) does not lead. in this approach. to a smoother precursor Career value of {ο Γι).," namely It is clear that the increasing relevance of Alfvénn heating $\zeta$ approaching 1) does not lead, in this approach, to a smoother precursor (larger value of $\Rs/\Rt$ )."
 In fact. the energv (ransfer [rom (he waves to (he plasma. while heating (he plasma and reducing ils compressibilitv. is also accompanied by. a decrease of VW. the ratio of magnetic/plasma pressure.," In fact, the energy transfer from the waves to the plasma, while heating the plasma and reducing its compressibility, is also accompanied by a decrease of $W$, the ratio of magnetic/plasma pressure."
 The latter is the parameter which controls the magnetic feedback. which is then reduced.," The latter is the parameter which controls the magnetic feedback, which is then reduced."
 The net effect is a slight increase of {τω for intermediate values of ¢=0.5— 0.8. Onlv if Q is verv close to 1 the shock is less modified (han the adiabatie solution with, The net effect is a slight increase of $\Rt$ for intermediate values of $\zeta=0.5-0.8$ Only if $\zeta$ is very close to 1 the shock is less modified than the adiabatic solution with
 (vauderIruit1971.Condon1992:Yuneta," \citep[][]{vanDerKruit71,vanDerKruit73,deJong85,Helou85,Condon92,Yun01}."
l.2001).. 520 (Condonetal.1991: (c.g...Cram1998:Mobasherctal.1999).," $z \approx 0$ \citep{Condon91b,Yun01,Bell03}. \citep[e.g.,][]{Cram98,Mobasher99}."
 low-: at hieh :., $z$ at high $z$.
 There have been several couflicting results observationallv., There have been several conflicting results observationally.
 A umber of studies have fouud that the FRC holds uuchaugedor with little evolution at high redshifts (e.9.. Appletonetal.2001:Thar2008:al.2010:Youngerot 2010: Persic&Rephacli2007 Sugeest radio-dim ULIRGs at high :).," A number of studies have found that the FRC holds unchangedor with little evolution at high redshifts (e.g., \citealt{Appleton04,Ibar08,Rieke09,Murphy09,Younger09,Garn09,Sargent10,Ivison10,Younger10}; \citealt{Persic07} suggest radio-dim ULIRGs at high $z$ )."
 Subiuillimeter ealaxies. however. seen to be radio-bright. by a factor of 3 (dlxováesetal.2006:Vlaliakis2007:Sajinactphy2009:Michalowskietal.2009. 2010)).," Submillimeter galaxies, however, seem to be radio-bright, by a factor of $\sim 3$ \citealt{Kovacs06,Vlahakis07,Sajina08,Murphy09,Seymour09,Murphy09c,Michalowski09,Michalowski10}) )."
" In particular. Aburphnwetal.(20094) aud Michalowskietal.(2009) argue that their samples of submillimeter galaxies are intrinsically radio bright with respect to the local FRC. with uo significant coutamination from radio bright AGN,"," In particular, \citet{Murphy09} and \citet{Michalowski09} argue that their samples of submillimeter galaxies are intrinsically radio bright with respect to the local FRC, with no significant contamination from radio bright AGN."
 Tn addition to the work on individual star-foriuiug ealaxies. there have also been new investigations into both the receutlv-resolved FIR aud the unresolved CIIz radio backgrounds.," In addition to the work on individual star-forming galaxies, there have also been new investigations into both the recently-resolved FIR and the unresolved GHz radio backgrounds."
 The FIR background was detected by CODE aud has long been attributed to star-formatiou (seothereviewsbvIauser&Dwek2001:Lagacheetal. 2005).," The FIR background was detected by COBE and has long been attributed to star-formation \citep[see the reviews by][]{Hauser01,Lagache05}."
 The starformation origin ofthe FIRbackground was recently confirmed by BLAST (Devlin 2009)...," The star-formation origin ofthe FIRbackground was recently confirmed by BLAST \citep{Devlin09,Pascale09}. ."
 A detection of the extragalactic GIIz radio backgrouud has also Όσοι, A detection of the extragalactic GHz radio background has also been
"The differential equation (47)) can be solved by iteration. and (he corrections to ZU"" can be found in powers of A.","The differential equation \ref{Cdotp}) ) can be solved by iteration, and the corrections to $Z^{(\,0)}$ can be found in powers of $\lambda$."
" The first order correction is given by and the second order correction is given bv ;The coefficients∙− ὃς⊏↓⊐ and 5;,(3) in. equations. (52))⋅↜↜ and (53))NE are given. in. appendix A.."," The first order correction is given by and the second order correction is given by The coefficients $b^{\,(1)}_{n,k}$ and $b^{\,(2)}_{n,k}$ in equations \ref{Z(1)}) ) and \ref{Z(2)}) ) are given in appendix \ref{appB}."
 They depend on the initial conditions but do not depend on the length of DNA., They depend on the initial conditions but do not depend on the length of DNA.
" The coefficient C, is given by where for simplicity. we omit the «quantum mumber m keeping in mind that n=0."," The coefficient $U^{\,(2)}_{n}$ is given by where for simplicity, we omit the quantum number $m$ keeping in mind that $m=0$."
" G, in equation (54)) refers to all eigenvectors wilh eigenvalues equal to £,, Clearly. if the eigenvector |i.0.0) is not degenerate. we have G,,={ir}."," $G_{n}$ in equation \ref{U(2)}) ) refers to all eigenvectors with eigenvalues equal to $\mathcal{E}_{n,\,0,\,0}^{\,0}$ Clearly, if the eigenvector $|n,\,0,\,0\rangle $ is not degenerate, we have $ G_n=\{n\}$."
 The coellicients pit are zero except lor f&=0.42 (see appendix A)).," The coefficients $b^{\,(1)}_{n,k}$ are zero except for $k=0,\pm 2$ (see appendix \ref{appB}) )."
" Since the imaginary part £,4 is hey. an oscillatory term with frequency 244 appears in Z!P."," Since the imaginary part $\mathcal{E}_{n,\,k,\,0}^{\,0}$ is $k\,\omega _0$ , an oscillatory term with frequency $2\,\omega _0$ appears in $Z^{(\,1)}$."
 In fact. [rom equation (47)) we expect that oscillatory terms with frequencies (20.do.sc:.2puy} appear in the expression of Z.," In fact, from equation \ref{Cdotp}) ) we expect that oscillatory terms with frequencies $\{2\,\omega _0,\,4\,\omega _0,\,\cdots\,,2p\,\omega
_0\}$ appear in the expression of $Z^{(\,p)}$."
 The appearance of oscillatory terms is. in fact. an artifact of coupling between bending and twisting in an anisotropic DNA |?]..," The appearance of oscillatory terms is, in fact, an artifact of coupling between bending and twisting in an anisotropic DNA \cite{Farshid}."
 This is the main difference between the partition functions of an isotropic ancl an anisotropic DNA., This is the main difference between the partition functions of an isotropic and an anisotropic DNA.
 Although. as we will show in the next section. this difference is not detectable in experiments. at least if the DNA is long enough.," Although, as we will show in the next section, this difference is not detectable in experiments, at least if the DNA is long enough."
 Using equations (8)). (12)). (22)). and (25)) the average end-to-end extension of the DNA can be calculated as |?.?] ," Using equations \ref{Etot1}) ), \ref{Green}) ), \ref{Geq}) ), and\ref{Z1}) ) the average end-to-end extension of the DNA can be calculated as \cite{Marko, Nelson}
 "
ealaxies.,galaxies.
 Eveu in this unrealistic case of not allowine for the presence of the gas. we believe the trend to be hardly significant in view of the uucertamties.," Even in this unrealistic case of not allowing for the presence of the gas, we believe the trend to be hardly significant in view of the uncertainties."
 Siuce some correction for the eas mass as a function of morphological type must be made. we cannot claim that we find iu evidence for a change in the velocity anisotropy with IIubble type.," Since some correction for the gas mass as a function of morphological type must be made, we cannot claim that we find any evidence for a change in the velocity anisotropy with Hubble type."
 Fie., Fig.
 3 shows the axis ratio of the velocity ellipsoid of all the galaxies versus their rotation velocity., 3 shows the axis ratio of the velocity ellipsoid of all the galaxies versus their rotation velocity.
" Iu view of the fact that the two dispersions that eo iuto this ratio are deteriuued from different observational data (TRL youn integral properties such as total Ilunimosity aud auplitude of the rotation curve: 954, from photometric scale parameters and surface brightuess) and that we have made rather smuplifvius asstuuptious. the scatter is relmarkably πια."," In view of the fact that the two dispersions that go into this ratio are determined from different observational data $\sigma _{\rm R,h}$ from integral properties such as total luminosity and amplitude of the rotation curve; $\sigma _{\rm z,h}$ from photometric scale parameters and surface brightness) and that we have made rather simplifying assumptions, the scatter is remarkably small."
 No svstematic trends are visible (uud would probably not be significant!), No systematic trends are visible (and would probably not be significant!)
 in the data., in the data.
 The points closest to unitv im the dispersion ratio eenerally have low rotation velocities and inferred velocity dispersions., The points closest to unity in the dispersion ratio generally have low rotation velocities and inferred velocity dispersions.
" Oue of these (V5, = 95 kins lio,nog = 0.75) is NGCDh023."," One of these $V_{\rm rot}$ = 95 km $^{-1}$, $\sigma _{\rm z,h} / \sigma _{\rm R,h}$ = 0.75) is NGC5023."
 Bottema ct al. (, Bottema et al. (
1986) have shown that the stars aud the eas in this ealaxy are effectively coexistent: the radialand vertical distributions are very simular.,1986) have shown that the stars and the gas in this galaxy are effectively coexistent; the radial vertical distributions are very similar.
 This would nuplv that the velocity dispersions of the eas aud the stars are the same., This would imply that the velocity dispersions of the gas and the stars are the same.
 The vertical velocity dispersion found here is about 20 aus +. which is significantly higher than that observed in larger spirals.," The vertical velocity dispersion found here is about 20 km $^{-1}$, which is significantly higher than that observed in larger spirals."
 It would be of interest to measure the velocity dispersion in this galaxy., It would be of interest to measure the velocity dispersion in this galaxy.
 Since the III would be expected to have an isotropic velocity distribution from collisions between clouds. the vertical dispersion should be equal to that in the line of sight iu edge-on galaxies.," Since the HI would be expected to have an isotropic velocity distribution from collisions between clouds, the vertical dispersion should be equal to that in the line of sight in edge-on galaxies."
 lu this section we will critically discuss the uncertainties in our approach., In this section we will critically discuss the uncertainties in our approach.
 e We have discussed above that the power-aw nature of the Tully-Fisher relation (Eq. (, $\bullet $ We have discussed above that the power-law nature of the Tully-Fisher relation (Eq. (
11)) would iuplv a noulinear form of the magnitude version of Bottema’s relation (Eq. (,11)) would imply a nonlinear form of the magnitude version of Bottema's relation (Eq. (
2)).,2)).
 We have used it as an enipincal relation to help (together with Eq. (, We have used it as an empirical relation to help (together with Eq. (
1)) to estimate the radial velocity dispersions from the observed ο,1)) to estimate the radial velocity dispersions from the observed photometry.
 One may areue that it is iuternally cousisteut ο use instead of Eq. (, One may argue that it is internally consistent to use instead of Eq. (
2) a fit of tho form This has oulv a noticable effect on galaxies with faint Hsolute disk maguitudes.,2) a fit of the form This has only a noticable effect on galaxies with faint absolute disk magnitudes.
 We have repeated our analysis using such a fit aud fud no change in our results., We have repeated our analysis using such a fit and find no change in our results.
 To be more definite we repeat the table of the average axis ratio as a function of morphological type that we thenobtain., To be more definite we repeat the table of the average axis ratio as a function of morphological type that we thenobtain.
Figure 8. shows correlation functions (computed usine he techniques of Deusonetal. 2000)) for the same four uodels compared to both the predicted dark matter correlation function and the observed galaxy correlation unctio.,"Figure \ref{fig:xi} shows correlation functions (computed using the techniques of \citealt{ajbbias}) ) for the same four models, compared to both the predicted dark matter correlation function and the observed galaxy correlation function."
 As expected. all models do well at matching he data ou scales lweer than about 15 t\Mpe.," As expected, all models do well at matching the data on scales larger than about $1h^{-1}$ Mpc."
 Ou sinaller scales. all iiodels are cautibiassed? with respect o the dark matter. but they produce somewhat too much clusteriug.," On smaller scales, all models are `antibiassed' with respect to the dark matter, but they produce somewhat too much clustering."
 Bensonetal.(2000). found similar results for heir semi-aualvtie model., \citet{ajbbias} found similar results for their semi-analytic model.
 Model 8.3 gives. in fact. very similar clustering results to theirs (for the same ACDM cosmolosv).," Model 8.3 gives, in fact, very similar clustering results to theirs (for the same $\Lambda$ CDM cosmology)."
 The other models produce even strouger correlations on small scales. providing a worse match to the data.," The other models produce even stronger correlations on small scales, providing a worse match to the data."
 Model 8.3 does better than Model 8.2 because it places relatively fewer ealaxics iu clusters. thereby having many fewer pairs on small scales;," Model 8.3 does better than Model 8.2 because it places relatively fewer galaxies in clusters, thereby having many fewer pairs on small scales."
 We speculate that a model which performs even better at matching the observed Iunuinositv fiction (¢.¢. producing a sharper cut-off at bright maguitudes) may also do even better at matching the observed correlation function., We speculate that a model which performs even better at matching the observed luminosity function (e.g. producing a sharper cut-off at bright magnitudes) may also do even better at matching the observed correlation function.
 We have examined the key physics thought to be necessary to explain the shape of the galaxy. luninositv function in a cold dark matter universe., We have examined the key physics thought to be necessary to explain the shape of the galaxy luminosity function in a cold dark matter universe.
 While the cooling and condeusatiou of gas in a mereie hierarchy of dark matter halos remains the fundamental process through which galaxies form. we have demonstrated that at least two other processes must act to shape the hJuunuinositv function.," While the cooling and condensation of gas in a merging hierarchy of dark matter halos remains the fundamental process through which galaxies form, we have demonstrated that at least two other processes must act to shape the luminosity function."
 A model requires the inclusion of feedback moechauisus) (bevoud the heating resulting from the photoionization of the pregalactic eas) to flatten the faint eud of the huninosity function aud to suppress cooling at the ceutres of the massive halos of groups aud clusters., A model requires the inclusion of feedback mechanism(s) (beyond the heating resulting from the photoionization of the pregalactic gas) to flatten the faint end of the luminosity function and to suppress cooling at the centres of the massive halos of groups and clusters.
 If à fraction of the enerey liberated by supernovae aud winds goes iuto reheating disk gas and/or heating the diffuse eas halo. then the formation of faint galaxies is suppressed. resulting oeLa flattened faiut-cnd slope that matches the available observational data adequately.," If a fraction of the energy liberated by supernovae and winds goes into reheating disk gas and/or heating the diffuse gas halo, then the formation of faint galaxies is suppressed, resulting in a flattened faint-end slope that matches the available observational data adequately."
 These οςαπήσαν ou their own. however. are unable to produce a sharp cut-off at the bright end of the luminosity function.," These mechanisms on their own, however, are unable to produce a sharp cut-off at the bright end of the luminosity function."
 We lave shown that there are two possible (but quite extreme) processes that can achieve this: (1) thermal conduction at about or above the Spitzer rate: (2) expulsion of eas frou halos in superwinds at temperatures high cnough to prevent its subsequent recapture., We have shown that there are two possible (but quite extreme) processes that can achieve this: (1) thermal conduction at about or above the Spitzer rate; (2) expulsion of gas from halos in superwinds at temperatures high enough to prevent its subsequent recapture.
 The high value of A¢ong required to suppress the bright end of the hunnositv function is discouraging since it inplies both that the couductivity must be close to the Spitzer value (despite the presence of iG. magnetic fields in clusters: Naravan&Medvedev2001:Tayloretal.20023). aud that the effective teniperature eradicut must be somewhat steeper than the eradieuts observed in galaxy clusters (Allenetal.2001:Fabian.Voiet&Morris2002).," The high value of $\alpha_{\rm cond}$ required to suppress the bright end of the luminosity function is discouraging since it implies both that the conductivity must be close to the Spitzer value (despite the presence of $\mu G$ magnetic fields in clusters; \citealt{narayan01,taylor02}) ), and that the effective temperature gradient must be somewhat steeper than the gradients observed in galaxy clusters \citep{allen01, fabian02}."
. However. our inethod for calculating the effect of conduction is highly simplified.," However, our method for calculating the effect of conduction is highly simplified."
 In particular. there are two issues that are not well addressed.," In particular, there are two issues that are not well addressed."
 Firstly. our calculation is based ou the heat flux throuel a shell.," Firstly, our calculation is based on the heat flux through a shell."
 We have not considered the total exteut of the regiou in which conduction must be effective., We have not considered the total extent of the region in which conduction must be effective.
" We can define a radius Four such that the initial thermal euergv in the region Koool“oSFour d8 equal to the total enerev radiated roni the region r«rej. Where rego, ix the cooling radius in the presence of conduction."," We can define a radius $r_{\rm
out}$, such that the initial thermal energy in the region $r_{\rm
cool} <r< r_{\rm out}$ is equal to the total energy radiated from the region $r< r_{\rm cool}$, where $r_{\rm cool}$ is the cooling radius in the presence of conduction."
 Thermal enerev needs to © conducted from a radius at least as laree as rour du order to balance the radiative losses frou smaller racli., Thermal energy needs to be conducted from a radius at least as large as $r_{\rm out}$ in order to balance the radiative losses from smaller radii.
 For an isothermal halo with au r7 density profile. we Bud Peootour=rns where Log is the cooling radius calculated in the absence of conduction.," For an isothermal halo with an $r^{-2}$ density profile, we find $r_{\rm cool} r_{\rm out} =
r^{\prime 2}_{\rm cool}$, where $r^\prime_{\rm cool}$ is the cooling radius calculated in the absence of conduction."
 The radius rjr can be large. but the temperature eradieut that is required o transport heat effectively across this region 1s a stronglv declining function of radius.," The radius $r_{\rm
out}$ can be large, but the temperature gradient that is required to transport heat effectively across this region is a strongly declining function of radius."
 Thus. so lone as rj dies within the virialized region of the cluster. this is uulikelv o 1nodifv our solution siguiicautly.," Thus, so long as $r_{\rm out}$ lies within the virialized region of the cluster, this is unlikely to modify our solution significantly."
 Secondly. our method assunies that the logarithinic temperature eradieut within üesop Is constant.," Secondly, our method assumes that the logarithmic temperature gradient within $r_{\rm cool}$ is constant."
" If iustead. the eradieut is peaked iu his region. our method would underestimate the heat deposited iu the shell at 554,4."," If, instead, the gradient is peaked in this region, our method would underestimate the heat deposited in the shell at $r_{\rm
cool}$."
 These two simplifications Qvlich affect the required conduction coefficient iu opposite senses) are difficult to model accurately and without ad-hoc asstuuptions., These two simplifications (which affect the required conduction coefficient in opposite senses) are difficult to model accurately and without ad-hoc assumptions.
 Clearly. this is a problem that needs to be addressed by uuuerical sinmiations of cooling in conductive plasmas.," Clearly, this is a problem that needs to be addressed by numerical simulations of cooling in conductive plasmas."
" These would allow us to calibrate our simple model of conductive. heating and to infer what couductivitv is required. by removing the degeneracy between the shape of the halo temperature profile aud the suppression factor f, for the conductivity."," These would allow us to calibrate our simple model of conductive heating and to infer what conductivity is required, by removing the degeneracy between the shape of the halo temperature profile and the suppression factor $f_{\rm sp}$ for the conductivity."
 The alternative model invokes lighly cuerectic Usuperwiud outflows., The alternative model invokes highly energetic “superwind” outflows.
 The expulsion of gas from the halo reduces the reservoir of barvons avilable for cooliug at later times. and reduces the umber of stars formed by cach parcel of cold eas.," The expulsion of gas from the halo reduces the reservoir of baryons available for cooling at later times, and reduces the number of stars formed by each parcel of cold gas."
" However. the fraction of barvous required to be in this ""super-heated phase at 2=0 is quite high. aud the οποιον budget is exceptional."," However, the fraction of baryons required to be in this “super-heated” phase at $z=0$ is quite high, and the energy budget is exceptional."
 We found the energy budget of a promising superwiud modcl, We found the energy budget of a promising superwind model
of the luminosity function of dwarf svstems.,of the luminosity function of dwarf systems.
 We identify chvarl systems as those which satisfy the commonly accepted distance-Iuminositv definition of Tammann (1980)., We identify dwarf systems as those which satisfy the commonly accepted distance-luminosity definition of Tammann (1980).
 The entire survey is. described. in. details. elsewhere (Cavazzi οἳ al., The entire survey is described in details elsewhere (Gavazzi et al.
 1996b.c:: Boselli et. al.," 1996b,c; Boselli et al."
 LOOT: Scocdegeio et al., 1997; Scodeggio et al.
 1998: CGavazzi et al., 1998; Gavazzi et al.
 2000a: Doselli et. al., 2000a; Boselli et al.
 2000a hereafter referred to as Papers E and LL BOT. SOS. Papers IHE ancl IW) ancl we refer the reader to these papers for details concerning observations. data reduction. photometric calibration and image reduction. procedures of these 1157 galaxies.," 2000a – hereafter referred to as Papers I and II, B97, S98, Papers III and IV) and we refer the reader to these papers for details concerning observations, data reduction, photometric calibration and image reduction procedures of these 1157 galaxies."
 For the present study it is important to sav that azimuthally averaged: surface brightness profiles. were clerivedl and succesively fitted using either a de Vaucouleurs p paw. an exponential. a | disk: model or an exponential/de Vaucouleurs truncated model.," For the present study it is important to say that azimuthally averaged surface brightness profiles were derived and succesively fitted using either a de Vaucouleurs $r^{1/4}$ law, an exponential-law, a $+$ disk model or an exponential/de Vaucouleurs truncated model."
 Ehe. total magnitude of cach galaxy was obtained by adding to the Hux measured within the outermost significant isophote the Hux extrapolated to infinity along the model that fitted the outer parts of the galaxy., The total magnitude of each galaxy was obtained by adding to the flux measured within the outermost significant isophote the flux extrapolated to infinity along the model that fitted the outer parts of the galaxy.
 The typical internal error in the determination of Llp is £0.15 mag., The typical internal error in the determination of $\rm H_T$ is $\pm$ 0.15 mag.
" The cllective radius r, and the mean surface brightness within r (i.e. (n) of each ealaxv were computed in two ways (Paper V)."," The effective radius $r_e$ and the mean surface brightness within $r_e$ (i.e., $\mu_e$ ) of each galaxy were computed in two ways (Paper V)."
" The ""fitted"" values of the individual components were derived. from the incividual fitted profiles. extrapolated to zero and to infinity."," The “fitted” values of the individual components were derived from the individual fitted profiles, extrapolated to zero and to infinity."
" By contrast. the ""empirical values of the elective radius and surface brightness of the system were obtained locating the half-light point along the observed. light. profile. where the total amount of light is given by the total magnitude described. above. anc corrected for. secing according to Saglia. Beneder Dressler (1993)."," By contrast, the “empirical” values of the effective radius and surface brightness of the system were obtained locating the half-light point along the observed light profile, where the total amount of light is given by the total magnitude described above, and corrected for seeing according to Saglia, Bender Dressler (1993)."
" The ~empirical” values of r, and yy are used here.", The “empirical” values of $r_e$ and $\mu_e$ are used here.
 Typical internal errors in the determination of fogr. and fn. are ~—0.05 ancl 0.16 magareseec. respectively.," Typical internal errors in the determination of $log~r_e$ and $\mu_e$ are $\pm$ 0.05 and $\pm$ 0.16 $\rm mag~arcsec^{-1}$, respectively."
" Empirical values of the radii that enclose and of the total light were also determined. and their ratio defines the concentration index es, (de Vaucoulcurs 1977)."," Empirical values of the radii that enclose and of the total light were also determined, and their ratio defines the concentration index $c_{31}$ (de Vaucouleurs 1977)."
 Since part of the late-type galaxies. in he Virgo cluster were observed in the ν΄ -band. wir surface wightness. profiles were corrected for the mean Leb! color erm found by BOT (0.26 mag) before the determination of roo wd fie.," Since part of the late-type galaxies in the Virgo cluster were observed in the $\rm K^{\prime}$ -band, their surface brightness profiles were corrected for the mean $\rm K^{\prime}$ color term found by B97 (0.26 mag) before the determination of $r_e$ and $\mu_e$."
 For the late-type galaxies. accurately determined (double or single horned profile with high signal-to-noise ratio) linc-widths (a mean of the full-widths at the and levels of the maximum intensity) are taken from lomogencous [ow spatial resolution ΕΗ (i... A=21 cm) spectroscopic data-sets available in the literature (Scodeggio Gavazzi 1993 ancl references. therein).," For the late-type galaxies, accurately determined (double or single horned profile with high signal-to-noise ratio) line-widths (a mean of the full-widths at the and levels of the maximum intensity) are taken from homogeneous low spatial resolution HI (i.e., $\rm \lambda = 21~cm$ ) spectroscopic data-sets available in the literature (Scodeggio Gavazzi 1993 and references therein)."
 In. absence of 21 cm measurements or for Ll-deficient. spirals (llaàvnes Ciovanelli 1984). maximum rotational velocities are cerived from optical (i.e. Hào line. À=6563 A) major-axis rotation curves either derived by us (Gavazzi ct al.," In absence of 21 cm measurements or for HI-deficient spirals (Haynes Giovanelli 1984), maximum rotational velocities are derived from optical (i.e., $\rm H \alpha$ line, $\rm \lambda = 6563~\AA$ ) major-axis rotation curves either derived by us (Gavazzi et al."
 1999) or available in the literature., 1999) or available in the literature.
 Heassuringlv. no evidences of systematic differences in the measured. line-wicllhs either from. LIL or from Ia spectroscopic data are found for the subsample of non II-deficient objects with both measurements (Gavazzi et al.," Reassuringly, no evidences of systematic differences in the measured line-widths either from HI or from $\rm H \alpha$ spectroscopic data are found for the subsample of non HI-deficient objects with both measurements (Gavazzi et al."
 1999)., 1999).
" The values of Var, are derived from the widths. corrected for turbulent/z-motions along the 12.6kms+) according to Richter Luchtmeicr (1984) and cleprojected according to the Hubble. type-dependent Llolmberg formula given by Haynes Ciovanelli (1984)."," The values of $V_{Max}$ are derived from the line-widths, corrected for turbulent/z-motions along the $\rm -12.6~km~s^{-1}$ ) according to Richter Huchtmeier (1984) and deprojected according to the Hubble type-dependent Holmberg formula given by Haynes Giovanelli (1984)."
 For the early-tvpe galaxies. the values of the velocity dispersion are taken from the literature (SOs and references therein) and. homogenized. if necessary. according to the latter authors.," For the early-type galaxies, the values of the velocity dispersion are taken from the literature (S98 and references therein) and homogenized, if necessary, according to the latter authors."
 In the present analvsis. we exclude the dl and. ἄν ealaxies observed. by Cavazzi et al. (," In the present analysis, we exclude the dE and dS0 galaxies observed by Gavazzi et al. ("
2001) since it is still matter of debate whether their stellar. disk-component. is rotationally Dattened or not (e.g. Rix. Carollo Freeman 1999: Geha. Guhathakurta van der. Morel. 2001).,"2001) since it is still matter of debate whether their stellar disk-component is rotationally flattened or not (e.g. Rix, Carollo Freeman 1999; Geha, Guhathakurta van der Marel 2001)."
" By contrast. we select 197 earlv-tvpe galaxies and 210 latc-type galaxies. out of the surveved sample. of 1157. galaxies. according to the following criteria: 1) available homogeneous reliable measurements either of the central velocity. dispersion. or of the maximum rotational velocitw. for carly- and. late-type galaxies. respectively: 2) (only for the late-twpe systems) galaxy inclination between 30° ancl S5"". in order to limit any deprojection bias on Va, and a non-neeligible inclination correction of the photometric properties (if any). respectively: 3) goodness of the mono-dimensional (Le. radial) surface brightness profile fit. (Paper V). assured. by. the rejection threshold. 47.»=3.5."," By contrast, we select 197 early-type galaxies and 210 late-type galaxies, out of the surveyed sample of 1157 galaxies, according to the following criteria: 1) available homogeneous reliable measurements either of the central velocity dispersion or of the maximum rotational velocity, for early- and late-type galaxies, respectively; 2) (only for the late-type systems) galaxy inclination between $\rm 30^o$ and $\rm 85^o$, in order to limit any deprojection bias on $V_{Max}$ and a non-negligible inclination correction of the photometric properties (if any), respectively; 3) goodness of the mono-dimensional (i.e. radial) surface brightness profile fit (Paper V), assured by the rejection threshold $\rm \chi^2 = 3.5$."
 Though r. and yy. do not come from the fitting of the radial surface brightness profile. we adopt this criterion in order to select a sample. of swellbchaved” galaxies. be. of objects with photometric properties not highly alfected either by prominent structural features cilferent from bulge and disk or by peculiarities.," Though $r_e$ and $\mu_e$ do not come from the fitting of the radial surface brightness profile, we adopt this criterion in order to select a sample of “well-behaved” galaxies, i.e. of objects with photometric properties not highly affected either by prominent structural features different from bulge and disk or by peculiarities."
 Requirement limits the statisties of our sample hy and Large. so that we do not adopt any cut either in Vas or in ay. though literature sources suggest. that values of Vussx100kims Land of e«100kms.| are less reliable (but see PDdC).," Requirement 1 limits the statistics of our sample by and large, so that we do not adopt any cut either in $V_{Max}$ or in $\sigma_0$, though literature sources suggest that values of $V_{Max} \rm < 100~km~s^{-1}$ and of $\sigma_0 \rm < 100~km~s^{-1}$ are less reliable (but see PDdC)."
 The availability of reliable measurements Of Varus limits the statistics of galaxies later than Se but not that of SQaSab galaxies., The availability of reliable measurements of $V_{Max}$ limits the statistics of galaxies later than Sc but not that of S0a–Sab galaxies.
 No completeness is claimed for the resultant. sample of 407 galaxies. which is. therefore. exposed to the cluster population incompleteness bias (leerikorpi 1987. 1990).," No completeness is claimed for the resultant sample of 407 galaxies, which is, therefore, exposed to the cluster population incompleteness bias (Teerikorpi 1987, 1990)."
 Since the goal of the present paper is not to determine statistically accurate relations between the parameters of cilferent scaling relations but to discuss the relative distribution of each morphological class of galaxies within the s-space. the elfects of such a bias are less worrisonie.," Since the goal of the present paper is not to determine statistically accurate relations between the parameters of different scaling relations but to discuss the relative distribution of each morphological class of galaxies within the $\kappa$ -space, the effects of such a bias are less worrisome."
 For the sample here selected. Table 1. reproduces the relevant information as follows: 1} the galaxy denomination. from cither the “Catalogue of Galaxies and Clusters of Galaxies” of Zwicky et al.," For the sample here selected, Table 1 reproduces the relevant information as follows: 1) the galaxy denomination, from either the “Catalogue of Galaxies and Clusters of Galaxies” of Zwicky et al."
 (1961 CGCG) or from the “Virgo Cluster Catalogue” of Bineeeli. Sancage Tamamann (1985. VCC):," (1961--1968 – CGCG) or from the “Virgo Cluster Catalogue” of Binggeli, Sandage Tammann (1985 – VCC);"
munber of objects with au apparent axis ratio near or exactly equal to oue.,number of objects with an apparent axis ratio near or exactly equal to one.
 A close examination of the original Motte et al. (, A close examination of the original Motte et al. (
2001) data reveals that the objects which fall into this biu are well above the resolution Πιτ aud that this large umber is not a selection effect.,2001) data reveals that the objects which fall into this bin are well above the resolution limit and that this large number is not a selection effect.
 Since this data set has a number of axis ratios near p—1. it is interestiug to speculate whether or uot intrinsic oblate objects (rather than near-oblate triaxial objects) may agree with the observations.," Since this data set has a number of axis ratios near $p=1$, it is interesting to speculate whether or not intrinsic oblate objects (rather than near-oblate triaxial objects) may agree with the observations."
 We used two additional tests to investigate this hvpothesis., We used two additional tests to investigate this hypothesis.
 First. we fit the histogram of observed shapes with a curve aud carry out an analytic luverson to see if dtf ds consistent with a distribution of intrinsic oblate shapes.," First, we fit the histogram of observed shapes with a curve and carry out an analytic inversion to see if it is consistent with a distribution of intrinsic oblate shapes."
 The resulting intrinsic shape distribution C(q) docs go negative near qg=1 just as in the inversions performed ou the deuse core shape data of Jijina et al. (, The resulting intrinsic shape distribution $\psi(q)$ does go negative near $q=1$ just as in the inversions performed on the dense core shape data of Jijina et al. (
1999) and Lee Myers (1999) in Paper L This is due to the continuing presence of a decline in the observed axis ratio distribution o(p) towards p=1.,1999) and Lee Myers (1999) in Paper I. This is due to the continuing presence of a decline in the observed axis ratio distribution $\phi(p)$ towards $p=1$.
 To investigate further. we also experiment with an intrinsic axis distribution hat is Caussian in &. with £y=0.l and a=0.1. nit has a fixed value ¢=1 for all clouds. ic. he clouds are all oblate with various degrees of Hattenimg.," To investigate further, we also experiment with an intrinsic axis distribution that is Gaussian in $\xi$, with $\xi_0 = 0.4$ and $\sigma = 0.1$, but has a fixed value $\zeta = 1$ for all clouds, i.e., the clouds are all oblate with various degrees of flattening."
 In this case. our Monte Carlo program vields a probability distribution function which is plotted in Figure 11..," In this case, our Monte Carlo program yields a probability distribution function which is plotted in Figure \ref{mottebest}."
 The inverse \? values ‘or both the pure oblate objects and the best fit triaxial objects are z0.2., The inverse $\chi^2$ values for both the pure oblate objects and the best fit triaxial objects are $\approx 0.2$.
 The Motte et al. (, The Motte et al. (
2001) data. unlike the dense core data presented or reviewed iu 33.2. is close enough to being flat uear p=1 and has a small enough sample of objects that we cannot entirely exclude the pure oblate lypothesis on the basis of the 47 test.,"2001) data, unlike the dense core data presented or reviewed in 3.2, is close enough to being flat near $p=1$ and has a small enough sample of objects that we cannot entirely exclude the pure oblate hypothesis on the basis of the $\chi^2$ test."
 Tf just one of the six objects (interestingly. one object has an embedded class 0 protostar] is removed from the bin closest to p—1. the near-oblate triaxial objects provide a much better ft.," If just one of the six objects (interestingly, one object has an embedded class 0 protostar) is removed from the bin closest to $p=1$, the near-oblate triaxial objects provide a much better fit."
 Further observations ancl a larger sample will be necessary before the intrinsic shapes of these very deuse objects can be determined with certainty., Further observations and a larger sample will be necessary before the intrinsic shapes of these very dense objects can be determined with certainty.
 Nevertheless. we can conclude that molecular cloud coudeusatious are either oblate or near-oblate in shape.," Nevertheless, we can conclude that molecular cloud condensations are either oblate or near-oblate in shape."
 Tn order to test the reliabilitv of our results we, In order to test the reliability of our results we
In its most general form. the aim of the treatment described by Conway et al (1990)) is to find a way to decompose the dirty image into a sum of convolutions The problem is to calculate a set of beams B; for which this relation is true.,"In its most general form, the aim of the treatment described by Conway et al \cite{conway}) ) is to find a way to decompose the dirty image into a sum of convolutions The problem is to calculate a set of beams $B_i$ for which this relation is true."
 There are no doubt many ways to do this. but in the present section we are going to consider only the route which comes from expanding the frequency and time dependence of the sky brightness in a sum of basis functions.," There are no doubt many ways to do this, but in the present section we are going to consider only the route which comes from expanding the frequency and time dependence of the sky brightness in a sum of basis functions."
" Such an expansion is written where {ιν is the brightness function; r=(/.n) are direction. cosines of the angular displacementfrom the phase centre; v is frequency and ¢ time: Z,,(r) is a sky map of the (p.q)th component: and F,, and 7, are pth and qth members respectively of sets of basis functions."," Such an expansion is written where $I(\mathbf{r},\nu,t)$ is the brightness function; $\mathbf{r}=(l,m)$ are direction cosines of the angular displacementfrom the phase centre; $\nu$ is frequency and $t$ time; $I_{p,q}(\mathbf{r})$ is a sky map of the $(p,q)$ th component; and $F_p$ and $T_q$ are $p$ th and $q$ th members respectively of sets of basis functions."
 Earth-rotation and frequency synthesis will return a set of j=| to M measurements V; of the cross-correlations between antennas., Earth-rotation and frequency synthesis will return a set of $j=1$ to $M$ measurements $V_j$ of the cross-correlations between antennas.
 Ignoring for the sake of simplicity non-coplanarity. weights. the shape of the primary beam. and the spherical projection correction (1-r:r)? (see equation 1). each V; is related to I by a transform: Although each V; represents an average over a small time x bandwidth window. if this window is small enough. V; may be represented as a point sample of the visibility function at the spatial frequency uj.," Ignoring for the sake of simplicity non-coplanarity, weights, the shape of the primary beam, and the spherical projection correction $(1-\mathbf{r}\cdot\mathbf{r})^{-0.5}$ (see equation \ref{itotrue}) ), each $V_j$ is related to $I$ by a transform: Although each $V_j$ represents an average over a small time $\times$ bandwidth window, if this window is small enough, $V_j$ may be represented as a point sample of the visibility function at the spatial frequency $\mathbf{u}_j$ ."
 The total set V of visibility measurements can thus be written Expanding / in its basis functions gives. with some rearrangement: Fourier inversion of V. yields the dirty image D.," The total set $\mathbf{V}$ of visibility measurements can thus be written Expanding $I$ in its basis functions gives, with some rearrangement: Fourier inversion of $\mathbf{V}$ yields the dirty image $D$."
 This is indeed found to be à sum of convolutions: where Here the X symbol represents the Fourier transform., This is indeed found to be a sum of convolutions: where Here the $\mathfrak{F}$ symbol represents the Fourier transform.
 The two sums over p and q are easily collapsed to one. in which case equation + maps directly to equation 2..," The two sums over $p$ and $q$ are easily collapsed to one, in which case equation \ref{equ_f} maps directly to equation \ref{equ_a}."
 Clearly this requires that N2PxQ., Clearly this requires that $N=P \times Q$.
 Sault and Wieringa (1994)) developed an algorithm which. although it was set down only for N=2. is easily generalized to the following: The Sault-Wieringa deconvolution includes a matrix inversion.," Sault and Wieringa \cite{sault_wieringa}) )developed an algorithm which, although it was set down only for $N=2$, is easily generalized to the following: The Sault-Wieringa deconvolution includes a matrix inversion."
 If two or more beams from the set of N are identical. the matrix M is singular. te. uninvertible.," If two or more beams from the set of $N$ are identical, the matrix $\mathbf{M}$ is singular, i.e. uninvertible."
 If no two beams are exactly identical. but two or more are similar (have a normalized scalar product close to unity). M. will be formally invertible but can be expected to be ill-conditioned (1.e.. result in large errors in the final clean components).," If no two beams are exactly identical, but two or more are similar (have a normalized scalar product close to unity), $\mathbf{M}$ will be formally invertible but can be expected to be ill-conditioned (i.e., result in large errors in the final clean components)."
 Hence approximate orthogonality between beams is desirable: but if this be established. little further reduction in error is to be gained by enforcing complete orthogonality.," Hence approximate orthogonality between beams is desirable; but if this be established, little further reduction in error is to be gained by enforcing complete orthogonality."
 There may however be other reasons to manipulate the beams. even to the point of transforming them into ar orthonormal set. other than keeping the matrix M well-conditioned.," There may however be other reasons to manipulate the beams, even to the point of transforming them into an orthonormal set, other than keeping the matrix $\mathbf{M}$ well-conditioned."
 Two such circumstances are described here., Two such circumstances are described here.
 Firstly. the main aim of the Conway decomposition and subsequent vector cleaning is arguably to obtain a better image of the average sky brightness distribution.," Firstly, the main aim of the Conway decomposition and subsequent vector cleaning is arguably to obtain a better image of the average sky brightness distribution."
 This image is identical to the image of the zero-order beam coefficient if and only if every other beam is zero-valued at its centre - because a non-zero value of B;(0) equates to a non-zero average of the ith basis function over the frequency and time range of the observation., This image is identical to the image of the zero-order beam coefficient if and only if every other beam is zero-valued at its centre - because a non-zero value of $B_i(0)$ equates to a non-zero average of the $i$ th basis function over the frequency and time range of the observation.
 Thus in order to simplify the post-production of an average-brightness image. one would want to modify the set of beams before cleaning by subtracting B¢O)xBo/Bo(0) from each B; fori> 0.," Thus in order to simplify the post-production of an average-brightness image, one would want to modify the set of beams before cleaning by subtracting $B_i(0) \times B_0 / B_0(0)$ from each $B_i$ for $i > 0$ ."
 The second circumstance concerns the practicalities of computing the deconvolution., The second circumstance concerns the practicalities of computing the deconvolution.
 The Sault-Wieringa algorithm requires that N(N+1) images be kept inmemory during the iteration., The Sault-Wieringa algorithm requires that $N(N+1)$ images be kept inmemory during the iteration.
 For N= 2. as treated by Sault and Wieringa. this is à manageable number of images.," For $N=2$ , as treated by Sault and Wieringa, this is a manageable number of images."
 However. some of the," However, some of the"
According to equation (5). the CB disk can explain the loss rates of angular momentum seen in NN Ser for a large 0=0.1 and an ultra-high wind loss rate (107 Aiyr! ).,"According to equation (5), the CB disk can explain the loss rates of angular momentum seen in NN Ser for a large $\delta=0.1$ and an ultra-high wind loss rate $10^{-10}M_{\odot}\rm yr^{-1}$ )."
 The above order-of-magnitude estimate obviously contains substantial uncertainties in ó and the wind loss rates., The above order-of-magnitude estimate obviously contains substantial uncertainties in $\delta$ and the wind loss rates.
 Firstly. the loss rates of angular momentum relies strongly on the stellar wind loss rates. which may be overestimated by Mullanetal.(1992).," Firstly, the loss rates of angular momentum relies strongly on the stellar wind loss rates, which may be overestimated by \cite{mull92}."
". Based o the observations for several M dwarf flare stars. an upper limit of «107Mayr""! was derived (Lim&White1996.vandenOordDoyle 1997))."," Based on the observations for several M dwarf flare stars, an upper limit of $\sim 10^{-12}M_{\odot}\rm yr^{-1}$ was derived \cite{lim96,oord97}) )."
 Analysis of the data from and observations showed that. the M 5.5 dwarf Proxima Centauri. has a wind loss rate of ~1074—107A£.yr! (Woodetal.2001.Wargelin&Drake 2002)).," Analysis of the data from and observations showed that, the M 5.5 dwarf Proxima Centauri has a wind loss rate of $\sim
10^{-14}-10^{-15}M_{\odot}\rm yr^{-1}$ \cite{wood01,warg02}) )."
 Assuming that the white dwarf acecretes wind material through Bondi-Hoyle accretion. Debes(2006) presented a wind loss rates range of ~107—1079M.yr7! for three M. dwarfs.," Assuming that the white dwarf accretes wind material through Bondi-Hoyle accretion, \cite{debe06} presented a wind loss rates range of $\sim 10^{-14}-10^{-16}M_{\odot}\rm yr^{-1}$ for three M dwarfs."
 We expect that future observations on P. Cyent profiles. optical and molecular emission lines. infrared and radio excesses. and absorption lines can present further constrain for the wind loss rates of NN Ser (Lamers&Cassinelli 1999)).," We expect that future observations on P Cygni profiles, optical and molecular emission lines, infrared and radio excesses, and absorption lines can present further constrain for the wind loss rates of NN Ser \cite{lame99}) )."
 Secondly. even if the wind loss rates derived by Mullanetal.(1992) are the same with NN Ser. the CB disk mechanism still requires a large 6. which is about 2-3 orders of magnitude larger than that used by Spruit&Taam2001..," Secondly, even if the wind loss rates derived by \cite{mull92} are the same with NN Ser, the CB disk mechanism still requires a large $\delta$, which is about 2-3 orders of magnitude larger than that used by \cite{spru01}."
 In a word. such wind loss rates and ó-values are incredibly large. so it seems that the presence of a CB disk is not the main cause for the period change of NN Ser.," In a word, such wind loss rates and $\delta$ -values are incredibly large, so it seems that the presence of a CB disk is not the main cause for the period change of NN Ser."
 Recently. Brinkworth et al. (," Recently, Brinkworth et al. ("
2006) suggested that the standard nagnetic braking model may explain the period change observed in NN Ser if the magnetic braking cut-off was ignored.,2006) suggested that the standard magnetic braking model may explain the period change observed in NN Ser if the magnetic braking cut-off was ignored.
 In this letter. we estimate the loss rates of angular nomentum via magnetic braking by an analytic approach.," In this letter, we estimate the loss rates of angular momentum via magnetic braking by an analytic approach."
" Our result shows that. even if M dwarf in NN Ser possesses a strong nagnetic field of 4000 G and an ultra-high wind loss rates of ~I0""Mayr!. the loss rates of angular momentum via nagnetic braking are an order of magnitude less than that of observation."," Our result shows that, even if M dwarf in NN Ser possesses a strong magnetic field of $4000$ G and an ultra-high wind loss rates of $\sim
10^{-10}M_{\odot}\rm yr^{-1}$, the loss rates of angular momentum via magnetic braking are an order of magnitude less than that of observation."
 However. for the same wind loss rates. if a large fraction (~ 10%) of wind loss was input the CB disk. the loss rates of angular momentum seen in NN Ser can be interpreted by the tidal torques caused by the gravitational interaction between the CB disk and the binary.," However, for the same wind loss rates, if a large fraction $\sim 10\%$ ) of wind loss was input the CB disk, the loss rates of angular momentum seen in NN Ser can be interpreted by the tidal torques caused by the gravitational interaction between the CB disk and the binary."
 However. the stellar wind loss rates of M dwarfs determine if a CB disk can account for the period change of NN Ser.," However, the stellar wind loss rates of M dwarfs determine if a CB disk can account for the period change of NN Ser."
 Several authors have subsequently derived the wind loss rates of 2-6 magnitudes lower than the one given by Mullan et al. (, Several authors have subsequently derived the wind loss rates of 2-6 magnitudes lower than the one given by Mullan et al. (
1992) (Lim&White1996.vandenOordDoyle1997.Woodetal.2001.Wargelin&Drake2002.Debes (2006))).,"1992) \cite{lim96,oord97,wood01,warg02,debe06}) )."
 Based on recent inferred wind loss rates for M. dwarfs. the CB disk is not the main mechanism causing the period change of NN Ser.," Based on recent inferred wind loss rates for M dwarfs, the CB disk is not the main mechanism causing the period change of NN Ser."
 If we can not explore a more efficient mechanism extracting angular momentum from the binary. the presence of a third body in a long orbit around NN Ser may be the best candidate mechanism to cause its period change (Brinkworthetal.(2006))).," If we can not explore a more efficient mechanism extracting angular momentum from the binary, the presence of a third body in a long orbit around NN Ser may be the best candidate mechanism to cause its period change \cite{brin06}) )."
 Though a CB disk is ruled out in NN Ser. the existence of CB disks might be a key issue in studying the evolution of the CVs.," Though a CB disk is ruled out in NN Ser, the existence of CB disks might be a key issue in studying the evolution of the CVs."
 As a result of a continuum contribution of the dust emission. the CB disk may be detected in the L waveband (Spruit&Taam2001)).," As a result of a continuum contribution of the dust emission, the CB disk may be detected in the L waveband \cite{spru01}) )."
 Recently. Hayasaki Okazaki (2009) suggested a new channel to probe a CB disk. in. which the emission profiles may be caused to be variable by prograde and nonaxisymmetric waves.," Recently, Hayasaki Okazaki (2009) suggested a new channel to probe a CB disk, in which the emission profiles may be caused to be variable by prograde and nonaxisymmetric waves."
 Through interferometric observations. the direct imaging of CB disks has been successfully obtained in some young binaries such as GG Tau (Dutrey.Guilloteau&Simon1994)) and UY Aur (Duvertetal.1998)).," Through interferometric observations, the direct imaging of CB disks has been successfully obtained in some young binaries such as GG Tau \cite{dutr94}) ) and UY Aur \cite{duve98}) )."
 When the Spitzer data for CVs with a strong magnetic field were analyzed. the flux density of four and five polars in mid-infrared was discovered to be in excess. respectively.," When the Spitzer data for CVs with a strong magnetic field were analyzed, the flux density of four and five polars in mid-infrared was discovered to be in excess, respectively."
 Howell et al. (, Howell et al. (
2006) and Brinkworth et al. (,2006) and Brinkworth et al. (
2007) proposed that the CB dust disks may be the best origin of these excess (but the source of optically thin cyclotron cannot be ruled out).,2007) proposed that the CB dust disks may be the best origin of these excess (but the source of optically thin cyclotron cannot be ruled out).
 Recently. Dubus et al. (," Recently, Dubus et al. ("
2007) found that the infrared emission from the magnetic CVs AE Aqr is obviously larger than the expected value from the companion. and they thought that the thermal emission from the CB material might be a candidate.,"2007) found that the infrared emission from the magnetic CVs AE Aqr is obviously larger than the expected value from the companion, and they thought that the thermal emission from the CB material might be a candidate."
 Therefore. as the progenitor of CVs. NN Ser may also be surrounded by a CB disk.," Therefore, as the progenitor of CVs, NN Ser may also be surrounded by a CB disk."
 We expect further detailed multi-waveband observations for this pre-CVs to confirm or negate our idea in the future., We expect further detailed multi-waveband observations for this pre-CVs to confirm or negate our idea in the future.
iree characteristics in hyclrodynamics (see. Landau Lifschitz 1966).,"three characteristics in hydrodynamics (see, Landau Lifschitz 1966)."
 We ect this fourth wave purely as a result [the non-planar nature of the svstem., We get this fourth wave purely as a result of the non-planar nature of the system.
 Lt formis because. as 16 forward shock moves outwards it sweeps up an increasing mount of interstellar matter per unit distance.," It forms because, as the forward shock moves outwards it sweeps up an increasing amount of interstellar matter per unit distance."
 This means i (he forward shock does not move outwards as [ast s it would in the planar case. and the reverse shock is ormed to decelerate material behind the forward shock to 16 appropriate speed.," This means that the forward shock does not move outwards as fast as it would in the planar case, and the reverse shock is formed to decelerate material behind the forward shock to the appropriate speed."
 When the rarefaction reaches r=0 it is rellected. and enhanced., When the rarefaction reaches $r=0$ it is reflected and enhanced.
 This rellected rarefaction” can be seen clearly at |—3 in figure 2.., This “reflected rarefaction” can be seen clearly at $t=3$ in figure \ref{early_times}.
 This rarefaction will eventually catch up with the reverse shock/blastwave system (see figure 4. and 6.13)., This rarefaction will eventually catch up with the reverse shock/blastwave system (see figure \ref{second_hydro} and \ref{hydro_results}) ).
 When the rarefaction catehes up with the reverse shock. the ram-pressure of the material entering this shock is drastically reduced. because it. has been rarefied: and decelerated.," When the rarefaction catches up with the reverse shock, the ram-pressure of the material entering this shock is drastically reduced, because it has been rarefied and decelerated."
: Hen ‘cit can no longer support the thermal pressure between he forward and reverse shocks., Hence it can no longer support the thermal pressure between the forward and reverse shocks.
 Asa result. the material between these two shocks expands.," As a result, the material between these two shocks expands."
 Since the rame-pressure of he material entering the forward shock has not changed (assuming constant external density). this necessitates the reverse shock slowing down with respect to the rest-frame of the initial blast.," Since the ram-pressure of the material entering the forward shock has not changed (assuming constant external density), this necessitates the reverse shock slowing down with respect to the rest-frame of the initial blast."
 Indeed. it will actually begin propagating towards the origin.," Indeed, it will actually begin propagating towards the origin."
 Lhe speed at which it does this depends on the initial value of jj. since thiJa determines the strength of the initial (and so the rellectec rarefaction.," The speed at which it does this depends on the initial value of $\eta$, since this determines the strength of the initial (and so the reflected) rarefaction."
 For example. if 1 is very small. then the fore due to the pressure eradient. will produce a relatively small increase in velocity of the material in the initial sphere.," For example, if $\eta$ is very small, then the force due to the pressure gradient will produce a relatively small increase in velocity of the material in the initial sphere."
 llence the rarefaction will be weak., Hence the rarefaction will be weak.
 LE on the other hand. g ds large then the force due to the pressure egracicnt will accelerate the blast material to high velocities very quickly. producing a very strong rarefaction.," If, on the other hand, $\eta$ is large then the force due to the pressure gradient will accelerate the blast material to high velocities very quickly, producing a very strong rarefaction."
 For the conditions in (24)refinitial it becomes sulliciently strong to cause ejected material to How back towards the origin also., For the conditions in \\ref{initial} it becomes sufficiently strong to cause ejected material to flow back towards the origin also.
 When the reverse shock reaches r=0 dt rebounds and. as it propagates outwards again. it weakens.," When the reverse shock reaches $r=0$ it rebounds and, as it propagates outwards again, it weakens."
 Once this shock is sulliciently weak to be ignored. we have reached the self-similar stage of evolution.," Once this shock is sufficiently weak to be ignored, we have reached the self-similar stage of evolution."
 Prior to this point the finite radius of the initial blast plays a part. and hence there is à significant length-scale in the svstem.," Prior to this point the finite radius of the initial blast plays a part, and hence there is a significant length-scale in the system."
 Lf the blast was initiallv of zero radius then the whole process described above would happen infinitely quickly (or. equivalently. would not happen at all).," If the blast was initially of zero radius then the whole process described above would happen infinitely quickly (or, equivalently, would not happen at all)."
 We can relate the above “hydrodynamical” picture with the one used. by. for example. Rees Alésszarros (1992).. as follows.," We can relate the above “hydrodynamical” picture with the one used by, for example, Rees Mésszárros \shortcite{reesmeszaros92}, as follows."
 The coasting radius. 2. is reached when al material has been accelerated. down the pressure gradien of the ingoing rarefaction.," The coasting radius, $R_c$, is reached when all material has been accelerated down the pressure gradient of the ingoing rarefaction."
" “This. of course. never occurs. bu one can celine Z2, as being the radius when “most” of the material has been accelerated."," This, of course, never occurs, but one can define $R_c$ as being the radius when “most” of the material has been accelerated."
 The deceleration radius. Ay. is then the radius a which the reflected. rarefaction catches up with the reverse shock.," The deceleration radius, $R_d$, is then the radius at which the reflected rarefaction catches up with the reverse shock."
 This is when the material between the forward. anc reverse shock expands back towards the origin. necessarily decelerating significantly as it does so.," This is when the material between the forward and reverse shock expands back towards the origin, necessarily decelerating significantly as it does so."
 We discuss the results of the simulations in two sections., We discuss the results of the simulations in two sections.
 The first deals with the detailed byelrodynamic evolution of the blastwave., The first deals with the detailed hydrodynamic evolution of the blastwave.
 The second. concerns the observed. spectra. and light-curves., The second concerns the observed spectra and light-curves.
 Lere we show the hvdrodynamie aspect of the results of our simulations., Here we show the hydrodynamic aspect of the results of our simulations.
 Figure 3. shows the distribution of proper density. velocity and. pressure alter 1107 seconds.," Figure \ref{first_hydro} shows the distribution of proper density, velocity and pressure after $1\times10^5$ seconds."
 We can see the two rarefactions mentioned in (25)rethydro 5c. , We can see the two rarefactions mentioned in \\ref{hydro_disc}. .
heheadofthereflected rarefactiontiesaltlhelocat," The head of the reflected rarefaction lies at the location of the peak velocity, with its tail at $r=0$ ."
ionofth« light-seconds., The original rarefaction lies between the peak of velocity and the rise in the density and pressure plots at $\sim 1\times10^5$ light-seconds.
 The forward shock can be identified as the right-most rise in pressure and density. while the reverse shock is just to the left of this.," The forward shock can be identified as the right-most rise in pressure and density, while the reverse shock is just to the left of this."
" Figure 4. shows the same plots as figure 3..but for a time of 7«10"" seconds."," Figure \ref{second_hydro} shows the same plots as figure \ref{first_hydro}, ,but for a time of $7 \times 10^6$ seconds."
 Llere wecan see the reverse shock, Here wecan see the reverse shock
aand vvalues of the NIZS were adopted to enable the estimation of the ionic abundances of the NI region.,and values of the NES were adopted to enable the estimation of the ionic abundances of the NF region.
 From the results of the slit αν physical parameters (‘Table 8)). one can notice the very low regional variation of theii].," From the results of the slit G physical parameters (Table \ref{results}) ), one can notice the very low regional variation of the."
. On the other hand. the spatial variation of the is significant.," On the other hand, the spatial variation of the is significant."
 These results should be compared with those coming from the same region of the spectroscopic maps., These results should be compared with those coming from the same region of the spectroscopic maps.
 The quantities shown with brackets inTables. are the corresponding mean values from the spectroscopic map for the region where the slit €: was placed., The quantities shown with brackets inTable \ref{results} are the corresponding mean values from the spectroscopic map for the region where the slit G was placed.
 As we were not able to calculate a map. the results of this. parameter refer only to the slit €. These results (those obtained directly from the slit and those obtained [rom the maps) are in agreement and. with the exception of the estimate of the NER. region (discrepancy of ~2 ) all of them show cliscrepancy of ~ 10% or less.," As we were not able to calculate a map, the results of this parameter refer only to the slit G. These results (those obtained directly from the slit and those obtained from the maps) are in agreement and, with the exception of the estimate of the NIR region (discrepancy of $\sim$ $\%$ ), all of them show discrepancy of $\sim$ $\%$ or less."
 In particular. the spatial variation encountered in the analysis of the slit €i. can be clearly visualized. in the map (Figure. 7)).," In particular, the spatial variation encountered in the analysis of the slit G, can be clearly visualized in the map (Figure \ref{temden}) )."
 Phe absence of variation ofni]. from region to region. as shown by the slit G results. can also be visualized on the results obtained [rom the map.," The absence of variation of, from region to region, as shown by the slit G results, can also be visualized on the results obtained from the map."
 Note that the histogram of this map is much more concentrated around the mean value than the histogram., Note that the histogram of this map is much more concentrated around the mean value than the histogram.
 The 31 emission-line maps that were constructed using the spectroscopic mapping technique are listed in Table 1.., The 31 emission-line maps that were constructed using the spectroscopic mapping technique are listed in Table \ref{mapintens}.
 The corresponding lluxes and intensities. of the entire nebula (NN). as well as the adopted: SNR cut-olf values (see Section 3.1) are also given in this table.," The corresponding fluxes and intensities, of the entire nebula (WN), as well as the adopted SNR cut-off values (see Section 3.1) are also given in this table."
 The emission-line map of Ilo was already. shown in Figure 3.., The emission-line map of $\alpha$ was already shown in Figure \ref{hacontour}.
 Other maps namely: Lhe. O iu] 5007AL. Na] 65844 and S u] 6731 are shown here. in Figure 5..," Other maps –namely: $\beta$, [O ] 5007, [N ] 6584 and [S ] 6731 – are shown here, in Figure \ref{linemaps}."
 After creating the emission-line maps. we caleulated the c(11:7) map using the package. Ho.," After creating the emission-line maps, we calculated the $\beta$ ) map using the package. $\alpha$,"
 H7 and H9 maps (weighted by their fluxes) and the Cardellietal.(1950) extinction curve were all considered in deriving the 1) map.," $\gamma$ and $\delta$ maps (weighted by their fluxes) and the \citet{b3}
 extinction curve were all considered in deriving the $\beta$ ) map."
 Phe variation of 1) across the nebula can be seen in ligure 6.., The variation of $\beta$ ) across the nebula can be seen in Figure \ref{cbeta}.
 The spectroscopic map clearly shows that c(L:7) is not constant throughout NGC 40. and the corresponding histogram shows its dispersion.," The spectroscopic map clearly shows that $\beta$ ) is not constant throughout NGC 40, and the corresponding histogram shows its dispersion."
 The mean value computed from this map. which includes only valid values (of the pixels that survived the noise-mask cleaning) is 0.42.," The mean value computed from this map, which includes only valid values (of the pixels that survived the noise-mask cleaning) is 0.42."
 The spatial variation of c(113). seen in Figure 6.. suggests that the amount of dust across the nebula is not constant and/or the dust grains have different characteristics from region to region (Spitzer1998:Monteiroetal.," The spatial variation of $\beta$ ), seen in Figure \ref{cbeta}, suggests that the amount of dust across the nebula is not constant and/or the dust grains have different characteristics from region to region \citep{spitzer,b14}."
2005).. Note that in studying a portion of the nebula Cleggetal.(1983). found c(11:7) 20.70., Note that in studying a portion of the nebula \citet{b4} found$\beta$ $=$ 0.70.
 In our map this region corresponds to an area where c(11.3) values are higher than average with minimum and maximum values of —0.22 anc 1.03. respectively whose median. 0.62. is in agreement with Clegeetal. (1983).," In our map this region corresponds to an area where $\beta$ ) values are higher than average –with minimum and maximum values of $\sim$ 0.22 and $\sim$ 1.03, respectively– whose median, 0.62, is in agreement with \citet{b4}. ."
. Pottaschctal.(2003). and. Alleretal. (1972)... using cata from various regions of the nebula. found 11550.005," \citet{b17} and \citet{b2}, , using data from various regions of the nebula, found $\beta$ $=$ 0.605"
eas fractions such that larger gas fraction progenitors result in remnants with larger ratios of stellar mass to dynamical mass.,gas fractions such that larger gas fraction progenitors result in remnants with larger ratios of stellar mass to dynamical mass.
 In the next experiment we let gas fraction vary as a [function of mass., In the next experiment we let gas fraction vary as a function of mass.
 We fix the gas mass of the largest progenitor (G3) such that the ratio of gas mass to stellar mass is 0.25., We fix the gas mass of the largest progenitor (G3) such that the ratio of gas mass to stellar mass is 0.25.
 Then we let the barvonic gas fraction. vary as à power law with the barvonic mass. MiΛιν (ἂν suggested in 2)).," Then we let the baryonic gas fraction vary as a power law with the baryonic mass, $M_{\rm
 gas}/M_{\rm baryons}\propto M_{\rm baryons}^{-\gamma}$ (as suggested in \citet{Dekel06}) )."
 We use values of > equal to 0. 0.5. and. 1.0.," We use values of $\gamma$ equal to 0, 0.5, and 1.0."
 In Figure 2(b) we show the scaling relations of the remnants produced by this series of progenitors., In Figure \ref{fig:toyGasPower} we show the scaling relations of the remnants produced by this series of progenitors.
 Each line of remnants is fixed to the largest mass remnant. but the slope of the size-mass and. EJ relations clearly depends on the value chosen for 5.," Each line of remnants is fixed to the largest mass remnant, but the slope of the size-mass and FJ relations clearly depends on the value chosen for $\gamma$."
 Non-zero values of + allow for significant rotations in all of the plotted projections of the FP., Non-zero values of $\gamma$ allow for significant rotations in all of the plotted projections of the FP.
 Phe rotation in the size-mass relation is the direction of rotation required if one is to create ellipticals from mergers of disks that follow the observed relations., The rotation in the size-mass relation is the direction of rotation required if one is to create ellipticals from mergers of disks that follow the observed relations.
 Additionally. the fundamental plane relation rotates away from the virial relation in the same direction as the observed. tilt.," Additionally, the fundamental plane relation rotates away from the virial relation in the same direction as the observed tilt."
 For reference. the slope of the observed. tilt is shown with a dashed. line.," For reference, the slope of the observed tilt is shown with a dashed line."
 The tilt. required. is slightly. overshot by. the ~=| case. suggesting that a slightly shallower power law slope would reproduce the observed tilt.," The tilt required is slightly overshot by the $\gamma=1$ case, suggesting that a slightly shallower power law slope would reproduce the observed tilt."
 This result is compatible with the gas fraction power of 0.7 suggested. by 7.., This result is compatible with the gas fraction power of 0.7 suggested by \citet{Dekel06}.
 Phus within our model a gas fraction gradient is capable of creating a tilt in the fundamental plane., Thus within our model a gas fraction gradient is capable of creating a tilt in the fundamental plane.
 Our model relies on the virial relation to. caleulate sizes and velocity. dispersion., Our model relies on the virial relation to calculate sizes and velocity dispersion.
 However. in our model the central dark matter [fraction is caleulated assuming that no dissipation occurs within the dark matter halo. and this aleets our caleulation of o.," However, in our model the central dark matter fraction is calculated assuming that no dissipation occurs within the dark matter halo, and this affects our calculation of $\sigma$."
 The break from virial scaling results [rom this changing central dark matter fraction. with more σας rich progenitors producing a Larger dillerence between the dissipational barvons and. dissipationless clark matter resulting in a lower central dark matter fraction.," The break from virial scaling results from this changing central dark matter fraction, with more gas rich progenitors producing a larger difference between the dissipational baryons and dissipationless dark matter resulting in a lower central dark matter fraction."
 For large values o£ 5 some curvature is also introduced into the scaling relations., For large values of $\gamma$ some curvature is also introduced into the scaling relations.
 Since both the disk and elliptical scaling relations are approximately power laws. this puts a constraint on the strength of the gas fraction. variation allowed by the model if we want to reproduce the observed scaling relations.," Since both the disk and elliptical scaling relations are approximately power laws, this puts a constraint on the strength of the gas fraction variation allowed by the model if we want to reproduce the observed scaling relations."
 Hlowever. the expected. value of 5.=0.7 only produces a mocdest amount of curvature.," However, the expected value of $\gamma=0.7$ only produces a modest amount of curvature."
 The merger model contains several parameters with uncertain values because of the uncertainty in the feedback oescription. used. by the merger. simulations., The merger model contains several parameters with uncertain values because of the uncertainty in the feedback prescription used by the merger simulations.
 Because of his uncertainty. the values of the model parameters might require adjustment.," Because of this uncertainty, the values of the model parameters might require adjustment."
 In order to understand the ellect of these »uwameters we vary them svstematically ancl examine the results of these variations on the remnant scaling relations., In order to understand the effect of these parameters we vary them systematically and examine the results of these variations on the remnant scaling relations.
 We begin by varving the star formation cllicicney xwameter. ej1:4.," We begin by varying the star formation efficiency parameter, $e_{\rm
 1:1}$."
 Phe calibrated value of this parameter (from he simulations) is 0.55. but for the experiments below we use values of 0.1. 0.5. ancl 1.0.," The calibrated value of this parameter (from the simulations) is 0.55, but for the experiments below we use values of 0.1, 0.5, and 1.0."
 First. we assume a constant eas-to-stellar-mass ratio of 0.5 across the idealized. galaxy series.," First, we assume a constant gas-to-stellar-mass ratio of 0.5 across the idealized galaxy series."
 Increasing ο will increase the number of stars that form: however. it has little effect on the remnant scaling relations (Figure 3(a))).," Increasing $e_{\rm
 1:1}$ will increase the number of stars that form; however, it has little effect on the remnant scaling relations (Figure \ref{fig:cnewConst}) )."
" Specifically, none of the relations experience significant rotation as a result of the adjustment."," Specifically, none of the relations experience significant rotation as a result of the adjustment."
 For all relations an increase in ey.) simply results in a slight shift toward higher stellar mass., For all relations an increase in $e_{\rm 1:1}$ simply results in a slight shift toward higher stellar mass.
 lor the second. experiment with ep... we introduce a mass-dependent gas fraction according to the power law relation used above. using the expected value of Ξ0.7.," For the second experiment with $e_{\rm 1:1}$, we introduce a mass-dependent gas fraction according to the power law relation used above, using the expected value of $\gamma=0.7$."
 For this series. adjusting ον produces rotations of the scaling relations.," For this series, adjusting $e_{\rm 1:1}$ produces rotations of the scaling relations."
 Specilicallv. changing ey. has a greater elfect on the mergers with a larger gas fraction. resulting in rotations in the size-mass and FJ relations and a slight tilting in the FP (Figure 3(b))).," Specifically, changing $e_{\rm 1:1}$ has a greater effect on the mergers with a larger gas fraction, resulting in rotations in the size-mass and FJ relations and a slight tilting in the FP (Figure \ref{fig:cnewPower}) )."
 Another parameter for which feedback. could: produce some uncertainty is Ch. which sets the importance of the radiative energy term.," Another parameter for which feedback could produce some uncertainty is $C_{\rm rad}$, which sets the importance of the radiative energy term."
 Since the C4 parameter is decoupled from the equation that determines the number of new stars. acjusting Ομ results in no dillerence in final mass.," Since the $C_{\rm rad}$ parameter is decoupled from the equation that determines the number of new stars, adjusting $C_{\rm rad}$ results in no difference in final mass."
 However. an increase of the parameter results in a significant reduction of size and increase in velocity dispersion for the remnants.," However, an increase of the parameter results in a significant reduction of size and increase in velocity dispersion for the remnants."
 The same constant gas fraction ancl mass-cepencdent gas fraction merger series used for the star formation parameter series are plotted in Figures 4(a) απ 4(b).. respectively. with Cy... taking values of 1.0 (black). 3.0 (red) ancl 5.0 (blue).," The same constant gas fraction and mass-dependent gas fraction merger series used for the star formation parameter series are plotted in Figures \ref{fig:cradConst} and \ref{fig:cradPower}, respectively, with $C_{\rm rad}$ taking values of 1.0 (black), 3.0 (red) and 5.0 (blue)."
 Thevalue of Ch. determined by fitting to the merger simulations was 2.75., Thevalue of $C_{\rm rad}$ determined by fitting to the merger simulations was 2.75.
 As with ey... rotation in the scaling relations is only seen for the series with a mass-dependent gas fraction.," As with $e_{\rm 1:1}$, rotation in the scaling relations is only seen for the series with a mass-dependent gas fraction."
" Llere. a significant rotation is created in the size-mass and FJ relations. but adjusting C5, never introduces a tilt in the FP."," Here, a significant rotation is created in the size-mass and FJ relations, but adjusting $C_{\rm rad}$ never introduces a tilt in the FP."
 This is because the mocel is built on the assumption of the virial theorem. and the only portion of the model that violates this assumption is the formula for calculating the change in central clark matter fraction. which is then used to adjustJ the velocity dispersion.," This is because the model is built on the assumption of the virial theorem, and the only portion of the model that violates this assumption is the formula for calculating the change in central dark matter fraction, which is then used to adjust the velocity dispersion."
1 ChangingBIS Cy. does not alfect this 1portion of the moclel., Changing $C_{\rm rad}$ does not affect this portion of the model.
 The Sloan Digital Sky Survey (SDSS) (2?) has provided exquisite statistics on galaxy scaling relations in the local universe., The Sloan Digital Sky Survey (SDSS) \citep{York00} has provided exquisite statistics on galaxy scaling relations in the local universe.
 ? show that for local galaxies the size clistribution [or cach type of galaxy at a given. stellar mass is. log-normal., \citet{Shen03} show that for local galaxies the size distribution for each type of galaxy at a given stellar mass is log-normal.
 Fhev provide fitting functions for the medians of the distributions for both earlv- and late-twpe galaxies., They provide fitting functions for the medians of the distributions for both early- and late-type galaxies.
" For Iate-type galaxies the median (£2) is described by where 5;= Ol. a=O14. 2=0.39. and M,=LOM AL."," For late-type galaxies the median ${\bar R}$ ) is described by where $\gamma=0.1$ , $\alpha=0.14$, $\beta=0.39$, and $M_0=3.98 \times
10^{10}\msun$ ."
 A comparison of this distribution to that of 7.. also from SDSS. demonstrates a discrepancy. despite the act that the samples contain significant overlap.," A comparison of this distribution to that of \citet{Barden05}, also from SDSS, demonstrates a discrepancy, despite the fact that the samples contain significant overlap."
 Specifically. a comparison of the stellar-niass size ridge lino in ? with the igure in Shen et al..," Specifically, a comparison of the stellar-mass size ridge line in \citet{Somerville08a} with the figure in Shen et al.,"
 correcting for the conversion between disk scale length and half light radius. shows that the Shen et al.," correcting for the conversion between disk scale length and half light radius, shows that the Shen et al."
 distribution is a factor of 1.5 smaller in radius or a given mass., distribution is a factor of $\sim 1.5$ smaller in radius for a given mass.
 ? find a similar ollset between their analysis of SDSS and the results of Shen et ab.," \citet{Dutton10} find a similar offset between their re-analysis of SDSS and the results of Shen et al.,"
 ancl argue hat this was primarilv due to their use of circular rather han elliptical apertures., and argue that this was primarily due to their use of circular rather than elliptical apertures.
 For this work. we scale the fitting unction of Shen et al.," For this work, we scale the fitting function of Shen et al."
 to match the normalization of? and ? , to match the normalization of\citet{Barden05} and \citet{Dutton10}. .
For earlv-tvpe galaxies the median radius is described, For early-type galaxies the median radius is described by
heliocentric distances. in view to indications given by the Pioncer-anomaly.,"heliocentric distances, in view to indications given by the Pioneer-anomaly."
" We started with a halo-densitv-profile poxxr’ where n is a real number. Substituting this expression into the spherical Poisson-equation leads to the following expression for the gravitational force connected with the DM-halo If this force is constant over heliocentric distances. n has to be chosen equal to 1 and the integration constant C,—0."," We started with a halo-density-profile $\rho_{DM}\propto r^n$ where $n$ is a real number, Substituting this expression into the spherical Poisson-equation leads to the following expression for the gravitational force connected with the DM-halo If this force is constant over heliocentric distances, $n$ has to be chosen equal to $-1$ and the integration constant $C_1=0$."
 This then leads to the followingdensitv-prolile where ry=1AU and po is the density at ry. that causes a constant additional acceleration towards the centre.," This then leads to the followingdensity-profile where $r_0=1~\mathrm{AU}$ and $\rho_0$ is the density at $r_0$, that causes a constant additional acceleration towards the centre."
 The question is how the halo-mass can be selected such that the orbits of the outer planets. like Uranus. persist?," The question is how the halo-mass can be selected such that the orbits of the outer planets, like Uranus, persist?"
" For that purpose ?.— used data from the ephemoeries of DIZ200 (?) that contain Uranus! ephemoeries down to an accuracy of LO""AU in radial distance.", For that purpose \citet{14} used data from the ephemeries of DE200 \citep{23} that contain Uranus' ephemeries down to an accuracy of $10^{-5}\mathrm{AU}$ in radial distance.
 Phe halo-mass enclosed within a given distance can be caleulated via With that the halo-niass is fixed by the value of po., The halo-mass enclosed within a given distance can be calculated via With that the halo-mass is fixed by the value of $\rho_0$.
 Calculating the deviation of the orbit. of Uranus from the pure Ixeplerian case for different po leads to the results shown in bie., Calculating the deviation of the orbit of Uranus from the pure Keplerian case for different $\rho_0$ leads to the results shown in Fig.
 1., 1.
" Lt is obvious that a racial distance deviation of the order of LO7AU is given for an enclosed halo-mass. within 50AU. «10""M. that corresponds to pj2244.10""M.pe"," It is obvious that a radial distance deviation of the order of $10^{-5}~\mathrm{AU}$ is given for an enclosed halo-mass, within $50~\mathrm{AU}$, $<10^{-6}~\mathrm{M_{\odot}}$ that corresponds to $\rho_0\approx 4.4\times10^{5}~\mathrm{M_{\odot}\,pc^{-3}}$."
 Such a halo-mass is in good agreement with the results from an investigation done by 77..," Such a halo-mass is in good agreement with the results from an investigation done by \citet{15,14}."
 Using this enclosed. mass delivers a racial acceleration-component of the order of 10.L7nsec=2 which is two orders of magnitude smaller than the measured anomalous Is a Dark-Matter halo with a densitv-prolile as given by cqn. (," Using this enclosed mass delivers a radial acceleration-component of the order of $10^{-12}~\mathrm{m\,sec^{-2}}$ which is two orders of magnitude smaller than the measured anomalous Is a Dark-Matter halo with a density-profile as given by eqn. ("
4) in good agreement with a general Navarro-Frenk-\White (NEW) profile (2?2?)??,"4) in good agreement with a general Navarro-Frenk-White (NFW) profile \citep{16,17,18}?"
 The profile is given where ες is the scale radius of the halo ancl povpie is a constant density.," The NFW-profile is given where $r_s$ is the scale radius of the halo and $\rho_{0,NFW}$ is a constant density."
 For a=51 and 3= this prolile reduces to a standard NEW-prolile dn the limit of small distances compared to the seale radius (r«s ry) this profile leads to the desired i-prolile., For $\alpha=\gamma=1$ and $\beta=3$ this profile reduces to a standard NFW-profile In the limit of small distances compared to the scale radius $r<<r_s$ ) this profile leads to the desired $\frac{1}{r}$ -profile.
" Compared {ο Pioneer-like distances (20TO AU) ry has to be choosen very large. e.g. for 50AU. r,z5000AU."," Compared to Pioneer-like distances $20-70~\mathrm{AU}$ ) $r_s$ has to be choosen very large, e.g. for $r=50~\mathrm{AU}$, $r_s > 5000~\mathrm{AU}$."
 With this the constant acceleration @=2x6Gr;povpyàLO12msec leads to ΗΝΕΠ<47M.pe5 Usingin] a correlation between realistic Halo-parameters (Darbringhausen et.," With this the constant acceleration $a=2\pi Gr_s\rho_{0,NFW}\approx 10^{-12}~\mathrm{m\,sec^{-2}}$ leads to $\rho_{0,NFW}<47~\mathrm{M_{\odot}\,pc^{-3}}$ Using a correlation between realistic Halo-parameters (Darbringhausen et."
 ab.," al.,"
 in prepration). a halo with a scale racdus ry5000AU would have po.vri<30M.pe 7.," in prepration), a halo with a scale radius $r_s>5000~\mathrm{AU}$ would have $\rho_{0,NFW}<30~\mathrm{M_{\odot}\,pc^{-3}}$ ."
 This value and the one stimated for a scale radius Larger than 5000AU are of the same order of magnitude and it seems that the used. density. profile. (4) is à realistic approximation., This value and the one stimated for a scale radius larger than $5000~\mathrm{AU}$ are of the same order of magnitude and it seems that the used density profile (4) is a realistic approximation.
 The istance from the centre where the Newtonian eravitional force due to the central mass (the Sun) equals the racial acceleration due to the halo with a densitv-profile according to (4) is called. the critical raciius., The distance from the centre where the Newtonian gravitional force due to the central mass (the Sun) equals the radial acceleration due to the halo with a density-profile according to (4) is called the critical radius.
" This. radius turns out to be of the order of roi,550000AU. much larger than distances of about TO AU. so the gravitational contribution of such à halo to the central gravity is negligible at such distances and would not lead. to large daviations from pure Ixeplerian motion."," This radius turns out to be of the order of $r_{crit}\approx50000~\mathrm{AU}$, much larger than distances of about $70~\mathrm{AU}$ , so the gravitational contribution of such a halo to the central gravity is negligible at such distances and would not lead to large daviations from pure Keplerian motion."
 Objects expected to move at. distances of the, Objects expected to move at distances of the
nu For the (10.10)|10 runs we have e.=36.5 and οςfeC0.0.41). and for the (10.3)|10 runs we have 217 land eyfeC0. 0.69).,"by For the (10,10)+10 runs we have $v_c = 36.5$ and $v_{\infty}/{v_c} \in [0,0.41)$, and for the (10,3)+10 runs we have $v_c = 21.7$ and $v_{\infty}/{v_c} \in [0,0.69)$ ."
" The upper limit for ry, is determined by what might be an ""interesting"" encounter. that is the relative velocity between the binary and the single is boostecl during the three-body interaction."," The upper limit for $r_p$ is determined by what might be an `interesting' encounter, that is the relative velocity between the binary and the single is boosted during the three-body interaction."
 Fhis requires a close triple approach and hardening of the binary: previous work suggests that the maximum interaction distance between the binary and the single is a few times the binary separation1974)., This requires a close triple approach and hardening of the binary; previous work suggests that the maximum interaction distance between the binary and the single is a few times the binary separation.
. Our limit of GO au. or Ga. safely covered the full range of potentially interesting periastra.," Our limit of 60 au, or $6a$, safely covered the full range of potentially interesting periastra."
 After an initial run of 2000. experiments. we determined that no interesting encounters were taking place bevond ry=30 au for the (10.3)|10 case.," After an initial run of 2000 experiments, we determined that no interesting encounters were taking place beyond $r_p =30$ au for the (10,3)+10 case."
" After this an additional 1500 experiments were performed. drawn from the same cquasi-randonm. sampling series but. carrving out only. those runs with r,30 au."," After this an additional 1500 experiments were performed, drawn from the same quasi-random sampling series but carrying out only those runs with $r_p \le 30$ au."
 The (10.10)|]10. case. had a. few interesting encounters at larger periastra. so for this set all 5000 experiments were performed over the full. range.," The (10,10)+10 case had a few interesting encounters at larger periastra, so for this set all 5000 experiments were performed over the full range."
 The limit on ey is set by velocity dispersion of the Orion Nebula Cluster. @ ~231955).," The limit on $v_{\infty}$ is set by velocity dispersion of the Orion Nebula Cluster, $\sigma \sim$ 2–3."
 If the velocity dispersion in the region is Maxwellian. the integrated probability of an encounter with ος15 Cds less than 1 per cent with a 1D velocity. dispersion of 3kms1.," If the velocity dispersion in the region is Maxwellian, the integrated probability of an encounter with $v_{\infty} > 15$ is less than 1 per cent with a 1D velocity dispersion of 3."
 As noted above. strictly speaking the initial conditions are not chosen according to equal probabilities.," As noted above, strictly speaking the initial conditions are not chosen according to equal probabilities."
 Such a sampling would be proportional to the area of the surface clement orthogonal to ὃς. and is achieved. by a uniform sampling of 6° where b is the impact parameter.," Such a sampling would be proportional to the area of the surface element orthogonal to $v_{\infty}$, and is achieved by a uniform sampling of $b^2$ where $b$ is the impact parameter."
 However. he incderlving physical motivation for this work is such hat the stellar masses. range of interesting periastra. ancl ikelv encounter velocities place us in a gravitationally ocused. encounter regime. where the paths of the stars ceviate substantially from rectilinear motion (see figure 2)).," However, the underlying physical motivation for this work is such that the stellar masses, range of interesting periastra, and likely encounter velocities place us in a gravitationally focused encounter regime, where the paths of the stars deviate substantially from rectilinear motion (see figure \ref{ICschematic}) )."
 Following the familiar derivation in(2008).. in the two-body approximation the periastron separation between the binary and the single is related to he masses. impact. parameter and velocity at infinity via The second term in brackets is associated with the eravitational focusing of the orbits.," Following the familiar derivation in, in the two-body approximation the periastron separation between the binary and the single is related to the masses, impact parameter and velocity at infinity via The second term in brackets is associated with the gravitational focusing of the orbits."
" When this term is dominant. the right hand side is approximately linear in r7. in which case 5xr, to a good approximation."," When this term is dominant, the right hand side is approximately linear in $r_p$, in which case $b^2 \propto r_p$ to a good approximation."
 The largest ry we use is 60 au. and the smallest value of the focusing term. occurs with ex=15 in the (10.3)|10 runs. where it takes a value of approximately 181 au.," The largest $r_p$ we use is 60 au, and the smallest value of the focusing term occurs with $v_{\infty} = 15$ in the (10,3)+10 runs, where it takes a value of approximately 181 au."
 Thus our entire parameter range is in a strongly focused. regime. ancl our uniform sampling of ry is very close to the equal-probability sampling. which is formally proportional to b=.," Thus our entire parameter range is in a strongly focused regime, and our uniform sampling of $r_p$ is very close to the equal-probability sampling, which is formally proportional to $b^2$."
 We can use our setup as a reasonable proxy for one specifically tailored to determining scattering outcome cross sections. and we do this in Appendix |. to verily that our results are in agreement with previous work.," We can use our setup as a reasonable proxy for one specifically tailored to determining scattering outcome cross sections, and we do this in Appendix \ref{scatteringappendix} to verify that our results are in agreement with previous work."
 The goal of these experiments is to determine if there are regions in parameter space that can lead to the retention of disc material in a binarv-single encounter that has a large inal relative velocity., The goal of these experiments is to determine if there are regions in parameter space that can lead to the retention of disc material in a binary-single encounter that has a large final relative velocity.
 In. general. an encounter between a xunarv and a single star can result in one of two outcomes: ionisation of the svstem into three single stars. or an end state consisting of a binary and a single.," In general, an encounter between a binary and a single star can result in one of two outcomes: ionisation of the system into three single stars, or an end state consisting of a binary and a single."
 The latter yossibility. can be further divided. into a I[lxby. in. which he initially single star remains single. or an exchange in which one of the original binary members is displaced. by he intruder.," The latter possibility can be further divided into a flyby, in which the initially single star remains single, or an exchange in which one of the original binary members is displaced by the intruder."
 For our choice of initial conditions ionisation is energetically forbidden. as the internal energy. of. the ‘nay is greater than the kinetic energy associated with he binarysingle orbit. Le. ex«6.," For our choice of initial conditions ionisation is energetically forbidden, as the internal energy of the binary is greater than the kinetic energy associated with the binary–single orbit, i.e. $v_{\infty} < v_c$."
 All of our experiments must terminate in a binary and a single., All of our experiments must terminate in a binary and a single.
 The interplay of three bodies in a scattering event can » quite complex ancl last for an unpredictable length of ime1993).. and some way to determine he end of a simulation is required beyond integrating for a ixed period.," The interplay of three bodies in a scattering event can be quite complex and last for an unpredictable length of time, and some way to determine the end of a simulation is required beyond integrating for a fixed period."
 During each experiment we track the size of the hree stars’ configuration. measured by their total moment of inertia in the center of momentum frame. We terminate the runs when two criteria are met.," During each experiment we track the size of the three stars' configuration, measured by their total moment of inertia in the center of momentum frame, We terminate the runs when two criteria are met."
 First. in the two body approximation (i.c. when the binary is treated as its center of mass) the binarysingle. orbit is hyperbolic.," First, in the two body approximation (i.e. when the binary is treated as its center of mass) the binary–single orbit is hyperbolic."
 Second. 500 vears have past since the Last minimum in Js. which we then define as the time of the scattering.," Second, 500 years have past since the last minimum in $I_3$, which we then define as the time of the scattering."
 At this point we have the three stars arranged as a binary and a single. each component surrounded: (or not) by a cloud. of cise particles.," At this point we have the three stars arranged as a binary and a single, each component surrounded (or not) by a cloud of disc particles."
 In. physical units. the integrations range from about 10 to 107 vears. roughly following a power law as /. between those limits.," In physical units, the integrations range from about $10^3$ to $10^4$ years, roughly following a power law as $t^{-3}$ between those limits."
 In order to determine final remnant dise membership. we rely on a circularisation scheme similar to one that has been used in previous work2006).," In order to determine final remnant disc membership, we rely on a circularisation scheme similar to one that has been used in previous work."
. At the end of the simulation. the binary is treated as à single body at its center of mass.," At the end of the simulation, the binary is treated as a single body at its center of mass."
 Disc particles that are energetically bound to this center of mass have passed the first cut., Disc particles that are energetically bound to this center of mass have passed the first cut.
 These then have their orbital angular momentunir calculated. and a Weplerian orbital. period determined.," These then have their orbital angular momentum calculated, and a Keplerian orbital period determined."
 In other applications. the dise particles may. be. place on circular orbits corresponding to their specific angular momentum. the argument being that viscous ellects. anc shocks between flows of material on crossing orbits wil damp any eecentricity.," In other applications, the disc particles may be placed on circular orbits corresponding to their specific angular momentum, the argument being that viscous effects and shocks between flows of material on crossing orbits will damp any eccentricity."
 In this way a circularised and settle disc can be reconstructed without simulating hvdrodynamic forces for long time periods., In this way a circularised and settled disc can be reconstructed without simulating hydrodynamic forces for long time periods.
 Because of the specific constraints of the presen problem. some care must be taken anc we do not directly reconstruct the dise profile in this way.," Because of the specific constraints of the present problem, some care must be taken and we do not directly reconstruct the disc profile in this way."
 Instead. we impose two additional cuts to determine the final cise membership.," Instead, we impose two additional cuts to determine the final disc membership."
 First. the orbital period of the disc particle about the binary must be less than 500 vears. the time between the scattering event and the present day.," First, the orbital period of the disc particle about the binary must be less than 500 years, the time between the scattering event and the present day."
 Second. the periastron of the particles orbit around. the binary center ofmass must. be less than 50 au. the observed size of the disc.," Second, the periastron of the particle's orbit around the binary center ofmass must be less than 50 au, the observed size of the disc."
 These dual constraints ensure that the dise. particle will have passed, These dual constraints ensure that the disc particle will have passed
"as absorbed or unabsorbed using Nj,=107 em7 as dividing value (44 unabsorbed AGN. 18 absorbed AGN).","as absorbed or unabsorbed using $N_H = 10^{22}$ $^{-2}$ as dividing value (44 unabsorbed AGN, 18 absorbed AGN)."
 In the same left panel of Figure 6 we have also reported the fraction of obscured AGN as recently computed by Akylasetal.(2006) using a sample of AGN selected in the hard keV band down to a flux limit of 6x107! (open squares). about a factor one hundred below our flux limit.," In the same left panel of Figure \ref{ratio} we have also reported the fraction of obscured AGN as recently computed by \cite{akylas2006} using a sample of AGN selected in the hard 2-8 keV band down to a flux limit of $6\times 10^{-16}$ (open squares), about a factor one hundred below our flux limit."
 The data points computed by Akylasetal.(2006) have been corrected for the different volumes sampled from absorbed and unabsorbed AGN (due to the absorption) in a similar way as done here., The data points computed by \cite{akylas2006} have been corrected for the different volumes sampled from absorbed and unabsorbed AGN (due to the absorption) in a similar way as done here.
" Although the HBSS sample and the Akylasetal.(2006) show a similar trend of decreasing F as a function of the intrinsic luminosity. the fractions computed at z=0 using the HBSS sample are systematically below (~ a factor 2 for L,>10% )) than those reported in etal. (2006)."," Although the HBSS sample and the \cite{akylas2006}
 show a similar trend of decreasing F as a function of the intrinsic luminosity, the fractions computed at z=0 using the HBSS sample are systematically below $\sim$ a factor 2 for $L_x > 10^{43}$ ) than those reported in \cite{akylas2006}."
. However the data points reported in Akylasetal.(2006) have been computed without taking into account possible differences in the cosmological evolution properties of the absorbed and unabsorbed AGN population., However the data points reported in \cite{akylas2006} have been computed without taking into account possible differences in the cosmological evolution properties of the absorbed and unabsorbed AGN population.
 This effect. that we have already shown as of the second order for the HBSS AGN sample. could be very important for the Akylasetal.(2006) sample since their objects are at a significantly higher z compared to the HBSS AGN sample.," This effect, that we have already shown as of the second order for the HBSS AGN sample, could be very important for the \cite{akylas2006} sample since their objects are at a significantly higher z compared to the HBSS AGN sample."
 To test this effect in Figure 6 (middle panel) the Akylasetal.(2006) points have been rescaled to z=0 using the mean redshift in each luminosity bins (T. Akylas. private communication) and a cosmological evolution of F according to the model proposed by Treister&Urry(2006) CFx(1+ 2)°.," To test this effect in Figure \ref{ratio} (middle panel) the \cite{akylas2006} points have been rescaled to z=0 using the mean redshift in each luminosity bins (T. Akylas, private communication) and a cosmological evolution of F according to the model proposed by \cite{treister2006} $F
\propto (1+z)^{0.4}$ )."
 A much better agreement with our results is clearly evident. suggesting a possible evolution of the fraction of absorbed AGN with the redshift.," A much better agreement with our results is clearly evident, suggesting a possible evolution of the fraction of absorbed AGN with the redshift."
 Finally in Figure 6 (right panel) we compare F with that required to produce the cosmic X-ray background according to the new synthesis model reported in Gillietal.(2007) (long dashed line: best fit: short dashed lines: one c error range: both computed and predicted F ratios refer only to absorbed AGN with Nj; below 107 em77): we discuss this comparison in section 8., Finally in Figure \ref{ratio} (right panel) we compare F with that required to produce the cosmic X-ray background according to the new synthesis model reported in \cite{gilli2007} (long dashed line: best fit; short dashed lines: one $\sigma$ error range; both computed and predicted F ratios refer only to absorbed AGN with $N_H$ below $10^{24}$ $^{-2}$ ); we discuss this comparison in section 8.
" Α second important and debated issue on the AGN astrophysics is related to their intrinsic Ny, distribution. Le. the Ny, distribution of the AGN family computed taking into account the selection effects related to the photoelectric absorption,"," A second important and debated issue on the AGN astrophysics is related to their intrinsic $N_H$ distribution, i.e. the $N_H$ distribution of the AGN family computed taking into account the selection effects related to the photoelectric absorption."
 To compute this distribution we have proceeded as follows., To compute this distribution we have proceeded as follows.
 We have first split the HBSS AGN sample in four bins of absorbing column densities up to Ny = 107 em? (Ny = 107—102: Lor!=1077: 107= 102: 107= em.," We have first split the HBSS AGN sample in four bins of absorbing column densities up to $N_H$ = $10^{24}$ $^{-2}$ $N_H$ = $10^{20} - 10^{21}$; $10^{21} - 10^{22}$; $10^{22} - 10^{23}$ ; $10^{23}
- 10^{24}$ $^{-2}$ )."
" Second. we have computed the integral luminosity function using the objects in each bin of Nj, and the 1/V, method as Ciscussed in Section 3.2."," Second, we have computed the integral luminosity function using the objects in each bin of $N_H$ and the $1/V_a$ method as discussed in Section 3.2."
" Third. using these XLFs we have Cuetermined the density of objects in each Nj, bin having a luminosity above ~3x107 (ie. around the luminosity of the faintest absorbed AGN in the HBSS sample)."," Third, using these XLFs we have determined the density of objects in each $N_H$ bin having a luminosity above $\sim 3\times 10^{42}$ (i.e. around the luminosity of the faintest absorbed AGN in the HBSS sample)."
 Finally o—n order to obtain the Nj; distribution (reported in Figure7 cpper panel. as solid line) the density in each Nj; bin has been ormalized to the total density of AGN with Nj; between 107? ," Finally in order to obtain the $N_H$ distribution (reported in Figure\ref{int_nh} upper panel, as solid line) the density in each $N_H$ bin has been normalized to the total density of AGN with $N_H$ between $10^{20}$ "
is the probability of creating a massive EC like 22119.,is the probability of creating a massive EC like 2419.
 Due to the limited field of view of tie Hubble Space Telescope. most extragalactic studies on GCs cover oilv (a part of) te optica| disk of the respective galaxies.," Due to the limited field of view of the Hubble Space Telescope, most extragalactic studies on GCs cover only (a part of) the optical disk of the respective galaxies."
 An ouer halo object like 22119 would be found ouly by €lance if it is projected onto the main body of a galaxy., An outer halo object like 2419 would be found only by chance if it is projected onto the main body of a galaxy.
 Another reason or incompleteuess is the cli[Iiculty of cistinguishiug ECs from backg‘ound galaxies., Another reason for incompleteness is the difficulty of distinguishing ECs from background galaxies.
 Therefore. a nuuber of surveys ayplied a size limit of about 10 pc to reduce the contaimdiuatioln oL background. galaxies.," Therefore, a number of surveys applied a size limit of about 10 pc to reduce the contamination of background galaxies."
 Thereby these strveys exclude all NCC22119-like EC's rol their GC catalogues., Thereby these surveys exclude all 2419-like ECs from their GC catalogues.
 As 1jasslve galaxy-galaxy interactions are expected to have beeu more iuimerous iu the past. a large number of 22119-like oljects probably await their detection in he outer halos oL various galaxien.," As massive galaxy-galaxy interactions are expected to have been more numerous in the past, a large number of 2419-like objects probably await their detection in the outer halos of various galaxies."
 We conclue that 22119 can be well explained by the merged cluster complex scenario., We conclude that 2419 can be well explained by the merged cluster complex scenario.
 Measurements of the proper motion of 22[19 are iudispensable to further study the proposed scenario aud to j»oteutially associate 22119 with one of the stellar streams iu the outer Galactic halo., Measurements of the proper motion of 2419 are indispensable to further study the proposed scenario and to potentially associate 2419 with one of the stellar streams in the outer Galactic halo.
 We thank Manuel Metz for providing bis ecode and lis for excellent support., We thank Manuel Metz for providing his code and his for excellent support.
 We thank tlie anouyinous referee for his helpful commeuts tliat helped us to improve the paper siguilicautly., We thank the anonymous referee for his helpful comments that helped us to improve the paper significantly.
 The work of this paper was supported by DEC Cirauts 11635/11-1 and 11635/29-1., The work of this paper was supported by DFG Grants 1635/14-1 and 1635/29-1.
enerey range.,energy range.
" Equation (12)) is approximately. expressed as (0/0I~1=Ta and 03/05~ul—p""+Tic τι) ∐≼↲≺∢≀↧↴∏⋟∖⊽≼↲⋟∖⊽∡∖↽∐≺∢∐↕⋅∪∏⋅∪∐≺∢∪∪∐∐≸↽↔↴≺⇂∪∐↓↕∐≀↧↴∩↲⋟∖⊽↕∐⊔↥↕⋟∖⊽≼↲∐≼↲↕⋅↖⊂↽↔↴⋡∖↽↕⋅≀↧↴∐≸≟≼↲⊤⋯⊓↥↴∿↴⊤⋝∖∙∖↓↓⊤↕⇂⋅∖↓↓∙ ≼↲≺⇂∏≀↧↴∐∪∐⊔⊥⇄⋝⇄⋟∣↽≻≼↲≺⊲∪∐∐↲⊳∖⊽↼∖⊽∾⊤⋝∖∙∖↓↓≬⊋↥↓↓∙∣⋅⊡≻↕⋅∣↙∖∕∖⋊⊤∣∣⋅⊔∐↲↕∐∙↿≼↲≺∢∐∪∐↥≼↲↕⋅↕∐∣↽≻≼↲∐≀↧↴∖↽≼↲⊳∖⊽≀↧↪∖⇁≬⊋↥⊔∙⇪∖"," Equation \ref{eq12}) ) is approxmately expressed as $\partial / \partial t \sim t^{-1} = \tau^{-1}_{\rm dyn}$ and $\partial \dot{\gamma} / \partial \gamma \sim \tau^{-1}_{\rm cool} = (\tau^{-1}_{\rm syn} + \tau^{-1}_{\rm IC} + \tau^{-1}_{\rm ad})$ ) Because synchrotron cooling dominates in this energy range $\tau_{\rm cool} \sim \tau_{\rm syn} < \tau_{\rm dyn}$ , equation \ref{eq21}) ) becomes $N \sim \tau_{\rm syn} Q_{\rm{inj}}$."
↶⇩↴↙⋪⊒⋅ ⋟∖⊽∪⊔⋯↴∟∖∖↶↵↙⋪−↓∕−⋅⊟≻↕⋅∕∕∖∕∖⊤∣∣⋅⊔∐↲∐↥∙↿≼↲≺∢⊔∪∐∩↲↕⋅↕∐∣↽≻≼↲∐≀↧↴∖⇁≼↲⋟∖⊽≀↧↪∖⊽⇁⊳⋝9 ⋅⋅⋅ ο”.," For $t < \tau_0$, the injection term behaves as $Q_{\rm{inj}} \propto \gamma^{- p_2}$, so that $N \propto \gamma^{- p_2 - 1} t^2$ ."
"..↽⋡⋝∆−∶⋉≱⋡⊳ for n=⋅2.5. so that Αα02.127,"," For $t > \tau_0$ , the injection term behaves as $Q_{\rm{inj}} \propto \gamma^{- p_2} t^{-7/3}$ for $n = 2.5$, so that $N \propto \gamma^{- p_2 - 1} t^{2/3}$."
" This is the reason why the particle number increases with time and the particle distribution is softer than the injection distribution for >10"".", This is the reason why the particle number increases with time and the particle distribution is softer than the injection distribution for $\gamma > 10^8$ .
 We- next examine. the steacinessn ofB the particlesn number forB 107L7<4<10? shown in. Figure5 3.., We next examine the steadiness of the particles number for $10^2 < \gamma < 10^5$ shown in Figure \ref{f3}.
" For /€Ty. because To,|©TadaclTagIv 1n equation (21)). we have NVx5$.Pt."," For $t < \tau_0$, because $\tau_{\rm cool} \sim \tau_{\rm ad} \sim \tau_{\rm dyn}$ in equation \ref{eq21}) ), we have $N \propto \gamma^{- p_1} t$."
 For Ty.because (he injection term more rapidly decreases wilh time (han the adiabatic cooling term. equation (12)) is approximated by When we asstune a form Vx5. 7/7. we obtain d=1—a.," For $t > \tau_0$, because the injection term more rapidly decreases with time than the adiabatic cooling term, equation \ref{eq12}) ) is approximated by When we assume a form $N \propto \gamma^{-\alpha} t^{\beta}$ , we obtain $\beta = 1 - \alpha$."
" For a=p,1.5. we have jH——(.5."," For $\alpha = p_1 = 1.5$, we have $\beta = - 0.5$."
 The particle number increases until /~75. and (hen it decreases slowly with lime as Vx/P? for 10?<4<107.," The particle number increases until $t \sim \tau_0$, and then it decreases slowly with time as $N \propto t^{-0.5}$ for $10^2 < \gamma < 10^5$."
" The feature of the particle distribution for 10""<><LO“ shown in Figure 3. is complex because the dominant cooling process changes with time as seen in Figure 4..", The feature of the particle distribution for $10^5 < \gamma < 10^8$ shown in Figure \ref{f3} is complex because the dominant cooling process changes with time as seen in Figure \ref{f4}.
 Until an age of a few thousand. vears. the feature is similar to that for 5>10 (equation (21)) with Teool© Ta). Le. the particle number increases with time and the particle distribution is softer than the injection distribution.," Until an age of a few thousand years, the feature is similar to that for $\gamma > 10^8$ (equation \ref{eq21}) ) with $\tau_{\rm cool} \sim \tau_{\rm syn}$ ), i.e., the particle number increases with time and the particle distribution is softer than the injection distribution."
 After that. the feature becomes similar to that[or 10?«410° for />7s (equation (22)))and the particle number decreases with time.," After that, the feature becomes similar to thatfor $10^2 < \gamma < 10^5$ for $t > \tau_0$ (equation \ref{eq22})))and the particle number decreases with time."
 Because the time when Taq7744is different for dillerent energy. the particle distribution becomes harder thano5.72.| at an age of LOkvr.," Because the time when $\tau_{\rm ad} \sim \tau_{\rm syn}$is different for different energy, the particle distribution becomes harder than$\propto \gamma^{-p_2 - 1}$ at an age of 10kyr."
skewed. the quariles provide a better indication of the spread iu the disribution than the saudard deviation.,"skewed, the quartiles provide a better indication of the spread in the distribution than the standard deviation."
" The nonualization wih the ""total scatter allows us Oo conrpare the 1uporance of parameters between he lice mcelinations.", The normalization with the “total” scatter allows us to compare the importance of parameters between the three inclinations.
 Tt should be noted hat the non-linear character of the moclel. and the opposiιο effects of certam xurinueters can male t10 ratio of the normalized quarile ranges larecr than unity.," It should be noted that the non-linear character of the model, and the opposing effects of certain parameters can make the ratio of the normalized quartile ranges larger than unity."
 Table 1 shows for three values of he inclination the result of 10000 realizatious of cach paralncter. draw Youn a uniform cistribition.," Table \ref{model_var-tab} shows for three values of the inclination the result of 10000 realizations of each parameter, drawn from a uniform distribution."
 The magnetic field streneth. electron: density. fliug factor. turinlent leneth scale. aud the vertical thickness of the disk were varied hy an order of magnitudo. as dudicated in the footnote o Table L.," The magnetic field strength, electron density, filling factor, turbulent length scale, and the vertical thickness of the disk were varied by an order of magnitude, as indicated in the footnote to Table \ref{model_var-tab}."
 The ratio of raudoni to regular magnetic Ποια streugth (fp) was varied over a smaller range (0.7 o LO), The ratio of random to regular magnetic field strength $f_{\rm B}$ ) was varied over a smaller range (0.7 to 4.0).
 At low inchations. the normalized quartile range for variation of fp is 1.01. while the normalized quartile ranges of all other paraueters are less than Wl.," At low inclinations, the normalized quartile range for variation of $f_{\rm B}$ is 1.01, while the normalized quartile ranges of all other parameters are less than 0.1."
 Clearly. the ratio of raudom to regular magnetic ficld dominates the fractional polarization of the model or small iuclinations.," Clearly, the ratio of random to regular magnetic field dominates the fractional polarization of the model for small inclinations."
 At 7=607. fj is still the most iuportant parameter. but other parameters such as the regular magnetic field strereth and the clectrou density )oconie nore important.," At $i=60\degr$, $f_{\rm B}$ is still the most important parameter, but other parameters such as the regular magnetic field strength and the electron density become more important."
" A (=75"". fp ixstill uuportant. mt the parameters that define Ro=of;By2h/cosi are almost equally important."," At $i=75\degr$, $f_{\rm B}$ is still important, but the parameters that define $\mathcal{R} = n_e f_i B_\| 2h/\cos i$ are almost equally important."
" The relative 1uportance of Hel f. I. and 27 is simuar oat;—τοῦ, because they contribute equally to R. although subtle differences occur because of the dependence ou omg."," The relative importance of $n_e$, $f_i$, $B$, and $2h$ is similar at $i=75\degr$, because they contribute equally to $\mathcal R$ , although subtle differences occur because of the dependence on $\sigma_{\rm RM}$."
 The turbulent scale leneth Jiu. is the parameer in our mode that is least constraime by observations., The turbulent scale length $l_{turb}$ is the parameter in our model that is least constrained by observations.
 Table 1 shows that its effect Ol onr restIts is insubstaulal., Table \ref{model_var-tab} shows that its effect on our results is insubstantial.
 The simplest model is a disk with uniforli piarineters throughout that can be represeuted by a set of concentric annuli. al with the same integrated polarization properties.," The simplest model is a disk with uniform parameters throughout that can be represented by a set of concentric annuli, all with the same integrated polarization properties."
 The model makes no assuniptious about the magneic field structure in the center of the disk., The model makes no assumptions about the magnetic field structure in the center of the disk.
 This is no a significant simplification for most spiral ealaxies. wwiore nost of the polarized euissiou originates in the disk.," This is not a significant simplification for most spiral galaxies, where most of the polarized emission originates in the disk."
 Fiewre 1. shows a graphic represcutation of polarized intensity at a represcutative subset of locations (a ring) i he disk for model Lin Table 5 at melinatious A=10 ands=60°., Figure \ref{spiral_proj-fig} shows a graphic representation of polarized intensity at a representative subset of locations (a ring) in the disk for model 1 in Table \ref{model_par-tab} at inclinations $i=40\degr$ and $i=60\degr$.
 Thin lines iudicate the magnitude and direction of the maguetic field component in the plane of the sky. By.," Thin lines indicate the magnitude and direction of the magnetic field component in the plane of the sky, $B_\bot$ ."
 Thick lines represeut polarization vectors., Thick lines represent polarization vectors.
 Open aud filled circles represcut the conronent of the regular iuagnuetic field aloug the line of sight. By.," Open and filled circles represent the component of the regular magnetic field along the line of sight, $B_\|$."
 At low inclination (Figure laa). the path leneth through the disk is reatively small aud the iunc-of-sieht component of the regiar Ποια is also small.," At low inclination (Figure \ref{spiral_proj-fig}a a), the path length through the disk is relatively small and the line-of-sight component of the regular field is also small."
 The polarized intensity iu Figure laa ds fairly uniformi across the disk aud relatively high., The polarized intensity in Figure \ref{spiral_proj-fig}a a is fairly uniform across the disk and relatively high.
" At higher inclination. the pah leneth through the disk iucreasecs. aud he liuc-of-sigh component of the reeular maeuetic fik lnhcreases, iu articular near the major axis."," At higher inclination, the path length through the disk increases, and the line-of-sight component of the regular magnetic field increases, in particular near the major axis."
 The polarized iucusity is snaller evervwhere iu the disk. but most strongVv near the major axis.," The polarized intensity is smaller everywhere in the disk, but most strongly near the major axis."
" Here. the lue-ofsight compoient of the azimuthal regular field dis Luweest. so Faraday rotation ls strongest and the conugxneut D, (Equation 1)) is SETles."," Here, the line-of-sight component of the azimuthal regular field is largest, so Faraday rotation is strongest and the component $B_\bot$ (Equation \ref{P0-eq}) ) is smallest."
 Faraday depolarization is therefore strougest rear the major axis. aud the intrinsic polarization of the Cluission is snaller than el«where in the disk.," Faraday depolarization is therefore strongest near the major axis, and the intrinsic polarization of the emission is smaller than elsewhere in the disk."
 Faraday rotation of the plane of pola‘ization is also stronger near je Major axis in Figure L., Faraday rotation of the plane of polarization is also stronger near the major axis in Figure \ref{spiral_proj-fig}.
 The model Stokes (Q aud C incusities. calculated * solvius Equation 2. for every line of sight through jo disk. are iuteerated over the disk to predict he volarized iuteusitv of an uuresolve spiral galaxy.," The model Stokes $Q$ and $U$ intensities, calculated by solving Equation \ref{P-eq} for every line of sight through the disk, are integrated over the disk to predict the polarized intensity of an unresolved spiral galaxy."
 The integration over the disk recuces to a one-dimensional Munerical integration over azimuthal anele for the svuuuetre models under οςumsideration., The integration over the disk reduces to a one-dimensional numerical integration over azimuthal angle for the symmetric models under consideration.
 The model iu Figure laa has integrated fractiona polarization Ty=7.9 while the model in Figure [bb has integrated fractional polarization Wy17.054.," The model in Figure \ref{spiral_proj-fig}a a has integrated fractional polarization $\Pi_0 = 7.9\%$ , while the model in Figure \ref{spiral_proj-fig}b b has integrated fractional polarization $\Pi_0 = 17.0\%$."
 Despite the strouger depolarization auvwhere iu the disk at inclination / GU. the polarizalou is stronger at 7=607 than at 7=Lo because of the sinaller degree of svuuuetrv of the polarized eiissionu.," Despite the stronger depolarization anywhere in the disk at inclination $i =
60\degr$ , the polarization is stronger at $i =
60\degr$ than at $i = 40\degr$, because of the smaller degree of symmetry of the polarized emission."
 The model predictious for Ty aud 0j are incependeut of the spiral pitch anele of t1e magnetic field., The model predictions for $\Pi_0$ and $\thetaB$ are independent of the spiral pitch angle of the magnetic field.
 For a disk with coustant thickness and uniforii properties. the path leugth through t1e disk depends ouly on inclination. aud the polarized intensity depeids only on the angle oft1C reeular component of the nuwnetie field with the line of seht.," For a disk with constant thickness and uniform properties, the path length through the disk depends only on inclination, and the polarized intensity depends only on the angle of the regular component of the magnetic field with the line of sight."
The effect of apitch arele of the magnetic field. is to change the azimuthal augle in the disk where the line of sight makes a certain auge with the regular magnetic,"The effect of apitch angle of the magnetic field, is to change the azimuthal angle in the disk where the line of sight makes a certain angle with the regular magnetic"
recomputed in a single-configuration approximation. the differences with Drake are reduced to and. ASL also does somewhat better (3%)).,"recomputed in a single-configuration approximation, the differences with Drake are reduced to and AS1 also does somewhat better )."
 The latter result suggests that perhaps lakine into account core relaxation effects does not necessarily lead (0 improved radiative data., The latter result suggests that perhaps taking into account core relaxation effects does not necessarily lead to improved radiative data.
 This hypothesis is confirmed by a comparison of available lifetime measurements in 1e- and Li-like ions with ASI and AS? (see Table 6))., This hypothesis is confirmed by a comparison of available lifetime measurements in He- and Li-like ions with AS1 and AS2 (see Table \ref{lifet}) ).
 The computed lifetimes for these »=2 levels are sensitive to the wavefuntions because most of them involve optically forbidden decay lhannels., The computed lifetimes for these $n=2$ levels are sensitive to the wavefuntions because most of them involve optically forbidden decay channels.
 Although the agreement of both ASI and AS? with experiment is within approximately1054... it is not clear which is the most accurate.," Although the agreement of both AS1 and AS2 with experiment is within approximately, it is not clear which is the most accurate."
 As a conclusion. we are only confident that the accuracy of the HERI -A- values is at around the level.," As a conclusion, we are only confident that the accuracy of the HFR1 $A$ -values is at around the level."
 This suggested level of accuracy is further supported by a comparison of the IFRI elvalues ereater than LO! £1 in Ar ions with those computed by in (he IIER2 and MCDET approximations., This suggested level of accuracy is further supported by a comparison of the HFR1$A$ -values greater than $10^{13}$ $^{-1}$ in Ar ions with those computed by \citet{bie00} in the HFR2 and MCDF1 approximations.
 In spite of their fine tuning of the transition malrix elements with (he experimental energy levels in WFR. (he general agreement is well within except for the lew problematic transitions listed in Table 7..," In spite of their fine tuning of the transition matrix elements with the experimental energy levels in HFR2, the general agreement is well within except for the few problematic transitions listed in Table \ref{aval}."
 It max be seen that for Gransitions in species wilh N=5 and N=7. ΗΕ and ΠΗΓΗΣ are in reasonable agreement in contrast to MCDFI.," It may be seen that for transitions in species with $N=5$ and $N=7$, HFR1 and HFR2 are in reasonable agreement in contrast to MCDF1."
 For Vo=6. the scatter is large which is surely due tostrong acinixture of the upper IK-vacancy levels produced by (he spin-orbit interaction.," For $N=6$, the scatter is large which is surely due tostrong admixture of the upper K-vacancy levels produced by the spin-orbit interaction."
 Ad-values ealeulated by Chen&Crasemann(1988) for B-like Ar using the MCDE method agree within with HERI although on average they are 1056 smaller., $A$ -values calculated by \citet{che88} for B-like Ar using the MCDF method agree within with HFR1 although on average they are $\sim$ smaller.
 However. we find that those computed for C-like Ar bv Chenetal. (1997).. as shown in Fie. 9..," However, we find that those computed for C-like Ar by \citet{che97}, , as shown in Fig. \ref{chen-A},"
 are higher., are higher.
 We also include in this plot the MCDET --values by Biémontοἱal.(2000) which are within of HERI if the problematic values of Table 7 ave excluded., We also include in this plot the MCDF1 $A$ -values by \citet{bie00} which are within of HFR1 if the problematic values of Table \ref{aval} are excluded.
 Moreover. there are several transitions by Chen et al.," Moreover, there are several transitions by Chen et al."
 that show differences larger than a factor of 2 with WFR which have not been taken into accountin (his comparison., that show differences larger than a factor of 2 with HFR1 which have not been taken into accountin this comparison.
 The comparison of the IIERI A-values with (hose caleulated by Faenovetal.(1994) using the method for ions with 12€Z16 and 4xN<9 shows a wide scatter: some Gransitions agree to better than while large discrepancies are found for others.," The comparison of the HFR1 $A$ -values with those calculated by \citet{fae94} using the method for ions with $12\leq
Z\leq 16$ and $4\leq N\leq 9$ shows a wide scatter: some transitions agree to better than while large discrepancies are found for others."
 Auger widths of K-vacancy levels are determined by including all the decay channels Cel. where C are all the η=2 valence configurations of the (NV— 1)-electron daughter ion and /« 4. D," Auger widths of K-vacancy levels are determined by including all the decay channels $C\epsilon l$, where $C$ are all the $n=2$ valence configurations of the $(N-1)$ -electron daughter ion and $l\leq 4$ ."
iémontetal.(2000) have computed with and theMCDF code Auger widths for IX-vacaney states in Ar ions with 3<N<9 (data sets referred to as IIER2 and," \citet{bie00} have computed with and theMCDF code Auger widths for K-vacancy states in Ar ions with $3\leq
N\leq 9$ (data sets referred to as HFR2 and"
of NLACIHIOs which would. produce the same optical depth.,of MACHOs which would produce the same optical depth.
 Basically. this reduction can be understood. because most microlensing is due to lenses within about 20kpc of the Sun for either configuration.," Basically, this reduction can be understood because most microlensing is due to lenses within about $20 \kpc$ of the Sun for either configuration."
 Phe very thick disk has less mass bevond that distance than a halo., The very thick disk has less mass beyond that distance than a halo.
 In acelition. we note that since the halo of the Galaxy extends far beyond the LAC. a standard halo distribution of NLACTIIOs must be abruptly: cut olf at SOkpe in order to avoid a much larger total mass in NLACTIIOs which would be even more dillieult to reconcile with a white cwarl scenario.," In addition, we note that since the halo of the Galaxy extends far beyond the LMC, a standard halo distribution of MACHOs must be abruptly cut off at $50 \kpc$ in order to avoid a much larger total mass in MACHOs which would be even more difficult to reconcile with a white dwarf scenario."
 Strong [lattening of the microlensing population also leaves its mark on the variation of optical depth as a function of direction. (Sackett.DP.&Could.A.1993:EriemanScoc-cimarro 1994).," Strong flattening of the microlensing population also leaves its mark on the variation of optical depth as a function of direction \cite{sackettgould,JoshRoman}."
". In Figure 4 we show à=rsc/TzLuc às A ""unction of ..", In Figure 4 we show $\alpha=\tau_{SMC}/\tau_{LMC}$ as a function of $h_z$ .
 For very Uat disks (.z Q.3kpc) a is the same for both models., For very flat disks $h_z \approx 0.3$ kpc) $\alpha$ is the same for both models.
 All the lensing is local. the global configuration of the NLACTIOs is irrelevant. and the limiting ormula for lensing through a thin disk can be applied.," All the lensing is local, the global configuration of the MACHOs is irrelevant, and the limiting formula for lensing through a thin disk can be applied."
 This xediets a value Tea/TL=80(θενο)sim(bue) 1.60.," This predicts a value $\tau_{\rm SMC}/\tau_{\rm LMC}=
{sin^2(b_{\rm LMC})}/{sin^2(b_{\rm SMC})} = 0.60$ ."
 As fr. increases however.the configuration becomes loss lat and lensing occurs further from the observer.," As $h_z$ increases however,the configuration becomes less flat and lensing occurs further from the observer."
 Since the ine of sight towards the SAIC probes closer to the galactic center. with increasing scale height the SMC clireetion passes hrough denser material than the LMC line of sight and so o increases to about. 1.0 by νι= 3.0kpe for the exponential disk model.," Since the line of sight towards the SMC probes closer to the galactic center, with increasing scale height the SMC direction passes through denser material than the LMC line of sight and so $\alpha$ increases to about $1.0$ by $h_z=3.0$ kpc for the exponential disk model."
 For the Alestel disk the density increases. loss stronely with decreasing radius and so this cllect is not as large. with à reaching only 0.75 for h.= 3.0kpc.," For the Mestel disk the density increases less strongly with decreasing radius and so this effect is not as large, with $\alpha$ reaching only $0.75$ for $h_z=3.0$ kpc."
 By comparison. for a standard. spherical halo ase1.5: for a flattened (EG) halo az1.0.," By comparison, for a standard spherical halo $\alpha\approx 1.5$; for a flattened (E6) halo $\alpha\approx 1.0$."
 The MLACIHIO and EROS collaborations have recently announced the first detection. of a microlensing event towards the SAIC., The MACHO and EROS collaborations have recently announced the first detection of a microlensing event towards the SMC.
 While it is not possible το craw conclusions [rom a single event. an estimate of the ratio of TeacATL may be determined within the next 5r vears or sO.," While it is not possible to draw conclusions from a single event, an estimate of the ratio of $\tau_{SMC}/\tau_{LMC}$ may be determined within the next 5 years or so."
 The distribution of event durations for a typical fat. clisk model is shown in Figure 5 as a solid line., The distribution of event durations for a typical fat disk model is shown in Figure 5 as a solid line.
 For comparison. the distribution for a standard isothermal halo is also shown as a dashed line.," For comparison, the distribution for a standard isothermal halo is also shown as a dashed line."
 Lt is clear that distinguishing between these models on the basis of event. durations will require miu events., It is clear that distinguishing between these models on the basis of event durations will require many events.
 The cistribution of events with clistance given in Figure 6 shows more clearly the dilferences between the two models., The distribution of events with distance given in Figure 6 shows more clearly the differences between the two models.
 Very thick disk mociels concentrate the lensing much closer to the observer with a tvpical distance of perhaps 5 kpe., Very thick disk models concentrate the lensing much closer to the observer with a typical distance of perhaps 5 kpc.
 In the standard halo case the typical distance is closer to 15 kpe., In the standard halo case the typical distance is closer to 15 kpc.
 Although (as discussed in the next section) the fractional rate of parallax events is small. it is possible that the two models could be distinguished with relatively lower events based on the distances derived.," Although (as discussed in the next section) the fractional rate of parallax events is small, it is possible that the two models could be distinguished with relatively fewer events based on the distances derived."
 The canonical microlensing light curve is based on a number of assumptions. among which is a constant transverse velocity.," The canonical microlensing light curve is based on a number of assumptions, among which is a constant transverse velocity."
 Since microlensing events have a non-zero duration. the motion of the Earth in its orbit around the Sun breaks this idealization.," Since microlensing events have a non-zero duration, the motion of the Earth in its orbit around the Sun breaks this idealization."
 For most microlensing events the resulting modification of the light curve is small., For most microlensing events the resulting modification of the light curve is small.
 For longer events. however. the ellect of the Earth's motion Is more apparent.," For longer events, however, the effect of the Earth's motion is more apparent."
 The detection of such a mocificationto the standard light curve is interesting because it allows one to partially break, The detection of such a modificationto the standard light curve is interesting because it allows one to partially break
Figure B2 shows the full 3-D model for both observations for three different viewingdirections?.,Figure \ref{integ2} shows the full 3-D model for both observations for three different viewing.
". I emphasize that the model is derived more or less straightforward from the observed spectra, with in principle the single assumption that the integration of the field inclination is reasonable."," I emphasize that the model is derived more or less straightforward from the observed spectra, with in principle the single assumption that the integration of the field inclination is reasonable."
" If the model properties are projected to the surface at z=0 km, one has exactly the vector field and thermodynamic properties that gave the best-fit to the observed Stokes profiles in — including the weak line blends — 3 infrared and 4 visible spectral lines."," If the model properties are projected to the surface at z=0 km, one has exactly the vector field and thermodynamic properties that gave the best-fit to the observed Stokes profiles in – including the weak line blends – 3 infrared and 4 visible spectral lines."
 The model(s) show some interesting peculiarities and give rise to several interesting questions that could be addressed by analyzing them., The model(s) show some interesting peculiarities and give rise to several interesting questions that could be addressed by analyzing them.
" The observation close to disc center (7.8.2003, 6? heliocentric angle) is very uniform all around the spot, whereas in the other case there is a much larger difference between center and limb side, where the flow channels appear to be much more elevated."," The observation close to disc center (7.8.2003, $^\circ$ heliocentric angle) is very uniform all around the spot, whereas in the other case there is a much larger difference between center and limb side, where the flow channels appear to be much more elevated."
" The background component exhibits a ragged subsurface structure, where less inclined and steeper fields coincide with an increased field strength."," The background component exhibits a ragged subsurface structure, where less inclined and steeper fields coincide with an increased field strength."
 This could be closely related to the question if these “spines” (?) are co-spatial to darker or brighter filaments., This could be closely related to the question if these “spines” \citep{lites+etal1993} are co-spatial to darker or brighter filaments.
" In general, a study on the relation of intensity to this specific geometry would be interesting, because positive as well negative correlations between field strength, inclination, and intensity have been found up to now."," In general, a study on the relation of intensity to this specific geometry would be interesting, because positive as well negative correlations between field strength, inclination, and intensity have been found up to now."
" Before an intense study on the question of the validity of the integration of inclination has been performed, I refrain from speculating further at this point."," Before an intense study on the question of the validity of the integration of inclination has been performed, I refrain from speculating further at this point."
 The 3-D models show some similarity to the artists sketch of a sunspot in Fig., The 3-D models show some similarity to the artists sketch of a sunspot in Fig.
" 4 of ?,, but I remark that they are derived (directly) from observations here."," 4 of \citet{weiss+etal2004}, but I remark that they are derived (directly) from observations here."
" To investigate the temporal evolution, I used a time-series taken after the map on 9th of August."," To investigate the temporal evolution, I used a time-series taken after the map on 9th of August."
" Figure 12 shows a small subsection of the full field-of-view (FOV) at the DOT together with a co-temporal observation taken at the VTT from 9:36 to 10:40 UT, after the map analyzed to derive the field topology."," Figure \ref{teempevol} shows a small subsection of the full field-of-view (FOV) at the DOT together with a co-temporal observation taken at the VTT from 9:36 to 10:40 UT, after the map analyzed to derive the field topology."
" This is the upper part of the FOV containing the sunspot which was not used in ?,, where the data properties and alignment method are discussed in more detail."," This is the upper part of the FOV containing the sunspot which was not used in \citet{beck+etal2006d}, where the data properties and alignment method are discussed in more detail."
" The images show a peculiarity of the penumbral dynamics that I think has not been given enough attention up to now: the global structure of the sunspot, i.e., the boundary between umbra and penumbra marked with a white rectangle, does not evolve at all in around 1 hour, whereas the intensity pattern of bright penumbral grains (PGs) evolves much faster on scales below 30 minutes (cf."," The images show a peculiarity of the penumbral dynamics that I think has not been given enough attention up to now: the global structure of the sunspot, i.e., the boundary between umbra and penumbra marked with a white rectangle, does not evolve at all in around 1 hour, whereas the intensity pattern of bright penumbral grains (PGs) evolves much faster on scales below 30 minutes (cf."
 also Appendix Appendix C:))., also Appendix \ref{appb}) ).
 This suggests that the dynamical evolution does not change the geometry., This suggests that the dynamical evolution does not change the geometry.
" In the context of the previous sections, this could be interpreted as a static background component with a dynamic flow channel component."," In the context of the previous sections, this could be interpreted as a static background component with a dynamic flow channel component."
" The penumbra has been subject of many studies, which in most cases did not agree in their results."," The penumbra has been subject of many studies, which in most cases did not agree in their results."
" The observational findings are converging in some points, which I think I can substantiate further by the results of this investigation."," The observational findings are converging in some points, which I think I can substantiate further by the results of this investigation."
 The observations agree that the topology of the penumbra is complex., The observations agree that the topology of the penumbra is complex.
" The Evershed flow happens along the nearly horizontal flow channels, whereas the average field inclination isnot horizontal (e.g. ?).."," The Evershed flow happens along the nearly horizontal flow channels, whereas the average field inclination is horizontal \citep[e.g.][]{bellot+etal2004}. ."
 The Stokes V profiles of Figs., The Stokes V profiles of Figs.
" 2 and clearly show that at a resolution of 1"" at least two independent magnetic components are present in each pixel.", \ref{vneutral} and \ref{invcomp} clearly show that at a resolution of 1” at least two independent magnetic components are present in each pixel.
" This could be an artifact due to the spatial resolution, but if the picture of the uncombed penumbra is valid, it will be the caseresolved."," This could be an artifact due to the spatial resolution, but if the picture of the uncombed penumbra is valid, it will be the case."
 As long as the flow channels are not optically thick and located inside the formation heightof, As long as the flow channels are not optically thick and located inside the formation heightof
illal or equal o that of Galactic disk M dwarls.,than or equal to that of Galactic disk M dwarfs.
 We note also the contrast between our result aud ilje success [ouid by Ixoerueretal.(1999).. who found that three of ten L brown dwarf targets Wwere resolved ito near-equal-Iuuinosity systems with separations of 5-10. A.U. — we would have detected equalunmluosity svstenis in that range of separations.," We note also the contrast between our result and the success found by \citet{keckl}, who found that three of ten L brown dwarf targets were resolved into near-equal-luminosity systems with separations of 5-10 A.U. – we would have detected equal-luminosity systems in that range of separations."
 The JOSS]bility that the higli-velocity. 1jetal-poor stars have a low bina'N [raction dates back {κ| Oort(1926).. who found that high velocity sla* were cleficient in visual biuaries.," The possibility that the high-velocity, metal-poor stars have a low binary fraction dates back to \citet{o26}, who found that high velocity stars were deficient in visual binaries."
 More recently. Abt&Wilia11(1987) argued hat both visual aud spectroscopic binary fr:TEion of Population LU Sals Is OLly that of Population I stars.," More recently, \citet{aw87} argued that both visual and spectroscopic binary fraction of Population II stars is only that of Population I stars."
" Hf so. liis is a signature of the [ornatiol of the Galactic halo — 5""keretal.(1985) have shown that clisruptlo1 of halo binaries is insiglülicant."," If so, this is a signature of the formation of the Galactic halo — \citet{stryker} have shown that disruption of halo binaries is insignificant."
 (1982) ald others. howeve2 have areied that the iilo binary fraction jiu fac comparable {κ) that of he clisk.," \citet{stryker} and others, however, have argued that the halo binary fraction is in fact comparable to that of the disk."
 Carneyetal.(1901) have fouid tla at least of th ipmje of halo FC tbclwarls are sy}»ectroscopic bina‘ies with periods less th:ux 3000 cays., \cite{carney} have found that at least of their sample of halo FG subdwarfs are spectroscopic binaries with periods less than 3000 days.
 This 1S el1c:ito the yectroscopic b=.ary [fraction of lecal disk: Co cdwarls (Dugienuoy in the salle pejod rauge.," This is identical to the spectroscopic binary fraction of local disk G dwarfs \citep{dm91,mgdm92} in the same period range."
 Cuüvei our ΠΟ number statistics. our data are coiSISent with eitlier ne'enario.," Given our small number statistics, our data are consistent with either scenario."
" Our d:ita and the C dw""arf data taken together strongly suMODecest that he binary fraction οἱ greater tlan that iu the clisk.", Our data and the G dwarf data taken together strongly suggest that the binary fraction is not greater than that in the disk.
 On the basis of imaging of wide binaries in IC 318. Duchene. argue that loose associations exhibi an excess of binaries with respect otl denser opeu clusters (IC 315. Trapezium. tle Pleiades) aud the sola: neighborhood.," On the basis of imaging of wide binaries in IC 348, \citet{dbs99} argue that loose associations exhibit an excess of binaries with respect to both denser open clusters (IC 348, Trapezium, the Pleiades) and the solar neighborhood."
 They oces that the disk binary frequency depeuds ou stellar cersity wihin tle cluster (or perhaps je οher parameter wlich. also controls the density)., They suggest that the disk binary frequency depends on stellar density within the cluster (or perhaps some other parameter which also controls the density).
 If this scenari) ls COrect. and if it applies ¢» the ialo. it suggests tlab imost halo stars form iu chIslers ο: densitles comparable to or greater lian the typical disk star formation region.," If this scenario is correct, and if it applies to the halo, it suggests that most halo stars form in clusters of densities comparable to or greater than the typical disk star formation region."
 Qir results SugeestMOD) hat further study of the binary [racjon of ο stars of all masses will )e proitable., Our results suggest that further study of the binary fraction of halo stars of all masses will be profitable.
 À few more M subdwarls are available for study wibh OO parsecs: significant improvement in tle satuple size requires exteudiug tle sample out 100 parsecs — increasing jiunbers of such subdwarls are being identified., A few more M subdwarfs are available for study within 50 parsecs; significant improvement in the sample size requires extending the sample out to 100 parsecs – increasing numbers of such subdwarfs are being identified.
 Iu acdit1011 {ο Image. a ‘acial velocity monitoring campaign is ueede« to search [or closer objects.," In addition to imaging, a radial velocity monitoring campaign is needed to search for closer objects."
 Compa‘json of such data to higlier mass halo stars (Carneyetal.1991) and data for disk stars in a variety of enviromenuts 1lay provide au iniportant constraint on the ormation and subsequent. evolution of the Galactic halo., Comparison of such data to higher mass halo stars \citep{carney} and data for disk stars in a variety of enviroments may provide an important constraint on the formation and subsequent evolution of the Galactic halo.
 The importance of density ou the sta ‘formation process aud the subseqrent evolution of halo binary systems also ueeds to be investigatect., The importance of density on the star formation process and the subsequent evolution of halo binary systems also needs to be investigated.
 We have found that color trausformatious of WEPC2 F555W and FssOLP to eround V.I photometry are consisteut with predictions.," We have found that color transformations of WFPC2 F555W and F850LP to ground V,I photometry are consistent with predictions."
 This supports analysis of WEPC?2 color-iuaguitude diagraum of globular clusters., This supports analysis of WFPC2 color-magnitude diagrams of globular clusters.
 We fiud no companious to a sample of nine isolated. nearby M subcdwarfs aud one tertiary M subdwarl., We find no companions to a sample of nine isolated nearby M subdwarfs and one tertiary M subdwarf.
 A binary fraction as high as that for similar mass disk M dwarf caunot be ruled out ou the basis of such a stall sample. but the lack of observed binaries," A binary fraction as high as that for similar mass disk M dwarf cannot be ruled out on the basis of such a small sample, but the lack of observed binaries"
detailed physics.,detailed physics.
 In particular. since the model is axisymmetric. i will not correctly describe any small scale clumping in the flow.," In particular, since the model is axisymmetric, it will not correctly describe any small scale clumping in the flow."
 In the following sub-sections we first discuss the relevance of our results to the interpretation of X-ray spectra (Section 4.13)., In the following sub-sections we first discuss the relevance of our results to the interpretation of X-ray spectra (Section \ref{sect:obs}) ).
 We then comment on the comparison of our spectra to those obtained from the parametrized models used in Papers I and II (Section 4.21) before discussing the implications of our work for the modelling of line-driven winds (Section 4.3)) and. finally. highlighting some of the outstanding questions in Section 4.4..," We then comment on the comparison of our spectra to those obtained from the parametrized models used in Papers I and II (Section \ref{sect:param_comp}) ) before discussing the implications of our work for the modelling of line-driven winds (Section \ref{sect:theory}) ) and, finally, highlighting some of the outstanding questions in Section \ref{sect:more_work}."
 Our first application of a Monte Carlo code to the modelling of the X-ray spectra of AGN (2). was motivated by the identification of narrow. blueshifted absorption lines in the Fe K band (e.g.?)..," Our first application of a Monte Carlo code to the modelling of the X-ray spectra of AGN \citep{sim05b} was motivated by the identification of narrow, blueshifted absorption lines in the Fe K band \citep[e.g.][]{pounds03}."
 Such features are the least ambiguous signature of a fast. highly-ionized outflow.," Such features are the least ambiguous signature of a fast, highly-ionized outflow."
 This study confirms that such features can arise in a plausible disk wind geometry., This study confirms that such features can arise in a plausible disk wind geometry.
 Our calculations suggest that narrow. blueshifted Ka absorption lines will manifest in systems with line-driven disk winds for a limited range of orientations (very roughly A@~210 deg. centred around moderate inclination angles of @~57 deg).," Our calculations suggest that narrow, blueshifted $\alpha$ absorption lines will manifest in systems with line-driven disk winds for a limited range of orientations (very roughly $\Delta
\theta \sim 2 - 10$ deg, centred around moderate inclination angles of $\theta
\sim 57$ deg)."
 For an isotropic distribution of observed orientations. this would suggest that only a modest fraction of sources (somewhere around ~3.15 per cent) should show any such absorption lines.," For an isotropic distribution of observed orientations, this would suggest that only a modest fraction of sources (somewhere around $\sim 3 - 15$ per cent) should show any such absorption lines."
 The fraction in the observed sample of X-ray bright AGN would be expected to be somewhat higher since very high inclination systems are likely excluded — but it should still be a minority., The fraction in the observed sample of X-ray bright AGN would be expected to be somewhat higher since very high inclination systems are likely excluded – but it should still be a minority.
" Thus the absence of this “smoking gun"" signature of outflow is not evidence against the presence of a fast wind and the calibration factor required to convert the fraction of objects with observed narrow line features to the fraction with powerful disk winds may be large.", Thus the absence of this “smoking gun” signature of outflow is not evidence against the presence of a fast wind and the calibration factor required to convert the fraction of objects with observed narrow line features to the fraction with powerful disk winds may be large.
 Moreover. comparing the spectra obtained from. the two timesteps we considered demonstrates the absorption line properties should be significantly variable on. timescales comparable to Af~5 years.," Moreover, comparing the spectra obtained from the two timesteps we considered demonstrates the absorption line properties should be significantly variable on timescales comparable to $\Delta t \sim
5$ years."
 Thus. even if the flow is persistent. re-observations of particular objects are not expected to yield very similar absorption line properties over timescales of years: for a fixed observer orientation. the line blueshifts. widths and equivalent-widths can all change significantly.," Thus, even if the flow is persistent, re-observations of particular objects are not expected to yield very similar absorption line properties over timescales of years: for a fixed observer orientation, the line blueshifts, widths and equivalent-widths can all change significantly."
 This is consistent with observations of e.g. PGI2114143. an object where blueshifted Fe Ka absorption has been claimed but in which the absorptionproperties have varied between multiple observations made over the course of the last decade (seee.g.222?)..," This is consistent with observations of e.g. PG1211+143, an object where blueshifted Fe $\alpha$ absorption has been claimed but in which the absorptionproperties have varied between multiple observations made over the course of the last decade \citep[see
 e.g.][]{pounds03,pounds05,pounds07,pounds09}."
 Our current radiative transfer simulations do not constrain the level of absorption line variability expected on much shorter timescales (e.g. on the scale of typical X-ray exposures of several kiloseconds)., Our current radiative transfer simulations do not constrain the level of absorption line variability expected on much shorter timescales (e.g. on the scale of typical X-ray exposures of several kiloseconds).
 Detailed consideration of shorter timescales will require a more extensive. tightly-spaced sequence of snapshots and investigation of the role played by both small-scale structure in the flow (which will not be well-represented in the axisymmetric simulation considered here) and intrinsic. short time-scale variability of the primary X-ray source.," Detailed consideration of shorter timescales will require a more extensive, tightly-spaced sequence of snapshots and investigation of the role played by both small-scale structure in the flow (which will not be well-represented in the axisymmetric simulation considered here) and intrinsic, short time-scale variability of the primary X-ray source."
" We would like to note. however. that (1) variations in the wind structure itself occur on a very wide range of timescales. at least as short as ~10s — thus we expect that some degree of variability will also be present on much shorter timescales than the time difference between the two snapshots used here: and (i1) short time-scale variability (timescales <10° s) is much more likely to manifest in the absorption lines than any emission features since the light-crossing time for the simulation (0.01 yr 2310"" s) sets a lower limit for the timescale on which the emission from the outflow should show significant variability."," We would like to note, however, that (i) variations in the wind structure itself occur on a very wide range of timescales, at least as short as $\sim 10^5$ s – thus we expect that some degree of variability will also be present on much shorter timescales than the time difference between the two snapshots used here; and (ii) short time-scale variability (timescales $\simlt
10^5$ s) is much more likely to manifest in the absorption lines than any emission features since the light-crossing time for the simulation $\sim 0.01$ yr $= 3 \times 10^5$ s) sets a lower limit for the timescale on which the emission from the outflow should show significant variability."
 Whilst narrow absorption features appear for only a limited range of observer orientations. other spectroscopic signatures associated with emission/reflection by the wind are predicted to appear for ai] inclination angles:," Whilst narrow absorption features appear for only a limited range of observer orientations, other spectroscopic signatures associated with emission/reflection by the wind are predicted to appear for inclination angles:"
relations. the K-band ellective parameters being obtained from the cireular aperture estimates of Mobasher οἱ al. (,"relations, the K-band effective parameters being obtained from the circular aperture estimates of Mobasher et al. ("
1999).,1999).
 I£ the comparison of these two data-sets is helcl as representative of the systematic elfects due to the cdillerent data analysis. we infer that the adoption of circular aperture estimates of the effective. parameters. causes a systematic decrease of the sj and # coordinates (ef.," If the comparison of these two data-sets is held as representative of the systematic effects due to the different data analysis, we infer that the adoption of circular aperture estimates of the effective parameters causes a systematic decrease of the $\kappa_1$ and $\kappa_3$ coordinates (cf."
 σαι., Equ.
 1 and 3)., 1 and 3).
 This results in a reduced. slope of the FP in the &-3pace notation and contributes to justify the discrepancy between us and PDdt. Spiral and Im/DCD galaxies form two distinct classes in the HQ Ha plane. the latter having a mean elfective mass-to-light ratio (in solar units) larger by a factor of2.," This results in a reduced slope of the FP in the $\kappa$ -space notation and contributes to justify the discrepancy between us and PDdC. Spiral and Im/BCD galaxies form two distinct classes in the $\kappa_1$ $\kappa_3$ plane, the latter having a mean effective mass-to-light ratio (in solar units) larger by a factor of 2."
 Taken as a whole. the Iate-type galaxies have a mean value of s; equal to 0.656. ic. à mean effective mass-to-light ratio (in solar units) equal to 2.," Taken as a whole, the late-type galaxies have a mean value of $\kappa_3$ equal to 0.656, i.e., a mean effective mass-to-light ratio (in solar units) equal to 2."
 This figure is of the value of the mean total mass-to-light ratio (in solar units) determined by CPB for a sample of 426 Iate-tvpe galaxies., This figure is of the value of the mean total mass-to-light ratio (in solar units) determined by GPB for a sample of 426 late-type galaxies.
 “Phis large discrepancy has not a statistical origin., This large discrepancy has not a statistical origin.
 First. 1e total mass-to-lieht ratios of GDPD were determined. under the same assumptions of virial equilibrium and spherical symmetry as in Sect.," First, the total mass-to-light ratios of GPB were determined, under the same assumptions of virial equilibrium and spherical symmetry as in Sect."
 2. at the 25 D-magaresee7 Isophotal radius £0)... and not at infinity," 2, at the 25 $\rm mag~arcsec^{-2}$ isophotal radius $R_{opt}$, and not at infinity."
 As à consequence. the mass-to-light ratios quoted in GP are about [ess than the total ones. on average.," As a consequence, the mass-to-light ratios quoted in GPB are about less than the total ones, on average."
" From he definitions of total ancl ellective mass and. luminosity. Aly and Ly respectively. it is straightforward to determine hat M./L,=2rfIus Αρ."," From the definitions of total and effective mass and luminosity, $M_T$ and $L_T$ respectively, it is straightforward to determine that $M_e/L_e = 2 r_e/R_{opt} \times M_T/L_T$ ."
 Whatever the Hubble ype of the galaxy is. on average. Ropes=5.3d0.08 (Paper V). so that we expect that the mean elfective mass-o-light ratio is of the mean total mass-to-lieht ratio. on average.," Whatever the Hubble type of the galaxy is, on average, $R_{opt}/r_e = 5.3 \pm 0.08$ (Paper V), so that we expect that the mean effective mass-to-light ratio is of the mean total mass-to-light ratio, on average."
 Second. we note that the maximum rotational velocities were not corrected for. turbulent/z-motions by CPB. so that the estimates of the total mass-to-light ratios further exceed those of the ellective mass-to-lisht ratio [or the low-mass objects.," Second, we note that the maximum rotational velocities were not corrected for turbulent/z-motions by GPB, so that the estimates of the total mass-to-light ratios further exceed those of the effective mass-to-light ratio for the low-mass objects."
 We conclude that the two estimates are consistent within the assumptions and the uncertainties of the observations., We conclude that the two estimates are consistent within the assumptions and the uncertainties of the observations.
 What do these two estimates tell us about the radial behaviour of the mass-to-light ratio?, What do these two estimates tell us about the radial behaviour of the mass-to-light ratio?
 The mass of a spiral ealaxy within a given ealactocentric distance lays with high confidence between the estimates given by a Llat disk modcl and a spherical one and is between 60. anc of the mass estimate determined through the assumption of spherical symmetry. (Lequeux 1983)., The mass of a spiral galaxy within a given galactocentric distance lays with high confidence between the estimates given by a flat disk model and a spherical one and is between 60 and of the mass estimate determined through the assumption of spherical symmetry (Lequeux 1983).
 According to this author. the overestimate due to this assumption is probably much reduced: at. galactocentric distances as large as the optical radius. where spherical. components. dominate the potential.," According to this author, the overestimate due to this assumption is probably much reduced at galactocentric distances as large as the optical radius, where spherical components dominate the potential."
 Hence. the difference between the average estimates of the ellective and total mass-to-light ratios may suggest that the actual mass-to-light ratio increases with ealactocentric distance.," Hence, the difference between the average estimates of the effective and total mass-to-light ratios may suggest that the actual mass-to-light ratio increases with galactocentric distance."
" A linear fit to the data of all the galaxies later than S0a which minimizes the dispersion in both axes gives: Formally this relation corresponds (ο the scaling relations Ad,L,x-iDGO09320,026, Lianc EM1Lx»LUElud cp", A linear fit to the data of all the galaxies later than S0a which minimizes the dispersion in both axes gives: Formally this relation corresponds to the scaling relations $M_e/L_e \propto M_e^{-0.093 \pm 0.026}$ and $M_e/L_e \propto L_e^{-0.103 \pm 0.032}$ .
"""Phe sieht.n dependencees of⋅ the elective""M mass- ratio on ellective mass ancl luminosity are mareinally significant.", The slight dependences of the effective mass-to-light ratio on effective mass and luminosity are marginally significant.
 We note that the adoption of velocity corrections for turbulent/z-motions gives us some protection against a systematic overestimate of the mass of the Sed.Im/DCD galaxies. where such motions are not negligible with respect to the rotational velocity.," We note that the adoption of velocity corrections for turbulent/z-motions gives us some protection against a systematic overestimate of the mass of the Scd–Im/BCD galaxies, where such motions are not negligible with respect to the rotational velocity."
 Phe incompleteness bias which allects our sample may justify even higher. mass-to-light ratios for these galaxies. since we better observe low-mass objects of higher luminosity.," The incompleteness bias which affects our sample may justify even higher mass-to-light ratios for these galaxies, since we better observe low-mass objects of higher luminosity."
 On the other ened. Lequeux (1983) shows that the discrepancy between the estimates of the mass-to-light ratio given by a Hat clisk model and a spherical one depends on its rotation curve.," On the other end, Lequeux (1983) shows that the discrepancy between the estimates of the mass-to-light ratio given by a flat disk model and a spherical one depends on its rotation curve."
 In a disk where he rotation curve increases linearly until a racial distance a. where it reaches its maximum. and stavs [lat at larger raclii. his assumption leads to a discrepancy. increasing from 40 ο when e ranges between O and the optical radius.," In a disk where the rotation curve increases linearly until a radial distance $a$, where it reaches its maximum, and stays flat at larger radii, this assumption leads to a discrepancy increasing from 40 to when $a$ ranges between 0 and the optical radius."
 Since rotation curves seem to peak at larger radial distances with decreasing mass of the svstem (Persic. Salucci Stel 1996). it is reasonable to assume that our estimates of the cllective mass-to-light ratio for the SedIm/BCD galaxies may be svstematicallv in excess by an additional with respect to those of earlier and. more. massive. [ate-types.," Since rotation curves seem to peak at larger radial distances with decreasing mass of the system (Persic, Salucci Stel 1996), it is reasonable to assume that our estimates of the effective mass-to-light ratio for the Scd–Im/BCD galaxies may be systematically in excess by an additional with respect to those of earlier and more massive late-types."
 Furthermore. setting the velocity at. the elective. radius equal to the maximum velocity may Iead to an overestimate of the dvnamical mass of these systems. as discussed. in Sect.," Furthermore, setting the velocity at the effective radius equal to the maximum velocity may lead to an overestimate of the dynamical mass of these systems, as discussed in Sect."
 2., 2.
 Alternatively. the decrease of the cynamical mass-o-light ratio with mass may be attributed to increasing extinction. as an ellect of the mass-metallicity relation (Zaritsky. Wennieutt Lluchra 1994).," Alternatively, the decrease of the dynamical mass-to-light ratio with mass may be attributed to increasing extinction, as an effect of the mass-metallicity relation (Zaritsky, Kennicutt Huchra 1994)."
 At present. there are no estimates of such an elleet. obtained from moclelling both sincmatics and radiative transfer and we assume that these ellects are very small in the ποσαΕν.," At present, there are no estimates of such an effect, obtained from modelling both kinematics and radiative transfer and we assume that these effects are very small in the near-IR."
 Hence. we conclude hat the validity and interpretation of the scaling relations involved by Equ.," Hence, we conclude that the validity and interpretation of the scaling relations involved by Equ."
 14 are dubious., 14 are dubious.
 In this projection of the &-space. the distribution of the E and SO galaxies is elongated. in the direction. of the Ho axis. so that Joox(AL./L.)I for these objects (Pie.," In this projection of the $\kappa$ -space, the distribution of the E and S0 galaxies is elongated in the direction of the $\kappa_2$ axis, so that $I_e \propto (M_e/L_e)^{-3}$ for these objects (Fig."
 2a)., 2a).
 A similar clistribution is found by PDdC aad. BBEN., A similar distribution is found by PDdC and BBFN.
 Therefore. we conclude that the higher is the mass of an clliptical/lenticular galaxy the higher is its mean cllective mass-to-lieht ratio and the lower is its cllective surface intensity. whatever the pass-band is.," Therefore, we conclude that the higher is the mass of an elliptical/lenticular galaxy the higher is its mean effective mass-to-light ratio and the lower is its effective surface intensity, whatever the pass-band is."
 S0a galaxies distribute ina similar way to the earlv-types., S0a galaxies distribute ina similar way to the early-types.
 For the late-twpe galaxies. the coordinates #2 and a; are," For the late-type galaxies, the coordinates $\kappa_2$ and $\kappa_3$ are"
"by(e.g.,Zhang&Beacom2004;Cuocoetal.2007) where we use Eq. (9))","by\citep[e.g.,][]{Zhang2004, Cuoco2007}
 where we use Eq. \ref{eq:galaxy auto-power}) )"
" for C7? in this expression; Cy,g==1.5x107°fa sr is the galaxy shot noise."," for $C_\ell^{gg}$ in this expression; $C_{N,g} = \Omega_{\rm sky} / N_g = 1.5 \times
10^{-5} f_{\rm sky}$ sr is the galaxy shot noise."
 The errors for are plotted as a dashed curve in Fig. 3((, The errors for $C_\ell^{\gamma g}$ are plotted as a dashed curve in Fig. \ref{fig:C_l}( (
"b), which shows C7?similar prospects to the case of auto-power spectrum, for detecting the galaxy clustering in the CGB anisotropy.","b), which shows similar prospects to the case of auto-power spectrum, for detecting the galaxy clustering in the CGB anisotropy."
 The sweet spot is slightly wider than that for the auto-power spectrum., The sweet spot is slightly wider than that for the auto-power spectrum.
" In the calculations for both the mean intensity and anisotropy, we assumed that the y-ray emissivity of all galaxies at the same redshift is the same, rescaled from the emissivity of the Milky Way using the cosmic star-formation rate as well as the gas-mass fraction."," In the calculations for both the mean intensity and anisotropy, we assumed that the $\gamma$ -ray emissivity of all galaxies at the same redshift is the same, rescaled from the emissivity of the Milky Way using the cosmic star-formation rate as well as the gas-mass fraction."
 This implicitly assumes that all the galaxies of interest are Milky-Way-like in their y-ray properties., This implicitly assumes that all the galaxies of interest are Milky-Way-like in their $\gamma$ -ray properties.
" Although this is clearly not true for all galaxies, what it really amounts to is assuming thatphotons emitted by star-forming galaxies come from Milky-Way-like, properly de-evolved sources."," Although this is clearly not true for all galaxies, what it really amounts to is assuming that emitted by star-forming galaxies come from Milky-Way–like, properly de-evolved sources."
 This in turn is not an unreasonable assumption., This in turn is not an unreasonable assumption.
" Milky- objects are rich in both star formation and gas, so they are Way-likeexpected to be the most y-ray bright among normal star-forming galaxies of the same epoch (see,e.g.,Pavlidou&Fields 2001)."," Milky-Way-like objects are rich in both star formation and gas, so they are expected to be the most $\gamma$ -ray bright among normal star-forming galaxies of the same epoch \citep[see, e.g.,][]{Pavlidou2001}."
". This is the reasoning behind taking, as a first approximation, all normal galaxies contributing to the CGB to have a single luminosity at a given redshift, instead of using a luminosity function."," This is the reasoning behind taking, as a first approximation, all normal galaxies contributing to the CGB to have a single luminosity at a given redshift, instead of using a luminosity function."
" A notable exception to this general rule is that of starburst galaxies, which, depending on the details of cosmic ray confinement, could individually be one to two orders of magnitude brighter in y-rays than the typical Milky-Way-like galaxy of the same cosmic epoch, as well as have harder energy spectra at high energies (see,e.g.,Thompson,Quataert,&Waxman 2007)."," A notable exception to this general rule is that of starburst galaxies, which, depending on the details of cosmic ray confinement, could individually be one to two orders of magnitude brighter in $\gamma$ -rays than the typical Milky-Way--like galaxy of the same cosmic epoch, as well as have harder energy spectra at high energies \citep*[see, e.g.,][]{Thompson2007}."
". However starburst galaxies would be best treated as a distinct source class as far as their anisotropy properties are concerned—compared to normal star-forming galaxies, the population of starburst galaxies consists of few and bright sources, and the anisotropy at small angular scales could be considerably stronger, even if the overall contribution of starbursts to the CGB is lower."," However starburst galaxies would be best treated as a distinct source class as far as their anisotropy properties are concerned—compared to normal star-forming galaxies, the population of starburst galaxies consists of few and bright sources, and the anisotropy at small angular scales could be considerably stronger, even if the overall contribution of starbursts to the CGB is lower."
 We will return to this issue in a future publication., We will return to this issue in a future publication.
" Until this point, we have concentrated on photons of E=300 MeV, as the y-ray energy flux spectrum due to normal galaxies peaks at this energy (see Fig. 1))."," Until this point, we have concentrated on photons of $E = 300$ MeV, as the $\gamma$ -ray energy flux spectrum due to normal galaxies peaks at this energy (see Fig. \ref{fig:spectrum}) )."
" We now also discuss the results for higher energy photons E—1 GeV. At this energy, although the energy flux from star- galaxies is lower, the LAT effective area increases to 8000 cm?, and also the angular resolution improves to ~0°8 (Atwoodetal.2009)."," We now also discuss the results for higher energy photons $E = 1$ GeV. At this energy, although the energy flux from star-forming galaxies is lower, the LAT effective area increases to 8000 $^2$, and also the angular resolution improves to $\sim$ $\fdg$ 8 \citep{lat09}."
". In Fig. 6,,"," In Fig. \ref{fig:C_l_1GeV},"
 we show the same plots as Fig., we show the same plots as Fig.
 3 but for E=1 GeV photons.," \ref{fig:C_l}
 but for $E = 1$ GeV photons."
" We find that especially for the cross-correlation, the detection prospects are still pretty good even though the number of photons received would decrease."," We find that especially for the cross-correlation, the detection prospects are still pretty good even though the number of photons received would decrease."
" In addition, the multipole range for the detection becomes larger, above 4=100 for C7?."," In addition, the multipole range for the detection becomes larger, above $\ell = 100$ for $C_\ell^{\gamma g}$."
" Although we fixed the galaxy bias to be Όρω=1.11 throughout (Afshordietal.2004),, the relevant value of the bias might be different."," Although we fixed the galaxy bias to be $b_{\rm gal} = 1.11$ throughout \citep{Afshordi2004}, the relevant value of the bias might be different."
" This is because while 544; refers to all galaxies, we are not interested in elliptical galaxies, faint dwarfs, or gas-poor dwarfs, which do not emit significant amount of 4-rays."," This is because while $b_{\rm gal}$ refers to all galaxies, we are not interested in elliptical galaxies, faint dwarfs, or gas-poor dwarfs, which do not emit significant amount of $\gamma$ -rays."
" Thus, the bias of star-forming -ray- bright galaxies might differ from that of all the galaxies as inferred from galaxy catalogs."," Thus, the bias of star-forming $\gamma$ -ray-bright galaxies might differ from that of all the galaxies as inferred from galaxy catalogs."
" However, our results are not very sensitive to the value of bga; as long as the true value is not significantly different from 1."," However, our results are not very sensitive to the value of $b_{\rm gal}$ as long as the true value is not significantly different from 1."
 The emission from individual galaxies we have considered is entirely due to the interaction between cosmic rays and interstellar gas and light; any contribution from point sources within galaxies has not been accounted for., The emission from individual galaxies we have considered is entirely due to the interaction between cosmic rays and interstellar gas and light; any contribution from point sources within galaxies has not been accounted for.
" However, using y-ray observations of the Milky Way for guidance, we expectthat the contribution of point sources to the total gamma-ray emission of a star-forming galaxy is small."," However, using $\gamma$ -ray observations of the Milky Way for guidance, we expectthat the contribution of point sources to the total gamma-ray emission of a star-forming galaxy is small."
" First, the relative intensity of the diffuse flux is much higher than the total emission due to resolved point sources in the Milky Way (see,e.g.,Hartmanetal. 1999)."," First, the relative intensity of the diffuse flux is much higher than the total emission due to resolved point sources in the Milky Way \citep[see,
e.g.,][]{Hartman1999}."
". Second, the good agreement between the Milky Way diffuse emission as measured byFermi LAT and GALPROP, indicates that in the Milky Way point sources are not a dominant component in the diffuse emission, at least at mid-Galactic latitudes."," Second, the good agreement between the Milky Way diffuse emission as measured by LAT and GALPROP, indicates that in the Milky Way point sources are not a dominant component in the diffuse emission, at least at mid-Galactic latitudes."
" The situation can be very different for early-type galaxies with little star formation, in which most y-ray emission would arise from nonthermal processes in older populations of stellar remnants, such as millisecond pulsars."," The situation can be very different for early-type galaxies with little star formation, in which most $\gamma$ -ray emission would arise from nonthermal processes in older populations of stellar remnants, such as millisecond pulsars."
 However the contribution of early-type galaxies to the CGB is expected to be very small., However the contribution of early-type galaxies to the CGB is expected to be very small.
 We also comment on the nonlinear part of the galaxy power spectrum., We also comment on the nonlinear part of the galaxy power spectrum.
 The angular scales where such nonlinearity becomes important are £z10? for C7? and €zz100 for C;?.," The angular scales where such nonlinearity becomes important are $\ell
\approx 10^3$ for $C_\ell^{\gamma\gamma}$ and $\ell \approx 100$ for $C_\ell^{\gamma g}$ ."
" Remembering that the angular resolution of Fermi- for 1 GeV photons corresponds roughly to £= 100, the"," Remembering that the angular resolution of }-LAT for 1 GeV photons corresponds roughly to $\ell \approx 100$ , the"
correction to absolute proper motions.,correction to absolute proper motions.
 The refercuce stars (rius and cutire field) are used to map plate positions iuto one another as well as CCD positions into the photographic positions., The reference stars (ring and entire field) are used to map plate positions into one another as well as CCD positions into the photographic positions.
 For one field. #2136. we had a slightly differcut iuput catalog. as this field was measured carly ou. together with our Paper IV. clusters. since both epoch plates existed.," For one field, $\# 436$, we had a slightly different input catalog, as this field was measured early on, together with our Paper IV clusters, since both epoch plates existed."
" However, at that time. we realized that although we can obtain a reliable correction for the absolute proper motion for this field. the motion of cluster NGC 6111 was unreliable."," However, at that time, we realized that although we can obtain a reliable correction for the absolute proper motion for this field, the motion of cluster NGC 6441 was unreliable."
 This cluster is more distaut. aud the time baseline for the plates is ouly 22 vears (Tab.," This cluster is more distant, and the time baseline for the plates is only 22 years (Tab."
 1)., 1).
 So. we took several CCD frames centered ou the cluster in 2007 to iniprove the mean motion of the cluster.," So, we took several CCD frames centered on the cluster in 2007 to improve the mean motion of the cluster."
 The strategy used to make the input catalog was simular to the one preseuted above: however instead ofUCAC2 aud 2MASS. we used the Guide Star Catalog (CSC) L1 (Lasker et al.," The strategy used to make the input catalog was similar to the one presented above; however instead of UCAC2 and 2MASS, we used the Guide Star Catalog (GSC) 1.1 (Lasker et al."
 1990) and the USNO-À2.0 catalog (Monet et al., 1990) and the USNO-A2.0 catalog (Monet et al.
 1998)., 1998).
 For cluster stars. we derived a catalog based ou a coarse scan centered ou the cluster of the deepest SPAL plate.," For cluster stars, we derived a catalog based on a coarse scan centered on the cluster of the deepest SPM plate."
 During these lone PDS scans (up to 21 hours) we monio a set of 8 to LO stars that are used to correct for thermal dift., During these long PDS scans (up to 24 hours) we monitor a set of 8 to 10 stars that are used to correct for thermal drift.
 Positions. iustrumental magnitudes and other inuaage parameters are derived with the Yale centering routines that fit a two-dimensional Ciuussiau function to the image profile (Lee van Altena 1983).," Positions, instrumental magnitudes and other image parameters are derived with the Yale centering routines that fit a two-dimensional Gaussian function to the image profile (Lee van Altena 1983)."
 The CCD system mounted on the double astroeraph consists of two main cameras: a UN x Us PixelVision (PV) camera (15 mücron pixel) iu the focal plane of the vellow lens and an Apogee LIN x Ls (21 micron pixel) camera in the focal plane of the blue lens., The CCD system mounted on the double astrograph consists of two main cameras: a 4K x 4K PixelVision (PV) camera (15 micron pixel) in the focal plane of the yellow lens and an Apogee 1K x 1K (24 micron pixel) camera in the focal plane of the blue lens.
 Later. the Apogee camera was replaced with an Apogee Alta 39 x 2k (12 micron pixel) camera.," Later, the Apogee camera was replaced with an Apogee Alta 2K x 2K (12 micron pixel) camera."
 The PV's feld of view is (0.937«0.937 with a scale of 0.83/pix., The PV's field of view is $0.93\arcdeg \times 0.93\arcdeg$ with a scale of 0.83”/pix.
 The Apogee Alta camera covers a 0.3987&0.387 area with a scale of O71/pix., The Apogee Alta camera covers a $0.38\arcdeg \times 0.38\arcdeg$ area with a scale of 0.74”/pix.
 The PV data were used for both astrometry and photometry. while the Apogee data were used only for photometry.," The PV data were used for both astrometry and photometry, while the Apogee data were used only for photometry."
 The observations are taken with the diffraction erating oriented at 157. thus cusuring a ανασα range of 10 mae (1.0.. 6 from the CCD plus 1 from the erating).," The observations are taken with the diffraction grating oriented at $45\arcdeg$, thus ensuring a dynamical range of 10 mag (i.e., 6 from the CCD plus 4 from the grating)."
 Exposure times are 120 sec. reaching the same depth as the first-epoch plates.," Exposure times are 120 sec, reaching the same depth as the first-epoch plates."
 Between 3 aud 6 frames are taken on each cluster in addition to the survey CCD frames taken for cach SPM field (Tab., Between 3 and 6 frames are taken on each cluster in addition to the survey CCD frames taken for each SPM field (Tab.
 1)., 1).
 These have exposures of 30. 60 and 120 sec.," These have exposures of 30, 60 and 120 sec."
 The astrometric reduction of the CCD data is thoroughly described iu Paper V: here we briefly micution ouly the steps applied., The astrometric reduction of the CCD data is thoroughly described in Paper V; here we briefly mention only the steps applied.
 The CCD data are corrected for bias. dark (ouly in he case of the Apogee frames is it significant) ar Hat fielding.," The CCD data are corrected for bias, dark (only in the case of the Apogee frames is it significant) and flat fielding."
 SExtractor (Bertin Arnuouts 1996) is used for object detectious. aperture photometry anc xelininary xv centers.," SExtractor (Bertin Arnouts 1996) is used for object detections, aperture photometry and preliminary x,y centers."
 Final κιν ceuters are derived by fitting two-dimensional elliptical Gaussian fictions to iuaee mteusities.," Final x,y centers are derived by fitting two-dimensional elliptical Gaussian functions to image intensities."
 These image ceuters have a positiona xecision of ~20 imas per sinele iase. for V—715.," These image centers have a positional precision of $\sim 20$ mas per single image, for $V=7-15$."
 Two other corrections of the CCD positions are applic ovr fune., Two other corrections of the CCD positions are applied per frame.
 The first is a correction for the optical Πο] anele distortion (OFAD)., The first is a correction for the optical field angle distortion (OFAD).
 This correction is determines yon stacked residuals into UCAC2. and is applied as a mask to the CCD data (sec Paper V).," This correction is determined from stacked residuals into UCAC2, and is applied as a mask to the CCD data (see Paper V)."
 The secouc correction refers to the positious of different eratine-order dnages that must be placed on a common svsteni with those of the ceutral-order images., The second correction refers to the positions of different grating-order images that must be placed on a common system with those of the central-order images.
 We found offsets between the average positioniofsvunuuetric nuage orders and the position of the central order. but these offsets are not related to the magnitude of the object (as ds the case for photographic pl:ies).," We found offsets between the average position of symmetric image orders and the position of the central order, but these offsets are not related to the magnitude of the object (as is the case for photographic plates)."
 Therefore these offsets were corrected as such. a simple offset between differeut inage order svstenis (see also Paper V).," Therefore these offsets were corrected as such, a simple offset between different image order systems (see also Paper V)."
 The next step is to link all of the CCD frames for a even SPAM field from the main survey to produce a 67«67 CCD pseudo-plate., The next step is to link all of the CCD frames for a given SPM field from the main survey to produce a $6\arcdeg\times6\arcdeg$ CCD pseudo-plate.
 This is «ifercut frou our procedure adopted in Paper V. where cach individual CCD frame was mapped into a 1iaster first-epoch plate.," This is different from our procedure adopted in Paper V, where each individual CCD frame was mapped into a master first-epoch plate."
 The linking of the CCD frames was deveoped for the construction of the SPALL catalog aud is described in Carard et al. (, The linking of the CCD frames was developed for the construction of the SPM4 catalog and is described in Girard et al. (
2010).,2010).
 Iu brief. the mask-correctec CCD x.v positions of cach frame are transformed onto he system of the UCAC?2 to facilitate pasting together tιο roughly 50 to LOO frames (depending on whether the field had two-fold or single coverage] that comprise a 67«67 SPM field.," In brief, the mask-corrected CCD x,y positions of each frame are transformed onto the system of the UCAC2 to facilitate pasting together the roughly 50 to 100 frames (depending on whether the field had two-fold or single coverage) that comprise a $6\arcdeg\times6\arcdeg$ SPM field."
 An iterative overlap method is curplovec to perform this task using Tycho? stars as an external reference system to eusure that svstematics from the individual frame overlaps do not accumulate., An iterative overlap method is employed to perform this task using Tycho2 stars as an external reference system to ensure that systematics from the individual frame overlaps do not accumulate.
 In this manner. an artificial pseudo-plate” is built up from CCD frames.," In this manner, an artificial ""pseudo-plate"" is built up from CCD frames."
 The CCD frames that contribute to anv one fields pseudo-plate may actually span two to three vears” range in epoch whereas an actual plate has a single epoch., The CCD frames that contribute to any one field's pseudo-plate may actually span two to three years' range in epoch whereas an actual plate has a single epoch.
 For this reason. once prelunuünary proper imetions are determined frou a secoud-epoch pseucdo-plate. an improved pseudo-plate is coustructed. one +that incorporates the proeliniuaryv proper motions prior to pasting the fraunes together iu a new overlap solution.," For this reason, once preliminary proper motions are determined from a second-epoch pseudo-plate, an improved pseudo-plate is constructed, one that incorporates the preliminary proper motions prior to pasting the frames together in a new overlap solution."
 This sinele-cpoch pseudo-plate cau then be treated the same as a real secoud-epoch plate in the reduction process to vield final proper-amotio- determinatious., This single-epoch pseudo-plate can then be treated the same as a real second-epoch plate in the reduction process to yield final proper-motion determinations.
 The CCD BW photometiy is derived from aperture photometry calibrated into Tycho? (corrected to the Johnson system) aud several other external catalogs suc[um as the Guide Star Photometric Catalog ID (Ducciarelli et al., The CCD $BV$ photometry is derived from aperture photometry calibrated into Tycho2 (corrected to the Johnson system) and several other external catalogs such as the Guide Star Photometric Catalog II (Bucciarelli et al.
 2001)., 2001).
 When no CCD photometry is available. we use photographic photometry from the first-epoch plates calibrated on Tycho2.," When no CCD photometry is available, we use photographic photometry from the first-epoch plates calibrated on Tycho2."
 For our purposes in this paper. we use however 2\LASS photometry.," For our purposes in this paper, we use however 2MASS photometry."
 To obtain proper motions we use the ceutral-plate overlap icethod described for iustance by Cirard et al. (, To obtain proper motions we use the central-plate overlap method described for instance by Girard et al. (
1989).,1989).
 Thus. we trausform all measurements CCD pseudo-plate. ou-cluster CCD frames. photographic positions of various nage eratine-ordcer svstenis iuto oue master photographic plate dist which ids chosen to be a visual plate with the ceutralorder image.," Thus, we transform all measurements — CCD pseudo-plate, on-cluster CCD frames, photographic positions of various image grating-order systems — into one master photographic plate list which is chosen to be a visual plate with the central-order image."
 This transformation is a polvnonual function of x.v coordinates of up to 5th order. aud it Uses stays with magnitudes between V.—10 aud 17 distributed nuiformly over the field and with a ligher density iu a ving around each chluster.," This transformation is a polynomial function of x,y coordinates of up to 5th order, and it uses stars with magnitudes between $V = 10$ and 17 distributed uniformly over the field and with a higher density in a ring around each cluster."
 The uuuber of reference stars for different epoch measuremcuts ranges between 500 and 6000 stars. with a mean average maenitude roughlye between V—Ll and 16.," The number of reference stars for different epoch measurements ranges between 500 and 6000 stars, with a mean average magnitude roughly between $V = 14$ and 16."
 A linear least-squares fit of positions as a fiction of time eives the proper motion of cach object., A linear least-squares fit of positions as a function of time gives the proper motion of each object.
 Measurements that differ by more than 0.2” from the best fit line are rejected as outliers., Measurements that differ by more than $0.2\arcsec$ from the best fit line are rejected as outliers.
 The formal properanotion crror is given by the scatter around, The formal proper-motion error is given by the scatter around
aud is relatively weak. aud the iiaximanua teniperature iu he bubble occurs mnuuediatelv postshock.,"and is relatively weak, and the maximum temperature in the bubble occurs immediately postshock."
 The solution with the cashed Lue las some characteristics of cach of he ]t is', The solution with the dashed line has some characteristics of each of the other solutions.
" gasloadec from μπα] radius. which other leads solutions,to the maximuun bubble temperature occurrins againear the center,", It is mass-loaded from small radius which again leads to the maximum bubble temperature occurring near the center.
" However. the mass loading πο essws severeupovere (Qj,(P,= 6.5) GH);and its ⋅⊀radial dependence steeper (A= 3) than for the solution with the solid Tine. πο hat there is a large fall in density between the switch-ou radius for mass loacing andj."," However, the mass loading is less severe $\Phi_{b} = 6.5$ ) and its radial dependence steeper $\lambda = -3$ ) than for the solution with the solid line, so that there is a large fall in density between the switch-on radius for mass loading and $x_{is}$."
 This leads to a steep rise oe Lenussivity from the ner shock to the bubble ceuter iu simular fashion to the solution with the dotted linc., This leads to a steep rise in emissivity from the inner shock to the bubble center in a similar fashion to the solution with the dotted line.
 The bottom panels of Fie., The bottom panels of Fig.
 7 show results where there is no inner shock and where the mass loading region directly connects to the contact discoutinuity., \ref{fig:xray_ab} show results where there is no inner shock and where the mass loading region directly connects to the contact discontinuity.
 The Npél amber profiles for these solutions are displayed ∖∖∖⊳∖↴∖∖∖⋅⋅iy the bottourright⋅ paucl of DpFig. .6.., The Mach number profiles for these solutions are displayed in the bottom-right panel of Fig. \ref{fig:machno}.
 As can be «cen. qu temperature profiles are approximately flat over their respective mass loading regions. aud are very simular iu shape to each other.," As can be seen, the temperature profiles are approximately flat over their respective mass loading regions, and are very similar in shape to each other."
 This coutrasts with the behaviour of their cuuissivity profiles. where it is clear that the solution," This contrasts with the behaviour of their emissivity profiles, where it is clear that the solution"
 (Bertin&Arnouts1996) to the pre- and post-PSF- images. rebinned by a factor of two to produce 071182 pixels.," \citep{1996A&AS..117..393B} to the pre- and post-PSF-subtracted images, rebinned by a factor of two to produce 182 pixels."
 A lo threshold above the sky level. equivalent to a surface-brightness threshold jg.221.1magaaresec 2. was employed with a Gaussian detection kernel matched to the seeing of the target frame.," A $\sigma$ threshold above the sky level, equivalent to a surface-brightness threshold $\mu_K \simeq 21.1\,$ $^{-2}$, was employed with a Gaussian detection kernel matched to the seeing of the target frame."
 Cols., Cols.
 6and 7 of Table |. list the seeing and surface- thresholds for each target frame., 6and 7 of Table \ref{tab:obs} list the seeing and surface-brightness thresholds for each target frame.
 Visual inspection of the target frames confirmed the effectiveness of the analysis and the resultant objects catalogues were not sensitive to small changes in the detection parameters., Visual inspection of the target frames confirmed the effectiveness of the analysis and the resultant objects catalogues were not sensitive to small changes in the detection parameters.
 All the detected objects in the frames were inspected visually and a small number (10) at the extreme edges of the frames. or resulting from a faint satellite trail in one target frame. were eliminated.," All the detected objects in the frames were inspected visually and a small number $\simeq$ 10) at the extreme edges of the frames, or resulting from a faint satellite trail in one target frame, were eliminated."
 The number of objects detected in each targe frame (typically 210) was too small for the morphologica image classitication provided by to prove reliable., The number of objects detected in each target frame (typically $\simeq$ 10) was too small for the morphological image classification provided by to prove reliable.
 Consequently. all objects with A<< 18.5 were classified visually.," Consequently, all objects with $K \le$ 18.5 were classified visually."
 PSF-titting was employed in the few cases where any doub concerning the classification arose., PSF-fitting was employed in the few cases where any doubt concerning the classification arose.
 The parameter was used to provide the magnitude estimate for the detected objects., The parameter was used to provide the magnitude estimate for the detected objects.
 The magnitudes of the quasars were taken from the values provided by the routine., The magnitudes of the quasars were taken from the values provided by the routine.
 After applying the zero-points for each target frame (Section 22)) we detect {ν=20.0 objects in all frames. with the catalogues from the longest exposures in the best seeing containing objects as faint as fy=21.0.," After applying the zero-points for each target frame (Section \ref{sec:obs}) ) we detect $K=20.0$ objects in all frames, with the catalogues from the longest exposures in the best seeing containing objects as faint as $K=21.0$."
 Magnitude errors are estimated from the detected electrons per object and an additional approximation. to take account of the uncertainty in the sky- determination. calculated by shifting the sky-level under the total area of the image by pper cent oftqe 10 fluctuations in the sky background.," Magnitude errors are estimated from the detected electrons per object and an additional approximation, to take account of the uncertainty in the sky-background determination, calculated by shifting the sky-level under the total area of the image by per cent of the $1\sigma$ pixel-to-pixel fluctuations in the sky background."
 Table 2. presents the catalogue of nearest neighbour galaxies. including galaxies within 6700 of each quasar.," Table \ref{tab:galcat} presents the catalogue of nearest neighbour galaxies, including galaxies within 0 of each quasar."
 Cols., Cols.
 2. 3. and 4 give the quasar-galaxy separations in areseconds and Col.," 2, 3, and 4 give the quasar-galaxy separations in arcseconds and Col."
 5 gives the galaxy A -band magnitude., 5 gives the galaxy $K$ -band magnitude.
 The tinal column specities whether the galaxy is the first-. second-. third- or fourth-nearest neighbour to the quasar.," The final column specifies whether the galaxy is the first-, second-, third- or fourth-nearest neighbour to the quasar."
 The total sky coverage of the 36 fields. each covering a 4778 region. excluding a 1700 strip at the frame edges where the image catalogues will be incomplete. is aaremin?.," The total sky coverage of the 36 fields, each covering a $47\farcs8
\times 47\farcs8$ region, excluding a 0 strip at the frame edges where the image catalogues will be incomplete, is $^2$."
 Excluding a 6700 radius circle centred on each of the 35 quasars. which will be used in subsequent analysis of galaxies associated with the quasar absorber. reduces the area to aaremin?.," Excluding a 0 radius circle centred on each of the 35 quasars, which will be used in subsequent analysis of galaxies associated with the quasar absorber, reduces the area to $^2$."
 The number of galaxies is relatively small but the number-counts (Table 3)) are consistent with the results of the K20 survey and the compendium of A-band imaging results presented by Cimattietal.(2002).., The number of galaxies is relatively small but the number-counts (Table \ref{tab:nm}) ) are consistent with the results of the K20 survey and the compendium of $K$ -band imaging results presented by \citet{2002A&A...392..395C}.
 The contribution of stars to the counts fainter than ἐν=18.5 at the high Galactic latitudes of the fields is expected to be small CS5 per cent) (Cimattietal.2002). and all objects fainter than {ν=18.5 are treated as “galaxies” in subsequent statistical analysis.," The contribution of stars to the counts fainter than $K=18.5$ at the high Galactic latitudes of the fields is expected to be small $\la 5\,$ per cent) \citep{2002A&A...392..395C} and all objects fainter than $K=18.5$ are treated as `galaxies' in subsequent statistical analysis."
 The large number of widely-separated fields reduces the impact of large scale structure on the number-counts but. nonetheless. the Poisson errors associated with the observed numbers of galaxies underestimate the uncertainties given the clustering of galaxies.," The large number of widely-separated fields reduces the impact of large scale structure on the number-counts but, nonetheless, the Poisson errors associated with the observed numbers of galaxies underestimate the uncertainties given the clustering of galaxies."
 The selection of the absorber sample deliberately included a bias towards quasars with redshifts well above those of the absorbers., The selection of the absorber sample deliberately included a bias towards quasars with redshifts well above those of the absorbers.
 A small sample of quasars without known intervening absorption line systems was also imaged to provide an empirical control sample., A small sample of quasars without known intervening absorption line systems was also imaged to provide an empirical control sample.
" The median redshift of the quasar sample is 2,,,,/,,71.65 and only five quasars possess redshifts 2«1.4.", The median redshift of the quasar sample is $z_{median}$ =1.65 and only five quasars possess redshifts $z < 1.4$.
 There are three independent results which consistently indicate a low level of contamination of the number-magnitude counts by galaxies physically associated with the quasars themselves., There are three independent results which consistently indicate a low level of contamination of the number–magnitude counts by galaxies physically associated with the quasars themselves.
 Firstly. the spectroscopic results from the K20 survey show only 9pper cent of their fy20.0 sample to possess redshifts >1.5 Cimattietal.(2002)..," Firstly, the spectroscopic results from the K20 survey show only per cent of their $K\le 20.0$ sample to possess redshifts $z > 1.5$ \cite{2002A&A...391L...1C}."
 Secondly. the small control sample of five quasars with 2—1.5 contains just a single galaxy detected within a radius of 6700.," Secondly, the small control sample of five quasars with $z \simeq 1.5$ contains just a single galaxy detected within a radius of 0."
" Finally. the number of galaxies detected within 6700 of the absorber sampο quasars as a function of quasar redshift also provides no evidence for signiticant contamination: 16 galaxies were detected around the 15 quasars with 2«ομως With I4 galaxies detected around the 15 quasars with 2>z,,,,.5,,: and of the five quasars with 2«1.4. two have no detected galaxies."," Finally, the number of galaxies detected within 0 of the absorber sample quasars as a function of quasar redshift also provides no evidence for significant contamination: 16 galaxies were detected around the 15 quasars with $z < z_{median}$, with 14 galaxies detected around the 15 quasars with $z > z_{median}$; and of the five quasars with $z < 1.4$, two have no detected galaxies."
 The A-band magnitudes of host galaxies of quasars with 12oxX 2. which are not strong radio sources and possess absolute magnitudes within the range covered by our sample. are typically A~19 (e.g.Falomoetal.2004:Kotilainen2006)..," The $K$ -band magnitudes of host galaxies of quasars with $1 \le z \le
2$ , which are not strong radio sources and possess absolute magnitudes within the range covered by our sample, are typically $K \sim 19$ \citep[e.g.][]{2004ApJ...604..495F, 2006NewAR..50..772K}."
" While no account of the radio properties of the quasars was taken when selecting the sample. only one of the quasars (SDSS J120300.96+063440.8 at 222.182. with a ratio of radio to /-band optical flux //;c 3.3) is a strong radio source (41,71.0Iveziéetal. 20024.."," While no account of the radio properties of the quasars was taken when selecting the sample, only one of the quasars (SDSS J120300.96+063440.8 at $z$ =2.182, with a ratio of radio to $i$ -band optical flux $R_i \simeq 3.3$ ) is a strong radio source \citep[$R_i > 1.0$][]{2002AJ....124.2364I}."
 Although the expected magnitudes of the quasar host galaxies lie above the magnitude limit of our object catalogues (A.= 20.0).the size and surface brightness properties of the host galaxies effectively preclude their detection via the techniques employed to identify potential absorber host galaxies.," Although the expected magnitudes of the quasar host galaxies lie above the magnitude limit of our object catalogues $K=20.0$ ),the size and surface brightness properties of the host galaxies effectively preclude their detection via the techniques employed to identify potential absorber host galaxies."
 The quasar host galaxies are physically large. with half-light radii typically exceeding 170. and the surface brightnesses are low. not least because of the," The quasar host galaxies are physically large, with half-light radii typically exceeding $1\farcs0$ , and the surface brightnesses are low, not least because of the"
increasing trend are consistent with observations.,increasing trend are consistent with observations.
" We note that, when non-LTE effect taken into account, Na abundance of some stars for which high [Na/Fe] value is reported decreases to [Na/Fe]~—0.2 (Andrievskyetal."," We note that, when non-LTE effect taken into account, Na abundance of some stars for which high $\abra{Na}{Fe}$ value is reported decreases to $\abra{Na}{Fe}\sim -0.2$ \citep{Andrievsky07}."
 2007).. [Cr/Fe| shows a decreasing trend as decreasing metallicity., $\abra{Cr}{Fe}$ shows a decreasing trend as decreasing metallicity.
" The predicted relative abundance is not consistent with the observations of EMP stars, as pointed out by Kobayashietal.(2006)."," The predicted relative abundance is not consistent with the observations of EMP stars, as pointed out by \citet{Kobayashi06}."
. We note that the sample of Hondaetal.(2004) is distributed around [Cr/Fe]=0 and consistent with model results., We note that the sample of \citet{Honda04} is distributed around $\abra{Cr}{Fe}=0$ and consistent with model results.
" However, the First Stars sample and Aoki's sample show clear decreasing trend with small scatter."," However, the First Stars sample and Aoki's sample show clear decreasing trend with small scatter."
" In the models in this paper, Zn is mainly produced by O-Ne-Mg SNe since Wanajoetal. predict a large Zn yield for O-Ne-Mg SNe."," In the models in this paper, Zn is mainly produced by O-Ne-Mg SNe since \citet{Wanajo09} predict a large Zn yield for O-Ne-Mg SNe."
" Hypernovae(2009) are also important sources of Zn, especially at very low metallicity."," Hypernovae are also important sources of Zn, especially at very low metallicity."
" For EMP stars, all observational subsamples show similar abundance distribution and they are consistent with the model result."," For EMP stars, all observational subsamples show similar abundance distribution and they are consistent with the model result."
 Observations show an increasing trend of [Zn/Fe] as decreasing metallicity., Observations show an increasing trend of $\abra{Zn}{Fe}$ as decreasing metallicity.
 Both subsamples by the First Stars group and Aoki et al., Both subsamples by the First Stars group and Aoki et al.
 also show clear increasing trend with small scatter., also show a clear increasing trend with small scatter.
 The model aresult shows flat distribution and predicts lower [Zn/Fe] at—2., The model result shows flat distribution and predicts lower $\abra{Zn}{Fe}$ at.
" Recentry, Yamadaetal.(2011) shows that a decrease in [Zn/Fe] above [Fe/H]>—2.2 may be due to changeover of the IMF from high mass to low mass."," Recentry, \citet{Yamada11} shows that a decrease in $\abra{Zn}{Fe}$ above $\feoh>-2.2$ may be due to changeover of the IMF from high mass to low mass."
 The IMF changeover lowers the frequency of hypernova and lowers the [Zn/Fe]., The IMF changeover lowers the frequency of hypernova and lowers the $\abra{Zn}{Fe}$.
 The contribution from hypernovae is discussed again with resultsof the model without hypernovae in Section ??.., The contribution from hypernovae is discussed again with resultsof the model without hypernovae in Section \ref{hyperS}.
" At [Fe/H]=-2 to -—1, the model predict higher [Zn/Fe] than observations."," At $\feoh=-2$ to $-1$, the model predict higher $\abra{Zn}{Fe}$ than observations."
 Zn thought to be overproduced by O-Be-Mg SNe., Zn thought to be overproduced by O-Be-Mg SNe.
 Criterion to be O-Ne-Mg SNe is not yet revealed (Herwig2005) and the number of O-Ne-Mg SNe can be smaller., Criterion to be O-Ne-Mg SNe is not yet revealed \citep{Herwig05} and the number of O-Ne-Mg SNe can be smaller.
 Predicted scatter of Zn is larger than other elements., Predicted scatter of Zn is larger than other elements.
 This is because hypernovae and O-Ne-Mg SNe eject matter with high but normal SNe with mass m>20Mo eject a small [Zn/Fe]amount of Zn., This is because hypernovae and O-Ne-Mg SNe eject matter with high $\abra{Zn}{Fe}$ but normal SNe with mass $m>20\msun$ eject a small amount of Zn.
 Figures 7 and 8 show predicted abundance ratio distributions by models using different IMF's., Figures \ref{CK} and \ref{LK} show predicted abundance ratio distributions by models using different IMFs.
 Model CK predicts similar typical abundance ratio to Model KK., Model CK predicts similar typical abundance ratio to Model KK.
" O, Mg and Si, are mainly provided by stars with mass heavier than 20Mo and iron is ejected by all SNe II and SNe Ia. For EMP stars, [a/Fe] depends on fraction of stars with >20Mc among SNe II and it dependsa on the IMF."," O, Mg and Si, are mainly provided by stars with mass heavier than $20\msun$ and iron is ejected by all SNe II and SNe Ia. For EMP stars, $\alphafe$ depends on a fraction of stars with $>20\msun$ among SNe II and it depends on the IMF."
" For Models KK and CK, typical mass of stars is quite different but the slope of the IMFs at mass range to be SNe II (10—50 Mo) is similar, as seen in Fig. 1.."," For Models KK and CK, typical mass of stars is quite different but the slope of the IMFs at mass range to be SNe II $10-50\msun$ ) is similar, as seen in Fig. \ref{IMFs}. ."
 Relative frequency of heavier (>20 Mo) and lighter (<20 Mc) SNe II are similar for both IMFs and typical, Relative frequency of heavier $>20\msun$ ) and lighter $<20\msun$ ) SNe II are similar for both IMFs and typical
The robustness of the derived luminosity has been explored » considering two low-redshift objects in the list of RR with detections in all bands (RAS 07380.2342 and IRAS 18216|6418).,The robustness of the derived luminosity has been explored by considering two low-redshift objects in the list of RR with detections in all bands (IRAS 07380–2342 and IRAS 18216+6418).
 Similarly to the approach adopted here. he Et luminosities have been derived by Γη from a multi-component model fit of the SED. and are found to agree o within with the values determined by the method oescribed by Sanders Mirabel (1996).," Similarly to the approach adopted here, the IR luminosities have been derived by RR from a multi-component model fit of the SED, and are found to agree to within with the values determined by the method prescribed by Sanders Mirabel (1996)."
 We conclude that estimates of the total LR luminosity are fairly insensitive o the choice of the method. used. although the relatively ow value we obtain for (coupled with the quite large uncertainties in the Ht Uuxes) indicates that this object can only be formally considered as a candidate LIVLIC at this stage.," We conclude that estimates of the total IR luminosity are fairly insensitive to the choice of the method used, although the relatively low value we obtain for (coupled with the quite large uncertainties in the IR fluxes) indicates that this object can only be formally considered as a candidate HyLIG at this stage."
 CGravitational lensing is known to enhance the luminosity in à number of IIvLICGs (e.g.. Serjeant 1995).," Gravitational lensing is known to enhance the luminosity in a number of HyLIGs (e.g., Serjeant 1995)."
 While our data do not allow us to rule out lens magnification at this stage. this possibility can be explored in the future via high-resolution4S1 imaging or by secking for intervening Me LE absorbers in. high-quality. mocdoerate-resolution spectroscopic data (e.g. Goodrich 1996).," While our data do not allow us to rule out lens magnification at this stage, this possibility can be explored in the future via high-resolution imaging or by seeking for intervening Mg II absorbers in high-quality, moderate-resolution spectroscopic data (e.g., Goodrich 1996)."
 We compare in Figure 4 the SED of with a sample of LvblGs with optical evidence for quasar activity., We compare in Figure 4 the SED of with a sample of HyLIGs with optical evidence for quasar activity.
 It can be seen that Gvhich is the cast Luminous in this subset) presents a relative excess in he far-LR., It can be seen that (which is the least luminous in this subset) presents a relative excess in the far-IR.
 Interestingly. the strongest. outlier. (BR. 1202W725) is also the most luminous (RR).," Interestingly, the strongest outlier (BR 1202--0725) is also the most luminous (RR)."
 This trend of hotter colour temperature with increasing luminosity might suggest an increasing contribution [from ACG:N emission. at. high uminoslties (see also Llaas 2000)., This trend of hotter colour temperature with increasing luminosity might suggest an increasing contribution from AGN emission at high luminosities (see also Haas 2000).
 However. such an ellect is not apparent in the sample of quasars studied by ουσία (2000).," However, such an effect is not apparent in the sample of quasars studied by Polletta (2000)."
 Phe detection of a large reservoir of molecular gas in Bl 12020725 (Ohta 1996). but not in PG 1634)706 (Barvainis 1998) also seems to be at variance with this simple picture.," The detection of a large reservoir of molecular gas in BR 1202–0725 (Ohta 1996), but not in PG 1634+706 (Barvainis 1998) also seems to be at variance with this simple picture."
 We also show in Fig.4 the mean SED for raclio-quiet quasars in the UVSX sample (elvis 1994)., We also show in Fig.4 the mean SED for radio-quiet quasars in the UVSX sample (Elvis 1994).
 Lt can be seen that displays a significant far-LR excess compared to this population. hence giving credence to the existence ofa starburst contributing to the Ht output.," It can be seen that displays a significant far-IR excess compared to this population, hence giving credence to the existence of a starburst contributing to the IR output."
 Indicative of the unsuallv strong level of LR emission from is the fact that a number of more powerful quasars in the optical regime are member of the HNLIC class (MeMahon 1999)., Indicative of the unsually strong level of IR emission from is the fact that a number of more powerful quasars in the optical regime are member of the HyLIG class (McMahon 1999).
 Assuming a Salpeter initial mass function. we derive from the luminosity of the starburst component a current star-formation rate in the range: 1-7 105 hu AL. 1. depending. upon the stellar low- aud hieh-mass cutolls assumed (see Thronson Telesco 1986).," Assuming a Salpeter initial mass function, we derive from the luminosity of the starburst component a current star-formation rate in the range: 1-7 $\times$ $^{3}$ $h_{65}^{-2}$ $_{\odot}$ $^{-1}$, depending upon the stellar low- and high-mass cutoffs assumed (see Thronson Telesco 1986)."
Over the last vear or so. different groups have presente simulations aimed at studvine the ellect of radiative cooling and feedback on the N ray properties of the ICM.,"Over the last year or so, different groups have presented simulations aimed at studying the effect of radiative cooling and feedback on the $X$ –ray properties of the ICM."
 Mos of these studies are based on simulations which follow the eas hydrodynamics within the full volume of a cosmologica box (e.g.. Muanwong et al.," Most of these studies are based on simulations which follow the gas hydrodynamics within the full volume of a cosmological box (e.g., Muanwong et al."
 2002: Dave ct al., 2002; Davé et al.
 2002: Kav ο al., 2002; Kay et al.
 2002), 2002).
 One common result of these simulations. which agrees with what we find in our analysis. is that the effec of cooling is able to alleviate or even solve the discrepancy between simulated ancl observed VY ray scaling properties of clusters and. groups. but the fraction of barvons convertec into stars is too large.," One common result of these simulations, which agrees with what we find in our analysis, is that the effect of cooling is able to alleviate or even solve the discrepancy between simulated and observed $X$ –ray scaling properties of clusters and groups, but the fraction of baryons converted into stars is too large."
 To remedy this problem. \luanwong et al. (," To remedy this problem, Muanwong et al. ("
"2002) preheated the eas by adding 1.5 keV therma energv to all the gas particles at cs,=4.",2002) pre–heated the gas by adding 1.5 keV thermal energy to all the gas particles at $z_h=4$.
 As a result. rey found. that the cold. fraction in. groups and. clusters is decreased. [rom 15 per cent to 0.4 per cent. which is," As a result, they found that the cold fraction in groups and clusters is decreased from 15 per cent to 0.4 per cent, which is"
"around ""50 Mey/nucleon. and are accompanied with emission of 5 at 431 and 478 keV. Lt ijs possible that. the ~ lines observed sometimes around this energy. (Cilfanov et al.","around 50 Mev/nucleon, and are accompanied with emission of $\gamma-$ lines at 431 and 478 keV. It is possible that the $\gamma-$ lines observed sometimes around this energy (Gilfanov et al."
 1991. Sunvaev et αἱ.," 1991, Sunyaev et al."
 1992) are another signature of ion illumination (Alartinn et al., 1992) are another signature of ion illumination n et al.
 1994a.b).," 1994a,b)."
 This work was done in the context of Human Capital and Mobility network “Accretion onto compact objects’. CLIRA-," This work was done in the context of Human Capital and Mobility network `Accretion onto compact objects', CHRX-CT93-0329."
Radio relies are filamentary structures often located in the periphery of galaxy clusters.,Radio relics are filamentary structures often located in the periphery of galaxy clusters.
 It is proposed that large radio relics trace shock waves generated by cluster merger events (22)..," It is proposed that large radio relics trace shock waves generated by cluster merger events \citep{1998A&A...332..395E, 2001ApJ...562..233M}."
 At the shock front particles from the thermal gas are accelerated to relativistic energies by DSA mechanism in a first-order Fermi process (22222222?)..," At the shock front particles from the thermal gas are accelerated to relativistic energies by DSA mechanism in a first-order Fermi process \citep{1977DoSSR.234R1306K, 1977ICRC...11..132A, 1978MNRAS.182..147B, 1978MNRAS.182..443B, 1978ApJ...221L..29B, 1983RPPh...46..973D, 1987PhR...154....1B, 1991SSRv...58..259J, 2001RPPh...64..429M}."
 In the presence of a magnetic field these particles emit synchrotron radiation at radio wavelengths., In the presence of a magnetic field these particles emit synchrotron radiation at radio wavelengths.
 Another possibility mentioned by ?.. is that the shock re-accelerates relativistic fossil electrons injected previously into the ICM by for example AGN.," Another possibility mentioned by \cite{2005ApJ...627..733M}, is that the shock re-accelerates relativistic fossil electrons injected previously into the ICM by for example AGN."
 They note that from an observational point of view. this case will probably be indistinguishable from the direct shock acceleration mentioned above.," They note that from an observational point of view, this case will probably be indistinguishable from the direct shock acceleration mentioned above."
 An alternative scenario has been recently proposed. namely that relics arise from emission of secondary cosmic ray electrons (?)..," An alternative scenario has been recently proposed, namely that relics arise from emission of secondary cosmic ray electrons \citep{2010arXiv1011.0729K}."
" Some smaller radio relics (< S00kpe) have been been explained by old (""fossil) radio plasma from à. previous episode of AGN activity.", Some smaller radio relics $\lesssim 500$ kpc) have been been explained by old (“fossil”) radio plasma from a previous episode of AGN activity.
 These sources are called (see2.foranoverviewoftheclassificationdif-fuseradio sources)..," These sources are called \citep[see][for an overview of 
the classification of diffuse radio sources]{2004rcfg.proc..335K}."
 The fossil radio plasma could also have been compressed. creating a radio (22)..," The fossil radio plasma could also have been compressed, creating a radio \citep{2001A&A...366...26E, 2002MNRAS.331.1011E}."
 Both radio phoenices and AGN relies. are characterized by a very steep (ας—1.5. Εν«v. where « 15 the spectral index) and curved radio spectra due to synchrotron and Inverse Compton (IC) losses.," Both radio phoenices and AGN relics, are characterized by a very steep $\alpha \lesssim -1.5$, $F_{\nu} \propto \nu^{\alpha}$, where $\alpha$ is the spectral index) and curved radio spectra due to synchrotron and Inverse Compton (IC) losses."
 In the hierarchical. model of structure formation. galaxy cluster grow by the accretion of gas from the surrounding intergalactic medium (IGM) and through mergers with other clusters and galaxy groups., In the hierarchical model of structure formation galaxy cluster grow by the accretion of gas from the surrounding intergalactic medium (IGM) and through mergers with other clusters and galaxy groups.
 Large radio relies are exclusively found in disturbed clusters. indicative of merger activity.," Large radio relics are exclusively found in disturbed clusters, indicative of merger activity."
 This supports the idea that shocks generated during cluster merger events can be responsible for the non-thermalradio emission., This supports the idea that shocks generated during cluster merger events can be responsible for the non-thermalradio emission.
 Hydrodynamical models of structure formation. including particle acceleration mechanisms (e.g..2222) make predictions about the location. orientation and radio power of relics in merging clusters.," Hydrodynamical models of structure formation, including particle acceleration mechanisms \citep[e.g.,][]{2007MNRAS.375...77H, 2008MNRAS.391.1511H, 2008MNRAS.385.1242P, 2009MNRAS.393.1073B} make predictions about the location, orientation and radio power of relics in merging clusters."
 Amongst the several dozen radio relics known to date (e.g...22222222). there are a few rare double relicsystems. with two relies located symmetrically oi opposite sites of the cluster center (e.g..22222??).. ," Amongst the several dozen radio relics known to date \citep[e.g., ][]{2009A&A...508...75V, 2009ApJ...697.1341R, 2009A&A...507..639P, 2008A&A...486..347G, 2008A&A...489...69B, 2001ApJ...548..639K, 1999NewA....4..141G, 1991A&A...252..528G}, there are a few rare double relicsystems, with two relics located symmetrically on opposite sites of the cluster center \citep[e.g., ][]{2010Sci...330..347V, 2010arXiv1011.4985B, 2009A&A...494..429B, 2009A&A...506.1083V, 2007A&A...463..937V, 2006Sci...314..791B, 1997MNRAS.290..577R}."
These double relics can be used to constrain the merger geometry and timescales involved (?).., These double relics can be used to constrain the merger geometry and timescales involved \citep{1999ApJ...518..603R}.
 If radio relies. trace. outward traveling shock waves in which DSA takes place. then the radio plasma in the post-shock region should have a steeper spectrum due to IC and synchrotron losses.," If radio relics trace outward traveling shock waves in which DSA takes place, then the radio plasma in the post-shock region should have a steeper spectrum due to IC and synchrotron losses."
 For a relic seer close to edge-on. the luminosity profile across the width of the relic can then be used to constrain the magnetic fields strength at the location of the shock (2?).. ," For a relic seen close to edge-on, the luminosity profile across the width of the relic can then be used to constrain the magnetic fields strength at the location of the shock \citep[][]{2005ApJ...627..733M, 2010arXiv1004.2331F}."
This is because the downstream luminosity profileshould directly reflect the synchrotron losses. which in turn depend on the magnetic field strength.," This is because the downstream luminosity profileshould directly reflect the synchrotron losses, which in turn depend on the magnetic field strength."
 In ? we presented observations of a double relic in the merging clusterJ2242.8+5301.. which provided evidence for DSA in galaxy cluster merger shocks.," In \cite{2010Sci...330..347V} we presented observations of a double relic in the merging cluster, which provided evidence for DSA in galaxy cluster merger shocks."
 For the largest relic we derived a magnetic field strength of about 5—7 u Gauss by modeling the relic’s luminosity profile across the width of the relic (although a strength of about 1.2 Gauss could not be completely ruled out)., For the largest relic we derived a magnetic field strength of about 5--7 $\mu$ Gauss by modeling the relic's luminosity profile across the width of the relic (although a strength of about 1.2 $\mu$ Gauss could not be completely ruled out).
 Because there are only a few double relies systems known. we carried out an extensive search in the 1.4 GHz NVSS (?).. 325 MHz WENSS (?).. and 74 MHz VLSS (?) surveys for the presence of are-like radio structures around X-ray selected galaxy clusters from the ROSAT All-Sky Survey.," Because there are only a few double relics systems known, we carried out an extensive search in the 1.4 GHz NVSS \citep{1998AJ....115.1693C}, 325 MHz WENSS \citep{1997A&AS..124..259R}, and 74 MHz VLSS \citep{2007AJ....134.1245C} surveys for the presence of arc-like radio structures around X-ray selected galaxy clusters from the ROSAT All-Sky Survey."
 This search already resulted in the discovery of several new radio relics. see ???.. ," This search already resulted in the discovery of several new radio relics, see \cite{2009A&A...506.1083V, 2009A&A...508...75V, 2009A&A...505..991V}."
In this paper we present the discovery of a double relic in the galaxy cluster which showed faint elongated structures in both NVSS and WENSS images., In this paper we present the discovery of a double relic in the galaxy cluster which showed faint elongated structures in both NVSS and WENSS images.
 The layout of this paper is as follows., The layout of this paper is as follows.
 In Sect., In Sect.
 2 we give an overview of the observations and the data reduction., \ref{sec:obs-reduction} we give an overview of the observations and the data reduction.
 In Sect., In Sect.
 3 we present the radio and spectral index maps as well as optical images around the radio sources., \ref{sec:results} we present the radio and spectral index maps as well as optical images around the radio sources.
 In Sect., In Sect.
 + wediscuss the merger scenario and the magnetic field strength at the location of the relics., \ref{sec:discussion} wediscuss the merger scenario and the magnetic field strength at the location of the relics.
 We end with conclusions in Sect. 5.., We end with conclusions in Sect. \ref{sec:conclusion}. .
" Throughout this paper we assume a ACDM cosmology with Hy=71 km s! Mpe7!. O,,= 0.3. and Q4= 0.7."," Throughout this paper we assume a $\Lambda$ CDM cosmology with $H_{0} = 71$ km $^{-1}$ $^{-1}$ , $\Omega_{m} = 0.3$ , and $\Omega_{\Lambda} = 0.7$ ."
 All images are in the J2000 coordinate system., All images are in the J2000 coordinate system.
information content in these features is rich. and provides iuportant constraints on the dynamical history of these ealaxies.,"information content in these features is rich, and provides important constraints on the dynamical history of these galaxies."
 With these factors in mund. if is mteresting to study the diffuse lieht around elliptical galaxies m a cluster environment.," With these factors in mind, it is interesting to study the diffuse light around elliptical galaxies in a cluster environment."
 As part of our ongoing survey for ICL in the Virgo cluster (Milos 2005). we have obtained deep. wide-field nuagiug of the Virgo cllipticals AIST (NGC L186). MSG (NCC 1106). M81 (NGC. 137D. M89 (NGC. 1552). and ALLO (NGC 1172).," As part of our ongoing survey for ICL in the Virgo cluster (Mihos 2005), we have obtained deep, wide-field imaging of the Virgo ellipticals M87 (NGC 4486), M86 (NGC 4406), M84 (NGC 4374), M89 (NGC 4552), and M49 (NGC 4472)."
 These galaxies. all occupy different environments within the cluster (sec. Binegecli 1999 for a review of the structure of he Virgo Cluster).," These galaxies all occupy different environments within the cluster (see, Binggeli 1999 for a review of the structure of the Virgo Cluster)."
 As the central dominant elliptical in the Virgo cluster. ALS? lives near the ceuter of the cluster potential well (as defined by the X-ray enission: Bolainecr 1991). and represeuts the center of the uost massive suberoup of galaxies in the Vireo Cluster.," As the central dominant elliptical in the Virgo cluster, M87 lives near the center of the cluster potential well (as defined by the X-ray emission; Bohringer 1994), and represents the center of the most massive subgroup of galaxies in the Virgo Cluster."
" AISG and MSIE lie ~1.3"" (370 to the nortlisvest of MST: they are separated youn cach other by. ((T8 kpe) iu projection. close enough that. at faint surface briehtuesses. their extended lalos appear to ucree together iuto a conunon euvelope of light (Milos 2005)."," M86 and M84 lie $\sim1.3$ (370 to the northwest of M87; they are separated from each other by (78 kpc) in projection, close enough that, at faint surface brightnesses, their extended halos appear to merge together into a common envelope of light (Mihos 2005)."
 This is likely a projection effect. however. as distance estimates from surface brightness fluctuations place M81 about 1 Mpe behind. M86 (Moi 2007).," This is likely a projection effect, however, as distance estimates from surface brightness fluctuations place M84 about 1 Mpc behind M86 (Mei 2007)."
 Tudeed. from a combined optical aud. N-ray analysis of the cluster. Schiudler (1999) suggest that M86 sits at the center of its own subcluster of galaxies mereiue with the main body of the cluster.," Indeed, from a combined optical and X-ray analysis of the cluster, Schindler (1999) suggest that M86 sits at the center of its own subcluster of galaxies merging with the main body of the cluster."
 MIS9 lies ~1.2° ((335 kpe) to the East of M87 aud is the least Iuninuous of our selected elliptical galaxies., M89 lies $\sim1.2$ (335 kpc) to the East of M87 and is the least luminous of our selected elliptical galaxies.
 Finally. wine tto the south of ALS7. ALLO as the brightest. elliptical in Virgo. aud defines the ceuter of another distinct Virgo subgroup (cluster D) which is dominated by spiral ealaxies (Bingech. Tanuuaun. Saudage 1987).," Finally, lying to the south of M87, M49 is the brightest elliptical in Virgo, and defines the center of another distinct Virgo subgroup (cluster B) which is dominated by spiral galaxies (Binggeli, Tammann, Sandage 1987)."
 The different dynanücal environments these ellipticals find themselves iu is likely to trauslate to differences im the structure of their extended Iuminous halos., The different dynamical environments these ellipticals find themselves in is likely to translate to differences in the structure of their extended luminous halos.
 lu this work. we study tιο diffuse outer halos of hese elipticals. searching for ticlal structures that may race the dynamical histories of these galaxies.," In this work, we study the diffuse outer halos of these ellipticals, searching for tidal structures that may trace the dynamical histories of these galaxies."
 We use our deep inaging to fit and subtract a sinooth elliptical fit to cach ealaxw’s light profile. and ideutifv tidal features in the residual images (for a similar approach. sec. Canalizo 2007).," We use our deep imaging to fit and subtract a smooth elliptical fit to each galaxy's light profile, and identify tidal features in the residual images (for a similar approach, see, Canalizo 2007)."
 We then measure the total huninosity aud peak surface brightuess of each of the cataloged features., We then measure the total luminosity and peak surface brightness of each of the cataloged features.
 We describe the observational dataset and analysis techuiqucs ii 822. aud detail the results for cach ealaxy in 8233.," We describe the observational dataset and analysis techniques in 2, and detail the results for each galaxy in 3."
 Finally. we cud with a discussion of these features in the more general contest of the luerarchical asscunbly of galaxies aud galaxy clusters iu &1I.," Finally, we end with a discussion of these features in the more general context of the hierarchical assembly of galaxies and galaxy clusters in 4."
 The nuagiug data preseuted here were taken as part of our ongoing survey for diffuse intracluster light iu the Virgo cluster (sec. Afihos 2005. 2009: Rudick 2010) using Case Western Reserve Uulversitvs 0.6/0.9012. Burrell Schiaidt telescope located at itt Peal National Observatory.," The imaging data presented here were taken as part of our ongoing survey for diffuse intracluster light in the Virgo cluster (see, Mihos 2005, 2009; Rudick 2010) using Case Western Reserve University's 0.6/0.9m Burrell Schmidt telescope located at Kitt Peak National Observatory."
 The data were takeu over the course of three observiug seasons in Spring 2001. 2005. and 2006.," The data were taken over the course of three observing seasons in Spring 2004, 2005, and 2006."
 ALS6 aud M81 were mnuaeed in Spring 20014. ALS9 in Spring 2005. N19 in Spring 2006. aud M87 in both Spring 2001 and 2005 (see Table 13).," M86 and M84 were imaged in Spring 2004, M89 in Spring 2005, M49 in Spring 2006, and M87 in both Spring 2004 and 2005 (see Table \ref{obsdata}) )."
 In all seasons. the data were taken uuder dark. photometric conditions at airmasses less than |," In all seasons, the data were taken under dark, photometric conditions at airmasses less than 1.5."
" The SITe 2015x1096 CCD iaees a field of view of0.75""x 1.5udug 1.15"" pixels. aud we build a larger mosaic by dithering our observations by up to one degree per feld."," The SITe 2048x4096 CCD images a field of view of x using $1.45\arcsec$ pixels, and we build a larger mosaic by dithering our observations by up to one degree per field."
 Individual exposures are 9008 long. aud mosaics are iade using 45117 dithered exposures im each field.," Individual exposures are 900s long, and mosaics are made using 45–117 dithered exposures in each field."
 Observations are taken through the Washington M filter. which is simular to Jolusou V but bluer bv ~ 300 aand cuts out the strong and variable sky ciissiou line at [O I| ΑΡΛΤΤΑ.," Observations are taken through the Washington M filter, which is similar to Johnson V but bluer by $\sim$ 300 and cuts out the strong and variable sky emission line at [O I] $\lambda5577$."
", To construct accurate flat fields. we tage blank sky fields (typically SO.120 per season) at nearly the same iour angle and declination as Virgo observations."," To construct accurate flat fields, we image blank sky fields (typically 80–120 per season) at nearly the same hour angle and declination as Virgo observations."
 This observing pattern reduces the effect on the flat ficlds of any flexure in the telescope system., This observing pattern reduces the effect on the flat fields of any flexure in the telescope system.
 Each might sky πασο ad a 900s exposure time. aud the brightuess of the night sky varied frou 1100-1500 ADU in the images.," Each night sky image had a 900s exposure time, and the brightness of the night sky varied from 1100-1500 ADU in the images."
 IRAF’s OBJALASIS task was used to mash. stars and ealaxies on he blank sky images. after which an ieratfivo process was applied to fit and remove planar eracdicuts in the skv levels before median combining the skies to create a super sky flat (sce Feldicier 2002 aud Ruclick 2010 for complete details).," IRAF's OBJMASK task was used to mask stars and galaxies on the blank sky images, after which an iterative process was applied to fit and remove planar gradients in the sky levels before median combining the skies to create a super sky flat (see Feldmeier 2002 and Rudick 2010 for complete details)."
 Ouce flattened. the images are then star-subtracted to remove the exteuded wines of bright stars from the data.," Once flattened, the images are then star-subtracted to remove the extended wings of bright stars from the data."
 To coustruct the stellar poiut spread fiction. we start bv using short exposures of moderately bright stars to define he small-scale PSF (e« 307).," To construct the stellar point spread function, we start by using short exposures of moderately bright stars to define the small-scale PSF $r<30\arcsec$ )."
 At laveer scales ος 2307) we use 9008 exposures of aLeo to coustruct the PSF out or 0.1..., At larger scales $r>30\arcsec$ ) we use 900s exposures of $\alpha$ Leo to construct the PSF out to $r \sim 0.4$ .
 The resulting large-scale (7> 107) PSFs are shown in Figure 1.., The resulting large-scale $r>10\arcsec$ ) PSFs are shown in Figure \ref{psf}.
 Between the 2001 aud 2005 seasous. he priuary nurror was realuniized aud the interior of the telescope tube was flocked with black velvet to reduce scattered light.," Between the 2004 and 2005 seasons, the primary mirror was realuminized and the interior of the telescope tube was flocked with black velvet to reduce scattered light."
 These iiprovenieuts reduced the xightuess of stella wings by about 2.5 mae/aresec? at aree radius (rp~ 207.," These improvements reduced the brightness of stellar wings by about 2.5 $^2$ at large radius $r\sim
20\arcmin$ )."
 With the recoustructed PSF. we hen mask stars out to the radius where their scaled PSF falls below 3 ADU (jaye 28) and then subtract he extended wings out to 0.5 ADU (fare 30).," With the reconstructed PSF, we then mask stars out to the radius where their scaled PSF falls below 3 ADU $\approx 28$ ) and then subtract the extended wings out to 0.5 ADU $\approx
30$ )."
 For the 2001 data reduction. star subtraction was done on the," For the 2004 data reduction, star subtraction was done on the"
almosphere available to us. (,atmosphere available to us. (
2) The optical spectra were observed through (hin clouds so an empirical scaling factor was applied to the observed fluxes to match them to the synthetic spectrum (the latter was scaled to fit (he FUV spectrum).,2) The optical spectra were observed through thin clouds so an empirical scaling factor was applied to the observed fluxes to match them to the synthetic spectrum (the latter was scaled to fit the FUV spectrum).
 Fig., Fig.
 8 of 12004 shows the model fit to observed spectra. covering the interval toT800A.. including archivedUE spectra SWPI0905. covering to1973À.. and LWRO9590. covering (oÀ.. which were obtaàned on 1930 Dec. 27.," 8 of H2004 shows the model fit to observed spectra, covering the interval to, including archived spectra SWP10905, covering to, and LWR09590, covering to, which were obtained on 1980 Dec. 27."
 Fig., Fig.
 1 of this paper presents (he model fit to the same low stateZUE spectra in much greater detail (han in 112004., 1 of this paper presents the model fit to the same low state spectra in much greater detail than in H2004.
 Note that Fig., Note that Fig.
 8 of 1122004 is a logzritimnic plot while Fie., 8 of H2004 is a logaritmic plot while Fig.
 l of this paper plots flux directly., 1 of this paper plots flux directly.
 In producing Fig., In producing Fig.
 1. the spectra were divided by the same scaling factors applied in the I12004 plots (2.43x107? for the WD synthetic spectrum. 1.010.' for theZUE spectra). set by the fit to the FUSE spectrum.," 1, the spectra were divided by the same scaling factors applied in the H2004 plots	 $2.43{\times}10^{29}$ for the WD synthetic spectrum, $1.0{\times}10^{-13}$ for the spectra), set by the fit to the FUSE spectrum."
 The mean residual of the lit to the 877 points between and was 0.012 and the mean absolute residual was 0.038., The mean residual of the fit to the 877 points between and was 0.012 and the mean absolute residual was 0.038.
 These residuals apply to the scaled spectra., These residuals apply to the scaled spectra.
 An important conclusion from the Fig., An important conclusion from the Fig.
 1 fit is that there is no evidence for the presence of an accretion disk., 1 fit is that there is no evidence for the presence of an accretion disk.
 In a test of the sensitivity of the fit to added flux from a putative accretion disk. we find empirically that addition of 0.005 Παν units (Fig.," In a test of the sensitivity of the fit to added flux from a putative accretion disk, we find empirically that addition of 0.005 flux units (Fig."
 1 ordinates) produces a visually detectable displacement of the summed spectrum from the Fie., 1 ordinates) produces a visually detectable displacement of the summed spectrum from the Fig.
 1 fit., 1 fit.
 At3000A.. the secondary star makes a calculated contribution of to the svstem Παν.," At, the secondary star makes a calculated contribution of to the system flux."
 112004 fit an optical (unfiltered) light curve of MV Lav (their Fig., H2004 fit an optical (unfiltered) light curve of MV Lyr (their Fig.
 7)., 7).
 This fit was derived from the BINSYN spectral model described above., This fit was derived from the BINSYN spectral model described above.
 It assumes an orbital inclination for the CV of (=12° from Skillman.Patterson.&Thorstensen(1995.hereafterSPT95).., It assumes an orbital inclination for the CV of $i = 12{\arcdeg}$ from \citet*[hereafter SPT95]{spt95}.
 However. the corresponding amplitude of the model light eurve is too large.," However, the corresponding amplitude of the model light curve is too large."
 The orbital period light variation results from the variable presentation of the irradiated secondary component io the observer., The orbital period light variation results from the variable presentation of the irradiated secondary component to the observer.
 As the assumed inclination decreases from ;=12. the light amplitude decreases monotonicallv.," As the assumed inclination decreases from $i = 12{\arcdeg}$, the light amplitude decreases monotonically."
 An improved fit (Linnelletal.2005) implies à svstem inclination ol;—741°. which we adopt for this analysis.," An improved fit \citep{l2005} implies a system inclination of $i = 7{\pm}1{\arcdeg}$, which we adopt for this analysis."
 A remark is in order on the absolute accuracy of the results obtained in this paper., A remark is in order on the absolute accuracy of the results obtained in this paper.
 A Κον step is in the determination of the WD mass and radius in units of the solar values by comparison between the MV Lyr WD log g from our analvsis of the FUSE spectrum and the log gvalues lor the Ilamacda&Salpeter(1961). carbon. WD models.," A key step is in the determination of the WD mass and radius in units of the solar values by comparison between the MV Lyr WD log $g$ from our analysis of the FUSE spectrum and the log $g$values for the \citet*{hs61}
 carbon WD models."
 The mass ratio. q. comes from relatively uncertain radial velocitv measurements (SPT95). and (his value determines the mass of the secondary star and. since the secondary fills its Roche lobe. the size ol the secondary star.," The mass ratio, $q$, comes from relatively uncertain radial velocity measurements (SPT95), and this value determines the mass of the secondary star and, since the secondary fills its Roche lobe, the size of the secondary star."
 The fit of our svnthetic spectra to FUV data. in all cases. applies a scaling divisor. 2.43x107°. to observed. spectra which were divided by 1.0x1013 (see the ordinate labels).," The fit of our synthetic spectra to FUV data, in all cases, applies a scaling divisor, $2.43{\times}10^{29}$, to observed spectra which were divided by $1.0{\times}10^{-13}$ (see the ordinate labels)."
 The scaling divisor may be inaccurate by to1554., The scaling divisor may be inaccurate by to.
.. We present here an improved representation of the secondary. star. using tlie NextGen svuthelic spectra lor M stars. version 5 (Ilauschiklietal... 1999)..," We present here an improved representation of the secondary star, using the NextGen synthetic spectra for M stars, version 5 \citep{haus99}. ."
 We find a good [it to, We find a good fit to
The smearing of the reflection features by high velocities is a natural consequence of the presence of an inner accretion disc.,The smearing of the reflection features by high velocities is a natural consequence of the presence of an inner accretion disc.
 Undoubtedly. an inner accretion dise must exists in sources accreting above a few per cent of the Eddington ratio and thus. unlikely the smeared absorption model. the dise reflection model does not introduce any new (so far unobserved. if not for the soft excess interpretation itself) component to explain the soft excess.," Undoubtedly, an inner accretion disc must exists in sources accreting above a few per cent of the Eddington ratio and thus, unlikely the smeared absorption model, the disc reflection model does not introduce any new (so far unobserved, if not for the soft excess interpretation itself) component to explain the soft excess."
 The reflection interpretation just makes use of the basic ingredients of accretion theory. a powerful primary source of hard X-rays. and an optically thick accretion dise which reprocesses the irradiating flux into a reflection spectrum.," The reflection interpretation just makes use of the basic ingredients of accretion theory, a powerful primary source of hard X–rays, and an optically thick accretion disc which reprocesses the irradiating flux into a reflection spectrum."
 An additional external absorber may obviously mask this contribution and this may well be the case in some most extreme sources., An additional external absorber may obviously mask this contribution and this may well be the case in some most extreme sources.
 However. since disc reflection only requires the presence of an inner accretion dise and of an illuminating X-ray source. it is an unavoidable component in any reasonable accretion model for radiatively efficient AGN (and X—ray binaries).," However, since disc reflection only requires the presence of an inner accretion disc and of an illuminating X–ray source, it is an unavoidable component in any reasonable accretion model for radiatively efficient AGN (and X--ray binaries)."
 In fact (see e.g. Middleton. Done Gierlinsski 2007) when the smeared absorption model is applied to PG quasars and NLSIs. it always does require also a dise reflection component.," In fact (see e.g. Middleton, Done Gierlińsski 2007) when the smeared absorption model is applied to PG quasars and NLS1s, it always does require also a disc reflection component."
 If the dise reflection component alone can account for the spectral shape and variability of the sources. it is difficult to understand the need for an additional smeared absorber with problematic launching mechanism. extreme mass outflow rate. and rather unnatural relationship between column density and ionization.," If the disc reflection component alone can account for the spectral shape and variability of the sources, it is difficult to understand the need for an additional smeared absorber with problematic launching mechanism, extreme mass outflow rate, and rather unnatural relationship between column density and ionization."
 Since disc reflection invokes the presence of the accretion disc down to the last stable orbit. thermal emission from the disc should also be present and. given the small black hole masses and relatively high accretion rates in our IMBHs. such emission should peak in the soft X-rays.," Since disc reflection invokes the presence of the accretion disc down to the last stable orbit, thermal emission from the disc should also be present and, given the small black hole masses and relatively high accretion rates in our IMBHs, such emission should peak in the soft X–rays."
 Indeed. when a multicolor dise blackbody is included in the spectral models. a solution in which the soft excess is partly due to reflection and partly to dise blackbody with the theoretically expected temperature is found.," Indeed, when a multicolor disc blackbody is included in the spectral models, a solution in which the soft excess is partly due to reflection and partly to disc blackbody with the theoretically expected temperature is found."
 However. we point out that if thermal dise emission is present in the soft X-ray spectrum of these objects. its luminosity is far below the expected one for the given temperatures not only when reflection is invoked. but even when all the soft excess is modelled as a pure dise blackbody.," However, we point out that if thermal disc emission is present in the soft X–ray spectrum of these objects, its luminosity is far below the expected one for the given temperatures not only when reflection is invoked, but even when all the soft excess is modelled as a pure disc blackbody."
 It is actually difficult to distinguish between the two competing models (smeared absorption and dise reflection) by using spectral and variability information in the limited band—pass of (03-10 keV band) even in bright. well observed sources.," It is actually difficult to distinguish between the two competing models (smeared absorption and disc reflection) by using spectral and variability information in the limited band--pass of (0.3–10 keV band) even in bright, well observed sources."
 Moreover. our mini-sample of small mass BH is not well suited to investigate the problem due to the relatively low quality of the data.," Moreover, our mini–sample of small mass BH is not well suited to investigate the problem due to the relatively low quality of the data."
 High-energy data are crucial to test whether the X-ray spectrum above 10 keV is just the high-energy unabsorbed tail of the intrinsic power law continuum. or whether it is instead characterized by the presence of a Compton hump around 20-30 keV. related to X-ray reflection.," High–energy data are crucial to test whether the X–ray spectrum above 10 keV is just the high–energy unabsorbed tail of the intrinsic power law continuum, or whether it is instead characterized by the presence of a Compton hump around 20–30 keV, related to X–ray reflection."
 While signatures for the presence of X-ray reflection from the inner accretion dise are sometimes detected. the number of well observed sources above 10 keV is still too small to draw any clearcut conclusion (e.g. Miniutti et al 2007: Reeves et al 2007).," While signatures for the presence of X–ray reflection from the inner accretion disc are sometimes detected, the number of well observed sources above 10 keV is still too small to draw any clear–cut conclusion (e.g. Miniutti et al 2007; Reeves et al 2007)."
 Observations with the X-ray mission and with future missions such as (Ferrando et al., Observations with the X–ray mission and with future missions such as Simbol--X (Ferrando et al.
 2006) will most likely play a crucial role in that direction in the near future., 2006) will most likely play a crucial role in that direction in the near future.
 Given their relatively small black hole mass (i.e. small size). the observed IMBH are not surprisingly among the most variable in In particular. their excess variance m5: is among the largest obtained from AGN X-ray light curves.," Given their relatively small black hole mass (i.e. small size), the observed IMBH are not surprisingly among the most variable in In particular, their excess variance $\sigma^2_{\rm NXS}$ is among the largest obtained from AGN X–ray light curves."
 Our observations begin o fill a relatively poorly explored range of black hole masses in he v&x«—Mpag relationship and show that the X-ray variability ooperties of IMBH smoothly join with those of more massive Seyfert galaxies., Our observations begin to fill a relatively poorly explored range of black hole masses in the $\sigma^2_{\rm NXS}$ $M_{\rm BH}$ relationship and show that the X–ray variability properties of IMBH smoothly join with those of more massive Seyfert galaxies.
 The oz«—Mpg is consistent with a simple (well known? anti-correlation that can be explained with a universal PSD model in which the break frequencies (most importantly the high—Tequency one) scale with My.," The $\sigma^2_{\rm
NXS}$ $M_{\rm BH}$ is consistent with a simple (well known) anti–correlation that can be explained with a universal PSD model in which the break frequencies (most importantly the high--frequency one) scale with $M^{-1}_{\rm BH}$."
 However. such functional form or vg is known to be only a zeroth-order approximation (see T Hardy et al 2006) and the universal PSD model suffers also for other uncertainties that do not allow to properly account for the scatter in the relationship.," However, such functional form for $\nu_{\rm H}$ is known to be only a zeroth–order approximation (see $^{\rm c}$ Hardy et al 2006) and the universal PSD model suffers also for other uncertainties that do not allow to properly account for the scatter in the relationship."
" Future longer observations of these and other IMBH in X-rays would allow to explicitly search for the high frequency break in the PSD. enabling us to extend the /u—AZigu- NL relationship pointed out by M* Hardy et al (2006) to the most crucial black hole mass range of A£yg:10""AL.."," Future longer observations of these and other IMBH in X–rays would allow to explicitly search for the high frequency break in the PSD, enabling us to extend the $\nu_{\rm
H}$ $M_{\rm BH}$ $\dot M_{\rm{acc}}$ relationship pointed out by $^{\rm c}$ Hardy et al (2006) to the most crucial black hole mass range of $M_{\rm BH} \leq 10^6~M_\odot$."
 Based on observations obtained with XMM-Newton. an ESA Science mission with instruments and contributions directly funded by ESA Member States and NASA.," Based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA."
 We would like to thank the referee for her/his suggestions that improved our work., We would like to thank the referee for her/his suggestions that improved our work.
 GM thanks the UK STFC and the French CNRS for partial support., GM thanks the UK STFC and the French CNRS for partial support.
 GM also thanks the Spanish Ministerio de Ciencia e InnovaciGnn and CSIC for support through a Ramónn y Cajal contract., GM also thanks the Spanish Ministerio de Ciencia e Innovaciónn and CSIC for support through a Ramónn y Cajal contract.
 ACF thanks the Royal Society for support., ACF thanks the Royal Society for support.
The cosmic microwave background° m(CALB) 3provides one of he cornerstones of the cosmological concordance moclel.,The cosmic microwave background (CMB) provides one of the cornerstones of the cosmological concordance model.
 ⊳∖Phe statisticalD. properties. of our cosmological. models have o match those of the CMD arpin order to give° an admissible⊀⊲ model., The statistical properties of our cosmological models have to match those of the CMB in order to give an admissible model.
 sThus. it is ⊀⊀⋅of utmost importance⊀ to reliably. extract he statistical2. properties. of. the Ar»CM.," Thus, it is of utmost importance to reliably extract the statistical properties of the CMB."
 A main. obstacle is. he foreground.. emissionT. of. our galaxy and of. other sources which. restrict. the area of the sky. available. for⋅ a sullicientIvD. clean CMD. signal. tthe full sky. CAIB signal has to oe masked.," A main obstacle is the foreground emission of our galaxy and of other sources which restrict the area of the sky available for a sufficiently clean CMB signal, the full sky CMB signal has to be masked."
" One path of statistical analysis leads to the Fourier. space in. which. the CMD Alpis decomposed with. respect o spherical: harmonics: 35,090)uno where the masked. sky. leacks o à coupling. between the Fourierun modes since: no full⋅ sky CAIB AIDis available.", One path of statistical analysis leads to the Fourier space in which the CMB is decomposed with respect to spherical harmonics $Y_{lm}(\hat n)$ where the masked sky leads to a coupling between the Fourier modes since no full sky CMB is available.
. In this. paper. we do not delve into. these dillieulties. where upon an extensive literature exists. but instead.. follow. the alternative: path which. allows an analysis. in. the. pixel space.24. which in .turn is moreout. adapted . to à masked sky.," In this paper, we do not delve into these difficulties, where upon an extensive literature exists, but instead follow the alternative path which allows an analysis directly in the pixel space, which in turn is more adapted to a masked sky."
 vThis analysis ow-orderis based on the temperature two-point. correlation. function. )C'(J). which Eis defined. as where 027) is the temperature [fluctuation in the direction of the unit vector #.," This analysis is based on the temperature two-point correlation function $C(\vartheta)$, which is defined as where $\delta T(\hat n)$ is the temperature fluctuation in the direction of the unit vector $\hat n$."
 Phe most direct way to deal with a mask is just to use only those pixels which are outside the mask., The most direct way to deal with a mask is just to use only those pixels which are outside the mask.
 In this wav it was discovered by the CODE team (?) that the correlation function (04) possesses surprisingly low power at large angles J607.," In this way it was discovered by the COBE team \citep{Hinshaw_et_al_1996}
 that the correlation function $C(\vartheta)$ possesses surprisingly low power at large angles $\vartheta \gtrsim 60^\circ$."
" A surprising observation is mace by using the ILC map. which represents a Full sky CMD map obtained by the WALAP: team ,(?).."," A surprising observation is made by using the ILC map, which represents a full sky CMB map obtained by the WMAP team \citep{Gold_et_al_2010}."
 .Computing the correlation. function⋅. 6) using. à mask leads to à correlation. function⋅⊀ having⊀ very low power at large scales. whereas using. the complete LLC. map leads to à correlation. function⋅. which. possesses higher. large scale power being. compatible. with: the concordance model ο(?)..," Computing the correlation function $C(\vartheta)$ using a mask leads to a correlation function having very low power at large scales, whereas using the complete ILC map leads to a correlation function which possesses higher large scale power being compatible with the concordance model \citep{Spergel_et_al_2003}."
 One has to decide. which. correlation. function.⋅. C'(;à) corresponds to the true AIDCMD sky: the one which Da:is based on the sale pixels. tthose outside the mask. or the other one. which would imply that most of the large scale power is generated by those areas. hidden by the galaxy. bby those pixels. which. have experienced.. much larger corrections.," One has to decide which correlation function $C(\vartheta)$ corresponds to the true CMB sky: the one which is based on the safe pixels, those outside the mask, or the other one, which would imply that most of the large scale power is generated by those areas hidden by the galaxy, by those pixels which have experienced much larger corrections."
 “This question has recently stimulated: much discussions.. citepC'opigrtererschiarzstarkmeanms06.C'opigulererschwearzstarkmeanmot ο?," This question has recently stimulated much discussions, \\citep{Copi_Huterer_Schwarz_Starkman_2006,Copi_Huterer_Schwarz_Starkman_2008,%
Copi_Huterer_Schwarz_Starkman_2010,Hajian_2007,%
Aurich_Janzer_Lustig_Steiner_2007,Aurich_Lustig_Steiner_2009,%
Sarkar_Huterer_Copi_Starkman_Schwarz_2010,%
Bennett_et_al_2010,%
Efstathiou_Ma_Hanson_2009,Pontzen_Pei iris_2010."
 emphasise. that one has to start with. the eut. sky. before the⋅ correlation function⊀ C'(9)⋅⊀ is⊀ computed.. the directly. multipoles have. to be reconstructed.," \cite{Efstathiou_Ma_Hanson_2009} emphasise that one has to start with the cut sky, but before the correlation function $C(\vartheta)$ is computed the low-order multipoles have to be reconstructed."
 In this wav.BN à stable result is. obtained. as long as the mask is. not too large.," In this way, a stable result is obtained as long as the mask is not too large."
 sPhe obtained. correlation. function⋅ ⊀⊀is then the one with. Large »wver ab large scales., The obtained correlation function is then the one with large power at large scales.
 For the details of the method see ?7.. ller," For the details of the method see \cite{deOliveira-Costa_Tegmark_2006,Bielewicz_Gorski_Banday_2004}."
e we summarise only the most important. ingredients., Here we summarise only the most important ingredients.
" The data vector” containing only the pixel values outside he mask is related. to the spherical harmonic coefficients Ap, represented as @ by where Y;; denotes the corresponding values of Yrs) ", The data vector $\vec x$ containing only the pixel values outside the mask is related to the spherical harmonic coefficients $a_{lm}$ represented as $\vec a$ by where $Y_{ij}$ denotes the corresponding values of $Y_{l_jm_j}(\hat n_i)$ 
Coudenused cores are compact dense regions of molecular clouds that have a high cohuuu density. coutrast to hei surrounding nediuu.,	Condensed cores are compact dense regions of molecular clouds that have a high column density contrast to their 	surrounding medium.
 They are regions of star ornation and appear to be plivsicallv very similar to Bok-elobules (?7).. ense. almost spherically shaped. highly conrpact molecular clouds surrounded by uouanuolecular hin interstellar eas (?)..," They 	are regions of star formation and appear to be physically very similar to Bok-globules \citep{Bok1947}, dense, 	almost spherically shaped, highly compact molecular clouds surrounded by non-molecular thin 	interstellar gas \citep{Curry2000}."
 The formaion of the condensed. cores is potentially iuke« to the turbulent motion of the molecular eas that produces a selfsimilar inulti-fractal density structure with a loe-normal distribution of the local density., 	The formation of the condensed cores is potentially linked to the turbulent motion of the molecular gas that 	produces a self-similar multi-fractal density 	structure with a log-normal distribution of the local density.
 Iu us scenario. the cores are formed out of massive density chhancements that became selfsgravitatiug and stable against the turbulent motion.," In this scenario, the cores are formed out of massive 	density enhancements that became self-gravitating and stable against the turbulent motion."
 Turbuleuce naturally xoduces a mess distribution of clouds simular to that observed in the ISM ane is understood to be the origin of 1ο initial mass function (INTF) of the stars (sec references iu ?))., Turbulence naturally 	produces a mass distribution of clouds similar to that observed in the ISM and is understood to be the origin 	of the initial mass function (IMF) of the stars (see references in \citet{Fischera2008}) ).
 Because the cores are highly opaque. they are uost casily studied iu he far infrared (FIR) or subnua reeiue by observing the dust enüssion spectra where ie cores are still optically thin.," 	 	Because the cores are highly opaque, they are most easily studied in the far infrared (FIR) or submm regime 	by observing the dust emission spectrum where the cores are still optically thin."
 Survevs of molecular clouds performed in the FIR/subuun (as are possible usine BLAST. HIERSCTIEL. and ALMA) are essential o our understanding of the very carly evolutionary oocess of star formation and will help us to uulock he mvsterv of the origin of the IMIF (e.go. 22 )).," 	Surveys of molecular clouds performed in the FIR/submm (as are possible using BLAST, HERSCHEL, and ALMA) 	are essential to our understanding of the very early 	evolutionary process of star formation and will help us to 	unlock the mystery of the origin of the IMF (e.g. \citet{Netterfield2009, Olmi2009}) )."
 The iuterpretatiou. jiowever. of tje dust cCluission spectra. ix coniplicated w both radiative transfer effects and the παπονὰ. dust xoperties nm he molecular phase of the ISM.," 	The interpretation, however, of the dust emission spectrum 	is complicated by both radiative transfer effects and the unknown dust properties in the molecular phase of 	the ISM."
" Both effects lead to uncertainties nu particular in the measurement of the core lasses, Which is he main observable cerived by modeling the SED."," Both effects lead to uncertainties in particular in the measurement of the core masses, which is the main 	observable derived by modeling the SED."
 This causes a major problem in σαήλιο information about the efficiency of star formation. the stellar mass. or tle masses produced within a core of a certain mass.," This causes a major problem 	in gaining information about the efficiency of star formation, the stellar mass, or the masses 	produced within a core of a certain mass."
 The radiative trauster also further affects the surface brielituess profile of the core as eraius in the cloud are heated by a eraduallv chaneine radiation field (7?)..," 	The radiative transfer also further affects the surface brightness profile of the core as grains in the cloud are 	heated by a gradually changing radiation field \citep{Fischera2008,Nutter2009}."
 Observationally. cores display. if described by a single temperature model. a large variation in dust temperatures.," 	 	Observationally, cores display, if described by a single temperature model, a large variation in dust temperatures."
 This is a direct consequence not oulv of their eravitational state. but also of their local environment.," 	This is a direct consequence not only of their gravitational state, but also of their local environment."
 Some cores are exclusively heated by an external radiatiou field while others have already formed a protostellar object in the center aud are therefore also heated from the inside., 	Some cores are exclusively heated by an external 	radiation field while others have already formed a protostellar object in the center and are therefore also 	heated from the inside.
 Cores with a wari central object therefore have on average a higher dust temperature (?).., Cores with a warm central object therefore have on average a higher dust temperature \citep{Olmi2009}.
 The SEDs of iuterstellar clouds aud. cores have Όσοι extensively studied in the past (22777?7).. although with different cuuphases.," 	 The SEDs of interstellar clouds and cores have been extensively studied in the past \citep{Bernard1992,Bernard1993,Evans2001, Stamatellos2003,Stamatellos2004,Fischera2008}, although with different emphases."
 7. studied the radiative transfer using a physical dust model and derived the brightness profiles and SEDs of interstellar clouds while makiug simplified assuniptious about the scattered light and density profiles in clouds (a flat ceuter aud a power law further out)., \citet{Bernard1992} studied the radiative transfer using a physical dust model and derived the brightness profiles and SEDs of interstellar clouds while making simplified assumptions about the scattered light and density profiles in clouds (a flat center and a power law further out).
 They conclude tha the observed brightness profiles cannot be caused by radiative transter effects alone. ?.. ?7..," They concluded that the observed brightness profiles cannot be caused by radiative transfer effects alone. \citet{Evans2001}, \citet{Stamatellos2003},"
 aud ? studied the mfrared. emission from cores to obtain more robust estimates of their dust masses., and \citet{Stamatellos2004} studied the infrared emission from cores to obtain more robust estimates of their dust masses.
 Their calculations focused. on the radiative transfer aspects aud used a siuplifed dust re-cnussion iuodel based on the mean dust properties that they adopted from ?.., Their calculations focused on the radiative transfer aspects and used a simplified dust re-emission model based on the mean dust properties that they adopted from \citet{Ossenkopf1994}.
 7. studied the dependence of the SED derived or stable isothermal selEeravitatiug interstellar clouds on the radiation Ποια and the external pressure iu the interstellar imuediun., \citet{Fischera2008} studied the dependence of the SED derived for stable isothermal self-gravitating interstellar clouds on the radiation field and the external pressure in the interstellar medium.
 These caleulatious were based on a physical dust model of interstellar dust eraius., These calculations were based on a physical dust model of interstellar dust grains.
 The radiative trausfer problem was solved by accurately considering the complications caused by the scattered light to provide (as can also be ound in the work of ?)) profiles ofthe surface brightucss or the whole SED., The radiative transfer problem was solved by accurately considering the complications caused by the scattered light to provide (as can also be found in the work of \citet{Stamatellos2003}) ) profiles of the surface brightness for the whole SED.
 ? studied the SEDs of cores embedded: im optical hick dense spherical clouds aud the present work can be conipared to theirs., \citet{Stamatellos2003} studied the SEDs of cores embedded in optical thick dense spherical clouds and the present work can be compared to theirs.
 There are. however. basic differences.," There are, however, basic differences."
 Iu their model. the eiaut molecular cloud. (GAIC) is not uodeled as a self-eravitatiug eutitv but as a homogeneous euse sphere aud the pressure inside the GAIC is assumed. o be independent of the extinction of the cloud.," In their model, the giant molecular cloud (GMC) is not modeled as a self-gravitating entity but as a homogeneous dense sphere and the pressure inside the GMC is assumed to be independent of the extinction of the cloud."
 Iu this paper. I relate the SEDs of passively heated condensed cores to their plysical euviromnoeut.," In this paper, I relate the SEDs of passively heated condensed cores to their physical environment."
 The caleulations rest upon comparable studies of interstellar clouds that are either spherical (1) Or cvlndrical (Fischera. iun prep.)," The calculations rest upon comparable studies of interstellar clouds that are either spherical \citep{Fischera2008} or cylindrical (Fischera, in prep.)"
 in shape aud are modeled as, in shape and are modeled as
efficieucy correction introduces some variations in tle best-fit values of the scaling factors. that should have an amplituce around (Espositoetal.1999).,"efficiency correction introduces some variations in the best-fit values of the scaling factors, that should have an amplitude around \citep{esp99}."
. For each data set we ran the likelihood analysis twice. first with the scaling factors fixed to the values founcl in the allsky analysis (Eq. 7)).," For each data set we ran the likelihood analysis twice, first with the scaling factors fixed to the values found in the allsky analysis (Eq. \ref{3}) ),"
 aud then allowing the scaling factor to freely vary., and then allowing the scaling factor to freely vary.
 Variable scaling [actors should provide a better representation of the diffuse galactic emission. for they can balauce errors iu the efficiency correction aud they cau correct inappropriate large-scale structure iu the mocel ol diffuse emission.," Variable scaling factors should provide a better representation of the diffuse galactic emission, for they can balance errors in the spark-chamber efficiency correction and they can correct inappropriate large-scale structure in the model of diffuse emission."
 On the other baucl. one may expect an auti-correlation between the best-fit flux. from and the best-fit value of Gaya. which is the dominant parameter for the intensity of the expected difltse emission from the inner galaxy.," On the other hand, one may expect an anti-correlation between the best-fit flux from and the best-fit value of $\gm$, which is the dominant parameter for the intensity of the expected diffuse emission from the inner galaxy."
 Therefore tle mean relative amplitude of variations in Cj over N viewlug periods should not significantly exceed1056., Therefore the mean relative amplitude of variations in $\gm$ over $N$ viewing periods should not significantly exceed.
.. We thus monitor the variations iu the best-fit values of Cpu to ensure that variations iu the measured flux from are not caused by an uurealistically extreme value of Cqug., We thus monitor the variations in the best-fit values of $\gm$ to ensure that variations in the measured flux from are not caused by an unrealistically extreme value of $\gm$.
 The results of the likelihood aualysis ruus for the iudividual viewing periods as well as for the combined data set are stunmarized iu table 3.., The results of the likelihood analysis runs for the individual viewing periods as well as for the combined data set are summarized in table \ref{t3}.
 The scaling parameter of diffuse emission. Gy. has best-fit values that are characterized by =0.106 so the scatter in Gay is at a level cominensurate with the systematic error in the absolute determination of EGRETs ellective area at the time of measurement. thus uot iudicating any additional systematic problem.," The scaling parameter of diffuse emission, $\gm$, has best-fit values that are characterized by =0.106 so the scatter in $\gm$ is at a level commensurate with the systematic error in the absolute determination of EGRET's effective area at the time of measurement, thus not indicating any additional systematic problem."
" We- can perform"" a L7 X7-test to determine. how well the measured fIuxes iun the i21 viewingn periodsn are compatible with a constant flux.", We can perform a $\chi^2$ -test to determine how well the measured fluxes in the 24 viewing periods are compatible with a constant flux.
 The best-fit coustaut flux would be, The best-fit constant flux would be
 (Tou2 sub-L. Christensenetal.2004;Savaglio2008)). (Bloometal.2002;," $T_{90}\gtrsim 2$ $L_*$ \citealt{hf99,cba02,bck+03,ldm+03,chg04,sgl08}) \citep{bkd02,fls+06}."
 z©0.3. (Staneketal.2006:Savaglio2008).. (Bergeretal.2007a).. Eichleretal.1989;Narayan1992)). (Foxetal.2005).," $z\lesssim 0.3$ \citep{sgb+06,sgl08}, \citep{bfk+07}. \citep{bpc+05,ffp+05,gso+05,bpp+06}. \citealt{elp+89,npp92}) \citep{ffp+05}."
. Subsequent to the discovery of the first short GRB afterglows and hosts. we have shown that à substantial fraction of these events (1/3—2/3) reside at higher redshifts than previously suspected. z20.7 (Bergeretal.20070:Cenkoetal. 2008).," Subsequent to the discovery of the first short GRB afterglows and hosts, we have shown that a substantial fraction of these events $1/3-2/3$ ) reside at higher redshifts than previously suspected, $z\gtrsim 0.7$ \citep{bfp+07,cbn+08}."
. Spectroscopic observations indicate that a substantial fraction of these galaxies are undergoing active star formation., Spectroscopic observations indicate that a substantial fraction of these galaxies are undergoing active star formation.
 Indeed. of the current sample of short GRBs localized to better than a few areseconds (23 bursts). z456€ reside in star forming galaxies compared to only z10% in ellipticalfollow-up.," Indeed, of the current sample of short GRBs localized to better than a few arcseconds (23 bursts), $\approx 45\%$ reside in star forming galaxies compared to only $\approx 10\%$ in elliptical."
.. This result raises the question of whether some short GRBs are related to star formation activity rather than an old stellar population. and if so. whether the star formation properties are similar to those in long GRB host galaxies.," This result raises the question of whether some short GRBs are related to star formation activity rather than an old stellar population, and if so, whether the star formation properties are similar to those in long GRB host galaxies."
 The answer will shed light on the diversity of short GRB progenitors. in particular their age distribution and the possibility of multiple progenitor populations.," The answer will shed light on the diversity of short GRB progenitors, in particular their age distribution and the possibility of multiple progenitor populations."
 Here we present optical spectroscopy of short GRB host galaxies and measure their luminosities. metallicities. and star formation rates refsec:obs and refsec:prop)).," Here we present optical spectroscopy of short GRB host galaxies and measure their luminosities, metallicities, and star formation rates \\ref{sec:obs} and \\ref{sec:prop}) )."
 We then assess their specific star formation rates and luminosity-metallicity relation. and compare these results with the properties of long GRB hosts and field star forming galaxies refsec:disc)).," We then assess their specific star formation rates and luminosity-metallicity relation, and compare these results with the properties of long GRB hosts and field star forming galaxies \\ref{sec:disc}) )."
 Finally. we use these comparisons to draw conclusions about the progenitor population. and we outline future host galaxy studiesthatwill provide continued constraints on the progenitors refsec:cone)).," Finally, we use these comparisons to draw conclusions about the progenitor population, and we outline future host galaxy studiesthatwill provide continued constraints on the progenitors \\ref{sec:conc}) )."
" Throughoutthepaperwe use the standard cosmological parameters. Ho=70 km s! Mpc!. 0,= 0.27. and O42 0.73."," Throughoutthepaperwe use the standard cosmological parameters, $H_0=70$ km $^{-1}$ $^{-1}$ , $\Omega_m=0.27$ , and $\Omega_\Lambda=0.73$ ."
μοι of NGC 4472. taken from Davies (1993). who have measured the Meo ancl κος indices out to ~ 0.5 re for this galaxy.,"light of NGC 4472, taken from Davies (1993), who have measured the $_{2}$ and $<$ $>$ indices out to $\sim$ 0.5 $r_{\rm{e}}$ for this galaxy."
 To link the racial ranges covered by our data with that of Davies (1993) more completely. we have converted the οςTi colours of the raclially binned NCC. 4472 elobular clusters rom Geisler (1996) using Eqn. (4))," To link the radial ranges covered by our data with that of Davies (1993) more completely, we have converted the $C-T_{1}$ colours of the radially binned NGC 4472 globular clusters from Geisler (1996) using Eqn. \ref{eq:doug}) )"
 and the empirical relations of Broce IIuchra (1990)., and the empirical relations of Brodie Huchra (1990).
 For clarity we have omitted the error. bars on the converted photometry. but vpically the uncertainty in «Fez is  θε aand in Ales is ~ 0.03 mag.," For clarity we have omitted the error bars on the converted photometry, but typically the uncertainty in $<$ $>$ is $\sim$ 0.4 and in $_{2}$ is $\sim$ 0.03 mag."
 The conversion [rom €'—7i «pecdsnot a direct one. since Drodie Luchra (1990) calibrated Fe5270 with metallicity. as opposed to the mean of he Fe5270 and FEe5335> indices.," The conversion from $C-T_{1}$ to $<$ $>$ is not a direct one, since Brodie Huchra (1990) calibrated Fe5270 with metallicity, as opposed to the mean of the Fe5270 and Fe5335 indices."
 We have applied a correction of 0.3 to convert the Fe5270 prediction to «Lez, We have applied a correction of 0.3 to convert the Fe5270 prediction to $<$ $>$.
 converted elobular cluster colour data of Geisler ‘ll(Pi) et isin good agreement with our « : line-strengths al , The converted globular cluster colour data of Geisler (1996) is in good agreement with our $<$ $>$ line-strengths at all radii.
A shift of ~ 0.5 dex in «bez (corresponding to removing the blue globular clusters) would mate these data overlap with that ofthe nuclear line-strength measurements., A shift of $\sim$ 0.5 dex in $<$ $>$ (corresponding to removing the blue globular clusters) would make these data overlap with that of the nuclear line-strength measurements.
 The metal-rieh globular clusters appear to have similar iron abundances to the spheroid light., The metal-rich globular clusters appear to have similar iron abundances to the spheroid light.
 However. the situation for Mg» appears somewhat cillerent.," However, the situation for $_{2}$ appears somewhat different."
 Again. our cata are consistent with the indices predicted by the elobular cluster photometry of Geisler (1996).," Again, our data are consistent with the indices predicted by the globular cluster photometry of Geisler (1996)."
 Llowever. the GC's are olfset. cownwards from the spheroid data of Davies (1993) by ~ -0.10 mae at the same radii.," However, the GCs are offset downwards from the spheroid data of Davies (1993) by $\sim$ -0.10 mag at the same radii."
" Assuming the data of Geisler (1996) traces the behaviour of the CC's MM to 0.5 ro. then even after applving an additive shift of ""m0.05 mag (for the metal-rich GC's). there is still a dilference iden 05 mag between the GCs and spheroid light."," Assuming the data of Geisler (1996) traces the behaviour of the GCs inwards to 0.5 $_{e}$, then even after applying an additive shift of 0.05 mag (for the metal-rich GCs), there is still a difference of $\sim$ 0.05 mag between the GCs and spheroid light."
 lt is that there is a metallicity gracient in our co-ackded data. in the sense that Meo and «bez weaken with increasing ealactocentric radius.," It is evident that there is a metallicity gradient in our co-added data, in the sense that $_{2}$ and $<$ $>$ weaken with increasing galactocentric radius."
 We see no significant trenc of changing flux in the spectra with radius. which coul possibly introduce an artificial radial gradient.," We see no significant trend of changing flux in the spectra with radius, which could possibly introduce an artificial radial gradient."
 Applying a weighted linear fit to the «Fez and Ales indices. we obtain A Fe/1]/4N log ri = -0.30 + 0.21 dex for «Fez aix A VFefl]/Alog r = -0.94 + 1.31 for Mg».," Applying a weighted linear fit to the $<$ $>$ and $_{2}$ indices, we obtain $\Delta$ $\Delta$ log $r$ = -0.30 $\pm$ 0.21 dex for $<$ $>$ and $\Delta$ $\Delta$ log $r$ = -0.94 $\pm$ 0.31 for $_{2}$."
 The steep gracien seen in Meg» is primarily driven by the outermost radial bin (which has the largest uncertainties)., The steep gradient seen in $_{2}$ is primarily driven by the outermost radial bin (which has the largest uncertainties).
Removing this poin [rom the fit vields a gradient of Fe/H]/4 log r = -0.45 + 0.19 dex., Removing this point from the fit yields a gradient of $\Delta$ $\Delta$ log $r$ = -0.45 $\pm$ 0.19 dex.
 Both of these values are consistent with the mean vient found by Geisler (1996) of A AA log r -0.4 + 0.2 dex. and the mean gradient found for (αςος in general of 4 Fe/L1]/4 log r = -0.5 dex (Ashman Zepf 1998).," Both of these values are consistent with the mean gradient found by Geisler (1996) of $\Delta$ $\Delta$ log $r$ = -0.4 $\pm$ 0.2 dex, and the mean gradient found for GCS's in general of $\Delta$ $\Delta$ log $r$ = -0.5 dex (Ashman Zepf 1998)."
 By comparison. the gradient from the spheroid data of Davies (1993) is A Ηλ log r = -0.20 + 0.10 dex. similar to the value found by [xim ((2000) using Washington photometry (for rx 180 arcsec).," By comparison, the gradient from the spheroid data of Davies (1993) is $\Delta$ $\Delta$ log $r$ = -0.20 $\pm$ 0.10 dex, similar to the value found by Kim (2000) using Washington photometry (for $r \le$ 180 arcsec)."
 To investigate this matter further. and to. directly compare the spheroid light with the globular cluster subpopulations. we have binned our globular clusters into a blue and red population. taking the colour cut to be CoTi = 1.625.," To investigate this matter further, and to directly compare the spheroid light with the globular cluster subpopulations, we have binned our globular clusters into a blue and red population, taking the colour cut to be $C-T_{1}$ = 1.625."
 We have further split cach of these two bins by radius into two equal components ancl show our results in Vig. 12, We have further split each of these two bins by radius into two equal components and show our results in Fig. \ref{fig:radial_plot.2}.
 The Mg» and cre indices decrease with increasing ealactocentric radius for the red and blue globular cluster. subpopulations., The $_{2}$ and $<$ $>$ indices decrease with increasing galactocentric radius for the red and blue globular cluster subpopulations.
 Formally. the radial gradients. of the clusters. [rom spectroscopy are. twice as steep às those determined from the photometric data.," Formally, the radial gradients of the clusters from spectroscopy are twice as steep as those determined from the photometric data."
 Llowever. the significance of this. particularly for the red elobular clusters (for which ~ 23) is marginal.," However, the significance of this, particularly for the red globular clusters (for which $\sim$ 23) is marginal."
 Measured in «ορ. the innermost red. cluster bin is comparable to the spheroid light from Davies (1993). whereas the Ales index of this bin is some 0.05 mag lower.," Measured in $<$ $>$, the innermost red cluster bin is comparable to the spheroid light from Davies (1993), whereas the $_{2}$ index of this bin is some 0.05 mag lower."
 In the lower panel of Fig. 12..," In the lower panel of Fig. \ref{fig:radial_plot.2},"
 we plot a vector corresponding to the maxiniunm correction expected for. Mg/Ee] overabundant ratios seen in the brightest elliptical galaxies. of which NCC 4472 is known to be allected (Worthey 1992: Henry Worthey 1999: Ixobavashi Arimoto 1999).," we plot a vector corresponding to the maximum correction expected for [Mg/Fe] overabundant ratios seen in the brightest elliptical galaxies, of which NGC 4472 is known to be affected (Worthey 1992; Henry Worthey 1999; Kobayashi Arimoto 1999)."
 If. we apply this maximum correction (0.05 mag) to the Mg» index of the GCs. then these cata become consistent with the spheroid cata of Davies (1993).," If we apply this maximum correction $\sim$ 0.05 mag) to the $_{2}$ index of the GCs, then these data become consistent with the spheroid data of Davies (1993)."
 Since the «Fez index of the globular clusters is consistent with that of the spheroid light with no correction. we tentatively conclude that the elobular clusters in NGC 4472 show no sign of non-solar Mg/Fc] ratios.," Since the $<$ $>$ index of the globular clusters is consistent with that of the spheroid light with no correction, we tentatively conclude that the globular clusters in NGC 4472 show no sign of non-solar [Mg/Fe] ratios."
 We return to this point in 165.4., We return to this point in $\S 5.4$.
 We now turn to the problem of deriving mean ages [or our globular clusters using the Worthey (1994). mocels., We now turn to the problem of deriving mean ages for our globular clusters using the Worthey (1994) models.
and both Wine aud EFF profiles in Figure 5. overlaved ou the data.,and both King and EFF profiles in Figure \ref{fig:Sky Sub} overlayed on the data.
 The kev difference between the wo Figures is that Figure [ shows the uu-backerotud subtracted data so that all of the data could be plotte ou the logarithunic scale., The key difference between the two Figures is that Figure \ref{fig:Sample Profiles} shows the un-background subtracted data so that all of the data could be plotted on the logarithmic scale.
 Note however. the profiles ploted in this manner do not resemble the standard Wine uxxdels. although they are.," Note however, the profiles plotted in this manner do not resemble the standard King models, although they are."
 Iu Figure 5 we again plot the bacserounc-subtracted xofiles. but here woe stop plottiug data and models ounce a radial bin has à negative backgrouid subtracted value cause the οσααι is undefined.," In Figure \ref{fig:Sky Sub} we again plot the background-subtracted profiles, but here we stop plotting data and models once a radial bin has a negative background subtracted value because the logarithm is undefined."
 Plotting only data ercater than the background. i.c. hose with positive vackeroundo subtracted values. resits in a misleading xofile.," Plotting only data greater than the background, i.e. those with positive background subtracted values, results in a misleading profile."
 The paramcter values for the fits are presented in Tade 2.., The parameter values for the fits are presented in Table \ref{tab:Structural Parameters}.
 The lo confidence intervals are defined using P veaid are therefore undefined in the cases where even he best fit model has 4? ereater than the corresponding value for the available deerees of freedom.," The $1\sigma$ confidence intervals are defined using $\chi^2$, and are therefore undefined in the cases where even the best fit model has $\chi^2$ greater than the corresponding value for the available degrees of freedom."
 Of the 201 clusters in our catalog. ¢xlv Ll are poorly deserihed bv a Wine xofile with oOoreater than confidence.," 	Of the 204 clusters in our catalog, only 44 are poorly described by a King profile with greater than confidence."
" Caven the size of our sample however. we expect from statistical cOousiderations hat a substantia iminiber of clusters tha are trulv weIL described by a lius profile will be rejστου, at this kvel."," Given the size of our sample however, we expect from statistical considerations that a substantial number of clusters that are truly well described by a King profile will be rejected at this level."
 We calculate hat only 19 clusters are fit sufficioeutv poorly that for each individual cluster he Wine profie can be rejectec as ab accurate descripion of their surface briehtuess xofile (this lait corresponds to rejecting thle profile with coufideuce)., We calculate that only 19 clusters are fit sufficiently poorly that for each individual cluster the King profile can be rejected as an accurate description of their surface brightness profile (this limit corresponds to rejecting the profile with confidence).
 Because hoh the Wine ane EFF profiles can ft clusers with exteuded radial surface xiehtuess profiles. the profile itself caunot be used to," Because both the King and EFF profiles can fit clusters with extended radial surface brightness profiles, the profile itself cannot be used to"
"continuum fluctuations, metal line contamination, damped systems and dealing with the resolution of the spectrograph and noise level in each of the redshift bins.","continuum fluctuations, metal line contamination, damped systems and dealing with the resolution of the spectrograph and noise level in each of the redshift bins."
" All these effects need to be properly taken into account, as a poor treatment would impact the obtained flux power in a non-trivial way."," All these effects need to be properly taken into account, as a poor treatment would impact the obtained flux power in a non-trivial way."
" In the following, we will use the flux power provided by the SDSS collaboration, introducing ""nuisance parameters"" for the resolution and noise in each redshift bin as suggested by ?,, and implicitly assuming that all the contaminants above have been either removed or properly modelled."," In the following, we will use the flux power provided by the SDSS collaboration, introducing “nuisance parameters” for the resolution and noise in each redshift bin as suggested by \cite{mcdonald05}, and implicitly assuming that all the contaminants above have been either removed or properly modelled."
" We compute the constraints from the SDSS flux power spectrum in a similar way to ? with the notable difference that we calculate the predicted flux statistics by expanding around a model with ~1 in the redshift range z=[2—4], while the original analysis was based on simulations with 4~1.6."," We compute the constraints from the SDSS flux power spectrum in a similar way to \cite{vielhaehnelt06} with the notable difference that we calculate the predicted flux statistics by expanding around a model with $\gamma \sim 1$ in the redshift range $z=[2-4]$, while the original analysis was based on simulations with $\gamma\sim 1.6$."
" Furthermore, the flux power is computed using a Taylor expansion to second instead of first order."," Furthermore, the flux power is computed using a Taylor expansion to second instead of first order."
 The parameters of the fiducial cosmological simulation are those of the B2 model in ?.., The parameters of the fiducial cosmological simulation are those of the B2 model in \cite{vielhaehnelt06}.
 As before the flux statistics have been corrected for box-size and resolution effects., As before the flux statistics have been corrected for box-size and resolution effects.
 We compute the derivatives required for the Taylor expansion by performing between four and six hydrodynamical simulations for every cosmological and astrophysical parameter considered., We compute the derivatives required for the Taylor expansion by performing between four and six hydrodynamical simulations for every cosmological and astrophysical parameter considered.
" In addition, we now allow for the effect of the reionization redshift, zre, and introduce this as an extra parameter."," In addition, we now allow for the effect of the reionization redshift, $z_{\rm re}$, and introduce this as an extra parameter."
 We interpolate between two very different reionization histories with ze~15 and ze~7.," We interpolate between two very different reionization histories with $z_{\rm re} \sim 15$ and $z_{\rm re} \sim
7$."
" We also introduce two extra parameters describing the redshift evolution of the thermal state of the IGM, the power-law index of the T' and vy relations at z>3 (a redshift range which is not probed by the PDF)."," We also introduce two extra parameters describing the redshift evolution of the thermal state of the IGM, the power–law index of the $T$ and $\gamma$ relations at $z>3$ (a redshift range which is not probed by the PDF)."
" 'The results for the power spectrum only analysis are summarised in the first two columns of Table [2] for a low redshift only sample, z=[2.2—9.6], and the full SDSS data set, z— [2.2—4.2]."," The results for the power spectrum only analysis are summarised in the first two columns of Table \ref{tab3} for a low redshift only sample, $z=[2.2-3.6]$, and the full SDSS data set, $z=[2.2-4.2]$ ."
" We decided to perform a separate analysis which omits the highest redshift bins following ?,, who obtained a somewhat poorer fit for the high redshift (z>3.6) PS estimates."," We decided to perform a separate analysis which omits the highest redshift bins following \cite{vielhaehnelt06}, who obtained a somewhat poorer fit for the high redshift $z>3.6$ ) PS estimates."
" Despite the fact that the flux statistics were calculated by expanding around a reference model with very different thermal history, in both instances the analysis still gives constraints on the cosmological parameters that are in agreement with the previous analysis of ?.."," Despite the fact that the flux statistics were calculated by expanding around a reference model with very different thermal history, in both instances the analysis still gives constraints on the cosmological parameters that are in agreement with the previous analysis of \cite{vielhaehnelt06}."
 This is rather reassuring., This is rather reassuring.
" However, there are some aspects of the results that need scrutiny."," However, there are some aspects of the results that need scrutiny."
" First, we note that for the flux power only the temperature at mean density, To, is significantly higher than that preferred by the PDF (and higher than expected for the photoionized IGM)."," First, we note that for the flux power only the temperature at mean density, $T_0$, is significantly higher than that preferred by the PDF (and higher than expected for the photoionized IGM)."
" Secondly, the value of og is now somewhat on the lower end of values allowed by the previous analysis of data and thus in better agreement with the CMB data (e.g. ?))."," Secondly, the value of $\sigma_8$ is now somewhat on the lower end of values allowed by the previous analysis of data and thus in better agreement with the CMB data (e.g. \citealt{komatsu08}) )."
" This is due to the degeneracy between og and  discussed in B08; allowing for y«1 means that the flux power can now be fitted by a slightly lower σε (but note that other parameters also have a a significant influence on the inferred og, most notably the mean flux level)."," This is due to the degeneracy between $\sigma_8$ and $\gamma$ discussed in B08; allowing for $\gamma<1$ means that the flux power can now be fitted by a slightly lower $\sigma_8$ (but note that other parameters also have a a significant influence on the inferred $\sigma_8$, most notably the mean flux level)."
" Overall the results from the new flux PS analysis are consistent with those inferred from the PDF alone except for the value of Το at z=3, which is several σ above that inferred from the best fit to the flux PDF."," Overall the results from the new flux PS analysis are consistent with those inferred from the PDF alone except for the value of $T_0$ at $z=3$, which is several $\sigma$ above that inferred from the best fit to the flux PDF."
 In the last column of Table [2] we show the constraints for a joint analysis of flux PDF and PS., In the last column of Table \ref{tab3} we show the constraints for a joint analysis of flux PDF and PS.
 Somewhat surprisingly the joint analysis prefers a larger value of og=0.9+0.02 with rather small errors., Somewhat surprisingly the joint analysis prefers a larger value of $\sigma_8=0.9\pm 0.02$ with rather small errors.
 We explicitly checked that this large value of og is related to the rather different Tj values that the PDF and PS favour., We explicitly checked that this large value of $\sigma_8$ is related to the rather different $T_0^A$ values that the PDF and PS favour.
" If we artificially remove the constraint of the temperature being simultaneously consistent with the somewhat discrepant temperatures favoured by the flux PDF and PS, the joint analysis gives og=0.86+0.03 with an improvement of Ax?—12."," If we artificially remove the constraint of the temperature being simultaneously consistent with the somewhat discrepant temperatures favoured by the flux PDF and PS, the joint analysis gives $\sigma_8=0.86\pm 0.03$ with an improvement of $\Delta \chi^2 = 12$."
 A not yet accounted for systematic error in the measurement of the flux PDF and/or PS appears to be a possible explanation for this discrepancy., A not yet accounted for systematic error in the measurement of the flux PDF and/or PS appears to be a possible explanation for this discrepancy.
 Alternatively the inconsistencies may suggest that a power—law T'—p relation is a poor approximation to the thermal state of the IGM and a wider range of physically motivated relations should be considered in future simulations., Alternatively the inconsistencies may suggest that a power--law $T-\rho$ relation is a poor approximation to the thermal state of the IGM and a wider range of physically motivated relations should be considered in future simulations.
 We have presented cosmological and astrophysical constraints derived from the K07 flux PDF measured from a set of 18 high-resolution QSO spectra whose statistical and systematic errors have been carefully estimated., We have presented cosmological and astrophysical constraints derived from the K07 flux PDF measured from a set of 18 high-resolution QSO spectra whose statistical and systematic errors have been carefully estimated.
 The flux PDF on its own provides tight constraints on the thermal state of the IGM and on cosmological parameters describing the linear dark matter PS., The flux PDF on its own provides tight constraints on the thermal state of the IGM and on cosmological parameters describing the linear dark matter PS.
" The results have been obtained by fitting the flux PDF at three different redshift bins in the range 2«z3 and for three different flux ranges F=[0.1—0.8], F=[0—0.9], and F=[0—1]."," The results have been obtained by fitting the flux PDF at three different redshift bins in the range $2<z<3$ and for three different flux ranges $F=[0.1-0.8]$, $F=[0-0.9]$, and $F=[0-1]$."
 There is good agreement between the analyses for the full flux range and the two restricted flux ranges and the results are consistentwith those derived in the simpler analysis made by B08., There is good agreement between the analyses for the full flux range and the two restricted flux ranges and the results are consistentwith those derived in the simpler analysis made by B08.
" An inverted temperature-density relation is favoured at the ~3c level (at z~ 3) if we consider the PDF for the full flux range, but the significance is reduced to 1—1.50 if we restrict the analysis to F=[0.1— 0.8]."," An inverted temperature-density relation is favoured at the $\sim 3\sigma$ level (at $z \sim 3$ ) if we consider the PDF for the full flux range, but the significance is reduced to $1-1.5\sigma$ if we restrict the analysis to $F=[0.1-0.8]$ ."
 The constraints for other parameters arein agreement with those presented in, The constraints for other parameters arein agreement with those presented in
lensing.,.
.. Flexion has two components denoted. first ancl second. [lexion. which are a shift of the image centroid and a representation of the “arciness” of the image respectively.," Flexion has two components denoted first and second flexion, which are a shift of the image centroid and a representation of the “arciness” of the image respectively."
 One main issue associated with shear-based eravitational lensing is that galaxies are intrinsically. elliptical in shape (ellipses at some inclination to the line-ol-sight seen in projection). so it is necessary to cliscntanele lens-inclueeck shear from the intrinsic shape.," One main issue associated with shear-based gravitational lensing is that galaxies are intrinsically elliptical in shape (ellipses at some inclination to the line-of-sight seen in projection), so it is necessary to disentangle lens-induced shear from the intrinsic shape."
 Resolved ealaxies. however. are not intrisincallv Blexed although systems undergoing a merger. or galaxies with substantial asvmmetrie sub-structure such as ai large. starforming region. may be mis-intepretecl as Dexion signals.," Resolved galaxies, however, are not intrisincally flexed – although systems undergoing a merger, or galaxies with substantial asymmetric sub-structure such as a large starforming region, may be mis-intepreted as flexion signals."
 It has been suggested. that Hexion may. provide a stronger. constraint on dark matter (Leonardetal.2007:Bacon.Amara&Read2010:Llawken&Bricle2009:LeonardIxing 2010).. ealaxy cluster mass mocels (Leonard.Kine&Wilkins and also ondefensing gravitational wave signals (Shapiroetal.2000). than shear on its own. notwithstanding the challenges in measuring Lexion (ο. Okura. Umetsu Futamase 2007. 2008: Goldberg Leonard 2007: Massey et al.," It has been suggested that flexion may provide a stronger constraint on dark matter \citep{leonard07,bacon09,hawken09,leonard10}, galaxy cluster mass models \citep{leonard09} and also on gravitational wave signals \citep{shapiro10} than shear on its own, notwithstanding the challenges in measuring flexion (e.g. Okura, Umetsu Futamase 2007, 2008; Goldberg Leonard 2007; Massey et al."
 2007: Irwin Shmakova 2006: Schneider Er 2008)., 2007; Irwin Shmakova 2006; Schneider Er 2008).
 Ina previous paper we presented analytic Llexion results for a range of popular mass density. profiles: Schwarzschild lens. singular isothermal sphere (SIS). Navarro-Frenk-White (NEW) profile and Sérrsic-like profiles (Lasky Fluke 2009: hereafter Paper D.," In a previous paper we presented analytic flexion results for a range of popular mass density profiles: Schwarzschild lens, singular isothermal sphere (SIS), Navarro-Frenk-White (NFW) profile and Sérrsic-like profiles (Lasky Fluke 2009; hereafter Paper I)."
 Our analytic solutions present a flexion formalism where we consider a two-dimensional (2D) field in the lens plane. which allows for the treatemoent of extended sources.," Our analytic solutions present a flexion formalism where we consider a two-dimensional (2D) field in the lens plane, which allows for the treatement of extended sources."
 ln this paper we extend our. previous work by considering the following key question: over what range of image/source sizes is the flexion approach valid?, In this paper we extend our previous work by considering the following key question: over what range of image/source sizes is the flexion approach valid?
 “Phat is. if flexion appears as a gradient of shear across an image. which is iplictly assumed to be zero for traditional weak-lensing analysis. how well can we recover IHexion for extende sources?," That is, if flexion appears as a gradient of shear across an image, which is implictly assumed to be zero for traditional weak-lensing analysis, how well can we recover flexion for extended sources?"
 The approach we use is via the rav-bundle metho introduced. by Fluke. Webster Mortlock (1999).," The approach we use is via the ray-bundle method introduced by Fluke, Webster Mortlock (1999)."
 Llere. bundles of light ravs with a known initial configuration are propagated through one or more lens planes. ane the deflection of cach light. ray is. determined. using the eravitational lens equation. see equation (1)) below.," Here, bundles of light rays with a known initial configuration are propagated through one or more lens planes, and the deflection of each light ray is determined using the gravitational lens equation, see equation \ref{eqn:tle}) ) below."
 The initial and final shapes of the bundles can now be usec to obtain numerical estimates for convergence. shear. magnification. first and second Iexion as a function of source size.," The initial and final shapes of the bundles can now be used to obtain numerical estimates for convergence, shear, magnification, first and second flexion as a function of source size."
 By starting with simple lens models. we use known analytic results to test the accuracy of our approach. and hence assess its applicability to cases where analytic llexion results do not exist (e.g. asymmetric mass profiles. such as from /*-bodv. dark matter halo simulations).," By starting with simple lens models, we use known analytic results to test the accuracy of our approach, and hence assess its applicability to cases where analytic flexion results do not exist (e.g. asymmetric mass profiles, such as from $N$ -body, dark matter halo simulations)."
 The paper is set out as follows: in Section. 2.. we summarise the key results for the analytic Hexion formalism.," The paper is set out as follows: in Section \ref{sct:flexform}, , we summarise the key results for the analytic flexion formalism."
 1n Section 3... we describe how the rav-bundle method can be used to obtain flexion along individual lines-of-sight.," In Section \ref{sct:RBM}, we describe how the ray-bundle method can be used to obtain flexion along individual lines-of-sight."
 We present the results of our numerical testing. and determine a range of image locations and bundle radii for which the flexion approximation is valid for a Sebwarzschild. lens nmociel.," We present the results of our numerical testing, and determine a range of image locations and bundle radii for which the flexion approximation is valid for a Schwarzschild lens model."
 We demonstrate the existence of Hexion zone. which defines a physical region where the Uexiona formalism is valid [or extended sources.," We demonstrate the existence of a flexion zone, which defines a physical region where the flexion formalism is valid for extended sources."
 In Section 4d. we present. caleulations of the size of the flexion zone as a function of lens mass. lens ancl source redshift.," In Section \ref{sct:discussion} we present calculations of the size of the flexion zone as a function of lens mass, lens and source redshift."
 We present our conclusions and identify future directions for this work in Section 5.., We present our conclusions and identify future directions for this work in Section \ref{sct:conclusion}.
 In this section. we summuarise relevant results of the flexion formalism — for full details. see Paper L ancl references therein.," In this section, we summarise relevant results of the flexion formalism – for full details, see Paper I and references therein."
 The thin-lens gravitational lens equation relates the location of a background. source and its image(s) due to an intervening mass distribution: For the simple case of a single lens at. the origin of the lens plane. £; is the image location in the image plane. g; is the source location in the source plane. and à; is the deflection angle.," The thin-lens gravitational lens equation relates the location of a background source and its image(s) due to an intervening mass distribution: For the simple case of a single lens at the origin of the lens plane, $\xi_i$ is the image location in the image plane, $\eta_i$ is the source location in the source plane, and $\tilde{\alpha}_i$ is the deflection angle."
 Phroughout this paper. indices ijk=1.2 signify the two-dimensional components. with summation assumed. over repeated. indices. and tensors are implicity functions of the image position. £;. unless otherwise indicated.," Throughout this paper, indices $i,j,k=1,2$ signify the two-dimensional components, with summation assumed over repeated indices, and tensors are implicity functions of the image position, $\xi_{i}$, unless otherwise indicated."
 The thin-lens approximation requires that the spatial extent of the Lens distribution be much smaller than the angular diameter distances between the observer. and lens. οι. observer and. source. Ds. and lens to source. Ds.," The thin-lens approximation requires that the spatial extent of the lens distribution be much smaller than the angular diameter distances between the observer and lens, $D_{L}$, observer and source, $D_{S}$, and lens to source, $D_{LS}$."
 X convenient scaling of the lens equation into angular coordinates uses the substitutions 3)=mDs. 0;=&οι and a;=DpD.à;. so we have the compact form: We introduce a further scaling for the lens equation in section 3.4.," A convenient scaling of the lens equation into angular coordinates uses the substitutions $\beta_i = \eta_i/D_{S}$, $\theta_i = \xi_i/D_{L}$ and $\alpha_i = \frac{D_{LS}}{D_{S}}\tilde{\alpha}_i$, so we have the compact form: We introduce a further scaling for the lens equation in section 3.4."
 As à mapping between the lens and source planes. equation (2)) is often rewritten in terms of its Jacobian matrix: where the matrix elements. are identified with the convergence. αν. and two orthogonal components of shear. σι and 5».," As a mapping between the lens and source planes, equation \ref{eqn:angle}) ) is often rewritten in terms of its Jacobian matrix: where the matrix elements are identified with the convergence, $\kappa$, and two orthogonal components of shear, $\gamma_1$ and $\gamma_2$."
 The magnification along a given line-of-sight. fi. is related to the area distortion of the lens mapping: where the total shear is 4—V; ὃν," The magnification along a given line-of-sight, $\mu$, is related to the area distortion of the lens mapping: where the total shear is $\gamma = \sqrt{\gamma_1^2 + \gamma_2^2}$."
 setting the location of the light rav as the origin of coordinates in the lens and source planes. one finds for small changes in the position of the light rav: The interpretation of this mapping is as follows: if the eracicnts of the shear anc convergence do not change significantly across the image. then the first-order weak lensing οσο is to producean additional ellipticitv in the shape of background: sources.," By setting the location of the light ray as the origin of coordinates in the lens and source planes, one finds for small changes in the position of the light ray: The interpretation of this mapping is as follows: if the gradients of the shear and convergence do not change significantly across the image, then the first-order weak lensing effect is to producean additional ellipticity in the shape of background sources."
 While this approach is, While this approach is
Llere we describe the calculation of the space density and X-rav Luminosity function from the sample of 20 non-magnetic CVs detected in the combined RBS anc NEP survey.,Here we describe the calculation of the space density and X-ray luminosity function from the sample of 20 non-magnetic CVs detected in the combined RBS and NEP survey.
 The results of this calculation are presented in the next section., The results of this calculation are presented in the next section.
 The most important assumption of the method. we use is that the observed CV. sample. is. representative of the underlying population., The most important assumption of the method we use is that the observed CV sample is representative of the underlying population.
 Whether this is a reasonable assumption is aclelressecl further in Section 5. and 6.., Whether this is a reasonable assumption is addressed further in Section \ref{sec:fluxl} and \ref{sec:disc}.
 The number of CVs per unit volume is of course a function of position in the Galaxy., The number of CVs per unit volume is of course a function of position in the Galaxy.
 We ignore the (weak) racial dependence of p. and assume that the vertical density profile is exponential with z the distance from the Galactic plane (i.e. b).," We ignore the (weak) radial dependence of $\rho$, and assume that the vertical density profile is exponential with $z$ the distance from the Galactic plane (i.e. $z=d \sin b$ )."
 The local space density is defined as py=p(0). the mid-plane value of p.," The local space density is defined as $\rho_0=\rho(0)$, the mid-plane value of $\rho$ ."
 The X-ray luminosity function. &(logLx) is defined so that where por. ds the local space density of CVs in the luminosity bin of width dlogLx centred on logLx.," The X-ray luminosity function, $\Phi\left(\mathrm{log}L_X\right)$ is defined so that where $\rho_{0,L_X}$ is the local space density of CVs in the luminosity bin of width $d\mathrm{log}L_X$ centred on $\mathrm{log}L_X$."
 In other words. py is the integral of & over logLx.," In other words, $\rho_0$ is the integral of $\Phi$ over $\mathrm{log}L_X$."
 In calculating po. we will compare two assumptions regarding Galactic scale height.," In calculating $\rho_0$, we will compare two assumptions regarding Galactic scale height."
 First. as in Pretoriusctal. (2007h).. we take f=120pe for long-period CVs. and 260pe or short-period svstenis. as a (quite crude) approximation of the fact that these are voung and old. populations.spectively’.," First, as in \cite{NEPrho}, we take $h=120\,\mathrm{pc}$ for long-period CVs, and $260\,\mathrm{pc}$ for short-period systems, as a (quite crude) approximation of the fact that these are young and old populations,."
.. Phe second py calculation uses a single scale wight of 260pe for all systems. and gives results that are not significantly dillerent. (see Section. 4.1)).," The second $\rho_0$ calculation uses a single scale height of $260\,\mathrm{pc}$ for all systems, and gives results that are not significantly different (see Section \ref{sec:rhoresult}) )."
 This implies hat the simpler approach of using only a single scale height is justified. and that is what we will assume in calculating c (the reason we require the simpler assumption for & will »o explained in Section 5.2)).," This implies that the simpler approach of using only a single scale height is justified, and that is what we will assume in calculating $\Phi$ (the reason we require the simpler assumption for $\Phi$ will be explained in Section \ref{sec:simphi}) )."
 ]nterstellar extinction is computed. by integrating the density of the interstellar medium along each line of sight to obtain the neutral hydrogen column density. Vy.," Interstellar extinction is computed by integrating the density of the interstellar medium along each line of sight to obtain the neutral hydrogen column density, $N_H$."
 We again assume only. vertical dependence in the density of gas: ic. We take Musa=IOpe (eg. Robinetal.2008:: Drimmoel&Spergel 2001)). and we fine pisaro by assuming ely=2mag/kpe for b=0 deg (Allen1976)latitudes... and Ng=1.79«1075em7. νοοἱ&Schmitt1995).," We again assume only vertical dependence in the density of gas; i.e., We take $h_{ISM}=140\,\mathrm{pc}$ (e.g. \citealt{RobinReyleDerriere03}; \citealt{DrimmelSpergel01}) ), and we find $\rho_{ISM,0}$ by assuming $A_V=2\,\mathrm{mag}/\mathrm{kpc}$ for $b=0$ deg \citep{apquant}, and $N_H=1.79 \times 10^{21}\,\mathrm{cm^{-2}}A_V$ \citep{PredehlSchmitt95}."
. As discussed in Section 2 we will assume a kd=LokeV thermal bremsstrahlune spectrum for all CVs in our sample.," As discussed in Section \ref{sec:xlum}, we will assume a $kT=10\,\mathrm{keV}$ thermal bremsstrahlung spectrum for all CVs in our sample."
 We will explain below that the p calculation uses the maximum distance at which a given CV could have been detected., We will explain below that the $\rho$ calculation uses the maximum distance at which a given CV could have been detected.
 Since this maximum distance depends. on the ratio of £x to the [lux limit. which may as well be expressed. as a ratio of count rate to limiting countrate. the assumed: X-ray spectral shape has very. little influence on 10. p calculation (only the interstellar absorption depends on the X-ray spectrum)," Since this maximum distance depends on the ratio of $F_X$ to the flux limit, which may as well be expressed as a ratio of count rate to limiting countrate, the assumed X-ray spectral shape has very little influence on the $\rho$ calculation (only the interstellar absorption depends on the X-ray spectrum)."
 Since the combined survey is complete (up to the variable Hux limit). we simply need to count the systems detected inside the observed volume to caleulate p (ancl clo the same in a set of luminosity bins to find 9).," Since the combined survey is complete (up to the variable flux limit), we simply need to count the systems detected inside the observed volume to calculate $\rho$ (and do the same in a set of luminosity bins to find $\Phi$ )."
 However. the dependence of p on z. as well as the flus- rather than volumce-Inmited nature of the sample need to be accounted for.," However, the dependence of $\rho$ on $z$, as well as the flux- rather than volume-limited nature of the sample need to be accounted for."
 Both these complications are taken care of by the well-known ται method (see citealtSchmidt68:: Felten 1976: Stobieetal. 1989: etal. 1993))., Both these complications are taken care of by the well-known $1/V_{max}$ method (see \\citealt{Schmidt68}; \citealt{Felten76}; \citealt{StobieIshidaPeacock89}; \citealt{TinneyReidMould93}) ).
 Our ain is to find not only a best estimate of po and o. but also to estimate the errors on both. accounting for all sources of statistical error (includingdistance errors. small number statistics. and observational error on fy or count rate).," Our aim is to find not only a best estimate of $\rho_0$ and $\Phi$, but also to estimate the errors on both, accounting for all sources of statistical error (includingdistance errors, small number statistics, and observational error on $F_X$ or count rate)."
" We describe in the following sections first. how we implement the 1/1,,,; method. and then the Monte Carlo simulation to find the uncertainties on our measurements. as well as the numerical tests we use to verily that the error estimate for py is correct."," We describe in the following sections first how we implement the $1/V_{max}$ method, and then the Monte Carlo simulation to find the uncertainties on our measurements, as well as the numerical tests we use to verify that the error estimate for $\rho_0$ is correct."
 Theuncertainty in O9 proves to be harder to estimate. and we will return to this issue in Sections 4.2. and 5.2..," Theuncertainty in $\Phi$ proves to be harder to estimate, and we will return to this issue in Sections \ref{sec:obsphi} and \ref{sec:simphi}."
" Vhe ος method. essentially allows the ""volume [mit of the survey to vary. according to the luminosities of the systems in the sample.", The $1/V_{max}$ method essentially allows the `volume limit' of the survey to vary according to the luminosities of the systems in the sample.
 For each observedsystem. we find the ceeneralized (ic. taking into account the exponential vertical density profile) maximum volume. citealt TinneyIteidMould93)).," For each observedsystem, we find the `generalized' (i.e., taking into account the exponential vertical density profile) maximum volume, \\citealt{TinneyReidMould93}) )."
 Lhe index j represents the CVs in our sample: Q is the solid. angle covered. by. the survey and a;= d;|sinb|/h. with d; themaximum distance at which €V j could have been detected (given its luminosity and the survey [iux limit).," The index $j$ represents the CVs in our sample; $\Omega$ is the solid angle covered by the survey and $x_j=d_j |\sin b|/h$ , with $d_j$ themaximum distance at which CV $j$ could have been detected (given its luminosity and the survey flux limit)."
 Equation + assumes the spatial dependence of p as given by equation L.., Equation \ref{eq:V} assumes the spatial dependence of $\rho$ as given by equation \ref{eq:z}. .
 V; is then the volume probed by the survey for sources with Ly the same as the observed. svstem j., $V_j$ is then the volume probed by the survey for sources with $L_X$ the same as the observed system $j$ .
 Because 6 (and in the case of the NEP survey. also the flux limit) is variable over £2. we," Because $b$ (and in the case of the NEP survey, also the flux limit) is variable over $\Omega$ , we"
The pattern speed of hhas been measured by several authors.,The pattern speed of has been measured by several authors.
" Cheminetal.(2003) have assumed that the inner ring-like feature found by Reganetal.(2002) but not by us, corresponds to the location of an ultra-harmonic resonance. Rand&Wallin(2004),"," \citet{chemin03} have assumed that the inner ring-like feature found by \citet{regan02} but not by us, corresponds to the location of an ultra-harmonic resonance. \citet{rand04},"
", using the BIMA SONG data and the Tremaine-Weinberg method, have measured a pattern speed of the bar of Q, —50*? kkm s! kpc!, in good agreement with our determination."," using the BIMA SONG data and the Tremaine-Weinberg method, have measured a pattern speed of the bar of $\Omega_{\rm p}=$ $^{+3}_{-8}$ km $^{-1}$ $^{-1}$, in good agreement with our determination."
" In the presence of an ILR, the torques should be negative between the CR of the bar and the ILR."," In the presence of an ILR, the torques should be negative between the CR of the bar and the ILR."
" For3627,, without an ILR, the torques are negative between the CR of the bar and the AGN, down to the resolution limit of our observations."," For, without an ILR, the torques are negative between the CR of the bar and the AGN, down to the resolution limit of our observations."
" Such a conclusion would be the natural outcome of a scenario in which a young and rapidly rotating bar has had no time to slow down due to secular evolution, and has not yet formed any ILR."," Such a conclusion would be the natural outcome of a scenario in which a young and rapidly rotating bar has had no time to slow down due to secular evolution, and has not yet formed any ILR."
" The presence of molecular gas inside the ILR of the primary bar, or where we expect that the ILR will form, makes aa potential of inner gas inflow."," The presence of molecular gas inside the ILR of the primary bar, or where we expect that the ILR will form, makes a potential of inner gas inflow."
" In this scenario, the gas there is certainly fueling the central region, and in a second step could fuel directly the AGN."," In this scenario, the gas there is certainly fueling the central region, and in a second step could fuel directly the AGN."
" Finding evidence of AGN fueling is proving to be quite challenging, perhaps because of the short-lived nature of the mechanisms responsible."," Finding evidence of AGN fueling is proving to be quite challenging, perhaps because of the short-lived nature of the mechanisms responsible."
" The molecular gas, traced by ?CO(1-0) and ""COQ-1) transitions, in the interacting barred LINER/Seyfert 2 galaxy iis distributed along a bar-like structure of 18"" ((~900 ppc) diameter (PA = 14°) with two peaks at the extremes."," The molecular gas, traced by $^{12}$ CO(1–0) and $^{12}$ CO(2–1) transitions, in the interacting barred LINER/Seyfert 2 galaxy is distributed along a bar-like structure of $\sim$ $\sim$ pc) diameter (PA = $^{\circ}$ ) with two peaks at the extremes."
" The 1.6um H-band 2MASS and 3.6m IRAC images of sshow a stellar bar in the nucleus with PA = —21, different from the PA (= 14°) of the molecular gas bar-like structure, suggesting that the gas is leading the stellar bar."," The $\mu$ m $H$ -band 2MASS and $\mu$ m -IRAC images of show a stellar bar in the nucleus with PA = $-21^{\circ}$, different from the PA (= $14^{\circ}$ ) of the molecular gas bar-like structure, suggesting that the gas is leading the stellar bar."
" Instead, the FUV emission of ddisplays an inner elongated (north/south) ring delimiting a hole around the nucleus and containing the '?CO ~18” bbar-like structure."," Instead, the FUV emission of displays an inner elongated (north/south) ring delimiting a hole around the nucleus and containing the $^{12}$ CO $\sim$ bar-like structure."
" This kind of anti-correlation between FUV, molecular gas, and the stellar bar is perhaps related to star formation efficiency and timescale variations in response to a spiral density wave."," This kind of anti-correlation between FUV, molecular gas, and the stellar bar is perhaps related to star formation efficiency and timescale variations in response to a spiral density wave."
" The gravity torques exerted by the stellar potential on the gas computed with the HST--NICMOS F160W image and our PdBI maps are negative within the inner kkpc, down to the resolution limit of our observations."," The gravity torques exerted by the stellar potential on the gas computed with the -NICMOS F160W image and our PdBI maps are negative within the inner kpc, down to the resolution limit of our observations."
" The torques computed with the Spitzer--IRAC iimage and BIMA ""CO map (with a resolution limit of 670 ppc) are also negative within the inner ~3 kkpc.", The torques computed with the -IRAC image and BIMA $^{12}$ CO map (with a resolution limit of $\sim$ pc) are also negative within the inner $\sim$ kpc.
" If the bar ends at ~3kkpc, with a pattern speed of the bar Q,~65 kkm s! kpc! then the CR of the bar would be at ~3.3 kkpc."," If the bar ends at $\sim$ kpc, with a pattern speed of the bar $\Omega_{\rm p}$$\sim$ km $^{-1}$ $^{-1}$ then the CR of the bar would be at $\sim$ kpc."
 There is no clear ring signature and we thus exclude the presence of an ILR., There is no clear ring signature and we thus exclude the presence of an ILR.
" Without an ILR, the torques are negative between the CR of the bar and the AGN, down to the resolution limit of our observations."," Without an ILR, the torques are negative between the CR of the bar and the AGN, down to the resolution limit of our observations."
" This scenario is compatible with a young/incipient bar which had no time to slow down from secular evolution, and has not yet formed any ILR."," This scenario is compatible with a young/incipient bar which had no time to slow down from secular evolution, and has not yet formed any ILR."
" lis a potential of inner gas inflow: the gas is certainly fueling the central region, and in a second step could fuel directly the AGN."," is a potential of inner gas inflow: the gas is certainly fueling the central region, and in a second step could fuel directly the AGN."
" lis the fifth NUGA galaxy, together with"," is the fifth NUGA galaxy, together with"
up for any galaxy with V>100 km s7!.,up for any galaxy with $V>100$ km $^{-1}$.
 2. show that for this process to work. none of the merging halos can be cuspy to start with. as only mergers between cored halos give a cored merger product.," \citet{BoylanKolchin:2004p8} show that for this process to work, none of the merging halos can be cuspy to start with, as only mergers between cored halos give a cored merger product."
 Any merger involving a cusp inevitably leads to a cuspy end-product., Any merger involving a cusp inevitably leads to a cuspy end-product.
 ?— also shows that the final slope always equals that of the steepest component., \citet{Dehnen:2005p837} also shows that the final slope always equals that of the steepest component.
 Setting up cored halos and ensuring that they remain cored is apparently not trivial., Setting up cored halos and ensuring that they remain cored is apparently not trivial.
 ? propose a different way to make halos cored: they note that merging gas clouds of ~10°M.. (for dwarfs) to ~10°M.. (for spirals) can disrupt cusps through dynamical friction., \citet{ElZant:2001p56} propose a different way to make halos cored: they note that merging gas clouds of $\sim 10^5\ M_{\odot}$ (for dwarfs) to $\sim 10^8\ M_{\odot}$ (for spirals) can disrupt cusps through dynamical friction.
 If this happens early enough in the universe (when halos were smaller). this process could be very efficient.," If this happens early enough in the universe (when halos were smaller), this process could be very efficient."
 Similar scenarios are presented in 2.., Similar scenarios are presented in \citet{Tonini:2006p59}.
 ?. in their study also argue that the effect of the baryons on the halo structure must be significant., \citet{RomanoDiaz:2008p70} in their study also argue that the effect of the baryons on the halo structure must be significant.
 They suggest that in the presence of baryons. initially a very steep cusp is formed (with à~ —2). which is then heated by sub-halos through dynamical friction. and. subsequently. from the inside out becomes shallower.," They suggest that in the presence of baryons, initially a very steep cusp is formed (with $\alpha \sim -2$ ), which is then heated by sub-halos through dynamical friction, and, subsequently, from the inside out becomes shallower."
 According to their analysis. the end result is a density profile that is less steep than a=—I1 in the inner few kpe. and may even be cored in the very center.," According to their analysis, the end result is a density profile that is less steep than $\alpha = -1$ in the inner few kpc, and may even be cored in the very center."
 ? take the opposite view., \citet{Jardel:2009p372} take the opposite view.
" They model the dynamical friction process. but argue that it is difficult to find ""free-floating"" baryon clumps massive enough to make this process happen. as these clumps must not be associated with dark matter (due to the cusp that will then be formed: see above)."," They model the dynamical friction process, but argue that it is difficult to find ``free-floating'' baryon clumps massive enough to make this process happen, as these clumps must not be associated with dark matter (due to the cusp that will then be formed; see above)."
 They note that work by ?. implies clump masses that are two orders of magnitude too small., They note that work by \citet{Kaufmann:2006p1262} implies clump masses that are two orders of magnitude too small.
 The processes just described are similar to those proposed by ??:; see also ?..," The processes just described are similar to those proposed by \citet{Mashchenko:2006p60, Mashchenko:2008p373}; see also \citet{Ricotti:2004p28}."
 They make it all happen in the early universe. when mass scales and the required. amount. of baryons were both smaller.," They make it all happen in the early universe, when mass scales and the required amount of baryons were both smaller."
 Their numerical. simulations suggest that cusps can be erased in the very early universe (z= 10) when (proto-) galaxies had approximately the size of the HI holes and shells observed in the disks of present-day. gas-rich spiral and dwarf galaxies.," Their numerical simulations suggest that cusps can be erased in the very early universe $z\la 10$ ) when (proto-) galaxies had approximately the size of the HI holes and shells observed in the disks of present-day, gas-rich spiral and dwarf galaxies."
 In objects that small. a random motion of only ~7 km s! (i.e.. equal to the HI velocity dispersion observed in local disk galaxies) is sufficient to disrupt the cusp and keep the halos cored until the present day.," In objects that small, a random motion of only $\sim 7$ km $^{-1}$ (i.e., equal to the HI velocity dispersion observed in local disk galaxies) is sufficient to disrupt the cusp and keep the halos cored until the present day."
 Note though that in a recent analysis. ὁ perform similar calculations. but find that halos remain cuspy. and suggest that differences in the simulation approach might be responsible for this.," Note though that in a recent analysis, \citet{Ceverino:2009p374} perform similar calculations, but find that halos remain cuspy, and suggest that differences in the simulation approach might be responsible for this."
 ? also argue against the idea of creating cores at high redshift., \citet{Chen:2008p375} also argue against the idea of creating cores at high redshift.
 Their argument is that cuspy halos cannot explain gravitational lensing results. but demand halos with an even steeper mass distribution (a singular isothermal sphere with slope «= —2).," Their argument is that cuspy halos cannot explain gravitational lensing results, but demand halos with an even steeper mass distribution (a singular isothermal sphere with slope $\alpha =
-2$ )."
 This means that if the halos of the elliptical galaxies that do the lensing indeed form with NFW-like profiles. these need to steepen over the course of their evolution. using some process for which the quiescent adiabatic contraction is the most likely candidate.," This means that if the halos of the elliptical galaxies that do the lensing indeed form with NFW-like profiles, these need to steepen over the course of their evolution, using some process for which the quiescent adiabatic contraction is the most likely candidate."
 LSB galaxies. on the other hand. need to experience vigorous bursts of early star formation that drive feedback to erase the initial cusp.," LSB galaxies, on the other hand, need to experience vigorous bursts of early star formation that drive feedback to erase the initial cusp."
 These scenarios are at odds with what we know about the evolution of these galaxies: ellipticals typically undergo a large amount of merging. with the associated vigorous star formation. as evidenced by their extensive old stellar populations.," These scenarios are at odds with what we know about the evolution of these galaxies: ellipticals typically undergo a large amount of merging, with the associated vigorous star formation, as evidenced by their extensive old stellar populations."
 LSB galaxies show no evidence at all for any kind of violent interactions. nor intense star formation.," LSB galaxies show no evidence at all for any kind of violent interactions, nor intense star formation."
 Dynamical friction and adiabatie. contraction thus seem to place demands on the evolution of elliptical and LSB galaxies contrary to what can be derived from their star formation histories., Dynamical friction and adiabatic contraction thus seem to place demands on the evolution of elliptical and LSB galaxies contrary to what can be derived from their star formation histories.
 ? and? show that introducing an elliptical disturbance in an NFW potential can lead to systematic (non-circular) motions that. when unrecognized. could be interpreted as evidence for a core.," \citet{Hayashi:2006p97} and \citet{Hayashi:2007p94} show that introducing an elliptical disturbance in an NFW potential can lead to systematic (non-circular) motions that, when unrecognized, could be interpreted as evidence for a core."
 Their arguments particularly apply to longsht Πα observations. where indeed the context of a velocity field is not available to gauge the validity of the circular motion assumption.," Their arguments particularly apply to longslit $\alpha$ observations, where indeed the context of a velocity field is not available to gauge the validity of the circular motion assumption."
 As described earlier. work on high-resolution velocity fields by ?.. ? and ? has put significant observational constraints on the strength of non-circular motions and the ellipticity of the (equatorial) potential.," As described earlier, work on high-resolution velocity fields by \citet{Gentile:2005p89}, \citet{Trachternach:2008p152} and \citet{KuzioDeNaray:2009p67} has put significant observational constraints on the strength of non-circular motions and the ellipticity of the (equatorial) potential."
 For a large sample of disk and dwarf galaxies. this potential is consistent with being round and the non-circular motions are too small to give the illusion of cores in long-slit observations.," For a large sample of disk and dwarf galaxies, this potential is consistent with being round and the non-circular motions are too small to give the illusion of cores in long-slit observations."
 The results from ? and? assume massless disks.," The results from \citet{Hayashi:2006p97} and \citet{Hayashi:2007p94}
 assume massless disks."
 ? present results from simulations of self-consistent massive disks in triaxial halos and find that the baryons cireularize the potential rapidly. even for low-mass disks. thus wiping out a large part of the tri-axiality signal.," \citet{Bailin:2007p66} present results from simulations of self-consistent massive disks in triaxial halos and find that the baryons circularize the potential rapidly, even for low-mass disks, thus wiping out a large part of the tri-axiality signal."
" ? also presents models of ""νου disks in tri-axial halos. and can approximate an observed LSB rotation curve by introducing tri-axiality in the halo."," \citet{Widrow:2008p58} also presents models of “live” disks in tri-axial halos, and can approximate an observed LSB rotation curve by introducing tri-axiality in the halo."
 In all these studies it would be interesting to compare simulated velocity fields with the observed ones., In all these studies it would be interesting to compare simulated velocity fields with the observed ones.
 As has become clear from the preceding discussion. modeling the long-slit rotation curves leaves too many ambiguities which only studies of the velocity fields can address.," As has become clear from the preceding discussion, modeling the long-slit rotation curves leaves too many ambiguities which only studies of the velocity fields can address."
 In an observational study. ? subject model NEW velocity fields to the DensePak observing procedure. and show that even in the presence of observational uncertainties the signature of an NFW velocity field can be observed.," In an observational study, \citet{KuzioDeNaray:2009p67}
 subject model NFW velocity fields to the DensePak observing procedure, and show that even in the presence of observational uncertainties the signature of an NFW velocity field can be observed."
 They show that axisymmetric NFW velocity fields are unable to reproduce the observed velocity fields for any combination of inclination and viewing angle., They show that axisymmetric NFW velocity fields are unable to reproduce the observed velocity fields for any combination of inclination and viewing angle.
 They derive NFW velocity fields in an elliptical potential. and show that the only way these can be made to resemble the observations is by having the observer's line of sight along the minor axis of the potential for 6 out of the 7 galaxies investigated. inconsistent with a random distribution of the line of sight.," They derive NFW velocity fields in an elliptical potential, and show that the only way these can be made to resemble the observations is by having the observer's line of sight along the minor axis of the potential for 6 out of the 7 galaxies investigated, inconsistent with a random distribution of the line of sight."
 ? also note that the kind of rapidly varying ellipticity of the potential as proposed by ? might help in better describing the data. but that the problem— of a preferred viewing angle will remain.," \citet{KuzioDeNaray:2009p67} also note that the kind of rapidly varying ellipticity of the potential as proposed by \citet{Hayashi:2007p94}
 might help in better describing the data, but that the problem of a preferred viewing angle will remain."
 For an elliptical potential with a random viewing angle. one also expects. once in a while. to observe a rotation curve that is steeper than the corresponding axisymmetric ΝΕ profile.," For an elliptical potential with a random viewing angle, one also expects, once in a while, to observe a rotation curve that is steeper than the corresponding axisymmetric NFW profile."
 Rotation curves like that are. however. exceedingly rare. if not absent. in the available observations.," Rotation curves like that are, however, exceedingly rare, if not absent, in the available observations."
 Rotation curves of LSB and late-type. gas-rich dwarf galaxies indicate the presence of constant-density or mildy cuspy (n~ —0.2) dark matter cores. contradicting the predictions of cosmological simulations.," Rotation curves of LSB and late-type, gas-rich dwarf galaxies indicate the presence of constant-density or mildy cuspy $\alpha \sim -0.2$ ) dark matter cores, contradicting the predictions of cosmological simulations."
 The most recent simulations still indicate resolved mass density slopes that are too steep to be easily reconciled with the observations (typically a—0.8 at a radius 0.1 kpe)., The most recent simulations still indicate resolved mass density slopes that are too steep to be easily reconciled with the observations (typically $\alpha \sim -0.8$ at a radius $\sim 0.1$ kpc).
 Claims of shallow slopes at even smaller radit depend on the validity of the analytical deseription chosen for the mass-density profile., Claims of shallow slopes at even smaller radii depend on the validity of the analytical description chosen for the mass-density profile.
 Whereas early HI observations and long-slit Ha rotation, Whereas early HI observations and long-slit $\alpha$ rotation
"tends to saturate al some asvmptotie value lor large A"".",tends to saturate at some asymptotic value for large $K'$.
" To understand what is happening. let us look at Figure 3 which shows the evolution of magnetic field during a hall-periocl for the case A""=1000. fy=0.5."," To understand what is happening, let us look at Figure 3 which shows the evolution of magnetic field during a half-period for the case $K' = 1000$, $f_d = 0.5$."
 In the plots of poloidal field. we have indicated the LIntitudes of last flux eruption with small arrows.," In the plots of poloidal field, we have indicated the latitudes of last flux eruption with small arrows."
 ILowever. the individual double rings are not usually discernable.," However, the individual double rings are not usually discernable."
 That is not surprising., That is not surprising.
 Flux eruption in the form of double rings keeps occuring al intervals of 7., Flux eruption in the form of double rings keeps occuring at intervals of $\tau$.
 Hence the latest double ring is merely superposed on (he field created bv the previous double rings and does not stand out. against the background of previously created field., Hence the latest double ring is merely superposed on the field created by the previous double rings and does not stand out against the background of previously created field.
 On looking al the plots of the toroidal field. it is clear that the toroidal field keeps weakening as we go to lower latitudes.," On looking at the plots of the toroidal field, it is clear that the toroidal field keeps weakening as we go to lower latitudes."
 This weakening of toroidal field at lower latitudes becomes more prominent as we make fy larger., This weakening of toroidal field at lower latitudes becomes more prominent as we make $f_d$ larger.
 This implies that [Iux eruption never lakes place al verv low latitudes and the dvnamo process is basically confined to hieher latitudes., This implies that flux eruption never takes place at very low latitudes and the dynamo process is basically confined to higher latitudes.
 Since it takes less time to transport magnetic flux through a limited range of latitudes. the dynamo period is shorter for non-zero fy.," Since it takes less time to transport magnetic flux through a limited range of latitudes, the dynamo period is shorter for non-zero $f_d$."
" la combination with this effect. an increasing A"" will make the erupted double rings stronger. thus reeveling toroidal flux to poloidal flux more efficiently."," In combination with this effect, an increasing $K'$ will make the erupted double rings stronger, thus recycling toroidal flux to poloidal flux more efficiently."
 This reduces the time period of the dvnamo as compared to the period in the limit of the CSD model. in which the toroidal field is brought to the surface by the meridional [low only near the equator and the whole range of latitiuices is involved.," This reduces the time period of the dynamo as compared to the period in the limit of the CSD model, in which the toroidal field is brought to the surface by the meridional flow only near the equator and the whole range of latitudes is involved."
 It may be noted that Durnev (1997) did not present anv plots of magnetic field configurations in his paper., It may be noted that Durney (1997) did not present any plots of magnetic field configurations in his paper.
 However. we clo get a deeper insight into the problem by looking ab such field configuration plots.," However, we do get a deeper insight into the problem by looking at such field configuration plots."
 For example. note that the direction of the poloidal field (clockwise or anti-clockwise) starts reversing al the time when we have an extended belt of strong toroidal field.," For example, note that the direction of the poloidal field (clockwise or anti-clockwise) starts reversing at the time when we have an extended belt of strong toroidal field."
 Durnev (1997) has presented several plots showing how the eruption latitude changes with (ime (Figures 710 in his paper)., Durney (1997) has presented several plots showing how the eruption latitude changes with time (Figures 7–10 in his paper).
" We present a similar plot in Figure 4 lor the case A""=1000. fy=0. corresponding to no flux depletion at the bottom as in the caleulations of Durnev (1997)."," We present a similar plot in Figure 4 for the case $K' = 1000$, $f_d = 0$, corresponding to no flux depletion at the bottom as in the calculations of Durney (1997)."
 IIere. we see (hat eruptions continue near (he pole lor some time al," Here, we see that eruptions continue near the pole for some time at"
 , 
are passive galaxies with no measurable cussion lines.,are passive galaxies with no measurable emission lines.
 Table 2 preseuts the emission line measurements of the romuining 87 used to construct the BPT diaerzun (7) of Figure L., Table \ref{elines} presents the emission line measurements of the remaining 87 used to construct the BPT diagram \citep{bpt81} of Figure \ref{bpt}.
" The dashed lines separate the star forming and Αν regions of ο, and the curved lines slow separations between star formingOm C5galaxies from the SDSS (?).. composite sources. and a theoretical upver ΠΕ for sources that cau be described by star fornire models (2)."," The dashed lines separate the star forming and AGN regions of \citet{ost06}, and the curved lines show separations between star forming galaxies from the SDSS \citep{kau03}, composite sources, and a theoretical upper limit for sources that can be described by star forming models \citep{kew02}."
. Ouly four are Sevfert ealaxies. aid 14 LINER.," Only four are Seyfert galaxies, and 14 LINER."
 Most cunission line galaxies fa lin tje star forming region. or in the transition region where star formation is still a domiuaut process.," Most emission line galaxies fall in the star forming region, or in the transition region where star formation is still a dominant process."
 Stirs. galaxies. and broad line ACN cau be differcutiated using their IRAC colors. (????)..," Stars, galaxies, and broad line AGN can be differentiated using their IRAC colors \citep{eis04,lac04,saj05,don08}."
 AGN are well separated because the power law of ACN ecinission is more red than the ealaxy spectrum in the 3.67022 channel. aud because there is a lack of PAIS in AGN.," AGN are well separated because the power law of AGN emission is more red than the galaxy spectrum in the $\mu$ m channel, and because there is a lack of PAHs in AGN."
 ? plot the IRAC colors as (8.0/0.5) vs (5.8/3.6) which separates objects with blue continua from objects with red continua: ACN tend to be red in both IRAC color filters., \citet{lac04} plot the IRAC colors as (8.0/4.5) vs (5.8/3.6) which separates objects with blue continua from objects with red continua; AGN tend to be red in both IRAC color filters.
 We plot the IRAC colors of our MIPS selected ealaxies in Fieure 5.., We plot the IRAC colors of our MIPS selected galaxies in Figure \ref{iracAGN}.
 The majority of bright IR sources avoid the AGN region. although four may be classified as AGN.," The majority of bright IR sources avoid the AGN region, although four may be classified as AGN."
 The predicted IRAC colors from template galaxies used in our SED fitting. at the redshift iuterval of the Coma Cluster. are also shown iu the figure.," The predicted IRAC colors from template galaxies used in our SED fitting, at the redshift interval of the Coma Cluster, are also shown in the figure."
 As can be seen. the template ACN (triangles) occupy approximately the same locus as defined ly ?..," As can be seen, the template AGN (triangles) occupy approximately the same locus as defined by \citet{lac04}."
 Using the radio-FIR correlation for star forming ealaxies of 7.. we cau determine the presence of radio-excess ACN.," Using the radio-FIR correlation for star forming galaxies of \citet{con92}, we can determine the presence of radio-excess AGN."
 We use the catalog of 1.1GIIz radio fluxes for Coma galaxies frou ? alc match the radio galaxies to our MIPS {μια ane Tau sources., We use the catalog of 1.4GHz radio fluxes for Coma galaxies from \citet{mil09} and match the radio galaxies to our MIPS $\mu$ m and $\mu$ m sources.
 The 1.L002 resolution is similar to tha of the 2tyan resolution. aud we match our sources purely on proximity in RA. Dec. iux redshift.," The 1.4GHz resolution is similar to that of the $\mu$ m resolution, and we match our sources purely on proximity in RA, Dec, and redshift."
 As shown in Figure 6.. sources well olow the relationship harbora radio excess. this is attributed to AGN emission.," As shown in Figure \ref{qval}, , sources well below the relationship harbora radio excess, this is attributed to AGN emission."
" Frou ?.. the Inuitiug ratios are Qe l= log (ομη ""ISος )o L40.27 and qry= log (Stopes δη αμ) ~ 2.3040.16."," From \citet{app04}, , the limiting ratios are $_{24}$ = log $_{24\mu m}$ $_{1.4GHz}$ $\sim$ $\,\pm\,$ 0.27 and $_{70}$ = log $_{70\mu m}$ $_{1.4GHz}$ ) $\sim$ $\,\pm\,$ 0.16."
Meylan ((2001).,Meylan (2001).
 Changes in the assumed flattening have little effect on the results below., Changes in the assumed flattening have little effect on the results below.
 The models are similar to those presented in Gebhardt ((2002)., The models are similar to those presented in Gebhardt (2002).
 They are axisymmetric. orbit-based models and so do not rely on a specified form for the distribution function.," They are axisymmetric, orbit-based models and so do not rely on a specified form for the distribution function."
 Thus. for an axisymmetric system. these models provide the most general solution.," Thus, for an axisymmetric system, these models provide the most general solution."
 The models require an input potential. in which. we run a set of stellar orbits covering the available phase space.," The models require an input potential, in which we run a set of stellar orbits covering the available phase space."
 We find a non-negative set of orbital weights that best matches both the photometry and kinematics to provide an overall \7 fit., We find a non-negative set of orbital weights that best matches both the photometry and kinematics to provide an overall $\chi^2$ fit.
 We vary the central black hole mass and re-fit., We vary the central black hole mass and re-fit.
 The orbit-based models store the kinematic and photometric results in both spatial and velocity bins., The orbit-based models store the kinematic and photometric results in both spatial and velocity bins.
 For Gl. we use 12 radial. 4 angular. and 13 velocity bins.," For G1, we use 12 radial, 4 angular, and 13 velocity bins."
 The data consist of the seven different STIS positions along a position angle uup from the major axis and one ground-based observation centered on the cluster., The data consist of the seven different STIS positions along a position angle up from the major axis and one ground-based observation centered on the cluster.
 The point-spread function. for both aand ground-based observations. are. included. directly into the models., The point-spread function for both and ground-based observations are included directly into the models.
 The program matches the luminosity density everywhere throughout the cluster to better than0., The program matches the luminosity density everywhere throughout the cluster to better than.
5%.. The quality of the fit is determined from the match to the velocity profiles., The quality of the fit is determined from the match to the velocity profiles.
 The data points consist of 7«13 STIS. velocity bins plus the one ground-based dispersion. making 92 total points.," The data points consist of $7\times13$ STIS velocity bins plus the one ground-based dispersion, making 92 total points."
 However. many of these points are correlated. since the smoothing used for the velocity profile extraction tends to correlate adjacent bins.," However, many of these points are correlated since the smoothing used for the velocity profile extraction tends to correlate adjacent bins."
 The reduction im the number of independent parameters is hard to estimate but is. generally around a factor of 2-4 (Gebhardt 22002)., The reduction in the number of independent parameters is hard to estimate but is generally around a factor of 2–4 (Gebhardt 2002).
 Figure 2 plots a two-dimensional map of the different models and the corresponding contours for 47., Figure 2 plots a two-dimensional map of the different models and the corresponding contours for $\chi^2$.
 The smallest value of 47 is 17: given the 92 parameters. the reduction of the independent parameters is about a factor of 5. higher than typical. which we attribute to the small radial extent of the data.," The smallest value of $\chi^2$ is 17; given the 92 parameters, the reduction of the independent parameters is about a factor of 5, higher than typical, which we attribute to the small radial extent of the data."
 The two independent parameters in the models are the BH mass and the stellar mass-to-light ratio (M /L)., The two independent parameters in the models are the BH mass and the stellar mass-to-light ratio $M/L$ ).
 The best-fit BH mass 1s 2.0(41.4.-0.8)10. with M/Ly = 2.6.," The best-fit BH mass is $2.0(+1.4,-0.8)\times10^4\,\Msun$ with $M/L_V$ = 2.6."
 Figure 3 shows the one-dimensional plot of 4 versus BH mass., Figure 3 shows the one-dimensional plot of $\chi^2$ versus BH mass.
 The difference in V between the zero BH mass model and the best fit is 3.0. implying a significance above for the BH detection.," The difference in $\chi^2$ between the zero BH mass model and the best fit is 3.0, implying a significance above for the BH detection."
 Spt Spt Spt Our best-fit model has a BH mass of 2.0«10M...," 5pt 5pt 5pt Our best-fit model has a BH mass of $2.0\times10^4\,\Msun$."
" We can place this measurement on the M,—c relation (Gebhardt 22000b: Ferrarese Merritt 2000) using the ground-based measurement of 5=25.141.7s!.", We can place this measurement on the $M_{\bullet}-\sigma$ relation (Gebhardt 2000b; Ferrarese Merritt 2000) using the ground-based measurement of $\sigma = 25.1\pm1.7$.
". Figure 4 plots the M,—0 correlation for nearby galaxies using the compilation and the linear relation given in Tremaine ((2002).", Figure 4 plots the $M_{\bullet}-\sigma$ correlation for nearby galaxies using the compilation and the linear relation given in Tremaine (2002).
 GI lies in excellent agreement with the extrapolation of the linear fit to the local galaxies., G1 lies in excellent agreement with the extrapolation of the linear fit to the local galaxies.
seen in the third. panel of 77. c librates around 322° with an amplitude smaller than 5°.,"seen in the third panel of 7, $\omega$ librates around $322^\circ$ with an amplitude smaller than $5^\circ$."
 To our best knowledge. there is no such an “asymmetrical” libration center of w being reported before.," To our best knowledge, there is no such an “asymmetrical” libration center of $\omega$ being reported before."
 However. in the case of Neptune ‘Trojan. there are at least two facts that must be taken into account in the analysis of the Wozai resonance.," However, in the case of Neptune Trojan, there are at least two facts that must be taken into account in the analysis of the Kozai resonance."
 First. the object is in a 1:1 mean motion resonance with Neptune. and second. there is more than one perturber on the asteroid's motion.," First, the object is in a 1:1 mean motion resonance with Neptune, and second, there is more than one perturber on the asteroid's motion."
 Thus we believe the Ixozai resonance here is more complicated and it deserves a careful investigation in future., Thus we believe the Kozai resonance here is more complicated and it deserves a careful investigation in future.
 As for the unstable eap at my~44° in the dynamical map. a close look at the orbits reveals that it is due to the apsiclal secular resonance vx.," As for the unstable gap at $i_0\sim 44^\circ$ in the dynamical map, a close look at the orbits reveals that it is due to the apsidal secular resonance $\nu_8$."
 A vs secular resonance happens when the precession rate of the Trojan's perihelion equals the fundamental frequency. gs of the solar svstem. which is mainly related to the apsidal precession of Neptune.," A $\nu_8$ secular resonance happens when the precession rate of the Trojan's perihelion equals the fundamental frequency $g_8$ of the solar system, which is mainly related to the apsidal precession of Neptune."
 Roughhy speaking. in a vs resonance. the Trojan's perihelion precesses at almost the same rate as Neptune's perihelion does. and the dillerence between the longitudes of perihelion zc oscillates around a constant value with a definite amplituce.," Roughly speaking, in a $\nu_8$ resonance, the Trojan's perihelion precesses at almost the same rate as Neptune's perihelion does, and the difference between the longitudes of perihelion $\varpi-\varpi_8$ oscillates around a constant value with a definite amplitude."
 We illustrate in Fig.SS the orbital evolution of a typical ‘Trojan initialized in the unstable eap to show the elfects of the vs resonance., We illustrate in 8 the orbital evolution of a typical Trojan initialized in the unstable gap to show the effects of the $\nu_8$ resonance.
 As shown in SS. e librates with a small amplitucle around the Lagrange point Lz witha¢(657.527) before 1.5710* vvr.," As shown in 8, $\sigma$ librates with a small amplitude around the Lagrange point $L_5$ with $\sigma\in(-65^\circ,
-52^\circ)$ before $1.57\times 10^7$ yr."
 Thanks to the protection of the 1:1 resonance. the evolutions of other orbital elements during this perioc are regular. e.g. e is nearlv constant ancl / varies aroun 44 with an amplitude of only ~4.," Thanks to the protection of the 1:1 resonance, the evolutions of other orbital elements during this period are regular, e.g. $a$ is nearly constant and $i$ varies around $\sim44^\circ$ with an amplitude of only $\sim4^\circ$."
 But there is one exception. the eccentricity e is increasing curing this perio and it reaches e=0.355 at 2—1.5710 vyr.," But there is one exception, the eccentricity $e$ is increasing during this period and it reaches $e=0.355$ at $T=1.57\times 10^7$ yr."
 We know tha he secular resonance related to the perihelion precession may clive the eccentricity up (Alurray&Dermott1999)., We know that the secular resonance related to the perihelion precession may drive the eccentricity up \citep{mur99}.
. In act. the vs secular resonance. characterized by a libration of x weasshown in the bottom panel of SS. is responsible or this cecentricity increasing.," In fact, the $\nu_8$ secular resonance, characterized by a libration of $\varpi - \varpi_8$ as shown in the bottom panel of 8, is responsible for this eccentricity increasing."
 Again. the high eccentricitv. this time owing to the Ux resonance. reduces the Trojan's perihelion distance. and hen the object is driven out by the strong perturbations during close encounters with Uranus.," Again, the high eccentricity, this time owing to the $\nu_8$ resonance, reduces the Trojan's perihelion distance, and then the object is driven out by the strong perturbations during close encounters with Uranus."
 We may note that after eaving the 1:1 mean motion resonance and before. being scattered far away. the object temporally experiences the ]xozai resonance again from MMyr to MMyr. with w oscillating. around. 180 this time.," We may note that after leaving the 1:1 mean motion resonance and before being scattered far away, the object temporally experiences the Kozai resonance again from Myr to Myr with $\omega$ oscillating, around $180^\circ$ this time."
 So far we discussed two mechanisms that alfect the secular behavior of Trojan orbits. be. the Wozai resonance and the # resonance.," So far we discussed two mechanisms that affect the secular behavior of Trojan orbits, i.e. the Kozai resonance and the $\nu_8$ resonance."
 Apart from the unstable regions due to these two mechanisms. some other chaotic subregions embedded: in. the dynamical. map can he seen. e.g. the blue (chaotic) are structures mentioned in 33.1.," Apart from the unstable regions due to these two mechanisms, some other chaotic subregions embedded in the dynamical map can be seen, e.g. the blue (chaotic) arc structures mentioned in 3.1."
 The possible mechanisms behind these structures are not. so obvious., The possible mechanisms behind these structures are not so obvious.
 However. since the orbital periods of Neptune and Uranus are very close to a 2:1 commensurability vyr ves vvr). the three-body mean motion resonance (Nesorny&Alorbidelli1998). between the Trojan and them is à good guess.," However, since the orbital periods of Neptune and Uranus are very close to a 2:1 commensurability yr yr), the three-body mean motion resonance \citep{nes98} between the Trojan and them is a good guess."
 For a Neptune Trojan. we expect that a. three-bocdy resonance may happen when A|AxAw~0.," For a Neptune Trojan, we expect that a three-body resonance may happen when $\dot\lambda+ \dot\lambda_8- \dot\lambda_7\sim 0$."
 The resonant angles associated with this resonance would be any combination of the form: where {ἐνἐκ are integers satisfving the cdXlembert rule: /|feἐκ=d.," The resonant angles associated with this resonance would be any combination of the form: where $l, l_7, l_8$ are integers satisfying the d'Alembert rule: $l+l_7+l_8=-1$."
 Dillerent resonances with cilferent combinations of /./; and fs may be responsible for the “multiplet” are structures in the dvnamical map.," Different resonances with different combinations of $l, l_7$ and $l_8$ may be responsible for the “multiplet” arc structures in the dynamical map."
 By testing the behavior of orbits. we find that several (but not. all) ‘Trojans initialized in the most distinct chaotic are may be related to the £F.τιés combination of 2. -3. 0.," By testing the behavior of orbits, we find that several (but not all) Trojans initialized in the most distinct chaotic arc may be related to the $l, l_7, l_8$ combination of 2, -3, 0."
 For these orbits the angle A|AsAzστοBey typically varies very slowly.," For these orbits the angle $\lambda+ \lambda_8-
\lambda_7 + 2\varpi- 3\varpi_7$ typically varies very slowly."
"- This is an ""order 5 resonance.", This is an “order 5” resonance.
 But in fact. as we will see in next section. those ares probably are not caused by the three-body resonance.," But in fact, as we will see in next section, those arcs probably are not caused by the three-body resonance."
 Lt is impossible απ unreasonable to check all the combinations of the integers {.τιἐκ for all orbits inside an interesting area.," It is impossible and unreasonable to check all the combinations of the integers $l, l_7, l_8$ for all orbits inside an interesting area."
 To obtain a global understanding of motion on the initial plane (05.75). we turn to a frequency analysis method in next section.," To obtain a global understanding of motion on the initial plane $(a_0,i_0)$, we turn to a frequency analysis method in next section."
 We have integrated thousands of Trojan orbits to construct the dynamical map and the filtered output. from the integrations contains valuable information about the global view of the motion on the initial plane., We have integrated thousands of Trojan orbits to construct the dynamical map and the filtered output from the integrations contains valuable information about the global view of the motion on the initial plane.
 We show in this part our Lrequeney analysis on three basic variables in the motion: the resonant argument in the form of cose and the non-singular variables & ancl q. which are related to the eccentricity e and inclination 7 through the relations: The speetra of these variables give information about the most important rates of the resonant argument. the perihelion longitude and the nodal longitude.," We show in this part our frequency analysis on three basic variables in the motion: the resonant argument in the form of $\cos\sigma$ and the non-singular variables $k$ and $q$ , which are related to the eccentricity $e$ and inclination $i$ through the relations: The spectra of these variables give information about the most important rates of the resonant argument, the perihelion longitude and the nodal longitude."
" We denote these three proper frequencies by f,.g and s hereafter."," We denote these three proper frequencies by $f_\sigma, g$ and $s$ hereafter."
 Typically. a power spectrum of cosahk or q ds very informative but. simultaneously. very complicated as well.," Typically, a power spectrum of $\cos\sigma, k$ or $q$ is very informative but simultaneously very complicated as well."
 ]t is a complicated: composition of peaks at all the forced [requencies. free frequencies. their. harmonics and. their combinations.," It is a complicated composition of peaks at all the forced frequencies, free frequencies, their harmonics and their combinations."
 Pherefore a. direct. look at a specific power spectrum may not be very helpful., Therefore a direct look at a specific power spectrum may not be very helpful.
 However. when we exam the continuous change of the spectrum with a parameter. some important features emerge.," However, when we exam the continuous change of the spectrum with a parameter, some important features emerge."
" This continuous change of a spectrum. defined as thespectrum, is caleulated in this paper."," This continuous change of a spectrum, defined as the, is calculated in this paper."
 We first list the fundamental frequencies. (Nobili.Mi-lani&Carpino1989) in the outer solar svstem in. Table 2., We first list the fundamental frequencies \citep{nob89} in the outer solar system in Table 2.
 One frequeney. not listed but important in the dynamics of Neptune Trojan is the frequency. of the quasi 2:1 mean motion resonance between Neptune and Uranus. fox.," One frequency not listed but important in the dynamics of Neptune Trojan is the frequency of the quasi 2:1 mean motion resonance between Neptune and Uranus, $f_{\rm 2N:1U}$."
 The value. determined. from our caleulation. is foray= 2z/vr. corresponding to a period of vvr.," The value determined from our calculation is $f_{\rm 2N:1U} = 2.3606 \times 10^{-4}\,2\pi$ /yr, corresponding to a period of yr."
 For each orbit initialized on a horizontal or vertical straight line on the (a0.0)plane. the EET is performed on the filtered output of & (or q.cosm) ancla power spectrum. is obtained.," For each orbit initialized on a horizontal or vertical straight line on the $(a_0,i_0)$plane, the FFT is performed on the filtered output of $k$ (or $q, \cos\sigma$ ) anda power spectrum is obtained."
 The leading terms in the spectrum are picked, The leading terms in the spectrum are picked
"although this dillerence is modest in comparison with the change in Zi, and. ὃς. and it goes in the opposite direction.","although this difference is modest in comparison with the change in $\zt_{\rm b}$ and $\zt_{\rm s}$, and it goes in the opposite direction."
 The above behaviour can be understood. using the analvtic expressions derived. in paper Lb. and reproduced in Appendix A..," The above behaviour can be understood using the analytic expressions derived in paper I, and reproduced in Appendix \ref{sec:appA}."
 Emploving the same reasoning as in our analvsis of Figs., Employing the same reasoning as in our analysis of Figs.
 4 and 5. in Section 4.2.1.. we emplov the height Zi of the base of the wind as a proxy for ὃς in this analysis.," \ref{fig:10_1} and \ref{fig:5_10} in Section \ref{subsubsec:sigH}, we employ the height $\zt_{\rm b}$ of the base of the wind as a proxy for $\zt_{\rm s}$ in this analysis."
 Using equations (AS)) and (N0)). we estimate that. to leacing order. bohzm(γι.|3D/(Yu|[7]) and Befam(YXS15Yup3/2140)/0X8.5Yuaps|/21050 ). where the subscripts ο) and 7- refer to the positive- and negative-polarity. cases. respectively.," Using equations \ref{eq:ht}) ) and \ref{eq:zb}) ), we estimate that, to leading order, ${\tilde
h}_+/{\tilde h}_- \approx (2\upo - |\beta|)/(2\upo + |\beta|)$ and $\zt_{\rm b +}/\zt_{\rm b -} \approx (\upo^2 + 5\upo |\beta|/2 +
\beta^2)/(\upo^2 - 5\upo |\beta|/2 + \beta^2)$ , where the subscripts `+' and `-' refer to the positive- and negative-polarity cases, respectively."
 Using also equations (83)) and (S4)). we hat. for the parameters adopted. in Figs.," Using also equations \ref{eq:upo}) ) and \ref{eq:betio}) ), we infer that, for the parameters adopted in Figs."
" δ and 9.. inferh./h|ezOSD and τιft,&2.28."," \ref{fig:5_2}
 and \ref{fig:5_3_1}, ${\tilde h}_+/{\tilde h}_- \approx 0.85$ and $\zt_{\rm b +}/\zt_{\rm b -} \approx 2.28$."
 These estimates are entirely consistent with the numerical results (For à fixed value of ο) shown in the two figures., These estimates are entirely consistent with the numerical results (for a fixed value of $\epsilon$ ) shown in the two figures.
" Furthermore. from equation CX3)) we confirm that [6,4/b,,4,| is >1 and hence (using equation AJ) that 6,1,στνο αυ. inclepencently of the sign of 2. reproducing the actual behaviour of the solutions in Fig. δι,"," Furthermore, from equation \ref{eq:B_rbB_phib}) ) we confirm that $|b_{r{\rm
b}}/b_{\phi{\rm b}}|$ is $\gg 1$ and hence (using equation \ref{eq:rphi_B}) ) that $b_{r{\rm b}} \approx \sqrt{2}/a_0$ , independently of the sign of $\beta$, reproducing the actual behaviour of the solutions in Fig. \ref{fig:5_2}."
" Setting ba,7ba. we then infer from equations CX3)) and CX8)) that ban.fbmhfh (=0.85 for the adopted. parameters)."," Setting $b_{r{\rm b+}}\approx
b_{r{\rm b-}}$, we then infer from equations \ref{eq:B_rbB_phib}) ) and \ref{eq:ht}) ) that $b_{\phi{\rm b}+}/b_{\phi{\rm b}-} \approx
{\tilde h}_+/{\tilde h}_-$ $\approx 0.85$ for the adopted parameters)."
 This conclusion. too. is consistent with the result exhibited in Fig. δ..," This conclusion, too, is consistent with the result exhibited in Fig. \ref{fig:5_2}."
" Although the specific angular momentum at the base of the flow is mostly magnetic (corresponding to the wind model parameter A being=> 1). the fact that ba,fb«1 does not imply that the value of A is larger in the negative- case."," Although the specific angular momentum at the base of the flow is mostly magnetic (corresponding to the wind model parameter $\lambda$ being $\gg
1$ ), the fact that $b_{\phi{\rm b}+}/b_{\phi{\rm b}-} < 1$ does not imply that the value of $\lambda$ is larger in the negative-polarity case."
" In fact. the converse is true. as can be seen using cquation (021). from which it follows that AfA(ba,fbonMp.fps ) "," In fact, the converse is true, as can be seen using equation \ref{eq:ele}) ), from which it follows that $\lambda_+/\lambda_-
\approx (b_{\phi{\rm b}+}/b_{\phi{\rm b}-})(\rhot_{\rm s -}/\rhot_{\rm s
+})$ ."
Given that pofp. is twpically bonfa (as the solutions in Fie.," Given that $\rhot_{\rm s -}/\rhot_{\rm s+}$ is typically $\gg
b_{\phi{\rm b}-}/b_{\phi{\rm b}+}$ (as the solutions in Fig."
 S. demonstrate). we find hat A/AÀ.," \ref{fig:5_2} demonstrate), we find that $\lambda_+/\lambda_- 
\gg 1$."
" Physically. the magnetic torque acting on he disc (x D.D,,) and corresponcinely the mass accretion rate and the rate of inward angular momentum advection are slightly larger in the negative-polarity case."," Physically, the magnetic torque acting on the disc $\propto B_z
B_\phi$ ) and correspondingly the mass accretion rate and the rate of inward angular momentum advection are slightly larger in the negative-polarity case."
 Llowever. he mass outllow rate is significantlv larger in this case and therefore the angular momentum (the angular momenttun per unit mass) has to be much smaller in order or the rate of inward (racial) and outward (vertical) angular momentum transport to balance cach other.," However, the mass outflow rate is significantly larger in this case and therefore the angular momentum (the angular momentum per unit mass) has to be much smaller in order for the rate of inward (radial) and outward (vertical) angular momentum transport to balance each other."
 An alternative wav of arriving at this conclusion is to consider the wind solutions that are self-consistentlv. matched. to these. disc solutions., An alternative way of arriving at this conclusion is to consider the wind solutions that are self-consistently matched to these disc solutions.
" The matched wind solutions lie on a £i= const curve in the «A wind parameter space (see equation 64)). and along such a curve values of κf, (seeequation 62)) correspond to valuesof A (see Fig."," The matched wind solutions lie on a $\xi_{\rm b}{'}=\;$ const curve in the $\kappa-\lambda$ wind parameter space (see equation \ref{eq:incl}) ), and along such a curve values of $\kappa \propto \rhot_{\rm s}$ (seeequation \ref{eq:kappa}) ) correspond to valuesof $\lambda$ (see Fig."
 2 in BPS2)., 2 in BP82).
 ↾↓∖↓∐⋅∪↓≻⇂⊲⊔⇍⋜↧↓⊔↓∪⊔⊀∐∪↓⋰↓⊔⋏∙≟∖∖⊽⋜↧⊳∖↓≻⋖⋅↓⋅⇂⋅∪↓⋅⊔↓∢⊾∠⇂⊔⊳∖⊀↓⊔⋏∙≟↓↕∢⋅⇀∖↓∖⊽∐↓≺⊲⇀∖↳∖↓ ↕↓↕≻⇂↓⋅⇂⇂↓↥↓∢⊾↓↥↿⊔↓∪⊔⊔∩⊾∠⇂∪⊔⇂↓⊔⊾↓⊳∶∫≻↓⊔∺↳∖↓⇀∖,"The optical monitoring was performed using the ANDICAM instrument mounted on the 1.3m SMARTS telescope in Cerro Tololo, Chile."
∐↾↓∖∺↿⋖⊾↓⋖⋅≻≼⇍⋖⋟↓≻∢⊾↕↓↕ ≺⊲⋖⊾↓⋅↓⋅∪↾↓∖∪↓∪⇂∪⋡≺⊲↓↥∐⋖⊾⋡↾↓∖∖∖⊽∪∐⋜⋯∠⇂∖↾∣⋯⊔∠⋖⊾⇀∖↓≻∪⋡∖⊔↓⋅⋖⊾⋡∖∪⇂⋅ wavere taken for each filter., Two B and V band exposures of were taken for each filter.
 Observations were made every four cays between 2006 December 1 and 2008 August 31 inclucling a daily sampling period between 2008 February 15 and April 28., Observations were made every four days between 2006 December 1 and 2008 August 31 including a daily sampling period between 2008 February 15 and April 28.
 Phe period of daily sampling in the optical was contained within the period of intensive X-ray monitoring., The period of daily sampling in the optical was contained within the period of intensive X-ray monitoring.
 We performed psf photometry on aanel four non-variable stars in the field of view using the task psf, We performed psf photometry on and four non-variable stars in the field of view using the task psf.
 We constructed relative flux light curves by dividing the Lux measured lor nucleus by the sum of the reference star. [luxes., We constructed relative flux light curves by dividing the flux measured for nucleus by the sum of the reference star fluxes.
. The errors were calculated by propagating the magnitude error produced by the psf task., The errors were calculated by propagating the magnitude error produced by the psf task.
 We confirmec that the relative Dux ol the reference stars was constant throughout the campaign., We confirmed that the relative flux of the reference stars was constant throughout the campaign.
 A D band image of aand the reference stars is shown in Fig. 2.., A B band image of and the reference stars is shown in Fig. \ref{image}.
 We note that the underlving galaxy Bux within the nuclear PSE is not subtracted from the AGN Iux. so a relatively small amount of starlight contamination remains.," We note that the underlying galaxy flux within the nuclear PSF is not subtracted from the AGN flux, so a relatively small amount of starlight contamination remains."
 We performed. aperture photometry on the reference stars ancl used the zero-point correction factors calculated or the SALARTS telescope every photometric night. ogether with the airmass of our observations. to calibrate wir magnitudes.," We performed aperture photometry on the reference stars and used the zero-point correction factors calculated for the SMARTS telescope every photometric night, together with the airmass of our observations, to calibrate their magnitudes."
 We converted these magnitudes into Ilux ensities at 5500 for the V. band and for D. assuming a flat spectrum (a= 0) within each band uxi used the total [flux of the four stars to calibrate the mcclative-Llux light curve of3783.," We converted these magnitudes into flux densities at 5500 for the V band and for B, assuming a flat spectrum $\alpha=0$ ) within each band and used the total flux of the four stars to calibrate the relative-flux light curve of."
 The final light. curve uxes were corrected. for foreground Galactic. extinction using ly=0.514 for D and ον=0.395 for V. (Schlegeletal., The final light curve fluxes were corrected for foreground Galactic extinction using $A_\lambda=0.514$ for B and $A_\lambda=0.395$ for V \citep{Schlegel}.
 1998).. Winkleretal.(1992). used several methods to estimate the extinction towards aan concluded. that it can be largely or completely accounted lor by the foreground Galactic value. we therefore mace no further correction to the Iluxes.," \citet{Winkleretal92}
 used several methods to estimate the extinction towards and concluded that it can be largely or completely accounted for by the foreground Galactic value, we therefore made no further correction to the fluxes."
 The calibrated. Band V. band. light curves are shown in the middle and bottom panels in Fig. 1..," The calibrated B and V band light curves are shown in the middle and bottom panels in Fig. \ref{lcs},"
 respectively., respectively.
 The psf photometry method was used. to include all the point source emission [rom the nucleus of the ACN while minimising the contribution from the host galaxy but it is likely that some contamination remains., The psf photometry method was used to include all the point source emission from the nucleus of the AGN while minimising the contribution from the host galaxy but it is likely that some contamination remains.
 We note however, We note however
Alieroquasis and ACNs are often considered as. close relatives with the same accretion/ejection processes Cole on (Mirabol&Rodriguez 1999)).,Microquasars and AGNs are often considered as close relatives with the same accretion/ejection processes going on \cite{mr1999}) ).
 To our knowledge. the Fig.," To our knowledge, the Fig."
 2 map is the first case where represcutatives of both families cau be simultaneously iuased aud resolved within the same primary beam thus eivine it a strong educational value., \ref{cd+d+b} map is the first case where representatives of both families can be simultaneously imaged and resolved within the same primary beam thus giving it a strong educational value.
 This fact also opeus a possibility for proper motion studies of Cyenus N-3 using future very sensitive interferometers with respect to the FR II core., This fact also opens a possibility for proper motion studies of Cygnus X-3 using future very sensitive interferometers with respect to the FR II core.
 The Ryle Telescope (Cambridge) has for some vears been used m a cspare-time” mode for monitoring of, The Ryle Telescope (Cambridge) has for some years been used in a `spare-time' mode for monitoring of
however Jablouka et al. (10996)),however Jablonka et al. \cite{jabl}) )
 measured values of Epv as low as 0.03 from spectrophotometry of elobular clusters in NGC 5128., measured values of $_{B-V}$ as low as 0.03 from spectrophotometry of globular clusters in NGC 5128.
 The extinction values for the PN are consistent with these values within the errors. except perhaps for PNZ55601.," The extinction values for the PN are consistent with these values within the errors, except perhaps for 5601."
 Towever it is puzzling that the values are systematically low: aly local extinction iu NGC 5128. or dust within the nebulae themselves. would lucrease the value above re baseline for the Calactic line of sight extinction.," However it is puzzling that the values are systematically low; any local extinction in NGC 5128, or dust within the nebulae themselves, would increase the value above the baseline for the Galactic line of sight extinction."
 Slit lossses through atmospheric refraction should not alone account for bias., Slit lossses through atmospheric refraction should not alone account for bias.
 Errors nav have arisen in subtraction of the underlying stellar continu whereby cussion line flux is lost to stellar sorption lines. although the effect would be to produce 1 lucreased extinction on account of he generally higher IL/ absorption equivalent width compared with Ie.," Errors may have arisen in subtraction of the underlying stellar continuum whereby emission line flux is lost to stellar absorption lines, although the effect would be to produce an increased extinction on account of the generally higher $\beta$ absorption equivalent width compared with $\alpha$."
 Tlowever oue of the PN (5621) docs show au extinction above the Calactic value. although with a substantial error. as does the fibuueut. which is however an extcuded object.," However one of the PN (5621) does show an extinction above the Galactic value, although with a substantial error, as does the filament, which is however an extended object."
 The extinction to the filament is in the rauge of values for the extinction cetermunued by Morgauti ct al. (19913):, The extinction to the filament is in the range of values for the extinction determined by Morganti et al. \cite{morg}) );
 the fibuneut is in the same vicinity as their Field 2 (see their Fig., the filament is in the same vicinity as their Field 2 (see their Fig.
 2) although about ten times lower surface briehtuess (compare their Table 1 for spectra)., 2) although about ten times lower surface brightness (compare their Table 4 for spectra).
 The [ο /TL7 ratio measured here is also situilar to the values measured by Morgauti et al. (1991))., The [O $\beta$ ratio measured here is also similar to the values measured by Morganti et al. \cite{morg}) ).
 The most probable explanation of the depressed reddening values is that the central wavelength of the euidiuns camera Des at one end of the range Is to Ta: bv tracking ou the nuage in the vicinity of the waveleugth around IL. fux is systematically lost frou the slit at Πα for airmasses ιο. ereater than 1.0.," The most probable explanation of the depressed reddening values is that the central wavelength of the guiding camera lies at one end of the range $\beta$ to $\alpha$; by tracking on the image in the vicinity of the wavelength around $\beta$, flux is systematically lost from the slit at $\alpha$ for airmasses much greater than 1.0."
 Subsequent to this conclusion we were informed that the euildius camera of the ESO 3.6m at the time of the observations was seusitive over the wavelcneth range 3700 to5000A., Subsequent to this conclusion we were informed that the guiding camera of the ESO 3.6m at the time of the observations was sensitive over the wavelength range 3700 to.
. The dereddened fluxes were formed emploviug the observed reddening. even if negative: this serves to colpcusate for the losses of the red part of the spectra.," The dereddened fluxes were formed employing the observed reddening, even if negative; this serves to compensate for the losses of the red part of the spectra."
 No specific correction for foreground (Galactic) reddening was eniploved., No specific correction for foreground (Galactic) reddening was employed.
 It is apparent tha the three brightest PN show 10 evidence for intrinsic reddening (within the substautial neasurement errors). which is probably not surprising eiven that they are the the brighltes PN observable in the ealaxy.," It is apparent that the three brightest PN show no evidence for intrinsic reddening (within the substantial measurement errors), which is probably not surprising given that they are the the brightest PN observable in the galaxy."
 Any extinction wouk move them to lower observed fixes: PN355621 is for example as intrinsically bright as LLOOL., Any extinction would move them to lower observed fluxes; 5621 is for example as intrinsically bright as 4001.
 The effect of local galactic extinction aud dust intrinsic to the PN must play a role iu shaping the PN ininositv function (Jacoby 1989))., The effect of local galactic extinction and dust intrinsic to the PN must play a role in shaping the PN luminosity function (Jacoby \cite{jac89}) ).
 With spectroscopy of he brightest PN. the effect of dust on the hwunuinositv Muction. aud heuce on the distance estimate through fittine of this function (Ciardullo et al. L989::," With spectroscopy of the brightest PN, the effect of dust on the luminosity function, and hence on the distance estimate through fitting of this function (Ciardullo et al. \cite{cia89};"
 see also Aleudez ct al. 19933).," see also Mendez et al. \cite{men}) ),"
 cau )o directly quautified., can be directly quantified.
 However if dust is associated with PN depeudent ou thei Iuuinosity it would be expected to have a stroug effect ou the PN huuinosity function., However if dust is associated with PN dependent on their luminosity it would be expected to have a strong effect on the PN luminosity function.
 Jacoby Ciardullo (1999)) in their study of PN in AL 31 have found a weak correlation between extinction aud Thuuinosity. which also exists for PN iu the LAIC.," Jacoby Ciardullo \cite{jaccia}) ) in their study of PN in M 31 have found a weak correlation between extinction and luminosity, which also exists for PN in the LMC."
 The surprising net effect on the PN huuimositv function is that the appareu peak brightuess is nearly iudepoeudeut of absolute peak brightuess., The surprising net effect on the PN luminosity function is that the apparent peak brightness is nearly independent of absolute peak brightness.
 Ou the basis of the |O IIH5007A//ILJ aud He II //ILJ ratios the excitation class can be defined (Dopita Aeatheringham 1990))., On the basis of the [O $\beta$ and He II $\beta$ ratios the excitation class can be defined (Dopita Meatheringham \cite{dom90}) ).
 A least squares fit of the effective temperature from photoionization models (Dopita Meatheringham 1991)) against excitation class for a mniform set of observations aud models ofMagellanic Cloud PN allows estimation of effective temperature., A least squares fit of the effective temperature from photoionization models (Dopita Meatheringham \cite{dom91b}) ) against excitation class for a uniform set of observations and models of Magellanic Cloud PN allows estimation of effective temperature.
 Use of this data set could be criticized suce the LMC and SMC have low metallicitics compared to Galactic or more metal rich galaxies. but the modelling of ACB evolution shows no strong dependence of stellar temiperature on imetallicity (Dopita et al. 1992)).," Use of this data set could be criticized since the LMC and SMC have low metallicities compared to Galactic or more metal rich galaxies, but the modelling of AGB evolution shows no strong dependence of stellar temperature on metallicity (Dopita et al. \cite{djv}) )."
 Table 5 lists the excitation class and indicative temperature of the PN in Cen-A. ρα.) could not have a reliably assigued stellar eni])oratire since its excitation class is high (based ou its ligh [ο T/L} ratio) vet it was too faint to detect Πο ((excitation class above 5.0 requires the We 7 ratio)., Table 5 lists the excitation class and indicative temperature of the PN in Cen-A. 5619 could not have a reliably assigned stellar temperature since its excitation class is high (based on its high [O $\beta$ ratio) yet it was too faint to detect He (excitation class above 5.0 requires the He $\beta$ ratio).
 These temperatures should be secu as upper limits. since if the nebulae are optically thin the high ionization ciission is enhanced: given the large line ratio errors the likely errors are at least -LOOOOLS. Even for he three brightest PN observed in NGC. 5128. he weak. diagnostic forbidden lines were uot detected: lus it i5 nof possible to measure accurate electrou enrperatures Yon the [O irafio) or densities (for example frou the 5 ratio).," These temperatures should be seen as upper limits, since if the nebulae are optically thin the high ionization emission is enhanced; given the large line ratio errors the likely errors are at least $\pm$ 10000K. Even for the three brightest PN observed in NGC 5128, the weak diagnostic forbidden lines were not detected; thus it is not possible to measure accurate electron temperatures (from the [O ratio) or densities (for example from the [S ratio)."
 Nevericless an attempt was made to estimate he oxveen abundance m order ο colupare it with other abuudance diagnostics (0.8. from stellar absorption lines)., Nevertheless an attempt was made to estimate the oxygen abundance in order to compare it with other abundance diagnostics (e.g. from stellar absorption lines).
 Dopita ct al. (1992)), Dopita et al. \cite{djv}) )
 presented a diagnostic diagram ofPN uctallicity effective temperature. in which the electron cluperture can be determined from he ο / ratio.," presented a diagnostic diagram of PN metallicity effective temperature, in which the electron temperture can be determined from the [O $\beta$ ratio."
 This plot was derived roni phnotoionizatioun models of a erid of optically thick PN: the effective. temperature cine deteriined from he at to the Magellanic Clo data (Dopita Aeathermeham 1991)., This plot was derived from photoionization models of a grid of optically thick PN; the effective temperature being determined from the fit to the Magellanic Cloud data (Dopita Meatheringham \cite{dom91b}) ).
 Iu Table he estimated values of the electron teniperature are isted: for PN#11902 and 5621 the range of effective cluperatures are out of range of the diagnostic plot. bu were extrapolated.," In Table 4 the estimated values of the electron temperature are listed; for 1902 and 5621 the range of effective temperatures are out of range of the diagnostic plot, but were extrapolated."
 Row 6 of Table [| lists the derived netallicities of the PN (all element abuudauces: scaled except IIehuni) based on the Dopita ct al. (1992))," Row 6 of Table 4 lists the derived metallicities of the PN (all element abundances scaled except Helium), based on the Dopita et al. \cite{djv}) )"
 calibration., calibration.
 From the electron temperature estimates (Table d£ row 5). the empirical O!! abundauces were determined fron the [ο T/T) ratios aud are listed in row T.," From the electron temperature estimates (Table 4 row 5), the empirical $^{++}$ abundances were determined from the [O $\beta$ ratios and are listed in row 7."
 A correction for the presence of O?! was riade using the ionization correction factor derived frou the | ratio (sinesbureh Barlow 1991)): the Heo/II ratio was asstuuecd fixed at 0.15., A correction for the presence of $^{3+}$ was made using the ionization correction factor derived from the $^{++}$ ratio (Kingsburgh Barlow \cite{kiba}) ); the He/H ratio was assumed fixed at 0.15.
 The Πο I, The He I
"galaxies residing in high overdensity regions have, for all mass bins, a greater D4000 value than galaxies in the lowest environment quartile.","galaxies residing in high overdensity regions have, for all mass bins, a greater D4000 value than galaxies in the lowest environment quartile."
" To study the influence of the mass and overdensity, we evaluated the differences of D4000 and EWo(H6) between the extreme quantiles of mass and environment and their significance."," To study the influence of the mass and overdensity, we evaluated the differences of D4000 and $EW_{0}(H\delta)$ between the extreme quantiles of mass and environment and their significance."
 The black points in the lower panels of each figure in Fig., The black points in the lower panels of each figure in Fig.
 8 show the difference in D4000 between high and low mass or environment regimes., \ref{fig:fig12} show the difference in D4000 between high and low mass or environment regimes.
" To derive a mean value for each mass and environment regime, we averaged the differences found in each redshift bin using their errors as weights; the red shaded area in Fig."," To derive a mean value for each mass and environment regime, we averaged the differences found in each redshift bin using their errors as weights; the red shaded area in Fig."
 8 represents the mean difference integrated as a function of redshift., \ref{fig:fig12} represents the mean difference integrated as a function of redshift.
" We defined the significance to be the distance of this integrated difference of D4000 between extreme quartiles of mass and environments in units of σ, where σ is the error in the integrated difference."," We defined the significance to be the distance of this integrated difference of D4000 between extreme quartiles of mass and environments in units of $\sigma$, where $\sigma$ is the error in the integrated difference."
" shows that the results are in agreement with those found in our color analysis: the dependence on mass is strong, with a mean (AD4000)=0.11+0.02 in a mass range 10.2<logio(M/Mo)S10.8 and a significance over 30 level (except for one overdensity bin), while the dependence on environment is weaker, with a mean (AD4000)=0.05+0.02 and much lower The mass incompleteness of our spectral analysis is not a problem."," shows that the results are in agreement with those found in our color analysis: the dependence on mass is strong, with a mean $\left<\Delta D4000\right>=0.11\pm0.02$ in a mass range $10.2\lesssim log_{10}(M/M_{\odot})\lesssim10.8$ and a significance over $3\sigma$ level (except for one overdensity bin), while the dependence on environment is weaker, with a mean $\left<\Delta D4000\right>=0.05\pm0.02$ and much lower The mass incompleteness of our spectral analysis is not a problem."
" Since we decided to divide our sample with a fixed mass cut as a function of redshift, the effect is a slight shift in the median value of mass at all redshifts in each mass bin, so that, for example, the median mass of low-mass galaxies change from logig(M/Mo)=10.1 to logio(M/Mo)=10.25 with increasing redshift."," Since we decided to divide our sample with a fixed mass cut as a function of redshift, the effect is a slight shift in the median value of mass at all redshifts in each mass bin, so that, for example, the median mass of low-mass galaxies change from $log_{10}(M/M_{\odot})=10.1$ to $log_{10}(M/M_{\odot})=10.25$ with increasing redshift."
 This shift in mass would have to be taken into account if one were trying to precisely establish the redshift evolution of D4000 at fixed mass., This shift in mass would have to be taken into account if one were trying to precisely establish the redshift evolution of D4000 at fixed mass.
" However, in our analysis we are only interested in identifying the main parameter relating mass to environment, so this shift should not affect our results."," However, in our analysis we are only interested in identifying the main parameter relating mass to environment, so this shift should not affect our results."
" Moreover, even by correcting for it considering the relative lack of massive galaxies at low redshift and of less massive ones at high redshift, would at most increase the range of mass explored in the different redshift A similar consideration has to be made for the metallicity."," Moreover, even by correcting for it considering the relative lack of massive galaxies at low redshift and of less massive ones at high redshift, would at most increase the range of mass explored in the different redshift A similar consideration has to be made for the metallicity."
" As pointed out before, the D4000 index depends on both the age and metallicity of a galaxy."," As pointed out before, the D4000 index depends on both the age and metallicity of a galaxy."
" Over the mass range probed here, we expect top find a"," Over the mass range probed here, we expect top find a"
The diagonal polynomials can be computed using EPhe first. few. polar Hermite. polvnomials. are listed.. in. .1..,The diagonal polynomials can be computed using The first few polar Hermite polynomials are listed in Table \ref{tab:hpolar}.
 Thev ⋅have a number of useful⋅ properties., They have a number of useful properties.
". Inrotation . particular.⊀ they are symmetric. ≜≜i.c. Ldn=£f and their: derivativeMN obey Dimensional1D"" polar""NU basis""1 functions'“fq can""el ben constructed3B* The radial dependence fyi)...Gr)] of the first. few polar shapelet functions is shown in Figure 10.."," In particular, they are symmetric, i.e. $H_{k,l}=H_{l,k}$ and their derivative obey Dimensional polar basis functions can be constructed as It is easy to check that these are orthonormal, i.e. that The radial dependence $|\chi_{n_l,n_r}(x)|$ of the first few polar shapelet functions is shown in Figure \ref{fig:polar}."
 ]t is useful to relate the angular momentum states |n.m to the cartesian states |nj.23.," It is useful to relate the angular momentum states $\vert n,m \rangle$ to the cartesian states $\vert n_{1}, n_{2} \rangle$."
" Using Equations (56)) and (60)) along with the binomial expansion. one can show that the transformation matrix between these two bases is given by only states with nj | no —n,|nyaremixed."," Using Equations \ref{eq:alar}) ) and \ref{eq:nrnl}) ) along with the binomial expansion, one can show that the transformation matrix between these two bases is given by This shows that only states with $n_1+n_2=n_r+n_l$ are mixed."
The first few|n. mj states aregiven in terms of [nino) states in Table 2..,"The first few $\vert n,m \rangle$ states are given in terms of $\vert n_1
n_2 \rangle$ states in Table \ref{tab:nm_states}."
 Figure 10. ltadial shapelet states are eigenstates of the angularthe momentum. they have simple rotational properties.," Because the polar shapelet states are eigenstates of the angular momentum, they have simple rotational properties."
 iok ta finite finite rotation an:by anarst: angleπμ p. the (G4)polar states EL Indeed. transform as where we have used the exponentiation (Eq. 36]])," Indeed, under a finite rotation by an angle $\rho$ , the polar states transform as where we have used the exponentiation (Eq. \ref{eq:rot_finite}] ])"
 of the generator. /? =4L(Eq. 32]]), of the rotation generator $\hat{R}=-i\hat{L}$ (Eq. \ref{eq:generators}] ])
 ↽ to operate a finite Tables rotation., to operate a finite rotation.
. In this⊀⋅∢ basis. ⊀↽finite rotations thus corresponds only to à phase factor.," In this basis, finite rotations thus corresponds only to a phase factor."
 Lt is. therefore. a simple. matter to rotate an arbitrary. function. f(x)., It is therefore a simple matter to rotate an arbitrary function $f({\mathbf x})$.
" First. we decompose it into polar shapelet coellicients fin,=perdife. with an appropriate shapelet scale 3."," First, we decompose it into polar shapelet coefficients $f_{n_r,n_l}=\langle n_r,n_l;\beta | f \rangle$, with an appropriate shapelet scale $\beta$."
" The cocllicicnts fi,=(nimi3h οἱ the rotated functionB. f’7!(x) are then given. simply. by )v contrast. operating a finite rotation in the cartesian basis requires an infinite number of applications of the 7? operator! (see Eq.4be 36|)I "," The coefficients $f_{n_r,n_l}'=\langle n_r,n_l;\beta | f' \rangle$ of the rotated function $f'({\mathbf x})$ are then given simply by By contrast, operating a finite rotation in the cartesian basis requires an infinite number of applications of the $\hat{R}$ operator (see Eq. \ref{eq:rot_finite}] ])"
and is. thus impractical., and is thus impractical.
.I On the other hand. convolutions do not have simple. analytical. expressions in the polar basis. as they do in the cartesian basis: (see refconvolution and Paper LL).," On the other hand, convolutions do not have simple analytical expressions in the polar basis, as they do in the cartesian basis (see \\ref{convolution} and Paper II)."
 The results of canthusbeconeenientlyusedtoconvert f romonebasistol heother. d," The results of \\ref{pol_cart}, , can thus be conveniently used to convert from one basis to the other, dependingon the operation to be performed."
An accretion disk is specified in BINSYN by an inner and outer radius. and the accretion disk is divided into a specified number of exlindrical annuli. with each annulus divided into a specified number of segments.,"An accretion disk is specified in BINSYN by an inner and outer radius, and the accretion disk is divided into a specified number of cylindrical annuli, with each annulus divided into a specified number of segments."
 Radiation characteristics of the accretion disk depend on a temperature profile. T(A). of the accretion disk annuli.," Radiation characteristics of the accretion disk depend on a temperature profile, $T(R)$, of the accretion disk annuli."
 We reserve (he term απαντά Model” to designate a TC) relation with 2=—0.75 for the Standard Model (Frank.Ning.&Raine1995.herealter," We reserve the term ""Standard Model"" to designate a $T(R)$ relation with $\beta=-0.75$ for the Standard Model \citep[hereafter FKR]{fkr95}."
ΕΙ]. Wis a normalizing laetor. (not a dilution factor): Wo=1.0 for the Standard Mlodel.," $W$ is a normalizing factor, (not a dilution factor); $W =1.0$ for the Standard Model."
 For default conditions. our definition is algebraically identical to the ΕΙ definition.,"	 For default conditions, our definition is algebraically identical to the FKR definition."
 The accretion disk is flared. in the sense that successive annuli step up in height between (he inner radius and a specified semi-height at the outer radius.," The accretion disk is flared, in the sense that successive annuli step up in height between the inner radius and a specified semi-height at the outer radius."
" Let // be (he semi-thickness al (he outer radius r,. and let 7j be the inner radius."," Let $H$ be the semi-thickness at the outer radius $r_a$, and let $r_b$ be the inner radius."
 Then the semi-thickness at racius r. f(r). is h()/H-(r-mn)yf(rgy-r)," Then the semi-thickness at radius $r$, $h(r)$, is $h(r)/H = (r-r_b)/(r_a-r_b)$."
 See Table L., See Table 1.
 IB caleulating a model for an accretion disk svstem. BINSYN. by default. assigns Z;y values to annuli based on the Standard Model. appropriate ο an assumed mass transfer rate.," In calculating a model for an accretion disk system, BINSYN, by default, assigns $T_{\rm eff}$ values to annuli based on the Standard Model, appropriate to an assumed mass transfer rate."
 An option permits modification of the assigned annulus τομ values to include calculated irradiation bv the WD. based on a bolometric albedo formalism.," An option permits modification of the assigned annulus $T_{\rm eff}$ values to include calculated irradiation by the WD, based on a bolometric albedo formalism."
 Calculation of a synthetic spectrum. for (he accretion disk. as part of the calculation of the svstem synthetic spectrum. involves interpolation among previously calculated. source spectra(wilh their individual Tr values) to produce a synthetic spectrum lor each annulus. for is Zip as assigned by DINSYN.," Calculation of a synthetic spectrum for the accretion disk, as part of the calculation of the system synthetic spectrum, involves interpolation among previously calculated source spectra	(with their individual $T_{\rm eff}$ values) to produce a synthetic spectrum for each annulus, for its $T_{\rm eff}$ as assigned by BINSYN."
 The accretion disk source spectra may consist largely of svithetic spectra for annulus models produced by TLUSTY (IIubeny. 1995).," The accretion disk source spectra may consist largely of synthetic spectra for annulus models produced by TLUSTY \citep{h88,hl95}."
. This caleulation is followed by integration over all annuli. with detailed allowance for Doppler shifts and sources of line broadening. and with proper allowance for visibility to the observer.," This calculation is followed by integration over all annuli, with detailed allowance for Doppler shifts and sources of line broadening, and with proper allowance for visibility to the observer."
 The number of source spectra (vpically will differ [rom the specified number of annuli., The number of source spectra typically will differ from the specified number of annuli.
 The programs finally output the calculated flix as function of wavelength for the individual objects as well as their sum. which represents the svstem svuthetic spectrum at the current orbital longitude.," The programs finally output the calculated flux as function of wavelength for the individual objects as well as their sum, which represents the system synthetic spectrum at the current orbital longitude."
 A parallel procedure produces svnthetic light values. repeated for a erid of orbital longitudes and so leads to light curves for specified wavelengths.," A parallel procedure produces synthetic light values, repeated for a grid of orbital longitudes and so leads to light curves for specified wavelengths."
 Additional details are in Linnell&πιουν(1996)., Additional details are in \citet*{lin96}.
. In fitting the optical spectra. II2004. found. two difficulties: (1) The polar Z;y of the secondary was cooler than 35001Ix. which is the temperature of the coolest (Ixurucz) model," In fitting the optical spectra, H2004 found two difficulties: (1) The polar $T_{\rm eff}$ of the secondary was cooler than 3500K, which is the temperature of the coolest (Kurucz) model"
Tevatron.,Tevatron.
 The BY theory can account for these differences (??).. however only new LHC data will select the proper symmetry-breaking mechanism.," The BY theory can account for these differences \citep{Palle7a,Palle7b}, however only new LHC data will select the proper symmetry-breaking mechanism."
 Formulating the theory of the local structure of spacetime as local SU(3)xSU(2)U(1) gauge theories. we choose the Einstein-Cartan theory as formulated by Sciama and Kibble to be the theory of the global structure of spacetime.," Formulating the theory of the local structure of spacetime as local $SU(3)\times 
SU(2)\times U(1)$ gauge theories, we choose the Einstein-Cartan theory as formulated by Sciama and Kibble to be the theory of the global structure of spacetime."
 Trautman was the first who realized the possibility of the nonsingular Einstein-Cartan (EC) cosmology (?).., Trautman was the first who realized the possibility of the nonsingular Einstein-Cartan (EC) cosmology \citep{Trautman}.
 In addition. there is more freedom to avoid noncausal Goedel cosmological solutions (?2)..," In addition, there is more freedom to avoid noncausal Goedel cosmological solutions \citep{Ray,Obukhov}."
 The Einstein-Cartan gravity is also a quantum theory of gravity but not in a sense of introducing the spin 2 local quantum field with the corresponding Heisenberg commutation rules., The Einstein-Cartan gravity is also a quantum theory of gravity but not in a sense of introducing the spin 2 local quantum field with the corresponding Heisenberg commutation rules.
 The quantum principle figures only through quantum mechanical spin densities at the first quantized level., The quantum principle figures only through quantum mechanical spin densities at the first quantized level.
 In this Note we attempt to make a connection between the chirally asymmetric weak interactions and possibly anisotropic Universe described by the Einstein-Cartan cosmology., In this Note we attempt to make a connection between the chirally asymmetric weak interactions and possibly anisotropic Universe described by the Einstein-Cartan cosmology.
 The EC gravity relates rotational degrees of freedom of matter and spacetime. 1.e. total angular momentum as a conserved quantity in the Special Theory of Relativity consisting of the orbital angular momentum and spin (??) of matter vs. torsion of spacetime.," The EC gravity relates rotational degrees of freedom of matter and spacetime, i.e. total angular momentum as a conserved quantity in the Special Theory of Relativity consisting of the orbital angular momentum and spin \citep{Bjorkena,Bjorkenb} of matter vs. torsion of spacetime."
 Spin. as an internal angular momentum of particles. is a quantum mechanical quantity. so it vanishes in the classical limit of the vanishing Planck constant.," Spin, as an internal angular momentum of particles, is a quantum mechanical quantity, so it vanishes in the classical limit of the vanishing Planck constant."
 One can introduce the angular momentum in General Relativity only as a nonconserved quantity and it does not obey tensorial transformations (?).., One can introduce the angular momentum in General Relativity only as a nonconserved quantity and it does not obey tensorial transformations \citep{Weinberg}.
 On the contrary. the EC theory of gravity Incorporates spin and angular momenta of matter and torsion of spacetime invariantly with respect to the general coordinate transformations of the enlarged general theory of relativity (22?)..," On the contrary, the EC theory of gravity incorporates spin and angular momenta of matter and torsion of spacetime invariantly with respect to the general coordinate transformations of the enlarged general theory of relativity \citep{Hehla,Hehlb,Hehlc}."
 Owing to the algebraic relation between spin and angular momentum vs. torsion. one can incorporate spin andangular momentum into the effective energy-momentum tensor (22222):," Owing to the algebraic relation between spin and angular momentum vs. torsion, one can incorporate spin andangular momentum into the effective energy-momentum tensor \citep{Ray,Obukhov,Hehla,Hehlb,Hehlc}: :"
ii) Randomly select a vector c according to PCr|8;) and a label e according to 1:234].,ii) Randomly select a vector $\underline{x}$ according to $P(\underline{x} | \theta_j)$ and a label $c$ according to $\{\beta_{k|j}\}$.
 The log of the joint data likelihood associated with this moclel is where ο)€P.., The log of the joint data likelihood associated with this model is where $c(\underline{x}) \in \tilde{\cal P}_c$.
 The model parameters A can be chosen to maximize the log-likelihood (1)) via the Expectation-Maximization (EM) algorithin (e.g. Duda.Wart.&Stork(2001)))., The model parameters $\Lambda$ can be chosen to maximize the log-likelihood \ref{newlik}) ) via the Expectation-Maximization (EM) algorithm (e.g. \citet{Duda}) ).
 since (he derivation of these EM equations is standard. their exposition is herein omitted.," Since the derivation of these EM equations is standard, their exposition is herein omitted."
 This model does not explicitly discover new class components. i.e. mixture components (hat are purely unlabeled.," This model does not explicitly discover new class components, i.e. mixture components that are purely unlabeled."
" However. suppose that. for a given component Mj. we have that 4;€ Land 9,); is also significantly greater (han theaverage value 5iEu|j»,"," However, suppose that, for a given component ${\cal M}_j$, we have that $\beta_{u | j}
\simeq 1$ and $\beta_{u|j}$ is also significantly greater than the value $\frac{1}{M} \sum\limits_{j'=1}^M \beta_{u|j'}$."
 In this case. (he fraction of uilabeled data owned by the component is unusually high.," In this case, the fraction of unlabeled data owned by the component is unusually high."
 We categorize these components as “honpredelined™. 1e. Mf;€Cy.," We categorize these components as “nonpredefined”, i.e. ${\cal M}_j \in {\bar{\cal C}}_{\rm pre}$."
 Such components are putative unknown class components., Such components are putative unknown class components.
" All other components are categorized as ""predefined"". representing known class data."," All other components are categorized as “predefined”, representing known class data."
" To summarize. we have the following strategy for class discoverv/outlier detectionin mixed data: 1) learn a mixture model to maximize the log likelihood (1)): 2) for each component. declare it. “nonpredefined” if J4;—(3532Jy)>ὃν otherwise. declare it ""predefined."," To summarize, we have the following strategy for class discovery/outlier detectionin mixed data: 1) learn a mixture model to maximize the log likelihood \ref{newlik}) ); 2) for each component, declare it “nonpredefined” if $\beta_{u | j} - (\frac{1}{M}
\sum\limits_{j'=1}^M \beta_{u|j'}) > \delta$; otherwise, declare it “predefined”."
 Here. ὁ is a suitably. chosen threshold.," Here, $\delta$ is a suitably chosen threshold."
" In. practice. we declare acomponent ""nonpredefined when its value 1; is closer to 1.0 than to the average value. Le... we choose ὃ--41-ᾱ-η)."," In practice, we declare acomponent “nonpredefined” when its value $\beta_{u|j}$ is closer to $1.0$ than to the average value, i.e., we choose $\delta = \frac{1}{2}(1 - \frac{1}{M}\sum\limits_{j'=1}^M
\beta_{u|j'})$."
 We have found this choice lor 9 to give reasonable results lor a variety of experimental conditions (lor dillerent datasets and lor dillerent fractious of labeled data)., We have found this choice for $\delta$ to give reasonable results for a variety of experimental conditions (for different data sets and for different fractions of labeled data).
 After applving this thresholding operation to each component. the resulting moclel is naturally applied (ο address several inference tasks: 1) standard classification of a given sample to one of the known classes: and 2) known vs. unknown class discrimination.," After applying this thresholding operation to each component, the resulting model is naturally applied to address several inference tasks: 1) standard classification of a given sample to one of the known classes; and 2) known vs. unknown class discrimination."
 For Classification to known classes. for a given sample c. we compute the posteriori probabilities," For classification to known classes, for a given sample $\underline{x}$ , we compute the probabilities"
"the five models, and for the Nordlund-Stein 3D hydrodynamic atmosphere quoted in Asplund,etal.(2005).","the five models, and for the Nordlund-Stein 3D hydrodynamic atmosphere quoted in \cite{aspat}."
. The semi-empirical stellar atmosphere models of Fontenlaοἱal.(2006) give curves similar to those of Nordlund- but are not plotted to reduce crowding.," The semi-empirical stellar atmosphere models of \cite{fontenla} give curves similar to those of Nordlund-Stein, but are not plotted to reduce crowding."
" The most striking feature in this figure is the difference between the low depth behavior of the models (an abrupt cliff at 7z1), and the3D-atmospheres (a gentler slope for lower 7)."," The most striking feature in this figure is the difference between the low depth behavior of the models (an abrupt cliff at $\tau \approx 1$ ), and the3D-atmospheres (a gentler slope for lower $\tau$ )."
" This is due to the use in the 1D models of the Schwarzschild criterion for convection, a local condition."," This is due to the use in the 1D models of the Schwarzschild criterion for convection, a local condition."
" À weakly-stable stratification cannot really hold back vigorous motion, as use of the local Schwarzschild criterion implies."," A weakly-stable stratification cannot really hold back vigorous motion, as use of the local Schwarzschild criterion implies."
" The micro- and macro-turbulent velocities, Gmi and πια, are parameters which were introduced long ago to account for the embarassment that, according to the Schwarzschild criterion, conventional solar atmospheres arenot convective at the surface."," The micro- and macro-turbulent velocities, $\zeta_{mi}$ and $\zeta_{ma}$, are parameters which were introduced long ago to account for the embarassment that, according to the Schwarzschild criterion, conventional solar atmospheres are convective at the surface."
" Note that if ὁ--{οQ,, then 1.9<¢€3.0km/s for the Sun (Cox2000)."," Note that if $\zeta = \sqrt{ \zeta_{mi}^2 +\zeta_{ma}^2 }$, then $ 1.9 \le \zeta \le 3.0 \rm \ km/s $ for the Sun \citep{aq00}."
. This is indicated by the vertical bounded line in Figure 4.., This is indicated by the vertical bounded line in Figure \ref{figasp}.
" The connection between this ¢ and the actual turbulent velocity due to convection is not simple, involving line-formation, photon escape, and inhomogeneous stellar surface layers."," The connection between this $\zeta$ and the actual turbulent velocity due to convection is not simple, involving line-formation, photon escape, and inhomogeneous stellar surface layers."
" Fortunately, multi-dimensional hydrodynamic atmospheres (Asplund2000;Nordlund&Stein2000) do provide a spectacular fit to line shapes, with no free parameters, so we identify the convective velocities well below the photosphere (optical depth 7= 3) in these simulations with those predicted by our hydro-dynamically consistent choice of mixing length parameter or."," Fortunately, multi-dimensional hydrodynamic atmospheres \citep{asp00,ns00} do provide a spectacular fit to line shapes, with no free parameters, so we identify the convective velocities well below the photosphere (optical depth $\tau \ga 3$ ) in these simulations with those predicted by our hydro-dynamically consistent choice of mixing length parameter $\alpha_{ML}$ ."
" This means we are essentially matching different 3D simulations in the region of adiabatic convection, where"," This means we are essentially matching different 3D simulations in the region of adiabatic convection, where"
For the investigation of the deconfinement phase transition expected to occur in neutron star iuatter at densities above the nuclear. saturation denusitv Ny—016fin’ several approaches το quark confinement dynanües have been discussed. SCC e.g. Dlaschkeetal.(1990).Blaschke(1999).Dragoοal.(1996) which lead to interesting couclusious or the properties of quark matter at üueh densitics.,"For the investigation of the deconfinement phase transition expected to occur in neutron star matter at densities above the nuclear saturation density $n_0=0.16~{\rm fm}^{-3}$ several approaches to quark confinement dynamics have been discussed, see e.g. \cite{bkt,b+99,drago} which lead to interesting conclusions for the properties of quark matter at high densities."
 Most of the approaches to quark decoufinennent in jieutronu star iuatter. however. use a thermodvuamical vae-nodel or the quark matter aud enmiplov a standard wo-pliase description of the equation of state (EOS) where the hadronic phase and the quark matter phase are modeled separately aud the resulting EOS is obtained x imposing Cübbs coucditions for phase equilibrium with he construut that ALVOL μπα: as well as electric charge of the system are couserved (Cleudeunius 1992. 1997).," Most of the approaches to quark deconfinement in neutron star matter, however, use a thermodynamical bag-model for the quark matter and employ a standard two-phase description of the equation of state (EOS) where the hadronic phase and the quark matter phase are modeled separately and the resulting EOS is obtained by imposing Gibbs' conditions for phase equilibrium with the constraint that baryon number as well as electric charge of the system are conserved (Glendenning 1992, 1997)."
 Siuce the focus of our work is the elucidation of qualitative features of signals for a possible decoufinement transition iu the pulsar timine. we will consider here such a rather standard. phenomenological model for an EOS with deconfinement transition.," Since the focus of our work is the elucidation of qualitative features of signals for a possible deconfinement transition in the pulsar timing, we will consider here such a rather standard, phenomenological model for an EOS with deconfinement transition."
" The otal pressure pCgr.D) as à thermodvuanical poteutia Is Given by where is the EOS of the relativistic 0wo inean-field model (Walecka model) for nuclear matter (Walecka 197I. Iapusta 1989). where the masses aud chemical poteutials have to be renormalized by the mean-values of the @ aud wo fields ni=1,GaP fh,=Hhguy."," The total pressure $p(\{\mu_i\},T)$ as a thermodynamical potential is given by where is the EOS of the relativistic $\sigma-\omega$ mean-field model (Walecka model) for nuclear matter (Walecka 1974, Kapusta 1989), where the masses and chemical potentials have to be renormalized by the mean-values of the $\sigma-$ and $\omega-$ fields $m_h^*=m_h-g_\sigma \bar \sigma$, $\mu_h^*=\mu_h-g_\omega \bar \omega_0$."
 The pressure for two-flavor quark matter within a bag model EOS is eiven by where B denotes the plenomenological bag pressure that cuforces quark confinement and the trausition to unclear matter at low deusities., The pressure for two-flavor quark matter within a bag model EOS is given by where $B$ denotes the phenomenological bag pressure that enforces quark confinement and the transition to nuclear matter at low densities.
 For our ποΊσα analyses in the present work. we asstue here a value of B=75Ιον Powhich allows us. ese. to discuss a neutron star of Lol solar masses with an exteuded quark matter core.," For our numerical analyses in the present work, we assume here a value of $B=75 ~{\rm MeV fm}^{-3}$ which allows us, e.g., to discuss a neutron star of $1.4$ solar masses with an extended quark matter core."
 Iu a neutron star. these phases of strongly interacting matter are dn 2 equilibrima with electrons and mnmons which contribute to the pressure balance with Iu the above OXpressiolis ply.T:mn;)=iτς).|plutT:m;) ds the partial pressure of the Fermion species { as a sun of particle and antiparticle coutributious defined by where wtih)=|n;Τεμέ.," In a neutron star, these phases of strongly interacting matter are in $\beta-$ equilibrium with electrons and muons which contribute to the pressure balance with In the above expressions $p^{id}_i(\mu_i,T;m_i)=p^{-}_i(\mu_i,T;m_i)+p^{+}_i(\mu_i,T;m_i)$ is the partial pressure of the Fermion species $i$ as a sum of particle and antiparticle contributions defined by where $x^{\pm}(k)=\sqrt{k^2+m_i^2}/T\pm \mu/T$."
 All the other thermodynamic quautities of interest can be derived from the pressure (021) as. eg.BS. the partial deusities of the species The chemical equilibziui due to the direct aud inverse decay processes miposes additional constraints on the values of the chemical potentials of leptonic and baryvoulc species (Cdendenning 1997. Sahakiau 1995).," All the other thermodynamic quantities of interest can be derived from the pressure \ref{pres}) ) as, e.g., the partial densities of the species The chemical equilibrium due to the direct and inverse $\beta$ - decay processes imposes additional constraints on the values of the chemical potentials of leptonic and baryonic species (Glendenning 1997, Sahakian 1995)."
 Onlv two incdependeut chemical potentials remain according to the correspouding two conserved charges of the system. the total barvou umber Vp as well as electrical charge Q The deconfinement transition is obtained following the construction which obeys the elobal conservation laws and allows one to find the volume fraction of the quark natter phase 4=ων in the inixed phase where μμμι]T)=polluiT). so that at given np aud T he total pressure under the coucitious (38)). (39)) Ina uaxiumn. see Clendcenning (1992. 1997).," Only two independent chemical potentials remain according to the corresponding two conserved charges of the system, the total baryon number $N_B$ as well as electrical charge $Q$ The deconfinement transition is obtained following the construction which obeys the global conservation laws and allows one to find the volume fraction of the quark matter phase $\chi=V_Q/V$ in the mixed phase where $p_H(\{\mu_h\},T) = p_Q(\{\mu_q\},T)$, so that at given $n_B$ and $T$ the total pressure under the conditions \ref{bn}) ), \ref{charge}) ) is a maximum, see Glendenning (1992, 1997)."
 Tn Fig., In Fig.
 l we show the model EoS with decoufinement ransition as described above., \ref{fig1} we show the model EoS with deconfinement transition as described above.
 Note that iu the density region of the phase transition there is a 1uonotonous increase of the pressure which gives rise to an extended uixed phase region m the compact star after solution of the equations of bydrodvuamic stability (13))., Note that in the density region of the phase transition there is a monotonous increase of the pressure which gives rise to an extended mixed phase region in the compact star after solution of the equations of hydrodynamic stability \ref{TOV}) ).
 For colmparison. the relativistic mean-field EoS of including 9 iuesons. hwperons and nmons Gucompressibility A=300 MeV. dotted Lue) and that including a decoufinement transition to quark matter in a bag model with Bo= MeV! απο shown. see also the monographs by Glendenming(1997) aud Weber (1999)..," For comparison, the relativistic mean-field EoS of \\cite{glen89} including $\varrho$ mesons, hyperons and muons (incompressibility $K=300$ MeV, dotted line) and that of \\cite{glen} including a deconfinement transition to three-flavor quark matter in a bag model with $B=180$ $^4$ are shown, see also the monographs by \cite{gbook} and \cite{fwbook}. ."
 N— p=|. $3)). $4. 5..," $N$ $p=1$ \ref{sec-Nvsp}) \ref{sec-observ} \ref{sec-intrins},"
the suggestion that (at least) some of them may trace stellar orbits. aud. continued searches for stellar streams or orbital modelling are necessary to go bevoud this preliminary work.,"the suggestion that (at least) some of them may trace stellar orbits, and continued searches for stellar streams or orbital modelling are necessary to go beyond this preliminary work."
" We lave searched the GC aud PN systems in the jiearby eiut elliptical galaxy. NGC 5128. for evidence of stellar subgroups and stella streams from niereiug events,"," We have searched the GC and PN systems in the nearby giant elliptical galaxy, NGC 5128, for evidence of stellar subgroups and stellar streams from merging events."
 Our results indicate there may be up to 4 x»teutial subgroups of GCs and L potential suberoups of PNe., Our results indicate there may be up to 4 potential subgroups of GCs and 4 potential subgroups of PNe.
 Two of the PNe subgroups overlap with two of he GC suberoups iu position aud velocity., Two of the PNe subgroups overlap with two of the GC subgroups in position and velocity.
 In order to iuprove the search for these suberoups in NGC 5128. we need ligher precision radial velocity measurements to nore concretely determine if these objects are grouped ogether.," In order to improve the search for these subgroups in NGC 5128, we need higher precision radial velocity measurements to more concretely determine if these objects are grouped together."
 By generating CC systems that inde that iu NGC 5128. we are able to assien the probability of our results cing a chance cucounter duc to the projection of these objects onto a 2-dimeusional plane.," By generating GC systems that mimic that in NGC 5128, we are able to assign the probability of our results being a chance encounter due to the projection of these objects onto a 2-dimensional plane."
 The probability of finding a fake subgroup within the CC population is <1. while the probablity of having a set of subgroups overlap is ~LI.," The probability of finding a fake subgroup within the GC population is $< 1\%$ , while the probablity of having a set of subgroups overlap is $\sim 4\%$."
 These results strongly sugeest that at cast some of these suberoups may indeed be real., These results strongly suggest that at least some of these subgroups may indeed be real.
 We have also searched for evidence of stellar streams x locating GCs and planetary nebalae that differ frou its neighbours in velocity space using a frieudless search algoritlin., We have also searched for evidence of stellar streams by locating GCs and planetary nebalae that differ from its neighbours in velocity space using a friendless search algorithm.
 We preseut our findings as potential tracers. rowever further work in orbital modelling as well as searches for very faint surface brieltuess features would ο necessary bevoud this point to further define the stellar streams.," We present our findings as potential tracers, however further work in orbital modelling as well as searches for very faint surface brightness features would be necessary beyond this point to further define the stellar streams."
 IAW. thanks Dr. Ibuvey Richer and W.E.IT. thauxs NSERC for their financial support., K.A.W. thanks Dr. Harvey Richer and W.E.H. thanks NSERC for their financial support.
 IK.AAW and W.E.II. thank Dr. Eric Peng for providing the nage of NGC 5128 in Figure 1.., K.A.W and W.E.H. thank Dr. Eric Peng for providing the image of NGC 5128 in Figure \ref{fig:subgroups_all}. .
-py (Wane | = ZIP συπο = M—— This set of equafions can be simplified by making he assumption that the turbulence is close to isotropy., - ( + + = - - - ( + )^2 )^2 = - - This set of equations can be simplified by making the assumption that the turbulence is close to isotropy.
 This allows us to neglect the time averaged pressure Huctuatious terms (sec for example ? )., This allows us to neglect the time averaged pressure fluctuations terms (see for example \citet{kato97}) ).
" We further assume hat the characteristic spatial variation scale of the Huctuatins components is sumaller than the local radius (ie terms of oxley αμ can be neglected compared o the ones of order 0,d4;0,0,).", We further assume that the characteristic spatial variation scale of the fluctuating components is smaller than the local radius (i.e terms of order $u^{'}_i u^{'}_j u^{'}_k / r$ can be neglected compared to the ones of order $\partial_r u^{'}_i u^{'}_j u^{'}_k$ ).
" The above equations then IOCOLIC, (Ou2/775 FILE The total turbulent kinetic energy. defined as 2M then obevs the following equation ih rausport. Céusideying,ouly, = ο.Vv = 5tμμ."," The above equations then become, = 2 - - ( + +, = - - = - The total turbulent kinetic energy, defined as k =, then obeys the following equation _t k = - r _r + - = 2 - ( + + = - - = - _t k = - r _r -"
delined as the ratio of magnetic to particle enerev flix according to: In the striped sind. the third. parameter. 5. depends on the phase-averaged magnetic field value via (he expression: Without loss of generality. we maychoose (09>0. so that 0€b I.,"defined as the ratio of magnetic to particle energy flux according to: In the striped wind, the third parameter, $\eta$, depends on the phase-averaged magnetic field value via the expression: Without loss of generality, we maychoose $\left<B'\right>\ge 0$, so that $0 \le b \le 1$ ."
 Both 5 and ji) are functions of latitude in the striped pulsar wind. since the spacing in phase of the current sheets varies.," Both $b$ and $\eta$ are functions of latitude in the striped pulsar wind, since the spacing in phase of the current sheets varies."
" At latitudes greater than the inclination angle between the magnetic and rotation axes. conventionally denoted by a. the sheets vanish (zero spacing). whereas on the equator, (hev are equally spaced. (separated in phase by 7)."," At latitudes greater than the inclination angle between the magnetic and rotation axes, conventionally denoted by $\alpha$, the sheets vanish (zero spacing), whereas on the equator, they are equally spaced (separated in phase by$\pi$ )."
 Thus. for given yg and b. the jump conditions can be solved for three of the four inpul parameters γα. g. b ancl 3s. provided thefourth is specilied.," Thus, for given $\mu$, $\sigma$ and $b$, the jump conditions can be solved for three of the four input parameters $u_{x0}$, $q$, $b$ and $\beta_>$, provided thefourth is specified."
 The wave frequency. normalized to «y. can then be constructed from (13)).," The wave frequency, normalized to $\omega_{\rm p}$, can then be constructed from \ref{linpolfrequency}) )."
 For cireular. polarization. the jump conditions can be solved. analytically (?)..," For circular polarization, the jump conditions can be solved analytically \citep{kirk10}. ."
 An example isplotted in Fig. 1l.. ," An example isplotted in Fig. \ref{circvsomega}, ,"
"which shows the relractive index ch’ω”=] το, the strength"," which shows the refractive index $ck'/\omega'=\beta_>$ , the strength"
" £—0.0278) (>10'7L.) 1.3 zz ο Πυ + Laud 4,=4.) (2=0.158) (6.1«1077 1) (Lyssi;21.0.1019 s+) log(Nyy)220.6. ουVy}>21 Nyy ina ", $z$ $> 10^{12} L_\odot$ $'$ $\approx$ $\sim$ $H_0$ $^{-1}$ $^{-1}$ $q_o = {1 \over 2}$ $z$ $6.1 \times 10^{43}$ $^{-1}$ $L_{\rm{1.37Ghz}} \approx 1.0 \times 10^{40}$ $^{-1}$ $\log(N_H) \approx 20.6$ $\log(N_H) > 21$ $N_H$ 
indication of the value of /3; can also be extracted [rom Fig.,indication of the value of $l_M$ can also be extracted from Fig.
 2 of Bechefal.(1995).. which shows the power spectra in the shearwise and spanwise directions.," 2 of \citet{Bech95}, which shows the power spectra in the shearwise and spanwise directions."
 However. the box size in these directions is large in terms of 5. and the resolution of the simulation does not allow the authors to really reach the inerlial part of the turbulent spectrum.," However, the box size in these directions is large in terms of $h$, and the resolution of the simulation does not allow the authors to really reach the inertial part of the turbulent spectrum."
" This is particularly noticeable for &, spectra in the middle of the flow (displaved in the y=82 quadrant of this ligure). which are nearly flat down to νι10. and drop precipitouslv for larger values ol hk because of numerical dissipation. as the limit resolution of the simulation is reached."," This is particularly noticeable for $k_x$ spectra in the middle of the flow (displayed in the $y=82$ quadrant of this figure), which are nearly flat down to $k_x
h\simeq 10$, and drop precipitously for larger values of $k$ because of numerical dissipation, as the limit resolution of the simulation is reached."
 The A. spectra behave sensibly better. more probably because the box is 2.5 times smaller in this direction. and show some indications that an inertial spectrum tries to develop for SSkh<30.," The $k_z$ spectra behave sensibly better, more probably because the box is 2.5 times smaller in this direction, and show some indications that an inertial spectrum tries to develop for $8\lesssim k_z h\lesssim 30$."
" Because h=Ay/2. this suggests that /,; in this simulation is at most within a [actor of ~3 of the order of magnitude estimate deduced from Eq. (17))."," Because $h=\Delta y/2$, this suggests that $l_M$ in this simulation is at most within a factor of $\sim 3$ of the order of magnitude estimate deduced from Eq. \ref{lm}) )."
 Note in passing (hat. for Couette flows. the inertial spectrum does not need (o be resolved in order for turbulence to be observed in numerical simulations: this is related to the existence of a large5 scale nonlinear mechanism which sustains turbulence. as mentioned in section ??.. and which is most likely at the origin of the more or less flat part of the spectra αἱ large scales.," Note in passing that, for Couette flows, the inertial spectrum does not need to be resolved in order for turbulence to be observed in numerical simulations; this is related to the existence of a large scale nonlinear mechanism which sustains turbulence, as mentioned in section \ref{plcou}, and which is most likely at the origin of the more or less flat part of the spectra at large scales."
for building a central SB. will be triggered by à non-axialsymmetric gravitational potential like in. interacting galaxies.,"for building a central SB, will be triggered by a non-axialsymmetric gravitational potential like in interacting galaxies."
 They argued that perturbed orbits of gas clouds caused by an encounter lead to enhanced cloud collisions within the galactic central region and trigger the formation of massive stars., They argued that perturbed orbits of gas clouds caused by an encounter lead to enhanced cloud collisions within the galactic central region and trigger the formation of massive stars.
 An alternative model for triggering a central SB was given by Jog Das (1992) and Jog Solomon (1992)., An alternative model for triggering a central SB was given by Jog Das (1992) and Jog Solomon (1992).
 The infall of giant molecular clouds (GMCs) into an intercloud medium with à higher mean pressure in the central regio drives a radiative shock into the GMCs and ignites the SB., The infall of giant molecular clouds (GMCs) into an intercloud medium with a higher mean pressure in the central region drives a radiative shock into the GMCs and ignites the SB.
 The inflow of gas from the galactic disk ts not only required for a central SB but also for fuelling an AGN., The inflow of gas from the galactic disk is not only required for a central SB but also for fuelling an AGN.
 It is. still under debate whether SBs are progenitors of AGN (Norma Seoville 1988) or whether both are different physical processes., It is still under debate whether SBs are progenitors of AGN (Norman Scoville 1988) or whether both are different physical processes.
 Weedman (1983) proposed that if a large number of massive stars form fast in a small central volume. the compact stellar remnants from these could act as aceretors.," Weedman (1983) proposed that if a large number of massive stars form fast in a small central volume, the compact stellar remnants from these could act as accretors."
 Also the stellar dynamical merging of a dense cluster of massive stellar remnants would plausibly form a blackhole nucleus (Rees 1984)., Also the stellar dynamical merging of a dense cluster of massive stellar remnants would plausibly form a blackhole nucleus (Rees 1984).
" The nuclei of several nearby galaxies. like NGC 1068. NGC 1097. and NGC 7469. can be resolved into a central AGN and a eircumnuclear SB ring (Keel 1985: Pérrez-Olea Colina 1996, hereafter PC96)."," The nuclei of several nearby galaxies, like NGC 1068, NGC 1097, and NGC 7469, can be resolved into a central AGN and a circumnuclear SB ring (Keel 1985; Pérrez-Olea Colina 1996, hereafter PC96)."
 Some host galaxies of quasars also exhibit evidence for SBs. such as 448 (Stockton 1990).," Some host galaxies of quasars also exhibit evidence for SBs, such as 48 (Stockton 1990)."
 Assuming an evolution from starbursts to AGNs during the interaction of galaxies one would expect more AGNs with the age of the merger process., Assuming an evolution from starbursts to AGNs during the interaction of galaxies one would expect more AGNs with the age of the merger process.
 Recent observations of ultraluminous IR galaxies with the infrared satellite ISO however do not show any obvious tendency of an increasing fraction of AGNs within interacting galaxies with advanced merging process (Lutz et al., Recent observations of ultraluminous IR galaxies with the infrared satellite ISO however do not show any obvious tendency of an increasing fraction of AGNs within interacting galaxies with advanced merging process (Lutz et al.
 1998; Genzel et al., 1998; Genzel et al.
 1998)., 1998).
 Half of the observed galaxies reveal both an AGN and starburst activity., Half of the observed galaxies reveal both an AGN and starburst activity.
 It seems more likely that more local and shorter term conditions like time-dependent compression of the cireumnuclear interstellar gas. the accretion rate onto the central black hole. and the associate radiation efficiency determine AGN or starburst dominated luminosities.," It seems more likely that more local and shorter term conditions like time-dependent compression of the circumnuclear interstellar gas, the accretion rate onto the central black hole, and the associate radiation efficiency determine AGN or starburst dominated luminosities."
 In this paper we present the spectral and imaging X-ray properties of NGC 4410 observed by the ROSAT Position Sensitive Proportional Counter (PSPC) and High Resolution Imager (HRI). respectively.," In this paper we present the spectral and imaging X-ray properties of NGC 4410 observed by the ROSAT Position Sensitive Proportional Counter (PSPC) and High Resolution Imager (HRI), respectively."
 We are able to resolve the two optical components in the ROSAT HRI image., We are able to resolve the two optical components in the ROSAT HRI image.
 The paper is structured as follows: In the next section we are considering the X-ray observations m general. detecting and trying to identify the emergent X-ray sources in the field and discussing the data reduction.," The paper is structured as follows: In the next section we are considering the X-ray observations in general, detecting and trying to identify the emergent X-ray sources in the field and discussing the data reduction."
 In Sect., In Sect.
 3 we concentrate on NGC 4410 presenting the HRI results at first before we study the spectral flux distribution of the PSPC data with particular concern of comparison with a sequence of X-ray radiation models., 3 we concentrate on NGC 4410 presenting the HRI results at first before we study the spectral flux distribution of the PSPC data with particular concern of comparison with a sequence of X-ray radiation models.
 The results are then discussed in Sect., The results are then discussed in Sect.
" 4 making use of a HST WFPC? image of NGC 4410a for a geometrical consideration of its inclination,", 4 making use of a HST WFPC2 image of NGC 4410a for a geometrical consideration of its inclination.
 The data presented in this paper were taken with the HRI and the PSPC detectors on board of the X-ray satellite ROSAT., The data presented in this paper were taken with the HRI and the PSPC detectors on board of the X-ray satellite ROSAT.
 This X-ray telescope is operating in the energy range of 0.1 to 2.4 keV. The spatial resolutions of the HRI is 1777., This X-ray telescope is operating in the energy range of 0.1 to 2.4 keV. The spatial resolutions of the HRI is 7.
" The point spread function (PSF) of this detector at the optical axis in combination with the telescope is3"".", The point spread function (PSF) of this detector at the optical axis in combination with the telescope is.
". The PSPC has a PSF of25"".", The PSPC has a PSF of.
", The two detectors have a field of view of παπά27.. respectively."," The two detectors have a field of view of and, respectively."
 For details concerning ROSAT and its instruments see the ROSAT User's Handbook (Briel et al., For details concerning ROSAT and its instruments see the ROSAT User's Handbook (Briel et al.
 1996)., 1996).
 NGC 4410 was observed on June 28-30. 1993 with the ROSAT PSPC detector for a total effective exposure time of 23.4 ksec.," NGC 4410 was observed on June 28-30, 1993 with the ROSAT PSPC detector for a total effective exposure time of 23.4 ksec."
 The total number of background-subtracted counts from the central source associated with NGC 4410 1s 87043231., The total number of background-subtracted counts from the central source associated with NGC 4410 is $\pm$ 31.
 Figure | shows the central oof the PSPC field of view., Figure 1 shows the central of the PSPC field of view.
 For the spectral analysis of the source we used the software package IDL., For the spectral analysis of the source we used the software package IDL.
 The source photons were extracted from a circular area of aaround the central source and corrected for telescope vignetting and detector dead-time., The source photons were extracted from a circular area of around the central source and corrected for telescope vignetting and detector dead-time.
 The spectrum of the source was binned according to a signal-to-noise ratio of ο., The spectrum of the source was binned according to a signal-to-noise ratio of 8.
" For the background correction we selected three uncontaminated circular areas close to NGC 4410 with radii of86"".. παπα141""."," For the background correction we selected three uncontaminated circular areas close to NGC 4410 with radii of, and."
. The background contributes an X-ray flux of (1.362-0.27) ets 7 in the ROSAT bandpass., The background contributes an X-ray flux of $\pm$ cts $^{-2}$ in the ROSAT bandpass.
 In order to fit a model spectrum to the PSPC data we used the X- spectral-fitting software package XSPEC (Arnaud 1996)., In order to fit a model spectrum to the PSPC data we used the X-ray spectral-fitting software package XSPEC (Arnaud 1996).
indicates that the “force-free” boundary condition gives good results as compared with those obtained using the “force-balance” conditionif the shape of the simulation reeion is not elougated im the + direction.,indicates that the “force-free” boundary condition gives good results as compared with those obtained using the “force-balance” condition the shape of the simulation region is not elongated in the $z-$ direction.
" Below. we investigate different runs for “force-frec™ outer boundary coucitions ou D,,. but for differeut shapes of the simulation region."," Below, we investigate different runs for “force-free” outer boundary conditions on $B_\phi$, but for different shapes of the simulation region."
 We noticed cmpirically that results of simulations depend significantly ou the shape of simulation region., We noticed empirically that results of simulations depend significantly on the shape of simulation region.
" The ratio between 2,44 to Zing, Is critical.", The ratio between $R_{max}$ to $Z_{max}$ is critical.
 We observed that when the region is elougated iu :. direction. then the flow has tendency to collimate.," We observed that when the region is elongated in $z-$ direction, then the flow has tendency to collimate."
 When the region is square. or spherical. or clongated iu r direction. then the outflow is almost spherical. that is. only shehtly collimated.," When the region is square, or spherical, or elongated in $r-$ direction, then the outflow is almost spherical, that is, only slightly collimated."
 Tere. we present results of simulations all with “force-free” outer boundary conditions but cdiffercut shapes of the simulation reelon.," Here, we present results of simulations all with “force-free” outer boundary conditions but different shapes of the simulation region."
 First. we investigated the case where the height of the region is the same as before. Ziq.= 200r;. but the region is πιο] wider. ονL70r;.," First, we investigated the case where the height of the region is the same as before, $Z_{max}=200 r_i$ , but the region is much wider, $R_{max}=170 r_i$."
 Figure 7 shows that in this case we got almost spherical outflow. which is verv different from the well-collimated outflow iu the narrow region at the same boundary conditions (Figures 6c. d).," Figure 7 shows that in this case we got almost spherical outflow, which is very different from the well-collimated outflow in the narrow region at the same boundary conditions (Figures 6c, d)."
6 We also performed similar simulatious in spherical coordinates with Roya:L70r;. and got sinülu result.," We also performed similar simulations in spherical coordinates with $R_{max}=170 r_i$, and got similar result."
 The question is why the dows are so differeut for different shapes of the simulation region?, The question is why the flows are so different for different shapes of the simulation region?
 Tn all cases the flow is super fast mmaegnetosonic i most of the region., In all cases the flow is super fast magnetosonic in most of the region.
 However. note that even if the flow is super fast magnetosonic. information can flow in from the boundaries to the siuulatioun region. if the Mach cones are directed inside the simulation region.," However, note that even if the flow is super fast magnetosonic, information can flow in from the boundaries to the simulation region, if the Mach cones are directed inside the simulation region."
" The Mach cone projected outo the poloidal plane has a half opening angle 42 which is where e,,, aud e5,, are the slow and fast maguetosouic velocities. respectively, which satisfy οἱtinCanalsfinx|eA)|3—( (with 3=B?/(lzp) and ση,=2 aud (Stayes(0|e2 is the “cusp” velocity (Polovin Douutskii 1980: Lovelace et al."," The Mach cone projected onto the poloidal plane has a half opening angle $\varphi$ which is where $c_{sm}$ and $c_{fm}$ are the slow and fast magnetosonic velocities, respectively, which satisfy $c_{s,fm}^4-c_{s,fm}^2(c_s^2+v_A^2)
+c_s^2 v_{Ap}^2=0$ (with $v_A^2 ={\bf B}^2/(4\pi\rho)$ and $v_{Ap}^2={\bf B}_p^2/(4\pi\rho)$ ) and $v_c \equiv v_{Ap} c_s/(v_A^2 +c_s^2)^{1/2}$ is the “cusp” velocity (Polovin Demutskii 1980; Lovelace et al."
 1986: Dogovalov 1997)., 1986; Bogovalov 1997).
 Figures 6 - 8 show the Mach coues ou the outer boundaries for different shapes of the simulation region., Figures 6 - 8 show the Mach cones on the outer boundaries for different shapes of the simulation region.
 We find that iu the case of an clongated region (Figure 6d) an esseutial part of the Mach cones is directed into the simulation region. whereas m the case of an alinost square rveeion (Fieure Th) ouly very small part of the Mach cones is directed into the region.," We find that in the case of an elongated region (Figure 6d) an essential part of the Mach cones is directed into the simulation region, whereas in the case of an almost square region (Figure 7b) only very small part of the Mach cones is directed into the region."
 Figure 8 shows that the most desirable ecometry - where information flows outward across the outer boundary - is obtained in spherical coordinates where all Mach cones are directed outward from the simulation region., Figure 8 shows that the most desirable geometry - where information flows outward across the outer boundary - is obtained in spherical coordinates where all Mach cones are directed outward from the simulation region.
 The clongated region is the least desirable and as discussed it eives artificial colliimatiou of the flow., The elongated region is the least desirable and as discussed it gives artificial collimation of the flow.
Note that the first stationary MIID flow solutious (Romanova et,Note that the first stationary MHD flow solutions (Romanova et
 fraanework (Jewelletal.2001:WandeltExik-senoetal.2001). to polarization.," framework \citep{jewell:2004, wandelt:2004, eriksen:2004} to polarization."
 The scientific importance of CMD polarization power spectra is high., The scientific importance of CMB polarization power spectra is high.
 For example. our current ποταιιο of the optical depth. amplitude. aud scalar spectral iudex hinges on what we kuow about the magnitude of the the low-f temperature aud polarization spectra from. t WALAP 3-vear data (Pageetal.2006).," For example, our current understanding of the optical depth, amplitude, and scalar spectral index hinges on what we know about the magnitude of the the $\ell$ temperature and polarization spectra from the WMAP 3-year data \citep{page:2006}."
. Also. a detection of large scale D modes would give a very exciting insight iuto primordial gravitational waves.," Also, a detection of large scale B modes would give a very exciting insight into primordial gravitational waves."
 Earlicr Cabbs analyses of unpolarized CMD data were described bv Wandeltetal.(2001):O°Dwyeral.(2000):Eriksenet(2004. 2006).," Earlier Gibbs analyses of unpolarized CMB data were described by \cite{wandelt:2004, odwyer:2004, eriksen:2004, eriksen:2006}."
. These efforts demonstrated that exact analyses are indeed feasible even for such large data sets as the WALAP data. which colmprise several iillion pixels.," These efforts demonstrated that exact analyses are indeed feasible even for such large data sets as the WMAP data, which comprise several million pixels."
 This is possible due to the verv favorable scaling of the Cübbs sampling algorithin., This is possible due to the very favorable scaling of the Gibbs sampling algorithm.
 While brute-force likelihood evaluations scale as OLNhe Ny being the umber of pixels in tho data set. AxGibbs sampler scales identically to the map making operation.," While brute-force likelihood evaluations scale as $\mathcal{O}(N_{\textrm{pix}}^3)$, $N_{\textrm{pix}}$ being the number of pixels in the data set, the Gibbs sampler scales identically to the map making operation."
" For the special case of uncorrelated nolse svinmnetric beams. this reduces further to On?xη, aud"," For the special case of uncorrelated noise and symmetric beams, this reduces further to $\mathcal{O}(N_{\textrm{pix}}^{3/2})$."
 Thus.even Plauck-sized data may be analyzed using these tools. as will be demonstrated im the present paper.," Thus, even Planck-sized data may be analyzed using these tools, as will be demonstrated in the present paper."
 Cübbs sampling thus provides au cficicnt route to the exact posterior (or likelihood)., Gibbs sampling thus provides an efficient route to the exact posterior (or likelihood).
 Moreover. it does not rely on anv ad-hoc approximatious.," Moreover, it does not rely on any ad-hoc approximations."
 Even for the analysis of temperature data. this proved tobe both an important and subtle issuc (Sperecletal.2006:Eriksen2006).," Even for the analysis of temperature data, this proved to be both an important and subtle issue \citep{spergel:2006,
 eriksen:2006}."
. Towever. if is critical for polarization measurements. because well-known approximate methods such as the," However, it is critical for polarization measurements, because well-known approximate methods such as the"
and it is not possible to judge if their low value for the slope is a consequence of the incompleteness.,and it is not possible to judge if their low value for the slope is a consequence of the incompleteness.
" ? studied the luminosity functions of open clusters in six nearby spiral galaxies constructed from HST archive images, and in the LMC from literature data."," \citet{slars} studied the luminosity functions of open clusters in six nearby spiral galaxies constructed from HST archive images, and in the LMC from literature data."
" Typically derived in the magnitude range [—10,—7], the CPDLF slope varies within ax04...0.6 mag""!."," Typically derived in the magnitude range $[-10,-7]$, the CPDLF slope varies within $a\approx0.4\dots0.6$ $^{-1}$."
 This result coincides with our finding for open clusters in the Milky Way., This result coincides with our finding for open clusters in the Milky Way.
" Further evidence for an agreement of the CPDLF slopes between Galactic and extragalactic clusters can be found e.g., in ?.."," Further evidence for an agreement of the CPDLF slopes between Galactic and extragalactic clusters can be found e.g., in \citet{grijs03}."
" The other interesting feature in our CPDLF is a deficiency of clusters for Jy,«—8 compared to the fitted power law.", The other interesting feature in our CPDLF is a deficiency of clusters for $I_{M_V}<-8$ compared to the fitted power law.
 A similar effect was observed by ? for extragalactic clusters., A similar effect was observed by \citet{slars} for extragalactic clusters.
 The corresponding present-day mass function CPDMF of 440 clusters is shown in Fig. 5.., The corresponding present-day mass function CPDMF of 440 clusters is shown in Fig. \ref{fig:histomf}.
 We note similar details in the ΟΡΡΜΕ that we have just observed for the CPDLF in Fig.5.., We note similar details in the CPDMF that we have just observed for the CPDLF in \ref{fig:histomf}.
" One recognises a quasi-linear portion in 7(M.) for 2.5, a turnover at about logM.=2, and a decrease for smaller masses."," One recognises a quasi-linear portion in $\eta(M_c)$ for $\log M_c>2.5$ , a turnover at about $\log M_c= 2$, and a decrease for smaller masses."
" Again, we stress that the turnover of the CPDMF can be considered as a real feature, since the determination is based on unbiased cluster data."," Again, we stress that the turnover of the CPDMF can be considered as a real feature, since the determination is based on unbiased cluster data."
" In the high-mass part of the histogram at logM.>2.5, the CPDMF can be expressed in a canonical power-law form as A fit of Eq."," In the high-mass part of the histogram at $\log M_c>2.5$, the CPDMF can be expressed in a canonical power-law form as A fit of Eq."
 1 to the observed mass function provides X=1.01+0.04 for the slope and logyn*=4.3+0.14 for the zero-point., \ref{eq:eta} to the observed mass function provides $\chi=1.01\pm0.04$ for the slope and $\log\eta^*=4.3\pm0.14$ for the zero-point.
" A deficiency of clusters at the high-mass end (logMe.2 4.0) is less pronounced than we observe for the luminosity function, and discrepancies to the fitted relation are almost within Poisson errors."," A deficiency of clusters at the high-mass end $\log M_c\gtrapprox 4.0$ ) is less pronounced than we observe for the luminosity function, and discrepancies to the fitted relation are almost within Poisson errors."
" Since all published data on mass functions of extragalactic clusters are based on the mass-luminosity relation used to convert the observed photometric or spectroscopic data into masses, only a formal comparison with our result is possible."," Since all published data on mass functions of extragalactic clusters are based on the mass-luminosity relation used to convert the observed photometric or spectroscopic data into masses, only a formal comparison with our result is possible."
" In ?,, the slopes of the CPDMFs are listed for open clusters observed in four galaxies."," In \citet{grijs03}, , the slopes of the CPDMFs are listed for open clusters observed in four galaxies."
" Within a mass range (10?,106Mo), a typical value of the CPDMF slope is α«2."," Within a mass range $(10^3,10^6\,M_\odot)$, a typical value of the CPDMF slope is $\alpha\approx2$."
" On the logarithmic scale, this corresponds to y~1 and agrees well with our results."," On the logarithmic scale, this corresponds to $\chi\approx1$ and agrees well with our results."
 We consider this result as indirect evidence of the coincidence of mass scales of Galactic and extragalactic clusters., We consider this result as indirect evidence of the coincidence of mass scales of Galactic and extragalactic clusters.
" Since star clusters evolve by changing the basic parameters (like mass and integrated luminosity), their mass and luminosity functions also undergo evolutionary changes."," Since star clusters evolve by changing the basic parameters (like mass and integrated luminosity), their mass and luminosity functions also undergo evolutionary changes."
" For stars, the impact of their evolution on the stellar mass and luminosity functions was revealed for the first time by ?,, who developed a receipt for the construction of stellar initial luminosity/mass functions from present-day distributions."," For stars, the impact of their evolution on the stellar mass and luminosity functions was revealed for the first time by \citet{salp55}, who developed a receipt for the construction of stellar initial luminosity/mass functions from present-day distributions."
" Compared to stars, the case of stellar clusters is rather complicated."," Compared to stars, the case of stellar clusters is rather complicated."
 The evolution of a cluster follows two independent time scales., The evolution of a cluster follows two independent time scales.
 The first one is the nuclear time scale that governs the evolution ofstars., The first one is the nuclear time scale that governs the evolution ofstars.
 The nuclear scale is primarily responsible for changing the cluster’s luminosity, The nuclear scale is primarily responsible for changing the cluster's luminosity
 , 
strucure in voids by providing a mapping beween the cosinological parameters in the wniverse as a whole aud the effective 1Οers within the void region.,structure in voids by providing a mapping between the cosmological parameters in the universe as a whole and the effective parameters within the void region.
 Thus. the formation and evolution of galaxies within voids gives us the opportinity to test he spherical collapse picture of halo formation (Press Schechter 1976) within lighhy underdeuse regions.," Thus, the formation and evolution of galaxies within voids gives us the opportunity to test the spherical collapse picture of halo formation (Press Schechter 1976) within highly underdense regions."
 Sreth vali e Weveaert (2001) explore a second evel of excursion When an underdeuse void is nested within a higher deusity regio, Sheth van de Weygaert (2004) explore a second level of excursion when an underdense void is nested within a higher density region.
 m is paper. we ieasure the void galaxy uass function in the Rojas et al. (," In this paper, we measure the void galaxy mass function in the Rojas et al. ("
200la) distant galaxy sample. aud comnre this t heoretical models of void nass funcious. in an attempt to understaud the euvironnieutal effects of low density regioIs ou galaxy formation.,"2004a) distant galaxy sample, and compare this to theoretical models of void mass functions, in an attempt to understand the environmental effects of low density regions on galaxy formation."
 In 2 we beeiu by introducing the SDSS void galaxy catalog., In \ref{sec:voidcat} we begin by introducing the SDSS void galaxy catalog.
" Next. in 3 we discuss lass Csination of the galaxies in this saiο,"," Next, in \ref{sec:massest} we discuss mass estimation of the galaxies in this sample."
 Because the SDSS does not include long slit spectroscopy we do not lave rotatio1 curves for our sample., Because the SDSS does not include long slit spectroscopy we do not have rotation curves for our sample.
 Thus. we use an inversion of the Tulls-Fisher relation to statistically estimate the rotational velocities of our spiral sample.," Thus, we use an inversion of the Tully-Fisher relation to statistically estimate the rotational velocities of our spiral sample."
 In l.. we prescut a theoretical basis for our expectations of the mass function based on a Press-Schechter model within an uuderdeuse region.," In \ref{sec:theory}, we present a theoretical basis for our expectations of the mass function based on a Press-Schechter model within an underdense region."
 We then preseut the comparison of theory with the measured mass function in 5.. and fud that “typical” void regions are consistent with an unbiased galaxy formation picture.," We then present the comparison of theory with the measured mass function in \ref{sec:results}, and find that “typical” void regions are consistent with an unbiased galaxy formation picture."
 We conclue with a discussion of future prospects., We conclude with a discussion of future prospects.
 To ostain a saiple o 110? void galaxies. we use data frou the Sloan Digital Sky Survey.," To obtain a sample of $^3$ void galaxies, we use data from the Sloan Digital Sky Survey."
 The SDSS is a wide-field plotometric aud spectroscopic survey., The SDSS is a wide-field photometric and spectroscopic survey.
 The completed survey will cover approximately 105 square degrees., The completed survey will cover approximately $10^{4}$ square degrees.
 CCD imaging of LOS ealaxies in five colors aud follow-up spectroscopy of 109 ealaxies with r«17.77 will be obtained., CCD imaging of $^8$ galaxies in five colors and follow-up spectroscopy of $^6$ galaxies with $r<17.77$ will be obtained.
 York et al. (, York et al. (
2000) provides au overview of he SDSS and Stoughton ct al. (,2000) provides an overview of the SDSS and Stoughton et al. (
2002) describes the carly data release (EDR) aud details about the photometric and spectroscopic measurements.,2002) describes the early data release (EDR) and details about the photometric and spectroscopic measurements.
 Strauss et al. (, Strauss et al. (
2001) describe the second data release (DR2).,2004) describe the second data release (DR2).
 Technical articles providing details of the SDSS include descriptions of the photometric camera (Camu ct al., Technical articles providing details of the SDSS include descriptions of the photometric camera (Gunn et al.
 1998). photometric analysis (Lupton ct al.," 1998), photometric analysis (Lupton et al."
 2102). the photometric svstem (Fukueita et al.," 2002), the photometric system (Fukugita et al."
 1996: Stith et al., 1996; Smith et al.
 2002). the photometric monitor (loge ct al.," 2002), the photometric monitor (Hogg et al."
 2001). astrouetric calibration (Pier et al.," 2001), astrometric calibration (Pier et al."
 2003). sclection of the galaxy. spectroscopic sauples (Strauss ct al.," 2003), selection of the galaxy spectroscopic samples (Strauss et al."
 2002: Eiseustei1 et al., 2002; Eisenstein et al.
 2001). and spectroscopic tiling (Blanton et al.," 2001), and spectroscopic tiling (Blanton et al."
 2003a)., 2003a).
 A thorough analysis of possible svstcmatic ujcertainties in the ealaxy samples is described m Scranton et al. (, A thorough analysis of possible systematic uncertainties in the galaxy samples is described in Scranton et al. (
2002).,2002).
 Galaxy photometry is k-corrected aud evolution corrected accorling to Blanton et al. (, Galaxy photometry is k-corrected and evolution corrected according to Blanton et al. (
20035).,2003b).
" We assume a 9,404 = 0.3. 0.7 cosmology aud IIubble's coustaut f=Πέ]00 -us !Mypet hroughout."," We assume a $\Omega_{\rm m}, \Omega_{\Lambda}$ = 0.3, 0.7 cosmology and Hubble's constant $h = H_0/ 100$ km $^{-1}$ $^{-1}$ throughout."
 Void galaxies are drawn from a sample referred to as (Blanton ot al., Void galaxies are drawn from a sample referred to as (Blanton et al.
 202). which is a subsample of he miblicly availalΊο DR2.," 2002), which is a subsample of the publicly available DR2."
 This sunple covers newly 2000 dee? aud contains 155.126 σαaxics.," This sample covers nearly 2000 $^2$ and contains 155,126 galaxies."
 We use a nearest ncieliOL alysis to fiuc ealaxies that reside iu regions of density coutrast dp/p<0.6 as αιjeasimmed on a scale of Th+AEpe., We use a nearest neighbor analysis to find galaxies that reside in regions of density contrast $\delta \rho / \rho < -0.6$ as measured on a scale of $h^{-1}$ Mpc.
 These are the void galaxies., These are the void galaxies.
 This choice of densiVv contrast ai nomenclature is consiseut with studies of voids iu more hrec-dimensional samples. m which individual void structures are identified using au objective algorithm (IIovle Voecley 2002. 2001.," This choice of density contrast and nomenclature is consistent with studies of voids in more three-dimensional samples, in which individual void structures are identified using an objective algorithm (Hoyle Vogeley 2002, 2004)."
 This definition fiuds voids in tre 20FCGRS. PSCz Survey and Updated Zwicky CataloOOo with typical radii of 12.5)! Mpe.," This definition finds voids in the 2dFGRS, PSCz Survey and Updated Zwicky Catalog with typical radii of $h^{-1}$ Mpc."
" These voids fil of the Udiverse and have mean ceusxitv dp/p-< 0.9, ", These voids fill of the Universe and have mean density $\delta \rho / \rho < -0.9$ .
As expected. he density aronud void galaxies (p«4) is hügher tran the mean ¢eusitv of a void (ορ) )ecause ealaxies are clusterce aud he few void. galaxies texd to lie close to the edex of the voids.," As expected, the density around void galaxies $\rho_{vg}$ ) is higher than the mean density of a void $\bar{\rho}_{void}$ ) because galaxies are clustered and the few void galaxies tend to lie close to the edges of the voids."
" Other techuiques suc1 as the method of ELAd Piran (199T) or use of tessellation techniques could also be used to find void galaxies but ""ureutle the ecometry o: the SDSS does not allow these techuiques to be used as the SDSS is xmv comprised o hin stripes which cannot wholly encompass the largest voids.", Other techniques such as the method of El-Ad Piran (1997) or use of tessellation techniques could also be used to find void galaxies but currently the geometry of the SDSS does not allow these techniques to be used as the SDSS is primarily comprised of thin stripes which cannot wholly encompass the largest voids.
 The exact process o pAelecting the void galaxies is described in detail iu Rojas et al. (, The exact process of selecting the void galaxies is described in detail in Rojas et al. (
200la}.,2004a).
 We provide a brief overview. as follows: First. a voUWue lanited sample with zj44=0.089 is constructed.," We provide a brief overview, as follows: First, a volume limited sample with $_{\rm max}=0.089$ is constructed."
 This is used to trace the distribution of the voids., This is used to trace the distribution of the voids.
 Auv galaxy in he full &8ux-Iunited sample with redshit Z«XZaax hat has less tli‘a three volune-Iimited neighbors in a sphere with radius Th tMpe and which docs uot lie close to the edge of the survev is considered a void galaxy., Any galaxy in the full flux-limited sample with redshift $<$ $_{\rm max}$ that has less then three volume-limited neighbors in a sphere with radius $h^{-1}$ Mpc and which does not lie close to the edge of the survey is considered a void galaxy.
 CGalaxics with more tha1 2 neighbors are called wall ealaxics, Galaxies with more than 3 neighbors are called wall galaxies.
" .Fηed galaxies that lie close to the survey boundary are removed from either sample as it is müpossible to tell if a galaxy is a void galaxy ""oor if its neighbors have not vet been observed.", Flux-limited galaxies that lie close to the survey boundary are removed from either sample as it is impossible to tell if a galaxy is a void galaxy or if its neighbors have not yet been observed.
 This produces a sample of 1.010 void galaxies and 12.732 wall galaxies.," This produces a sample of 1,010 void galaxies and 12,732 wall galaxies."
" These void aud wall galaxies have redshifts in the ranee 0.031«z<0.089 and have maenitudes in the rauge 22 cM,<1? (Rojas et al.", These void and wall galaxies have redshifts in the range $0.034 < z < 0.089$ and have magnitudes in the range $-22<$ $_{\rm r}<-17$ (Rojas et al.
 200La)., 2004a).
 The mass function of galaxies is oue of tho most seusitive probes of the effect of cuviromment on the erowth of structure., The mass function of galaxies is one of the most sensitive probes of the effect of environment on the growth of structure.
 The mass function is directly related to the linear erowth scale of structure and the power spectrum of the CDM distribution., The mass function is directly related to the linear growth scale of structure and the power spectrum of the CDM distribution.
 One of the complications in comparing a theoretical mass fiction to observations. is that the simplest theories generally map the mass function of Dark Matter halos. which are not directly observable.," One of the complications in comparing a theoretical mass function to observations, is that the simplest theories generally map the mass function of Dark Matter halos, which are not directly observable."
 Iu the following section. we discuss methods for using observations to estimate the halo masses.," In the following section, we discuss methods for using observations to estimate the halo masses."
 Many properties of galaxies. such as color. huuinositv and rotational velocity vary with morphology.," Many properties of galaxies, such as color, luminosity and rotational velocity vary with morphology."
 The surface brightuess profiles of the ciffereut imorphlological types are found to vary predictably. with spiral tvpes begin more compact and ellipticals beiug more extended.," The surface brightness profiles of the different morphological types are found to vary predictably, with spiral types begin more compact and ellipticals being more extended."
 Thesurface brightness profiles of galaxies be well approximated by the relation:, Thesurface brightness profiles of galaxies be well approximated by the relation:
will increase the Einstein radius aud boost the iuage separation A0.,will increase the Einstein radius and boost the image separation $\Delta\theta$.
 This boost becomes more pronounced for objects with flat iuner XM(«HR) profiles. like the NEW. NOL. W003 aud IKO1 density profiles (see Fig. 1)).," This boost becomes more pronounced for objects with flat inner $\bar{\Sigma}(<R)$ profiles, like the NFW, N04, H03 and K04 density profiles (see Fig. \ref{fig1}) )."
 While the density profiles themselves also change with u through the redshift evolution of the virial radius aud he concentration parameter. this has a münor effect on A. compared to impact of the X4.2) dependence.," While the density profiles themselves also change with $z_\mathrm{l}$ through the redshift evolution of the virial radius and the concentration parameter, this has a minor effect on $\Delta\theta$, compared to impact of the $\Sigma_\mathrm{c}(z_\mathrm{l},z_\mathrm{s})$ dependence."
 We Bud. that by allowing source redshifts as ligh as ος=5.0. he image separation of a 1019.AL. NEW-tvpe subbalo can be increased by a factor of up to zz30.," We find, that by allowing source redshifts as high as $z_\mathrm{s}=5.0$, the image separation of a $10^{10}\ M_\odot$ NFW-type subhalo can be increased by a factor of up to $\approx 30$."
 Even though lis boost factor may seeni large. the resulting mae separation is still only AO—10.9 aresecouds. aud lence ar below the observable rauge.," Even though this boost factor may seem large, the resulting image separation is still only $\Delta\theta\sim 10^{-6}$ arcseconds, and hence far below the observable range."
 For an M99 profile. the corresponding boost is only zz30%.," For an M99 profile, the corresponding boost is only $\approx 30\%$."
 Hence. subhalos need o have steep inner density profiles (of approximately the AI99 type) to become observable. even if a sample of uultiph-iuaged quasars with lens aud source redshifts chosen to maximize the subhalo image separations would )oconie available.," Hence, subhalos need to have steep inner density profiles (of approximately the M99 type) to become observable, even if a sample of multiply-imaged quasars with lens and source redshifts chosen to maximize the subhalo image separations would become available."
 The A0 estimates presented in the previous section are based on the asstuption that the subhalos cau be treated as isolated objects., The $\Delta\theta$ estimates presented in the previous section are based on the assumption that the subhalos can be treated as isolated objects.
 The effects of external convergence & and shear 5 due to the galaxy (and halo) hosting these subhalos have thereby heen ucelected., The effects of external convergence $\kappa$ and shear $\gamma$ due to the galaxy (and halo) hosting these subhalos have thereby been neglected.
 Youcharaetal.(2003) explored the cousequeces of non-zero & aud > iu the case of SIS subhalos aud found the external potential to have a nou-nueelicible impact ou the strong leusine properties of such objects., \citet{Yonehara et al.} explored the consequeces of non-zero $\kappa$ and $\gamma$ in the case of SIS subhalos and found the external potential to have a non-negligible impact on the strong lensing properties of such objects.
" However. their study suggests that the resulting mage separatious AO,.. ire typically within a factor of z3 from those derived in the case of &=ο0."," However, their study suggests that the resulting image separations $\Delta\theta_{\kappa,\gamma}$ are typically within a factor of $\approx 3$ from those derived in the case of $\kappa=\gamma=0$."
 If applied to the predictions. plotted iu Fig. 2..," If applied to the predictions plotted in Fig. \ref{fig2},"
 a boost factor of this magnitude would be iusufBcieut to challeuge our main results. namely that oulv subhalos with inner density profiles as steep as those of M99 (or SIS) models produce nage separations that can be resolved with current or planned telescopes.," a boost factor of this magnitude would be insufficient to challenge our main results, namely that only subhalos with inner density profiles as steep as those of M99 (or SIS) models produce image separations that can be resolved with current or planned telescopes."
 The question remains whether the boost factor can become considerably larecr for some of the more realistic deusitv profiles considered here., The question remains whether the boost factor can become considerably larger for some of the more realistic density profiles considered here.
 To investigate this. we use rav-tracing simulations to nuniericallv assess the distribution of figs.," To investigate this, we use ray-tracing simulations to numerically assess the distribution of $f_\mathrm{boost}$ ."
" For the macrolens (1.6. the halo aud galaxy hosting the subhalo) we adopt an SIS density profile with o,=150 kin ", For the macrolens (i.e. the halo and galaxy hosting the subhalo) we adopt an SIS density profile with $\sigma_v=150$ km $^{-1}$.
 At uo=0.5 and τς=2.0. the corresponds to a linear (angular) Equstein radius of 2.5 kpe (0.1 arcsec).," At $z_\mathrm{l}=0.5$ and $z_\mathrm{s}=2.0$, the corresponds to a linear (angular) Einstein radius of 2.5 kpc (0.4 arcsec)."
 Subhalos are then distributed within this structure. assuming an NEW profile with ο=10 for the subhalo component of the CDM in the macroleus.," Subhalos are then distributed within this structure, assuming an NFW profile with $c=10$ for the subhalo component of the CDM in the macrolens."
 Since the optical depth for image splitting bv sublalos is low (Youcharaetal.2003).. the Έως distribution is nof very sensitive to the exact spatial distrinition of the subhalos within the host hao.," Since the optical depth for image splitting by subhalos is low \citep{Yonehara et al.}, the $f_\mathrm{boost}$ distribution is not very sensitive to the exact spatial distribution of the subhalos within the host halo."
 For simpliciYe We assu all subhalos to have the sane nuam in Caci simulation. but repeat the simulations for ciffercut =bhlialo masses to explore the depeudence of fio ou the subhalo mass.," For simplicity, we assume all subhalos to have the same mass in each simulation, but repeat the simulations for different subhalo masses to explore the dependence of $f_\mathrm{boost}$ on the subhalo mass."
 The sources are asunued to be poiut-like aud are distributed on a regular grid iu the source plauc., The sources are assumed to be point-like and are distributed on a regular grid in the source plane.
 To assess the effects of maguification bias. two differcut cases are considered: one iu which no maguificatiou threshold is inposed. aud one in which ouly source positious which xoduce total magnifications ο10 are analyzed.," To assess the effects of magnification bias, two different cases are considered: one in which no magnification threshold is imposed, and one in which only source positions which produce total magnifications $\mu \geq 10$ are analyzed."
 Source xositious for which multiple πασος are not produced are always rejected., Source positions for which multiple images are not produced are always rejected.
 The vast majority of the resulting macrolmages turu out to be unaffected by the subhalos due to the ow optical depth. and are therefore discarded.," The vast majority of the resulting macroimages turn out to be unaffected by the subhalos due to the low optical depth, and are therefore discarded."
" The xoperties of the Eiustein ring of the sublialo is calculated or the remaining macronmiages. aud the image separation AO,. estimated frou its angular diameter."," The properties of the Einstein ring of the subhalo is calculated for the remaining macroimages, and the image separation $\Delta\theta_{\kappa,\gamma}$ estimated from its angular diameter."
" Tn the case of 5#0. the Einstein ring becomes an ellipse. aud Ad,,.- is then estimated along the major axis."," In the case of $\gamma\ne0$, the Einstein ring becomes an ellipse, and $\Delta\theta_{\kappa,\gamma}$ is then estimated along the major axis."
" This leads to a systematic overestimate of AY,-. which cusures that the resulting boost factors are conservative upper linüts."," This leads to a systematic overestimate of $\Delta\theta_{\kappa,\gamma}$, which ensures that the resulting boost factors are conservative upper limits."
 Iu the case of no magnification threshold. the resulting distribution of νυν Is showniu Fie.," In the case of no magnification threshold, the resulting distribution of $f_\mathrm{boost}$ is shownin Fig."
 9. for an M99 subhalo (solid line) aud an IOS subhalo (dashed). both," \ref{fig3} for an M99 subhalo (solid line) and an H03 subhalo (dashed), both"
reeions of relative success and failure of the method.,regions of relative success and failure of the method.
 The regions of parameter space where we have no simulated objects (usually because they. were too bright or faint to be in this GOODS-like sample} appear in white., The regions of parameter space where we have no simulated objects (usually because they were too bright or faint to be in this GOODS-like sample) appear in white.
 As can be seen. the differences in plots for different stretch ranges are minor. showing that the diversity in color and magnitude among SNe Ia does not affect the classification signilicantlv.," As can be seen, the differences in plots for different stretch ranges are minor, showing that the diversity in color and magnitude among SNe Ia does not affect the classification significantly."
 In the subsequent analysis. we mareinalize over the full range of streteh values.," In the subsequent analysis, we marginalize over the full range of stretch values."
 As can be seen in the top-left panel of Figure 4. (which is basically a weighted sum of ihe three panels of Figure 3)). the SN-ABC success rate on simulated SN La data is high. greater than 90%. in most regions of parameter space.," As can be seen in the top-left panel of Figure \ref{f:MCscss} (which is basically a weighted sum of the three panels of Figure \ref{f:MCstr}) ), the SN-ABC success rate on simulated SN Ia data is high, greater than $90\%$, in most regions of parameter space."
 The notable exception to this success is the population of 1-2 months old. relatively low-z. SNe.," The notable exception to this success is the population of 1-2 months old, relatively $z$, SNe."
As already. shown in (2002).. such SNe Ia have blue rest-frame colors that are similar to those of CC-SNe.,"As already shown in \citet{POZ_TP1}, such SNe Ia have blue rest-frame colors that are similar to those of CC-SNe."
 Furthermore. the older the SN. the fainter it is. and therefore it can be erroneously fitted more easily wilh vounger CC-SN (templates. which are intrinsically dimuner.," Furthermore, the older the SN, the fainter it is, and therefore it can be erroneously fitted more easily with younger CC-SN templates, which are intrinsically dimmer."
 This means that. by excluding objects [rom a sample below a certain z. one can obtain higher classification success rates.," This means that, by excluding objects from a sample below a certain $z$, one can obtain higher classification success rates."
 The top-left panel of Figure 5. shows. for the same simulated SNe Ia. the average Pi value (rather than the success rate) as a function of age and reclshilt.," The top-left panel of Figure \ref{f:MCavP} shows, for the same simulated SNe Ia, the average $P_{Ia}$ value (rather than the success rate) as a function of age and redshift."
" Clearly. most of the SNe are not only classified correctly but their classification has a high confidence. wilh an average P, ereater (han 0.8 in most regions."," Clearly, most of the SNe are not only classified correctly but their classification has a high confidence, with an average $P_{Ia}$ greater than $0.8$ in most regions."
" We also note. [rom a comparison of the top-left panels of Figures 4 and 5 that the average Pj, value follows quite well the actual success rate. meaning (hat it can serve as a reliable quality indicator."," We also note, from a comparison of the top-left panels of Figures \ref{f:MCscss} and \ref{f:MCavP} that the average $P_{Ia}$ value follows quite well the actual success rate, meaning that it can serve as a reliable quality indicator."
 We have searched [ου trends in the success rates of the classification as a function of all the other parameters. such as color. photometric errors. and extinction. and found no obvious correlations.," We have searched for trends in the success rates of the classification as a function of all the other parameters, such as color, photometric errors, and extinction, and found no obvious correlations."
 In (he three remaining panels of Figure 4.. we can see that the picture is more complex within the zoo of CC-SNe.," In the three remaining panels of Figure \ref{f:MCscss}, we can see that the picture is more complex within the zoo of CC-SNe."
 Most. (tvpe-II-P. SNe are correctly classified. being progressively better classified at later times.," Most type-II-P SNe are correctly classified, being progressively better classified at later times."
 This is (he complementary image of whal we see wilh tvpe Ia S5Ne., This is the complementary image of what we see with type Ia SNe.
 The colors of voung IH-DP SNe resemble those of Ia SNe about ἃ month past maximum light., The colors of young II-P SNe resemble those of Ia SNe about a month past maximum light.
 For this reason tvpe II-P SNe are also better classified al low z., For this reason type II-P SNe are also better classified at low $z$.
 The SN-ABC fails with tvpe-IHn SNe. with about half of them being erroneously classified as SNe la. This is the result of a degeneracy in color-amagnitude space between (hese two ivpes. and for which we have no straightlorward solution.," The SN-ABC fails with type-IIn SNe, with about half of them being erroneously classified as SNe Ia. This is the result of a degeneracy in color-magnitude space between these two types, and for which we have no straightforward solution."
 As already noted in 8??.. we clo not use in the SN-ABC a set of type Hn templates. because their addition. while improving the classification of SNe Hn as CC-SNe. would considerably hinder SN Ia classification.," As already noted in \ref{model}, we do not use in the SN-ABC a set of type IIn templates, because their addition, while improving the classification of SNe IIn as CC-SNe, would considerably hinder SN Ia classification."
 Tvpe Iln SNe likely result [rom the core-collapse of very massive stars (Gal-Yametal. 2006).. the," Type IIn SNe likely result from the core-collapse of very massive stars \citep{AGY_05gl}, , the"
In this paper we present the first results of our on-going spectroscopic survey of the eclipsing binarics from theSurvey (Pojmeaiski2002:Paezviiskietal. 2006).,"In this paper we present the first results of our on-going spectroscopic survey of the eclipsing binaries from the \citep{poj02,pacz06}."
. Our spectroscopic follow-up. to provide racial velocitics (RVs) was carried out with two high-resolution echelle spectrographs: the (UCLES) at the 3.9-m Australian Telescope (AAT) and the (CARAPEIE) at the the 192m SAAO Racelille telescope., Our spectroscopic follow-up to provide radial velocities (RVs) was carried out with two high-resolution echelle spectrographs: the (UCLES) at the 3.9-m Anglo-Australian Telescope (AAT) and the (GIRAFFE) at the the 1.9-m SAAO Radcliffe telescope.
 At the ACXP/UCLISS we were able to use the iodine cell o improve the radial velocity. precision and in consequence he precision in masses of the binary stars’ components down to a level better than0., At the AAT/UCLES we were able to use the iodine cell to improve the radial velocity precision and in consequence the precision in masses of the binary stars' components down to a level better than.
574... The available ASAS Whotometrv. when combined with our RVs. enables. us o obtain binary star models. parameterized with the absolute values of their orbital ancl physical parameters.," The available ASAS photometry, when combined with our RVs, enables us to obtain binary star models parameterized with the absolute values of their orbital and physical parameters."
 The spectroscopic observations. data reduction and the best-itting orbital/physical solutions for 15 detached. eclipsing yinarics (DEBs) from the ASAS database are. described rclow.," The spectroscopic observations, data reduction and the best-fitting orbital/physical solutions for 18 detached eclipsing binaries (DEBs) from the ASAS database are described below."
 The targets of this spectroscopic survey are. detached spectroscopic binaries with spectral types later than 15 for which precise RV measurements can be made., The targets of this spectroscopic survey are detached spectroscopic binaries with spectral types later than $\approx$ F5 for which precise RV measurements can be made.
 La order to select the appropriate targets. we proceeded as follows.," In order to select the appropriate targets, we proceeded as follows."
 The (ACVS:Pojmadski2002) was searched for DIZDs with with no obvious out-of-eclipse variations. possibly short-lasting eclipses and with 1.1.," The \citep[ACVS;][]{poj02}
 was searched for DEBs with with no obvious out-of-eclipse variations, possibly short-lasting eclipses and with $V-K>1.1$ ."
 Phere are 16 such stars in this paper., There are 16 such stars in this paper.
 Pwo other svstenis ASAS J010538-8003.7 (V.dy= 2.27) and ASAS J174626-1153.0 (V.ÁN= 2.74) are from ow separate observing program., Two other systems ASAS J010538-8003.7 $V-K=2.27$ ) and ASAS J174626-1153.0 $V-K=2.74$ ) are from our separate observing program.
 In order to select relatively bright objects and limit he exposure times but to still have a relatively large sample. we searched for binaries with V Ilmag.," In order to select relatively bright objects and limit the exposure times but to still have a relatively large sample, we searched for binaries with $V\le11\,$ mag."
 In Table 1 we present the basic characteristics of he targets discussed below., In Table \ref{tab_info} we present the basic characteristics of the targets discussed below.
 Fifteen stars turned out to be new variables whose eclipsing nature was first reported. in he ACVS., Fifteen stars turned out to be new variables whose eclipsing nature was first reported in the ACVS.
 All the systems have their ASAS photometry availableo, All the systems have their ASAS photometry available.
n-line’ The time-span of the ASAS photometry exceeds δ vears. hence.. a good phase coverage anc accurate »eriod. determination may. be expected.," The time-span of the ASAS photometry exceeds 8 years, hence a good phase coverage and accurate period determination may be expected."
 Llowever. the two xieghtest targets in our sample are not indicated in the ACVS as variables.," However, the two brightest targets in our sample are not indicated in the ACVS as variables."
 These are Al Phe CXSAS JOLO934-4615.9) and UX Alen CASAS. J053003-7614.9) previously characterized by Ancersenetal.(LOSS) and Andersenetal.(1989) respectively., These are AI Phe (ASAS J010934-4615.9) and UX Men (ASAS J053003-7614.9) previously characterized by \citet{and88} and \citet{and89} respectively.
 For AL Phe. our novel implementation of he iodine cell technique for spectroscopic binaries (Ixonacki2009) allows us to improve its parameters. especially masses. o an unprecedented level of precision.," For AI Phe, our novel implementation of the iodine cell technique for spectroscopic binaries \citep{Konacki:09::} allows us to improve its parameters, especially masses, to an unprecedented level of precision."
 For UN Men we have also obtained a higher precision in masses even though this system has wider spectral lines than AL Phe which reduces he attainable RV. precision., For UX Men we have also obtained a higher precision in masses even though this system has wider spectral lines than AI Phe which reduces the attainable RV precision.
 We have also substantially improved the characteristies of the third of the previously known eclipsing binaries in this sample W415 λα (CASASJL93044|1340.3:Brancewiez&Dworak1980) which until now was reported to have 2 times shorter period. a large brightness ratio ancl no secondary eclipse.," We have also substantially improved the characteristics of the third of the previously known eclipsing binaries in this sample – V415 Aql \citep[ASAS J193044+1340.3;][]{bra80} – which until now was reported to have 2 times shorter period, a large brightness ratio and no secondary eclipse."
 Spectra of the systems ASAS J010538 and ASAS J174626 were obtained during two runs in June (ASAS 010595) and October 2006 (ASAS 174626) with the 1.9-m Raclelille elescope and ΟΑΕΕ as à part of our low-mass eclipsing jnaries search. program., Spectra of the systems ASAS J010538 and ASAS J174626 were obtained during two runs in June (ASAS J010538) and October 2006 (ASAS J174626) with the 1.9-m Radcliffe telescope and GIRAFFE as a part of our low-mass eclipsing binaries search program.
 CLARE provides spectra with a resolution of 240000., GIRAFFE provides spectra with a resolution of $\simeq 40000$.
 Due to à relatively low throughput of he entire system. we used the exposure time of 3600s. The resulting signal-to-noise ratio (SNR) per collapsed spectral jxixel varied and depending on the observing conditions was 7-35 to 10 for both objects.," Due to a relatively low throughput of the entire system, we used the exposure time of $3600\,$ s. The resulting signal-to-noise ratio (SNR) per collapsed spectral pixel varied and depending on the observing conditions was $\sim$ 35 to $\sim$ 70 for both objects."
 The wavelength calibration was done in a standard manner with a Thr lamp exposure aken before and after a stellar exposure., The wavelength calibration was done in a standard manner with a ThAr lamp exposure taken before and after a stellar exposure.
 The rest of the objects were observed with the AAPSUCLES during 3 runs (11 nights) between September 2008. and January 2009., The rest of the objects were observed with the AAT/UCLES during 3 runs (11 nights) between September 2008 and January 2009.
 We used a 17 slit which provides a resolution of =60000.," We used a 1"" slit which provides a resolution of $\simeq 60000$."
 Most of the time we adopted an exposure time of 900s. In good seeing conditions we were able to obtain an SNR O0 For our typical target ancl an exposure without the iodine cell.," Most of the time we adopted an exposure time of $900\,$ s. In good seeing conditions we were able to obtain an $SNR \sim$ 90 for our typical target and an exposure without the iodine cell."
 However. usually the SNR was between 30 and. 65.," However, usually the SNR was between 30 and 65."
 ln bad. seeing conditions we obtained a SN?~30- 40 for the brightest targets and. no iodine cell in the light path., In bad seeing conditions we obtained a $SNR \sim$ 30-40 for the brightest targets and no iodine cell in the light path.
 I£ weather permitted we used. an iodine cell., If weather permitted we used an iodine cell.
 The exposures with the iodine cell had a SNR about lower than without the cell., The exposures with the iodine cell had a $SNR$ about lower than without the cell.
 Phe Thr lamp exposures were also taken throughout each night but not after every single stellar exposure., The ThAr lamp exposures were also taken throughout each night but not after every single stellar exposure.
 An iodine cell becomes useful when a SNR is ~50 or more., An iodine cell becomes useful when a $SNR$ is $\sim$ 50 or more.
 However. spectra with a SNA as low as ~30 taken through an iodine cell can still be reduced.," However, spectra with a $SNR$ as low as $\sim$ 30 taken through an iodine cell can still be reduced."
 For most of the nights at the AAT we had to deal with large (above 27) ancl variable seeing and it was not always possible to decide beforehand if it was practical to use the iodine cell for à elven target.," For most of the nights at the AAT we had to deal with large (above 2"") and variable seeing and it was not always possible to decide beforehand if it was practical to use the iodine cell for a given target."
 In consequence. we ended up with a number of exposures taken through the iodine cell with an SNA too low for high RV precision.," In consequence, we ended up with a number of exposures taken through the iodine cell with an $SNR$ too low for high RV precision."
 Fortunately. since the iodine cell approach for binary stars requires always taking pairs of exposures with and without the cell (Ixonacki2009.2005).. if we could not use or take an exposure with the cell we always πας one without the cell for cach target.," Fortunately, since the iodine cell approach for binary stars requires always taking pairs of exposures with and without the cell \citep{Konacki:09::,Konacki:05::}, if we could not use or take an exposure with the cell we always had one without the cell for each target."
 These were subsequently used to measure an RV with the usual Ελλη based approach., These were subsequently used to measure an RV with the usual ThAr based approach.
 In consequence. we have three types of RV clatasets based. entirely on the iodine cell. entirely on the Thar wavelength calibration or mixed sets when both types of calibrations are used to provide RVs.," In consequence, we have three types of RV datasets — based entirely on the iodine cell, entirely on the ThAr wavelength calibration or mixed sets when both types of calibrations are used to provide RVs."
 The raw ccd frames taken on both telescopes/spectrographs were reduced in a standard manner (bias subtraction.," The raw ccd frames taken on both telescopes/spectrographs were reduced in a standard manner (bias subtraction,"
the fraction of galaxies showing significant asymmetries 1 their light distribution (e.g.. Conselice2003:etal.2003)).,"the fraction of galaxies showing significant asymmetries in their light distribution (e.g., \citealt{conselice03,conselice03b}) )."
 The rationale behind the former approach ts that if à merger Is to occur. a companion must be present. anc therefore the close pair fraction Is related to the merger rate for the galaxies being considered.," The rationale behind the former approach is that if a merger is to occur, a companion must be present, and therefore the close pair fraction is related to the merger rate for the galaxies being considered."
 The latter methoc relies on the observation that if a galaxy has undergone a recent merger. it is likely to be morphologically disturbed. anc therefore an asymmetric light distribution would be a signpost of a recent merger.," The latter method relies on the observation that if a galaxy has undergone a recent merger, it is likely to be morphologically disturbed, and therefore an asymmetric light distribution would be a signpost of a recent merger."
 A critical discussion of these approaches may be found in DeProprisetal.(2007) and Genel (20082)., A critical discussion of these approaches may be found in \cite{depropris07} and \cite{genel08}.
 In this paper we derive the cynamically close pair fraction for galaxies in the 2SLAQ survey and determine an upper limit to their merger rate., In this paper we derive the dynamically close pair fraction for galaxies in the 2SLAQ survey and determine an upper limit to their merger rate.
 The benefit of using close pairs is that we are able to select major merger candidates between galaxies in a specified mass range (by appropriately choosing the luminosity of and magnitude difference between participating galaxies). derive a merger rate within a specified timescale (dependent on the chosen projected and velocity separations for the pair members and theoretical simulations) and identify ongoing merger candidates for later study.," The benefit of using close pairs is that we are able to select major merger candidates between galaxies in a specified mass range (by appropriately choosing the luminosity of and magnitude difference between participating galaxies), derive a merger rate within a specified timescale (dependent on the chosen projected and velocity separations for the pair members and theoretical simulations) and identify ongoing merger candidates for later study."
 Galaxy asymmetries tend to be more difficult to interpret in this fashion and usually require better quality imaging than we have available in our survey. especially for dry mergers (Belletal.2006a;Wen 2008).. to which the 2SLAQ survey Is most sensitive.," Galaxy asymmetries tend to be more difficult to interpret in this fashion and usually require better quality imaging than we have available in our survey, especially for dry mergers \citep{bell06a,wen09}, to which the 2SLAQ survey is most sensitive."
" Unlike asymmetries. galaxy pairs are sensitive to the merger fraction of ""progenitor"" halos and this quantity may be more directly compared to theoretical models etal. 2008a)."," Unlike asymmetries, galaxy pairs are sensitive to the merger fraction of `progenitor' halos and this quantity may be more directly compared to theoretical models \citep{genel08}."
. The structure of this paper is as follows: in the next section we present the data. describe the methodology and derive the pair fraction and an upper limit to the dry merger rate at the intermediate redshifts sampled by the 2SLAQ survey.," The structure of this paper is as follows: in the next section we present the data, describe the methodology and derive the pair fraction and an upper limit to the dry merger rate at the intermediate redshifts sampled by the 2SLAQ survey."
 We then discuss and compare our results in the context of galaxy formation models and recent work on the dry merger rate., We then discuss and compare our results in the context of galaxy formation models and recent work on the dry merger rate.
" We adopt the latest cosmological parameters with O4,=0.21, O4=(173 and Hy=100 km/s/Mpe."," We adopt the latest cosmological parameters with $\Omega_M=0.27$, $\Omega_{\Lambda}=0.73$ and $H_0=100$ km/s/Mpc."
 Unless otherwise stated. all absolute magnitudes quoted in the following are intended as including a term of |5log/ and all distance measures need to be referred to / (to the appropriate power).," Unless otherwise stated, all absolute magnitudes quoted in the following are intended as including a term of $+5\,\log h$ and all distance measures need to be referred to $h$ (to the appropriate power)."
 The data used in the 28LAQ survey consist of LRGs with jo«19.5 mag., The data used in the 2SLAQ survey consist of LRGs with $i < 19.8$ mag.
 from the original sample of Etsensteinet (2001).. selected by their yr and r/ colors to lie at 0.15<+«0.65 (see Fukugitaetal.1996. for a description of the SDSS filter system).," from the original sample of \cite{eisenstein01}, selected by their $g-r$ and $r-i$ colors to lie at $0.45 < z < 0.65$ (see \citealt{fukugita96} for a description of the SDSS filter system)."
 Photometry and astrometry for the target LRGs are derived from the SDSS Data Release | (Yorketal.2000:Abazajian2003) with improvements from the latest release available at the time of the spectroscopic observations (DR4 — Adelman-MeCarthyetal. 2006)).," Photometry and astrometry for the target LRGs are derived from the SDSS Data Release 1 \citep{york00,abazajian03} with improvements from the latest release available at the time of the spectroscopic observations (DR4 – \citealt{adelman06}) )."
 The objects lie in two long strips on the celestial equator. divided into several disconnected patches. each of which is between 10 and 30 deg? in area. for a total survey coverage of 182 deg.," The objects lie in two long strips on the celestial equator, divided into several disconnected patches, each of which is between 10 and 30 $^2$ in area, for a total survey coverage of 182 $^2$."
 Spectroscopy for candidate LRGs was carried out at the Anglo-Australian telescope using the 2dF facility (Lewisetal. 2002)., Spectroscopy for candidate LRGs was carried out at the Anglo-Australian telescope using the 2dF facility \citep{lewis02}.
. For objects in the main sample (Sample 8). it was found that most galaxies are within the specified redshift limits and were observed with high spectroscopic completeness (typically 87%).," For objects in the main sample (Sample 8), it was found that most galaxies are within the specified redshift limits and were observed with high spectroscopic completeness (typically $87\%$ )."
 A complete description of the data can be found in the general survey paper by Cannon et al. (, A complete description of the data can be found in the general survey paper by Cannon et al. (
2006; hereafter 0060).,2006; hereafter C06).
 Because we have highly complete spectroscopy. we can confirm that at least of our galaxies have K-type or LRG spectra. with no sign of star formation. while less than of the sample shows emission lines (Roseboometal.2006).," Because we have highly complete spectroscopy, we can confirm that at least of our galaxies have K-type or LRG spectra, with no sign of star formation, while less than of the sample shows emission lines \citep{roseboom06}."
. We can therefore use this sample to measure the dry merger rate., We can therefore use this sample to measure the dry merger rate.
 Following Wakeetal.(2006).. we computed the absolute magnitude for objects with reliable redshifts. 4|¢ corrected to the SDSS + band at :=0.2.," Following \cite{wake06}, we computed the absolute magnitude for objects with reliable redshifts, $k+e$ corrected to the SDSS $r$ band at $z=0.2$."
 This facilitates comparison with previous work on galaxy evolution and the merger rate from the SDSS (e.g.. Masjedietal.2006.2008)).," This facilitates comparison with previous work on galaxy evolution and the merger rate from the SDSS (e.g., \citealt{masjedi06,masjedi08}) )."
 Note that no correction for internal extinction. was applied to. these galaxies., Note that no correction for internal extinction was applied to these galaxies.
 We calculate close pair statistics following the formalism developed by Patton et al. (, We calculate close pair statistics following the formalism developed by Patton et al. (
2000. 2002: hereafter POO. P02) for the SSRS2 and CNOC? surveys.,"2000, 2002; hereafter P00, P02) for the SSRS2 and CNOC2 surveys."
 Here. we give an ‘algorithmic’ description of the procedures used. and show how we apply weights to correct for sources of incompleteness and the flux limited nature of the 2SLAQ survey.," Here, we give an `algorithmic' description of the procedures used, and show how we apply weights to correct for sources of incompleteness and the flux limited nature of the 2SLAQ survey."
 A fuller description of the method can be found in POO. PO2.," A fuller description of the method can be found in P00, P02."
" Let us consider a sample of Vy primary galaxies brighter than a limiting absolute magnitude 17, in some volume of space. and. in the same volume. a sample of V2 secondary galaxies brighter than a limiting absolute magnitude 175."," Let us consider a sample of $N_1$ primary galaxies brighter than a limiting absolute magnitude $M_1$ in some volume of space, and, in the same volume, a sample of $N_2$ secondary galaxies brighter than a limiting absolute magnitude $M_2$."
 The two samples may coincide (re. Mj.=Ao). as is often the case for redshift surveys: we then study ‘major’ mergers between galaxies of approximately similar luminosity.," The two samples may coincide (i.e., $M_1=M_2$ ), as is often the case for redshift surveys: we then study `major' mergers between galaxies of approximately similar luminosity."
 We are interested in knowing the fraction of galaxies in the secondary sample that are dynamically close to galaxies in the primary sample., We are interested in knowing the fraction of galaxies in the secondary sample that are dynamically close to galaxies in the primary sample.
" We define two galaxies to be dynamically close if they have a projected separation r,<204! kpe and a velocity difference of <500 kms +. as used by POO. Ρ02 and in subsequent work."," We define two galaxies to be dynamically close if they have a projected separation $r_p < 20\, h^{-1}$ kpc and a velocity difference of $< 500$ km $^{-1}$, as used by P00, P02 and in subsequent work."
 Of course. pair statistics are usually computed from redshift surveys. which are flux-limited rather than volume limited.," Of course, pair statistics are usually computed from redshift surveys, which are flux-limited rather than volume limited."
 We therefore need to account for the dependence of pair counts on the clustering properties and the mean density of galaxies in the sample. and to correct for sources of spatial and spectroscopic incompleteness.," We therefore need to account for the dependence of pair counts on the clustering properties and the mean density of galaxies in the sample, and to correct for sources of spatial and spectroscopic incompleteness."
 Because clustering is lummosity dependent (e.g.. Norbergetal. 2002)) we follow POO and restrict the analysis to a fixed range in luminosity. within which clustering properties are not expected to vary significantly. by imposing additional bright ΟΛΠε). and faint (ΑΓ) limits on the sample.," Because clustering is luminosity dependent (e.g., \citealt{norberg02}) ) we follow P00 and restrict the analysis to a fixed range in luminosity, within which clustering properties are not expected to vary significantly, by imposing additional bright $M_{bright}$ ) and faint $M_{faint}$ ) limits on the sample."
 This means that we derive a pair fraction (and merger rate) for galaxies within a specified range and ratio in luminosity., This means that we derive a pair fraction (and merger rate) for galaxies within a specified range and ratio in luminosity.
" In our case. we select galaxies with 0.15.<20.65 (where the survey is most complete) and with Afpigne=23 and My,,;=21.5 mag."," In our case, we select galaxies with $0.45 < z < 0.65$ (where the survey is most complete) and with $M_{bright}=-23$ and $M_{faint}=-21.5$ mag."
" Because the range of luminosities we survey Is small. we let 1/,,;,; coincide with AJ."," Because the range of luminosities we survey is small, we let $M_{faint}$ coincide with $M_2$."
 We also let the primary and secondary samples coincide. to select major mergers between galaxies of approximately equal luminosities (and. make full use of the spectroscopic sample).," We also let the primary and secondary samples coincide, to select major mergers between galaxies of approximately equal luminosities (and make full use of the spectroscopic sample)."
 Figure | shows the distribution of 2SLAQ galaxies in absolute magnitude vs. redshift. together with selection lines in magnitude and redshift (see below for details).," Figure 1 shows the distribution of 2SLAQ galaxies in absolute magnitude vs. redshift, together with selection lines in magnitude and redshift (see below for details)."
 The faint limit allows us to include most 2SLAQ galaxies at >0.15 and reaches slightly below the lumimosity of normal L galaxies at the mean survey redshift (or. similarly. below the turnover in the 2SLAQ LRG luminosity function of," The faint limit allows us to include most 2SLAQ galaxies at $z > 0.45$ and reaches slightly below the luminosity of normal $L^*$ galaxies at the mean survey redshift (or, similarly, below the turnover in the 2SLAQ LRG luminosity function of"
umtually consistent.,mutually consistent.
 Part of this inconsistency arises because the magnitudes refer to different phases in the Ixeplerian cycle., Part of this inconsistency arises because the magnitudes refer to different phases in the Keplerian cycle.
 With the well-known transformations (ESA 1997). standard photometric values for CL Aur in the Johnson system were calculated to be V—+11.62 aud (5—V)=+0.33 [rom the Tycho results.," With the well-known transformations (ESA 1997), standard photometric values for CL Aur in the Johnson system were calculated to be $V=+$ 11.62 and $(B-V)=+$ 0.33 from the Tycho results."
 These refer to some unkuowu Ixepleriau phase., These refer to some unknown Keplerian phase.
 These are uot. consistent with those iu Simbacl presumably. because of the large pliase-locked. variations in magnitude and color iudex of the binary., These are not consistent with those in Simbad presumably because of the large phase-locked variations in magnitude and color index of the binary.
 At present. CL Aur is known only as a neglected. eclipsing system composed of an A-type Primary aud a cooler companion.," At present, CL Aur is known only as a neglected eclipsing system composed of an A-type primary and a cooler companion."
 In order to derive photometric solutions aud to examine whetler the WOT suggestion is appropriate for the orbital period change. we decided to obtain light curves Wwμαhi multibaud photometry.," In order to derive photometric solutions and to examine whether the W07 suggestion is appropriate for the orbital period change, we decided to obtain light curves with multiband photometry."
 Iu this paper. we present the first mutual analyses of the O-C' diagram. aud the light curves.," In this paper, we present the first mutual analyses of the $O$ $C$ diagram and the light curves."
 New photometric observations of CL Aur were obtained using a SITe 2h. CCD camera aud a BVRE filter set attached to the 61-cin reflector at Sobaeksan Optical Astronomy Observatory (80AO) in Ixorea., New photometric observations of CL Aur were obtained using a SITe 2K CCD camera and a $BVRI$ filter set attached to the 61-cm reflector at Sobaeksan Optical Astronomy Observatory (SOAO) in Korea.
 The observations of the first season were mace on L1 nights τοι 2003 November to 2001 March ancl those of the secoud season ou δ nights [rom 200L December through 2005 February., The observations of the first season were made on 14 nights from 2003 November to 2004 March and those of the second season on 8 nights from 2004 December through 2005 February.
 The exposuretimes were 75—110 s for B. 15-85 s for V. 33-65 s for A. and 30—60 s for £. respectively. dependiug on weather conditions.," The exposuretimes were $-$ 140 s for $B$, $-$ 85 s for $V$ , $-$ 65 s for $R$, and $-$ 60 s for $I$, respectively, depending on weather conditions."
 The iustrument. and reduction method have been described by Lee et al. (, The instrument and reduction method have been described by Lee et al. (
2007) and a 2x2 binniug mode was selected.,2007) and a $\times$ 2 binning mode was selected.
 The nearby stars GSC 2303-112 Land GSC 2393-1118. imaged on the chip at the same time as the variable. were selected as comparison and check stars. respectively.," The nearby stars GSC 2393-1424 and GSC 2393-1418, imaged on the chip at the same time as the variable, were selected as comparison and check stars, respectively."
 Coordinates aud Tycho maguitudes for the three stars ol interest are given in Table 1., Coordinates and Tycho magnitudes for the three stars of interest are given in Table 1.
 The differential atinosphieric extinction amoug the three stars is uepglieible withiu observational error., The differential atmospheric extinction among the three stars is negligible within observational error.
 Measurements of the check aud comparison stars indicate tliat the latter remained coustant throughout the observing interval., Measurements of the check and comparison stars indicate that the latter remained constant throughout the observing interval.
 The Lo-values of the cispersious of the magnitude differences between them are about £0.01 imag for all baudpasses., The $\sigma$ -values of the dispersions of the magnitude differences between them are about $\pm$ 0.01 mag for all bandpasses.
 A total of 2717 individual observations was obtained among the four baudpasses (711 in B. 693 in V. 685 in A. and 658 iu £) aud a sample of them is listed in Table 2.," A total of 2747 individual observations was obtained among the four bandpasses (711 in $B$, 693 in $V$, 685 in $R$, and 658 in $I$ ) and a sample of them is listed in Table 2."
 The light curves of CL Aur defined by our CCD photometry are plotted in Figure 1 as clifferential magnitudesversus orbital phase. which was computed according to the ephemeris for our hot-spot moclel determined later in this article with the Wilsou-Deviuney svuthesis code (Wilson Devinney 1971. hereafter W-D).," The light curves of CL Aur defined by our CCD photometry are plotted in Figure 1 as differential magnitudes orbital phase, which was computed according to the ephemeris for our hot-spot model determined later in this article with the Wilson-Devinney synthesis code (Wilson Devinney 1971, hereafter W-D)."
 The filled aud open circles are the individual measures of the first aud second. observing seasons. respectively.," The filled and open circles are the individual measures of the first and second observing seasons, respectively."
 Our light curves from the first observing season had uot defiued secondary eclipse adequately., Our light curves from the first observing season had not defined secondary eclipse adequately.
 Except formally for the B bandpass. mean brightuess differences between tle two seasons (in the sense of Season 1 Season 2) are constant ancl smaller than the observational error of £0.01 mae: £0.01340.01E µιας For B. +0.00740.016 mag for V. 0.017 mag for F0. and —0.009270.015 mae for Z. respectively.," Except formally for the $B$ bandpass, mean brightness differences between the two seasons (in the sense of Season 1 Season 2) are constant and smaller than the observational error of $\pm$ 0.01 mag: $\pm$ 0.014 mag for $B$, $\pm$ 0.016 mag for $V$, $\pm$ 0.017 mag for $R$, and $-$ $\pm$ 0.015 mag for $I$ , respectively."
 Although we show no figureillustrating variability of the color indices. their phase-lockecl variations are large and intlie expected senses.," Although we show no figureillustrating variability of the color indices, their phase-locked variations are large and inthe expected senses."
 These variations, These variations
The measured slopes of the size distribution for m«mr are in excellent agreement with the model outlined in Sect. ??..,The measured slopes of the size distribution for $m\ll\mf$ are in excellent agreement with the model outlined in Sect. \ref{sec:distri:theory}.
" The simplest addition to this model is settling: as grains become larger, they start to settle towards the mid-plane."," The simplest addition to this model is settling: as grains become larger, they start to settle towards the mid-plane."
" However, turbulent mixing counteracts this systematic motion."," However, turbulent mixing counteracts this systematic motion."
 The vertical distribution of dust in a settling-mixing equilibrium can (close to the mid-plane) be estimated by a Gaussian distribution with a size-dependent dust scale heightἨα., The vertical distribution of dust in a settling-mixing equilibrium can (close to the mid-plane) be estimated by a Gaussian distribution with a size-dependent dust scale height.
". Smaller particles are well enough coupled to the gas to have the same scale height as the gas,H,,, while larger particles decouple and their scale height is decreasing with grain size, (seee.g.,2???) where the Stokes number is a dimensionless quantity which describes the dynamic properties of a suspended particle."," Smaller particles are well enough coupled to the gas to have the same scale height as the gas, while larger particles decouple and their scale height is decreasing with grain size, \citep[see e.g.,][]{Dubrulle:1995p300,Schrapler:2004p2394,Youdin:2007p2021} where the Stokes number is a dimensionless quantity which describes the dynamic properties of a suspended particle."
 Very small particles have a small Stokes number and are therefore well coupled to the gas., Very small particles have a small Stokes number and are therefore well coupled to the gas.
" Particles which have different properties (e.g., size or porosity) but the same behave aerodynamically the same."," Particles which have different properties (e.g., size or porosity) but the same behave aerodynamically the same."
" In our prescription of turbulence, is defined as the product of the particles stopping time r4 and the orbital frequency €."," In our prescription of turbulence, is defined as the product of the particles stopping time $\tau_\mathrm{st}$ and the orbital frequency $\Omega_\mathrm{k}$."
" We focus on the Epstein regime where the Stokes number can be approximated by with. being. the gas surface density: and being: the internal density of the particles which relates mass and size via m=4n/3p,a°, Settling starts to play a role as soon as the Stokes number becomes larger than the turbulence parameter αι which⋅ can be related to a certain size Eq."," We focus on the Epstein regime where the Stokes number can be approximated by with being the gas surface density and being the internal density of the particles which relates mass and size via $m=4\pi/3\rhos a^3$, Settling starts to play a role as soon as the Stokes number becomes larger than the turbulence parameter $\alphat$ which can be related to a certain size Eq."
 27 only holds within about one gas pressure scale height because the dust vertical structure higher up in the disk deviates from the a Gaussian profile (seealso???)..," \ref{eq:distri:asett} only holds within about one gas pressure scale height because the dust vertical structure higher up in the disk deviates from the a Gaussian profile \citep[see also][]{Dubrulle:1995p300,Schrapler:2004p2394,Dullemond:2004p390}. ."
" The mass-dependent dust scale height causes the number density distribution n(m) to depend on the vertical height, z."," The mass-dependent dust scale height causes the number density distribution $n(m)$ to depend on the vertical height, $z$."
" In disk-like configurations, it is therefore customary to consider the column density, Similar to Eq. 2,,"," In disk-like configurations, it is therefore customary to consider the column density, Similar to Eq. \ref{eq:distri:collisions1},"
 we can write the vertically integrated number of collisions as which gives the total number of collisions that take place over the entire column of the disks., we can write the vertically integrated number of collisions as which gives the total number of collisions that take place over the entire column of the disks.
" The dependence of the collisional probability on scale height, is now reflected in the modified kernel Cinm; derivation):: The point to realize here is that, due to the symmetry between Eq."," The dependence of the collisional probability on scale height, is now reflected in the modified kernel $\tilde{C}_{m_1,m_2}$ \citep[see][Appendix A for derivation]{Birnstiel:2010p9709}: The point to realize here is that, due to the symmetry between Eq."
" 2 and Eq. 29,"," \ref{eq:distri:collisions1} and Eq. \ref{eq:distri:collsions2},"
", the analysis in Sect.", the analysis in Sect.
" ?? holds also for disk-like configuration, if the kernel is now replaced by ο"," \ref{sec:distri:theory} holds also for disk-like configuration, if the kernel is now replaced by $\tilde{C}_{m_1,m_2}$."
 The resulting exponent α then concerns the column density dependence (N(m)em ?)., The resulting exponent $\alpha$ then concerns the column density dependence $N(m)\propto m^{-\alpha}$ ).
" If we consider the case that St>o, and substitute Eq.", If we consider the case that $\St>\alphat$ and substitute Eq.
 25 and Eq., \ref{eq:distri:h_dust} and Eq.
" 26 into Eq. 30,,"," \ref{eq:distri:st} into Eq. \ref{eq:distri:cmod_1},"
 we find that has an index v=1/6 for grain sizes largerthan ase and y=0 otherwise (it should be noted that H; and A are the dust scale heights whereas (m;/m) represents the function defined in Eq. 3))., we find that has an index $\nu = 1/6$ for grain sizes largerthan $a_\mathrm{sett}$ and $\nu=0$ otherwise (it should be noted that $H_1$ and $H_2$ are the dust scale heights whereas $h(m_2/m_1)$ represents the function defined in Eq. \ref{eq:distri:kernel_form}) ).
Several authors found correlations between gas-phase metallicity gradients and other global physical parameters of galaxies.,Several authors found correlations between gas-phase metallicity gradients and other global physical parameters of galaxies.
 The observed metallicity gradients are a function of the morphological type (??):: they are steep in late-type spirals and almost flat for early-type spirals.," The observed metallicity gradients are a function of the morphological type \citep{vilacostas92, marquez02}: they are steep in late-type spirals and almost flat for early-type spirals."
" Further, in the local Universe the absolute value of the gradients seems to decrease with increasing luminosity (less luminous galaxies have steeper metallicity profiles) as predicted by modeling (?) and verified by observations (??).."," Further, in the local Universe the absolute value of the gradients seems to decrease with increasing luminosity (less luminous galaxies have steeper metallicity profiles) as predicted by modeling \citep{prantzos00} and verified by observations \citep{garnett97, vanZee98}."
" Our high-redshift sample did not verify the latter correlations and we were not able to test a correlation with the morphological type, as we do not have that information for our MASSIV sample."," Our high-redshift sample did not verify the latter correlations and we were not able to test a correlation with the morphological type, as we do not have that information for our MASSIV sample."
" The right panel of shows no clear trend between the strength of the metallicity gradient and the kinematical type, nor any correlations with their close environment (isolated or interacting)."," The right panel of shows no clear trend between the strength of the metallicity gradient and the kinematical type, nor any correlations with their close environment (isolated or interacting)."
" We can however notice that i) among the isolated objects, the non-rotating galaxies have on average flatter gradients than rotating disks, and ii) the fraction of positive gradients is higher in interacting systems compared with isolated galaxies."," We can however notice that i) among the isolated objects, the non-rotating galaxies have on average flatter gradients than rotating disks, and ii) the fraction of positive gradients is higher in interacting systems compared with isolated galaxies."
 One of the two weak correlations that might be present in our sample is shown in the left panel of7., One of the two weak correlations that might be present in our sample is shown in the left panel of.
. The strength of the gradient seems to correlate with the velocity dispersion of the galaxy., The strength of the gradient seems to correlate with the velocity dispersion of the galaxy.
 The latter is derived on beam smearing corrected velocity dispersion maps obtained after velocity field modeling (see?) and thus reflects the true velocity dispersion of the gas., The latter is derived on beam smearing corrected velocity dispersion maps obtained after velocity field modeling \citep[see][]{epinat11} and thus reflects the true velocity dispersion of the gas.
" This apparent correlation seems to be driven by the fact that galaxies with high gas velocity dispersion show shallower, often positive, metallicity gradients."," This apparent correlation seems to be driven by the fact that galaxies with high gas velocity dispersion show shallower, often positive, metallicity gradients."
" This correlation has, to our knowledge, not been observed previously in the local universe, where the velocity dispersion in late-type objects is usually low with c,~20 km (?).."," This correlation has, to our knowledge, not been observed previously in the local universe, where the velocity dispersion in late-type objects is usually low with $\sigma_v \sim 20$ km \citep{epinat10}."
" Could turbulent physical conditions in the ISM of high-redshift galaxies be at the origin of the shallow, sometimes positive gradients?"," Could turbulent physical conditions in the ISM of high-redshift galaxies be at the origin of the shallow, sometimes positive gradients?"
" This question is difficult to address here, considering the relatively low spatial resolution of our data and the scatter in7."," This question is difficult to address here, considering the relatively low spatial resolution of our data and the scatter in."
". At face value, the positive gradients in our z~1.2 galaxies might be related to the perturbed physical conditions/motions in the ISM of ζ galaxies, as opposed to the continuous metallicity gradients observed in the relatively quiet ISM of the local spirals."," At face value, the positive gradients in our $z\sim 1.2$ galaxies might be related to the perturbed physical conditions/motions in the ISM of $z$ galaxies, as opposed to the continuous metallicity gradients observed in the relatively quiet ISM of the local spirals."
" Finally, we observe as well a tentative anti-correlation between the metallicity gradient of each galaxy and its integrated metallicity (see7,, right panel)."," Finally, we observe as well a tentative anti-correlation between the metallicity gradient of each galaxy and its integrated metallicity (see, right panel)."
 Metallicity gradients are more frequently negative in metal-rich galaxies and more frequently positive in low-metallicity galaxies., Metallicity gradients are more frequently negative in metal-rich galaxies and more frequently positive in low-metallicity galaxies.
" If real, this behaviour would support the scenario in which infall of metal-poor gas from the IGM into the center of the disks drives the positive gradients."," If real, this behaviour would support the scenario in which infall of metal-poor gas from the IGM into the center of the disks drives the positive gradients."
" This infall of pristine gas would be able to reverse the gradient by diluting the central gas metallicity, and lowering the overall metallicity of the galaxy at the same time."," This infall of pristine gas would be able to reverse the gradient by diluting the central gas metallicity, and lowering the overall metallicity of the galaxy at the same time."
 The main question would remain: where does the metal-poor gas come from?, The main question would remain: where does the metal-poor gas come from?
 Accretion of cold gas from the DM reservoir and/or interaction-triggered gas infall/capture from companions?, Accretion of cold gas from the DM reservoir and/or interaction-triggered gas infall/capture from companions?
" As suggested already by previous studies (eg.??),, during an interaction, metal-poor gas from the outskirts of the galaxy could radially flow towards the center and dilute the metallicity in the inner, high star-forming regions."," As suggested already by previous studies \citep[eg.][]{werk10, rupke10}, during an interaction, metal-poor gas from the outskirts of the galaxy could radially flow towards the center and dilute the metallicity in the inner, high star-forming regions."
" At the same time, metal-enriched gas could be transported to the outer parts during the interaction, overall resulting in a flattening of the metallicity gradient."," At the same time, metal-enriched gas could be transported to the outer parts during the interaction, overall resulting in a flattening of the metallicity gradient."
 The two scenarios explaining the positive metallicity gradients --- cold gas accretion and gas redistribution during interactions -— have in common that metal-poor gas needs to be transported efficiently to the center of the objects on time scales shorter than the star formation., The two scenarios explaining the positive metallicity gradients – cold gas accretion and gas redistribution during interactions – have in common that metal-poor gas needs to be transported efficiently to the center of the objects on time scales shorter than the star formation.
 We consider the possibility of infall of pristine gas onto the disk in the context of a chemical evolution model in order to explain the positive gradients., We consider the possibility of infall of pristine gas onto the disk in the context of a chemical evolution model in order to explain the positive gradients.
" Our toy model for the chemical evolution of galaxies assumes (i) an instantaneous recycling approximation (IRA), (ii) the infall of metal-free gas onto the"," Our toy model for the chemical evolution of galaxies assumes (i) an instantaneous recycling approximation (IRA), (ii) the infall of metal-free gas onto the"
Eighteen excellent black hole eandidates have been discovered so far in X-ray binaries (ARBs. AleChntock Remillard 2003).,"Eighteen excellent black hole candidates have been discovered so far in X-ray binaries (XRBs, McClintock Remillard 2003)."
 The compact stars in these binaries have masses (hat exceed the maximum mass of a neutron star (Glendenning 2000): therefore. it is generally assumed (hat they must be black holes.," The compact stars in these binaries have masses that exceed the maximum mass of a neutron star (Glendenning 2000); therefore, it is generally assumed that they must be black holes."
 The mass measurements certainly provide a strong argument lor considering (he objects to be black holes., The mass measurements certainly provide a strong argument for considering the objects to be black holes.
 ILowever. it would be prudent to keep an open mind on (his matter and to consider the possibility that the objects may be some kind of exotic stars Chat are composed of an as-vet unidentified form of exotic material.," However, it would be prudent to keep an open mind on this matter and to consider the possibility that the objects may be some kind of exotic stars that are composed of an as-yet unidentified form of exotic material."
 Until such a model is ruled out. the objects must be treated only as black hole candidates (BIICS). not true black holes.," Until such a model is ruled out, the objects must be treated only as black hole candidates (BHCs), not true black holes."
 Glendenning (2000) has discussed a number of forms of exotic matter that might be present in compact stars. and describes models made up of these kinds of matter.," Glendenning (2000) has discussed a number of forms of exotic matter that might be present in compact stars, and describes models made up of these kinds of matter."
 All of ihe models have a maximum mass (hat is well under ολ..., All of the models have a maximum mass that is well under $3M_\odot$.
 The models are. therefore. not relevant for DIICs in XRBs.," The models are, therefore, not relevant for BHCs in XRBs."
 There are other forms of compact stars. however. e.g. Q-stus (Miller. Shahbaz Nolan 1998. ad references (herein). (hat are in principle consistent with the observed objects.," There are other forms of compact stars, however, e.g. Q-stars (Miller, Shahbaz Nolan 1998, and references therein), that are in principle consistent with the observed objects."
 Can one show that such objects are ruled out?, Can one show that such objects are ruled out?
 One way to do this is to demonstrate (hat BIICs do not have hard surfaces., One way to do this is to demonstrate that BHCs do not have hard surfaces.
 If we could show this. then the objects nust have event horizons and must. therefore. be black holes.," If we could show this, then the objects must have event horizons and must, therefore, be black holes."
 Beginning with the work of Naravan. Garcia MeClintock (1997. 2002) and Garcia et al. (," Beginning with the work of Narayan, Garcia McClintock (1997, 2002) and Garcia et al. ("
2001). a iumber of studies iive attempted to prove this result (e... 9unyaev Revnivisey 2000; Naravan Που] 2002: Done Gierlinsky 2003).,"2001), a number of studies have attempted to prove this result (e.g., Sunyaev Revnivtsev 2000; Narayan Heyl 2002; Done Gierlinsky 2003)."
 We are concerned in (his paper with the work of Naravan Γον] (2002). who argued that BIICs should exhibit Type I X-ray bursts if Chev have surfaces.," We are concerned in this paper with the work of Narayan Heyl (2002), who argued that BHCs should exhibit Type I X-ray bursts if they have surfaces."
 We eive an update on Chat work in 844 of this paper and show that the calculations rule oul nodels of BIICs in which the objects have a hard surface on which accreting gas can collect., We give an update on that work in 4 of this paper and show that the calculations rule out models of BHCs in which the objects have a hard surface on which accreting gas can collect.
 This still leaves open the possibility (hat DIICs may be made up of some kind of exotic dark matter with which normal gas does not interact., This still leaves open the possibility that BHCs may be made up of some kind of exotic dark matter with which normal gas does not interact.
 That is. the dark matter may be “porous and permit accreting eas to fall through. and {ο collect at the center.," That is, the dark matter may be “porous” and permit accreting gas to fall through and to collect at the center."
 The dark Πιο{ον and the fermionic gas would (hen behave as (wo independent fluids (hat interact only via gravity., The dark matter and the fermionic gas would then behave as two independent fluids that interact only via gravity.
 Such models have been discussed in the literature. both for fermionic dark matter and bosonic dark matter (Lee Pang 1987: Zhang 1988: HLenriques et al.," Such models have been discussed in the literature, both for fermionic dark matter and bosonic dark matter (Lee Pang 1987; Zhang 1988; Henriques et al."
 1989. 1990a.b: Jin Zhang 1989. 1999).," 1989, 1990a,b; Jin Zhang 1989, 1999)."
 We reler to these objects as fermion-lermion stars and boson-fermion stars. respectively. where the first half of the name refers to the nature of the dark matter. and the second “lermion” in each name corresponds to the nucleonic gas component.," We refer to these objects as fermion-fermion stars and boson-fermion stars, respectively, where the first half of the name refers to the nature of the dark matter, and the second “fermion” in each name corresponds to the nucleonic gas component."
 If DIICs consist of either fermion-fermion or boson-fermion stars. would (hev have Type I bursts when ον accrete eas [rom a normal binary companion star?," If BHCs consist of either fermion-fermion or boson-fermion stars, would they have Type I bursts when they accrete gas from a normal binary companion star?"
 We attempt to answer this question., We attempt to answer this question.
 We describe in, We describe in
spectrum with a focus on individual Dine profiles.,spectrum with a focus on individual line profiles.
 In addition. we analyze the low-resolution. zeroth-order ACIS CCD spectrum. in order to determine the relative contributions of high-temperature thermal emission. and wind attenuation to the observed. spectral hardness.," In addition, we analyze the low-resolution, zeroth-order ACIS CCD spectrum in order to determine the relative contributions of high-temperature thermal emission and wind attenuation to the observed spectral hardness."
 These complementary analysis techniques provide information about the temperature and kinematics of the X-ray emitting plasma. about its spatial distribution. and about the wind niass-loss rate.," These complementary analysis techniques provide information about the temperature and kinematics of the X-ray emitting plasma, about its spatial distribution, and about the wind mass-loss rate."
 X-ray emission from © stars is attributed: to. three mechanisms: (1) Embedded Wind Shocks (EWS). generally assumed to be associated with the Line-Driving Instability (LDI) (Lucy&White1980:Owockietal.1988:Feld-meieretal.LOOT:Ixahn 2001): (2) Collicline Wind Shocks (CWS) in some binary svstems (Stevensetal.1992:Antokhinetal.2004:Pittard&Parkin PO10):: ancl (3) Alagnetically Confined Wind Shocks (ALICWS) for stars with significant dipole magnetic fields (Babel&Alontmerle1997:ud-Doula&Owocki2002:Cagnéetal. 2005).," X-ray emission from O stars is attributed to three mechanisms: (1) Embedded Wind Shocks (EWS), generally assumed to be associated with the Line-Driving Instability (LDI) \citep{lw1980,ocr1988,fpp1997,Kahn2001}; (2) Colliding Wind Shocks (CWS) in some binary systems \citep{Stevens1992,Antokhin2004,pp2010}; and (3) Magnetically Confined Wind Shocks (MCWS) for stars with significant dipole magnetic fields \citep{bm1997,uo2002,Gagne2005}."
. Of these. the EWS mechanism is assumed to operate in all O stars. while CWS may dominate in massive binaries with strong enough winds and MCWS in those small number of O stars with strong. large-scale magnetic fields.," Of these, the EWS mechanism is assumed to operate in all O stars, while CWS may dominate in massive binaries with strong enough winds and MCWS in those small number of O stars with strong, large-scale magnetic fields."
 Phe EWS mechanism produces plasma of several million degrees and is associated with relatively. soft X-ray emission. while the other two mechanisms produce stronger shocks. higher temperatures. and harder X-ray emission.," The EWS mechanism produces plasma of several million degrees and is associated with relatively soft X-ray emission, while the other two mechanisms produce stronger shocks, higher temperatures, and harder X-ray emission."
 However. it should be kept in mind that soft X-ray absorption by the bulk wind can harden the observed. X-rays from EWS in O stars with high mass-loss rates (Leuteneggeretal.2010).," However, it should be kept in mind that soft X-ray absorption by the bulk wind can harden the observed X-rays from EWS in O stars with high mass-loss rates \citep{Leutenegger2010}."
. In high-resolution N-rav spectra. the hallmark of embectdecl wind: shocks is broad. emission. lines (Ixahin.etal.2001:Cassinellict 2001).," In high-resolution X-ray spectra, the hallmark of embedded wind shocks is broad emission lines \citep{Kahn2001,Cassinelli2001}."
. ὃν analvzing the widths and profile shapes of individual X-rav. emission lines in the erating spectra of O stars. the kinematies of the hot. X-ray emitting plasma embedded in the warm. partially ionized bulk wind can be determined. testing the predictions of the EWS scenario.," By analyzing the widths and profile shapes of individual X-ray emission lines in the grating spectra of O stars, the kinematics of the hot, X-ray emitting plasma embedded in the warm, partially ionized bulk wind can be determined, testing the predictions of the EWS scenario."
 Furthermore. due to preferential absorption of red-shifted line photons from the lar hemisphere. of ο star winds. X-ray emission lines from embedded wind shocks have a characteristic blue-shifted ancl skeweel shape. in proportion to the characteristic wind optical depth (Owocki&Cohen 2001).," Furthermore, due to preferential absorption of red-shifted line photons from the far hemisphere of O star winds, X-ray emission lines from embedded wind shocks have a characteristic blue-shifted and skewed shape, in proportion to the characteristic wind optical depth \citep{oc2001}."
. lt recently. has been shown that a wind niass-loss rate can be determined by fitting the ensemble of derived. characteristic optical depths. given a model of the bulk wind X-ray opacity (Cohenetal.2010).," It recently has been shown that a wind mass-loss rate can be determined by fitting the ensemble of derived characteristic optical depths, given a model of the bulk wind X-ray opacity \citep{Cohen2010}."
.. The initial application of this technique to (O4 1f) provided a mass-loss rate determination that was roughly a factor of three lower than the traditional value derived from the strength of the emission under the assumption of a smooth. unclumped wind.," The initial application of this technique to (O4 If) provided a mass-loss rate determination that was roughly a factor of three lower than the traditional value derived from the strength of the emission under the assumption of a smooth, unclumped wind."
 This lower value is consistent with other recent poassessments (Pulsetal.2006) that. cdo account. for small-scale wind clumping. which allects density-squared cliagnostics such as emission. strength.," This lower value is consistent with other recent reassessments \citep{Puls2006} that do account for small-scale wind clumping, which affects density-squared diagnostics such as emission strength."
 Phe associated. clumping factors are consistent with those seen in numerical simulations of the LDI (Itunacres&Owocki2002:Dessart2005).," The associated clumping factors are consistent with those seen in numerical simulations of the LDI \citep{ro2002,do2005}."
. Indeed. there is à consensus emerging that many. if not all. O stars’ mass-Ioss rates must be lowered by. factors of several due to the ellects of clumping (Hamannctal. 2008).," Indeed, there is a consensus emerging that many, if not all, O stars' mass-loss rates must be lowered by factors of several due to the effects of clumping \citep{hfo2008}."
. In this context. the X-ray line profile mass-loss rate diagnostic is especially useful. as it is not allected by. small-scale clumping. as long as the individual clumps are optically thin to X-ravs (Cohenetal.2010).," In this context, the X-ray line profile mass-loss rate diagnostic is especially useful, as it is not affected by small-scale clumping, as long as the individual clumps are optically thin to X-rays \citep{Cohen2010}."
 oth. numerical simulations and the lack of significant observed: X-ray variability indicate that clumps in O star winds are on quite small scales. with sizes (<<Ay.," Both numerical simulations and the lack of significant observed X-ray variability indicate that clumps in O star winds are on quite small scales, with sizes $\ell \ll \Rstar$."
 Since even 1e entire wind of LD 93129.X is only marginally optically uck to bound-free absorption of X-rays. it is very likely that gsuch small clumps will be individually quite optically thin o NX-ravs.," Since even the entire wind of HD 93129A is only marginally optically thick to bound-free absorption of X-rays, it is very likely that such small clumps will be individually quite optically thin to X-rays."
 This means they cannot have much of the selt-ga1aciowing that woulcl reduce the exposure of wind material o X-ravs. and. would thus lead to a significant “porosity” reduction in the overall absorption.," This means they cannot have much of the self-shadowing that would reduce the exposure of wind material to X-rays, and would thus lead to a significant “porosity” reduction in the overall absorption."
 An important point here jen is that. while such porosity requires a strong clumping (with individual clumps that are optically thick). a elumpect wind need not be porous (if the clumps are optically 11D 93129A lies in the Trumpler 14 cluster in the Carina nebula. at à distance of 2.3 kpe. but with a modest. visual extinction of ely=2.3 (CTownslevctal.2011:Gagnéetal.2011).," An important point here then is that, while such porosity requires a strong clumping (with individual clumps that are optically thick), a clumped wind need not be porous (if the clumps are optically HD 93129A lies in the Trumpler 14 cluster in the Carina nebula, at a distance of 2.3 kpc, but with a modest visual extinction of $A_{\rm V}
= 2.3$ \citep{Townsley2011,Gagne2011}."
. It has a visual companion. LD 93129B. at a separation of2.77. with a spectral type of O3.5. and it also has a closer visual companion (LLD 93129Ab) detected using the LINE Fine Guidance Sensor (PGS) at a separation of (Nelanetal.2004.2010).," It has a visual companion, HD 93129B, at a separation of, with a spectral type of O3.5, and it also has a closer visual companion (HD 93129Ab) detected using the HST Fine Guidance Sensor (FGS) at a separation of \citep{Nelan2004,Nelan2010}."
. Vhis closer companion is also estimated to have a spectral type of O3.5., This closer companion is also estimated to have a spectral type of O3.5.
 Non-thermal racio emission has been detected. from. the system. presumably indicating the existence of colliding wind shocks (Denagliaetal. 2006).," Non-thermal radio emission has been detected from the system, presumably indicating the existence of colliding wind shocks \citep{Benaglia2006}."
. This motivated the initial CWS interpretation of low-resolution CCCD spectral measurements of the relatively hard X-rays from LID 93129. (Evansctal.2003).. although given the large separation of components Aa and Ab (over LOO AU zc1000 /2.)). any X-ray emission associatec with the wind interaction zone should be relatively weak anc the overall emission is likely dominated by EWS emission arising much closer to the photosphere of component Xa.," This motivated the initial CWS interpretation of low-resolution CCD spectral measurements of the relatively hard X-rays from HD 93129A \citep{Evans2003}, although given the large separation of components Aa and Ab (over 100 AU $\approx 1000$ ), any X-ray emission associated with the wind interaction zone should be relatively weak and the overall emission is likely dominated by EWS emission arising much closer to the photosphere of component Aa."
 Gagneοἱal.(2011) has recently suggested that only 10 to 15 percent of the X-ray emission is due to CWS X-ravs., \citet{Gagne2011} has recently suggested that only 10 to 15 percent of the X-ray emission is due to CWS X-rays.
 Furthermore. even the high wind mass-loss rate of LID 93129. significant attenuation of the soft. X-ray. emission is expected.," Furthermore, given the high wind mass-loss rate of HD 93129A, significant attenuation of the soft X-ray emission is expected."
 This paper represents an attempt to account for wind absorption when analyzing the ο properties., This paper represents an attempt to account for wind absorption when analyzing the star's X-ray properties.
 Detailed analysis and. modeling of the optical anc UV spectra of LID 3129 was presented by Taresch.et.al. (1997)., Detailed analysis and modeling of the optical and UV spectra of HD 93129A was presented by \citet{Taresch1997}.
. Phat work included an analysis of the interstellar absorption features in the UV. which vielded a hyclrogen column density measurement of Ny=2.51075 em? that is basically consistent with the observed redcdenine ancl inferred. extinction (Ny93.7a-1074 ? is implied hy the," That work included an analysis of the interstellar absorption features in the UV, which yielded a hydrogen column density measurement of $\NH = 2.5 \times
10^{21}$ $^{-2}$ that is basically consistent with the observed reddening and inferred extinction $\NH = 3.7 \times 10^{21}$ $^{-2}$ is implied by the"
For Sin10. the range of planetary radii over which this scaling relation is valid is 0.987?Hp1.4341.,"For $S_{\mbox{\small min}}~=~10$, the range of planetary radii over which this scaling relation is valid is $0.98~R_{\mbox{\small J}}~\le~R_{\mbox{\small p}}~\le~1.43 R_{\mbox{\small J}}$."
 The relation in Eqn., The relation in Eqn.
 15. allows us to scale our results for a range of planetary radii that encompasses the radii of the known transiting hot Jupiters without having to repeat the Monte Carlo simulations., \ref{eqn:empirical4} allows us to scale our results for a range of planetary radii that encompasses the radii of the known transiting hot Jupiters without having to repeat the Monte Carlo simulations.
" In Table 2 we present the results of the Monte Carlo simulations for the various sets of stars and orbital period ranges considered. as calculated for Sui,=LO. μη=1 and Hp1.2 //j."," In Table \ref{tab:limits} we present the results of the Monte Carlo simulations for the various sets of stars and orbital period ranges considered, as calculated for $S_{\mbox{\small min}} = 10$, $N_{\mbox{\small min}} = 1$ and $R_{\mbox{\small p}}~=~1.2~R_{\mbox{\small J}}$ ."
 We also include the value of 21 from Eqn., We also include the value of $A$ from Eqn.
 for each combination of star and planet type.," \ref{eqn:empirical4}
 for each combination of star and planet type."
 One can see thatwe expect to detect ~325 1-3 d very hot Jupiters. —131 3-5 d hot Jupiters and οἱ 5-10 d hot Jupiters from the transit survey based on the assumption that each star has a single planet of the specified type.," One can see thatwe expect to detect $\sim$ 325 1-3 d very hot Jupiters, $\sim$ 131 3-5 d hot Jupiters and $\sim$ 61 5-10 d hot Jupiters from the transit survey based on the assumption that each star has a single planet of the specified type."
 In reality. only a fraction /p of the stars considered in our Monte Carlo simulations harbour a planet of a specified type. instead of our assumed one planet per star.," In reality, only a fraction $f_{\mbox{\small p}}$ of the stars considered in our Monte Carlo simulations harbour a planet of a specified type, instead of our assumed one planet per star."
 Hence we must correct our calculations of the expected number of transiting planet detections by this factor., Hence we must correct our calculations of the expected number of transiting planet detections by this factor.
 We refer to. fp as the planet fraction., We refer to $f_{\mbox{\small p}}$ as the planet fraction.
 Since fp is an unknown quantity that we would like to estimate. we may use the fact that the transit survey in BRAOS has most likely sroduced a null result (although this is still to be confirmed) and place a signiticant upper limit on fp.," Since $f_{\mbox{\small p}}$ is an unknown quantity that we would like to estimate, we may use the fact that the transit survey in BRA05 has most likely produced a null result (although this is still to be confirmed) and place a significant upper limit on $f_{\mbox{\small p}}$."
 First of all we make the assumption that the actua number of transiting planet detections .V has a Poisson distribuion with expected value {ΝΔ} given by: The Poission distribution is detined by: For a null result. ο=0.," First of all we make the assumption that the actual number of transiting planet detections $X$ has a Poisson distribution with expected value $E(X)$ given by: The Poission distribution is defined by: For a null result, $x = 0$."
 Using this fact and substituting Eqn., Using this fact and substituting Eqn.
 16 into Eqn., \ref{eqn:EX} into Eqn.
 17 we get: In order to obtain an upper limit on fp at the significance level a we require: Hence. from Eqns.," \ref{eqn:poisson} we get: In order to obtain an upper limit on $f_{\mbox{\small p}}$ at the significance level $\alpha$ we require: Hence, from Eqns."
 18. and 19.. we derive: The values of tp that we derive in this manner for a=0.50. a=0.05 anda=0.01 are shown in Table 2..," \ref{eqn:PX0} and \ref{eqn:condition}, we derive: The values of $f_{\mbox{\small p}}$ that we derive in this manner for $\alpha = 0.50$, $\alpha = 0.05$ and $\alpha = 0.01$ are shown in Table \ref{tab:limits}. ."
 For example. for a=0.01. we place an upper limit of on the 1-3 d very hot Jupiter fraction based on the assumption that such planets have a typical radius of 1.2 £2).," For example, for $\alpha~=~0.01$, we place an upper limit of on the 1-3 d very hot Jupiter fraction based on the assumption that such planets have a typical radius of $1.2~R_{\mbox{\small J}}$ ."
 Our most conservative upper limits are obtained for a=0.01 and consequently these are the upper limits on fp that we consider in the discussion and conclusions., Our most conservative upper limits are obtained for $\alpha = 0.01$ and consequently these are the upper limits on $f_{\mbox{\small p}}$ that we consider in the discussion and conclusions.
 Finally. we derive how the upper limit on /p scales with Simin and /?p by using Eqn.," Finally, we derive how the upper limit on $f_{\mbox{\small p}}$ scales with $S_{\mbox{\small min}}$ and $R_{\mbox{\small p}}$ by using Eqn."
 15. in Eqn. 20:, \ref{eqn:empirical4} in Eqn. \ref{eqn:upperlim}:
 We have derived relatively stringent upper limits on the abundance of hot Jupiters for the tield of NGC 7789., We have derived relatively stringent upper limits on the abundance of hot Jupiters for the field of NGC 7789.
 The most stringent upper limit on. fp at à0.01 of is obtained for 1-3 d very hot Jupiters of radius 1.4£2)., The most stringent upper limit on $f_{\mbox{\small p}}$ at $\alpha~=~0.01$ of is obtained for 1-3 d very hot Jupiters of radius $1.4~R_{\mbox{\small J}}$.
 Por the Sun-like G stars. we obtain limits on fp ata=0.01 of for the 1-3 d very hot Jupiters and for the 3-5 d hot Jupiters (assuming Jp= 1.2/0].," For the Sun-like G stars, we obtain limits on $f_{\mbox{\small p}}$ at $\alpha~=~0.01$ of for the 1-3 d very hot Jupiters and for the 3-5 d hot Jupiters (assuming $R_{\mbox{\small p}} = 1.2 R_{\mbox{\small J}}$ )."
 Fig., Fig.
 6. shows plots of the upper limit on the planet fraction. /ρ at a significance level of as a function of star type (Fig. 660) , \ref{fig:limfig} shows plots of the upper limit on the planet fraction $f_{\mbox{\small p}}$ at a significance level of as a function of star type (Fig. \ref{fig:limfig1}) )
and orbital period (Fig. 6(5))), and orbital period (Fig. \ref{fig:limfig2}) )
 for an assmued planetary radius of1.2 fij., for an assmued planetary radius of$1.2~R_{\mbox{\small J}}$ .
 We also show the estimate by Butleretal.(2000). that ~ of nearby Sun-like stars (late F andG dwarfs) hosta 3-5 d hot Jupiter. as derived from radial velocity observations (dotted line).," We also show the estimate by \citet{but00}
 that $\sim$ of nearby Sun-like stars (late F andG dwarfs) hosta 3-5 d hot Jupiter, as derived from radial velocity observations (dotted line)."
 It is interesting to note that although the K stars are the most, It is interesting to note that although the K stars are the most
of laree ming noise.,of large timing noise.
 So. the pulsars rotation was modeled by polynomials including several frequency derivatives.," So, the pulsar's rotation was modeled by polynomials including several frequency derivatives."
 The (imine residuals after subtraction of the third-order polynomial for v and two frequency. derivatives 7 and 7 are shown in Figure 2((a)., The timing residuals after subtraction of the third-order polynomial for $\nu$ and two frequency derivatives $\dot\nu$ and $\ddot\nu$ are shown in Figure \ref{resid1}( (a).
 The corresponding rolation parameters for the model 1979.2009 are given in Table 2.., The corresponding rotation parameters for the model 1979–2009 are given in Table \ref{model}.
 The post-fit residuals displav a large quartic term with the amplitude approximately equal to half the pulsar period., The post-fit residuals display a large quartic term with the amplitude approximately equal to half the pulsar period.
 This plot shows that the residual curve has weak but well noticeable short-term ev¢lical structure over the entire lime span., This plot shows that the residual curve has weak but well noticeable short-term cyclical structure over the entire time span.
 This cvelical structure. become more discernible in the (üming residuals presented in Figure 2((b)., This cyclical structure become more discernible in the timing residuals presented in Figure \ref{resid1}( (b).
 The post-fit residuals obtained alter subtraction of a polynomial including » ancl three Irequency derivatives exhibit the three maxima of a large-scale structure., The post-fit residuals obtained after subtraction of a polynomial including $\nu$ and three frequency derivatives exhibit the three maxima of a large-scale structure.
 The timing model with higher-order derivatives. lor example. with [our or five Ireequency. derivatives. eives similar post-fit residuals aud does not remove this structure from (he timing residuals.," The timing model with higher-order derivatives, for example, with four or five frequency derivatives, gives similar post-fit residuals and does not remove this structure from the timing residuals."
 Its origin is uncertain., Its origin is uncertain.
 We pav attention to the short-term cvelieal structure superimposed on (his residual curve., We pay attention to the short-term cyclical structure superimposed on this residual curve.
 It contains 19 eveles which are located through the intervals approximately equal to 600 days., It contains 19 cycles which are located through the intervals approximately equal to 600 days.
 The properties of just (is evelical structure will be studied in detail in the following sections., The properties of just this cyclical structure will be studied in detail in the following sections.
 The changes in the rotation lrequeney with time are shown in Figure 2((c)., The changes in the rotation frequency with time are shown in Figure \ref{resid1}( (c).
 The curve A marks the frequency. residuals Av relative to the mean rotation parameters p. 7. and P over the 19792009 interval CIable 2)).," The curve A marks the frequency residuals $\Delta\nu$ relative to the mean rotation parameters $\nu$, $\dot\nu$ , and $\ddot\nu$ over the 1979–2009 interval (Table \ref{model}) )."
 The values of ν΄ were calculated [rom the local fits. performed to the pulse arrival limes over the intervals of ~ 300 davs.," The values of $\nu$ were calculated from the local fits, performed to the pulse arrival times over the intervals of $\sim$ 300 days."
 This interval is approximately equal to half a evele duration in the Uiming residuals., This interval is approximately equal to half a cycle duration in the timing residuals.
 The strong curvature ol the Av curve is due to the presence of higher-order frequeney derivatives which are not taken into account by the timing model., The strong curvature of the $\Delta\nu$ curve is due to the presence of higher-order frequency derivatives which are not taken into account by the timing model.
 The curve A clearly shows that the signature of the lrequency resicuals Av has a sawloolh-like character., The curve A clearly shows that the signature of the frequency residuals $\Delta\nu$ has a sawtooth-like character.
 This pattern is well appreciable over the interval 19912009., This pattern is well appreciable over the interval 1991–2009.
 The observed appearance of the Av changes indicates that the rotation frequency. of the pulsar underwent slow oscillations during all the observational interval., The observed appearance of the $\Delta\nu$ changes indicates that the rotation frequency of the pulsar underwent slow oscillations during all the observational interval.
 These slow oscillations in v eive rise (to cvelical changes in the timing residuals., These slow oscillations in $\nu$ give rise to cyclical changes in the timing residuals.
 Our purpose is (ο determine (he cause of slow oscillations in the pulsar's rotation frequency., Our purpose is to determine the cause of slow oscillations in the pulsar's rotation frequency.
 Because of the paucity of data between 1979 and 1936. the properties of this oscillatory structure will be investigated over (he time span from 1991 to2009 where there is a great deal of experimental data.," Because of the paucity of data between 1979 and 1986, the properties of this oscillatory structure will be investigated over the time span from 1991 to2009 where there is a great deal of experimental data."
at Buil. the common feature of all of these scenarios is that non-rotating dwarlL elliptical galaxies may have been significantly altered by their interaction with the cluster environment.,"at hand, the common feature of all of these scenarios is that non-rotating dwarf elliptical galaxies may have been significantly altered by their interaction with the cluster environment."
 Thus. it is possible that the galaxies which still retain their kinematic signature have been accreted relatively recently while the nou-rotating dwarl elliptical galaxy sample may contain galaxies with a wide range of cluster accretion times. from the very recent to several Civr in the past.," Thus, it is possible that the galaxies which still retain their kinematic signature have been accreted relatively recently while the non-rotating dwarf elliptical galaxy sample may contain galaxies with a wide range of cluster accretion times, from the very recent to several Gyr in the past."
 Since it is likely that the age of the dominant stellar population is indicative of the time of accretion. observations ol the stellar populatious iu these galaxies could provide iusight iuto the accretion timescales.," Since it is likely that the age of the dominant stellar population is indicative of the time of accretion, observations of the stellar populations in these galaxies could provide insight into the accretion timescales."
 Iu this paper. we analyze the past star formation activity in Virgo dwarf elliptical galaxies based ou the combination of stellar population svuthesis aid spectral svuthesis models.," In this paper, we analyze the past star formation activity in Virgo dwarf elliptical galaxies based on the combination of stellar population synthesis and spectral synthesis models."
 The imagiug aud spectroscopic observatious are described iu Section 2., The imaging and spectroscopic observations are described in Section 2.
 We discuss the derived optical structural parameters of the dwarf elliptical galaxies in Section 3., We discuss the derived optical structural parameters of the dwarf elliptical galaxies in Section 3.
 In Section 1l. we analyze the optical colors iu the context of situple stellar populatious.," In Section 4, we analyze the optical colors in the context of simple stellar populations."
 In Sectiou 5. optical spectra are analyzed in tlie context ol situple stellar population moclels to investigate typical timescales for chemical enricluneut.," In Section 5, optical spectra are analyzed in the context of simple stellar population models to investigate typical timescales for chemical enrichment."
 The ünplicatious [or the observed stellar population ages and eurichinent histories are discussed iu Section 6., The implications for the observed stellar population ages and enrichment histories are discussed in Section 6.
 The conclusions of the paper are sumauiarized in Sectiou 7., The conclusions of the paper are summarized in Section 7.
 Optical images were obtained of 16 dwarf elliptical galaxies with the VATT 1.811 aud the WIYN 3.9m telescopes., Optical images were obtained of 16 dwarf elliptical galaxies with the VATT 1.8m and the WIYN 3.5m telescopes.
 Optical spectra were obtained with the Palomar Sin telescope., Optical spectra were obtained with the Palomar 5m telescope.
 The kinematic results of the spectroscopic observations are presented in vauZeeetal.(2001):: here. we analyze the spectra in terms of stellar population moclels.," The kinematic results of the spectroscopic observations are presented in \citet{vSH04}; here, we analyze the spectra in terms of stellar population models."
 The sample selection aud observations are described in this section., The sample selection and observations are described in this section.
 As described in vanZeeetal.(2001).. the sample was selected to optimize the detection of rotational motion in dE galaxies.," As described in \citet{vSH04}, the sample was selected to optimize the detection of rotational motion in dE galaxies."
 Sixteen dwarl elliptical galaxies were selected from the Vireo Cluster Catalog (VCC.Biuggelietal.1985). based on their apparent luminosity (Guy« 15.5). morphological classification (dwarf elliptical or 90). and apparent ellipticity (e> 0.25).," Sixteen dwarf elliptical galaxies were selected from the Virgo Cluster Catalog \citep[VCC,][]{VCC} based on their apparent luminosity $_B < 15.5$ ), morphological classification (dwarf elliptical or dS0), and apparent ellipticity $\epsilon > 0.25$ )."
 The latter criterion was imposed to maximize the projected rotational velocity in the kinematic observations., The latter criterion was imposed to maximize the projected rotational velocity in the kinematic observations.
 Iu addition. the sample was restricted to those galaxies with rueasured recessional velocities tliat place them within the Vireo cluster. at an approximate distauce of 16.1 Mpc 2000).," In addition, the sample was restricted to those galaxies with measured recessional velocities that place them within the Virgo cluster, at an approximate distance of 16.1 Mpc \citep[e.g.,][]{Ke00}."
. Further details of the sample selection aud distribution of the galaxies within the Virgo cluster are clescribed in vanZeeetal.(200 1).., Further details of the sample selection and distribution of the galaxies within the Virgo cluster are described in \citet{vSH04}. .
We further investigate the elfects of changing the two main discriminators (the two [ux density ratios as described in Section 3.5)).,We further investigate the effects of changing the two main discriminators (the two flux density ratios as described in Section \ref{sec:res}) ).
 When changing both these cuts in favour of the SECs we ect an increase in the densities. but this is xwelv noticeable in the lowest redshift bin and increases the ighest redshift bin by just. 104.," When changing both these cuts in favour of the SFGs we get an increase in the densities, but this is barely noticeable in the lowest redshift bin and increases the highest redshift bin by just $10\%$."
 When changing the cuts he other way. in favour of the AGN. the densities decrease. rut only by a few percent at the lowest redshift and by 23% in the highest. redshift bin.," When changing the cuts the other way, in favour of the AGN, the densities decrease, but only by a few percent at the lowest redshift and by $23\%$ in the highest redshift bin."
 Clearly the clleet of changing he selection criteria is strongest in the highest redshift bin. out. this result is not. unexpected. since this bin. typically contains the lowest S/N radio sources and lowest number of sources.," Clearly the effect of changing the selection criteria is strongest in the highest redshift bin, but this result is not unexpected since this bin typically contains the lowest S/N radio sources and lowest number of sources."
 The lux ratio discriminators are least good at the uighest redshifts. and the radio morphology/spectral index methods cannot be applied. because most. objects are too zünt.," The flux ratio discriminators are least good at the highest redshifts, and the radio morphology/spectral index methods cannot be applied because most objects are too faint."
 Furthermore. these changes are generally smaller than he combined uncertainties from the ellects listed above ancl rence indicate that the ACGN/SECG discrimination criteria used in Section 3. are not the largest uncertainty in deriving he SERD at the highest recshift.," Furthermore, these changes are generally smaller than the combined uncertainties from the effects listed above and hence indicate that the AGN/SFG discrimination criteria used in Section \ref{sec.dia} are not the largest uncertainty in deriving the SFRD at the highest redshift."
 The results of our determination of the comoving star formation rate density of the Universe as a function. of redshift are presented in Table 5 ancl Figure 5..., The results of our determination of the comoving star formation rate density of the Universe as a function of redshift are presented in Table \ref{tab.sfrd} and Figure \ref{fig:sfrd}.
 These results agree well with the multi-wavelength sample fron(2004).. converted to a WKroupa LAUP. showing the rapid rise from the local value to a value over an order of magnitude larger at 2c1. followed by a flattening above 2o1.5.," These results agree well with the multi-wavelength sample from, converted to a Kroupa IMF, showing the rapid rise from the local value to a value over an order of magnitude larger at $z\ge 1$, followed by a flattening above $z\sim1.5$."
 We highlight the results of(2000).. as blue squares corrected to the same LAL ancl cosmology. who also derived. SER. comoving density from a deep VLA observation of several fields.," We highlight the results of, as blue squares corrected to the same IMF and cosmology, who also derived SFR comoving density from a deep VLA observation of several fields."
 Pheir results are consistent with ours at all recshifts., Their results are consistent with ours at all redshifts.
 perform similar corrections for instrumental cllects and for sources below the nominal detection limit. but have very. dillerent. AGN/SEC discrimination methods and less sophisticated: methods of redshift determination [lor sources without spectroscopic redshifts those authors use estimates [rom £ or {1ν΄ magnitudes. or have randoni assignments).," perform similar corrections for instrumental effects and for sources below the nominal detection limit, but have very different AGN/SFG discrimination methods and less sophisticated methods of redshift determination for sources without spectroscopic redshifts those authors use estimates from $I$ or $HK'$ magnitudes, or have random assignments)."
 Their uncertainties are relatively small as thev do not include uncertainties in sample variance., Their uncertainties are relatively small as they do not include uncertainties in sample variance.
 Our results are also consistent with the results of who use stacking of dillerent. galaxy types in the racio to derive SER. densities at. dillerent redshifts., Our results are also consistent with the results of who use stacking of different galaxy types in the radio to derive SFR densities at different redshifts.
 The largest uncertainty in our work is that [rom the evolution of the luminosity function. necessary to correct for the un-sampled part of the LE.," The largest uncertainty in our work is that from the evolution of the luminosity function, necessary to correct for the un-sampled part of the LF."
 ltecent studies of the star formation history of the Universe have not only measured. the rapid change in global SER density. but also the demographics of the star. forming ealaxies.," Recent studies of the star formation history of the Universe have not only measured the rapid change in global SFR density, but also the demographics of the star forming galaxies."
 Many. authors have observed the evolution of the distribution of star formation moving high mass galaxies at high. redshift to lower mass galaxies at lower redshifts2007)., Many authors have observed the evolution of the distribution of star formation moving high mass galaxies at high redshift to lower mass galaxies at lower redshifts.
. This ellect has been termed. “downsizing” and is analogous to (ancl possibly related to) the apparent shift of the peak number density of AGN to lower redshifts for lower X-ray. luminosities2003)., This effect has been termed “downsizing” and is analogous to (and possibly related to) the apparent shift of the peak number density of AGN to lower redshifts for lower X-ray luminosities.
. We are able to examine “downsizing” too with our unique racio-selected sample of star forming galaxies across 0«z2., We are able to examine “downsizing” too with our unique radio-selected sample of star forming galaxies across $0<z<2$.
" In this section we chose to look just at the contribution from the Lyacu,7105Ly galaxies where we are mostly complete up to 2= 2. Figure ία)."," In this section we chose to look just at the contribution from the $L_{\rm 1.4GHz}>10\times L_\star$ galaxies where we are mostly complete up to $z=2$ , Figure \ref{fig:zsfr}( (a)."
" The Liacusco10L, top end of the luminosity function represents the top 28% of the total SER density at. any redshift. for the best fitting. Mauch and Sadler (2007) LE assuming pure luminosity evolution."," The $L_{\rm 1.4GHz}>10\times L_\star$ top end of the luminosity function represents the top $28\%$ of the total SFR density at any redshift, for the best fitting Mauch and Sadler (2007) LF assuming pure luminosity evolution."
 llence we can divide cach SERD bin into the contribution by stellar mass including that of the local sample from., Hence we can divide each SFRD bin into the contribution by stellar mass including that of the local sample from.
(2007).. We onlv show the fractional. contribution bv [uminositv/SEIt density in Figure 6. but note that the distribution by number density is very similar.," We only show the fractional contribution by luminosity/SFR density in Figure \ref{fig:sfrdm}, but note that the distribution by number density is very similar."
 Hence. number density and luminosity density are both good tracers of downsizing.," Hence, number density and luminosity density are both good tracers of downsizing."
" While the sample shown in Figure 6 represents abou one quarter of the star formation occurring at a given cosmic epoch. the £446gcLO.L, sources are the most active a any redshift."," While the sample shown in Figure \ref{fig:sfrdm} represents about one quarter of the star formation occurring at a given cosmic epoch, the $L_{\rm 1.4GHz}>10\times L_\star$ sources are the most active at any redshift."
 We find that there is a dramatic change in the stellar mass of the galaxies contributing to this part of the luminosity function., We find that there is a dramatic change in the stellar mass of the galaxies contributing to this part of the luminosity function.
" The highest redshift bin is dominate by massive galaxies. log(CΔιz11.25. although at this redshift we are not quite complete to ιο,=lO.£L. and hence we mark points in this bin as limits."," The highest redshift bin is dominated by massive galaxies, $\log(M/M_\odot)>11.25$, although at this redshift we are not quite complete to $L_{\rm 1.4GHz}=10\times L_{\star}$ and hence we mark points in this bin as limits."
 In the Lowes redshift bin (from the 6d sample) we can see the dramatic. rapid rise in the number of the least massive galaxies.," In the lowest redshift bin (from the 6df sample) we can see the dramatic, rapid rise in the number of the least massive galaxies."
 We are even ableto see the rise and fall of the contribution from, We are even ableto see the rise and fall of the contribution from
required diffusion for the CRs.,required diffusion for the CRs.
 In $2 we determine the maximum energy of accelerated particles at shocks. in $33 we calculate the spectrum of cosmic rays in the vicinity of SNRs. in $44 we obtain the spectrum of gamma ray produced by the p-p interactions of the escaping cosmic rays in a nearby cloud and compare it with observations. $55. we check the self-consistency of our result by comparing the required the diffusion near SNRs and the streaming level allowed in the presence of turbulence.," In 2 we determine the maximum energy of accelerated particles at shocks, in 3 we calculate the spectrum of cosmic rays in the vicinity of SNRs, in 4 we obtain the spectrum of gamma ray produced by the p-p interactions of the escaping cosmic rays in a nearby cloud and compare it with observations, 5, we check the self-consistency of our result by comparing the required the diffusion near SNRs and the streaming level allowed in the presence of turbulence."
 The discussion and summary are provided in $866 and $7., The discussion and summary are provided in 6 and 7.
 In the Appendix we provide a list of notations used in the paper., In the Appendix we provide a list of notations used in the paper.
 Diffusive shock acceleration of energetic CR particles relies on the crucial process of amplification of MHD turbulence so that particles can be trapped at the shock front long enough to be accelerated to the high energy observed., Diffusive shock acceleration of energetic CR particles relies on the crucial process of amplification of MHD turbulence so that particles can be trapped at the shock front long enough to be accelerated to the high energy observed.
 One of the most popular scenarios that has been adopted in the literature is the streaming instability generated by the accelerated particles., One of the most popular scenarios that has been adopted in the literature is the streaming instability generated by the accelerated particles.
 However. in the highly nonlinear regime the fluctuations of magnetic field arising from the streaming instability get large and the classical treatment of the streaming instability i5 not applicable.," However, in the highly nonlinear regime the fluctuations of magnetic field arising from the streaming instability get large and the classical treatment of the streaming instability is not applicable."
 We circumvent the problem by proposing that the field amplification we consider does not arise from the streaming instability. but i$ achieved earlier through other processes. e.g. the interaction of the shock precursor with density perturbations preexisting in the interstellar medium (Beresnyak. Jones. Lazarian 2009).," We circumvent the problem by proposing that the field amplification we consider does not arise from the streaming instability, but is achieved earlier through other processes, e.g. the interaction of the shock precursor with density perturbations preexisting in the interstellar medium (Beresnyak, Jones, Lazarian 2009)."
 Due to the resonant nature of the streaming instability. the perturbations 68 arising from it are more efficient in scattering CRs compared to the large scale fluctuations produced by non-resonant mechanisms. e.g. the one in Beresnyak et al. (," Due to the resonant nature of the streaming instability, the perturbations $\delta B$ arising from it are more efficient in scattering CRs compared to the large scale fluctuations produced by non-resonant mechanisms, e.g. the one in Beresnyak et al. ("
2009).,2009).
 Therefore in this paper. we limit our discussions to the regime of 68< By. where By is the magnetic field that has already been amplified in the precursorregion?.," Therefore in this paper, we limit our discussions to the regime of $\delta B \la B_0$ , where $B_0$ is the magnetic field that has already been amplified in the precursor."
. When particles reach the maximum energy at a certain time. they escape and the growth of the streaming instability stops.," When particles reach the maximum energy at a certain time, they escape and the growth of the streaming instability stops."
 Therefore we can obtain the maximum energy by considering the stationary state of the evolution., Therefore we can obtain the maximum energy by considering the stationary state of the evolution.
 The steady state energy density of the turbulence W(K) at the shock is determined by where U is the shock speed. and the term on the l.h.s.," The steady state energy density of the turbulence $W(k)$ at the shock is determined by where $U$ is the shock speed, and the term on the l.h.s."
 represents the advection of turbulence by the shock flow., represents the advection of turbulence by the shock flow.
 và—BofvAruun and n are the Alfven speed and the ionized gas number density of the precursor region. respectively.," $v_A\equiv B_0/\sqrt{4\pi nm}$ and $n$ are the Alfven speed and the ionized gas number density of the precursor region, respectively."
 The plus sign represents the forward propagating Alfven waves and the minus sign refers to the backward propagating Alfven waves., The plus sign represents the forward propagating Alfven waves and the minus sign refers to the backward propagating Alfven waves.
 The terms on the rh.s., The terms on the r.h.s.
" describes the wave amplification by the streaming instability and damping with DD, as the corresponding growth and damping rates of the wave."," describes the wave amplification by the streaming instability and damping with $\Gamma_{cr}, \Gamma_d$ as the corresponding growth and damping rates of the wave."
 The distribution of accelerated particles at strong shocks is f(p)ocp., The distribution of accelerated particles at strong shocks is $f(p)\propto p^{-4}$.
 If taking into account the modification of the shock structure by the accelerated particles. the CR spectrum becomes harder.," If taking into account the modification of the shock structure by the accelerated particles, the CR spectrum becomes harder."
" Assume the distribution of CRs at the shock is fo(p)e«p"".", Assume the distribution of CRs at the shock is $f_0(p)\propto p^{-4+a}$.
 The nonlinear growth was studied by Ptuskin Zirakashvili (2005)., The nonlinear growth was studied by Ptuskin Zirakashvili (2005).
 It was demonstrated by Schlickeiser Shalchi (2008) that waves can grow or damp at the shock precursor depending on the the spatial boundary conditions., It was demonstrated by Schlickeiser Shalchi (2008) that waves can grow or damp at the shock precursor depending on the the spatial boundary conditions.
 If assuming an equal amount of forward and backward waves at the shock front. the forward wave will be growing and the backward wave will be efficiently damped in the upstream region.," If assuming an equal amount of forward and backward waves at the shock front, the forward wave will be growing and the backward wave will be efficiently damped in the upstream region."
 We therefore neglect the backward moving wave mode and consider here only the growing forward moving mode. which is the one that effectively contributes to the particle scattering.," We therefore neglect the backward moving wave mode and consider here only the growing forward moving mode, which is the one that effectively contributes to the particle scattering."
 The generalized growth rate of streaming instability then is where q is the charge of the particle. ο is the light speed. Pus=ZeBov1|Atομοι is the momentum of particles that resonate with the waves.," The generalized growth rate of streaming instability then is where $q$ is the charge of the particle, c is the light speed, $p_{res}=ZeB_0\sqrt{1+A^2}/c/k_{res}$ is the momentum of particles that resonate with the waves."
 A=68/By is wave amplitude normalized by the mean magnetic field strength Bo., $A=\delta B/B_0$ is wave amplitude normalized by the mean magnetic field strength $B_0$.
 is the diffusion coefficient of CRs. v and ry are the velocity and Larmor radius of the CRs.," is the diffusion coefficient of CRs, $v$ and $r_g$ are the velocity and Larmor radius of the CRs."
" The distribution function of CRs is where & measures the ratio of CR pressure at the shock and the upstream momentum flux entering the shock front. ; is the proton rest mass. and py, is the maximum momentum accelerated at the shock front."," The distribution function of CRs is where $\xi$ measures the ratio of CR pressure at the shock and the upstream momentum flux entering the shock front, $m$ is the proton rest mass, and $p_{max}$ is the maximum momentum accelerated at the shock front."
 H(p) is the Heaviside step function., $H(p)$ is the Heaviside step function.
 In the planar shock approximation. the distribution. of accelerated particles is at the upstream of the shock (x= 0) and f=fy at the downstream.," In the planar shock approximation, the distribution of accelerated particles is at the upstream of the shock $x\geq0$ ) and $f=f_0$ at the downstream."
" Insert Eqs.(3.. 4..5)) into Eq.(2)). one gets the following growth rate of the upstream forward moving wave at x=0. where C,=9/2/(4αλa). ro—mc/qiBo."," Insert \ref{crdiff}, \ref{f0}, \ref{f1}) ) into \ref{general}) ), one gets the following growth rate of the upstream forward moving wave at x=0, where $C_{cr}=9/2/(4-a)/(2-a)$, $r_0=m c^2/q/B_0$."
 The linear damping ts negligible since the medium should be highly ionized., The linear damping is negligible since the medium should be highly ionized.
" In fully ionized gas. there is nonlinear Landau damping. which. however. is suppressed due to the reduction of particles"" mean free path in the turbulent medium (see Yan Lararian 2011; Brunetti Lazarian 2011): we therefore neglect this process here."," In fully ionized gas, there is nonlinear Landau damping, which, however, is suppressed due to the reduction of particles' mean free path in the turbulent medium (see Yan Lararian 2011; Brunetti Lazarian 2011); we therefore neglect this process here."
 Background turbulence itself can cause nonlinear damping to the waves (Yan Lazarian 2002)., Background turbulence itself can cause nonlinear damping to the waves (Yan Lazarian 2002).
 Unlike hydrodynamical turbulence. MHD turbulence is anisotropic with eddies elongated along the magnetic field.," Unlike hydrodynamical turbulence, MHD turbulence is anisotropic with eddies elongated along the magnetic field."
 The anisotropy increases with the decrease of the scale (Goldreich Sridhar 1995)., The anisotropy increases with the decrease of the scale (Goldreich Sridhar 1995).
 Atthe scales of the Larmor radii rp of the cosmic rays. which are also the wavelengths Τά of the waves induced by the streaming instability. the scale," Atthe scales of the Larmor radii $r_L$ of the cosmic rays, which are also the wavelengths $1/k$ of the waves induced by the streaming instability, the scale"
is used.,is used.
 Note that the iron radius was determined using the radial metallicity profiles only and not using the metallicity maps., Note that the iron radius was determined using the radial metallicity profiles only and not using the metallicity maps.
 A trend between jet power and iron radius is evident over three decades in jet power., A trend between jet power and iron radius is evident over three decades in jet power.
 The low powered AGN outbursts Prec103ergs~! drive out material on a scale of a few tens of kiloparsecs., The low powered AGN outbursts $P_{\rm jet} \simeq 10^{43}\rm~erg~s^{-1}$ drive out material on a scale of a few tens of kiloparsecs.
" For exceptionally large outbursts with jet power exceeding 1046ergs~!, such as MS0735, metals from the core are being launched hundreds of kiloparsecs into the ICM."," For exceptionally large outbursts with jet power exceeding $10^{46}\rm~erg~s^{-1}$, such as MS0735, metals from the core are being launched hundreds of kiloparsecs into the ICM."
 To quantify this trend we fit a linear function to the logarithms of jet power and iron radius., To quantify this trend we fit a linear function to the logarithms of jet power and iron radius.
" Performing a least squares regression, the best fit plotted in Figure 3 takes the form where jet power is in units of 1044 ergs s-!."," Performing a least squares regression, the best fit plotted in Figure 3 takes the form where jet power is in units of $10^{44}$ ergs $^{-1}$."
 The RMS scatter about the fit is approximately 0.5 dex., The RMS scatter about the fit is approximately 0.5 dex.
" The correlation is strong and shows a fairly small scatter, although with only ten objects the true scatter about the mean is difficult to evaluate."," The correlation is strong and shows a fairly small scatter, although with only ten objects the true scatter about the mean is difficult to evaluate."
" The scatter will likely increase with the inclusion of additional clusters, which will be addressed in a future paper."," The scatter will likely increase with the inclusion of additional clusters, which will be addressed in a future paper."
" A spurious correlation between iron radius and jet power, which depends on the volume of the cavities, could arise due to the dependence of distance on both the linear diameter of the cavity systems and the iron radius."," A spurious correlation between iron radius and jet power, which depends on the volume of the cavities, could arise due to the dependence of distance on both the linear diameter of the cavity systems and the iron radius."
 This does not appear to be the case., This does not appear to be the case.
 The clusters we considered here all have been exposed deeply with Chandra., The clusters we considered here all have been exposed deeply with Chandra.
" We could have easily detected cool, metal-rich gas on all spatial scales of interest here, and at random angles with respect to the cavities and radio sources."," We could have easily detected cool, metal-rich gas on all spatial scales of interest here, and at random angles with respect to the cavities and radio sources."
 We did not., We did not.
" Hydra A, for example, has a complex cavity system that was created by at least three separate outbursts or a continuous outburst that has persisted for several hundred million years etal.2007)."," Hydra A, for example, has a complex cavity system that was created by at least three separate outbursts or a continuous outburst that has persisted for several hundred million years \citep{wis07}."
". The cavity systems considered separately(Wise have similar jet powers, but their centers lie at very different radii between 25 kpc and 250 kpc."," The cavity systems considered separately have similar jet powers, but their centers lie at very different radii between 25 kpc and 250 kpc."
" Nevertheless, Hydra A does not deviate significantly from the trend in Figure 3, implying that the measured iron radius is not a simple function of cavity size alone."," Nevertheless, Hydra A does not deviate significantly from the trend in Figure 3, implying that the measured iron radius is not a simple function of cavity size alone."
 In Figure 5 we have plotted the inner cavity position for all clusters in our sample versus the iron radius., In Figure 5 we have plotted the inner cavity position for all clusters in our sample versus the iron radius.
 In all cases the iron radius lies beyond the inner cavities., In all cases the iron radius lies beyond the inner cavities.
" This shows that the metallicity outflows are not simply tracing the current generation of AGN activity, but are maintained over multiple generations."," This shows that the metallicity outflows are not simply tracing the current generation of AGN activity, but are maintained over multiple generations."
 The iron radius may provide a reliable indicator of average jet power in a cluster where cavity power measurements are ambiguous., The iron radius may provide a reliable indicator of average jet power in a cluster where cavity power measurements are ambiguous.
 There are uncorrected systematic uncertainties in Figure 3., There are uncorrected systematic uncertainties in Figure 3.
" We have made no attempt to measure the additional power associated with shock fronts and faint ghost cavity systems, which would be difficult to do for the entire sample."," We have made no attempt to measure the additional power associated with shock fronts and faint ghost cavity systems, which would be difficult to do for the entire sample."
" The total jet power for objects such as MS0735 and Hydra A, which have detected shock fronts at high significance, are under reported here by roughly a factor of two (see McNamara Nulsen 2007 for a discussion)."," The total jet power for objects such as MS0735 and Hydra A, which have detected shock fronts at high significance, are under reported here by roughly a factor of two (see McNamara Nulsen 2007 for a discussion)."
 Including energy from the shocks effects the slope of the fit by ~20%., Including energy from the shocks effects the slope of the fit by $\sim 20\%$.
 We chose not to boost the power of these systems to avoid biasing them with respect to other systems., We chose not to boost the power of these systems to avoid biasing them with respect to other systems.
" Thus, only cavity power is given here for consistency."," Thus, only cavity power is given here for consistency."
" In addition, the iron radii given here are projected values."," In addition, the iron radii given here are projected values."
 Their true values may be underestimated in extreme cases by roughly a factor, Their true values may be underestimated in extreme cases by roughly a factor
desfdr is large and therefore. dOdr small in the central region (bv reason of solid body rotation).,$dv_\varphi/dr$ is large and therefore $d\Omega/dr$ small in the central region (by reason of solid body rotation).
 However. the high VD values at the centre make it dillicult to cistinguish between physical. erowth and. numerical errors.," However, the high $\nabla \cdot\textbf{B}$ values at the centre make it difficult to distinguish between physical growth and numerical errors."
 Since the Euler potentials are also unreliable in this region (see section 3.1.6)). it is not easy to decide which formalism is the most capable in describing the physics in the centre of the galaxy correctly.," Since the Euler potentials are also unreliable in this region (see section \ref{EULER}) ), it is not easy to decide which formalism is the most capable in describing the physics in the centre of the galaxy correctly."
" ""This is also true for the simulations including smoothing.", This is also true for the simulations including smoothing.
 Increasing the frequeney of smoothing tends to decrease the amplitude of the magnetic field. between 3 and 10 kpe. but has relatively little οσοι for larger raclii.," Increasing the frequency of smoothing tends to decrease the amplitude of the magnetic field between 3 and 10 kpc, but has relatively little effect for larger radii."
 Interestingly. the large increase of B in the centre is never smoothed away. which could indicate. that this behaviour is actually partly. physical.," Interestingly, the large increase of $\textbf{B}$ in the centre is never smoothed away, which could indicate, that this behaviour is actually partly physical."
 For the simulation which applies smoothing every 302 timesteps (red). the amplification of the field at rz3 kpe is similar to the simulations with Euler potentials.," For the simulation which applies smoothing every 30 timesteps (red), the amplification of the field at $r>3$ kpc is similar to the simulations with Euler potentials."
 Applying smoothing everv 5 timesteps (green). the amplification is considerably weaker than in the Euler potentials simulations. indicating that by such strong smoothing essential physics is lost. in agreement with earlier lindings by 7..," Applying smoothing every 5 timesteps (green), the amplification is considerably weaker than in the Euler potentials simulations, indicating that by such strong smoothing essential physics is lost, in agreement with earlier findings by \cite{GadgetMHD}."
 In the Following. we only consider the disc region (from 5 to 15 kpc). since the high. numerical divergence in the centre makes it dillicult to lower it to the value of the divergence seen in simulations with Euler potentials (i.e. h-|V-BJ/|B|e 1). without smoothing the magnetic field structure too much.," In the following, we only consider the disc region (from 5 to 15 kpc), since the high numerical divergence in the centre makes it difficult to lower it to the value of the divergence seen in simulations with Euler potentials (i.e. $h\cdot|\nabla\cdot\mathbf{B}|/|\mathbf{B}|\approx 1$ ), without smoothing the magnetic field structure too much."
 Fie., Fig.
 14. shows the evolution of the total magnetic field Ga=be|BF D2) within the disc with time for the dilferent. implementations., \ref{Bwithtime} shows the evolution of the total magnetic field $B_\mathrm{tot}=\sqrt{B_x^2+B_y^2+B_z^2}$ ) within the disc with time for the different implementations.
 The colour coding is the same as in Fig. 13.., The colour coding is the same as in Fig. \ref{Bwithr}.
 Xs before. for the simulation which applies smoothing every 30 timesteps (red). the amplification of the field is similar to the simulation with I2uler potentials.," As before, for the simulation which applies smoothing every 30 timesteps (red), the amplification of the field is similar to the simulation with Euler potentials."
 Llowever. the performance of these simulation is not. very convincing due to the “jumps” in the evolution caused. by the artificial periodic smoothing.," However, the performance of these simulation is not very convincing due to the “jumps” in the evolution caused by the artificial periodic smoothing."
 Applying smoothing every 5 timesteps (green). the amplification is as discussed. before lower than in the Euler potentials simulations.," Applying smoothing every 5 timesteps (green), the amplification is as discussed before lower than in the Euler potentials simulations."
Therefore. we developed other models with higher SFEs aud ciffercut SF duration.,"Therefore, we developed other models with higher SFEs and different SF duration."
 Since both dlrs aud BCDs harbor recent SF activities. we assumed that the SF is still going on at the present dav. aud therefore a short duration εἰ implies a late starting time (fe;d) of SF.," Since both dIrrs and BCDs harbor recent SF activities, we assumed that the SF is still going on at the present day, and therefore a short duration $d$ implies a late starting time $t_G-d$ ) of SF."
 We have examined the models with different SFIS by Vvarviis the SEE. duration. aud iufa Μπ," We have examined the models with different SFHs by varying the SFE, duration, and infall timescale."
 T restuts slow fvat only models with dierent SEEs are able o explain tre scatters in the abuudauce ratios., The results show that only models with different SFEs are able to explain the scatters in the abundance ratios.
 Fig. 19..," In Fig. \ref{Fig:contiSFZmu},"
 models with differcut SEEs for t1 Cases of no wind (let coluun). Loynal wind (middle column). axd lucta-ClLiced wind (epp.=0.9. viel: column) are shoWL.," models with different SFEs for the cases of no wind (left column), normal wind (middle column), and metal-enhanced wind $w_{\rm H,He}=0.3$, right column) are shown."
 Iu these models. to avoid reac.une a too high luctalici vat t10 wreseut time. a duration shorter than the aeaep Q the universe is assumed for the higrest SEE case.," In these models, to avoid reaching a too high metallicity at the present time, a duration shorter than the age of the universe is assumed for the highest SFE case."
 A short iufall timescale is adopted (7=1 Gyr) here. because it does not effect the evolutionary track. too much in the coutious SF scenario. especially when the SF starts late.," A short infall timescale is adopted $\tau=1$ Gyr) here, because it does not effect the evolutionary track too much in the continuous SF scenario, especially when the SF starts late."
 There are several conclusions that can be drawn frou Fig. 19:, There are several conclusions that can be drawn from Fig. \ref{Fig:contiSFZmu}:
 We have discussed in detail the chemical evolution of late-type cawarf galaxies (dwirf ireeular aud blue compact ealaxies) aud used the most recent data as a comparison., We have discussed in detail the chemical evolution of late-type dwarf galaxies (dwarf irregular and blue compact galaxies) and used the most recent data as a comparison.
" We have taken iuto account the measured abundances of sinele elements (eC. N. Ο S. Siaud Fe) as well as the gas μαses,"," We have taken into account the measured abundances of single elements (He,C, N, O, S, Si and Fe) as well as the gas masses."
" We have asstmed that the late-twpe dsvarf galaxies Oru by cold gas accretion aud sve run modes for different accvoted barvonie masses (10.109. aud QIUAF. 3,"," We have assumed that the late-type dwarf galaxies form by cold gas accretion and we run models for different accreted baryonic masses $10^{8}, 10^{9}$ and $10^{10}
M_{\odot}$ )."
 We have οςed both bursting and continuous 5ar femation., We have tested both bursting and continuous star formation.
 We heu have studied im detail the developeit of galactic winds by assunius a dark matcr halo which is asstmec. 10 nues the amount of of the barvonic nass ancl feedback YOu SNe and stellar winds., We then have studied in detail the development of galactic winds by assuming a dark matter halo which is assumed 10 times the amount of of the baryonic mass and feedback from SNe and stellar winds.
 Our main couchisions are:, Our main conclusions are:
Clusters of galaxies form in correspondence of the peaks of the primordial matter density field as a result of the gravitational collapse of both dark matter and baryons.,Clusters of galaxies form in correspondence of the peaks of the primordial matter density field as a result of the gravitational collapse of both dark matter and baryons.
 In the framework of the standard ccosmological model and the hierarchical clustering of the large scale structure formation they constitute both the most recent and the largest virialised objects of the Universe., In the framework of the standard cosmological model and the hierarchical clustering of the large scale structure formation they constitute both the most recent and the largest virialised objects of the Universe.
 Nowadays. it is clear that gravitation is not the only process that influences the physics of the intracluster medium (ICM. hereafter).," Nowadays, it is clear that gravitation is not the only process that influences the physics of the intracluster medium (ICM, hereafter)."
 The electrons of the ionized. plasma emit via free-free interaction with the protons. making clusters bright X-ray sources and allowing the gas to cool efficiently. particularly in the central regions.," The electrons of the ionized plasma emit via free-free interaction with the protons, making clusters bright X-ray sources and allowing the gas to cool efficiently, particularly in the central regions."
 During the last decade. the observations of the aand XX-ray satellites highlighted (πε presence of several interaction mechanisms between the galactic component and the ICM. showing that the evolution of the two is intimately tied.," During the last decade, the observations of the and X-ray satellites highlighted the presence of several interaction mechanisms between the galactic component and the ICM, showing that the evolution of the two is intimately tied."
 For instance. the aceretion of cold gas onto the brightest cluster galaxies (BCGs) at the cluster center is strongly suspected to fuel the super-massive blackholes they host.," For instance, the accretion of cold gas onto the brightest cluster galaxies (BCGs) at the cluster center is strongly suspected to fuel the super-massive blackholes they host."
 This process is able to trigger star-formation within the BCGs (O'Deaetal.2008:Pipino2009) and power episodic violent outbursts of their central active galactic nuclei (AGNs). whose energy injection into the ICM prevents the overcooling of the gas (Fabianetal.2006:McNamara&Nulsen 2007).," This process is able to trigger star-formation within the BCGs \citep{odea08,pipino09} and power episodic violent outbursts of their central active galactic nuclei (AGNs), whose energy injection into the ICM prevents the overcooling of the gas \citep{fabian06,mcnamara07}."
. AGNs feedback and other non-gravitational processes. such as supernovae (SNe) powered galactic winds (Kapfereretal.2006:Syacki&Springelaferio 2008).. preheating of the ICM (seee.g.Fang&Haiman 2008).. together with gravitational ones (re. galaxy-galaxy interactions. ram-pressure stripping. galaxy mergers) induce energy and matter exchanges between the galactic medium and the ICM.," AGNs feedback and other non-gravitational processes, such as supernovae (SNe) powered galactic winds \citep{kapferer06,sijacki06,schindler08}, , preheating of the ICM \citep[see e.g.][]{fang08}, together with gravitational ones (i.e. galaxy-galaxy interactions, ram-pressure stripping, galaxy mergers) induce energy and matter exchanges between the galactic medium and the ICM."
 To date these complex physical processes and their impact on the statistical cluster properties. thus on our understanding of structure formation (Voit2005) and use of the cluster population in cosmological studies (Mantzetal.2008;Vikhlininetal.2009;Mantz 2009).. are under serutinous observational and theoretical investigations (see.e.g..Arnaud2005:Borgani20082.andreferences therein)..," To date these complex physical processes and their impact on the statistical cluster properties, thus on our understanding of structure formation \citep{voit05} and use of the cluster population in cosmological studies \citep{mantz08,vikhlinin09,mantz09}, are under scrutinous observational and theoretical investigations \citep[see, e.g.,][and references
therein]{arnaud05,borgani08a}."
 The presence of heavy elements in the ICM is the most direct evidence and consequence of the ejection of galactic material., The presence of heavy elements in the ICM is the most direct evidence and consequence of the ejection of galactic material.
 Within clusters their abundance has been widely measured making use of X-ray observations (seethereviewsbySarazin1988:Arnaud2005:Werneretal.2008) with a typical abundance of 0.3 Z..," Within clusters their abundance has been widely measured making use of X-ray observations \citep[see the reviews
 by][]{sarazin88, arnaud05,werner08} with a typical abundance of 0.3 $ Z_\odot$."
 Stars and SNe constitute the most efficient way to produce and disperse metals., Stars and SNe constitute the most efficient way to produce and disperse metals.
 Heavy elements in the ICM originate from different processes:early enrichment (Aguirre&Schaye2007).. continuous injection from galaxy members and in situ production by intra-cluster stars (sourcesetal. 2009).," Heavy elements in the ICM originate from different processes:early enrichment \citep{aguirre07}, continuous injection from galaxy members and in situ production by intra-cluster stars \citep[sources of the
intra-cluster light, see][]{arnaboldi04,krick07,murante07,conroy07,dolag09}."
. The aforementioned processes do not discriminate between the natures of the ejected galactic material. therefore these enrichments are unambiguously linked also to the ejection of neutral gas and dust in the ICM.," The aforementioned processes do not discriminate between the natures of the ejected galactic material, therefore these enrichments are unambiguously linked also to the ejection of neutral gas and dust in the ICM."
 Observations indicate that in galactic environments dust is a minor component. with dust-to-gas ratio Maya/Meas70.01 (Mathisetal.1977) and it could be as low as Maya10-*10-7 in the ICM (Popescuetal.2000:Aguirre 2001).," Observations indicate that in galactic environments dust is a minor component, with dust-to-gas ratio $M_{\rm dust}/M_{\rm gas} \approx 0.01$ \citep{mathis77} and it could be as low as $M_{\rm dust}/M_{\rm gas} = 10^{-5}-10^{-4}$ in the ICM \citep{popescu00,aguirre01}."
. Nonetheless. dust particles have lifetimes long enough to be heated by collisions with the hot electrons and re-emit at the infrared (IR) wavelengths.," Nonetheless, dust particles have lifetimes long enough to be heated by collisions with the hot electrons and re-emit at the infrared (IR) wavelengths."
 In this way they can constitute an additional cooling agent of the gas (Montier&Girard2004) which might play an important role in ICM physics. as seen with the implementation of dust cooling in hydrodynamical simulations (daSilvaetal.2009).," In this way they can constitute an additional cooling agent of the gas \citep{montier04} which might play an important role in ICM physics, as seen with the implementation of dust cooling in hydrodynamical simulations \citep{dasilva09}."
. However obtaining observational constraints on the possible IR. signal coming from intracluster dust is a very challenging issue. since the average sky fluctuations caused by background galaxies and galactie cirrus clouds are comparable or even higher than the overall flux coming from a single cluster. which is anyway expected to be dominated by the dust emission from star-forming galaxies.," However obtaining observational constraints on the possible IR signal coming from intracluster dust is a very challenging issue, since the average sky fluctuations caused by background galaxies and galactic cirrus clouds are comparable or even higher than the overall flux coming from a single cluster, which is anyway expected to be dominated by the dust emission from star-forming galaxies."
 In fact. nowadays the only claimed (and still controversial) detection of this IR emission comes from the studieson the Coma cluster of Stickel 2002).. who measured a diffuse dust mass of," In fact, nowadays the only claimed (and still controversial) detection of this IR emission comes from the studieson the Coma cluster of \cite{stickel98,stickel02}, , who measured a diffuse dust mass of"
for the particular case of a neutron star. modeled as a Maclaurin spheroid.,for the particular case of a neutron star 	modeled as a Maclaurin spheroid.
 Cutleretal.(2003) calculated the “rigidity parameter™ b for a realistic NS structure. with a solid crust afloat on a liquid core.," \citet{cut03} calculated the “rigidity parameter” $b$ for a realistic NS structure, with a solid crust afloat on a liquid 	core."
 They solved the strain field that develops as the NS spins down and found that 6~1077. two orders of magnitude below theresult found by Baym&Pines(1971) for a simplified model.," They solved the strain field that develops as the NS spins down and found that $b\sim 10^{-7}$, two orders of magnitude 	below theresult found by \citet{baym71} for a simplified model."
 On the other hand. Horowitz&Kadau(2009) recently found through N-body simulations that the Coulomb lattice of the NS crust can support a maximum strain angle 6.~107. three orders of magnitude higher than the value estimated by Smoluchowski&Welch(1970).," On the other hand, \citet{hor09} recently found through N-body simulations that the 	Coulomb lattice of the NS crust can support a maximum strain angle $\theta_{c}\sim 10^{-1}$, three orders of magnitude 	higher than the value estimated by \citet{smo70}."
". Thus. for an NS of ~ΤΕΜ... the time-averaged crust-cracking luminosity is ἐς~10°°P_aa/P.engs!, where P.3o is the period derivative measured in units of 10— and Pa, is the period in units of 5 milliseconds."," Thus, for an NS of $\sim 1.4 M_{\odot}$, the time-averaged crust-cracking luminosity is $L_{cc}\sim 10^{26} \dot P_{-20}/P^3_{5\rm{ms}}~\mathrm{erg~s}^{-1}$ where $\dot P_{-20}$ is the period derivative measured 	in units of $10^{-20}$ and $P_{5\mathrm{ms}}$ is the period in units of 5 milliseconds."
 For a representative classical pulsar (PSR P~250 ms and P.«1076s«7l. so LLO?ergs7!. while for the MSP J0437-4715. P=5.76 ms and P=5.73x107?ss! so Lu.~4x107ergs7!.," For a representative classical pulsar 	(PSR $P\sim 250$ ms and $\dot P\sim 10^{-16}~\mathrm{s~s}^{-1}$, so $L_{cc}\sim 10^{25}~\mathrm{erg~s}^{-1}$, while for the MSP J0437-4715, $P= 5.76$ ms and $\dot P=5.73\times 10^{-20}~\mathrm{s~s}^{-1}$, so $L_{cc}\sim 4 \times 10^{25}~\mathrm{erg~s}^{-1}$."
 Comparing these results with the thermal emission from a pulsar with Τι~I1 Κ. L~I0?ergs! (ie. potentially detectable thermal emission from an NS in the solar neighborhood by the Hubble Space Telescope). we conclude that the crust-cracking mechanism does not produce detectable heating.," Comparing these results 	with the thermal emission from a pulsar with $T_s\sim10^5$ K, $L\sim 10^{29}~\mathrm{erg~s}^{-1}$ (i.e., potentially 	detectable thermal emission from an NS in the solar neighborhood by the Hubble Space Telescope), we conclude that the crust-cracking mechanism does not produce detectable heating."
" Additionally. the high critical strain angle obtained by Horowitz&Kadau(2009) requires the star to have an. initial deformation e,>&,~107! in order to cause any cracking of the crust."," 	Additionally, the high critical strain angle obtained by \citet{hor09} requires the star to have an 	initial deformation $\epsilon_0> \theta_c\sim 10^{-1} $ in order to cause any cracking of the crust."
" However. for plausible initial rotation periods of classical pulsars (Po>15 ms). their initial deformation is only &-ΡΕ10<1074, where Pj~0.5 ms is the Kepleriat period of the star."," However, for plausible initial rotation 	periods of classical pulsars $P_0>15$ ms), their initial deformation is only $\epsilon_0 \sim P_K^2/P_0^2 <10^{-3}$, where $P_K\sim 0.5$ ms is the Keplerian period of the star."
 Hence. the crust-cracking mechanism ts never activated in classical pulsars and probably operates only in MSPs with Po<2 ms.," Hence, the crust-cracking mechanism is never activated in classical pulsars 	and probably operates only in MSPs with $P_0<2$ ms."
 If the latter were the case. and now considering that all stresses in the crust are suddenly released. the internal thermal energy of the star is increasec by ~Ber104 erg. corresponding to an internal temperature of 107 K and a surface temperature of ~5xIO? K (Potekhiretal. 1997). which is dissipated within less than 10? vr.," If the latter were the case, and now considering that all stresses in the 	crust are suddenly released, the internal thermal energy of the star is increased by $\sim B\theta_c^2\sim 10^{44}$ erg, 	corresponding to an internal temperature of $10^7$ K and a surface temperature of $\sim 5\times 10^5$ K \citep{pot97}, which 	is dissipated within less than $10^7$ yr."
 Hence. in MSPs of 1077? yr. the increase in temperature due to catastrophic cracking is given by a narrow peak in the thermal evolution. which is unlikely to be detected because of the short timescale involved.," Hence, in MSPs of $10^{8-9}$ yr, the increase in temperature due to catastrophic 	cracking is given by a narrow peak in the thermal evolution, which is unlikely to be detected because of the short timescale 	involved."
 The relatively low temperatures in the interior. of NSs induce the formation of neutron Cooper pairs., 	The relatively low temperatures in the interior of NSs induce the formation of neutron Cooper pairs.
 These form a condensate with a macroscopic wave function., These form a condensate 	with a macroscopic wave function.
 A consequence of this is that the vorticity in the superfluid must. be concentrated in discrete vortex Imes. whose microscopic distribution allows the superfluid to approximate a macroscopic rigid rotation.," A consequence of this is that the vorticity in the superfluid must be concentrated in discrete 	vortex lines, whose microscopic distribution allows the superfluid to approximate a macroscopic rigid rotation."
 As the star spins down. the vortex lines must move outward.," 	As the star spins down, the vortex lines must move outward."
 As they move through the inner crust. they are pinned to the nuclear lattice until a critical velocity difference between the superfluid and the crust is reached.," As they move through the inner crust, they are pinned to the 	nuclear lattice until a critical velocity difference between the superfluid and the crust is reached."
 In this process. the and unpinning of the vortex lines with respect to the nuclei of the erystal lattice release energy that heats the star.," In this process, the and unpinning of the vortex lines with respect to the nuclei of the crystal lattice release energy that heats the star."
" energy-dissipation rate is given by (Alparetal.1984) where J/=ol, with J, the moment of inertia of the pinning layer and ©,=(Ως—Qo), an average over the pinning zone of the critical lag between the angular velocity O,. of the crust and the superfluid rotation rate Q,. Donati"," 	The energy-dissipation rate is given by \citep{alp84}
 	where $J\simeq \bar \omega I_p$, with $I_p$ the moment of inertia of the pinning layer and $\bar\omega_{cr}=(\Omega_s - \Omega_c)_{cr}$ an average over the pinning zone of the critical lag between the angular 	velocity $\Omega_c$ of the crust and the superfluid rotation rate $\Omega_s$."
&Pizzochero(2004) calculated the vortex-nucleus interaction in the inner crust of NSs with a semi-classical model., 	 	 \citet{don04} calculated the vortex-nucleus interaction in the inner crust 	of NSs with a semi-classical model.
 The density-dependent neutron pairing gaps used in the calculations are obtained from the Argonne —potential and Gogny effective interaction., The density-dependent neutron pairing gaps used in the calculations are obtained from the Argonne 	potential and Gogny effective interaction.
 Table | shows the pinning energy calculated with this model for five zones of the inner crust., Table \ref{tab:uno} shows the pinning energy calculated with this model 	for five zones of the inner crust.
 Similarly. Avogadroetal.(2008) calculated the nucleus interaction in the inner crust based on a Hartree-Fock-Bogoliubov quantum mean field theory.," Similarly, \citet{avo08} calculated the vortex-nucleus interaction in the inner crust based 	on a Hartree-Fock-Bogoliubov quantum mean field theory."
 Table 2. shows the pinning energy for this approach., Table \ref{tab:dos} shows the pinning energy for this approach.
 An important result of this. contrary to the prediction of the previous model. is that pinning of vortices on nuclei is. favored at low density in the inner crust.," An important result of this, contrary to the prediction of the previous model, is that pinning of vortices on nuclei is 	favored at low density in the inner crust."
 We used both results to calculate the excess angular momentum 4. which determines the luminosity for the vortex creep mechanism.," We used both results to calculate the excess angular momentum $J$, which determines the luminosity for the vortex creep mechanism."
 In addition. we used Eq. (," In addition, we used Eq. ("
58) of (1984) in the limit £pκΤ. where Exp is the pinning energy of a vortex on a nucleus. + is the radial coordinate. « is the quantum of circulation of each vortex. £ is the vortex coherence length. and Riys is the radius of the Wigner-Seitz cell.,"58) of \citet{alp84} in the limit $E_{NP} \gg kT$, where $E_{NP}$ is the pinning energy of a vortex on a nucleus, $r$ is the radial coordinate, $\kappa$ is the quantum of circulation of each vortex, $\xi$ is the vortex coherence length, and $R_{WS}$ is the radius of the Wigner-Seitz cell."
 In order to calculate this integral. we generate NS structure models for specific masses and linearly interpolate the values of Table | and 2. according to these models.," In order to calculate 	this integral, we generate NS structure models for specific masses and linearly interpolate the values of Table \ref{tab:uno} 	and \ref{tab:dos} according to these models."
" For simplicity. we do not take relativistic effects into account because the corrections involved are minor. re. (1— 0.8.with r, the Schwarzschild radius."," For simplicity, we do not take relativistic effects into account because the 	corrections involved are minor, i.e. $(1-r_g/R)^{1/2}\sim 0.8$ ,with $r_g$ the Schwarzschild radius."
" In this way. for an NS. of M~I.4M. and a typical range of equations of state we find that the excess of angular momentum is erg s, Thus. the vortex-creep luminosity L,.— |. where Q uis the angular velocity in units of 1077 s."," In this way, for an NS 	of $M\sim1.4M_\odot$ and a typical range of equations of state we find that the excess of angular momentum is $J\sim (10^{43}-10^{45})$ erg s. Thus, the vortex-creep luminosity $L_{vc}\simeq (10^{29}-10^{31})|\dot\Omega_{-14}|~\mathrm{erg~s}^{-1}$ , where $\dot\Omega_{-14}$ is the angular velocity 	derivative in units of $10^{-14}~\mathrm{s}^{-2}$ ."
 This is similar to the luminosity inferred from the observation of the MSP JO437-4715., This is similar to the luminosity inferred from the observation of the 	MSP J0437-4715.
the stellar masses derived. from their relation are robust against the effect. of dust. provided. the clust vectors. are parallel to the relation.,the stellar masses derived from their relation are robust against the effect of dust provided the dust vectors are parallel to the relation.
 Ehe reason is that the uneler-estimate of stellar mass arising from the attenuation in luminosity will be compensated. by the overproduction of stellar mass arising from the reddening in colour. therefore vielding comparable final stellar masses.," The reason is that the under-estimate of stellar mass arising from the attenuation in luminosity will be compensated by the overproduction of stellar mass arising from the reddening in colour, therefore yielding comparable final stellar masses."
 This balance might apply for [ace-on svstems. but could. not be the case for hiehly inclined svstems as the latter show a systematically higher ratio of attenuation to reddening.," This balance might apply for face-on systems, but could not be the case for highly inclined systems as the latter show a systematically higher ratio of attenuation to reddening."
 The overall consequence is that stellar masses could be under-estimated for a randomly oriented distribution bv the use of the Bell&deJong(2001) colour vs. mass-to-light ratio if cust is not taken into account.," The overall consequence is that stellar masses could be under-estimated for a randomly oriented distribution by the use of the \citet{bj01}
 colour vs. mass-to-light ratio if dust is not taken into account."
 Driveretal...(2007). have explored this in detail. ancl concluded: that while the masses are mocified somewhat the final stellar mass breakdown is not clrramatically altered.," \citet{driver07} have explored this in detail, and concluded that while the masses are modified somewhat the final stellar mass breakdown is not dramatically altered."
 The last three cobumns of Table 1. give the integrated stellar masses. the Iuminositv-weilghted. ages. and the luminosityv-weightecd metallicities for our sample of Abell 1367 &alaxies.," The last three columns of Table \ref{gal_prop_cal1} give the integrated stellar masses, the luminosity-weighted ages, and the luminosity-weighted metallicities for our sample of Abell 1367 galaxies."
 ligure 5. shows the relationship between the Iuminosity-weighted age and the integrated stellar mass for. our sample of Abell 1367 members., Figure \ref{mst_age} shows the relationship between the luminosity-weighted age and the integrated stellar mass for our sample of Abell 1367 members.
 Galaxies are. separated, Galaxies are separated
As mentioned above. once the merging history of the clark matter component has been calculated. it is possible to follow the evolution of the baryonic content in these halos forward in time.,"As mentioned above, once the merging history of the dark matter component has been calculated, it is possible to follow the evolution of the baryonic content in these halos forward in time."
 We assume each halo consists of three components: hot gas. cold gas and stars. where the latter two components can be distributed: among individual galaxies inside a single dark matter halo.," We assume each halo consists of three components: hot gas, cold gas and stars, where the latter two components can be distributed among individual galaxies inside a single dark matter halo."
 The stellar components of each galaxy are additional divided into bulge and disc. to allow morphological classifications of model galaxies.," The stellar components of each galaxy are additional divided into bulge and disc, to allow morphological classifications of model galaxies."
 In the Following. we describe how the evolution of each component is calculated.," In the following, we describe how the evolution of each component is calculated."
" Each branch of the merger tree starts at a progenitor mass of M,,;, and ends at a redshift of z:=0.", Each branch of the merger tree starts at a progenitor mass of $M_{min}$ and ends at a redshift of $z=0$.
 Initially. each halo is occupied by hot primordial gas which was captured in the potential well of the halo and shock heated to its virial temperature 75;=35.9[V(kms Ix. where V; is the circular velocity of the halo (White&jrErenk1991. IX99).," Initially, each halo is occupied by hot primordial gas which was captured in the potential well of the halo and shock heated to its virial temperature $T_{vir}=35.9\left[V_c/(\mbox{km s}^{-1}) \right]^2$ K, where $V_c$ is the circular velocity of the halo \citep[K99]{wf91}."
. SubsequentIy this hot gas component is allowed to raciatively cool and. settles down into a rotationally supported. eas disc at the centre of the halo. which we identily as the central galaxy (e.gSilk1977:White&Rees1978:White&Frenk 1991).," Subsequently this hot gas component is allowed to radiatively cool and settles down into a rotationally supported gas disc at the centre of the halo, which we identify as the central galaxy \citep[e.g][]{s77,wr78,wf91}."
. Phe rate at which hot gas cools down is estimated by calculating the cooling raclius inside he halo using the cooling functions provided by Sutherland&Dopita(1993). and the prescription in SOL., The rate at which hot gas cools down is estimated by calculating the cooling radius inside the halo using the cooling functions provided by \citet{sd93} and the prescription in S01.
 In the case ofa merger between halos we assume that all of the hot gas oesent in the progenitors ects shock heated to the virial emperature of the remnant halo. and that gas can only cool down onto the new central galaxy which is the central galaxy of the most massive progenitor halo.," In the case of a merger between halos we assume that all of the hot gas present in the progenitors gets shock heated to the virial temperature of the remnant halo, and that gas can only cool down onto the new central galaxy which is the central galaxy of the most massive progenitor halo."
 The central galaxy of he less massive halo will become a satellite galaxy orbiting inside the remnant halo., The central galaxy of the less massive halo will become a satellite galaxy orbiting inside the remnant halo.
 In this way. a halo can host multiple satellite galaxies. depending on the merging history of the 1alo. but will always only host one central galaxy onto which eas can cool.," In this way, a halo can host multiple satellite galaxies, depending on the merging history of the halo, but will always only host one central galaxy onto which gas can cool."
 Phe cold gas content in satellite galaxies is given by the amount present when they first became satellite ealaxies and does not increase. instead it. decreases due to ongoing star formation and supernova feedback.," The cold gas content in satellite galaxies is given by the amount present when they first became satellite galaxies and does not increase, instead it decreases due to ongoing star formation and supernova feedback."
 In the simplified picture adopted above. the amount of eas available to cool down is only limited by the universal barvon fraction Ομ=0.024 (Spergeletal.2003).," In the simplified picture adopted above, the amount of gas available to cool down is only limited by the universal baryon fraction $\Omega_b h^2=0.024$ \citep{sper03}."
 llowever. in the presence of a photoionising background the fraction of barvons captured. in halos is reduced. (e.g.2002) and we use the recipe of Somerville(2002)... which is based on a fitting formulae derived from hyclrodynamical simulations by Cnecdin(2000).. to estimate the amount of barvons in each halo.," However, in the presence of a photoionising background the fraction of baryons captured in halos is reduced \citep[e.g.][]{ns97,g00,ben02} and we use the recipe of \citet{som02}, which is based on a fitting formulae derived from hydrodynamical simulations by \citet{g00}, to estimate the amount of baryons in each halo."
 For the epoch of reionisation. we assunie ορίων= 20. which is in agreement with observations of the temperat correlation of the cosmic microwave background by ure-polarisation.Ixogutetal.(2003).," For the epoch of reionisation, we assume $z_{reion}=20$ , which is in agreement with observations of the temperature-polarisation correlation of the cosmic microwave background by \citet{ko03}."
" Once cooled gas has settled down in a disc. we allow for fragmentation and subsequent star formation according to a parameterised. elobal Schmidt-Ixennicutt. lav (Ixennicutt1998) ofthe form Al,=OMootνι Where a is a free parameter describing the cllicieney of the conversion of cold gas into stars. and ἐν is assumed to be the dynamical time of the galaxy and is approximated to be 0.1 times the dynamical time of the dark matter halo (Ix99)."," Once cooled gas has settled down in a disc, we allow for fragmentation and subsequent star formation according to a parameterised global Schmidt-Kennicutt law \citep{ken98} of the form $ \dot{M}_{*}=\alpha M_{cold}/t_{dyn,gal}$, where $\alpha$ is a free parameter describing the efficiency of the conversion of cold gas into stars, and $t_{dyn,gal}$ is assumed to be the dynamical time of the galaxy and is approximated to be 0.1 times the dynamical time of the dark matter halo (K99)."
 As in KOO we allow star formation only in halos of V.«350 km/s to avoid too bright central galaxies in clusters., As in K99 we allow star formation only in halos of $V_c < 350$ km/s to avoid too bright central galaxies in clusters.
 Feedback from supcrnovac plavs an important role in regulating star formation in small mass halos and in preventing too massive satellite galaxies from forming., Feedback from supernovae plays an important role in regulating star formation in small mass halos and in preventing too massive satellite galaxies from forming.
 We implement feedback based on the prescription presented in WOO with llere we introduce a second free parameter ce. which represents our lack of knowledge on the cllicicney with which the energy. [rom supernovae is going to reheat the cold. gas., We implement feedback based on the prescription presented in K99 with Here we introduce a second free parameter $\epsilon$ which represents our lack of knowledge on the efficiency with which the energy from supernovae is going to reheat the cold gas.
 The expected number of supernovae per solar mass of stars [ormed is given by psx=510%. taken as the value for the Scalo initial mass function (Scalo1986).. and We.=1013 erg is the energy output from cach supernova.," The expected number of supernovae per solar mass of stars formed is given by $\eta_{SN}=5 \times 10^{-3}$, taken as the value for the Scalo initial mass function \citep{sca86}, and $E_{SN}=10^{51}$ erg is the energy output from each supernova."
 We take Y; as the circular velocity of the halo in which the galaxy was last present as a central galaxy., We take $V_c$ as the circular velocity of the halo in which the galaxy was last present as a central galaxy.
 We allow for mergers between galaxies residing in a single halo., We allow for mergers between galaxies residing in a single halo.
 As mentioned earlier. cach halo is occupied. by. one central galaxy and a number of satellite galaxies depending on the past merging history of the halo.," As mentioned earlier, each halo is occupied by one central galaxy and a number of satellite galaxies depending on the past merging history of the halo."
 Whenever two halos merge. the galaxies inside them are going to merge on a tinie- which we calculate by estimating the time it would take the satellite to reach the centre of the halo under the cllects of dynamical friction.," Whenever two halos merge, the galaxies inside them are going to merge on a time-scale which we calculate by estimating the time it would take the satellite to reach the centre of the halo under the effects of dynamical friction."
 Satellites are assumed to merge only with central galaxies anc we set up their orbits in the halo according to the prescription of WOO. modified to use the Coulomb logarithm approximation of SOL.," Satellites are assumed to merge only with central galaxies and we set up their orbits in the halo according to the prescription of K99, modified to use the Coulomb logarithm approximation of S01."
 If the mass ratio between the two merging galaxies is MoatsfAlgats53.5 (Mauraz Algare) we declare the event as amajor merger and the remnant will be an elliptical galaxy and the stellar components ancl the gas will be treated according to the prescriptions below.," If the mass ratio between the two merging galaxies is $M_{gal,1}/M_{gal,2} 
\leq 3.5$ $M_{gal,1} \geq M_{gal,2}$ ) we declare the event as a merger and the remnant will be an elliptical galaxy and the stellar components and the gas will be treated according to the prescriptions below."
 In the case ofminor merger Muiωςc3.5 the cold gas in the disc of the smaller progenitor is assumed to settle down in the gas disc of the remnant ancl its stars contribute to the bulge component of the remnant (e.g. Ix09).," In the case of merger $M_{gal,1}/M_{gal,2} > 3.5$ the cold gas in the disc of the smaller progenitor is assumed to settle down in the gas disc of the remnant and its stars contribute to the bulge component of the remnant (e.g. K99)."
 ‘Toone&Toomre(1972) suggested that major mergers will lead to the formation of elliptical galaxies., \citet{tt72} suggested that major mergers will lead to the formation of elliptical galaxies.
 Indeed. detailed numerical simulations in the last decade seem to support this hypothesis (e.g.Barnes&Llernquist1992:Burkert:Naab2008.andreference therein).. and we will assume in the following that major mergers disrupt the discs in progenitor ealaxies. as seen in various numerical simulations. and relax to à spheroidal distribution.," Indeed detailed numerical simulations in the last decade seem to support this hypothesis \citep[e.g.][and reference therein]
{ba92,bn03}, and we will assume in the following that major mergers disrupt the discs in progenitor galaxies, as seen in various numerical simulations, and relax to a spheroidal distribution."
 Duringthe merger. any cold eas in the disces of the progenitor galaxies is assumed to be," Duringthe merger, any cold gas in the discs of the progenitor galaxies is assumed to be"
The Crab pulsar was the first pulsar detected as a consequence of its occasional bright. pulses (now known as Giant Radio Pulses) at radio wavelengths (Staelin Reifenstein 1968:: the first pulsar ever detected was PSR J19214+2153 Hewish et citehewish:1968)).,The Crab pulsar was the first pulsar detected as a consequence of its occasional bright pulses (now known as Giant Radio Pulses) at radio wavelengths (Staelin Reifenstein \cite{staelin:1968}; the first pulsar ever detected was PSR J1921+2153 Hewish et \\cite{hewish:1968}) ).
 Later on pulsations have been detected at optical wavelengths (Cocke et al.: 1969)), Later on pulsations have been detected at optical wavelengths (Cocke et al.; \cite{cocke:1969}) )
 and throughout the electromagnetic spectrum at X-rays and y-rays., and throughout the electromagnetic spectrum at X-rays and $\gamma$ -rays.
 One feature which is constant over the whole spectrum is the pulsed emission. but the details differ substantially.," One feature which is constant over the whole spectrum is the pulsed emission, but the details differ substantially."
 tthe strength of the interpulse. the presence of a pre-cursor to the main pulse (at low radio frequencies) change with wavelength.," the strength of the interpulse, the presence of a pre-cursor to the main pulse (at low radio frequencies) change with wavelength."
 However. the precise timing of the pulse over many orders of magnitude of energy imposes severe constraints on the emission regions (and mechanism).," However, the precise timing of the pulse over many orders of magnitude of energy imposes severe constraints on the emission regions (and mechanism)."
 For example Romani Yadigaroglu (1995)) have suggested that the pre-cursor originates at the polar cap. while the pulse and interpulse originate in the outer gap in the magnetosphere. with higher energy pulses being generated at significantly greater heights.," For example Romani Yadigaroglu \cite{romani:1995}) ) have suggested that the pre-cursor originates at the polar cap, while the pulse and interpulse originate in the outer gap in the magnetosphere, with higher energy pulses being generated at significantly greater heights."
 This should then be reflected in the timing of the pulses at different energies., This should then be reflected in the timing of the pulses at different energies.
 Small differences in pulse alignment allow to study the emission regions at relatively small scales (about 10 km per 0.001] phase in case of the Crab pulsar). and precise timing of pulsar light curves throughout the electromagnetic spectrum is thus a powerful tool to constrain theories of the spatial distribution of various emission regions: a time delay most naturally implies that the emission regions differ in position.," Small differences in pulse alignment allow to study the emission regions at relatively small scales (about 10 km per 0.001 phase in case of the Crab pulsar), and precise timing of pulsar light curves throughout the electromagnetic spectrum is thus a powerful tool to constrain theories of the spatial distribution of various emission regions: a time delay most naturally implies that the emission regions differ in position."
 In recent years. it has become clear that the main and secondary pulses of the Crab Pulsar (PSR J05344-2200) are not aligned in time at different wavelengths.," In recent years, it has become clear that the main and secondary pulses of the Crab Pulsar (PSR J0534+2200) are not aligned in time at different wavelengths."
 X-rays are leading the radio pulse by reported values of 344440 µς (Rots et citerots:2004:; RXTE data) and 280440 js (Kuiper et citekuiper:2003:: INTEGRAL data) and y-rays are leading the radio pulse by 241229 jis (Kuiper etcitekuiper:2003:; EGRET data., X-rays are leading the radio pulse by reported values of $\pm$ 40 $\mu$ s (Rots et \\cite{rots:2004}; RXTE data) and $\pm$ 40 $\mu$ s (Kuiper et \\cite{kuiper:2003}; INTEGRAL data) and $\gamma$ -rays are leading the radio pulse by $\pm$ 29 $\mu$ s (Kuiper et; EGRET data.
 The uncertainty in this value does not include the EGRET absolute timing uncertainty of better than 100 ys)., The uncertainty in this value does not include the EGRET absolute timing uncertainty of better than 100 $\mu$ s).
 At optical wavelengths. the observations presented a less coherent picture.," At optical wavelengths, the observations presented a less coherent picture."
 Sanwal (1999) has reported a time shift of 140 js (optical leading the radio)., Sanwal (1999) has reported a time shift of 140 $\mu$ s (optical leading the radio).
 The uncertaintt in this value is 20 4s in the determination of the optical peak and 75 ys in the radio ephemeris., The uncertainty in this value is 20 $\mu$ s in the determination of the optical peak and 75 $\mu$ s in the radio ephemeris.
 Shearer et ((2003)) have reported a lead of 100220 ys for simultaneous optical and radio observations of giant radio pulses., Shearer et \cite{shearer:2003}) ) have reported a lead of $\pm$ 20 $\mu$ s for simultaneous optical and radio observations of giant radio pulses.
 Golden et ((2000)) have reported that the optical pulse the radio pulse by ~80460 jus. Romani et ((2001)) conclude that the radi-) and optical peaks are coincident to better than 30 yes. but their error excludes the uncertainty of the radio ephemeris (150 1/8).," Golden et \cite{golden:2000}) ) have reported that the optical pulse the radio pulse by $\sim$ $\pm$ 60 $\mu$ s. Romani et \cite{romani:2001}) ) conclude that the radio and optical peaks are coincident to better than 30 $\mu$ s, but their error excludes the uncertainty of the radio ephemeris (150 $\mu$ s)."
 Oosterbroek et ((2006.. hereafter O06) have studied this issue in detail and found an optical lead of 2732100 ps. In this paper we will use simultaneous optical and radio observations at 2 GHz to further improve the accuracy of this value.," Oosterbroek et \cite{oosterbroek:2006}, hereafter O06) have studied this issue in detail and found an optical lead of $\pm$ 100 $\mu$ s. In this paper we will use simultaneous optical and radio observations at 2 GHz to further improve the accuracy of this value."
 We also study the possible changes in the peak emission coincident with Giant Radio Pulses (hereafter GP) as previously reported by Shearer et ((2003))., We also study the possible changes in the peak emission coincident with Giant Radio Pulses (hereafter GP) as previously reported by Shearer et \cite{shearer:2003}) ).
 Optical observations were obtained with S-Cam3 (Martin et citemartin:2006)) mounted on the ESA Optical Ground Station (OGS) telescope on Tenerife on September 16 and 17 2007., Optical observations were obtained with S-Cam3 (Martin et \\cite{martin:2006}) ) mounted on the ESA Optical Ground Station (OGS) telescope on Tenerife on September 16 and 17 2007.
 For test purposes the first two observations were obtained in the so-called FAST mode of the instrument., For test purposes the first two observations were obtained in the so-called FAST mode of the instrument.
 This mode only differs in the digital filter used to obtain the pulse shape of the photons., This mode only differs in the digital filter used to obtain the pulse shape of the photons.
 In S-Cam3 each photon gives rise to a bi-polar signal in the detector electronics chain., In S-Cam3 each photon gives rise to a bi-polar signal in the detector electronics chain.
 the zero-crossing of this signal is used to time tag the photon., the zero-crossing of this signal is used to time tag the photon.
 The instrumental delays in both modes were determined by triggering an LED using a GPS and registering the assigned time of the observed photons (see also O06)., The instrumental delays in both modes were determined by triggering an LED using a GPS and registering the assigned time of the observed photons (see also O06).
 The instrumental delay of S-Cam3 amounts, The instrumental delay of S-Cam3 amounts
17:48:53 and 21:08:57 UT. for a total on-source net exposure of 1ks.,"17:48:53 and 21:08:57 UT, for a total on-source net exposure of 1."
 ‘They were processed with. standard procedures v0.12.1). filtering and screening—- criteria hy using the package (v.6.1).," They were processed with standard procedures v0.12.1), filtering and screening criteria by using the package (v.6.6.1)."
 Moderate pile-up was opesent. so ποιος evens were extracted [rom an annular region (radii of 20 and 3 juxels. 1 pixel. ~rag 2736). while ickeground. events were extracted from an annular region (radii 120 and SO pixels) away from background: sources.," Moderate pile-up was present, so source events were extracted from an annular region (radii of 20 and 3 pixels; 1 pixel $\sim 2\farcs36$ ), while background events were extracted from an annular region (radii 120 and 80 pixels) away from background sources."
 An ΝΑΙ spectrum was extracted ancl ancillary response iles were eenerated wit1xrtmkarf. to account for cilferent extraction regions. vignetting and PSE corrections.," An XRT spectrum was extracted and ancillary response files were generated with, to account for different extraction regions, vignetting and PSF corrections."
 We used he spectral recistribution matrices vOLL in the Calibration Database maintained by HEASBARC., We used the spectral redistribution matrices v011 in the Calibration Database maintained by HEASARC.
 All spectra were rebinned with a minimum of 20 counts per cncrey bin., All spectra were rebinned with a minimum of 20 counts per energy bin.
 We retrieved the BAT claily licht. curves (1550 keV) available starting from ALJD=54754. from the BAT transient monitor (ανα οἱ al.," We retrieved the BAT daily light curves (15–50 keV) available starting from MJD=54754, from the /BAT transient monitor (Krimm et al."
 90060. 2008: itp:heasare.gslenasa.gov/docs/swift/results/transients/) ALC.," 2006, 2008; http://heasarc.gsfc.nasa.gov/docs/swift/results/transients/) page."
 The IBIS/ISGRI and BAT count rate of aare shown in Fig. Ll., The IBIS/ISGRI and BAT count rate of are shown in Fig. \ref{fig:lc}.
 Based on the LBIS data. the hard X-ray outburst started on October 10 at a Hux level of 10 mCrab (1840 keV) and lasted at least 14 days (last pointing at 4 mCrab).," Based on the IBIS data, the hard X-ray outburst started on October 10 at a flux level of 10 mCrab (18–40 keV) and lasted at least 14 days (last pointing at 4 mCrab)."
 This outburst is hence characterised by a fast increase of the Dux and a linear decay with a slope of | 0.134:0.01., This outburst is hence characterised by a fast increase of the flux and a linear decay with a slope of $-$ $\pm$ 0.01.
 An ppointing wit ino celeteetion was performed eight hours before the outburst started., An pointing with no detection was performed eight hours before the outburst started.
 We also averaged all our cata (from rev 724 to 731) collected: before the first source detection for a total of 500 ks. resulting in a 30 upper limit of mCrab (Fig. 1)).," We also averaged all our data (from rev 724 to 731) collected before the first source detection for a total of 500 ks, resulting in a $\sigma$ upper limit of 1 mCrab (Fig. \ref{fig:lc}) )."
 1n order o look for any possible 1spectral variability. we fitted the four averaged LBIS spectra with a simple power law.," In order to look for any possible spectral variability, we fitted the four averaged IBIS spectra with a simple power law."
 We obtained a constant value (within the errors) of the photon index (L 2) which indicates. in spite of the Hux variation. a steady spectral state.," We obtained a constant value (within the errors) of the photon index $\sim$ 2) which indicates, in spite of the flux variation, a steady spectral state."
 The lack of spectral parameter variation led us to average the IBIS spectra of cillerent revolutions., The lack of spectral parameter variation led us to average the IBIS spectra of different revolutions.
 The I8-100 keV averaged: spectrum is well ¢escribed. by a simple power law model with a slope as +E0.3., The 18-100 keV averaged spectrum is well described by a simple power law model with a slope as $2.2 \pm 0.3$.
 X mean LS100 keV: Hux o£ 1.5«10I⊏ can be derived., A mean 18–100 keV flux of $1.5\times 10^{-10}$ can be derived.
. The NIE spectrum can be fitted by an absorbed. power law model with a Ilvdrogen column density of Ny=LS(+0.6)1072 em.7., The XRT spectrum can be fitted by an absorbed power law model with a Hydrogen column density of ${\rm _H}=1.8 (\pm 0.6) \times 10^{22}$ $^{-2}$.
 The photon index is D=2.0d:0.5 and he resulting 210 keV absorbed and unabsorbed Ηχος are d and 95.2 2101. respectively.," The photon index is $\Gamma = 2.0 \pm 0.5$ and the resulting 2–10 keV absorbed and unabsorbed fluxes are $\sim$ 4.4 and $\sim$ 5.2 $\times 10^{-11}$, respectively."
" We note that the cderived Nu is higher than the absorption column of Uns1077"" cmE (Cornclisseetal.2002) [found by interpolating the LLL maps of Dickev Lockman (1990).", We note that the derived ${\rm _H}$ is higher than the absorption column of $0.83 \times 10^{22}$ $^{-2}$ \cite{corne02} found by interpolating the HI maps of Dickey Lockman (1990).
 In fact. the two values are perfectly consistent within the errors. given the large range of values (about 0.41.5.107 7) obtained in he box adopted to caleulate the Weighted. Average Ny (with the oll Column Density [rom the LIE maps.," In fact, the two values are perfectly consistent within the errors, given the large range of values (about $0.4-1.5 \times 10^{22}$ $^{-2}$ ) obtained in the box adopted to calculate the Weighted Average ${\rm _H}$ (with the nH Column Density from the HI maps."
 The joint LBIS and. NICE. spectrum (0.3.100. keV) was hen fitted with dillerent models., The joint IBIS and XRT spectrum (0.3–100 keV) was then fitted with different models.
 First we used an empirical model such as the power law (Fig. 2.. deff. ," First we used an empirical model such as the power law (Fig. \ref{fig:model}, ),"
then the more ohvsical. Comptonisation moclel., then the more physical Comptonisation model.
 Indeed. the 1200 keV spectrum of X-ray bursters in low/hard state is most likely oduced by the upscattering of soft seed. photons by a hot optically thin electron. plasma (ic. Barret et al.," Indeed, the 1–200 keV spectrum of X-ray bursters in low/hard state is most likely produced by the upscattering of soft seed photons by a hot optically thin electron plasma (i.e. Barret et al."
 2000 and references. therein)., 2000 and references therein).
 Aloreover. a black-bocky emission [rom he neutron star surface is also expected to be observed in he Lowhard. states of bursters (i.e. Natalucci et al.," Moreover, a black-body emission from the neutron star surface is also expected to be observed in the low/hard states of bursters (i.e. Natalucci et al."
 2000 ancl references therein)., 2000 and references therein).
 We tried to add a component to he two models., We tried to add a component to the two models.
 Phe best fit parameters and mean Iuxes are reported in Tab. 2.., The best fit parameters and mean fluxes are reported in Tab. \ref{tab:fit_sim}.
 Thus. using a physical thermal Coniptonisation model. (Litarchuk1994). in NSPEC. the electron temperature is not constrained. while a lower limit of ~24 keV (at 90%) can be inferred. (see Tab.," Thus, using a physical thermal Comptonisation model, \cite{tita94} in XSPEC, the electron temperature is not constrained, while a lower limit of $\sim$ 24 keV (at $90\%$ ) can be inferred (see Tab."
 2 and contour levels in Fig. 3))., \ref{tab:fit_sim} and contour levels in Fig. \ref{fig:cont}) ).
 This is consistent with the electrons temperature observed in burster systems. even brighter than 00..," This is consistent with the electrons temperature observed in burster systems, even brighter than \\cite{barret00}. ."
size of the svuthesized beam.,size of the synthesized beam.
 This procedure doesut work. or very meliued galaxies. so. as discussed in Sect.," This procedure doesn't work for very inclined galaxies, so, as discussed in Sect."
 2. for IKIX98 250 we assume a constaut velocity dispersiou of Sl, \ref{sec:obs} for KK98 250 we assume a constant velocity dispersion of 8.
uus L.For KK98 251 we find that. after putting in hese corrections. the estimated velocity dispersion is also sxSkinsο.," For KK98 251 we find that, after putting in these corrections, the estimated velocity dispersion is also $\approx 8$."
 Further. in the absence of auy mcasurement or ly. we asstuned d(üluthii))/dr=0 (i.e. hat the scale icieht does not change with radius).," Further, in the absence of any measurement for $\rm{h_z}$ , we assumed $\rm{d}(\ln(\rm{h_z}))/\rm{dr}=0$ (i.e. that the scale height does not change with radius)."
 Substituting these values back iu the Equ. (3)), Substituting these values back in the Eqn. \ref{eqn:ad}) )
" aud usine the fitted Caussiui xofile to the radial surface ceusity distribution. the ""asvnunetie drift” correction was calculated aud applied o the observes rotation velocities."," and using the fitted Gaussian profile to the radial surface density distribution, the “asymmetric drift"" correction was calculated and applied to the observed rotation velocities."
 For KI98 250 this correction is found to be small (less than 2.5 1)). compared to the errorbars on the rotation curve.," For KK98 250 this correction is found to be small (less than 2.5 ), compared to the errorbars on the rotation curve."
 Ou the other hand. the correction for IKI&98 251 is significant in the outer regions.," On the other hand, the correction for KK98 251 is significant in the outer regions."
 The “asvinmetric drift” corrected curve for Ίος 251 is shown in Fig. 6|[," The “asymmetric drift"" corrected curve for KK98 251 is shown in Fig. \ref{fig:vrot2}[ ["
D].,B].
" lu this section. we use the ""asvnuuetrne dift"" corrected rotation curves. derived in the last section. to derive nias models for IKIx98 250 and WIK9S 251."," In this section, we use the “asymmetric drift"" corrected rotation curves, derived in the last section, to derive mass models for KK98 250 and KK98 251."
 The coutributioun of the stellar mass to the observed rotation curves were computed by assuniue the galaxies to have exponential stellar disks. with a coustaut mass to light ratio (Y) iux au intrinsic thickuess ratio (qu) of 0.2.," The contribution of the stellar mass to the observed rotation curves were computed by assuming the galaxies to have exponential stellar disks, with a constant mass to light ratio $\Upsilon$ ) and an intrinsic thickness ratio $_0$ ) of 0.2."
 We further assiuned that the deusity distribution in the vertical (i) direction falls off like sechl?(:zy). with zy independent of ealacto-ceutric radius (see e.g. van der Iruit Searle 1981. de Gaijs Poletier 1997).," We further assumed that the density distribution in the vertical $z$ ) direction falls off like $^2(z/z_0)$, with $z_0$ independent of galacto-centric radius (see e.g. van der Kruit Searle 1981, de Grijs Peletier 1997)."
 The contribution of the gaseous disks to the observed rotation curves were calculated using the observed IIT surface mass density xofiles. with the III surface deusitv beige scaled by a factor of Ll to account for the contribution from helium.," The contribution of the gaseous disks to the observed rotation curves were calculated using the observed HI surface mass density profiles, with the HI surface density being scaled by a factor of 1.4 to account for the contribution from helium."
 There is little evidence that dwarf galaxies coutain substantial amounts of molecular eas (6.8. Isvacletal.1995.. Tavlorctal. 1998)). hence. no correction was niacde for molecular eas.," There is little evidence that dwarf galaxies contain substantial amounts of molecular gas (e.g. \cite{israel95}, \cite{taylor98}) ), hence, no correction was made for molecular gas."
" We also ucelecxd the contribution of ionize eas, if any."," We also neglected the contribution of ionized gas, if any."
 Since there is some evidence for similar vertical distributions of the III aud stellar disks (c.g. Bottema ct al., Since there is some evidence for similar vertical distributions of the HI and stellar disks (e.g. Bottema et al.
 1986). we assumed the IIT disks also to have a secl?(z/:z9) vertical profile. with an intrinsic thickness ratio of qy= 0.2.," 1986), we assumed the HI disks also to have a $^2(z/z_0)$ vertical profile, with an intrinsic thickness ratio of $q_0=0.2$ ."
 The circular velocities of the disk coluponents were computed using the formmlac given by Casertano(1983)., The circular velocities of the disk components were computed using the formulae given by \cite{casertano83}.
". For the dark matter halo. we considered two types of density profi""s viz."," For the dark matter halo, we considered two types of density profiles, viz."
 the moclified isothermal profile aud the NEW (Navarro et al., the modified isothermal profile and the NFW (Navarro et al.
 1996) profile., 1996) profile.
" For mass models using a modified isothermal halo. the free parameters are the halo ceutral density py. core radius r, aud the mass to light ratio of the stellar disk. Y."," For mass models using a modified isothermal halo, the free parameters are the halo central density $\rho_0$, core radius $_c$ and the mass to light ratio of the stellar disk, $\Upsilon$."
" For the NEW ποσο], the free parameters are the halo couceutration parameter c. e»oo (the circular velocity at the radius at which the halo deusitv is 200 times the critical density) aud the mass to liebt ratio of the stellar disk. Y."," For the NFW models, the free parameters are the halo concentration parameter c, $v_{200}$ (the circular velocity at the radius at which the halo density is 200 times the critical density) and the mass to light ratio of the stellar disk, $\Upsilon$."
 Mass model were fit using the CIPSY task ROTAIAS., Mass model were fit using the GIPSY task ROTMAS.
 Since we could trace enmissiou only from the brightest central regions of the galaxy in the I baud. we use the nore accurately determined V baud scale leneth for the nass modeling.," Since we could trace emission only from the brightest central regions of the galaxy in the I band, we use the more accurately determined V band scale length for the mass modeling."
 Fig. 9{[, Fig. \ref{fig:massmodel2}[ [
A] shows the best fit mass models or KI98 250.,A] shows the best fit mass models for KK98 250.
 The derived halo parameters are given iu Table 2.., The derived halo parameters are given in Table \ref{tab:halo}.
 For comparison. apart from the best fit mass uodel. the derived halo parameters are also eiven for the uaxinmn ΠΠ disk aud Y4=0.7 (which was obtained from the observed color x V-I- of ~1.3 usine he low metallicity Druzual & Charlot SPS inodel using a uodified Salpeter IME: Bell & de Joug 2001).," For comparison, apart from the best fit mass model, the derived halo parameters are also given for the maximum disk, minimum disk and $\Upsilon_V=0.7$ (which was obtained from the observed color $<$ $>$ of $\sim 1.3$ using the low metallicity Bruzual $\&$ Charlot SPS model using a modified Salpeter IMF; Bell $\&$ de Jong 2001)."
 The total dynamical mass of ΙΙΝ05 250. estimated from the last neasured poiut of the rotation curve is 22.6«1O°AE.. at lis radius more than of the mass of KK98 250 is dark.," The total dynamical mass of KK98 250, estimated from the last measured point of the rotation curve is $22.6\times 10^8 \rm{M}_\odot$ –at this radius more than of the mass of KK98 250 is dark."
 For mass models with au NEW halo. keeping Ἐν as a free paraicter iu the fit gave unphysical results.," For mass models with an NFW halo, keeping $\Upsilon_V$ as a free parameter in the fit gave unphysical results."
 Even after settiug Y3-= 0. no reasonable fit could be obtained.," Even after setting $\Upsilon_V=0$ , no reasonable fit could be obtained."
 As an illustration. Fig. 9 ," As an illustration, Fig. \ref{fig:massmodel2}[ ["
Aj shows an NEW fit to the data. keeping the concentration parameters e fixed to 1. Y4-—0.0 aud cogo chosen tominimize v,"A] shows an NFW fit to the data, keeping the concentration parameters c fixed to 1, $\Upsilon_V$ =0.0 and $v_{200}$ chosen tominimize $\chi^2$."
 As can be seen. even at these extreme values for the parameters. the quality of fit ls poor.," As can be seen, even at these extreme values for the parameters, the quality of fit is poor."
 Wo also fif mass models to ai hybrid rotation curve (see Fig. 5|[, We also fit mass models to a hybrid rotation curve (see Fig. \ref{fig:vrot1}[ [
B]). cousistiug of Πα data derived bv deBloketal.(2001) iu the inner regions of the ealaxy aud the vasvuuuectric dift corrected II rotation curve in the outer regions.,"B]), consisting of $\alpha$ data derived by \cite{deblok01} in the inner regions of the galaxy and the “asymmetric drift"" corrected HI rotation curve in the outer regions."
 Again. keeping Yy- as a free parameter in the fit eave unphysical results. hence it was fixed to the value of 0.2. obtained from the best fit isothermal halo model. derived using the III rotation curve alone.," Again, keeping $\Upsilon_V$ as a free parameter in the fit gave unphysical results, hence it was fixed to the value of 0.2, obtained from the best fit isothermal halo model, derived using the HI rotation curve alone."
 Iu any case. fixing Ty to a common value allows a meaniugful comparison of the halo parameters derived using both the rotation curves.," In any case, fixing $\Upsilon_V$ to a common value allows a meaningful comparison of the halo parameters derived using both the rotation curves."
 The derived halo parameters for the isothermal halo are eiven in Table 2.., The derived halo parameters for the isothermal halo are given in Table \ref{tab:halo}.
 The table also shows the isothermal halo parameters derivec bv deBloketal.(2001) using only the Πα rotation curve., The table also shows the isothermal halo parameters derived by \cite{deblok01} using only the $\alpha$ rotation curve.
 We note that apart from the (probably uot physically 10e2niugful) maxima disk case. the halo parameters derived from the ΤΗ rotation curve are in good agreement with one another. but that they are substantially different frou the paraimecters derived from. the Tvbrid or Πα rotation curves.," We note that apart from the (probably not physically meaningful) maximum disk case, the halo parameters derived from the HI rotation curve are in good agreement with one another, but that they are substantially different from the parameters derived from the Hybrid or $\alpha$ rotation curves."
" Iu this context it is worth repeating. that the discrepancy between the Ia rotation curve and the III rotation curve is largest at iuteriuediate radii aud not at παπαradii as one would have expected. if the IHE rotation curve suffered from beams πο,"," In this context it is worth repeating, that the discrepancy between the $\alpha$ rotation curve and the HI rotation curve is largest at intermediate radii, and not at smallradii as one would have expected, if the HI rotation curve suffered from beam smearing."
 Also shown in Fig. Ο , Also shown in Fig. \ref{fig:massmodel2}[ [
5) is the Ty=0. ΣΕΝ halo fit to the IIvbrid rotation curve.,"B] is the $\Upsilon_V=0$, NFW halo fit to the Hybrid rotation curve."
 As can be seen. this fit overestimates the observed rotationvelocity iu," As can be seen, this fit overestimates the observed rotationvelocity in"
of protocluster galaxies.,of protocluster galaxies.
 The aarcmin? CF+ is therefore used as the control field in the rest of this work., The $^{2}$ CF+ is therefore used as the control field in the rest of this work.
 A larger control field is required to determine the uncertainties due to the field-to-field variation of galaxy number counts., A larger control field is required to determine the uncertainties due to the field-to-field variation of galaxy number counts.
 For this purpose we use the ddeg? UDS., For this purpose we use the $^2$ UDS.
 Colour transformations are required to shift the observed UDS colours to HAWK-I colours since the UDS was observed with filters that have different passbands than HAWK-I filters., Colour transformations are required to shift the observed UDS colours to HAWK-I colours since the UDS was observed with filters that have different passbands than HAWK-I filters.
" These were determined using stellar population models of high-redshift galaxies, and by matching the galaxy number counts and colour distributions of the aand ppopulations in the UDS to the CF+ (ie., ensuring the UDS cumulative number counts in reffig:comparison match those of CF+)."," These were determined using stellar population models of high-redshift galaxies, and by matching the galaxy number counts and colour distributions of the and populations in the UDS to the CF+ (i.e., ensuring the UDS cumulative number counts in \\ref{fig:comparison} match those of CF+)."
" Therefore these transformations may not be suitable for sources with different colours, such as stars."," Therefore these transformations may not be suitable for sources with different colours, such as stars."
 The galaxy surface overdensity is theexcess surface density of galaxies., The galaxy surface overdensity $\Sigma_g$ is the surface density of galaxies.
" It is calculated as X,=(Lops— X)/X, where Lops is the observed surface density, and X is the expected surface density measured from the CF+ control field."," It is calculated as $\Sigma_g={(\Sigma_{obs}-\bar\Sigma)}/{\bar\Sigma}$ , where $\Sigma_{obs}$ is the observed surface density, and $\bar{\Sigma}$ is the expected surface density measured from the CF+ control field."
 The surface overdensity of the aand ggalaxies was measured within 3cco-moving Mpc (1.8) of the HzRGs., The surface overdensity of the and galaxies was measured within co-moving Mpc $\arcmin$ ) of the HzRGs.
 This distance corresponds to approximately the virial radius of a massive local cluster., This distance corresponds to approximately the virial radius of a massive local cluster.
" The fields were selected to include the HzRGs, so these galaxies were not included in either the oor ssample."," The fields were selected to include the HzRGs, so these galaxies were not included in either the or sample."
 The results are shown in feachpopulationarelistedinTable2.., The results are shown in \\ref{fig:inner_outer} and the number and overdensity of each population are listed in Table \ref{tab:overd}.
" field-to-field variations in the surface density measured from 10,000 randomly positioned cells within the UDS."," The error bars represent $\sigma$ field-to-field variations in the surface density measured from 10,000 randomly positioned cells within the UDS."
" The fields containing148,, aand aare at least 1o overdense in both aand ggalaxies."," The fields containing, and are at least $\sigma$ overdense in both and galaxies."
 The other 3 fields show no significant overdensity in either population., The other 3 fields show no significant overdensity in either population.
 The surface overdensity of the aand ggalaxies were also measured beyond 3’ of the HzRGs (see bottom panel of reffig:innerouter))., The surface overdensity of the and galaxies were also measured beyond $\arcmin$ of the HzRGs (see bottom panel of \\ref{fig:inner_outer}) ).
T herearenosigni ficantoverdensitiesint heouterregionso f anyfield MRC0406—244 has a s, There are no significant overdensities in the outer regions of anyfield so the overdensities near the radio galaxies are not caused by zeropoint errors or inadequate subtraction of stars.
light overdensity in ggalaxies within aand a 16 under-density in the outer regions., $\MRCofos$ has a slight overdensity in galaxies within and a $\sigma$ under-density in the outer regions.
 Therefore the 1.8’ cell around the radio galaxy is significantly overdense in comparison to its local surroundings suggesting mmay have several nearby companions., Therefore the $\arcmin$ cell around the radio galaxy is significantly overdense in comparison to its local surroundings suggesting may have several nearby companions.
 The spatial distribution of aand ggalaxies in the 6 radio galaxy fields are shown in reffig:spatialjist., The spatial distribution of and galaxies in the 6 radio galaxy fields are shown in \\ref{fig:spatial_dist}.
".Avisualinspectionofthesemapscon firmsthatthe fieldscontainingU: aandMRC ccontainsignificantlymoreALL-JHK aandJHK ggalaxiesthanex pected, whilstthe3 fieldscontaining aandMRC ddonot."," A visual inspection of these maps confirms that the fields containing, and contain significantly more and galaxies than expected, whilst the 3 fields containing, and do not."
 The significance of the galaxy overdensity is the joint probability of finding an overdensity in both aandppopulations., The significance of the galaxy overdensity is the joint probability of finding an overdensity in both andpopulations.
" Since the populations are not mutually exclusive, the significance of each population cannot be simply combined."," Since the populations are not mutually exclusive, the significance of each population cannot be simply combined."
" Instead 10,000 random 1.8' radius cells within the ddeg? UDS were used to determine the probability of finding a cell which is as dense as the regions surrounding the HzRGs in both aand ppopulations."," Instead 10,000 random $\arcmin$ radius cells within the $^{2}$ UDS were used to determine the probability of finding a cell which is as dense as the regions surrounding the HzRGs in both and populations."
" The probability of finding a 1.8’ radius cell within the UDS, with surface overdensities (2,5,) equal or greater than each of the radio galaxy fields is listed in the bottom row of Table 2.."," The probability of finding a $\arcmin$ radius cell within the UDS, with surface overdensities $\Sigma_{obs}$ ) equal or greater than each of the radio galaxy fields is listed in the bottom row of Table \ref{tab:overd}."
" Between and of all UDS regions were as dense as the 1.8’ radius cells around262,, oor2139292,, so these fields do not contain more galaxies than expected."," Between and of all UDS regions were as dense as the $\arcmin$ radius cells around, or, so these fields do not contain more galaxies than expected."
" The probability of finding regions asdense as those surrounding 148,, aand is ~ 0.3%,, so the number of galaxies in these fields deviate from the expected galaxy density by 30."," The probability of finding regions asdense as those surrounding , and is $\sim0.3$ , so the number of galaxies in these fields deviate from the expected galaxy density by $3\sigma$ ."
2004).,.
. llowever. Hui&Zhang(2002) has pointed out that it might be invalid to describe the ealaxy inürinsic alignments on large scales as a quadratic function of the density correlation.," However, \citet{hui-zha02} has pointed out that it might be invalid to describe the galaxy intrinsic alignments on large scales as a quadratic function of the density correlation."
 Their logic is as follows: Since the «quadratic scaling is based on the linear tidal torque theory which adopts a somewhat oversimplified assumption that the tidal field is Gaussian in the subsequent evolutionary stages. it should not be a good approximation to describe the ealaxv mürinsic alignments on large scales.," Their logic is as follows: Since the quadratic scaling is based on the linear tidal torque theory which adopts a somewhat oversimplified assumption that the tidal field is Gaussian in the subsequent evolutionary stages, it should not be a good approximation to describe the galaxy intrinsic alignments on large scales."
 In reality. (he densitv. [Inctuations will develop non-Gaussianity via gravity which would in turn lead to non-negligible contributions of je nonlinear-order of the tidal tensors to the generation of the galaxy angular momentum.," In reality, the density fluctuations will develop non-Gaussianity via gravity which would in turn lead to non-negligible contributions of the nonlinear-order of the tidal tensors to the generation of the galaxy angular momentum."
 Due to (his nonlinear effect on the galaxy angular momentum. their intrinsic spin alienments should be better approximated as linear scaling with the density correlation function.," Due to this nonlinear effect on the galaxy angular momentum, their intrinsic spin alignments should be better approximated as linear scaling with the density correlation function."
 Because je linear scaling of the densitv. correlation drops much slowly (han the euadratic scaling. (he intrinsic spin alignments would not be completely negligible even on large scales.," Because the linear scaling of the density correlation drops much slowly than the quadratic scaling, the intrinsic spin alignments would not be completely negligible even on large scales."
 Hf (heir ‘aims (urn out to be (true. then it will have a significant impact not only on the weak lensing ialvsis but also on our fundamental understanding of the evolution of the tidal alignments.," If their claims turn out to be true, then it will have a significant impact not only on the weak lensing analysis but also on our fundamental understanding of the evolution of the tidal alignments."
 In the light of their claims. the following questions naturally arise: Does the nonlinear tidal effect on the galaxy intrinsic alignments really exist to a non negligible degree?," In the light of their claims, the following questions naturally arise; Does the nonlinear tidal effect on the galaxy intrinsic alignments really exist to a non negligible degree?"
 1 so. al what epochs aud on which scales does its contribution begin to be sienilicant?," If so, at what epochs and on which scales does its contribution begin to be significant?"
 Does il depend on the intrinsic properties of the galaxies or dark halos?, Does it depend on the intrinsic properties of the galaxies or dark halos?
 Our goal here is (ο answer the above questions using both analvtical and numerical methods., Our goal here is to answer the above questions using both analytical and numerical methods.
 The outline of this paper is as follows: 82. we overview brielly the previous analytic moclel for the galaxy spin-spin alienmients based on (he linear (dal toreue theory. and propose a new model (o account lor the nonlinear tidal effect.," The outline of this paper is as follows: 2, we overview briefly the previous analytic model for the galaxy spin-spin alignments based on the linear tidal torque theory and propose a new model to account for the nonlinear tidal effect."
 83. we report a detection of the signals of the nonlinear tidal effect on the intrinsic spin alignments of dark matter halos simulated in N-body experiments ancl show how the signals depend on redshift. scale. aud the halo intrinsic property.," 3, we report a detection of the signals of the nonlinear tidal effect on the intrinsic spin alignments of dark matter halos simulated in N-body experiments and show how the signals depend on redshift, scale, and the halo intrinsic property."
 84. we summarize our results and discuss the implications of our work on the weak lensing effect.," 4, we summarize our results and discuss the implications of our work on the weak lensing effect."
 The linear tidal torque theory explains (hat unless a proto-halo has a perfectly spherical shape. it can acquire spin angular momentum at first order (through its tidal interaction with ihe surrounding matter (Doroshkevieh1970;White1934:Catelan&Theuns1996).," The linear tidal torque theory explains that unless a proto-halo has a perfectly spherical shape, it can acquire spin angular momentum at first order through its tidal interaction with the surrounding matter \citep{dor70,whi84,cat-the96}."
. The main prediction of the linear. tidal torque theory is Chat the proto-halo angular momentum, The main prediction of the linear tidal torque theory is that the proto-halo angular momentum
Pixels belonging to objects im the neighborhood of the primary objectbeing fit are masked out of the fitting area using the SExtractor segmentation nuage.,Pixels belonging to objects in the neighborhood of the primary object being fit are masked out of the fitting area using the SExtractor segmentation image.
 As noted earlier.the flux from the primary theobject that would have been iu those masked areas in absence of neighbors is nonetheless properly included iu the magnitude measurements because GIM2D imnaguitudes were obtained by iutegratiug the best-fit 110dols over all pixels.," As noted earlier, the flux from the primary object that would have been in those masked areas in the absence of neighbors is nonetheless properly included in the magnitude measurements because GIM2D magnitudes were obtained by integrating the best-fit models over all pixels."
 Systematic errors in the sky background level deterumination donünate the errors on the measured structural paraiicters., Systematic errors in the sky background level determination dominate the errors on the measured structural parameters.
 An erroneous sky level can also uusiead the bulge|disk decomposition algorithm iuto introducing wnplysical bulge or disk components., An erroneous sky level can also mislead the bulge+disk decomposition algorithm into introducing unphysical bulge or disk components.
 For exaniple. a very huge disk component would result from nuderestimating the sky level because the positive sky offset would look like such a component to the algoritlin.," For example, a very large disk component would result from underestimating the sky level because the positive sky offset would look like such a component to the algorithm."
 It is therefore critical to measure the best sky possible., It is therefore critical to measure the best sky possible.
 We initially adopted the SDSS sky background levels or our bulee|disk decompositions for the sake of consistency., We initially adopted the SDSS sky background levels for our bulge+disk decompositions for the sake of consistency.
 We used the sky levels even by the kevwor SKY iu the headers of the corrected images., We used the sky levels given by the keyword SKY in the headers of the corrected images.
 The sky evel for a given corrected frame was subtracted from al he CARD science postage stamp inages of the objects extracted frou this frame., The sky level for a given corrected frame was subtracted from all the GIM2D science postage stamp images of the objects extracted from this frame.
 The sky. level was then fixe o zero for the bulge|disk decompositions., The sky level was then fixed to zero for the bulge+disk decompositions.
 As discisscc ater. this procedure did not produce sky backerowk evels that were good enough for our decompositions.," As discussed later, this procedure did not produce sky background levels that were good enough for our decompositions."
 We then used sky backeround levels aud standard deviations determined by GINDD. GINI2D first uses all he pixels in the science thuubnal nuage flagged as vackeround pixels (flag value of zero) in the SExtractor seeieutation inage., We then used sky background levels and standard deviations determined by GIM2D. GIM2D first uses all the pixels in the science thumbnail image flagged as background pixels (flag value of zero) in the SExtractor segmentation image.
 CIARD further pruues this sample of background pixels by excluding amy backerouud κο that is closer than 12700 frouaay (primary Or ιοοπιο) object pixels., GIM2D further prunes this sample of background pixels by excluding any background pixel that is closer than 0 from (primary or neighboring) object pixels.
" This buffer zoue eusures that he fux from all SExtracted objectsot iu the image below all the 1.0-05,4, iophotes does sieuificautlv bias the nean background level upwards and artificially inflate Ohba:", This buffer zone ensures that the flux from all SExtracted objects in the image below all the $\sigma_{bkg}$ isophotes does not significantly bias the mean background level upwards and artificially inflate $\sigma_{bkg}$.
 A MULL of xy pixels was imposed ou the area of the sky 20.000.region.," A minimum of 20,000 sky pixels was imposed on the area of the sky region."
 Iu cases where the Munber of sky pixels in the iuput science thumbnail iuage was insufficient. the original SDSS corrected image was searched for the 20.000 sky pixels nearest to the object.," In cases where the number of sky pixels in the input science thumbnail image was insufficient, the original SDSS corrected image was searched for the 20,000 sky pixels nearest to the object."
 Background parameters were re-caleulated with GIMPD before fitting. aud the residual backerouud levels were then frozen to their recaleulated. values for the bulge|disk fits.," Background parameters were re-calculated with GIM2D before fitting, and the residual background levels were then frozen to their recalculated values for the bulge+disk fits."
 Galaxy structural parauicters were measured from bulee|disk decompositions performed using version 3.2 of the GIM2D software package(Simardetal.2002)., Galaxy structural parameters were measured from bulge+disk decompositions performed using version 3.2 of the GIM2D software package \citep{simard02}.
. We used the sui of a pure exponential disk aud a de Vaucouleurs bulge (Sérrsic iudex ο= 1) as our galaxy nuaee model., We used the sum of a pure exponential disk and a de Vaucouleurs bulge (Sérrsic index $n_b = 4$ ) as our galaxy image model.
 The free fitting paramcters of this model were the total flux £F in dataunits (DU). the bulge fraction B/T (= 0 for pure disk svstemis). the bulec senmui-najor axis effective radius οι the bulee ellipticity," The free fitting parameters of this model were the total flux $F$ in dataunits (DU), the bulge fraction $B/T$ $\equiv$ 0 for pure disk systems), the bulge semi-major axis effective radius $r_e$ , the bulge ellipticity"
and thus the stress energy tensor has the expansion As seen in the previous section. 8xG/c? increases the order by (wo so that the right-hand side of the Einstein equations are of second order and higher. thusthe fy equation to first order is so that the lowest order term of No is sourceless.,"and thus the stress energy tensor has the expansion As seen in the previous section, $8\pi G/c^2$ increases the order by two so that the right-hand side of the Einstein equations are of second order and higher, thusthe $t\varphi$ equation to first order is so that the lowest order term of $N$ is sourceless."
 We are [ree to choose N however we wish to make (he solution simplest. (hus we set. N—0.," We are free to choose $\stackrel{1}{N}$ however we wish to make the solution simplest, thus we set $\stackrel{1}{N}=0$."
 Wilh this selection the Einstein equations through third order become We see (hat o must be a constant so that we have Thus we see that the coupling to the angular momentum is of third order. there is no longer a nonlinear term in (he mass densitv'.. and we can identify," With this selection the Einstein equations through third order become We see that $\stackrel{2}{v}$ must be a constant so that we have Thus we see that the coupling to the angular momentum is of third order, there is no longer a nonlinear term in the mass , and we can identify"
"be obtained from the current J, by solving the linear set of equations given by Eq. 8,,","be obtained from the current $J_\nu$ by solving the linear set of equations given by Eq. \ref{matrix},"
 One of the key problems when obtaining an equilibrium solution iteratively is to decide when the solution has converged., One of the key problems when obtaining an equilibrium solution iteratively is to decide when the solution has converged.
" There are many ways in which we can check for convergence, but it is necessary to find a method that applies to all models and molecules."," There are many ways in which we can check for convergence, but it is necessary to find a method that applies to all models and molecules."
" It is important that the code does not quit prematurely before the model has actually converged, but on the other hand, it should not continue indefinitely because of minor random fluctuations in a single grid point somewhere."," It is important that the code does not quit prematurely before the model has actually converged, but on the other hand, it should not continue indefinitely because of minor random fluctuations in a single grid point somewhere."
" Given a sufficiently large number of grid points, the random nature of the code implies that some points will always deviate from the equilibrium populations."," Given a sufficiently large number of grid points, the random nature of the code implies that some points will always deviate from the equilibrium populations."
" In we therefore use a statistical criterion, and let the user decide how many iterations he or she will let the code run."," In we therefore use a statistical criterion, and let the user decide how many iterations he or she will let the code run."
 We have found empirically that 15-20 iterations a good value for most models and the default is thus set to 20., We have found empirically that 15-20 iterations a good value for most models and the default is thus set to 20.
 This can however easily be adjusted by the user according to preference and the problem at hand., This can however easily be adjusted by the user according to preference and the problem at hand.
" Figure 7 shows, as an example, the convergence history of a single grid point in a test run."," Figure \ref{statistics} shows, as an example, the convergence history of a single grid point in a test run."
" Panel a) shows the signal- ratio of the current iteration, where the signal is the current population and the noise is the standard deviation of the previous five iterations (shown in panel b), for each level."," Panel a) shows the signal-to-noise ratio of the current iteration, where the signal is the current population and the noise is the standard deviation of the previous five iterations (shown in panel b), for each level."
 The signal-to-noise ratio is seen to increase and then level out after about 10 iterations., The signal-to-noise ratio is seen to increase and then level out after about 10 iterations.
 It does however level out at different values for the different levels which makes it difficult to fix a certain value to reach., It does however level out at different values for the different levels which makes it difficult to fix a certain value to reach.
" Also, the signal-to-noise ratio fluctuates a lot (notice the log scale) which again makes it hard to decide whether or not the solution is stable."," Also, the signal-to-noise ratio fluctuates a lot (notice the log scale) which again makes it hard to decide whether or not the solution is stable."
" In panel c) we can see the populations averaged over the previous 5 iterations, and from this plot it is quite obvious that a stable solution (for this grid point) has been reached after the 12’th iteration."," In panel c) we can see the populations averaged over the previous 5 iterations, and from this plot it is quite obvious that a stable solution (for this grid point) has been reached after the 12'th iteration."
 The derivative of this curve is shown in panel d)., The derivative of this curve is shown in panel d).
" Because the signal-to-noise fluctuates randomly from one iteration to the next and the range in signal-to-noise values is large, we have chosen to consider the distribution throughout the entire model."," Because the signal-to-noise fluctuates randomly from one iteration to the next and the range in signal-to-noise values is large, we have chosen to consider the distribution throughout the entire model."
 The median value of this distribution tells us about how well converged the model is in general., The median value of this distribution tells us about how well converged the model is in general.
 We also consider the minimum value for the signal-to-noise for all levels and grid points., We also consider the minimum value for the signal-to-noise for all levels and grid points.
 Figure 8 shows the signal-to-noise distributions for the energy levels 0 — 6 individually and for all levels with a fractional population higher than 10:12., Figure \ref{medians} shows the signal-to-noise distributions for the energy levels 0 – 6 individually and for all levels with a fractional population higher than $10^{-12}$.
" We use this cut-off, because levels which are less populated only add unwanted noise."," We use this cut-off, because levels which are less populated only add unwanted noise."
 The differently colored histograms show the distributions with increasing iteration number., The differently colored histograms show the distributions with increasing iteration number.
" On top of the distributions, the corresponding median values are marked."," On top of the distributions, the corresponding median values are marked."
 All medians are seen to increase with increasing iterations with the median of the least converged level 2 ending up at a of 200 already at iteration 16., All medians are seen to increase with increasing iterations with the median of the least converged level 2 ending up at a signal-to-noise of 200 already at iteration 16.
" Still, the lowest value of the entire model is as low as 20, which means that for that particular level we make an error of at most5%."," Still, the lowest signal-to-noise value of the entire model is as low as 20, which means that for that particular level we make an error of at most."
. We find this acceptable and therefore stop the calculation at this point., We find this acceptable and therefore stop the calculation at this point.
" However, for better confidence, more photons and iterations can be used at the cost of calculation time."," However, for better confidence, more photons and iterations can be used at the cost of calculation time."
" Another test which the user can perform in order to evaluate the convergence, is to plot the spatial distribution of the least converged points (or, for instance, all points with a signal-to-noise less than 100) and make a statistical comparison with the global point distribution to see if the least converged points in any way are associated with particular regions of the model or if the least converged points simply are a random subset to the entire grid."," Another test which the user can perform in order to evaluate the convergence, is to plot the spatial distribution of the least converged points (or, for instance, all points with a signal-to-noise less than 100) and make a statistical comparison with the global point distribution to see if the least converged points in any way are associated with particular regions of the model or if the least converged points simply are a random subset to the entire grid."
 One particular situation that the user should be aware of is the very highly opaque regime., One particular situation that the user should be aware of is the very highly opaque regime.
 In this regime the radiation transfer problem becomes similar to the diffusion problem and this can cause a very slow drift of the populations toward the correct solution., In this regime the radiation transfer problem becomes similar to the diffusion problem and this can cause a very slow drift of the populations toward the correct solution.
 This drift may be so slow that the populations seem converged and this problem is inherent to radiation transfer codes., This drift may be so slow that the populations seem converged and this problem is inherent to radiation transfer codes.
" After convergence has been reached, the code ray-traces lines of sight through the model in order to obtain an image cube of the radiation that escapes from the surface."," After convergence has been reached, the code ray-traces lines of sight through the model in order to obtain an image cube of the radiation that escapes from the surface."
" The user provides the information on the source distance, source velocity, source orientation, and image resolution and units."," The user provides the information on the source distance, source velocity, source orientation, and image resolution and units."
" The orientation parameters are slightly more complicated than for 2D codes, where an inclination and position angle are enough to set the source orientation."," The orientation parameters are slightly more complicated than for 2D codes, where an inclination and position angle are enough to set the source orientation."
" In we also have a source rotation which allows us to view a 3D model from any direction, using the matrix where ϐ is the traditional inclination (0: face-on, 2/2: and ¢ is the azimuthal rotation."," In we also have a source rotation which allows us to view a 3D model from any direction, using the matrix where $\theta$ is the traditional inclination (0: face-on, $\pi/2$: edge-on) and $\phi$ is the azimuthal rotation."
" Rotation in the image plane is done afterwards, simply by rotating the image cube."," Rotation in the image plane is done afterwards, simply by rotating the image cube."
" For the raytracing we let the photons move in straight lines, rather than jumping from grid point to grid point."," For the raytracing we let the photons move in straight lines, rather than jumping from grid point to grid point."
 In this part of the code we therefore do not make use of the Delaunay triangulation but rather the Voronoi diagram., In this part of the code we therefore do not make use of the Delaunay triangulation but rather the Voronoi diagram.
 The entire volume of the Voronoi cell is represented by the populations of the corresponding grid point and so integration of Eq., The entire volume of the Voronoi cell is represented by the populations of the corresponding grid point and so integration of Eq.
 | becomes a matter of stepping through the source model and figuring out in which Voronoi cell the photon is., \ref{radtran} becomes a matter of stepping through the source model and figuring out in which Voronoi cell the photon is.
" From an algorithmic point of view, this comes down to a simple sorting, not of thousands of cells, but only of, on average, the 16 neighboring cells."," From an algorithmic point of view, this comes down to a simple sorting, not of thousands of cells, but only of, on average, the 16 neighboring cells."
 The step size is chosen as a fraction of the cell size in order to avoid accidentally missing a cell by stepping over it., The step size is chosen as a fraction of the cell size in order to avoid accidentally missing a cell by stepping over it.
" Also, we need to sample variations in the velocity field across the cell in order to get a smooth spectrum."," Also, we need to sample variations in the velocity field across the cell in order to get a smooth spectrum."
" This is a very fast process compared to moving through a regular grid, but not as fast as moving along the Delaunay lines, which is why this transport method is not used when determining the level populations."," This is a very fast process compared to moving through a regular grid, but not as fast as moving along the Delaunay lines, which is why this transport method is not used when determining the level populations."
"(the numbers are conjectural, we show them for illustrative purposes only).","(the numbers are conjectural, we show them for illustrative purposes only)."
" The more massive star (the progenitor of the pulsar), evolves and becomes a red supergiant (RSG): At this point, it starts transferring mass to the other component in the inner binary."," The more massive star (the progenitor of the pulsar), evolves and becomes a red supergiant (RSG): At this point, it starts transferring mass to the other component in the inner binary."
" In such a situation, mass transfer is generally unstable, and the envelope of the RSG is expected to engulf the companion and lead to a common envelope (CE) phase, where the helium core of the RSG and the inner companion are embedded in the envelope of the RSG."," In such a situation, mass transfer is generally unstable, and the envelope of the RSG is expected to engulf the companion and lead to a common envelope (CE) phase, where the helium core of the RSG and the inner companion are embedded in the envelope of the RSG."
" Because of friction with the envelope, the orbit of this embedded binary will decay, releasing orbital energy in the process."," Because of friction with the envelope, the orbit of this embedded binary will decay, releasing orbital energy in the process."
" If this energy is sufficient to eject the envelope, this will leave a much closer binary consisting of a helium star and the more-or-less unaffected inner companion e.g., ?): If the outer component of the triple system is close enough, it may also be affected by this CE phase, since the envelope will greatly expand because of the orbital energy that is being deposited within it (toradiiof~5—10AU;see,e.g., ?)."," If this energy is sufficient to eject the envelope, this will leave a much closer binary consisting of a helium star and the more-or-less unaffected inner companion \citep[see, e.g.,][]{bv91}: If the outer component of the triple system is close enough, it may also be affected by this CE phase, since the envelope will greatly expand because of the orbital energy that is being deposited within it \citep[to radii of $\sim 5-10\,$AU; see, e.g.,][]{pod01}."
 It will also be engulfed by the expanding envelope and will also experience a spiral-in phase ?.., It will also be engulfed by the expanding envelope and will also experience a spiral-in phase \cite{ev86}.
 This will produce a much closer triple system., This will produce a much closer triple system.
" Without realistic hydrodynamical simulations, it is difficult to determine the post-CE parameters."," Without realistic hydrodynamical simulations, it is difficult to determine the post-CE parameters."
" Here, we will consider two potential outcomes, which we will discuss in more detail later: or Eventually, the He core will explode in a supernova and produce a NS."," Here, we will consider two potential outcomes, which we will discuss in more detail later: or Eventually, the He core will explode in a supernova and produce a NS."
" The sudden mass loss associated with this event will make the orbits of the other two components wider and somewhat eccentric: or This event could be either a normal Fe-core collapse supernova (SN) or an electron-capture (e-capture) supernova (see?,andfurtherreferencestherein)..", The sudden mass loss associated with this event will make the orbits of the other two components wider and somewhat eccentric: or This event could be either a normal Fe-core collapse supernova (SN) or an electron-capture (e-capture) supernova \citep[see][and further references therein]{plp+04}.
" Given the fact that the system remained bound after the explosion, it is not likely that the SN produced a major kick, nor large fractional mass loss, particularly under scenario ""a"","," Given the fact that the system remained bound after the explosion, it is not likely that the SN produced a major kick, nor large fractional mass loss, particularly under scenario ""a"","
section 5)).,section \ref{flare}) ).
 Interval 3 covers the remaining portion of the observation. during which the mean Εις increased steacily.," Interval 3 covers the remaining portion of the observation, during which the mean flux increased steadily."
 Accompanving the changes in ux were significant variations in pulse profile ancl spectral shape., Accompanying the changes in flux were significant variations in pulse profile and spectral shape.
 Historically GN 114 has shown evidence of a correlation between torque state ancl pulse. profile shape (GreenhillGallowayandStorey 1998)., Historically GX 1+4 has shown evidence of a correlation between torque state and pulse profile shape \cite{gre98}.
. Throughout the period of spin-up curing t[une 1970s pulse profiles were typically brighter at the trailing edge. with respect to the primary minimum: e.g. Doty. Hollman and Lewin (LOS1).," Throughout the period of spin-up during the 1970s pulse profiles were typically brighter at the trailing edge with respect to the primary minimum; e.g. Doty, Hoffman and Lewin \shortcite{dot81}."
. Since then. measured pulse profiles have instead: usually been leacling-cclee bright. with less pronounced. asymmetry: e.g. Greenhill et al. (1993).," Since then, measured pulse profiles have instead usually been leading-edge bright, with less pronounced asymmetry; e.g. Greenhill et al. \shortcite{gre93}."
 During interval 1 the pulse. profile was observed. to. be leacing-edge bright. similar to other observations since the 1980s.," During interval 1 the pulse profile was observed to be leading-edge bright, similar to other observations since the 1980s."
 Pulsations all but. ceased. curing interval 2. and in interval 3 the shape of the profile had changed dramatically ancl resembled the trailine-edee bright profiles typically observed curing the 1970s (Cilesetal.1999).," Pulsations all but ceased during interval 2, and in interval 3 the shape of the profile had changed dramatically and resembled the trailing-edge bright profiles typically observed during the 1970s \cite{gil99}."
. The count rate spectra taken during cach interval are shown in Fig., The count rate spectra taken during each interval are shown in Fig.
 Ibb. The overall spectral shape changed significantly over the course of the observation. with the spectrum becoming harder in intervals 2 and 3 compared to interval 1.," \ref{fig1}b b. The overall spectral shape changed significantly over the course of the observation, with the spectrum becoming harder in intervals 2 and 3 compared to interval 1."
 The iron Iluorescence line at around. 6.4 keV appears more prominent in the second ancl third. intervals., The iron fluorescence line at around 6.4 keV appears more prominent in the second and third intervals.
 lron line enhancement during intervals 2 and 3 is also apparent in the spectral ratios. Fig.," Iron line enhancement during intervals 2 and 3 is also apparent in the spectral ratios, Fig."
 lec. These ratios were calculated: by subtracting the background: spectrum. (including a component to account for the emission. from the galactic plane: see section 3)) from the source spectrum. [or each interval and dividing the resulting spectra for intervals 2 and 3 by that ofinterval 1., \ref{fig1}c c. These ratios were calculated by subtracting the background spectrum (including a component to account for the emission from the galactic plane; see section \ref{spec}) ) from the source spectrum for each interval and dividing the resulting spectra for intervals 2 and 3 by that of interval 1.
 Because the countrate drops olf steeply above LO keV the spectral bins must be mace correspondingly larger to achieve a reliable ratio., Because the countrate drops off steeply above 10 keV the spectral bins must be made correspondingly larger to achieve a reliable ratio.
 The datapoint in the highest energy. hand for cach curve was obtained from. LENE cata. while the lower energy. ratios are calculated from PCA data.," The datapoint in the highest energy band for each curve was obtained from HEXTE data, while the lower energy ratios are calculated from PCA data."
 Phe decrease in Hux observed from interval 1 to 2 and 3 becomes more pronounced at energies below 6 keV. Above 15 keV the spectral ratios are almost constant with energy., The decrease in flux observed from interval 1 to 2 and 3 becomes more pronounced at energies below 6 keV. Above 15 keV the spectral ratios are almost constant with energy.
 Instrumental background. from cosmic ray interactions aud as a result of passages close to the SAA are estimated using the software. provided bv theANTE Guest Observer Facility (GOL).," Instrumental background from cosmic ray interactions and as a result of passages close to the SAA are estimated using the software, provided by the Guest Observer Facility (GOF)."
" Due to the proximity of the source to the galactie plane. an additional component which takes into account the so-called. ""galactic ridge” emission must be included. in any spectral. model."," Due to the proximity of the source to the galactic plane, an additional component which takes into account the so-called `galactic ridge' emission must be included in any spectral model."
 “Phe model for this component used. in our fits is identical to that. fitted to survey data from this region (ValiniaanclMarshall1998) with normalisations and abundance fitted to spectra taken during slews to and from the source during this observation., The model for this component used in our fits is identical to that fitted to survey data from this region \cite{val98} with normalisations and abundance fitted to spectra taken during slews to and from the source during this observation.
 A secondary instrumental effect which must be taken into account to obtain the lowest possible residuals in the mocol fit is a consequence of the Nenon οσο absorption feature., A secondary instrumental effect which must be taken into account to obtain the lowest possible residuals in the model fit is a consequence of the Xenon L-edge absorption feature.
 This feature is modelled in our spectrum by a multiplicative edge model component with energy fixed at 4.83 keV. Candidate spectral models were tested by fitting to the count rate spectrum to minimise x72 using the spectral fitting package version LO (Arnaucl1996)., This feature is modelled in our spectrum by a multiplicative edge model component with energy fixed at 4.83 keV. Candidate spectral models were tested by fitting to the count rate spectrum to minimise $\chi^{2}$ using the spectral fitting package version 10 \cite{xspec}.
.. In. &eneral each model takes the form of one (or more) continuum components with a gaussian component necessary to simulate the iron. line emission. and ᾱ- multiplicative component to account for absorption by cold matter along," In general each model takes the form of one (or more) continuum components with a gaussian component necessary to simulate the iron line emission, and a multiplicative component to account for absorption by cold matter along"
"by a two-dimensional Maxwell-Boltzmann distribution, P(Vo)~Voe-(νονο” so under transformation, the distribution of V2, and hence rperi, is exponential.","by a two-dimensional Maxwell-Boltzmann distribution, $P(\vt) \sim \vt {\rm e}^{-(\vt-V_o)^2}$, so under transformation, the distribution of $\vt^2$, and hence $\rperi$, is exponential."
 Note that considering orbits in extended host halo profiles will modify this exponential distribution somewhat (see the Appendix)., Note that considering orbits in extended host halo profiles will modify this exponential distribution somewhat (see the Appendix).
 We next explore how satellite orbital distributions depend on halo mass at z=0., We next explore how satellite orbital distributions depend on halo mass at $z=0$.
" We first examined the dependence on host halo mass by selecting satellite halos in the mass range 1019010151Mo, and we used the large dynamic range of the simulation to explore the dependence across four decades in halo mass."," We first examined the dependence on host halo mass by selecting satellite halos in the mass range $10^{10.0-10.5}\hmsol$, and we used the large dynamic range of the simulation to explore the dependence across four decades in halo mass."
" Figure 3 shows the distribution of circularity and pericenter, as in Fig. 1,,"," Figure \ref{fig:circ_rperi_dist_mhost} shows the distribution of circularity and pericenter, as in Fig. \ref{fig:circ_rperi_dist},"
 but for two host halo mass ranges., but for two host halo mass ranges.
" The distributions clearly change shape, being skewed to both lower circularity and lower pericenter for more massive host halos, which drives the average/median of the distributions (vertical lines) down."," The distributions clearly change shape, being skewed to both lower circularity and lower pericenter for more massive host halos, which drives the average/median of the distributions (vertical lines) down."
 Figure 4 demonstrates explicitly the dependence of average circularity and median pericenter on host halo mass., Figure \ref{fig:circ_rperi_mhost} demonstrates explicitly the dependence of average circularity and median pericenter on host halo mass.
" Circularity shows no dependence up to ~3x101?5!Ms, but above this mass satellite orbits become less circular with increasing host halo mass, with average circularity dropping nearly 2096 across the mass range."," Circularity shows no dependence up to $\sim3\times10^{12}\hmsol$, but above this mass satellite orbits become less circular with increasing host halo mass, with average circularity dropping nearly $20\%$ across the mass range."
" Interestingly, the turnover corresponds to the value of M., the characteristic halo mass scale of collapse, at z—0.? Median pericenter decreases more strongly with host halo mass, falling by more than a factor of 2 across the mass range and showing no rollover at low mass."," Interestingly, the turnover corresponds to the value of $M_*$, the characteristic halo mass scale of collapse, at $z=0$ Median pericenter decreases more strongly with host halo mass, falling by more than a factor of 2 across the mass range and showing no rollover at low mass."
" Overall, satellite orbits are both more radial and plunge deeper into their host halo at higher host halo mass."," Overall, satellite orbits are both more radial and plunge deeper into their host halo at higher host halo mass."
 Similarly Fig.," Similarly, Fig."
 5 (top and middle) shows the host halo mass dependence of satellite average tangential and radial velocity., \ref{fig:vt_vr_vtot_mhost} (top and middle) shows the host halo mass dependence of satellite average tangential and radial velocity.
 Both velocity components remain below the host halo virial velocity at all mass scales., Both velocity components remain below the host halo virial velocity at all mass scales.
" Tangential velocity monotonically declines with host halo mass, falling by 3096, implying that satellite accretion contributes angular momentum less efficiently onto higher mass halo."," Tangential velocity monotonically declines with host halo mass, falling by $30\%$, implying that satellite accretion contributes angular momentum less efficiently onto higher mass halo."
" Radial velocity declines rapidly with host halo mass up to 10?57! Mo, beyond which it remains nearly flat."," Radial velocity declines rapidly with host halo mass up to $\sim3\times10^{12}\hmsol$ , beyond which it remains nearly flat."
 'These trends explain the host halo mass dependence of circularity and pericenter., These trends explain the host halo mass dependence of circularity and pericenter.
" Below ~3x10?h!Ma, both Vo and V. decline with host halo mass, giving rise to constant circularity."," Below $\sim3\times10^{12}\hmsol$, both $\vt$ and $\vr$ decline with host halo mass, giving rise to constant circularity."
" At fixed circularity (eccentricity) and Meat, Tperi/RvirοςV2/Mj/S. (Eq. 4)),"," At fixed circularity (eccentricity) and $\ms$, $\rperi/\rvir \propto \vt^2/\mh^{4/3}$ (Eq. \ref{eq:rperi}) ),"
 so rperi continues to decline rapidly with mass., so $\rperi$ continues to decline rapidly with mass.
" Above ~3x107?A!Mo, declining Ve and constant V. cause both circularity and pericenter to decline with mass."," Above $\sim3\times10^{12}\hmsol$, declining $\vt$ and constant $\vr$ cause both circularity and pericenter to decline with mass."
" Additionally, Fig."," Additionally, Fig."
 5 (bottom) shows the host halo mass dependence of satellite average total velocity., \ref{fig:vt_vr_vtot_mhost} (bottom) shows the host halo mass dependence of satellite average total velocity.
" While satellite infall is usually ‘hotter’ than the host halo virial velocity, the magnitude of this effect decreases with host halo mass, falling by 2096 over the mass range."," While satellite infall is usually `hotter' than the host halo virial velocity, the magnitude of this effect decreases with host halo mass, falling by $20\%$ over the mass range."
" Interestingly, this leads to a crossover such that satellites infalling onto halos >10!5!Mg are instead on average ‘colder’ than the host halo."," Interestingly, this leads to a crossover such that satellites infalling onto halos $>10^{14}\hmsol$ are instead on average `colder' than the host halo."
 This mass trend is driven by the interplay of halo mass with its environment., This mass trend is driven by the interplay of halo mass with its environment.
" High-mass halos generically dominate the local potential field, and so satellites naturally fall in with velocity comparable to the halo virial velocity."," High-mass halos generically dominate the local potential field, and so satellites naturally fall in with velocity comparable to the halo virial velocity."
" By contrast, many low-mass halos reside in proximity to higher"," By contrast, many low-mass halos reside in proximity to higher"
"with the masses derived in this work except for WD1544—377, whose mass is smaller when calculated from its gravitational redshift.","with the masses derived in this work except for $-$ 377, whose mass is smaller when calculated from its gravitational redshift."
" However, Kawkaetal.(2007) inferred the spectroscopic mass of this star, together with those of WD1620-391 and WD1659-531, that are in good agreement with our results."," However, \cite{kaw07} inferred the spectroscopic mass of this star, together with those of $-$ 391 and $-$ 531, that are in good agreement with our results."
 WD0913+442 was studied by Karletal.(2005) and Bergeronetal.(2001)., $+$ 442 was studied by \cite{kar05} and \cite{ber01}.
 The former inferred the spectroscopic mass of the white dwarf and the latter used photometry and the trigonometric parallax to estimate the mass., The former inferred the spectroscopic mass of the white dwarf and the latter used photometry and the trigonometric parallax to estimate the mass.
" In both cases, the results are compatible with the value derived here."," In both cases, the results are compatible with the value derived here."
The two main differences between ZB's model and ours are the following.,The two main differences between ZB's model and ours are the following.
 First. ZB's multiple-1mage interpretation is different from ours: they claim to find a fifth image of AI. plus six additional multiple-image systems (their 5-10). all of which do not pass the strict criteria described in refsec:model:: in addition. ZB do not identify our systems A6 and A7.," First, ZB's multiple-image interpretation is different from ours: they claim to find a fifth image of A1, plus six additional multiple-image systems (their 5–10), all of which do not pass the strict criteria described in \\ref{sec:model}; in addition, ZB do not identify our systems A6 and A7."
" Second. ZB's analysis contains no spectroscopic or photometrie redshift information for their multiple images and. more importantly. ZB do not treat these unknown redshifts as free parameters in their model — their model contains just 6 free parameters. which describe the cluster mass distribution,"," Second, ZB's analysis contains no spectroscopic or photometric redshift information for their multiple images and, more importantly, ZB do not treat these unknown redshifts as free parameters in their model – their model contains just 6 free parameters, which describe the cluster mass distribution."
 We attempt to reproduce ZB's flat profile by fitting a model to all of their multiple image identifications. including the putative fifth image of system Al (marked by a black circle in the AT.2 panel of Fig.," We attempt to reproduce ZB's flat profile by fitting a model to all of their multiple image identifications, including the putative fifth image of system A1 (marked by a black circle in the A1.2 panel of Fig."
 1)., 1).
 We treat the redshifts of all multiple images as free parameters., We treat the redshifts of all multiple images as free parameters.
" The resulting best-fit ~ZB-constrained™ model has an image-plane rms of (6j;=1.2” , mmore than twice that of our fiducial model. dominated by the fifth image of Al and ZB's systems ὃ--10."," The resulting best-fit “ZB-constrained” model has an image-plane rms of $\langle\sigma_i\rangle=1.2\arcsec$ , more than twice that of our fiducial model, dominated by the fifth image of A1 and ZB's systems 5--10."
 The density profile associated with this model is shown in Fig., The density profile associated with this model is shown in Fig.
 4. and is in fact than ours., \ref{fig:prof} and is in fact than ours.
 However. once redshifts are no longer included as free parameters in the fit. but fixed at values that differ. to varying degrees. from the true. measured values. the sensitivity of the density profile to a chosen set of fixed redshift values becomes apparent.," However, once redshifts are no longer included as free parameters in the fit, but fixed at values that differ, to varying degrees, from the true, measured values, the sensitivity of the density profile to a chosen set of fixed redshift values becomes apparent."
 We demonstrate this by setting the redshifts of Al. A2. A3. and A+ to z21.5. 1.6. 1.8. and 1.8. tto values that are permitted by the model uncertainties but are in fact not the measured ones.," We demonstrate this by setting the redshifts of A1, A2, A3, and A4 to $z=1.5$, $1.6$, $1.8$, and $1.8$, to values that are permitted by the model uncertainties but are in fact not the measured ones."
 The density profile (Fig. 4)), The density profile (Fig. \ref{fig:prof}) )
 resulting from these erroneous assumptions tis nearly flat. with ~—0.14.," resulting from these erroneous assumptions is nearly flat, with $\gamma\sim-0.14$."
 We conclude that ZB's claim of a flat density. profile is highly sensitive to the details of the method by which they chose to assign fixed redshifts to multiple-image systems., We conclude that ZB's claim of a flat density profile is highly sensitive to the details of the method by which they chose to assign fixed redshifts to multiple-image systems.
 These problems may have been compounded by, These problems may have been compounded by
remains one of the most direct and quantitative measure of the dark energy available to us today.,remains one of the most direct and quantitative measure of the dark energy available to us today.
 Future all-sky missions such as Planck will provide an excellent possibility to extend these studies to higher contidence regime., Future all-sky missions such as Planck will provide an excellent possibility to extend these studies to higher confidence regime.
 While the above studies are mainly focussed on large angular scales. where the ISW effect plays an important role. at small angular scales. the presence of clusters and probably the associated filamentary network in which they reside can also affect both CMB maps through the Sunyaev-Zeldovich effect (Sunyaev&Zeldovich1980) as well as through the X-ray maps via bremsstrahlung.," While the above studies are mainly focussed on large angular scales, where the ISW effect plays an important role, at small angular scales, the presence of clusters and probably the associated filamentary network in which they reside can also affect both CMB maps through the Sunyaev-Zeldovich effect \citep{SZ} as well as through the X-ray maps via bremsstrahlung."
 Cross-correlation analysis of the diffuse soft X-ray background maps ofROSAT with WMAP Ist year data were performed by 2004)..," Cross-correlation analysis of the diffuse soft X-ray background maps of ROSAT with WMAP 1st year data were performed by \citep{Die1,Die2}."
 This study was motivated by the fact that hot gas in clusters can be more easily detected by cross-correlating X-ray and CMB maps., This study was motivated by the fact that hot gas in clusters can be more easily detected by cross-correlating X-ray and CMB maps.
 Although no evidence was found of this effect it opens the possibility of detecting such an effect in future high-resolution CMB maps., Although no evidence was found of this effect it opens the possibility of detecting such an effect in future high-resolution CMB maps.
 All these act as a motivation for development of a generic techniques to cross-correlate high-resolution CMB maps with other maps from LSS surveys., All these act as a motivation for development of a generic techniques to cross-correlate high-resolution CMB maps with other maps from LSS surveys.
 In this paper we focus on cross-correlating two or three different datasets. but the challenges are similar to those arising from a single dataset.," In this paper we focus on cross-correlating two or three different datasets, but the challenges are similar to those arising from a single dataset."
 For example. the estimation of the power spectrum from a single high-resolution map poses a formidable numerical problem in terms of computational requirements.," For example, the estimation of the power spectrum from a single high-resolution map poses a formidable numerical problem in terms of computational requirements."
 Typically two different methods are followed., Typically two different methods are followed.
 The first os the non-linear maximum likelihood method. or its quadratic variant. which can be applied to smoothed degraded maps. as it is not possible to directly invert a full pixel covariance matrix (Tegmark1997).," The first os the non-linear maximum likelihood method, or its quadratic variant, which can be applied to smoothed degraded maps, as it is not possible to directly invert a full pixel covariance matrix \citep{teg}."
.. To circumvent this problem a pseudo-C; s (PCL) technique was invented (Hivonetal.2002) which is unbiased though remains suboptimal., To circumvent this problem a ${\cal C}_{\ell}$ s (PCL) technique was invented \citep{Hiv} which is unbiased though remains suboptimal.
 In recent analysis has shown how to optimize these estimators which can then be used to analyse high-resolution maps in a very fast and accurate way.," In recent analysis \citet{Efs1,Efs2} has shown how to optimize these estimators which can then be used to analyse high-resolution maps in a very fast and accurate way."
 We generalize the PCL-based approach here to compute the cross-correlation of different data sets., We generalize the PCL-based approach here to compute the cross-correlation of different data sets.
 The method developed here is completely general and can be applied to an arbitrary number ofdata sets., The method developed here is completely general and can be applied to an arbitrary number of data sets.
 For example. our formalism can analyse the degree of cross-correlation among various CMB surveys observing the same region of the sky with different noise levels and survey strategies.," For example, our formalism can analyse the degree of cross-correlation among various CMB surveys observing the same region of the sky with different noise levels and survey strategies."
 For near-Gaussian fields. two-point analysis from any cosmological survey provides the bulk of the cosmological information.," For near-Gaussian fields, two-point analysis from any cosmological survey provides the bulk of the cosmological information."
 Nevertheless. going one step further. at the level of three-point correlation. the detection of departure from Gaussianity in the CMB can probe both primary non-Gaussianity see (e.g. Munshi&Heavens (2009))) as well as the mode-coupling effects due to secondaries.," Nevertheless, going one step further, at the level of three-point correlation, the detection of departure from Gaussianity in the CMB can probe both primary non-Gaussianity see (e.g. \cite{MuHe09}) ) as well as the mode-coupling effects due to secondaries."
 The possibility of further improving a detection of primordial non-Gaussianity with CMB maps. given current hints with WMAP data (Yadav&Wandelt2008:Smith.SenatoreZaldarriaga2009). provides further motivation in this direction.," The possibility of further improving a detection of primordial non-Gaussianity with CMB maps, given current hints with WMAP data \citep{YaWa08,SmSeZa09}, provides further motivation in this direction."
 One of the prominent contributions to the secondary non-Gaussianity is the coupling of weak lensing and sources of secondary contributions such as SZ (Goldberg&Spergel1999:CoorayHu2000).," One of the prominent contributions to the secondary non-Gaussianity is the coupling of weak lensing and sources of secondary contributions such as SZ \citep{GoldbergSpergel99,CoorayHu}."
. Although weak lensing produces a characteristic signature in the CMB angular power spectrum. its detection has proved to be difficult internally from CMB power spectrum alone.," Although weak lensing produces a characteristic signature in the CMB angular power spectrum, its detection has proved to be difficult internally from CMB power spectrum alone."
 The non-Gaussianity imprinted by lensing into the primordial CMB remains below the detection level of current experiments. although with Planck the situation is likely to improve.," The non-Gaussianity imprinted by lensing into the primordial CMB remains below the detection level of current experiments, although with Planck the situation is likely to improve."
 The difficulty originates mainly due to the fact that such detections are linked to the four-point statistics of the lensing potential., The difficulty originates mainly due to the fact that such detections are linked to the four-point statistics of the lensing potential.
 However cross-correlating CMB data with external tracers means lensing signals can be probed at the level of the mixed bispectrum., However cross-correlating CMB data with external tracers means lensing signals can be probed at the level of the mixed bispectrum.
 After the first unsuccessful attempt to cross-correlate WMAP against SDSS. recent efforts by Smith.Zahn&Dore(2007) have found a clear signal of weak lensing of the CMB. by cross-correlating WMAP against NVSS which covers a significant fraction of the sky.," After the first unsuccessful attempt to cross-correlate WMAP against SDSS, recent efforts by \cite{SmZaDo00} have found a clear signal of weak lensing of the CMB, by cross-correlating WMAP against NVSS which covers a significant fraction of the sky."
 Their work also underlines the link between three-point statistics estimators and the estimators for weak lensing effects on CMB., Their work also underlines the link between three-point statistics estimators and the estimators for weak lensing effects on CMB.
 The study of non-Gaussianity is primarily focused on the bispectrum (Heavens1998). however in practice it is difficult to probe the entire configuration dependence in the harmonic space from noisy data.," The study of non-Gaussianity is primarily focused on the bispectrum \citep{Heav98}, however in practice it is difficult to probe the entire configuration dependence in the harmonic space from noisy data."
 The cumulant correlators are multi-point correlators collapsed to probe two-point statistic., The cumulant correlators are multi-point correlators collapsed to probe two-point statistic.
 These were introduced in the context of analyzing galaxy clustering by Szapudi&Szalay(1999). and were later found to be useful for analyzing projected surveys such as APM (Munshi.Melott&Coles2000).," These were introduced in the context of analyzing galaxy clustering by \citet{Szapudi}, and were later found to be useful for analyzing projected surveys such as APM \citep{Mun}."
. Being two-point statistics they can be analyzed in the multipole space by defining an associated power-spectrum., Being two-point statistics they can be analyzed in the multipole space by defining an associated power-spectrum.
 Recent studies by Cooray(2006) and Cooray.Li&Melchiorri(2008) have shown its wider applicability including e.g. in 21em studies., Recent studies by \cite{Cooray3} and \citet{Cooray8} have shown its wider applicability including e.g. in 21cm studies.
 However. the multi-spectrum elements defined in multipole space are difficult to estimate directly from the data because of their complicated response to partial sky coverage and inhomogeneous noise. as well as associated high redundancy in the information content.," However, the multi-spectrum elements defined in multipole space are difficult to estimate directly from the data because of their complicated response to partial sky coverage and inhomogeneous noise, as well as associated high redundancy in the information content."
 However such issues are well understood in the context of power-spectrum analysis., However such issues are well understood in the context of power-spectrum analysis.
 Borrowing from previous results. in this paper we show how the cross-power spectrum and the skew spectrum can be studied in real data in an optimal way.," Borrowing from previous results, in this paper we show how the cross-power spectrum and the skew spectrum can be studied in real data in an optimal way."
 We concentrate on two effects: the cross-correlation power spectrum. which is recovered by cross-correlating two different (but possibly correlated) data sets. focussing on weak lensing effects on the CMB. and secondly the contributions to the skew spectrum from foreground effects.," We concentrate on two effects: the cross-correlation power spectrum, which is recovered by cross-correlating two different (but possibly correlated) data sets, focussing on weak lensing effects on the CMB, and secondly the contributions to the skew spectrum from foreground effects."
 The relation of such cross-power spectrum estimators with higher-order such as the bispectrum is also discussed in the context of methods known as pseudo-C 7s and quadratic estimators., The relation of such cross-power spectrum estimators with higher-order multi-spectra such as the bispectrum is also discussed in the context of methods known as $C_l$ s and quadratic estimators.
 We derive the error-covariance matrices and diseuss their validity in the signal- and noise-dominated regimes and comment on their relationship to the Fisher matrix., We derive the error-covariance matrices and discuss their validity in the signal- and noise-dominated regimes and comment on their relationship to the Fisher matrix.
 This layout of the paper is as follows: in $22 we use the formalism based on Pseudo-C; analysis for power-spectra to study the cross-correlation power spectrum of different data sets., This layout of the paper is as follows: in 2 we use the formalism based on ${\cal C}_{\ell}$ analysis for power-spectra to study the cross-correlation power spectrum of different data sets.
 While we keep the analysis completely general. it is specialized for the ease of near all-sky analysis and use it to compute the signal-to-noise and the covariance of estimated Cys for various tracers with Planck-type all-sky experiments.," While we keep the analysis completely general, it is specialized for the case of near all-sky analysis and use it to compute the signal-to-noise and the covariance of estimated ${\cal C}_l$ s for various tracers with Planck-type all-sky experiments."
" Possibilities of using various weights which can make the pseudo-C, approach near optimal in limiting cases of the signal-dominated regime or the noise-dominated regime are also discussed.", Possibilities of using various weights which can make the ${\cal C}_{\ell}$ approach near optimal in limiting cases of the signal-dominated regime or the noise-dominated regime are also discussed.
 In $33 we continue our discussion on Pseudo-C; but generalize it to the analysis of the skew spectrum., In 3 we continue our discussion on ${\cal C}_{\ell}$ but generalize it to the analysis of the skew spectrum.
 Such an estimator can handle he partial sky coverage and noise in a very straightforward way., Such an estimator can handle the partial sky coverage and noise in a very straightforward way.
 However in general it remains sub-optimal., However in general it remains sub-optimal.
" In the high-/ regime where mode-mode coupling ean be modelled using a fraction of sky fon, proxy one can make such an estimator nearly optimum using a suitable weighting.", In the $l$ regime where mode-mode coupling can be modelled using a fraction of sky $f_{sky}$ proxy one can make such an estimator nearly optimum using a suitable weighting.
 After à very brief introduction to various physical effects in S44 which introduce mode-mode coupling that leads to CMB bispeetra. we move on to develop a crude but fast estimator for the skew spectrum in 355.," After a very brief introduction to various physical effects in 4 which introduce mode-mode coupling that leads to CMB bispectra, we move on to develop a crude but fast estimator for the skew spectrum in 5."
 Section $66 is devoted to developing the mixed bispectrum analysis in an optimal way by introducing inverse covariance Weighting of the data., Section 6 is devoted to developing the mixed bispectrum analysis in an optimal way by introducing inverse covariance weighting of the data.
 We analyze both one-point and two-point collapsed bispectral analysis., We analyze both one-point and two-point collapsed bispectral analysis.
 The one-point estimator or the mixed skewness is introduced - being a one point estimator it compresses all available information in a bispectrum to a single number., The one-point estimator or the mixed skewness is introduced - being a one point estimator it compresses all available information in a bispectrum to a single number.
 Next. we introduce he mixed skew spectrum which compresses various components of a bispectrum to a power spectrum in an optimum way.," Next, we introduce the mixed skew spectrum which compresses various components of a bispectrum to a power spectrum in an optimum way."
 Next. in $77. the general ormalism of bispectral analysis is used for specific cases of interest.," Next, in 7, the general formalism of bispectral analysis is used for specific cases of interest."
" In this section we generalise results from pseudo-C, power spectrum estimation of a single field with partial sky coverage. to cross-power spectra of"," In this section we generalise results from ${\cal {C}}_\ell$ power spectrum estimation of a single field with partial sky coverage, to cross-power spectra of"
 A fundamental computational problem in astrophysics is the motion of a cloud. of gas forming a protostar in an ambient medium which is tvpically lower in density by a factor of <1077., A fundamental computational problem in astrophysics is the motion of a cloud of gas forming a protostar in an ambient medium which is typically lower in density by a factor of $< 10^{12} $.
 The ambient. medium. can therefore be treated as a vacuum to an excellent: approximation., The ambient medium can therefore be treated as a vacuum to an excellent approximation.
 The simulation of such a eas cloud is more οΠο than many of the stancarc battery of test. problems considered in computational astrophysics., The simulation of such a gas cloud is more difficult than many of the standard battery of test problems considered in computational astrophysics.
 Exact. or very accurate. solutions for the motion of these gas clouds are rare and this creates further cdillieulties in assessing the accuracy of a numerical algorithm.," Exact, or very accurate, solutions for the motion of these gas clouds are rare and this creates further difficulties in assessing the accuracy of a numerical algorithm."
 In this paper we fill this gap in test cases by stucying solutions and simulations for the class of models which we have called Tov Stars., In this paper we fill this gap in test cases by studying solutions and simulations for the class of models which we have called Toy Stars.
 They are. first and foremost. a tool for studying the accuracy of computational algorithms relevan to astrophysical gas dynamics but they. also provide an interesting class of dynamical systems where exact solutions can be found.," They are, first and foremost, a tool for studying the accuracy of computational algorithms relevant to astrophysical gas dynamics but they also provide an interesting class of dynamical systems where exact solutions can be found."
 “Phe fundamental aspects of “Tow Stars ane a variety of one dimensional solutions have been cliscussec by?., The fundamental aspects of Toy Stars and a variety of one dimensional solutions have been discussed by.
. The key features are that they are gas masses where compressibility is. included: without. approximation. but gravity is replaced by a force derived (rom the potentia where vis a constant. m; is themass of particle 7 and it is assumed that there are N masses.," The key features are that they are gas masses where compressibility is included without approximation, but gravity is replaced by a force derived from the potential where $\nu$ is a constant, $m_i$ is themass of particle $i$ and it is assumed that there are $N$ masses."
 The equation of motion of particle j in the absence of other forces is where AZ is the total mass and the origin is the centre of mass., The equation of motion of particle $j$ in the absence of other forces is where $M$ is the total mass and the origin is the centre of mass.
 Remarkably. as first noted by Newton2).. the particles moveindependently about the centre of mass of the particle system.," Remarkably, as first noted by Newton, the particles move about the centre of mass of the particle system."
 Two particles in a binary Tov Star system move on orbits given by the solutions of the following equation for the relative coordinate r—ryτο These solutions are closed. Lissajous figures which include elliptical orbits., Two particles in a binary Toy Star system move on orbits given by the solutions of the following equation for the relative coordinate ${\bf r = r_1 - r_2}$ These solutions are closed Lissajous figures which include elliptical orbits.
 The equations of motion of a gaseous system in a Γον Star force are the acceleration equation where O7=Mp. P is the pressure and. p the density. and the continuity. equation IP=Αρ this equation. together with the continuity equation is identical to the equation for small oscillations of water in a lake with paraboloidal bottom.," The equations of motion of a gaseous system in a Toy Star force are the acceleration equation where $\Omega^2 = M \nu $, $P$ is the pressure and $\rho$ the density, and the continuity equation If $P = K \rho^2$ this equation together with the continuity equation is identical to the equation for small oscillations of water in a lake with paraboloidal bottom."
 This equation has been studied by and?7.. but. the most. important contributions were made by and7.," This equation has been studied by and, but the most important contributions were made by and."
. In this paper we focus on the aspects of these equations. which are most important for astrophysical problems. ancl generalise to the case where P= p.," In this paper we focus on the aspects of these equations which are most important for astrophysical problems, and generalise to the case where $P = K \rho^\gamma$ ."
 In the following we first consider the small amplitude, In the following we first consider the small amplitude
"that iis not entirely ""dead"" but is forming stars in the spiral arms.",that is not entirely “dead” but is forming stars in the spiral arms.
 The amount of star formation is difficult to quantify and depends on the assumed reddening: assuming £(B—V)~0.3 itis ~20 yr!., The amount of star formation is difficult to quantify and depends on the assumed reddening; assuming $E(B-V)\sim 0.3$ it is $\sim 20$ $^{-1}$.
" The WFC3 grism and imaging data of mmay provide ""smoking gun"" evidence for minor mergers as an important growth mechanism of massive galaxies: lis à massive. compact galaxy at z~2 which is interacting with a ~IO. less massive companion."," The WFC3 grism and imaging data of may provide “smoking gun” evidence for minor mergers as an important growth mechanism of massive galaxies: is a massive, compact galaxy at $z\sim 2$ which is interacting with a $\sim 10\times$ less massive companion."
 The quiescent spectrum of the primary galaxy is qualitatively consistent with the spectra of other compact high redshift galaxies and with the old stellar ages of present-day early-type galaxies., The quiescent spectrum of the primary galaxy is qualitatively consistent with the spectra of other compact high redshift galaxies and with the old stellar ages of present-day early-type galaxies.
 This mode of growth has been proposed by several recent studies to explain the size difference between massive galaxies at high redshift and low redshift (e.g.. 2009: 2009).," This mode of growth has been proposed by several recent studies to explain the size difference between massive galaxies at high redshift and low redshift (e.g., 2009; 2009)."
 Nearby ellipticals have gradients in. their color and metallicity. such that they are bluer and more metal-poor at larger radi (e.g..Franx.Hlingworth. 1989).," Nearby ellipticals have gradients in their color and metallicity, such that they are bluer and more metal-poor at larger radii (e.g., 1989)."
 Interestingly. we can begin to address the origin of these gradients with the kind of data that we are now getting from HST.," Interestingly, we can begin to address the origin of these gradients with the kind of data that we are now getting from HST."
 The relatively strong oxygen lines and weak H./ of the infalling galaxy imply logR53—|. and a metallicity that is z1/3 times the Solar value 2005).," The relatively strong oxygen lines and weak $\beta$ of the infalling galaxy imply $\log R_{23}\sim 1$, and a metallicity that is $\gtrsim 1/3$ times the Solar value 2005)."
 The spectrum extracted from the disk of hhas. by contrast. no detected oxygen limes and an unambiguous detection of H./.," The spectrum extracted from the disk of has, by contrast, no detected oxygen lines and an unambiguous detection of $\beta$."
 It has logR»s<=0. which implies a Solar or super-Solar metallicity.," It has $\log R_{23}\lesssim 0$, which implies a Solar or super-Solar metallicity."
 Qualitatively these results are consistent with the idea that the metallicity gradients of elliptical galaxies reflect a gradual increase with, Qualitatively these results are consistent with the idea that the metallicity gradients of elliptical galaxies reflect a gradual increase with
Since the detection of the first extra-solar planet orbiting a solar-like star in 1995. 51 Pee,"Since the detection of the first extra-solar planet orbiting a solar-like star in 1995, 51 Peg"
features.,features.
 Our results show that these modes are not excited bv the racdiation-warpiug torque., Our results show that these modes are not excited by the radiation-warping torque.
 The two lowest-order ΗΕΝΤ precession 1iodes involve vertical motions of the iuner edee of the disk., The two lowest-order HFGM precession modes involve vertical motions of the inner edge of the disk.
 This offers a possible wav of exciting them., This offers a possible way of exciting them.
 Iu order to excite steadily either of these two modes. a torque acting ou the inner edee of the disk would have to match he variation of their phases with azimuth as well as heir frequencies.," In order to excite steadily either of these two modes, a torque acting on the inner edge of the disk would have to match the variation of their phases with azimuth as well as their frequencies."
 Ou the other hand. coupling of the vertical motion to the radiation field. maeuetic field. or surface of a neutron star nav instead damp these nodes.," On the other hand, coupling of the vertical motion to the radiation field, magnetic field, or surface of a neutron star may instead damp these modes."
 The two lowest DFCOAL modes might also be excited w repetitive impulsive disturbance of the ier disk., The two lowest HFGM modes might also be excited by repetitive impulsive disturbance of the inner disk.
 If. however. such disturbances affect the immer portion of the disk as well as its iunerimost edee. they may excite the broad spectrum of underdamped UTFCAL modes. rather than one or two such modes. producing a broac spectrum rather than a QPO.," If, however, such disturbances affect the inner portion of the disk as well as its innermost edge, they may excite the broad spectrum of underdamped HFGM modes, rather than one or two such modes, producing a broad spectrum rather than a QPO."
 Resonaut excitation of the m)>2 [IFGM nodes appears difficult. because hey do not disturb the inner edee of the disk.," Resonant excitation of the $m>2$ HFGM modes appears difficult, because they do not disturb the inner edge of the disk."
 In order to excite these nodes steadily. the driiugs force would have to match closely the extremely rapid variation of their plases with radius and azimuth. as well as their frequencies.," In order to excite these modes steadily, the driving force would have to match closely the extremely rapid variation of their phases with radius and azimuth, as well as their frequencies."
 The highest-order ITFGAL modes do not appear o»ronising as a niecliaudsun for producing quasi-periodic oscillations i X-rav brightuess. because they are very ightly wound spiral corrugations within a narrow anuulus centered at a racius  5 times larger than the radius ofthe immer edge of the accretion disk aud do iot affect the accretion disk at its iuner edge.," The highest-order HFGM modes do not appear promising as a mechanism for producing quasi-periodic oscillations in X-ray brightness, because they are very tightly wound spiral corrugations within a narrow annulus centered at a radius $\sim\,$ 5 times larger than the radius of the inner edge of the accretion disk and do not affect the accretion disk at its inner edge."
 Ou their race. the lowest-order ΠΕΝΤΕ modes appear more capable of causing oscillations iu the N-rayv cussion. or example by modulating the accretion onto the compact object.," On their face, the lowest-order HFGM modes appear more capable of causing oscillations in the X-ray emission, for example by modulating the accretion onto the compact object."
 Ainore complete exploration of the detailed properties of the Ligl-order radiation-awarping LFCM modes. LFGAIR modes. aud. IIECOM. modes will be preseuted elsewhere.," A more complete exploration of the detailed properties of the high-order radiation-warping LFGM modes, LFGMR modes, and HFGM modes will be presented elsewhere."
 We are erateful to Philip Maloney. Cole Miller. and Dimitrios Psaltis for may helpful coments. aud to Cole Miller for computing the moments of inertia used in Ll.," We are grateful to Philip Maloney, Cole Miller, and Dimitrios Psaltis for many helpful comments, and to Cole Miller for computing the moments of inertia used in 4."
 This work was supported in part bv NSF erants AST 93-15133 aud AST 96-18521 aud by NASA eraut NAC 5-2925., This work was supported in part by NSF grants AST 93-15133 and AST 96-18524 and by NASA grant NAG 5-2925.
This is the only galaxy with spectroscopic confirmation in the sample of Stiavellietal.(2005).,This is the only galaxy with spectroscopic confirmation in the sample of \citet{st5}.
. We detect a clear (~ 150) emission line (see Fig. 1)), We detect a clear $\sim 15 \sigma$ ) emission line (see Fig. \ref{fig:target1}) )
" which we identify as aat ZLya=5.973+0.002, in good agreement with the redshift ZLya=5.970 reported by Stiavellietal. (2005)."," which we identify as at $z_{\rm Ly\alpha}=5.973\pm 0.002$, in good agreement with the redshift $z_{\rm Ly\alpha}=5.970$ reported by \citet{st5}. ."
". The total line flux is Fuya=22+1.5x10? eerg s~*cm~?,, measured by integrating over ~23 ((~800 kms)) of the spectrum; it is not possible to compare with the data by Stiavellietal.(2005) because these authors did not report a measurement of the line flux."," The total line flux is $F_{\rm Ly\alpha}=22 \pm 1.5\,\times 10^{-18}$ erg $^{-1}$, measured by integrating over $\sim 23$ $\sim 800$ ) of the spectrum; it is not possible to compare with the data by \citet{st5}
 because these authors did not report a measurement of the line flux."
" The lline flux corresponds to a luminosity [γα=8.640.6x107? eerg s! in our cosmology, and a star formation rate SFRr,4=7.8t0.5 yr! with the conversion (and caveats) given above (see MMeTable 1))."," The line flux corresponds to a luminosity $L_{\rm Ly\alpha}=8.6\pm 0.6\,\times 10^{42}$ erg $^{-1}$ in our cosmology, and a star formation rate $_{\rm Ly\alpha}= 7.8\pm 0.5$ $_{\sun}$ $^{-1}$ with the conversion (and caveats) given above (see Table \ref{mag}) )."
" As can be seen from Fig. 2,,"," As can be seen from Fig. \ref{fig:target2},"
 we detect a weak and narrow emission line which we interpret as eemission at z=5.676+0.002., we detect a weak and narrow emission line which we interpret as emission at $z = 5.676\pm 0.002$.
" With a line flux 4.91.1x107! eerg s!cm,, the detection is significant at the ~4.5c level."," With a line flux $F_{\rm Ly\alpha}=4.9\pm 1.1 \times 10^{-18}$ erg $^{-1}$, the detection is significant at the $\sim 4.5 \sigma$ level."
" Although the line is weak, it does fall in a relatively clean region of the spectrum, free from obvious residuals from the subtraction of sky emission lines (see top panel of Fig. 2))."," Although the line is weak, it does fall in a relatively clean region of the spectrum, free from obvious residuals from the subtraction of sky emission lines (see top panel of Fig. \ref{fig:target2}) )."
" The corresponding luminosity and star formation rate are, respectively, Liy4=1.740.4x10? eerg s! and SFRiya= 1.6+40.4MMg yr! (see Table 1))."," The corresponding luminosity and star formation rate are, respectively, $L_{\rm Ly\alpha}=1.7 \pm 0.4 \times 10^{42}$ erg $^{-1}$ and $_{\rm Ly\alpha} = 1.6\pm 0.4$ $_{\sun}$ $^{-1}$ (see Table \ref{mag}) )."
 The line has ~150 aafter correcting for the instrumental resolution., The line has $\simeq 150$ after correcting for the instrumental resolution.
" Although this galaxy is relatively close to the QSO sight-line, at a projected distance of kkpc, no aabsorption at its redshift was reported by either Ryan- nor Simcoeetal.(2011)."," Although this galaxy is relatively close to the QSO sight-line, at a projected distance of kpc, no absorption at its redshift was reported by either \citet{rw6} nor \citet{si+11}."
". At a projected distance of kkpc, this galaxy is the closest to the QSO sight-line among the three galaxies targeted by our observations."," At a projected distance of kpc, this galaxy is the closest to the QSO sight-line among the three galaxies targeted by our observations."
" We detect a weak emission line centred at λους=8168 AA,, in a clean region of the spectrum, free from strong sky line residuals (see Fig. 3))."," We detect a weak emission line centred at $\lambda_{\rm obs} = 8168$ , in a clean region of the spectrum, free from strong sky line residuals (see Fig. \ref{fig:target3}) )."
" We identify the feature as eemission at z=5.719+0.002, with a flux Flya=4.340.9x1075 eerg s! ((~4.80 level detection)."," We identify the feature as emission at $z = 5.719 \pm 0.002$, with a flux $F_{\rm Ly\alpha}=4.3 \pm 0.9 \times 10^{-18}$ erg $^{-1}$ $\sim 4.8 \sigma$ level detection)."
" This corresponds to a luminosity Ίπγα=1.530.3x10“ eerg s! and star formation rate SFRL,4=1.40.3 yr!.", This corresponds to a luminosity $L_{\rm Ly\alpha}=1.5 \pm 0.3\times 10^{42}$ erg $^{-1}$ and star formation rate $_{\rm Ly\alpha}= 1.4 \pm 0.3$ $_{\sun}$ $^{-1}$.
" The emission line MMGredshift differs by Av=—214 ffrom the redshift zaps=5.7238+0.0001 of the strongest absorption system in the spectrum of the QSO, with column density ,22.8x10! citeprw6.."," The emission line redshift differs by $\Delta v = -214$ from the redshift $z_{\rm abs} = 5.7238 \pm 0.0001$ of the strongest absorption system in the spectrum of the QSO, with column density $= 2.3\,\times 10^{14}$ \\citep{rw6}."
" More recently, Simcoeetal.(2011) reported Zabs=5.72438, corresponding to Av=—240kms,, and =8.9x10!Nery ffor this absorber, measured from near-IR spectra obtained with the Folded Port Infrared Echellette (FIRE) instrument on the mm Magellan telescope."," More recently, \citet{si+11} reported $z_{\rm abs} = 5.72438$, corresponding to $\Delta v = -240$, and $= 3.9\,\times 10^{14}$ for this absorber, measured from near-IR spectra obtained with the Folded Port Infrared Echellette (FIRE) instrument on the m Magellan telescope."
" The velocity difference between the eemission line and the ssystem may be due to random error (~ 2-30)and/or systematic errors in the wavelength scale of either the FORS2 spectrum reported here or the near-IR spectra analysed by Ryan-Weber,Pettini&Madau(2006)and Simcoeetal.(2011)..", The velocity difference between the emission line and the system may be due to random error $\sim 2$ $3 \sigma$ )and/or systematic errors in the wavelength scale of either the FORS2 spectrum reported here or the near-IR spectra analysed by \citet{rw6} and \citet{si+11}.
" Alternatively, it may be an indication that the geometry of the outflowing (or perhaps inflowing) gas associated with this galaxy is not spherically symmetric."," Alternatively, it may be an indication that the geometry of the outflowing (or perhaps inflowing) gas associated with this galaxy is not spherically symmetric."
 The velocity offset could be larger if the, The velocity offset could be larger if the
and. for simple poles. their residues are Here we have simplified the expression by defining the determinant factor The arguments as to the choice of contours apply exactly as before. since the imaginary part of the poles remains unchanged from Eq. (18)),"and, for simple poles, their residues are Here we have simplified the expression by defining the determinant factor The arguments as to the choice of contours apply exactly as before, since the imaginary part of the poles remains unchanged from Eq. \ref{eq:derivation_poles}) )"
 to Eq. (58))., to Eq. \ref{eq:bivar_derivation_poles}) ).
" Thus. poles with positive C,5 factors lie within the lower contour. whereas those with negative C,» lie within the upper contour."," Thus, poles with positive $C_{n2}$ factors lie within the lower contour, whereas those with negative $C_{n2}$ lie within the upper contour."
" The corresponding Heaviside factors encoding this behaviour are H(é)H(C,>) andH(-&)H(-C,.).", The corresponding Heaviside factors encoding this behaviour are $H(\xi_2)H(C_{n2})$ and$H(-\xi_2)H(-C_{n2})$.
" The winding numbers are wy,=| for the upper and w,,=--ἰ for the lower contour.", The winding numbers are $w_n=1$ for the upper and $w_n=-1$ for the lower contour.
 So we obtain the full integral as The remaining task is to calculate the second integral., So we obtain the full integral as The remaining task is to calculate the second integral.
 For ease of notation. we will substitute s;—s and introduce the new variables Then. the second integral can be reduced to the calculation of the term This integral has poles at η=-1Brn.," For ease of notation, we will substitute $s_1 \rightarrow s$ and introduce the new variables Then, the second integral can be reduced to the calculation of the term This integral has poles at $s_{nm} = -\iu \, \beta_{nm}$."
 For simple poles. the residues are Furthermore. the choice of contours is also very similar to the previous procedure.," For simple poles, the residues are Furthermore, the choice of contours is also very similar to the previous procedure."
" We will again close the contour with semi-circles m either the upper or the lower half-plane. and the purely Imaginary poles s,,=—15,,; lead. by the same convergence argument. to Heaviside factors H(o,)H(Bj) for the contour in the lower half-plane and H(—o,)H(-f,,) for the contour in the upper half-plane."," We will again close the contour with semi-circles in either the upper or the lower half-plane, and the purely imaginary poles $s_{nm} = -\iu \, \beta_{nm}$ lead, by the same convergence argument, to Heaviside factors $H(\alpha_n)H(\,\beta_{nm})$ for the contour in the lower half-plane and $H(-\alpha_n)H(-\beta_{nm})$ for the contour in the upper half-plane."
" With the usual winding numbers w,=+1. the integral is Reinserting this result into the full expression (61)). the bivariate probability distribution function is where we used a shorthand notation for all of the Heaviside factors: Finally. we can bring this expression to a more symmetric form by reinserting the £,,, and shifting around some factors: This derivation is only valid if. in both integrations. none of the poles vanish or are of higher order."," With the usual winding numbers $w_n = \pm 1$, the integral is Reinserting this result into the full expression \ref{eq:bivar_derivation_firstintegral}) ), the bivariate probability distribution function is where we used a shorthand notation for all of the Heaviside factors: Finally, we can bring this expression to a more symmetric form by reinserting the $\beta_{nm}$ and shifting around some factors: This derivation is only valid if, in both integrations, none of the poles vanish or are of higher order."
 But like we do for the univariate distribution in appendix Appendix A:.. we can find corrections to get the most general result.," But like we do for the univariate distribution in appendix \ref{sec:multipoles}, , we can find corrections to get the most general result."
 In. this, In this
the three principal structures in the May98 and May&JJune98 amplitude spectrum. at 650 s. 370 s and 230 s. aswon). andwy.,"the three principal structures in the May98 and June98 amplitude spectrum, at 650 s, 370 s and 230 s, as, and."
 However. we show below that each of these is a multiplet consisting of more than one frequency.," However, we show below that each of these is a multiplet consisting of more than one frequency."
 In Table 2 we list all the signals present in each amplitude spectrum., In Table 2 we list all the signals present in each amplitude spectrum.
 Each signal consists of a set of aliases (ambiguities caused by gaps in the data). and Table 2 lists only the highest- alias for each signal.," Each signal consists of a set of aliases (ambiguities caused by gaps in the data), and Table 2 lists only the highest-amplitude alias for each signal."
 There is ambiguity in the aliases (the highest-amplitude alias is not necessarily the true frequency). so each frequency cw in Table 2 should be read as a set of frequencies w|n11.575 Hz. where n=c1.x2.c3... and Az is the dominant |-day alias.," There is ambiguity in the aliases (the highest-amplitude alias is not necessarily the true frequency), so each frequency $\omega $ in Table 2 should be read as a set of frequencies $\omega + n \times 11.57 \mu$ Hz, where $n=\pm1,\pm2,\pm3, ...$, and $\mu$ Hz is the dominant 1-day alias."
 The procedure for determining the amplitudes and frequencies of the signals in the amplitude spectrum is as follows., The procedure for determining the amplitudes and frequencies of the signals in the amplitude spectrum is as follows.
 First. the mean and second-order trends (due to sky transparency) are removed from the light-curves. and then the amplitude spectrum is calculated.," First, the mean and second-order trends (due to sky transparency) are removed from the light-curves, and then the amplitude spectrum is calculated."
" Then. assuming there are no aliasing ambiguities. the frequency of the highest peak is fitted to the data and subtracted (a process known as ""pre-whitening)."," Then, assuming there are no aliasing ambiguities, the frequency of the highest peak is fitted to the data and subtracted (a process known as `pre-whitening')."
 The amplitude spectrum of the residuals is then computed and the process repeated until the data are consistent with noise., The amplitude spectrum of the residuals is then computed and the process repeated until the data are consistent with noise.
 The frequencies found in this way (linear combinations as well as principal frequencies) are then fitted, The frequencies found in this way (linear combinations as well as principal frequencies) are then fitted
Fig.,Fig.
 4) on a color-color diagram., 4) on a color-color diagram.
 In particular. the figure shows (vpical (J—H) vs.(HH —ἐν) value [or MT-M.5 (horizontal stripes region) and M8 or later (vertical stripes region) cwarls.," In particular, the figure shows typical $(J-H)$ vs. $(H-K_{s}$ ) value for M7-M7.5 (horizontal stripes region) and M8 or later (vertical stripes region) dwarfs."
" Most. MT-MT.5 chwarfs are around (47—IN...H)=(0.45.0.62) whereas M8-MS8.5 cbwarls are around (47—NJID)=(0.42.0.74) with similar J—ἰν, colors (although. as the vertical striped region indicates. a few M8 or later stars may have singificantlv hieher numbers)."," Most M7-M7.5 dwarfs are around $(H-K_{s}, J-H)=(0.45, 0.62)$ whereas M8-M8.5 dwarfs are around $(H-K_{s}, J-H)=(0.42,0.74)$ with similar $J-K_{s}$ colors (although, as the vertical striped region indicates, a few M8 or later stars may have singificantly higher numbers)."
 The black star in the figure shows the colors (ff—Ay.II)=(0.42x:0.10.0.74+0.07) of ihe 2MASS counterpart of the source 2XMM J043527.2-144301. indicating a spectral class of M8-M8.5.," The black star in the figure shows the colors $(H-K_{s}, J-H)=(0.42\pm0.10,0.74\pm0.07)$ of the 2MASS counterpart of the source 2XMM J043527.2-144301, indicating a spectral class of M8-M8.5."
". We note that (ο properly confirm the spectral (wpe of the source dedicated spectroscopic observations are necessary,", We note that to properly confirm the spectral type of the source dedicated spectroscopic observations are necessary.
 To determine the distance of the source. we estimated the absolute magnitude [rom the PATASS (C/—IN.) color using the relation [rom Gizis οἱ al. (," To determine the distance of the source, we estimated the absolute magnitude from the 2MASS $(J-K_{s})$ color using the relation from Gizis et al. ("
"2000). Aj,=7.5934-2.25x(JJ—ἰν.). with a scatter of ¢=0.36 magnitudes.","2000), $M_{k}=7.593+2.25\times(J-K_{s})$, with a scatter of $\sigma=0.36$ magnitudes."
 The relation is valid for only MT and later dwarls over the color range., The relation is valid for only M7 and later dwarfs over the color range.
" The source 2NMM J043527.2-144201. value of (J—IN.)=(1.160.10) eives − − ⇀∪∕⋅∶∐∟≻↓−∪⋅−≻−≻⋅⊄↧∐≼⇂∏∖⊽∐↥∩⊔∐↲⋟∖⊽↥≀↧↴∐≺⇂≀↧↴↕⋅≼⇂≺∐⋟∖⊽↥≀↧↴∐≺∢≼↲∐↕⋯⇂∏↥∏⋟∖⊽≼↲≺⇂∏≀↧↴⊔∪∐⋖⋡∣∣∣∕⋅−⇀⋃∕⋅∶↱≻↥∪↖≺↽↔↴↙↓≑⋝ we eel d,—(6T.X13) pc."," The source 2XMM J043527.2-144301 value of $(J-K_{s})=(1.16\pm0.10)$ gives $M_{k}=10.21\pm0.22$ , and using the standard distance modulus equation $(m_{k}-M_{k}=5\log \frac{d_{k}}{10})$, we get $d_{k}=(67.\pm13)$ pc."
 We note that. this distance 1s signilicantlv shorter (han the measured distance of MDBM?20 (112215 pe «d161521 pe). indicating (hat source is nol part of MBM?20. but in [ront of it.," We note that this distance is significantly shorter than the measured distance of MBM20 $(112\pm15$ pc $<d<161\pm21$ pc), indicating that source is not part of MBM20, but in front of it."
 As discussed in (he next sessions. (his is consistent with the spectral analvsis of the flares and their inferred luminosity.," As discussed in the next sessions, this is consistent with the spectral analysis of the flares and their inferred luminosity."
 Ii our subsequent. analysis we use the distance derived from the 2ATASS (JJ—N.). although we will also briefly discuss thepossibility that. instead. source 2NMM J043527.2-144301.: is part of MDMO20.," In our subsequent analysis we use the distance derived from the 2MASS $(J-K_{s})$, although we will also briefly discuss thepossibility that, instead, source 2XMM J043527.2-144301 is part of MBM20."
" Using the relation for Dolometric Correction (2.07); [rom Legget (2001). we also obtained a bolometric magnitude of Mj=U3.32dE0.43). which leads to a bolometric Inminositv of Loy=(1.4d0.6)x10"" erg st."," Using the relation for Bolometric Correction $(B.C.)_k$ from Legget (2001), we also obtained a bolometric magnitude of $M_{bol} = (13.32\pm 0.43)$, which leads to a bolometric luminosity of $L_{bol}=(1.4\pm0.6)\times 10^{30}$ erg $^{-1}$."
 We then used the near-IR. colors to estimate the radius. elfective temperature ancl mass of the source 2XMM J043527.2-144301.," We then used the near-IR colors to estimate the radius, effective temperature and mass of the source 2XMM J043527.2-144301."
" Assiuming a tvpical ultracool age of 7 «2 (o 3 Gvrs. we used the relation from Dalin οἱ al.(2002). R/R.=0.088+NM0.000700(16.2m—AL,2°. which predies radii lor objects with age between 1 Gyr and 5 Gyr over range 12-16.5 in My. to caleulated Che radius of the source: With the calculated values of luminosity and radius. we also determined the effective temperature of the source as 7;jj=(24792275) I. which is (vpical for an ultracool M dw."," Assuming a typical ultracool dwarfs age of $\tau<$ 2 to 3 Gyrs, we used the relation from Dahn et al.(2002), $R/R_{\odot}=0.088+0.00070(16.2-M_{bol})^{2.9}$, which predics radii for objects with age between 1 Gyr and 5 Gyr over the range 12-16.5 in $M_{bol}$, to calculated the radius of the source: With the calculated values of luminosity and radius, we also determined the effective temperature of the source as $T_{eff}=(2479\pm275)$ K, which is typical for an ultracool M dwarf."
" Using (he relationships lor Mass vs. Al, aud Mass vs. speetral-(wpe Irom Chabrier et al. (", Using the relationships for Mass vs. $_k$ and Mass vs. spectral-type from Chabrier et al. (
2000 - their Figs.,2000 - their Figs.
 9 10 respectivelv). we found (hat the mass of 2NMM J043527.2-144301. is inthe range (0.007.—0.082.U.. ). suggesting that the object is near the stellar/substellar (ransilion.," 9 10 respectively), we found that the mass of 2XMM J043527.2-144301 is inthe range $(0.079 M_{\odot} - 0.083 M_{\odot})$ , suggesting that the object is near the stellar/substellar transition."
This triple system is the most intrigmine of the three proeranm stars.,This triple system is the most intriguing of the three program stars.
 Its CATÀ-like spectra show that the three conrponeuts are quite simular in femiperature. eravity and huunünositv (cf.," Its GAIA-like spectra show that the three components are quite similar in temperature, gravity and luminosity (cf."
 Fig., Fig.
 1)., 1).
 Tweho-2 photometry (BVoy = 0.163 trausformis to (5Vy) = 0.39 and. supposing all three components have equal temperatures. it sugeests Fl spectral types. in good agreeineut with the F5 ype reported in SIMIBAD and the spectral appearance in Fie.," Tycho-2 photometry $(B-V)_{\rm T}$ = 0.463 transforms to $(B-V)_{\rm J}$ = 0.39 and, supposing all three components have equal temperatures, it suggests $-$ F4 spectral types, in good agreement with the $-$ F5 type reported in SIMBAD and the spectral appearance in Fig."
 l., 1.
 The adopted Dug. was 6500 I. Eclipses are quite well mappe by Lp photometry aud the secondary cluperature was thus adjusted.," The adopted $T_{\rm eff,1}$ was 6500 K. Eclipses are quite well mapped by $H_{\rm P}$ photometry and the secondary temperature was thus adjusted."
" The contribution of the hird body to the Πο curve was taken iuto account wv adding a constant third lieht. 7, = 29(46)% of the otal fux."," The contribution of the third body to the light curve was taken into account by adding a constant third light, $l_{3}$ = $\pm$ of the total flux."
" The derived temperatures (Tug. = 6500 Ix. Tigo = 6155 IK). masses (AL, = Mo = 1.0L AL.) aud radii (Ry = Lao R.. Ro = LSER.) show that the coniponeu.. of the close dunry are virtually identical (within the quoted formal errors) and mareially evolved away from the MS."," The derived temperatures $T_{\rm
eff,1}$ = 6500 K, $T_{\rm eff,2}$ = 6455 K), masses $M_{1}$ = $M_{2}$ = 1.04 $M_{\odot}$ ) and radii $R_{1}$ = 1.80 $R_{\odot}$, $R_{2}$ = 1.84 $R_{\odot}$ ) show that the components of the close binary are virtually identical (within the quoted formal errors) and marginally evolved away from the MS."
 The third yodyv 11621 racial velocity IB kau/sec) is consistent with the svstemic velocity of the close pair (NV. = 156405 kin/sec)., The third body mean radial velocity $-13\pm1$ km/sec) is consistent with the systemic velocity of the close pair $_{\gamma}$ = $-15.6\pm0.5$ km/sec).
 A period search has failed to reveal a clear periodicity in the radial velocities of the third )ody. Which linited ranec of radial velocities displaved in our spectra (21 iau/sec} cau be caused by au orbital period much longer than the time spanned by our observations (3.2 vr) and/or a low orbital ποιαοι.," A period search has failed to reveal a clear periodicity in the radial velocities of the third body, which limited range of radial velocities displayed in our spectra (21 km/sec) can be caused by an orbital period much longer than the time spanned by our observations (3.2 yr) and/or a low orbital inclination."
 The three targets were chosen withou restricfions on peculiarities or variability and faint chough so that Tycho 2 photometry is useful oulv iu providing lean colors and uot epoch data., The three targets were chosen without restrictions on peculiarities or variability and faint enough so that Tycho 2 photometry is useful only in providing mean colors and not epoch data.
 Oulv ZZp data were therefore available to aap the lehteurve. which compromised the accuracy of derived effective. temperatures of the components (both the absolute scale ane the differcuce).," Only $H_P$ data were therefore available to map the lightcurve, which compromised the accuracy of derived effective temperatures of the components (both the absolute scale and the difference)."
 Even under such limitations (aiming to simulate CATA observations of targets more difficult that those explored in Paper I aud II of this series) reasonable solutions have been achieved for all the three targets. with the distance nuplied by the orbital modeling within the uucertaimty bar of the Ilipparcos parallax for all the three stars. including the equal uasses triple svsteiu.," Even under such limitations (aiming to simulate GAIA observations of targets more difficult that those explored in Paper I and II of this series) reasonable solutions have been achieved for all the three targets, with the distance implied by the orbital modeling within the uncertainty bar of the Hipparcos parallax for all the three stars, including the equal masses triple system."
" This reassuring external aud independent cleck reinforces the expectation of a high impact of CALA observations for the derivation of fundamental stellar properties frou, observations of eclipsing binaries. aud the direct use of CATA observations of eclipsing binarics as a valuable measure of distances mn itself."," This reassuring external and independent check reinforces the expectation of a high impact of GAIA observations for the derivation of fundamental stellar properties from observations of eclipsing binaries, and the direct use of GAIA observations of eclipsing binaries as a valuable measure of distances in itself."
leads to (where the radio power is measured at. 1.4 ΟΙ and given in W/llz/sr]. units)) which shows that racdüo luminosity. and black hole mass are very loosely correlated since the dependence — ifany — between these two quantities is much weaker than in the black hole/optical luminosity The above results can be interpreted as evidence for the fact that while optical/nuclear emission is directly related to the mass of the black hole that produces the quasar signal. radio luminosity is not.,"leads to (where the radio power is measured at 1.4 GHz and given in [W/Hz/sr] units), which shows that radio luminosity and black hole mass are very loosely correlated since the dependence – if any – between these two quantities is much weaker than in the black hole/optical luminosity The above results can be interpreted as evidence for the fact that while optical/nuclear emission is directly related to the mass of the black hole that produces the quasar signal, radio luminosity is not."
" Black hole mass in RL quasars merely plavs a marginal ""threshold"" role whereby. for à given optical luminosity. only the more massive quasars will develop significant radio activity."," Black hole mass in RL quasars merely plays a marginal “threshold” role whereby, for a given optical luminosity, only the more massive quasars will develop significant radio activity."
 However. once the activity is triggered. there is no significant evidence for à connection between black hole mass and the level of radio output. (see also Magliocchetti et al.," However, once the activity is triggered, there is no significant evidence for a connection between black hole mass and the level of radio output (see also Magliocchetti et al."
 2004)., 2004).
 We have made use of a homogeneous sample of  300. 0.32443. radio-Ioud quasars drawn from the FURST and 2dEP QSO survevs to estimate possible dependences of radio activity on black-hole mass.," We have made use of a homogeneous sample of $\sim 300$ , $0.3\simlt {\rm z}\simlt 3$, radio-loud quasars drawn from the FIRST and 2dF QSO surveys to estimate possible dependences of radio activity on black-hole mass."
" By analyzing composite spectra [or the populations of racio-quiet and. racdio-Ioud. QSOs chosen to have the same recshift and luminosity distribution we find with high statistical significance that racio-loucl quasars are on average associated to black holes of masses SLOPEC about twice as large as those obtained for racdio-quiet quasars (7LOSPFE PONT, "," By analyzing composite spectra for the populations of radio-quiet and radio-loud QSOs – chosen to have the same redshift and luminosity distribution – we find with high statistical significance that radio-loud quasars are on average associated to black holes of masses $\sim 10^{8.56\pm 0.04}{\rm M_\odot}$, about twice as large as those obtained for radio-quiet quasars $\sim 10^{8.30\pm 0.06}{\rm M_\odot}$ )."
The above result. is also verified when one splits1 the two samples in luminosity bins., The above result is also verified when one splits the two samples in luminosity bins.
 In fact. we observe a clear dependence of black hole mass on optical luminosity of the form log(Ae)1.=S.57(40.06) 0.27(£0.06)(Aly|24.5) and Log(=8.43(£0.05) O.32(ED.0G)(Alpp|24.5). respectively forRO the case of radio-loud απ raclio-quict quasars.," In fact, we observe a clear dependence of black hole mass on optical luminosity of the form ${\rm log \left(\frac{M_{BH}}
{M_\odot}\right)_{RL}}= 8.57(\pm0.06) -0.27(\pm 0.06) ({\rm M_B} + 24.5)$ and ${\rm log \left(\frac{M_{BH}}{M_\odot}\right)_{RQ}}= 8.43(\pm0.05) -
0.32(\pm 0.06) ({\rm M_B} + 24.5)$, respectively for the case of radio-loud and radio-quiet quasars."
 “These trends run parallel το each other. implying that radio-loud quasars are associated o black holes about 1.4. times more massive than hose producing the radio-quiet case fuminosifies.," These trends run parallel to each other, implying that radio-loud quasars are associated to black holes about $1.4$ times more massive than those producing the radio-quiet case ."
" On the other hand. in the case. of. radio- quasars. we only find. evidence for a marginal (if any) dependence of the black hole mass on radio power (log(m)=SGOCIEO.0G)|0.15(3-0.08)(log,,PP—25)) Our results allow a number of important. conclusions o be i) There exists à strong correlation between level of optical/nuclear emission. ancl mass of the black hole producing the quasar."," On the other hand, in the case of radio-loud quasars, we only find evidence for a marginal (if any) dependence of the black hole mass on radio power ${\rm log \left(\frac{M_{BH}}{M_\odot}\right)_{RL}}= 8.60(\pm0.06) +
0.15(\pm 0.08) ({\rm \log_{10}P} -25)$ Our results allow a number of important conclusions to be i) There exists a strong correlation between level of optical/nuclear emission and mass of the black hole producing the quasar."
 The same correlation holds for both racdio-loud and racio-quict quasars. but with. dilferent i) Raclio-loucl quasars are on average more massive than radio quiet ones at all (optical) ii) Black hole mass plays a partial. threshold. role in determining the radio activity that. gives rise to the population of radio-loud. quasars.," The same correlation holds for both radio-loud and radio-quiet quasars, but with different ii) Radio-loud quasars are on average more massive than radio quiet ones at all (optical) iii) Black hole mass plays a partial, threshold, role in determining the radio activity that gives rise to the population of radio-loud quasars."
 Our findings are further support for the existence — at cach given optical luminosity ofa threshold black hole mass associated with the onset of significant radio activity such as that of radio-Ioud QSOs: however. once the activity is triggered. there appears to be very little evidence for a connection between black hole mass and level of racio output (see also Alaglioechetti et al.," Our findings are further support for the existence – at each given optical luminosity – of a threshold black hole mass associated with the onset of significant radio activity such as that of radio-loud QSOs; however, once the activity is triggered, there appears to be very little evidence for a connection between black hole mass and level of radio output (see also Magliocchetti et al."
 An important issue to stress is Chat. while the absolute values associated to the various quantities analvzed in this paper might be somehow allected by calibration effects (see e.g. section 5). all the results that compare the two populations of raclio-louc and raclio-quict quasars are not. as any dilference in the zero-point calibrations would cancel out during the comparison process.," An important issue to stress is that, while the absolute values associated to the various quantities analyzed in this paper might be somehow affected by calibration effects (see e.g. section 5), all the results that compare the two populations of radio-loud and radio-quiet quasars are not, as any difference in the zero-point calibrations would cancel out during the comparison process."
" Even though the analvzed samples are too small to investigate for any presence of a dillerent. cosmological evolution of the two RQ and RL populations. the above statement. together with our choice of selecting. two samples that were ascindistinguishable"" as possible (in number of sources. luminosity and. redshift distributions). give us confidence in the reliability of the results."," Even though the analyzed samples are too small to investigate for any presence of a different cosmological evolution of the two RQ and RL populations, the above statement, together with our choice of selecting two samples that were as“indistinguishable” as possible (in number of sources, luminosity and redshift distributions), give us confidence in the reliability of the results."
 As a final remark we note that. since we have chosen two samples matched in optical luminosity. the fact that RL quasars harbor on average more massive black holes implies that these sources accrete at a lower fraction of their Eddington limit than their RQ counterparts.," As a final remark we note that, since we have chosen two samples matched in optical luminosity, the fact that RL quasars harbor on average more massive black holes implies that these sources accrete at a lower fraction of their Eddington limit than their RQ counterparts."
 Whether this result can be seen as evidence that racio-loucl and raclio-quict quasars are two distinct populations or whether this can simply be interpreted by saving that radio-Ioud quasars mark a different (possibly later) stage of evolution of raclio-quict quasars is still unclear and we plan to tackle this issue in a forthcoming paper., Whether this result can be seen as evidence that radio-loud and radio-quiet quasars are two distinct populations or whether this can simply be interpreted by saying that radio-loud quasars mark a different (possibly later) stage of evolution of radio-quiet quasars is still unclear and we plan to tackle this issue in a forthcoming paper.
 The authors wish to thank Paola Marziani lor extremely interesting cliscussions aud Cianlraneo De Zotti lor a carelul reading of the manuscript., The authors wish to thank Paola Marziani for extremely interesting discussions and Gianfranco De Zotti for a careful reading of the manuscript.
 Financial support lor RBAL was provided by NASA through Hubble Fellowship. grant LLLOLISLOLA awarded by the Space Science Lustitute. Which is by the Association of TelescopeUniversities lor Research in Astronomy. operateddne. lor NASA. under contract NAN 5-26555.," Financial support for RBM was provided by NASA through Hubble Fellowship grant HF-01154.01-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555."
 Wealso thank the anonymous releree to help improving therobustness ol the results of this paper., Wealso thank the anonymous referee to help improving therobustness of the results of this paper.
establish possible scenarios where (he constraints (detection at TeV. nou-cetection αἱ GeV) could be satisfied.,"establish possible scenarios where the constraints (detection at TeV, non-detection at GeV) could be satisfied."
 A discussion of these results and a comparison with the similar case of ONR. W28 with nearby MCs (AICs) is given ad the end., A discussion of these results and a comparison with the similar case of SNR W28 with nearby MCs (MCs) is given at the end.
 We searched for gamma ravs emitted by the HESS J1858—020 analvzing the publicly available ~28 months of Fermi-LAT data in the energv range LOO MeV - 100 GeV. from 4 Ang 2008 to 19 November 2010.," We searched for gamma rays emitted by the HESS J1858+020 analyzing the publicly available $\sim28$ months of -LAT data in the energy range 100 MeV - 100 GeV, from 4 Aug 2008 to 19 November 2010."
 The search is performed by means of the binned likelihood spectral analysis. using the official tool (gtlike) released by the Ferim--LAT collaboration SScence Tools v9r17p0).," The search is performed by means of the binned likelihood spectral analysis, using the official tool ) released by the -LAT collaboration Science Tools )."
" All the data. software. and diffuse models used for this analvsis are available from the. SScience Support Events from the “Pass 6 Diffuse"" class were selected. i.e. the event class with the greatest purity of gamma rays. having the most stringent backeround rejection (see details in Atwood et al."," All the data, software, and diffuse models used for this analysis are available from the Science Support Events from the “Pass 6 Diffuse” class were selected, i.e. the event class with the greatest purity of gamma rays, having the most stringent background rejection (see details in Atwood et al."
 2009)., 2009).
" The ""Pass 6 v3 Diffuse"" instrument response functions (RFs) were applied in the analysis (Rando 2009)."," The “Pass 6 v3 Diffuse"" instrument response functions (IRFs) were applied in the analysis (Rando 2009)."
 We selected events wilh energv £2100 MMeV in a square aligned with celestial coordinates. inscribed inside a circular region of interest (ROI) of 15° radius. centered on the ILIZ.S.5. source.," We selected events with energy $E>$ MeV in a square aligned with celestial coordinates, inscribed inside a circular region of interest (ROI) of $^{\circ}$ radius, centered on the H.E.S.S. source."
 The good time intervals are clefined such that the ROI does not eo below the gamma-rav-bright Earth limb (defimed at 105° from the Zenith angle). ancl that the source is abwavs inside the LAT field of view. namely in a cone angle of 667.," The good time intervals are defined such that the ROI does not go below the gamma-ray-bright Earth limb (defined at $^{\circ}$ from the Zenith angle), and that the source is always inside the LAT field of view, namely in a cone angle of $^{\circ}$."
 Source detection significance is determined using the Test-Statistie (TS) value. 775=—2(Ly—L4). which compares the likelihood ratio of models including an additional source. L4. with the null-hvpothesis of background only. Li (Mattox οἱ al.," Source detection significance is determined using the Test-Statistic (TS) value, $TS = -2(L_0 -
L_1)$, which compares the likelihood ratio of models including an additional source, $L_1$ , with the null-hypothesis of background only, $L_0$ (Mattox et al."
 1996)., 1996).
 To apply the likelihood analvsis. a spectral-spatial model containing dilluse ancl sources was created.," To apply the likelihood analysis, a spectral-spatial model containing diffuse and point-like sources was created."
 Using the IFGL Catalog we have 93 sources closer than 20° and 5 closer than 3° from the HESS J13584-020 position., Using the 1FGL Catalog we have 93 sources closer than $^o$ and 5 closer than $^o$ from the HESS J1858+020 position.
 For the Galactic diffuse emission we used the spectral-spatial model vv02.fit. which is the one used by the -LAT collaboration in order to build the Fermi-LAT First Source Catalog CAbdo οἱ al.," For the Galactic diffuse emission we used the spectral-spatial model v02.fit"", which is the one used by the -LAT collaboration in order to build the -LAT First Source Catalog (Abdo et al."
 2010a; LFGL as relerred to hereafter)., 2010a; 1FGL as referred to hereafter).
" The isotropic diffuse emission was mocdelled by the spectrum described in the ""isotropicvv02.txt file."," The isotropic diffuse emission was modelled by the spectrum described in the v02.txt"" file."
 Thenormalization factors of these, Thenormalization factors of these
Observations of long gamama-ray bursts (GRBs) by a number of spacecrafts during the last decades revealed that their > -rav prompt eniüssion is over after 10.100 s. Llowever. alter the launch of (Gehrelsctal. 2004)) evidence is accumulating that the central engine of the GRB sources could. still be active hours after the main burst.,"Observations of long gamma-ray bursts (GRBs) by a number of spacecrafts during the last decades revealed that their $\gamma$ -ray prompt emission is over after $\sim10-100$ s. However, after the launch of \citealt{Gehrels04}) ) evidence is accumulating that the central engine of the GRB sources could still be active hours after the main burst."
 This is mainly linked to the discovery of large amplitude. episocic re-brightenings with typical κ)ον0.2 in the ~33% of X-rav afterglows: the X-ray [ares (see Chincarinietal.2010.. C10 hereafter. for a recent compilation).," This is mainly linked to the discovery of large amplitude, episodic re-brightenings with typical $\Delta t/t \sim 0.2$ in the $\sim 33\%$ of X-ray afterglows: the X-ray flares (see \citealt{Chincarini10}, C10 hereafter, for a recent compilation)."
 The temporal properties of X-ray. [lares make it difficult to interpret the observed. emission in the framework of the external shock scenario (see e.g. Lazzati&Perna 2007))., The temporal properties of X-ray flares make it difficult to interpret the observed emission in the framework of the external shock scenario (see e.g. \citealt{Lazzati07}) ).
 Moreover. the strict analogv Found. by Marguttietal.(2010b) (ALLO hereafter) between the temporal and. spectral behaviour of X-ray flares ancl prompt emission pulses strongly suggests à common. internal origin.," Moreover, the strict analogy found by \cite{Margutti10b} (M10 hereafter) between the temporal and spectral behaviour of X-ray flares and prompt emission pulses strongly suggests a common, internal origin."
 Phe direct implication is that [ares directly trace the activity of the central engine., The direct implication is that flares directly trace the activity of the central engine.
 To account for the details of the Hare emission. GRB central engines (CLE) are required to have the following basic properties (C10. MIO ancl references therein):," To account for the details of the flare emission, GRB central engines (CE) are required to have the following basic properties (C10, M10 and references therein):"
"and M describe how the mass is distributed, hence our choice for naming S the shape tensor.","and $\mat{M}$ describe how the mass is distributed, hence our choice for naming $\mat{S}$ the shape tensor."
 The tensors I and M have the same eigenvectors., The tensors $\mat{I}$ and $\mat{M}$ have the same eigenvectors.
" If m is an eigenvalue of M, then tr(M)—m is an eigenvalue of I."," If $m$ is an eigenvalue of $\mat{M}$ , then $\mathrm{tr}(\mat{M}) - m$ is an eigenvalue of $\mat{I}$."
 The detailed meaning of the eigenvalues depends on the integration volume and the mass distribution (i.e. density profile)., The detailed meaning of the eigenvalues depends on the integration volume and the mass distribution (i.e. density profile).
" For example, for a thin ellipsoidal shell (a thin homoeoid) of uniform density, the eigenvalues of M are Mgga?/3, and Mgsc?/3 (Mzgg is the mass in the ellipsoidal Mg?/"," For example, for a thin ellipsoidal shell (a thin homoeoid) of uniform density, the eigenvalues of $\mat{M}$ are $M_\mathrm{ES}a^2/3, M_\mathrm{ES}b^2/3$ and $M_\mathrm{ES}c^2/3$ $M_\mathrm{ES}$ is the mass in the ellipsoidal shell)."
"3Whereas for an ellipsoid of uniform density the eigenvaluesshell). are Mga?/5,Mg?/5 and Mgc?/5 (Mg is the mass in the ellipsoid)."," Whereas for an ellipsoid of uniform density the eigenvalues are $M_\mathrm{E}a^2/5, M_\mathrm{E}b^2/5$ and $M_\mathrm{E}c^2/5$ $M_\mathrm{E}$ is the mass in the ellipsoid)."
" Unfortunately, the tensor M is often inaccurately denoted as the moment of (Equationinertia (3)))tensor in the astronomy and astrophysics literature."," Unfortunately, the tensor $\mat{M}$ (Equation \ref{eq:M}) )) is often inaccurately denoted as the moment of inertia tensor in the astronomy and astrophysics literature."
" This probably goes back to ? (Page 494, Equation 8-11), where M was called the moment of inertia tensor."," This probably goes back to \cite{1987gady.book.....B} (Page 494, Equation 8-11), where $\mat{M}$ was called the moment of inertia tensor."
" Fortunately, this was corrected in the second edition (?,page796,EquationD- 39).."," Fortunately, this was corrected in the second edition \citep[page 796, Equation D-39]{2008gady.book.....B}."
 The shape tensor can be generalized by using an additional weight function w(r) By setting w(r)=1 and choosing p(r) to be the mass density we obtain our standard definition (Equation (5))., The shape tensor can be generalized by using an additional weight function $w(\vec{r})$ By setting $w(\vec{r}) = 1$ and choosing $\rho(\vec{r})$ to be the mass density we obtain our standard definition (Equation \ref{eq:shapetensor}) )).
 Other choices are also possible., Other choices are also possible.
" For example, a weighting by number with p(r)=— being the number density (which is, of course, *7,ó(requivalentrx) to the mass density weighting if all the particles have equal "," For example, a weighting by number with $\rho(\vec{r}) = \sum_k \delta(\vec{r} - \vec{r}_k)$ being the number density (which is, of course, equivalent to the mass density weighting if all the particles have equal mass)."
"Or p(r)=$7,6(r— where is the local mass).density of the particle like in ?.. rx)/p", Or $\rho(\vec{r}) = \sum_k \delta(\vec{r} - \vec{r}_k)/\rho_k$ where $\rho_k$ is the local density of the particle like in \cite{2008MNRAS.385.1859W}.
"xIf one is p;interested in the shape of a matter distribution where the particles or volume elements can have different mass (e.g. for gas and stars), it is essential ato use as the mass density."," If one is interested in the shape of a matter distribution where the particles or volume elements can have a different mass (e.g. for gas and stars), it is essential to use $\rho(\vec{r})$ as the mass density."
" Here, we only use as the p(r)mass density."," Here, we only use $\rho(\vec{r})$ as the mass density."
" Throughout the paper, we use p(r)the elliptical radius rey for distances from the center for ellipsoidal shapes."," Throughout the paper, we use the elliptical radius $r_\mathrm{ell}$ for distances from the center for ellipsoidal shapes."
 The elliptical radius raj also Equation is the major axis of the local (seehomoeoid or ellipsoid., The elliptical radius $r_\mathrm{ell}$ (see also Equation \ref{eq:rell}) )) is the semi-major axis of the local homoeoid or ellipsoid.
(10))) We concentrate on 6 different methods for determining the shape of a matter distribution (see also Table 1))., We concentrate on 6 different methods for determining the shape of a matter distribution (see also Table \ref{tab:methodsummary}) ).
 These methods differ by using a different integration volume V and different weight functions w(r)., These methods differ by using a different integration volume $V$ and different weight functions $w(\vec{r})$.
" For calculating the shape at a distance rey, in the methods with a starting letter S, the integration is over an ellipsoidal shell volume centered at rey (in logarithmic space)."," For calculating the shape at a distance $r_\mathrm{ell}$ , in the methods with a starting letter S, the integration is over an ellipsoidal shell (homoeoid) volume centered at $r_\mathrm{ell}$ (in logarithmic space)."
" In the (homoeoid)methods with first letter E, the integration is over the whole enclosed ellipsoidal volume within rey."," In the methods with first letter E, the integration is over the whole enclosed ellipsoidal volume within $r_\mathrm{ell}$."
" For the different weight functions w(r), we use (1) w(r)=1, (2) w(r)=τὸ and (3) w(r)=rab."," For the different weight functions $w(\vec{r})$, we use (1) $w(\vec{r}) = 1$, (2) $w(\vec{r}) = r^{-2}$ and (3) $w(\vec{r}) = r_\mathrm{ell}^{-2}$."
" 'The elliptical radius is given by where (zen;Yell;Zen) are the coordinates of the volume element or particle in the eigenvector coordinate system of the ellipsoid, i.e. rey corresponds to the semi-major axis a of the ellipsoid surface through that particle or volume element."," The elliptical radius is given by where $(x_\mathrm{ell},y_\mathrm{ell},z_\mathrm{ell})$ are the coordinates of the volume element or particle in the eigenvector coordinate system of the ellipsoid, i.e. $r_\mathrm{ell}$ corresponds to the semi-major axis $a$ of the ellipsoid surface through that particle or volume element."
" Additionally, we also check for the importance of the removal of subhalos."," Additionally, we also check for the importance of the removal of subhalos."
" Cases where we removed the subhalos are marked with a —, cases where they remained by a +."," Cases where we removed the subhalos are marked with a –, cases where they remained by a +."
" In order to calculate the local shape at a distance rej from the center, we use an iteration method (e.g. and start with a spherically symmetric integration volume (shell or sphere)."," In order to calculate the local shape at a distance $r_\mathrm{ell}$ from the center, we use an iteration method \citep[e.g.][]{1991ApJ...368..325K,1991ApJ...378..496D,1992ApJ...399..405W} and start with a spherically symmetric integration volume (shell or sphere)."
 Then the shape tensor is calculated according to the different methods., Then the shape tensor is calculated according to the different methods.
 By diagonalizing S we get the eigenvectors and eigenvalues at distance rey., By diagonalizing $\mat{S}$ we get the eigenvectors and eigenvalues at distance $r_\mathrm{ell}$.
 The eigenvectors give the directions of the semi-principal axes., The eigenvectors give the directions of the semi-principal axes.
" The eigenvalues of S for the method S1 are a?/3, b?/3 and c?/3 where a, b and c are the semi-principal axes with a>bc — at least in the thin homoeoid approximation where the density is uniform."," The eigenvalues of $\mat{S}$ for the method S1 are $a^2/3$, $b^2/3$ and $c^2/3$ where $a$, $b$ and $c$ are the semi-principal axes with $a \geq b \geq c$ – at least in the thin homoeoid approximation where the density is uniform."
" Hence, the square roots of the eigenvalues are proportional to the lengths of the semi-principal axes for method S1 and we can readily calculate the axis ratios b/a and c/a."," Hence, the square roots of the eigenvalues are proportional to the lengths of the semi-principal axes for method S1 and we can readily calculate the axis ratios $b/a$ and $c/a$."
" For method S3 we expect to get the same axis ratios as for method S1 since dividing by the semi-major axis a=raj squared, which is a constant for a thin ellipsoidal shell, just changes the geometrical meaning and normalization of the eigenvalues but not the axis ratios."," For method S3 we expect to get the same axis ratios as for method S1 since dividing by the semi-major axis $a=r_\mathrm{ell}$ squared, which is a constant for a thin ellipsoidal shell, just changes the geometrical meaning and normalization of the eigenvalues but not the axis ratios."
 For the other methods it is not clear what the detailed geometrical meaning of the eigenvalues is., For the other methods it is not clear what the detailed geometrical meaning of the eigenvalues is.
" For the methods that use the enclosed ellipsoidal volume, this will also depend on the mass density profile."," For the methods that use the enclosed ellipsoidal volume, this will also depend on the mass density profile."
 The r-? weighting projects the volume elements dV onto the unit sphere., The $r^{-2}$ weighting projects the volume elements $V$ onto the unit sphere.
 This projection complicates the physical interpretation of this method., This projection complicates the physical interpretation of this method.
 It is generally assumed though that the eigenvalues of S in these casesare still proportional to the semi-major axes squared., It is generally assumed though that the eigenvalues of $\mat{S}$ in these casesare still proportional to the semi-major axes squared.
" Hence, we calculate the axis ratio for the other methods the same way as for methods S1 and S3 - as it is generally done in the literature."," Hence, we calculate the axis ratio for the other methods the same way as for methods S1 and S3 – as it is generally done in the literature."
 We then keep the length of the semi-major axis fixed (but the orientation can change) and calculate S again by summing over all particles within the new deformed integration volume (homoeoid or ellipsoid) with semi-major axis α=rey and axis ratios b/a and c/a but with the new orientation., We then keep the length of the semi-major axis fixed (but the orientation can change) and calculate $\mat{S}$ again by summing over all particles within the new deformed integration volume (homoeoid or ellipsoid) with semi-major axis $a=r_\mathrm{ell}$ and axis ratios $b/a$ and $c/a$ but with the new orientation.
 For the shape determination we allow volume elements or particles to be in several bins/shells., For the shape determination we allow volume elements or particles to be in several bins/shells.
 Of course this is naturally the case when using an enclosed ellipsoidal volume., Of course this is naturally the case when using an enclosed ellipsoidal volume.
 It is alsonecessary when using an ellipsoidal shell since neighboring shells can overlap due to slightly different orientation and axis ratios., It is alsonecessary when using an ellipsoidal shell since neighboring shells can overlap due to slightly different orientation and axis ratios.
 This iteration is repeated untilconvergence is reached., This iteration is repeated untilconvergence is reached.
 As a convergence criterion we require that the fractional difference between two iteration steps in both axis ratios is smaller than 107°., As a convergence criterion we require that the fractional difference between two iteration steps in both axis ratios is smaller than $10^{-3}$ .
" For methods using the shape tensor, it is important to use an iteration method that allows the algorithm to"," For methods using the shape tensor, it is important to use an iteration method that allows the algorithm to"
"+3Hp, — Γβφρ. ,(2)with ρε the energy density of CDM p,and where a prime denotes a derivative with respect to conformal time.",+3 = + with $\rho_c$ the energy density of CDM and where a prime denotes a derivative with respect to conformal time.
" The dimensionless function where m. is the mass of a CDM particle, fully specifies the interaction."," The dimensionless function - where $m_{c}$ is the mass of a CDM particle, fully specifies the interaction."
 Note that we define densities as p=81Gp and that the scalar field ¢ is normalized in units of the reduced Planck mass M=(8«G)!., Note that we define densities as $\rho \equiv 8 \pi G \rho$ and that the scalar field $\phi$ is normalized in units of the reduced Planck mass $M = (8 \pi G)^{-1/2}$.
" The scalar field energy density is pg=2j+U(¢) and we consider two choices of potentials: U($) = Uod"" U($)) = Uoe(6) where Uo and *a are constants.", The scalar field energy density is $\rho_{\phi} = \frac{\phi'^2}{2 a^2} + U(\phi)$ and we consider two choices of potentials: ) = U_0 ) = U_0 where $U_0$ and $\alpha$ are constants.
" In the present work we limit our investigation to the models specified in Table [I]: one model with a potential given by (0) and with a constant coupling @= 0.2, labelled as “RP”, and two models with an exponential potential with constant coupling 8—0.2 and variable coupling (65)β(4)=0.4-e?®, labelled “EXP005” and “EXP010a2”, respectively (see?,foradetaileddiscus-siononvariablecoupling models).."," In the present work we limit our investigation to the models specified in Table \ref{Simulations_Table}: one model with a potential given by \ref{U_def_ipl}) ) and with a constant coupling $\beta = 0.2$ , labelled as “RP”, and two models with an exponential potential \ref{U_def_exp}) ) with constant coupling $\beta = 0.2$ and variable coupling $\beta (\phi ) = 0.4\cdot e^{2\phi }$, labelled “EXP005"" and “EXP010a2"", respectively \citep[see][for a detailed discussion on variable coupling models]{Baldi_2010}."
" Coupled dark energy models have been widely studied in the literature (717,andreferencestherein)."," Coupled dark energy models have been widely studied in the literature \citep[][and references therein]{Wetterich_1995, Amendola_2000, Mangano_etal_2003, pettorino_baccigalupi_2008}."
" The interaction imprints specific features on the growth of cosmic structures, as it has been shown both within spherical collapse models (??) and at the nonlinear level by means of N-body simulations for constant (??) and variable couplings 8($) (?).."," The interaction imprints specific features on the growth of cosmic structures, as it has been shown both within spherical collapse models \citep{Wintergerst_pettorino_2010, Mainini_bonometto_2006} and at the nonlinear level by means of N-body simulations for constant \citep{Baldi_etal_2010, Maccio_etal_2004} and variable couplings $\beta (\phi )$ \citep{Baldi_2010}."
" In particular, the interaction determines an enhancement of structure formation due to the presence of a long range fifth-force acting between coupled massive particles."," In particular, the interaction determines an enhancement of structure formation due to the presence of a long range fifth-force acting between coupled massive particles."
" In addition to this effect, conservation of momentum turns into an extra acceleration directly proportional to the peculiar velocity of coupled particles; at the nonlinear level, it has been shown that this velocity dependent term can determine a reduction of the concentration of halos if the coupling function β(9) is positive (seeagain??).."," In addition to this effect, conservation of momentum turns into an extra acceleration directly proportional to the peculiar velocity of coupled particles; at the nonlinear level, it has been shown that this velocity dependent term can determine a reduction of the concentration of halos if the coupling function $\beta (\phi)$ is positive \citep[see again][]{Baldi_etal_2010, Baldi_2010}."
" These effects are encoded in the modified newtonian acceleration equation for coupled dark matter particles: where { and j are indices that span over all the particles of the simulation, p is the momentum of the i-th particle, and Gi; is the effective gravitational constant between the i-th and the j-th coupled particles = 2(9))], where Gy is the usual Newtonian value."," These effects are encoded in the modified newtonian acceleration equation for coupled dark matter particles: where $i$ and $j$ are indices that span over all the particles of the simulation, $\vec{p}$ is the momentum of the $i$ -th particle, and $\tilde{G}_{ij}$ is the effective gravitational constant between the $i$ -th and the $j$ -th coupled particles = )], where $G_{N}$ is the usual Newtonian value."
" In this Letter, we estimate how the probability of finding very massive clusters comparable to the XMMU J2235.3-2557 detection by ? and? at z~1.4 is modified in the presence of a coupling between dark energy and CDM as compared to the standard ACDM case."," In this Letter, we estimate how the probability of finding very massive clusters comparable to the XMMU J2235.3-2557 detection by \citet{Jee_etal_2009} and \citet{Rosati_etal_2009} at $z\sim 1.4$ is modified in the presence of a coupling between dark energy and CDM as compared to the standard $\Lambda $ CDM case."
" With this aim, we use the modified version of the cosmological N-body code (?) presented in ? and ?,, to which we refer for further details, to investigate nonlinear structure formation within the models described in Table[Il."," With this aim, we use the modified version of the cosmological N-body code \citep{gadget-2} presented in \citet{Baldi_etal_2010} and \citet{Baldi_2010}, to which we refer for further details, to investigate nonlinear structure formation within the models described in Table \ref{Simulations_Table}."
" We make use of the following sets of simulations: The former set of simulations includes the cosmological fraction of uncoupled baryons on which hydrodynamical forces are computed with theHydrodynamics (17) algorithm, while the latter ones are pure CDM simulations."," We make use of the following sets of simulations: The former set of simulations includes the cosmological fraction of uncoupled baryons on which hydrodynamical forces are computed with the \citep{Springel_Hernquist_2002,gadget-2} algorithm, while the latter ones are pure CDM simulations."
 The two sets of simulations start at z=60 with exactly the same initial conditions for each set of runs., The two sets of simulations start at $z=60$ with exactly the same initial conditions for each set of runs.
" This is a conservative setup, since the effects of enhanced growth that we are investigating would be more pronounced if a normalization at decoupling (z~1100) had been adopted."," This is a conservative setup, since the effects of enhanced growth that we are investigating would be more pronounced if a normalization at decoupling $z\sim 1100$ ) had been adopted."
 We remark that this normalization is different from the one adopted in most of the simulations discussed in ? and ?:: in these works the amplitude of linear density fluctuations was normalized in order to have the same og at the present time., We remark that this normalization is different from the one adopted in most of the simulations discussed in \citet{Baldi_etal_2010} and \citet{Baldi_2010}: in these works the amplitude of linear density fluctuations was normalized in order to have the same $\sigma _{8}$ at the present time.
" In the present study, instead, we choose all the models with the same initial normalization of the power spectrum, which will necessarily result in different values of ca at z—0 for the different cosmological models."," In the present study, instead, we choose all the models with the same initial normalization of the power spectrum, which will necessarily result in different values of $\sigma _{8}$ at $z=0$ for the different cosmological models."
 It is important to notice that all our models start at high redshift with a normalization of the Power Spectrum which is in full accordance with the latest WMAP7 determination of the scalar perturbations amplitude from CMB data alone (?).., It is important to notice that all our models start at high redshift with a normalization of the Power Spectrum which is in full accordance with the latest WMAP7 determination of the scalar perturbations amplitude from CMB data alone \citep{wmap7}.
" Given this setup, we study the halo mass function at different redshifts for the groups identified in each simulation with a Friends-of-Friends (FoF) algorithm with a linking length λ=0.2xd, where d is the mean particle spacing."," Given this setup, we study the halo mass function at different redshifts for the groups identified in each simulation with a Friends-of-Friends (FoF) algorithm with a linking length $\lambda = 0.2 \times \bar{d}$, where $\bar{d}$ is the mean particle spacing."
" We show that the interaction between dark energy and CDM results in a significantly larger number of massive halos at any epoch, with respect to ACDM."," We show that the interaction between dark energy and CDM results in a significantly larger number of massive halos at any epoch, with respect to $\Lambda$ CDM."
 In Fig. (1)), In Fig. \ref{cumulative_massfunctions}) )
 we show the evolution of the halo mass function at different redshifts in the three low resolution simulations described in Table T, we show the evolution of the halo mass function at different redshifts in the three low resolution simulations described in Table \ref{Simulations_Table}.
he bottom panel of each plot shows the enhancement of [I].halo number density in coupled dark energy models with respect to ACDM., .The bottom panel of each plot shows the enhancement of halo number density in coupled dark energy models with respect to $\Lambda $ CDM.
" As it clearly appears inall the plots, the number density of halos of any mass is larger in coupled dark energy models, both for constant"," As it clearly appears inall the plots, the number density of halos of any mass is larger in coupled dark energy models, both for constant"
prius.,prisms.
 NARVAL was used iu polarimetric mode with a PA»ectral resolution of about 65000., NARVAL was used in polarimetric mode with a spectral resolution of about 65000.
 Stokes 7 (unpolarised) and Stokes V. (circular polarisation) parameters were obtained by means of [ sub-exposures between which the retarders (Fresnel rhonibs) were rotated i order to exchauge the beams in the whole iustriunueut aud to reduce spurious polarization signatures., Stokes $I$ (unpolarised) and Stokes $V$ (circular polarisation) parameters were obtained by means of 4 sub-exposures between which the retarders (Fresnel rhombs) were rotated in order to exchange the beams in the whole instrument and to reduce spurious polarization signatures.
" We aimed to get long exposures, up to 6100s. ou our bright targets in order to be able to detect ultra-weak or complex magnetic fields."," We aimed to get long exposures, up to 6400s, on our bright targets in order to be able to detect ultra-weak or complex magnetic fields."
 lu order to avoid saturation of the CCD we mace short sub exposures (6.8. Lor 8 second subexposures for each Stokes V. series in the case of Sirius)., In order to avoid saturation of the CCD we made short sub exposures (e.g. 4 or 8 second subexposures for each Stokes $V$ series in the case of Sirius).
 During the techuical tests and science demonstration time. naguctic and nou magnetic stars were observed which showed that NARVAL works properly and is 230 times nore efücieut than the previous mstruneut. MusiCoS (Baudvaud Bohlin 1992. Donati ct al.," During the technical tests and science demonstration time, magnetic and non magnetic stars were observed which showed that NARVAL works properly and is 30 times more efficient than the previous instrument, MuSiCoS (Baudrand Böhhm 1992, Donati et al."
 1999). which was used by Shorlin et al. (," 1999), which was used by Shorlin et al. ("
2002).,2002).
 Since then. a ereat iuuber of new results have been obtained that confi 16 hieh scieutific efficiency of ESPaDOuS aud NARVAL e.g. in Donati Landstreet 2009).," Since then, a great number of new results have been obtained that confirm the high scientific efficiency of ESPaDOnS and NARVAL (e.g. in Donati Landstreet 2009)."
 The extraction of je spectra was done usine Libre-ESpRIT (Donati ct al., The extraction of the spectra was done using Libre-ESpRIT (Donati et al.
 1997). a fully automatic reduction package iustalled at the TBL.," 1997), a fully automatic reduction package installed at the TBL."
 Iu order to carry out the Zeeman analysis. Least-Squares Decouvolution analysis (LSD. Donati ct al.," In order to carry out the Zeeman analysis, Least-Squares Deconvolution analysis (LSD, Donati et al."
 1997) was applied to all observations., 1997) was applied to all observations.
 We used line masks with solar abundances. logg = L temperatures close to the values eiven by Shorlin et al. (," We used line masks with solar abundances, $\log g$ = 4, temperatures close to the values given by Shorlin et al. ("
2002: see our Table 1). aud included. lines with a ceutral depth exeater than of the continua.,"2002; see our Table 1), and included lines with a central depth greater than of the continuum."
 For our sample. this method enabled us to average frou about 500 (lighest temperature HegMu star) to about 5000 (coolest Ai star) lines aud to obtain Stoke:CS V profiles with signal-to-noise ratio (S/N) imereased by a factor of about 10 to 10.," For our sample, this method enabled us to average from about 500 (highest temperature HgMn star) to about 5000 (coolest Am star) lines and to obtain Stokes $V$ profiles with signal-to-noise ratio (S/N) increased by a factor of about 10 to 40."
 We performed a statistical test for the detection of Stokes V. Zeeman signatures: the reduced. 47statistic is computed for zero signal iu the Stokes V. profile. both iuside aud outside the spectral line (Donati ct al.," We performed a statistical test for the detection of Stokes $V$ Zeeman signatures: the reduced $\chi^2$statistic is computed for zero signal in the Stokes $V$ profile, both inside and outside the spectral line (Donati et al."
 1997)., 1997).
 The statistics are then converted iuto detection probabilities (false alavin probability)., The statistics are then converted into detection probabilities (false alarm probability).
" Also mincluded in the output are ""diagnostic uull spectra iV (conibinations of sub-exposures iu which real V. signatures should cancel out). which are in principle featureless. and therefore serve to diagnose the presence of spurious contributions to the Stokes V spectra."," Also included in the output are “diagnostic null” spectra $N$ (combinations of sub-exposures in which real $V$ signatures should cancel out), which are in principle featureless, and therefore serve to diagnose the presence of spurious contributions to the Stokes $V$ spectra."
 We then computed the longitudinal maeuetic field B; in C. using the first-order moment imoethod adapted to LSD profiles (Rees aud Semel 1979. Donati ct al.," We then computed the longitudinal magnetic field $B_{l}$ in G, using the first-order moment method adapted to LSD profiles (Rees and Semel 1979, Donati et al."
 1997. Wade et al.," 1997, Wade et al."
 2000)., 2000).
 The integration range used to compute Bp corresponds to the first and last poiut in the Stokes £ profile for which the flax was lower than 154 of the masinuun depth. except for the SB2 stars for which it was optimized mamually.," The integration range used to compute $B_{l}$ corresponds to the first and last point in the Stokes $I$ profile for which the flux was lower than $\%$ of the maximum depth, except for the SB2 stars for which it was optimized manually."
 For a few selected stars we coustructed line masks that matched the stellar spectrum in detail. by modifving individual line depths iu the mask. using data provided x VALD (Ixupka ct al.," For a few selected stars we constructed line masks that matched the stellar spectrum in detail, by modifying individual line depths in the mask, using data provided by VALD (Kupka et al."
 1999)., 1999).
 While these custom masks ιαπαν provided a better represeutation of the Stokes { and V spectra. they did not result in auy chauge in the detection diagnosis. or anv sguificaut iniprovenient in the ongitudinal field upper limit.," While these custom masks naturally provided a better representation of the Stokes $I$ and $V$ spectra, they did not result in any change in the detection diagnosis, or any significant improvement in the longitudinal field upper limit."
 As a consequence. all results xeseuted here correspoud tosolar abuudauce Bue masks.," As a consequence, all results presented here correspond tosolar abundance line masks."
" Finally, we imeasured for each star (generally the xmv) the radial velocity RV from the averaged LSD Stokes J profile. using a eaussian fit."," Finally, we measured for each star (generally the primary) the radial velocity $RV$ from the averaged LSD Stokes $I$ profile, using a gaussian fit."
" The long term stability of NARVAL is about 30 nis (ο,ο, Aiierre et al.", The long term stability of NARVAL is about 30 m/s (e.g. Aurièrre et al.
" 2009a) but the absolute uucertantv of individual measurements relative to the local standard of rest is about ld luis +,", 2009a) but the absolute uncertainty of individual measurements relative to the local standard of rest is about 1 km $^{-1}$.
 Table 1 eives for cach star its Womaenitude. spectral class. dnask temperature used. esin’. and. for cach observation. the date. ILJD. (corresponding to the RV. nuüeasureient). nuinber of exposures and total exposure time. RV. and the inferred longitudinal magnetic field with its standard error im C. Our aim is to search for magnetic fields on non Ap/Bp A-type stars in order to establish definitively the eap of the maguetic dichotomy.," Table 1 gives for each star its $V$ magnitude, spectral class, mask temperature used, $v \sin i$, and, for each observation, the date, HJD (corresponding to the $RV$ measurement), number of exposures and total exposure time, $RV$, and the inferred longitudinal magnetic field with its standard error in G. Our aim is to search for magnetic fields on non Ap/Bp A-type stars in order to establish definitively the gap of the magnetic dichotomy."
 Shorlin ct al. (, Shorlin et al. (
2002) showed the ercat influence of the value of esin? on the sensitivity of a magnetic survey usine high-resolution spectropolarimetry.,2002) showed the great influence of the value of $v \sin i$ on the sensitivity of a magnetic survey using high-resolution spectropolarimetry.
 Tn order to reduce the errors in our survey. we choose here to observe the most promising objects already: observed by Shorlin et al. (," In order to reduce the errors in our survey, we choose here to observe the most promising objects already observed by Shorlin et al. ("
2002).,2002).
 Ai stars are frequeutlve found iu close binaries (Alt Levy 1985). likely because tidal iuteractions im such systems slow stellar rotation and thereby reduce rotational nunxing.," Am stars are frequently found in close binaries (Abt Levy 1985), likely because tidal interactions in such systems slow stellar rotation and thereby reduce rotational mixing."
 This is also the case for Πσλ[αι stars (Rvabchikova 1998)., This is also the case for HgMn stars (Ryabchikova 1998).
 This property does not hamper our study. but the interesting cases of the SB2 stars 32 Vir aud A Vir are discussed in detail iu Sect.3.2.," This property does not hamper our study, but the interesting cases of the SB2 stars 32 Vir and $\lambda$ Vir are discussed in detail in Sect.3.2."
" No Zeeman detection was obtained for anv of our sample stars. since false alarm probability was always greater than 7, apart from the case of 32 Vir which is discussed in Sect."," No Zeeman detection was obtained for any of our sample stars, since false alarm probability was always greater than $^{-3}$, apart from the case of 32 Vir which is discussed in Sect."
 3.2., 3.2.
 The results are discussed further for Am aud HgMa stars in Sect., The results are discussed further for Am and HgMn stars in Sect.
 3.2 and 3.3 respectively., 3.2 and 3.3 respectively.
 A stars are cool A-type stars that can be considered as “ordinary” slowly rotating BA-stars (Takeda ct al., Am stars are cool A-type stars that can be considered as ”ordinary” slowly rotating A-stars (Takeda et al.
 200s)., 2008).
 A laree nunuber of Ai stars deserve a seusitive magnetic survev with NARVAL: we observed 12 of them. amone them the bright star Sirius.," A large number of Am stars deserve a sensitive magnetic survey with NARVAL; we observed 12 of them, among them the bright star Sirius."
 Our main selection criterion for the stars observed was low esin. which we required to be zualler than 50 kimi 1 . aud is often wich smaller.," Our main selection criterion for the stars observed was low $v \sin i$ , which we required to be smaller than 50 km $^{-1}$ , and is often much smaller."
 Our sample stars are generally on the main sequence.," Our sample stars are generally on the main sequence,"
chwarl with an estimated mass of 20.014 M. (2). andisrightatthelithiumdepletionedgeinthePleaides(?).,"dwarf with an estimated mass of $\sim$ $\Msun$ \citep{bihain2010}, and is right at the lithium depletion edge in the Pleaides \citep{stauffer1998}."
.C respectively. andiheirsubstellarnalureiscon firmedthroughthepresenecoflilhium(t)..," Calar 3 and Teide 1, two M8 dwarfs, have estimated masses of $\sim$ $\Msun$ and $\sim$ $\Msun$ \citep[at 
d=120\,pc;][]{bihain2010}, respectively, and their substellar nature is confirmed through the presence of lithium \citep{rebolo1996}."
 1 13- T," HII 1348B has the same spectral type as Calar 3 and Teide 1, and we therefore conclude that is also substellar."
I 13484 is a double-Iined spectroscopic binary (?).. and hence an upper mass limit for the primary can be obtained by assuming (that both components are VV stars.," Future optical spectroscopy could confirm the presence of lithium in HII 1348B. HII 1348A is a double-lined spectroscopic binary \citep{queloz1998}, and hence an upper mass limit for the primary can be obtained by assuming that both components are V stars."
 With the mass of a single VV star being ~0.65A/. (2).. the SB2 star HIT 1348Àab has a mass ol c 11.344..," With the mass of a single V star being $\sim$ $\Msun$ \citep{zakhozhaj1998}, the SB2 star HII 1348Aab has a mass of $\sim$ $\Msun$."
. A more precise mass estimate can be obtained using the 2—V. colors of III 1348Àa and HII 1243Àb (1.05 and 1.35. respectively) given by ?..," A more precise mass estimate can be obtained using the $B-V$ colors of HII 1348Aa and HII 1348Ab (1.05 and 1.35, respectively) given by \citet{queloz1998}."
" The colors roughly translate Lo masses of 7250.07A. and 0.55260.05M, . respectively. vielding a total estimated mass of 1.22+0.00.1\/. for IHE 1348Àab."," The colors roughly translate to masses of $\pm$ $\Msun$ and $\pm$ $\Msun$, respectively, yielding a total estimated mass of $\pm$ $\Msun$ for HII 1348Aab."
 Adopting the latter mass for the5B2 component. the mass ratio of HIE 1347B to IHE 1347Àab is between 0.0430.052 (Table 2)).," Adopting the latter mass for theSB2 component, the mass ratio of HII 1347B to HII 1347Aab is between 0.043–0.052 (Table \ref{tab:info}) )."
 This is the lowest among the known Pleiad multiples (??).. and is comparable to that of very. low-mass ratio binaries in the field (7)..," This is the lowest among the known Pleiad multiples \citep{bouvier1997, bouy2006}, and is comparable to that of very low-mass ratio binaries in the field \citep{faherty2011}."
 I] 1348B is a new AIS brown dwarl member of the Pleiades. and (he fist substellar companion discovered around a Pleiades star.," HII 1348B is a new M8 brown dwarf member of the Pleiades, and the first substellar companion discovered around a Pleiades star."
 Given that no other substellar companions were discovered in the ?— survey al similar or wider separations. it is worth considering whether HII 1348B may be unusually weakly bound. compared (to other binary svstems in ihe Pleiades or in the field.," Given that no other substellar companions were discovered in the \citet{bouvier1997} survey at similar or wider separations, it is worth considering whether HII 1348B may be unusually weakly bound, compared to other binary systems in the Pleiades or in the field."
 ? found a total of 28 stellar binaries in the Pleiades in their CLIFT AO survey., \citet{bouvier1997} found a total of 28 stellar binaries in the Pleiades in their CHFT AO survey.
 HST survevs of verv low mass stars and brown clwarls conducted by ?2/— and ?/— revealed three additional binaries., HST surveys of very low mass stars and brown dwarfs conducted by \citet{martin2003} and \citet{bouy2006} revealed three additional binaries.
 In Figure 8 we compare the binding energies of these svstems. and those of field AM binaries (???).. to the binding enerev of HII 13434/D. As can be seen. TI 1348A/B sits in the middle of the loeus [οι stellar binaries. and is comparably or more lightly bound even than the three very low mass Pleiacles binaries.," In Figure \ref{fig:Ebind} we compare the binding energies of these systems, and those of field A–M binaries \citep{close1990, close2003, close2007}, to the binding energy of HII 1348A/B. As can be seen, HII 1348A/B sits in the middle of the locus for stellar binaries, and is comparably or more tightly bound even than the three very low mass Pleiades binaries."
 What is more. substellar companions up to LO times further away [rom their primaries would still be well above the minimum stellar binding energy in the Pleiacles.," What is more, substellar companions up to 10 times further away from their primaries would still be well above the minimum stellar binding energy in the Pleiades."
 The dearth of known brown dwarl companions to stars in the Pleiacles may thus be attributable to the lack of a follow-up sensitive aud comprehensive high-contrast imagine survey of the cluster., The dearth of known brown dwarf companions to stars in the Pleiades may thus be attributable to the lack of a follow-up sensitive and comprehensive high-contrast imaging survey of the cluster.
 Simall samples of Pleiades stars have since been observed in deep survevs bv 7. and ?.. with no new brown dwarf companion detections.," Small samples of Pleiades stars have since been observed in deep surveys by \citet[23 stars;][]{metchev2009} and \citet[14 stars;][]{tanner2007}, , with no new brown dwarf companion detections."
 However. a much," However, a much"
from the one-sigma period uncertainty).,from the one-sigma period uncertainty).
 Our new aand ddata. and the / spectra we wish to model for abundances. cannot be accurately phased with the older measurements without improving the precision of the period.," Our new and data, and the $I$ spectra we wish to model for abundances, cannot be accurately phased with the older measurements without improving the precision of the period."
 In principle. the period can be improved both by fitting our new mmeasurements to the five measurements used by ?.. and by optimising the fit of our new ddata to the well-determined variations of this field moment as measured by both the Fe and the Nd line.," In principle, the period can be improved both by fitting our new measurements to the five measurements used by \citet{LM2000}, and by optimising the fit of our new data to the well-determined variations of this field moment as measured by both the Fe and the Nd line."
 In practice. however. the variation of wwith phase is too sparsely sampled by both the older field measurements and our own for comparison to allow us to refine the period.," In practice, however, the variation of with phase is too sparsely sampled by both the older field measurements and our own for comparison to allow us to refine the period."
 This problem is made more difficult for HD 318107 by the very different values of tthat are found at any particular phase by only moderately different measurement methods., This problem is made more difficult for HD 318107 by the very different values of that are found at any particular phase by only moderately different measurement methods.
 Hence we turn to the new ddata., Hence we turn to the new data.
 Fortunately the numerous vvalues as measured by Fe 6149 aand by Nd 6145 vvary in significantly different ways. and from ? we have convenient polynomials describing the variations of wwith phase for these two elements.," Fortunately the numerous values as measured by Fe 6149 and by Nd 6145 vary in significantly different ways, and from \citet{MM2000} we have convenient polynomials describing the variations of with phase for these two elements."
 Note that in Table 2 of ? the coefficients A of the polynomials for the two spectral lines have been inadvertently exchanged (private communication with Mathys)., Note that in Table 2 of \citet{MM2000} the coefficients $A$ of the polynomials for the two spectral lines have been inadvertently exchanged (private communication with Mathys).
 Varying the period through the range allowed by the uncertainty of +0.0021 d. we find that our new mmeasurements fall Very nicely on the appropriate polynomials for a limited range of periods.," Varying the period through the range allowed by the uncertainty of $\pm 0.0021$ d, we find that our new measurements fall very nicely on the appropriate polynomials for a limited range of periods."
 The best fit as judged by the γ΄ of the fit for Fe is P=9.7087+0.0012 d. while both Nd lines agree on P=9.7089+0.0007 d. for a conservative global average of P=9.7088+0.0007 d. and an adopted zero point of JD 2449397.828.," The best fit as judged by the $\chi^2$ of the fit for Fe is $P = 9.7087 \pm 0.0012$ d, while both Nd lines agree on $P = 9.7089 \pm 0.0007$ d, for a conservative global average of $P = 9.7088 \pm 0.0007$ d, and an adopted zero point of JD 2449397.828."
 This reduces the phase uncertainty of our new data with respect to the data from the 1990s to about £0.03 cycle., This reduces the phase uncertainty of our new data with respect to the data from the 1990s to about $\pm 0.03$ cycle.
 All phases reported here are on this system., All phases reported here are on this system.
 A comparison of our new ddata to the polynomials of ? 1s shown in the upper two panels of Figure l.., A comparison of our new data to the polynomials of \citet{MM2000} is shown in the upper two panels of Figure \ref{magfield}.
 It is clear from this figure that the agreement of our data with the previous mmeasurements Is very satisfactory. and 1t is also obvious why significant phase shifts of especially the Nd data rapidly lead to decreased quality of the fit between the two data sets. so that the new period is accurately determined.," It is clear from this figure that the agreement of our data with the previous measurements is very satisfactory, and it is also obvious why significant phase shifts of especially the Nd data rapidly lead to decreased quality of the fit between the two data sets, so that the new period is accurately determined."
 The improved period is then used to phase the older ddata shown by ? with the new measurements., The improved period is then used to phase the older data shown by \citet{LM2000} with the new measurements.
 The results are shown in the bottom panel of Figure |.., The results are shown in the bottom panel of Figure \ref{magfield}.
 Several points emerge from this figure., Several points emerge from this figure.
 First. the new data are generally consistent with the older measurements provided that we use the metal line vvalue from FORSI] at phase 0.91.," First, the new data are generally consistent with the older measurements provided that we use the metal line value from FORS1 at phase 0.91."
 At this phase the Balmer line field strength is about 2500 G higher than the older measurement at almost the same phase., At this phase the Balmer line field strength is about 2500 G higher than the older measurement at almost the same phase.
 Secondly. the variations of both aand ((from ὁ=0.5 to ὁ=1.0) appear to be rather non-sinusoidal.," Secondly, the variations of both and (from $\phi = 0.5$ to $\phi = 1.0$ ) appear to be rather non-sinusoidal."
 These facts. as discussed above. very strongly suggest that either the detailed metal abundance distributions or the field geometry. or probably both. are complex.," These facts, as discussed above, very strongly suggest that either the detailed metal abundance distributions or the field geometry, or probably both, are complex."
 This star appears to belong to the small sample of stars. including HD 32633 (?).. HD 37776 (?).. HD 133880 (?).. HD 137509 (?).. and r Sco (?) in which the magnetic field may depart in an important way from the generally dipolar topology of the magnetic fields of most Ap stars. (," This star appears to belong to the small sample of stars, including HD 32633 \citep{hd32633}, HD 37776 \citep{Kochetal10}, HD 133880 \citep{Landstreet1990}, HD 137509 \citep{kochukhov2006}, and $\tau$ Sco \citep{donati2006} in which the magnetic field may depart in an important way from the generally dipolar topology of the magnetic fields of most Ap stars. ("
The field and surface He distribution of the outstandingly peculiar magnetic He-strong star HD 37776 have recently been mapped by ?.. and the resulting map reveals a quite astonishing degree of complexity.),"The field and surface He distribution of the outstandingly peculiar magnetic He-strong star HD 37776 have recently been mapped by \citet{Kochetal10}, and the resulting map reveals a quite astonishing degree of complexity.)"
 Thirdly. the fact that the FORSI metal line vvalue agrees with the older metal line measurement. while the Balmer line mmeasurement does not. is certainly consistent with the idea that the difference between the two FORSI vvalues is due to the combination of a rather complex field distribution and substantial differences in the way that the field is sampled by the presumably uniformly distributed H and the strongly patchy metal distributions.," Thirdly, the fact that the FORS1 metal line value agrees with the older metal line measurement, while the Balmer line measurement does not, is certainly consistent with the idea that the difference between the two FORS1 values is due to the combination of a rather complex field distribution and substantial differences in the way that the field is sampled by the presumably uniformly distributed H and the strongly patchy metal distributions."
 It ts clear that it would be extremely interesting to obtain V (and probably Q and U spectra) of this star with rather fine phase resolution. at least of order 0.05 cycle. to make it possible to explore more fully the field and abundance distribution structure.," It is clear that it would be extremely interesting to obtain $V$ (and probably $Q$ and $U$ spectra) of this star with rather fine phase resolution, at least of order 0.05 cycle, to make it possible to explore more fully the field and abundance distribution structure."
 To model the spectrum of HD 318107 we use the magnetic spectrum synthesis programme ZEEMAN (??)..," To model the spectrum of HD 318107 we use the magnetic spectrum synthesis programme ZEEMAN \citep{L1988,L1989}."
 This programme is designed to compute the emergent spectrum of à star of specified παπά logg. with a specified magnetic. field. strength and geometry (currently characterized as a sum of colinear dipole. quadrupole. and octupole. at a specified anglef to the rotation axis).," This programme is designed to compute the emergent spectrum of a star of specified and $\log g$, with a specified magnetic field strength and geometry (currently characterized as a sum of colinear dipole, quadrupole, and octupole, at a specified angle $\beta$ to the rotation axis)."
 Either a uniform surface abundance distribution or a distribution which ts a simple function only of latitude in the frame of reference of the magnetic axis can be specified., Either a uniform surface abundance distribution or a distribution which is a simple function only of latitude in the frame of reference of the magnetic axis can be specified.
 The parameters of the magnetic field model are chosen to match the observed field strength measurements of aand aas a function of phase. generally as described by ?..," The parameters of the magnetic field model are chosen to match the observed field strength measurements of and as a function of phase, generally as described by \citet{LM2000}."
 The magnetic model can be further tested by comparison. of computed line profiles to observed ones in cases such as HD 318107 where line splitting is an important line broadening mechanism., The magnetic model can be further tested by comparison of computed line profiles to observed ones in cases such as HD 318107 where line splitting is an important line broadening mechanism.
 In principle. since ZEEMAN computes all four Stokes parameters. comparison could be made with observed polarised spectra. but this possibility is not implemented at present.," In principle, since ZEEMAN computes all four Stokes parameters, comparison could be made with observed polarised spectra, but this possibility is not implemented at present."
 The abundance variation with magnetic latitude is currently specified in the form of uniform abundance values on each of one to six rings of equal extent in latitude., The abundance variation with magnetic latitude is currently specified in the form of uniform abundance values on each of one to six rings of equal extent in latitude.
 The abundance of one element at a time. and its variation with latitude. can be varied by the programme to optimise the fit to a set of spectral," The abundance of one element at a time, and its variation with latitude, can be varied by the programme to optimise the fit to a set of spectral"
not in GALEN | 3844 (lable 4)).,not in GALEX $+$ 3844 (Table \ref{tbl_bin}) ).
 We estimated the probability of a given frequency relative to the probability of the peak frequency following Pressetal.(1992). and determined the le (66%)) error bars on the period. of the photometric variations for GALEN | 4727: and 2M | 3759: For both stars. the period. of photometric variations is equal. within error bars. to the measurec orbital period. thereby. validating the method.," We estimated the probability of a given frequency relative to the probability of the peak frequency following \citet{pre1992} and determined the $\sigma$ ) error bars on the period of the photometric variations for GALEX $+$ 4727: and 2M $+$ 3759: For both stars, the period of photometric variations is equal, within error bars, to the measured orbital period, thereby validating the method."
 Figure 4 shows the NSVS light) curves for GALEN 1 4727. and GALLEN | 3844 folded. on the orbital period with an arbitrary phase adjustment so that &=0 corresponds to the inferior conjunction of the primary star (sclB)., Figure \ref{fig_phot} shows the NSVS light curves for GALEX $+$ 4727 and GALEX $+$ 3844 folded on the orbital period with an arbitrary phase adjustment so that $\Phi=0$ corresponds to the inferior conjunction of the primary star (sdB).
 “Phe distant. NSVS epoch ( 1999) preclucecl phasing with the current. orbital ephemeris (Table 4))., The distant NSVS epoch ( 1999) precluded phasing with the current orbital ephemeris (Table \ref{tbl_bin}) ).
 The light. curve of GALEN | 4727 is fitted with the sine curve: that we interpret as a rellection. effect. on a. late- secondary star. (Section 4)., The light curve of GALEX $+$ 4727 is fitted with the sine curve: that we interpret as a reflection effect on a late-type secondary star (Section 4).
 The variations in GALEN 2349] 3844. are not significant with a mean magnitude of «m=12.281x0.003 and a semi-amplituce of Nimm/2=0.009+0.004., The variations in GALEX $+$ 3844 are not significant with a mean magnitude of $<m>=12.281\pm0.003$ and a semi-amplitude of $\Delta m/2=0.009\pm0.004$.
 Our analysis of the spectroscopic observations of the primary stars is based on a grid of non-L'TE models ancl synthetic spectra calculated using PLUSTY/SYNSPEC (IIubeny&Lanz1995:&Lubeny 1995).," Our analysis of the spectroscopic observations of the primary stars is based on a grid of non-LTE models and synthetic spectra calculated using TLUSTY/SYNSPEC \citep{hub1995,lan1995}."
. The grid covers the elective. temperature from. Z;4;=21000 to 35000 Ix. (in steps of 1000. I). the surface. gravity. [rom logg=4.75 to 6.25 (in steps of 0.25). and the helium abundance from," The grid covers the effective temperature from $T_{\rm eff}=21000$ to 35000 K (in steps of 1000 K), the surface gravity from $\log{g}=4.75$ to 6.25 (in steps of 0.25), and the helium abundance from"
Since we deal with the oplically thin region outside the neutrino sphere in this paper. we do not have to solve (he transport equation for neutrinos.,"Since we deal with the optically thin region outside the neutrino sphere in this paper, we do not have to solve the transport equation for neutrinos."
 We assume that (he neutrino distribution functions are approximated bv the Fermi-Dirac distribution with a vanishing chemical potential: where the geometrical [actor is taken into account for normalization., We assume that the neutrino distribution functions are approximated by the Fermi-Dirac distribution with a vanishing chemical potential; where the geometrical factor is taken into account for normalization.
 Note Chat although the angular dependence in the above distribution Iunction is assumed {ο be isotropic. it is entirely irrelevant for (he absorption and emission rates.," Note that although the angular dependence in the above distribution function is assumed to be isotropic, it is entirely irrelevant for the absorption and emission rates."
" We further assume lor simplicity in the following that the luminosity £,. temperature 7), ancl neutrino sphere r, are related bv the following equation. where σ is the Stefan-Doltzmann constant."," We further assume for simplicity in the following that the luminosity $L_{\nu}$, temperature $T_{\nu}$ and neutrino sphere $r_{\nu}$ are related by the following equation, where $\sigma$ is the Stefan-Boltzmann constant."
 In order (o clearly see the linear growths of the instability. it is critically important (o use a well-defined unperturbed state as an initial condition for simulations.," In order to clearly see the linear growths of the instability, it is critically important to use a well-defined unperturbed state as an initial condition for simulations."
 For this purpose. we employ the spherically svuunetric steady accretion flows through the standing shock wave in (his paper.," For this purpose, we employ the spherically symmetric steady accretion flows through the standing shock wave in this paper."
 Following(2005). we solve the ime-independent hyvdrodynamical equations Irom the shock front down to the inner boundary.," Following, we solve the time-independent hydrodynamical equations from the shock front down to the inner boundary,"
more rapidly in the beginning. caused by the rapid increase of the turbulent sub-grid energy (see Fig. 9)).,"more rapidly in the beginning, caused by the rapid increase of the turbulent sub-grid energy (see Fig. \ref{esubcomp}) ),"
 in contrast to the models without front-tracking., in contrast to the models without front-tracking.
 This. in fact. is in agreement with ones expectations because the tracked front has more structure and. therefore. a larger surface area.," This, in fact, is in agreement with ones expectations because the tracked front has more structure and, therefore, a larger surface area."
 However. already after O.5s the total energy released by nuclear burning in all our present models 1s high enough to lead to an overall expansion of the white dwarf. as was discussed in the previous subsections.," However, already after 0.5s the total energy released by nuclear burning in all our present models is high enough to lead to an overall expansion of the white dwarf, as was discussed in the previous subsections."
 Consequently. the sub-grid energy drops again and so does the nuclear energy generation rate.," Consequently, the sub-grid energy drops again and so does the nuclear energy generation rate."
 So in total less energy is produced in comparison to the models without tracking. which reach their peak values of both the energy generation and the sub-grid energy about a factor of two later and. therefore. expand later.," So in total less energy is produced in comparison to the models without tracking, which reach their peak values of both the energy generation and the sub-grid energy about a factor of two later and, therefore, expand later."
 An exception is our model B5., An exception is our model B5.
 Here the energy generation rate rises so fast that the star 1s already unbound at the time when bulk expansion sets in., Here the energy generation rate rises so fast that the star is already unbound at the time when bulk expansion sets in.
 In addition to the higher sub-grid energy production during the early stages of the simulations. we observe that most of the turbulence is generated in a very thin region around the flame. resulting in extremely high turbulence intensities near the front and a further increase in the burning speed (Fig. 10)).," In addition to the higher sub-grid energy production during the early stages of the simulations, we observe that most of the turbulence is generated in a very thin region around the flame, resulting in extremely high turbulence intensities near the front and a further increase in the burning speed (Fig. \ref{subspeed}) )."
 This is caused by the fact that the transition between the rising bubbles of hot. light ashes and the dense. cold fuel is quite thin ( 2A). which leads to a well-localized shear flow and turbulent energy generation. as one would expect in reality.," This is caused by the fact that the transition between the rising bubbles of hot, light ashes and the dense, cold fuel is quite thin $\approx 2\Delta$ ), which leads to a well-localized shear flow and turbulent energy generation, as one would expect in reality."
 In Niemeyer's simulations. in contrast. the transition was smeared out over several cells because of the employed reactive-diffusive flame model: consequently. the turbulent flame propagation speed was underestimated.," In Niemeyer's simulations, in contrast, the transition was smeared out over several cells because of the employed reactive-diffusive flame model; consequently, the turbulent flame propagation speed was underestimated."
 In the present paper we have presented first results obtained by applying a new numerical technique to. thermonuclear explosions of Chandrasekhar-mass C+O white dwarfs., In the present paper we have presented first results obtained by applying a new numerical technique to thermonuclear explosions of Chandrasekhar-mass C+O white dwarfs.
 Our code differs from those used previously in the atrophysics literature in that it follows the propagation of the burning front explicitly by means of a level set funetion., Our code differs from those used previously in the atrophysics literature in that it follows the propagation of the burning front explicitly by means of a level set function.
 Our approach has the advantage that numerical diffusion of the front i5 largely avoided and that the structure of burning regions 1s resolved down to a few grid zones. which is an important issue In numerical simulations of combustion.," Our approach has the advantage that numerical diffusion of the front is largely avoided and that the structure of burning regions is resolved down to a few grid zones, which is an important issue in numerical simulations of combustion."
 Moreover. in principle. an extension of the code is possible. making use of the fact that the thermodynamic properties in mixed cells can be reconstructed from the conservation laws of mass. energy. and momentum. tf the burning velocity of the front is known.," Moreover, in principle, an extension of the code is possible, making use of the fact that the thermodynamic properties in mixed cells can be reconstructed from the conservation laws of mass, energy, and momentum, if the burning velocity of the front is known."
 Such a code could also be applied to the Type Ia supernova problem and would. for the first time. allow to include individual nuclear reactions in a meaningful way. and we are presently working o this extension.," Such a code could also be applied to the Type Ia supernova problem and would, for the first time, allow to include individual nuclear reactions in a meaningful way, and we are presently working on this extension."
 Since our aim. was to demonstrate that deflagrations 1 Mey white dwarfs car lead to explosions which have th[27 properties of some Gf not of typical) Type Ia supernovae. th[27 outcome so far is disappointing.," Since our aim was to demonstrate that deflagrations in $_{\text{Ch}}$ white dwarfs can lead to explosions which have the properties of some (if not of typical) Type Ia supernovae, the outcome so far is disappointing."
 Our models produce eve less nickel and less energy than those computed with simpler and less accurate numerical schemes., Our models produce even less nickel and less energy than those computed with simpler and less accurate numerical schemes.
 In retrospect the reaso for this finding ts obvious., In retrospect the reason for this finding is obvious.
" For a ""healthy"" explosion it 1non not sufficient to accelerate the burning front beyond what 1 predicted by previous numerical experiments. at least not 1 multi-dimensional models."," For a “healthy” explosion it is not sufficient to accelerate the burning front beyond what is predicted by previous numerical experiments, at least not in multi-dimensional models."
 In fact. more rapid burning may under certain circumstances result in an expansion and cooling of the white dwarf large amounts of nuclear fuel are consumed.," In fact, more rapid burning may under certain circumstances result in an expansion and cooling of the white dwarf large amounts of nuclear fuel are consumed."
 Our centrally tgnited models and the one with a single off-center blob are examples., Our centrally ignited models and the one with a single off-center blob are examples.
 The question. therefore. remains whether or no our simulations rule out the deflagration scenario for typical Type Ia supernovae.," The question, therefore, remains whether or no our simulations rule out the deflagration scenario for typical Type Ia supernovae."
 Possible short-comings of the present numerical approach. such as the artificial symmetry assumption or the still insufficient numerical resolution. have already been mentioned.," Possible short-comings of the present numerical approach, such as the artificial symmetry assumption or the still insufficient numerical resolution, have already been mentioned."
 Here improvements will be possible with increasing computer power in the near future., Here improvements will be possible with increasing computer power in the near future.
 It might also be worthwhile to investigate the behaviour of the simulations with varied parameter sets. e.g. for different chemical compositions or a slightly increased turbulent flame speed. since both of these quantities are not known exactly.," It might also be worthwhile to investigate the behaviour of the simulations with varied parameter sets, e.g. for different chemical compositions or a slightly increased turbulent flame speed, since both of these quantities are not known exactly."
 A second open question concerns our model of turbulent combustion., A second open question concerns our model of turbulent combustion.
 Here it is not clear at all. if one of our basic assumptions. namely that in the presence of reactions the turbulence spectrum Is given by the Kolmogorov law remains valid.," Here it is not clear at all, if one of our basic assumptions, namely that in the presence of reactions the turbulence spectrum is given by the Kolmogorov law remains valid."
 Although in the limit of very high turbulence intensity experiments seem to support our hypothesis more work needs to be done., Although in the limit of very high turbulence intensity experiments seem to support our hypothesis more work needs to be done.
 Also. significant burning is still possible at low densities mm the. so-called distributed regime. and even a transition to a detonation Is not ruled out there (?)..," Also, significant burning is still possible at low densities in the so-called distributed regime, and even a transition to a detonation is not ruled out there \citep{niemeyer-woosley-97}."
 Finally. white dwarfs at the onset of the explosion might look rather different from the ones we have used as initial conditions.," Finally, white dwarfs at the onset of the explosion might look rather different from the ones we have used as initial conditions."
" URCA-neutrino emission and non stationary convection during the evolution just prior to the explosion have already been mentioned as likely sources of large uncertainties,", URCA-neutrino emission and non stationary convection during the evolution just prior to the explosion have already been mentioned as likely sources of large uncertainties.
 Also. whether the star reaches the Chandrasekhar-mass by accretion or by merging with a companion will make a big difference.," Also, whether the star reaches the Chandrasekhar-mass by accretion or by merging with a companion will make a big difference."
 For example. rotation in some form may directly affect the propagation of the deflagration front.," For example, rotation in some form may directly affect the propagation of the deflagration front."
 All. these, All these
magnetic field Bo in magnetized turbulent environments.,magnetic field $\Bv_{0}$ in magnetized turbulent environments.
" When the grain moves together with the wave along Bo, it is subject to magnetic mirror forces —(mv? where v, is the grain velocity component perpendicular/2B)V|B, to Bo."," When the grain moves together with the wave along $\Bv_{0}$, it is subject to magnetic mirror forces $-(mv_{\perp}^{2}/2B)\nabla_{\|}\Bv$, where $v_{\perp}$ is the grain velocity component perpendicular to $\Bv_{0}$."
" In the plasma reference, the back and forth collisions of the grain with the moving magnetic mirrors increase grain energy because the head-on collisions are more frequent than trailing collisions (see e.g., Fisk "," In the plasma reference, the back and forth collisions of the grain with the moving magnetic mirrors increase grain energy because the head-on collisions are more frequent than trailing collisions (see e.g., Fisk 1976)."
"The resonance condition for a grain with velocity v 1976).reads where vj=vp is the grain velocity component parallel to B, and w is the wave frequency (see Fisk 1976; Schlickeiser Miller 1998)."," The resonance condition for a grain with velocity $\vv$ reads where $v_{\|}=v\mu$ is the grain velocity component parallel to $\Bv$, and $\omega$ is the wave frequency (see Fisk 1976; Schlickeiser Miller 1998)."
" For fast MHD modes in low-§ plasma, the dispersion relation is w=kVa (see Cho et al."," For fast MHD modes in $\beta$ plasma, the dispersion relation is $\omega=k V_{\A}$ (see Cho et al."
" 2002), and the required velocity for TTD corresponds to vj=vA/cos8."," 2002), and the required velocity for TTD corresponds to $v_{\|}=v_{\A}/\cos\theta$."
" Thus, if vj2Va, TTD can be efficient to accelerate grains to large velocities."," Thus, if $v_{\|}\ge V_{\A}$, TTD can be efficient to accelerate grains to large velocities."
" In the NLT limit, the diffusion coefficient for TTD is given by (see Appendix C) ]"," In the NLT limit, the diffusion coefficient for TTD is given by (see Appendix C) ]."
 In Figure 3 we present D as a function of the cosine of the grain pitch angle µ DIIobtained using the QLT and NLT., In Figure \ref{Dpp_mu_TTD} we present $D_{pp}^{\TTD}$ as a function of the cosine of the grain pitch angle $\mu$ obtained using the QLT and NLT.
 Two values of the grain velocity v=1.5Va and 3.5Va are considered., Two values of the grain velocity $v=1.5~V_{\A}$ and $3.5~V_{\A}$ are considered.
" It can be seen that in the former case, Dy)P increases with decreasing jj until pp=v/Va, and drops sharply to zero for jj<v/Va because the resonance condition (19)) is not satisfied."," It can be seen that in the former case, $D_{pp}^{\TTD}$ increases with decreasing $\mu$ until $\mu=v/V_{\A}$, and drops sharply to zero for $\mu<v/V_{\A}$ because the resonance condition \ref{eq:resTTD}) ) is not satisfied."
" In contrast, the broadening of the resonance condition in the latter case allows grains with i«V4/v to have resonant interactions with waves, resulting in finite DIT even at p.=0."," In contrast, the broadening of the resonance condition in the latter case allows grains with $\mu<V_{\A}/v$ to have resonant interactions with waves, resulting in finite $D_{pp}^{\TTD}$ even at $\mu=0$."
" Therefore, TTD is usually neglected in the QLT because the gyroresonance tends to accelerate grains in the perpendicular direction to Bo, resulting in 44=0, for which —0."," Therefore, TTD is usually neglected in the QLT because the gyroresonance tends to accelerate grains in the perpendicular direction to $\Bv_{0}$, resulting in $\mu=0$, for which $D_{pp}^{\TTD}\rightarrow 0$."
" However, TTD can play an important role inDTP driving grain motion when the fluctuations of guiding center are taken into account."," However, TTD can play an important role in driving grain motion when the fluctuations of guiding center are taken into account."
" Consider an ensemble of grains with the same mass m, moving in the uniform magnetic field with theirdifferent pitch angles µ."," Consider an ensemble of grains with the same mass $m$, moving in the uniform magnetic field with theirdifferent pitch angles $\mu$."
" From the equation of motion, mdv/dt=+ R, where R is the random force, we can obtain—mv/tarag where (v?) is the grain velocity dispersion averaged over the ensemble of grains, A(v) is the rate of energy gain YL03)."," From the equation of motion, $mdv/dt=-mv/t_{\drag}+R$ , where $R$ is the random force, we can obtain where $\langle v^{2}\rangle$ is the grain velocity dispersion averaged over the ensemble of grains, $A(v)$ is the rate of energy gain (see YL03)."
" (seeWhen the scattering is less efficient than the the cosine of the grain pitch angle 4=cosf changes slowly during acceleration, and A(v) is given by where Dpp(p,μ) is the diffusion coefficient."," When the scattering is less efficient than the the cosine of the grain pitch angle $\mu=\cos\beta$ changes slowly during acceleration, and $A(v)$ is given by where $D_{pp}(p,\mu)$ is the diffusion coefficient."
" When the scattering is more efficient than the acceleration, the pitch angle can be rapidly redistributed through pitch angle diffusion during the acceleration (i.e., diffusion approximation)."," When the scattering is more efficient than the acceleration, the pitch angle can be rapidly redistributed through pitch angle diffusion during the acceleration (i.e., diffusion approximation)."
 The rate of energy gain (Eq. , The rate of energy gain (Eq. \ref{eq:Av}) )
"is then determined by the averaged value D, of 23))μ) over the isotropic distribution of µ (see Dung Dyp(p,Schlickeiser 1990ab): We consider in the present paper zero helicity turbulence with D,— 0."," is then determined by the averaged value $D_{p}$ of $D_{pp}(p,\mu)$ over the isotropic distribution of $\mu$ (see Dung Schlickeiser 1990ab): We consider in the present paper zero helicity turbulence with $D_{\mu p}=0$ ."
" When is known, we solve Equation (22)) iteratively to get Dy,convergent velocities."," When $D_{pp}$ is known, we solve Equation \ref{eq:dv-dt}) ) iteratively to get convergent velocities."
 (1970:1979). alain Cuistafssouctal.(1975) Tsuji(1976).. (IlohvegerL970:Coustatssoual.1975).. WoO). (I&urucz1992):Castelli.Caratton.&I&urucz1997). UWausc," \citeyearpar{kurucz70,kurucz79} \citet{gustafssonetal75} \citet{tsuji76}, \citeyearpar{kurucz92a,kurucz95} \citep{holweger70, gustafssonetal75}, $_2$ \citep{kurucz92b,castellietal97}."
hildtetal.(19994.b) rave presented their PIOENTIN/NestCen eid of model atinospheres for dwart aud giaut stars.," \citet{hau99a,hau99b} have presented their PHOENIX/NextGen grid of model atmospheres for dwarf and giant stars."
 Allard.Hauschildt.&Selaweitzer(2000) extended he original bulk of models to the pre-muaiu-sequence (pre-MS). evolution at the low-iass regune., \citet{allardetal00} extended the original bulk of models to the pre-main-sequence (pre-MS) evolution at the low-mass regime.
 With its 500 million atomic aud molecular ines aud a spherical geometry treatiuent of stellar structure. the NextGen library is arguablv the nost advanced. one currently available in the iterature.," With its 500 million atomic and molecular lines and a spherical geometry treatment of stellar structure, the NextGen library is arguably the most advanced one currently available in the literature."
 As the low-temperature plivsical reeinie is suitable. sampled. with models as cool as Jig=2000 Ix. these may possibly fll the σα) assure a homogenous coverage of the stellar fundamental parameters across the whole IL-R diaeram.," As the low-temperature physical regime is suitably sampled, with models as cool as $\mteff = 2000$ K, these may possibly fill the gap assuring a homogenous coverage of the stellar fundamental parameters across the whole H-R diagram."
 Given the relevance of the I&urucz aud IHauschildt contributions. it could be of special interest. at this stage. to carry out a combined analysis of the ATLAS NNestGen codes. iu order to check their mutual capabilities to match spectroplotometiic properties of real stars and assess selfÉ-consisteucv in their input physics.," Given the relevance of the Kurucz and Hauschildt contributions, it could be of special interest, at this stage, to carry out a combined analysis of the ATLAS NextGen codes, in order to check their mutual capabilities to match spectrophotometric properties of real stars and assess self-consistency in their input physics."
 Our analysis follows the IbLuuschildt (1999a) xelinimaryv discussion. and will be carried out in two steps.," Our analysis follows the Hauschildt \citeyearpar{hau99a} preliminary discussion, and will be carried out in two steps."
" After a brief cescription of the nain features of each theoretical dataset 22), we will first trv a fit to observations of cluplate stars and compare model outputs 33)."," After a brief description of the main features of each theoretical dataset 2), we will first try a fit to observations of template stars and compare model outputs 3)."
" This will rely ou an original optimization oxocedure. that also provides an estimate of the fit uncertainty across the(Τμ,logg.. |M/TIJ)) ohase space."," This will rely on an original optimization procedure, that also provides an estimate of the fit uncertainty across the, ) phase space."
 The best fits will allowto establish aneffectivetemperature scale aud a calibration of he bolometric correction scale LL)., The best fits will allowto establish aneffectivetemperature scale and a calibration of the bolometric correction scale 4).
 In, In
Finally. it is noteworthy that the solid line in Figs.,"Finally, it is noteworthy that the solid line in Figs."
 | and 2 does not match well the upper boundary of the region occupied by barum and Te-poor S stars. thus suggesting that for these classes of post-mass-transfer binaries. tidal processes and periastron mass-transfer were. as expected. not the only ones to operate.," \ref{Fig:elogP_M} and \ref{Fig:elogP_panels} does not match well the upper boundary of the region occupied by barium and Tc-poor S stars, thus suggesting that for these classes of post-mass-transfer binaries, tidal processes and periastron mass-transfer were, as expected, not the only ones to operate."
 Mass transfer and interaction with à cireumbinary disc must have played a role for these (2).., Mass transfer and interaction with a circumbinary disc must have played a role for these \citep{Frankowski-2007a}.
 One mild barium star (HD 77247: P= stud: e= 0.09) deviates markedly from the rest of the sample of barium stars., One mild barium star (HD 77247: $P = 80.5$ d; $e = 0.09$ ) deviates markedly from the rest of the sample of barium stars.
 One may wonder whether the location of HD 77247 in the ddiagram along the periastron envelope of K giants Is just accidental. or whether it indicates instead that this system might not be a post-mass-transfer system after all. as are the other barium stars. but that its barium anomaly may rather be inherited from the gas out of which it formed. and be unrelated to its binary nature.," One may wonder whether the location of HD 77247 in the diagram along the periastron envelope of K giants is just accidental, or whether it indicates instead that this system might not be a post-mass-transfer system after all, as are the other barium stars, but that its barium anomaly may rather be inherited from the gas out of which it formed, and be unrelated to its binary nature."
 HD 77247 would thus join the small number of (mostly dwarf) bartum stars with no evidence for being binaries (seethereviewby?.andindividualcasesdis-al..1992. 2000)..," HD 77247 would thus join the small number of (mostly dwarf) barium stars with no evidence for being binaries \citep[see the review by][ and individual cases discussed by Tomkin et al. 1989, Edvardsson et al. 1993, North et al., 1992, 2000]{Jorissen-03}."
 Binary post-AGB stars (??) are the immediate descendants of the binary M giants (Fig. 3)).," \nocite{Tomkin-89,Edvardsson-93,North-92,North-00}
 Binary post-AGB stars \citep{VanWinckel-03,VanWinckel-2007} are the immediate descendants of the binary M giants (Fig. \ref{Fig:binaryscenario}) ),"
 and indeed they share almost exactly the same location in the (οlogP) diagram., and indeed they share almost exactly the same location in the $(e - \log P)$ diagram.
 The ΜΑΗ + A system SS Lep already mentioned in Sect., The M4III + A system SS Lep already mentioned in Sect.
 2.1] is very interesting in this respect. since it shares with post-AGB stars the presence of a circumbinary disc and its position ina group of binaries with the shortest orbital periods among both families.," \ref{Sect:evolution} is very interesting in this respect, since it shares with post-AGB stars the presence of a circumbinary disc and its position in a group of binaries with the shortest orbital periods among both families."
 It may thus be considered as à system linking binary M giants and post-AGB systems in the sense that the M-giant component in SS Lep should shortly evolve into a post-AGB star., It may thus be considered as a system linking binary M giants and post-AGB systems in the sense that the M-giant component in SS Lep should shortly evolve into a post-AGB star.
 On the contrary. one may wonder whether some among the post-AGB stars from panel 4 in Fig.," On the contrary, one may wonder whether some among the post-AGB stars from panel 4 in Fig."
 2. with circular orbits and P~200 d like SS Lep (these are HD 101584. HD 213985 and IRAS 05208-2035. although in the case of HD 101584. the eccentricity isnot well constratned) would not be genuie AGB stars. but rather be accreting main-sequence or white- stars which have swollen to giant dimensions in RLOF systems (asexpectedwhentheaccretingmain-sequercestar 1996)..," \ref{Fig:elogP_panels} with circular orbits and $P \sim 200$ d like SS Lep (these are HD 101584, HD 213985 and IRAS 05208-2035, although in the case of HD 101584, the eccentricity isnot well constrained) would not be genuine post-AGB stars, but rather be accreting main-sequence or white-dwarf stars which have swollen to giant dimensions in RLOF systems \citep[as expected when the accreting
 main-sequence star has a
radiative envelope:] [ or when the WD accretion rate is large enough to
 trigger shell H-burning: Paczy\'nski \& Rudak 1980, Iben \&
 Tutukov 1996]{Kippenhahn77,Jorissen-03}. ."
 The post-AGB stars 1 those, The post-AGB stars in those
not complete. nor necessarily representative of the overall population. but the biases are qualitatively uuderstood and the sample is still far larger than auv for which detailed structural paraiueter fits are available.,"not complete, nor necessarily representative of the overall population, but the biases are qualitatively understood and the sample is still far larger than any for which detailed structural parameter fits are available."
" For the crossideutification prescuted in Table Ἐν, we identify the closest cluster iu projection from the BicaandDutra(2000) catalog which contaius clusters. association. and some other sources such as planetary uecbulae."," For the crossidentification presented in Table \ref{tab:Names and Positions}, we identify the closest cluster in projection from the \cite{bica} catalog which contains clusters, association, and some other sources such as planetary nebulae."
 For matches. the coordinates typically Πο by a few arcsec. well within the quoted general uucertaimty of LO arcsec (BicaaudDutra (2000))).," For matches, the coordinates typically differ by a few arcsec, well within the quoted general uncertainty of 10 arcsec \cite{bica}) )."
 Although we fit both Nine and EFF profiles to our clusters. we place ereater emphasis on the ing profiles for several reasons.," 	 	Although we fit both King and EFF profiles to our clusters, we place greater emphasis on the King profiles for several reasons."
 First. the full set of Ising models include profiles with exteuded wines.," First, the full set of King models include profiles with extended wings."
 The largest concentration models we fit resemble a power Law profile with an effective index simular to the typical EFF profile (seo. Figure 1))., The largest concentration models we fit resemble a power law profile with an effective index similar to the typical EFF profile (see Figure \ref{fig:profile comparison}) ).
 Second. previous studies have ouly demonstrated that the yonneest LMC clusters. those with age «300 Myr. are better fitby an EFF profile. while over half of our cluster gjuple is estimated to be older (Bafelski&Zaritsky2001).," Second, previous studies have only demonstrated that the youngest LMC clusters, those with age $<300$ Myr, are better fit by an EFF profile, while over half of our cluster sample is estimated to be older \citep{rz}."
. Finally. focusing on a sinele family of models allows for a more straightforward coluparison across the sample.," Finally, focusing on a single family of models allows for a more straightforward comparison across the sample."
 Our decision to enplasize he Nine profile is certainly open to critique. particularly if the data were to favor the EFF profile.," Our decision to emphasize the King profile is certainly open to critique, particularly if the data were to favor the EFF profile."
 Our results indicate that this is not the case., Our results indicate that this is not the case.
 Ifthe surface brightuess xofiles of vouug clusters are better fit bv softened oower law profiles. we should fud these clusters more successfully fit by increasingly concentrated Ius models.," If the surface brightness profiles of young clusters are better fit by softened power law profiles, we should find these clusters more successfully fit by increasingly concentrated King models."
" However, our analysis shows Wine models are uot only statistically satisfactory fits for ~ of the clusters. mit also are ecuerally superior fits than EFF profiles for he bulk of the sample (see 833.2)."," However, our analysis shows King models are not only statistically satisfactory fits for $\sim$ of the clusters, but also are generally superior fits than EFF profiles for the bulk of the sample (see 3.2)."
 The usual approach of fitting a model profile o the surface density of a cluster is complicated by he incompletencss of our stella catalog that results roni crowding iun the centers of many clusters;, 	 	 	The usual approach of fitting a model profile to the surface density of a cluster is complicated by the incompleteness of our stellar catalog that results from crowding in the centers of many clusters.
 We overcome this difficulty by fitting models to the surface xiehtuess profile rather than attempting the difficult and inherently uncertain task of defining aud applviug an incompleteness correction., We overcome this difficulty by fitting models to the surface brightness profile rather than attempting the difficult and inherently uncertain task of defining and applying an incompleteness correction.
 We choose to work with the V-baud images because they are the deepest of our set. and because V. ds more sensitive to the uuderlviug stellar populations than cither (© or D while being less seusitive to foreground contanunating stars than 7.," We choose to work with the $V$ -band images because they are the deepest of our set, and because $V$ is more sensitive to the underlying stellar populations than either $U$ or $B$ while being less sensitive to foreground contaminating stars than $I$."
 Furthermore. use of V allows us to compare directly to previous studies (Isoutizasetal.1982:[onutizasCihuore2003b) without concern for possible color eracieuts.," Furthermore, use of $V$ allows us to compare directly to previous studies \citep{kon82, kon83, kon86, mac03b} without concern for possible color gradients."
 Obtaining— an accurate determination of cach clusters center is the first step im constructing the surface brightness profile., 	 	Obtaining an accurate determination of each cluster's center is the first step in constructing the surface brightness profile.
" We use the approximate coordinates even in our catalog to extract a 350""< inaese of the cluster.", We use the approximate coordinates given in our catalog to extract a $^{\prime\prime} \times 350^{\prime\prime}$ image of the cluster.
 A precise center is determined by calculating the bhunuinositv-weiehted centroid., A precise center is determined by calculating the luminosity-weighted centroid.
 To avoid spurious results due to coutamination bv other clusters or bright foreground stars. we constrain the calculation to pixels within 207 of the approximate center aud exclude pixel values that are 3000 counts above the mode of the entire frame (typical mode values are between 100 and 200 counts).," To avoid spurious results due to contamination by other clusters or bright foreground stars, we constrain the calculation to pixels within $^{\prime\prime}$ of the approximate center and exclude pixel values that are 3000 counts above the mode of the entire frame (typical mode values are between 100 and 200 counts)."
 We iterate four times. with cach successive run using the previous huuinosityv-weighted ceuter.," We iterate four times, with each successive run using the previous luminosity-weighted center."
 The derived centers are stable., The derived centers are stable.
 For sole mregular clusters. we adjust the ceuter to match a visually identified ceuter that corresponds to central condensation of stars. rather than a broader bpuuinositv ceutroid.," For some irregular clusters, we adjust the center to match a visually identified center that corresponds to central condensation of stars, rather than a broader luminosity centroid."
 This adjustment is typically not more than a few arcsec., This adjustment is typically not more than a few arcsec.
 As has been previously noted (FreukaudFall 1982).. many SAIC clusters areelliptical.," 	 	As has been previously noted \citep{FF}, , many SMC clusters areelliptical."
 The nature of this ellipticitv. whether it is funcamentally counected to age or luninosity. is debated (Elson1991:vaudeu 1981)..," The nature of this ellipticity, whether it is fundamentally connected to age or luminosity, is debated \citep{e91, van84}. ."
 Despite the couclusion frou LElsou(1991) that the asphericity primarilyresults, Despite the conclusion from \cite{e91} that the asphericity primarilyresults
excess fy=0.54mag/0.02magd!20.07yr.,"excess $t_\mathrm{g} = 0.54\,\mathrm{mag}/0.02\,\mathrm{mag\,d}^{-1}=0.07\,\mathrm{yr}$."
" Since the brightness of CCMa was for two years prior to the decline, we assume the relativelyinitial steadysurface density of the disk was nearly the steady-state solution, X(r,to)=No(r/R)?? (Bjorkman&Carciofi2005)."," Since the brightness of CMa was relatively steady for two years prior to the decline, we assume the initial surface density of the disk was nearly the steady-state solution, $\Sigma(r,t_0) = \Sigma_0 (r/R)^{-2.0}$ \citep{bjo05}."
". To match the initial AV, we Xo=1.64-0.5 whose error is dominated by the requireuncertainty in the gcminclination?, angle (i= 0°-30°)."," To match the initial $\Delta V$, we require $\Sigma_0 = 1.6 \pm 0.5 \,\mathrm{g}\,\mathrm{cm}^{-2}$, whose error is dominated by the uncertainty in the inclination angle $i=0^\circ$ $30^\circ$ )."
 This implies a pre-decline disk mass 2xXR?In(r/R)23x10? interior to r=10.," This implies a pre-decline disk mass $M_\mathrm{d}=2\pi\Sigma_0 R^2\ln(r/R) = 3\times 10^{-9}\,M_\sun$ interior to $r=10\,R$."
" To produce the initial steady-stateMo disk, we run for a long time with a constant mass injection rate, M."," To produce the initial steady-state disk, we run for a long time with a constant mass injection rate, $\dot M$."
" Note that X depends on the ratio M/a, so whenever we change the disk viscosity parameter, a, we adjust M to maintain the desired value for 3o."," Note that $\Sigma_0$ depends on the ratio ${\dot M}/\alpha$, so whenever we change the disk viscosity parameter, $\alpha$, we adjust $\dot M$ to maintain the desired value for $\Sigma_0$."
" After achieves steady-state, we turn off the mass M= 0) and let the disk dissipate."," After achieves steady-state, we turn off the mass injection (by setting $\dot M = 0$ ) and let the disk dissipate."
 Figure 2 injectionshows(by the settingdecline in the V-band excess as a function of time., Figure \ref{fig:DiskDissipation} shows the decline in the $V$ -band excess as a function of time.
" Note that as the viscosity parameter a increases, the disk dissipates more rapidly."," Note that as the viscosity parameter $\alpha$ increases, the disk dissipates more rapidly."
 Initially there is a rapid decline as the inner disk (where the V-band excess is produced) adjusts from outflow to infall and is reaccreted., Initially there is a rapid decline as the inner disk (where the $V$ -band excess is produced) adjusts from outflow to infall and is reaccreted.
" Subsequently, the remaining mass of the disk is drained via quasi-steady-state accretion, and the V-band excess continues to slowly drop to zero."," Subsequently, the remaining mass of the disk is drained via quasi-steady-state accretion, and the $V$ -band excess continues to slowly drop to zero."
" Given the model curves in Figure 2,, we fit the Phase I portion of the observed light curve (see Fig. 1))"," Given the model curves in Figure \ref{fig:DiskDissipation}, we fit the Phase I portion of the observed light curve (see Fig. \ref{fig:LightCurve}) )"
 by adjusting two a and fg., by adjusting only two parameters: $\alpha$ and $t_0$.
" Table 2 lists the best-fitting onlyvalue of {0 for each parameters:value of o and the reduced chi-squared value for the Phase I data, y7."," Table \ref{tab:ModelFits} lists the best-fitting value of $t_0$ for each value of $\alpha$ and the reduced chi-squared value for the Phase I data, $\chi^2_\mathrm{I}$."
" Additionally, we list the reduced chi-squared values of the extrapolation of the fit through Phase II, x7, as well as the reduced chi-squared for the entire data set, x7."," Additionally, we list the reduced chi-squared values of the extrapolation of the fit through Phase II, $\chi^2_\mathrm{II}$, as well as the reduced chi-squared for the entire data set, $\chi^2$."
" Finally, each model curve is shown in comparison to the observations in Figure 1.."," Finally, each model curve is shown in comparison to the observations in Figure \ref{fig:LightCurve}."
 The overall best fit to the Phase I data is a=1.0+0.2 confidence interval)., The overall best fit to the Phase I data is $\alpha = 1.0\pm0.2$ confidence interval).
" Note that when we extrapolate the fit to Phase II, the fit is still reasonable, requiring a large value of o, albeit with a larger uncertainly."," Note that when we extrapolate the fit to Phase II, the fit is still reasonable, requiring a large value of $\alpha$, albeit with a larger uncertainly."
" As may be seen in Figure 1,, our model fits quite well the detailed shape of the V-band decline observed in CCMa."," As may be seen in Figure \ref{fig:LightCurve}, our model fits quite well the detailed shape of the $V$ -band decline observed in CMa."
" Since the V-band excess is produced in the innermost parts of the disk (typicallyrSS2R,Carciofi2011),, we infer that the viscous decretion disk model correctly predicts the time-dependent evolution of the disk density (at least at small radii)."," Since the $V$ -band excess is produced in the innermost parts of the disk \citep[typically $r \lesssim 2\,R$,][]{car11}, we infer that the viscous decretion disk model correctly predicts the time-dependent evolution of the disk density (at least at small radii)."
" Not only does the model reproduce the early decline (Phase J), it also reproduces the slow disk-drainingrapid (Phase II) with a single physical model."," Not only does the model reproduce the rapid early decline (Phase I), it also reproduces the slow disk-draining (Phase II) with a single physical model."
" Furthermore, there is no evidence that the value of o changed from Phase I to Phase II, despite the rather large change in physical conditions in the disk shown in Figure 3.."," Furthermore, there is no evidence that the value of $\alpha$ changed from Phase I to Phase II, despite the rather large change in physical conditions in the disk shown in Figure \ref{fig:DiskStructure}."
" When the mass injection ceases, the disk readjusts most quickly at small radii."," When the mass injection ceases, the disk readjusts most quickly at small radii."
" This is because the viscous diffusion timescale, tgοςr'/2a7!, increases with radius."," This is because the viscous diffusion timescale, $t_\mathrm{diff} \propto r^{1/2} \alpha^{-1} $, increases with radius."
" Reaccretion of material from the inner disk occurs because the turbulent viscosity transports angular momentum outward, transferring angular momentum from the inner disk to the outer."," Reaccretion of material from the inner disk occurs because the turbulent viscosity transports angular momentum outward, transferring angular momentum from the inner disk to the outer."
" Hence, the outer of the disk continue to expand while the inner parts move partsinward."," Hence, the outer parts of the disk continue to expand while the inner parts move inward."
 This produces simultaneous inflow in the inner disk and outflow in the outer disk., This produces simultaneous inflow in the inner disk and outflow in the outer disk.
" As a function of time, the stagnation point (the division between inflow and"," As a function of time, the stagnation point (the division between inflow and"
the energy range to 2.9-20kkeV. The hydrogen column density. Nyy. towards 3341 was fixed to that found by the SSS and MPC measurements (1.7- 1077 7. Christian SSwank 1997).,"the energy range to keV. The hydrogen column density, $_{\rm H}$, towards 3+1 was fixed to that found by the SSS and MPC measurements $\cdot$ $^{22}$ $^{-2}$, Christian Swank 1997)."
 Large amplitude. high coherence brightness oscillations have been observed during various X-ray bursts in. other LMXBs (see Strohmayer 1998. 2000).," Large amplitude, high coherence brightness oscillations have been observed during various X-ray bursts in other LMXBs (see Strohmayer 1998, 2000)."
 In our search for possible burst oscillations we made fast Fourier transforms (FFTs) of data segments ranging from 0.25ss to 2ss long during the burst. with time steps of ss (so-called sliding FFTs).," In our search for possible burst oscillations we made fast Fourier transforms (FFTs) of data segments ranging from s to s long during the burst, with time steps of s (so-called sliding FFTs)."
 We used the 64 spectral channel and 16 j/see data set. and limited our search to the 50 to HHz frequency range.," We used the 64 spectral channel and 16 $\mu$ sec data set, and limited our search to the 50 to Hz frequency range."
 We performed the search in the whole PCA energy range kkeV). as well as in a relatively high energy range kkeV).," We performed the search in the whole PCA energy range keV), as well as in a relatively high energy range keV)."
 The light curve of the burst at low energies is single-peaked. whereas at high energies it is double-peaked (Fig.," The light curve of the burst at low energies is single-peaked, whereas at high energies it is double-peaked (Fig."
 2a.b).," 2a,b)."
 The corresponding hardness curve (Fig., The corresponding hardness curve (Fig.
 2c) shows that the burst first hardens. softens. hardens again. and then gradually softens again.," 2c) shows that the burst first hardens, softens, hardens again, and then gradually softens again."
 Our search for burst oscillations yielded negative results., Our search for burst oscillations yielded negative results.
 Previous burst oscillations were found mainly during the rise to burst maximum and after the radius-expansion phase (see Strohmayer 1998. 2000).," Previous burst oscillations were found mainly during the rise to burst maximum and after the radius-expansion phase (see Strohmayer 1998, 2000)."
 Using the 0.25ss long FFTs in the full energy range. we derive upper limits on the modulation amplitude of burst oscillations of ~45% aat the start of the rise. ~ aat the maximum of the burst. and ~20% jjust after the radius expansion phase.," Using the s long FFTs in the full energy range, we derive upper limits on the modulation amplitude of burst oscillations of $\sim$ at the start of the rise, $\sim$ at the maximum of the burst, and $\sim$ just after the radius expansion phase."
 The upper limits in the kkeV energy band are ~60%.. ~20%.. and ~25%.. respectively.," The upper limits in the keV energy band are $\sim$, $\sim$, and $\sim$, respectively."
 The 25s long FFTs give more stringent upper limits of ~16%.. ~6%.. and ~9%.. respectively. for the full energy range. whereas we derive ~24%.. ~7%.. and ~10“.. respectively. in the kkeV energy band.," The s long FFTs give more stringent upper limits of $\sim$, $\sim$ , and $\sim$, respectively, for the full energy range, whereas we derive $\sim$, $\sim$, and $\sim$, respectively, in the keV energy band."
 The net burst spectra ttotal burst spectrum minus persistent spectrum) were satisfactorily (a less than ~2) modeled by black-body emission., The net burst spectra total burst spectrum minus persistent spectrum) were satisfactorily $\chi^2_{\rm red}$ less than $\sim$ 2) modeled by black-body emission.
 The results are shown in Fig., The results are shown in Fig.
 3., 3.
" À dip in the black-body temperature. T),),. ~2 ss after the burst onset is apparent. simultaneous with an increase of a factor of ~2 in the black-body radius. Ri."," A dip in the black-body temperature, $_{\rm bb}$, $\sim$ s after the burst onset is apparent, simultaneous with an increase of a factor of $\sim$ 2 in the black-body radius, $_{\rm bb}$."
" The total increase/decrease phase of Ri, lasts only ~ ssec.", The total increase/decrease phase of $_{\rm bb}$ lasts only $\sim$ sec.
 We note that the X-ray spectral analysis during bursts can be significantly hampered when the persistent emission contains a black-body contribution from the same surface of the neutron star that emits the burst emission (van Paradijs LLewin 1985)., We note that the X-ray spectral analysis during bursts can be significantly hampered when the persistent emission contains a black-body contribution from the same surface of the neutron star that emits the burst emission (van Paradijs Lewin 1985).
 In that case our spectral fits to the net burst spectra may contain systematic errors in the black-bodv temperature and radius. especially near the end of the burst.," In that case our spectral fits to the net burst spectra may contain systematic errors in the black-body temperature and radius, especially near the end of the burst."
 We therefore repeated our spectral analysis to the total burst spectra. fixing the non black-body component in the persistent emission (see Table 1).," We therefore repeated our spectral analysis to the total burst spectra, fixing the non black-body component in the persistent emission (see Table 1)."
 The black-body component. which now includes all emission from the neutron star surface. is left free.," The black-body component, which now includes all emission from the neutron star surface, is left free."
 This procedure only slightly alters our estimated black-body flux., This procedure only slightly alters our estimated black-body flux.
 The absence of significant differences between the two methods is mainly due the fact that the burst is sufficientlystronger than the persistent emission (which ts reflected by, The absence of significant differences between the two methods is mainly due the fact that the burst is sufficientlystronger than the persistent emission (which is reflected by
enission [rom accretion onto a neutron star or black hole via Roche lobe overflow from a low mass companion (Persic&Rephaeli2002).,emission from accretion onto a neutron star or black hole via Roche lobe overflow from a low mass companion \citep{persic}.
. Assuming the lifetime of a single burst of star formation is approximately 10 vears. the X-ray emission from HIMXDs are expected to dominate the hard spectra because the low mass stars have not had time to evolve away from ihe main sequence and to come into Roche lobe contact (Persicοἱal.2004)..," Assuming the lifetime of a single burst of star formation is approximately $^8$ years, the X-ray emission from HMXBs are expected to dominate the hard spectra because the low mass stars have not had time to evolve away from the main sequence and to come into Roche lobe contact \citep{persic2}."
. As a result. the spectra of the galaxies should reflect (he properties of IINMAXDs with average Dc 1.01.4 (Persicetal.2004.andreferencestherein)..," As a result, the spectra of the galaxies should reflect the properties of HMXBs with average $\Gamma \simeq$ 1.0–1.4 \citep[and references therein]{persic2}."
 llowever. in mergers. multiple events of starbursts may occur due (to recurrent tidal interactions (Persicetal.2004)..," However, in mergers, multiple events of starbursts may occur due to recurrent tidal interactions \citep{persic2}."
 In (his scenario. the low mass companions in binaries formecl in the earlier starburst events have had time to evolve and. therefore. the N-rav enussion trom LMXDs may also contribute to the hard. X-ray. spectra.," In this scenario, the low mass companions in binaries formed in the earlier starburst events have had time to evolve and, therefore, the X-ray emission from LMXBs may also contribute to the hard X-ray spectra."
 To determine the significance of this contribution. mass estimates from Veilleuxetal.(2002) were used in conjunction with Equation 7 of Colbertetal.(2004) ιο approximate the SER. based on the global hard X-ray. Iuninosity.," To determine the significance of this contribution, mass estimates from \citet{vei02} were used in conjunction with Equation 7 of \citet{colbert} to approximate the SFR based on the global hard X-ray luminosity."
 The LMXD-subtracted SFRs are within ~3% of the SFRs found. without Καρίαςο of the contribution of LAINBs., The LMXB-subtracted SFRs are within $\sim$ of the SFRs found without subtraction of the contribution of LMXBs.
 Therefore. the LMXDs do not contributed significantly to the X-ray luminosity.," Therefore, the LMXBs do not contributed significantly to the X-ray luminosity."
 Based on (he peaks of (he histograms in Figure 13. and (he above discussion. the spectra of our sources max. well be dominated by contributions [rom IINEXDs.," Based on the peaks of the histograms in Figure \ref{fig:hist2} and the above discussion, the spectra of our sources may well be dominated by contributions from HMXBs."
 This implies that the weak sources are starburst dominated. as suggested by their values of log(EF»yojv/Fyn) (Figures 11. and 14)).," This implies that the weak sources are starburst dominated, as suggested by their values of $\mathrm{F_{2 - 10~keV}/F_{FIR}}$ ) (Figures \ref{fig:ptakplot} and \ref{fig:sfr}) )."
" If. we assume that the luminosity in the hard. X-ray bod is solely due to X-ray binaries with luminosities = LO"" eres |. then the galaxies in our sample contain 10* 10"" binaries that contribute to the X-ray emission."," If we assume that the luminosity in the hard X-ray band is solely due to X-ray binaries with luminosities $\gtrsim$ $^{37}$ ergs $^{-1}$, then the galaxies in our sample contain $^3$ $^5$ binaries that contribute to the X-ray emission."
 Assuming a universal stellar initial mass function and star formation rate. these values are 4170 times the number of X-ray binaries in (he nearby starburst galaxies M82 and NGC 253 which in turn have 416 limes (he number of binaries in the Milky Way (Persic&Rephaeli2002).," Assuming a universal stellar initial mass function and star formation rate, these values are 4–170 times the number of X-ray binaries in the nearby starburst galaxies M82 and NGC 253 which in turn have 4–16 times the number of binaries in the Milky Way \citep{persic}."
.. If ultraluminous X-ray sources (ULXs) contribute to the emission. then a smaller number of X-ray binaries would be required.," If ultraluminous X-ray sources (ULXs) contribute to the emission, then a smaller number of X-ray binaries would be required."
 On the other hand. the hard. X-ray. emission may result [rom thermal bremsstrahlung from a hot wind driven bv either astarburst or an AGN.," On the other hand, the hard X-ray emission may result from thermal bremsstrahlung from a hot wind driven by either astarburst or an AGN."
 For low abundances. the dominant enission process of a thermal gas is. of course. bremsstirahlung.," For low abundances, the dominant emission process of a thermal gas is, of course, bremsstrahlung."
 Rapkeetal.(2002) and Rupke et al.(2005a.b.¢) have shown evidence for galactic winds in the 1-Jv. sample.," \citet{rupke02} and Rupke et al.(2005a,b,c) have shown evidence for galactic winds in the 1-Jy sample."
 The spectrum of thermal bremsstrahlung is almost “flat” with P ~1.2 for E < kT. This value of I coincides with the peak of the histograms of observed photon indices in Figures 12 and 13.., The spectrum of thermal bremsstrahlung is almost “flat” with $\Gamma \sim$ 1.2 for E $\lesssim$ kT. This value of $\Gamma$ coincides with the peak of the histograms of observed photon indices in Figures \ref{fig:hist} and \ref{fig:hist2}. .
are detected.,are detected.
 There is a clear reduction in detection probability for AGN having absorbing columns above 107? em7. and this etfect is more marked at low-z.," There is a clear reduction in detection probability for AGN having absorbing columns above $10^{23.5}$ $^{-2}$, and this effect is more marked at $z$."
 The plot shows that the survey is able to detect the majority of moderately luminous AGN(log£ys»> 44). with moderate-absorption (21.5 «logV;;« 22.5) up to z=3.5.," The plot shows that the survey is able to detect the majority of moderately luminous AGN$L_{0.5-2} \ge 44$ ), with moderate-absorption $21.5 < $ $N_H < 22.5$ ) up to $z\approx 3.5$."
 Fig., Fig.
 3. shows the fraction. as a function of absorption. of all input sources that are matched to output sources in the simulated images.," \ref{nh_det_frac} shows the fraction, as a function of absorption, of all input sources that are matched to output sources in the simulated images."
 This highlights the small ditferences in detection wobability between the two spectral models., This highlights the small differences in detection probability between the two spectral models.
 The addition of a reflection component in the AGN spectra has a rather small etfect on the detectability of simulated sources., The addition of a reflection component in the AGN spectra has a rather small effect on the detectability of simulated sources.
 The dependence of the selection function on T can be seen in tig. 4.," The dependence of the selection function on $\Gamma$ can be seen in fig. \ref{gamma_det_frac},"
 which shows the fraction of simulated input sources with output counterparts. as a function of spectral slope.," which shows the fraction of simulated input sources with output counterparts, as a function of spectral slope."
 It can be seen hat the spectral slope of an AGN has a small but measurable bearing on its probability of detection., It can be seen that the spectral slope of an AGN has a small but measurable bearing on its probability of detection.
" A strong increase in detection probability is seen for very hard sources (P 118. 10wever, the inset histogram shows that very few of these objects are predicted by the e(D) model."," A strong increase in detection probability is seen for very hard sources $\Gamma < 1.4$ ), however, the inset histogram shows that very few of these objects are predicted by the $g(\Gamma)$ model."
 We have used the 0.5—2 keV de- flux to normalise the model spectra. and so the hard-slope AGN have a relatively high countrate above 2 keV. and are more likely to be detected.," We have used the 0.5–2 keV de-absorbed flux to normalise the model spectra, and so the hard-slope AGN have a relatively high countrate above 2 keV, and are more likely to be detected."
 This ettect is larger for moderate to heavily absorbed sources. since they are primarily detected at these harder energies.," This effect is larger for moderate to heavily absorbed sources, since they are primarily detected at these harder energies."
" The impact on the overall selection function is largest for the /(N,,) models containing the largest fraction of absorbed sources. Le. the A=8. A=REC) models."," The impact on the overall selection function is largest for the $f(N_H)$ models containing the largest fraction of absorbed sources, i.e. the $R=8$, $R=R(z)$ models."
 Constraints on {ΕΛΑ} models can be made from analysis of X-ray colour (i.e hardness ratio) distributions., Constraints on $f(N_H)$ models can be made from analysis of X-ray colour (i.e hardness ratio) distributions.
" For example. Perolaetal.(2004) compared the Nj, of sources determined from full spectral fits. with the Vj, estimated using a hardness ratio method (over the 0.5—10 keV range). and showed that they were in good agreement for logVj;>22."," For example, \citet{perola04} compared the $N_H$ of sources determined from full spectral fits, with the $N_H$ estimated using a hardness ratio method (over the 0.5–10 keV range), and showed that they were in good agreement for $N_H > 22$."
" For this study we define the hardness ratios HRI=(Rus>—Ro»os)/tRos os) HRI=(Rys—Rosο)δν+>) and ARS=(Rsag—Riοqo+Re 5). where Ry.4, I5 the source count rate. corrected for vignetting. in the given energy band."," For this study we define the hardness ratios $HR1 = (R_{0.5-2}-R_{0.2-0.5})/(R_{0.5-2}+R_{0.2-0.5})$ , $HR2=(R_{2-5}-R_{0.5-2})/(R_{2-5}+R_{0.5-2})$ and $HR3=(R_{5-10}-R_{2-5})/(R_{5-10}+R_{2-5})$ , where $R_{E_{min}-E_{max}}$ is the source count rate, corrected for vignetting, in the given energy band."
 The corresponding measurement errors are denoted by Oye. Tue. Ores respectively.," The corresponding measurement errors are denoted by $\sigma_{HR1}$, $\sigma_{HR2}$, $\sigma_{HR3}$ respectively."
 The count rates. hardness ratios. and errors are computed within using the combined dataset from the MOSI. MOS? and pn cameras.," The count rates, hardness ratios, and errors are computed within using the combined dataset from the MOS1, MOS2 and pn cameras."
 If any hardness ratio measurement is undetermined (zero countrates in two energy bands). we set it to 0.0+1.0.," If any hardness ratio measurement is undetermined (zero countrates in two energy bands), we set it to $0.0 \pm 1.0$."
" The dependence of HRI. HR2 and HR3 on absorption is illustrated in fig. ὃν,"," The dependence of $HR1$, $HR2$ and $HR3$ on absorption is illustrated in fig. \ref{colour_nh_ranges},"
" which shows the measured colour-colour distributions of ""output"" simulated sources grouped into a number of Ny, bins.", which shows the measured colour-colour distributions of “output” simulated sources grouped into a number of $N_H$ bins.
" For each Ny, bin. we have over-plotted the ""perfect"" z- in colour-colour space for an AGN with mid-bin absorption. T=1.9. and 0<z«5."," For each $N_H$ bin, we have over-plotted the “perfect” $z$ -track in colour-colour space for an AGN with mid-bin absorption, $\Gamma = 1.9$, and $0 < z < 5$."
 Both the width of the Nj; bins. and the range of Tin the simulated sources. act to distribute sources about his track.," Both the width of the $N_H$ bins, and the range of $\Gamma$ in the simulated sources, act to distribute sources about this track."
 The relative density of the distribution along the track is mostly determined by the evolution of the XLF. which peaks above z=1.5.," The relative density of the distribution along the track is mostly determined by the evolution of the XLF, which peaks above $z=1.5$ ."
 In addition. a significant amount of scatter is caused by measurement uncertainties within the source detection process. yarticularly for the faintest sources.," In addition, a significant amount of scatter is caused by measurement uncertainties within the source detection process, particularly for the faintest sources."
 We see from the left-most upper panel of fig. S..," We see from the left-most upper panel of fig. \ref{colour_nh_ranges},"
 that the colour distribution of output simulated sources with log;«21.5 is compact. and approximately centered on (HRI.HR2) = (0.2.-0.5).," that the colour distribution of output simulated sources with $N_H < 21.5$ is compact, and approximately centered on $HR1,HR2$ ) = (0.2,-0.5)."
 The study of sources in the Lockman hole by Mainierietal.(2002).. found that the vast majority of AGN in this part of hardness ratio space had broad line optical counterparts and. at most. weak absorption (logN;<21.5) in their X-ray spectra.," The study of sources in the Lockman hole by \citet{mainieri02}, found that the vast majority of AGN in this part of hardness ratio space had broad line optical counterparts and, at most, weak absorption $N_H<21.5$ ) in their X-ray spectra."
 In contrast most of the identified AGN having hard X-ray colours had narrow line optical counterparts. although only a small fraction of the hard sources had optical identifications.," In contrast most of the identified AGN having hard X-ray colours had narrow line optical counterparts, although only a small fraction of the hard sources had optical identifications."
" Examination of the three upper right panels reveals that the moderately to heavily absorbed sources (logy,> 21.5). occupy a measurably ditterent region of HRI. A2 space compared to their less absorbed counterparts."," Examination of the three upper right panels reveals that the moderately to heavily absorbed sources $N_H>21.5$ ), occupy a measurably different region of $HR1$ $HR2$ space compared to their less absorbed counterparts."
" In particular, HA] is sensitive to absorption in the range 21.5 «ΙοσΝ«23.5. and HR2 to absorption above logN;,= 22.5."," In particular, $HR1$ is sensitive to absorption in the range $21.5<$ $N_H<23.5$, and $HR2$ to absorption above $N_H=22.5$ ."
 In the study of Georgantopoulosetal.(2004).. the hardness ratio between the 0.5—2 and 2-8 keV bands did not appear to separate the broad and narrow line AGN: however. relatively few of the harder AGN in thissample had spectroscopic identifications.," In the study of \citet{georga04}, the hardness ratio between the 0.5–2 and 2–8 keV bands did not appear to separate the broad and narrow line AGN; however, relatively few of the harder AGN in thissample had spectroscopic identifications."
 DellaCecaetal.(2004). showed that the majority of AGN with broad line counterparts fall in the range 70.75«HR2< -0.35. consistent with the location of the low absorption AGN 21.5) produced by our simulations.," \citet{dellaceca04} showed that the majority of AGN with broad line counterparts fall in the range $-0.75 < HR2 < -0.35$ , consistent with the location of the low absorption AGN $N_H<21.5$ ) produced by our simulations."
 As we would expect. the majority of thesimulated. faint unabsorbed AGN do not have good measurements of HAS.," As we would expect, the majority of thesimulated faint unabsorbed AGN do not have good measurements of $HR3$."
 These sources have noise dominated countrate measurements above 2 keV. and hence have HA3 measurements randomly scattered in the interval [-1.1].," These sources have noise dominated countrate measurements above 2 keV, and hence have $HR3$ measurements randomly scattered in the interval $[-1,1]$."
" Of the simulated AGN having logN;,>23.5. it is only the most luminous (Los»>107 erg ! y. that are detectable in our survey. as shown in figs."," Of the simulated AGN having $N_H>23.5$, it is only the most luminous $L_{0.5-2}>10^{44}$ erg $^{-1}$ ), that are detectable in our survey, as shown in figs."
 2. and 3.., \ref{det_frac_zL} and \ref{nh_det_frac}.
" The bottom right hand panel illustrates that ΠΗΛΟ is sensitive to absorption above logN,,=23.5 forall but the highest redshift AGN.", The bottom right hand panel illustrates that $HR3$ is sensitive to absorption above $N_H = 23.5$ for all but the highest redshift AGN.
 Hard band X-ray count rates were well determined for sources in the bright sample of Caccianigaetal. (2004).. and of the four objects with a higher count rate in the 4.5—7.5 keV band than inthe 2—L.5 keV band. three were associated with narrow line optical counterparts. and onewith a Seyfert 1.9 galaxy.," Hard band X-ray count rates were well determined for sources in the bright sample of \citet{caccianiga04}, , and of the four objects with a higher count rate in the 4.5–7.5 keV band than inthe 2–4.5 keV band, three were associated with narrow line optical counterparts, and onewith a Seyfert 1.9 galaxy."
 Figure 6 shows the HAL HR2 Cupper row) andHR? HR3 (lower row) distributions produced by three of the {ΑΛ} models., Figure \ref{colours_sims_models} shows the $HR1$ $HR2$ (upper row) and$HR2$ $HR3$ (lower row) distributions produced by three of the $f(N_H)$ models.
" The most immediately noticeable difference between the plots. is the fraction of sources that appear to the right of HRI=0.6 for thevarious /CV,;) models."," The most immediately noticeable difference between the plots, is the fraction of sources that appear to the right of $HR1 = 0.6$ for thevarious $f(N_H)$ models."
are required to confirm this observation.,are required to confirm this observation.
 Surveys of star-forming regions show that the frequency of wide (2500 AU) binary pairs declines smoothly with system mass (?).. and we find no evidence that the high order multiplicity of our systems changes with total system mass.," Surveys of star-forming regions show that the frequency of wide $\ga$ 500 AU) binary pairs declines smoothly with system mass \citep{Kraus2009}, and we find no evidence that the high order multiplicity of our systems changes with total system mass."
 It therefore seems plausible that perhaps all protostellar cores undergoing freefall collapse could fragment into multiple systems (as reviewed by ?)) on any length scale. but the probability of this collapse occurring at a given length scale (.e. the probability of achieving a Jeans-critical overdensity) declines with decreasing characteristic density. and hence with decreasing total mass of the core and the resulting binary system.," It therefore seems plausible that perhaps all protostellar cores undergoing freefall collapse could fragment into multiple systems (as reviewed by \citealt{Bodenheimer2001}) ) on any length scale, but the probability of this collapse occurring at a given length scale (i.e. the probability of achieving a Jeans-critical overdensity) declines with decreasing characteristic density, and hence with decreasing total mass of the core and the resulting binary system."
 The two resulting fragments would be otherwise unremarkable. so they would then evolve and further fragment in à manner like low-mass protostars that are not in wide binary pairs.," The two resulting fragments would be otherwise unremarkable, so they would then evolve and further fragment in a manner like low-mass protostars that are not in wide binary pairs."
 This idea would explain both the rarity of wide systems and the similarity between their components and other low-mass stars., This idea would explain both the rarity of wide systems and the similarity between their components and other low-mass stars.
 However. other proposed models could also match the observations. such as the mutual ejection hypothesis of ?.. which postulates that wide binary systems could form via simultaneous ejection from the natal cluster on a similar trajectory.," However, other proposed models could also match the observations, such as the mutual ejection hypothesis of \citet{Kouwenhoven2010}, which postulates that wide binary systems could form via simultaneous ejection from the natal cluster on a similar trajectory."
 The validity of such a mechanism should be tested as part of large-scale star formation simulations (e.g. ??)).," The validity of such a mechanism should be tested as part of large-scale star formation simulations (e.g. \citealt{Bate2009, Offner2009}) )."
 The increase in high-order-multiplicity for the very widest binaries. if confirmed. could offer a sensitive new test for formation models.," The increase in high-order-multiplicity for the very widest binaries, if confirmed, could offer a sensitive new test for formation models."
 We find 1I new close companions in our survey of 36 M-dwarf binaries with separations >SOQAU. giving a bias-corrected high-order-multiple fraction of 457 for these wide systems.," We find 11 new close companions in our survey of 36 M-dwarf binaries with separations $>$ 500AU, giving a bias-corrected high-order-multiple fraction of ${45}^{+18}_{-16}$ for these wide systems."
" The close-binary fractions and 0%close-binary mass ratios of our wide binary targets are. statistically indistinguishable whether they are above or below the ? empirical “unusually wide"" mass cutoff.", The close-binary fractions and close-binary mass ratios of our wide binary targets are statistically indistinguishable whether they are above or below the \citet{Reid2001} empirical “unusually wide” mass cutoff.
 We do. however. find marginally significant evidence for an evolution of high-order-multiplicity following the form of the ?. Jeans-length binding energy relations.," We do, however, find marginally significant evidence for an evolution of high-order-multiplicity following the form of the \citet{Faherty2010} Jeans-length binding energy relations."
 The unusually wide binaries’ close-companion separations are not significantly different from. the. normal-binary sample., The unusually wide binaries' close-companion separations are not significantly different from the normal-binary sample.
 The close-binary component separation distribution is strongly peaked at separations «30. AU. but we do not see See a strong peak towards even closer systems.," The close-binary component separation distribution is strongly peaked at separations $<$ 30 AU, but we do not see see a strong peak towards even closer systems."
 Almost all the detected companions have similar masses to their primaries. although two very low mass companions. including a candidate brown dwarf. were found at relatively large separations.," Almost all the detected companions have similar masses to their primaries, although two very low mass companions, including a candidate brown dwarf, were found at relatively large separations."
" We find 2c evidence for an increased high-order-multiple fraction for the widest targets in our survey. with a high-order-multiple fraction of2173 for systems with separations up to 2000AU. compared to 7773,% for systems with separations >4000AU."," We find $\sigma$ evidence for an increased high-order-multiple fraction for the widest targets in our survey, with a high-order-multiple fraction of ${21}^{+17}_{-7}$ for systems with separations up to 2000AU, compared to ${77}^{+9}_{-22}$ for systems with separations $>$ 4000AU."
 Three of the four widest binary targets in the survey are high-order-multiples. while we find only one triple system from eight systems with a wide separation « 1000AU.," Three of the four widest binary targets in the survey are high-order-multiples, while we find only one triple system from eight systems with a wide separation $<$ 1000AU."
 It is possible that the widest binaries do in fact need higher total masses to survive. leading to a higher probability of finding extra components in the systems.," It is possible that the widest binaries do in fact need higher total masses to survive, leading to a higher probability of finding extra components in the systems."
 Larger sample sizes are required to confirm this., Larger sample sizes are required to confirm this.
 Our results indicate several potentially exciting paths forward in studying unusually wide binary systems., Our results indicate several potentially exciting paths forward in studying unusually wide binary systems.
 The high frequency of high-order multiples of the widest systems in our sample should be confirmed with larger surveys. and even wider systems should be surveyed to see if the frequency continues to increase.," The high frequency of high-order multiples of the widest systems in our sample should be confirmed with larger surveys, and even wider systems should be surveyed to see if the frequency continues to increase."
 Our sample will also be pushed to much lower total system masses under better LGS observational conditions. and the existing sample should be surveyed with high-dispersion spectroscopy to search for extremely close binary companions.," Our sample will also be pushed to much lower total system masses under better LGS observational conditions, and the existing sample should be surveyed with high-dispersion spectroscopy to search for extremely close binary companions."
 We are particularly grateful to both the Palomar and Keck staff for helping us acquire these targets under difficult conditions., We are particularly grateful to both the Palomar and Keck staff for helping us acquire these targets under difficult conditions.
 N.M.L. is supported by a Dunlap Fellowship at University of Toronto., N.M.L. is supported by a Dunlap Fellowship at University of Toronto.
 S.D.. K.G.S.. and A.W. acknowledge funding support through NSF grant AST-0909463.," S.D., K.G.S., and A.A.W. acknowledge funding support through NSF grant AST-0909463."
 This research has made use of the SIMBAD database. operated at CDS. Strasbourg. France.," This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France."
The rotational. positional anc derived. parameters. for PSR JISO0G 2125 are given in Table 1..,"The rotational, positional and derived parameters for PSR $-$ 2125 are given in Table \ref{tb:posnparam}."
 Phese parameters are obtained by modoel-ftting the Jodrell Bank pulse POAs using/pulsar., These parameters are obtained by model-fitting the Jodrell Bank pulse TOAs using.
princeton.edu/tempo... All uncertainties are twice the standard. values., All uncertainties are twice the standard values.
 The rotational frequeney of the pulsar. increased between October 1999 and. December 2000. indicating that a elitch iwl occurred.," The rotational frequency of the pulsar increased between October 1999 and December 2000, indicating that a glitch had occurred."
" ""The nature of the event is. summarised in Figure 1.", The nature of the event is summarised in Figure \ref{fg:glitch}.
 The rotational frequencies versus time are Xotted in Figure laa. Lt is clear that sometime during the 430 dav gap between observations. approximately TOO days of normal spin-clown were reversed.," The rotational frequencies versus time are plotted in Figure \ref{fg:glitch}a a. It is clear that sometime during the 430 day gap between observations, approximately 700 days of normal spin-down were reversed."
 Assuming. as argued ater. that this occurred in a single event. the step change in rotation rate was Av/vz16«10°.," Assuming, as argued later, that this occurred in a single event, the step change in rotation rate was $\Delta \nu/\nu \approx
 16\times10^{-6}$."
 The frequencies or the final two pre-eliteh Jodrell Bank observations were obtained by determining the shift in the pulse profile across he integration time of ~20 minutes., The frequencies for the final two pre-glitch Jodrell Bank observations were obtained by determining the shift in the pulse profile across the integration time of $\sim$ 20 minutes.
 ALL other [frequencies were obtained from a least-squares fit of a timing model ο 4.8 adjacent TOAs. keeping positional parameters anc he frequency derivative fixed with the epoch set to the mic-point of the “POAs.," All other frequencies were obtained from a least-squares fit of a timing model to 4–8 adjacent TOAs, keeping positional parameters and the frequency derivative fixed with the epoch set to the mid-point of the TOAs."
 The cllect of subtracting the e-eliteh. rotational frequeney ancl frequeney derivative. determined. from the Jodrell Bank data. is shown in Figure lbb. Fo view structure in the post-eliteh residuals. an olfse is subtracted from the post-fit data and the scale expandec wea factor of 100 (Figure lec).," The effect of subtracting the pre-glitch rotational frequency and frequency derivative, determined from the Jodrell Bank data, is shown in Figure \ref{fg:glitch}b b. To view structure in the post-glitch residuals, an offset is subtracted from the post-fit data and the scale expanded by a factor of 100 (Figure \ref{fg:glitch}c c)."
 The post-egliteh rotationa requency clecavs with time over a few hundred. clavs., The post-glitch rotational frequency decays with time over a few hundred days.
 The changing frequency derivative is shown in Figure Lele. The ast observation prior to the glitch was obtained at Jodrel Dank on MJD 51462 and the first. observation alter the eliteh was obtained at Parkes on ALJD 51894 (indicated by dotted lines in Figure 1))., The changing frequency derivative is shown in Figure \ref{fg:glitch}d d. The last observation prior to the glitch was obtained at Jodrell Bank on MJD 51462 and the first observation after the glitch was obtained at Parkes on MJD 51894 (indicated by dotted lines in Figure \ref{fg:glitch}) ).
 Unfortunately. the large interva »etween the Jodrell Bank ancl Parkes observations prevents extrapolation of the pre- ancl post- elitch pulse ephemoerides without pulse period. ambiguities.," Unfortunately, the large interval between the Jodrell Bank and Parkes observations prevents extrapolation of the pre- and post- glitch pulse ephemerides without pulse period ambiguities."
 We can therefore. only deduce that the eliteh occurred sometime between the two clates., We can therefore only deduce that the glitch occurred sometime between the two dates.
 ‘Table 2. gives the pre-elitch value of the frequency. 9. ancl its first and second derivatives extrapolated to the epoch of the first observation after the eliteh (ALJD 51894).," Table \ref{tb:param} gives the pre-glitch value of the frequency, $\nu$, and its first and second derivatives extrapolated to the epoch of the first observation after the glitch (MJD 51894)."
 This able also contains the analogous post-eglitch parameters eiven for the same epoch and the instantaneous changes at he elitch., This table also contains the analogous post-glitch parameters given for the same epoch and the instantaneous changes at the glitch.
 For the pre-gliteh data. 7 rellects timing noise. rowever in the post-elitch data. i describes both the timing noise and the recovery from the glitch.," For the pre-glitch data, $\ddot{\nu}$ reflects timing noise, however in the post-glitch data, $\ddot{\nu}$ describes both the timing noise and the recovery from the glitch."
" No other glitch eventsave visible in the data limiting the magnitudes of any elitches o less than Aviv&10.""."," No other glitch eventsare visible in the data limiting the magnitudes of any glitches to less than $\Delta \nu/\nu \approx 
 10^{-9}$."
 In some cases. elitches may »* confused. with timing noise particularly. when there are arge gaps between observations.," In some cases, glitches may be confused with timing noise particularly when there are large gaps between observations."
 The timing residuals. of SR 2125 show small amounts of timing noise: the »e- and post-elitch residuals (Fable 2)) have root-mean-square values of 3.4 and 8.2 ms respectively., The timing residuals of PSR $-$ 2125 show small amounts of timing noise; the pre- and post-glitch residuals (Table \ref{tb:param}) ) have root-mean-square values of 3.4 and 8.2 ms respectively.
 As the pre- ancl post-elitch data sets are only 1 vear in length. these its may under-estimate the amount oftiming noise which may have been absorbed in the rotational parameters. or »osition.," As the pre- and post-glitch data sets are only $\sim$ 1 year in length, these fits may under-estimate the amount oftiming noise which may have been absorbed in the rotational parameters or position."
 In particular. the position given in Table 1. may be in error by more than the quoted formal uncertainty.," In particular, the position given in Table \ref{tb:posnparam} may be in error by more than the quoted formal uncertainty."
 Even i£ PSR. 1500 2125 had similar timing noise properties to SR | 32. which is known to exhibit extreme amounts of timing noise (7).. its apparent fractional [requeney change hrough the data would still be less than 10. 7.," Even if PSR $-$ 2125 had similar timing noise properties to PSR $+$ 32, which is known to exhibit extreme amounts of timing noise , its apparent fractional frequency change through the data would still be less than $\sim
 10^{-8}$ ."
 Ehis would, This would
ccloud (Wrightctal.2001).. iniplius higher deusities.,"cloud \citep{wright01}, implying higher densities."
 A higher deusitv would result iu a higher collision rate. thus keeping the pumping at a ligher rate eventually resulting iu more stable maser intensities.," A higher density would result in a higher collision rate, thus keeping the pumping at a higher rate eventually resulting in more stable maser intensities."
" Note that Yusef-Zadehetal.(2001). show hat deusities »>100 cmP are needed for chuup-clunip collisions to produce MMITz pumping. which is slightly higher than the C-shock post-regiou density of à)210 ciu."" for the SNR masers (Lockettetal.1999:Wardle1999)."," Note that \cite{yusefzadeh01} show that densities $n>10^6$ $^{-3}$ are needed for clump-clump collisions to produce MHz pumping, which is slightly higher than the C-shock post-region density of $n\simeq10^5$ $^{-3}$ for the SNR masers \citep{lockett99,wardle99}."
. What the exact pumping couditious and the pumping rate really are is difficul to calculate. aud depends on the ortho-para Z7» ratio in the region.," What the exact pumping conditions and the pumping rate really are is difficult to calculate, and depends on the ortho-para $H_2$ ratio in the region."
 Both Lockettetal.(1999) aud Pavlakis&I&vlafis(1996) have found that collisions with paral. cau strouelv suppress the 1720 AMI inversion., Both \citet{lockett99} and \citet{pavlakis96} have found that collisions with $_2$ can strongly suppress the 1720 MHz inversion.
 Ortho- and Ils are thought to be formed ou grains with a ratio of 3:1., Ortho- and $_2$ are thought to be formed on grains with a ratio of 3:1.
 At low temperatures (T=10 K) proton exchange reztion convert ortho-IT. into para-Is. makiug he para-IH» beime the dominaut species.," At low temperatures $T=10$ K) proton exchange reaction convert $_2$ into $_2$, making the $_2$ being the dominant species."
" As the temperature incr‘cases, there is less of a difference. but still with ρατα-Πο dominating (Offer&vanDishoeck 1992)..."," As the temperature increases, there is less of a difference, but still with $_2$ dominating \citep{offer92}. ."
 However. to create the 1720 MITz maser ouly a small amount of ortho-IIL» is required. since the collision rate for ortho-ITo ustally is larger by a factor of 2-3 than the para rates (Offer&vanDishoeck1992).," However, to create the 1720 MHz maser only a small amount of $_2$ is required, since the collision rate for $_2$ usually is larger by a factor of 2-3 than the para rates \citep{offer92}."
. The equilibrimu ratio or ortho-xwa Ilis 9\«1TU;T. which is equal to 1 for a temperature T=Ti KK. nuplvine the temperature shoud be cooler than this value.," The equilibrium ratio for ortho-para $_2$ is $9\times e^{-170/T}$, which is equal to 1 for a temperature $T=77$ K, implying the temperature should be cooler than this value."
 This is cousisteu with a lieh density euviroumoeut in the CND where the gas temerature is thermalized with the dust temperatures of IIs (DBeckliuetal.1982:Alezeeretal. 1989).. although: molecular studies of the CND imply excitation cluperatures anvwhere between 50-200Is. (CCliistoplieretal.2005:Jacksonal.1993:Wightet2001:Coil&IIo1999. 2000).," This is consistent with a high density environment in the CND where the gas temperature is thermalized with the dust temperatures of K \citep{becklin82,mezger89}, although molecular studies of the CND imply excitation temperatures anywhere between K \citep{christopher05,jackson93,wright01,coil99,coil00}."
 Coil&IIo(2000) κο NIT4(2.2) NIT4(L.1). ratios to derive rotational gas temperatures between 20-70 EK. mostly iu the outer regious of the CND.," \citet{coil00}
 use $_3$ $_3$ )(1,1) ratios to derive rotational gas temperatures between 20-70 K, mostly in the outer regions of the CND."
 Perhaps. next to path-leusth eecoimoetry. ID. this is à reason that 1720 MIIZz niasers are not seen all across the CND: if temperatures are too high the 1720 ΑΠ enüssion will be suppressed.," Perhaps, next to path-length geometry I), this is a reason that 1720 MHz masers are not seen all across the CND; if temperatures are too high the 1720 MHz emission will be suppressed."
 We have preseuted the first fux monitoring study of 1720 MIIz ΟΠ masers associated with au SNR., We have presented the first flux monitoring study of 1720 MHz OH masers associated with an SNR.
 Iu total five epochs of the 1720 MITz ΟΠ mascrs in the GC were obtained. aud used to estimate the maser flux im cdiffercut reeions of the CC.," In total five epochs of the 1720 MHz OH masers in the GC were obtained, and used to estimate the maser flux in different regions of the GC."
 We find that the typical variability is very low. but that the northeasteru SNR/ISAD masers have a higher variability than the other masers.," We find that the typical variability is very low, but that the northeastern SNR/ISM masers have a higher variability than the other masers."
 We speculate this is because the |50 cloud is located behind the SNR. and the maser cluission travels through ai louger path leugth of urbuleut gas before reaching the observer.," We speculate this is because the $+50$ cloud is located behind the SNR, and the maser emission travels through a longer path length of turbulent gas before reaching the observer."
 At other ocations across the SNR the masers probably arise at he near side of the SNR with less material between the naser aud the observer. aud therefore show a 1ο lower evel of variability.," At other locations across the SNR the masers probably arise at the near side of the SNR with less material between the maser and the observer, and therefore show a much lower level of variability."
 Sinularly low variability levels are ound for the CND masers consistent with the CND being ocated in front of EEast., Similarly low variability levels are found for the CND masers consistent with the CND being located in front of East.
 The low variability of the CND iaser agrees with a scenario where the Muupine ix provided by relatively large clips (sizes 71 AU)., The low variability of the CND maser agrees with a scenario where the pumping is provided by relatively large clumps (sizes $>1$ AU).
 TheNational Radio Astronomy Observatory is a ‘acility of the National Science Foundation operated under cooperative agreement by Associated Universities. Iuc.," TheNational Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc."
p value of 0.11 are shown in Fig.,$p-$ value of 0.14 are shown in Fig.
 5., 8.
 This agrees with katzetal.(2011). where the two directions toward M23 and M5 in the anti-Galactocenter region show similar [Fe/T]| distributions.," This agrees with \citet{katz11}
 where the two directions toward M3 and M5 in the anti-Galactocenter region show similar $\feh$ distributions."
 Since GL is located inside of C5. similar CDFs indicate the variation of metallicity with X is [Fe/II]not detectable.," Since G4 is located inside of G5, similar $\feh$ CDFs indicate the variation of metallicity with X is not detectable."
 Similarly. C2 and C3 have siuular |Z| distributions with little or mo X variation within the eroup. and a INS test vields a po value of 0.33 for the |Fe/II| CDFEs based on stars with 1<|Z|«3 kpe.," Similarly, G2 and G3 have similar $|Z|$ distributions with little or no X variation within the group, and a KS test yields a $p-$ value of 0.33 for the $\feh$ CDFs based on stars with $1< |Z| <3$ kpc."
 Again. G2 is located inside of C3 and similar CDFs indicate X differences between C2 and 3 do not have a sieuificaut effect ou their metallicity distributions.," Again, G2 is located inside of G3 and similar CDFs indicate X differences between G2 and G3 do not have a significant effect on their metallicity distributions."
 Similar |Fe/II| CDEs are found for C3 aud Gl. but this is not the case for the comparison between Cl and C5.," Similar $\feh$ CDFs are found for G3 and G4, but this is not the case for the comparison between G1 and G5."
 Fig., Fig.
 9 shows the similar |Z| but different. |Fe/II] CDFs tween Cl and C5. beme the two extreme cases i opposite VY directious.," 9 shows the similar $|Z|$ but different $\feh$ CDFs between G1 and G5, being the two extreme cases in opposite $X$ directions."
 For 0.7<οο. αἱ aud €5 have exactly the same CDEs while at both cues he differences in the |Fo/TII| CDFs are significant.," For $-0.7 < \feh < -0.4$, G1 and G5 have exactly the same CDFs while at both ends the differences in the $\feh$ CDFs are significant."
 Two xossilble reasons may explain the special case of GL., Two possible reasons may explain the special case of G1.
 It has con suggested that the effect of |Fo/TI] variation with X cannot be neglected for a scale length of the thick disk )etween 2 and Ekpce., It has been suggested that the effect of $\feh$ variation with X cannot be neglected for a scale length of the thick disk between 2 and 4 kpc.
 Alternatively. it is expected that C1 ws a high contribution of stars at both the metal poor end aud the metal rich eud. from the bulee population with a wide metallicity range of 2.0<[Fe/T]«0.5. which will steepen the eradieut.," Alternatively, it is expected that G1 has a high contribution of stars at both the metal poor end and the metal rich end from the bulge population with a wide metallicity range of $-2.0 < \feh < 0.5$, which will steepen the gradient."
 In addition. it seeuis that Gil also has a special kincmatic distribution iu Fig.," In addition, it seems that G1 also has a special kinematic distribution in Fig."
 10. which shows the radial velocity distributious for five eroups with Cl haviug the largest radial velocity rauge and a peak siguificautly different from the other eroups.," 10, which shows the radial velocity distributions for five groups with G1 having the largest radial velocity range and a peak significantly different from the other groups."
 Therefore. Cl is not included m this study.," Therefore, G1 is not included in this study."
 We lave estimated. the metallicity eradieut for the thick disk population iu two wavs using RUB stars selected frou SDSS DRBRS8 data., We have estimated the metallicity gradient for the thick disk population in two ways using RHB stars selected from SDSS DR8 data.
 The first method is based ou the Gaussian peal of the metallicity distribution in five |Z] bius by subtracting the coutribution from the thin disk aud halo via the Desaucoon Galaxy model., The first method is based on the Gaussian peak of the metallicity distribution in five $|Z|$ bins by subtracting the contribution from the thin disk and halo via the Besançoon Galaxy model.
 The slope is 0.190.041 dex with aniutercept of 0.31 , The slope is $-0.12\pm0.01$ dex $^{-1}$ with an intercept of $-0.34$ 
"Since its discovery in 1844 (?),, Sirius B has been a tantalizing object.","Since its discovery in 1844 \citep{1844MNRAS...6R.136B}, Sirius B has been a tantalizing object."
" While its close proximity to the Sun makes it ideal for detailed study, its binary companion, Sirius A, is the brightest star in the night-sky, complicating observations of Sirius B. With a A mag of 10"," While its close proximity to the Sun makes it ideal for detailed study, its binary companion, Sirius A, is the brightest star in the night-sky, complicating observations of Sirius B. With a $\Delta$ mag of $\sim$ 10"
(unclear in the case of Sevfert 1. disk im the case of Sevtert 2 and Cold galaxies) by Πα cussion aud (c) the contamination of the W-band magnitudes by οσοσρυτ Claission.,"(nuclear in the case of Seyfert 1, disk in the case of Seyfert 2 and Cold galaxies) by $\alpha$ emission and (c) the contamination of the $V$ -band magnitudes by $_{4959,5007}$ emission."
 Seyfert Ls show positive eradieuts for all colours. (BV). (5.ΠΟ OL). which are most likely due to the presence of a “naked” ACN in their centers. that blueus significantly their imclear colours (see also Figure 2 of Paper ID).," Seyfert 1s show positive gradients for all colours, $(B-V)$, $(B-R)$, $(V-I)$, which are most likely due to the presence of a “naked” AGN in their centers, that bluens significantly their nuclear colours (see also Figure 2 of Paper II)."
 The reeative colour eradicuts in Sevfert 28 are comparable o those found iu normal galaxies. for which stellar opulationu age and metallicity effects are the main contributors (DeJong 1996)).," The negative colour gradients in Seyfert 2s are comparable to those found in normal galaxies, for which stellar population age and metallicity effects are the main contributors \cite{jong96c}) )."
 In Sevtert 2s. reddening of the ceutral regions due to dust obscuration could tuther steepen their colour eracicuts.," In Seyfert 2s, reddening of the central regions due to dust obscuration could further steepen their colour gradients."
 Supporting evidence to the latter is the progressive fatteniug (less negative) of the colour eradicuts towards longer wavelengths. (, Supporting evidence to the latter is the progressive flattening (less negative) of the colour gradients towards longer wavelengths. (
i) The Cold sample galaxies all show negative outwards colour eracicuts.,ii) The Cold sample galaxies all show negative outwards colour gradients.
 They are less steep than he Seyfert 2 eradieuts and are comparable for the (B5. Ryand(VRR) colours., They are less steep than the Seyfert 2 gradients and are comparable for the $(B-R)$ and $(V-R)$ colours.
 These two facts are likely indicating that dust extinction aud star formation are nore evenly distributed throughout these objects. (, These two facts are likely indicating that dust extinction and star formation are more evenly distributed throughout these objects. (
i) There is no well-defined correlation between colour eradicuts and morphological type (vith perhaps he exception of the Sevtert 2 (V.I) exadicuts).,iii) There is no well-defined correlation between colour gradients and morphological type (with perhaps the exception of the Seyfert 2 $(V-I)$ gradients).
 The lack of correlation with morphological type for he Wari Sevterts. most likely tudicates that the aperture colour eradieuts are affected by both the ACN and dust extinction. rather than simply reflecting stellar age and metallicity eradicuts.," The lack of correlation with morphological type for the Warm Seyferts, most likely indicates that the aperture colour gradients are affected by both the AGN and dust extinction, rather than simply reflecting stellar age and metallicity gradients."
 \lorphological nuissclassifications. due to the complex host morphologies. is another Likely reason for the lack of correlations with T. in particular for the highly disturbed. interacting Cold sample galaxies.," Morphological missclassifications, due to the complex host morphologies, is another likely reason for the lack of correlations with T, in particular for the highly disturbed, interacting Cold sample galaxies."
 We used the isophotal fitting results from Paper ΤΠ. to derive colours at each radius from the azimauthally averaged isophotal maeuitudes.," We used the isophotal fitting results from Paper III, to derive colours at each radius from the azimuthally averaged isophotal magnitudes."
 We are mainly interested in isolating the host colour eradieuts. thus we ouly use 16 data for radii larger than 2 kpe out to the gp=25 μας 7.," We are mainly interested in isolating the host colour gradients, thus we only use the data for radii larger than 2 kpc out to the $\mu_{B}$ =25 mag $^{-2}$."
 For elliptical galaxies. it is common to ot radial colour profiles versus log radius because rese are essentially linear functious.," For elliptical galaxies, it is common to plot radial colour profiles versus log radius because these are essentially linear functions."
 However. this is rot the case for our objects and thus we choose to represent colour eradieuts iu linear radius space.," However, this is not the case for our objects and thus we choose to represent colour gradients in linear radius space."
 We ien derived the colour eracieuts trom the slope of the radial colour profiles., We then derived the colour gradients from the slope of the radial colour profiles.
 Here à represeuts the seuiauajor axis lenetl and the surface colour., Here $\alpha$ represents the semi-major axis length and the surface colour.
 In this wav. we measured colour eradieuts through weighted least-square fitting of a first-order polvnonual. using the surface photomietry errors to weigh the data.," In this way, we measured colour gradients through weighted least-square fitting of a first-order polynomial, using the surface photometry errors to weigh the data."
 Inspection of the colour xofiles iu the Appendix of Paper HL. shows that there is almost always a break in the profiles. particularly well-defined in the case of Sevfert Is.," Inspection of the colour profiles in the Appendix of Paper III, shows that there is almost always a break in the profiles, particularly well-defined in the case of Seyfert 1s."
 We thus decided o fit most colour profiles in two regions.inner audouter frou the break location. which is defined to f the point where the inner (linear) geradieut stops fitting the data points.," We thus decided to fit most colour profiles in two regions, and from the break location, which is defined to be the point where the inner (linear) gradient stops fitting the data points."
 The outer portion of the xofile is then fitted from the larger radi isvards, The outer portion of the profile is then fitted from the larger radii inwards.
 The eracicnts obtained in this way. are presented in Table 1. (subscripts7 ancO for the immer/outer eracicuts. respectively) aud im Figures 5 - 12 (subscriptsmand out).," The gradients obtained in this way, are presented in Table \ref{tab2} (subscripts and for the inner/outer gradients, respectively) and in Figures \ref{f3} - \ref{f5} (subscripts and )."
 Define the break poiut frou the ΠΙΟ: fits has the advantage that is less affected bv the preseuce of structure in the galactic disks., Defining the break point from the inner fits has the advantage that is less affected by the presence of structure in the galactic disks.
 The breals radius (n kpc) is also listed in Table 1.., The break radius (in kpc) is also listed in Table \ref{tab2}.
 When only oue line is fitted to the totality of the profile. this is considered asovter disk eradieut.," When only one line is fitted to the totality of the profile, this is considered as disk gradient."
 The median. mean and standard deviations of the colour gradieut distributions are listed in Table 3..," The median, mean and standard deviations of the colour gradient distributions are listed in Table \ref{tab3}."
 The uncertainties in the caleulated eradicuts are comparable for the different samples and for the various colours., The uncertainties in the calculated gradients are comparable for the different samples and for the various colours.
 The median errors are: 0.008 for audAe. 0001 forpAa.. O.OLF for aud aud 0.019 foroAa.," The median errors are: 0.008 for and, 0.004 for, 0.017 for and and 0.019 for."
. The errors in the outer eracdieuts are lareer bv a factor of —10. duc to the presence of structure in the disks aud to sky subtraction uucertainties.," The errors in the outer gradients are larger by a factor of $\sim$ 10, due to the presence of structure in the disks and to sky subtraction uncertainties."
 Comparison of the median errors quoted above and the values listed in Tables 1. and 3. indicates that the mer (5. V)aud (D.R) exadieuts are well defined (with errors at the ~ level or less). while the inner (CV.PR) aud all the outer eradicuts are very small (Hat colour profiles). comparable to their associated errors. ," Comparison of the median errors quoted above and the values listed in Tables \ref{tab2} and \ref{tab3}, indicates that the inner $(B-V)$ and $(B-R)$ gradients are well defined (with errors at the $\sim$ level or less), while the inner $(V-R)$ and all the outer gradients are very small (flat colour profiles), comparable to their associated errors. ("
G) All surface colour gradients are flatter (inner eracicuts are flatter bv factors of 2 to 5) compared to the integrated ones. the former being less affected,"i) All surface colour gradients are flatter (inner gradients are flatter by factors of 2 to 5) compared to the integrated ones, the former being less affected"
We focus here on the objects that are overluminous in radio with respect to the empirical radio - X-ray correlation.,We focus here on the objects that are overluminous in radio with respect to the empirical radio - X-ray correlation.
 We note that there might be some uncertainties in the computation of their parameters., We note that there might be some uncertainties in the computation of their parameters.
" In particular, A1213 displays a peculiar diffuse emission, and its size and radio power is lower than that of classical giant radio halos."," In particular, A1213 displays a peculiar diffuse emission, and its size and radio power is lower than that of classical giant radio halos."
" Even if Giovanninietal.2009 showed that small-size radio halos have the same properties as giant radio halos, data of higher statistical quality are necessary to confirm this result."," Even if \cite{gio09} showed that small-size radio halos have the same properties as giant radio halos, data of higher statistical quality are necessary to confirm this result."
" In addition, the cluster 0217-70, as discussed by Brownetal.2011,, is on the galactic plane therefore the X-ray luminosity could be affected by an unusually high absorption."," In addition, the cluster 0217+70, as discussed by \cite{bro11}, is on the galactic plane therefore the X-ray luminosity could be affected by an unusually high absorption."
" On the other hand, the uncertainties in the determination of the radio power and the X-ray luminosity in the cluster A1351 (Giovanninietal. 2009)) are smaller than the deviations from the correlation (however see Giacintuccietal. 2009))."," On the other hand, the uncertainties in the determination of the radio power and the X-ray luminosity in the cluster A1351 \cite{gio09}) ) are smaller than the deviations from the correlation (however see \cite{gia09}) )."
" In the case of A523, we are aware that the redshift is not well known, since only the redshift of the BCG is available."," In the case of A523, we are aware that the redshift is not well known, since only the redshift of the BCG is available."
" However, to be consistent with the correlation between the radio power and the X-ray luminosity, the clusters should be at a redshift of ~ 0.2."," However, to be consistent with the correlation between the radio power and the X-ray luminosity, the clusters should be at a redshift of $\sim$ 0.2."
 Fig., Fig.
" 3 shows the predicted values of the B;-R-1.4 and 2.0 for the predicted early-type galaxies at z=0.0 and z=0.2, respectively (see Fig."," \ref{fig:3}
 shows the predicted values of the $B_j$ $R$ =1.4 and 2.0 for the predicted early-type galaxies at $z=0.0$ and $z=0.2$, respectively (see Fig."
 1 of Brown et al., 1 of Brown et al.
 2000 and refs., \cite{bro00} and refs.
 therein) after a 0.2 mag decorrection for the Galactic absorption., therein) after a 0.2 mag decorrection for the Galactic absorption.
" Although these predictions cannot be used to provide a redshift estimate, they are useful to show to the reader the difference expected in the color-magnitude relation fora z~0.2 cluster, thus strongly favouring the location of A523 at much lower distance."," Although these predictions cannot be used to provide a redshift estimate, they are useful to show to the reader the difference expected in the color–magnitude relation for a $z\sim0.2$ cluster, thus strongly favouring the location of A523 at much lower distance."
" Moreover, at z = 0.2, the halo size would be ~ 2.4 Mpc, the largest radio halo known to date (see Giovanninietal. 2009))."," Moreover, at z = 0.2, the halo size would be $\sim$ 2.4 Mpc, the largest radio halo known to date (see \cite{gio09}) )."
 The radio halo in A523 therefore represents a robust case of a giant radio halo clearly identified with an X-ray underluminous cluster., The radio halo in A523 therefore represents a robust case of a giant radio halo clearly identified with an X-ray underluminous cluster.
 As discussed in Sect., As discussed in Sect.
" 2, the X-ray and optical distribution is similar (bimodal) but not in perfect agreement."," 2, the X-ray and optical distribution is similar (bimodal) but not in perfect agreement."
" The thermal gas distribution is shifted with respect to the galaxy distribution; this is more evident for the smaller and more compact NNE clump, where the position of the BCG is not at the center of the gas distribution."," The thermal gas distribution is shifted with respect to the galaxy distribution; this is more evident for the smaller and more compact NNE clump, where the position of the BCG is not at the center of the gas distribution."
" A higher quality X- image is necessary to investigate whether the peculiarity of A523 could be related to the possibility that the compact NNE group just crossed the SSW cluster as in the case of the Bullet cluster (1E0657-56, Markevitchetal.2002)), and this strong and recent interaction affected in a different way the gas and galaxy distribution."," A higher quality X-ray image is necessary to investigate whether the peculiarity of A523 could be related to the possibility that the compact NNE group just crossed the SSW cluster as in the case of the Bullet cluster (1E0657-56, \cite{mar02}) ), and this strong and recent interaction affected in a different way the gas and galaxy distribution."
 We conclude that there is firm observational evidence that giant radio halos can be associated with low luminosity X-ray clusters., We conclude that there is firm observational evidence that giant radio halos can be associated with low luminosity X-ray clusters.
 These halos are overluminous in radio by at least an order of magnitude with respect to that expected from the extrapolation of the observed radio power - X-ray luminosity., These halos are overluminous in radio by at least an order of magnitude with respect to that expected from the extrapolation of the observed radio power - X-ray luminosity.
" The radio - X-ray correlation is consistent with reacceleration models, which have been extensively discussed in the literature (Cassano 2010 and refs therein) and supported by the observations (e.g. Giovanninietal.2009))."," The radio - X-ray correlation is consistent with reacceleration models, which have been extensively discussed in the literature (Cassano 2010 and refs therein) and supported by the observations (e.g. \cite{gio09}) )."
" In the framework of these models, the radio emitting particles in cluster radio halos gain energy from merger-driven turbulence in the ICM."," In the framework of these models, the radio emitting particles in cluster radio halos gain energy from merger-driven turbulence in the ICM."
" Turbulence development on timescales of the order of 1 Gyr is necessary to reaccelerate electrons to the energies needed to emit the observed synchrotron radiation at GHz frequencies, thus giant radio halos are expected to be strictly connected to massive systems that have undergone strong merging processes."," Turbulence development on timescales of the order of 1 Gyr is necessary to reaccelerate electrons to the energies needed to emit the observed synchrotron radiation at GHz frequencies, thus giant radio halos are expected to be strictly connected to massive systems that have undergone strong merging processes."
" In the framework of turbulent reacceleration models, Cassano 2010 suggests that very steep spectrum radio halos should exist that are detectable only at low frequencies, and be less luminous than predicted by the radio - X-ray correlation."," In the framework of turbulent reacceleration models, Cassano 2010 suggests that very steep spectrum radio halos should exist that are detectable only at low frequencies, and be less luminous than predicted by the radio - X-ray correlation."
" The radio halo in A523, and a few similar objects, are instead more luminous in radio than predicted by the radio - X-ray correlation."," The radio halo in A523, and a few similar objects, are instead more luminous in radio than predicted by the radio - X-ray correlation."
" These powerful radio halos, associated with clusters of low X-ray luminosity, do not appear to be described well by current models, hence are likely to represent a new class of objects, raising new questions about the origin of radio halos."," These powerful radio halos, associated with clusters of low X-ray luminosity, do not appear to be described well by current models, hence are likely to represent a new class of objects, raising new questions about the origin of radio halos."
" They could be either young halos or clusters at a special time of the merger event, when particle acceleration processes have a higher efficiency (see Brunetti&Lazarian 2011))."," They could be either young halos or clusters at a special time of the merger event, when particle acceleration processes have a higher efficiency (see \cite{bru11}) )."
 Another possibility is that the X-ray luminosity might not be in these cases a good indicator of the previous cluster merging activity., Another possibility is that the X-ray luminosity might not be in these cases a good indicator of the previous cluster merging activity.
" We note that the non-thermal diffuse radio emission in A523 does not follow the optical and the X-ray emission, unlike most other radio halos."," We note that the non-thermal diffuse radio emission in A523 does not follow the optical and the X-ray emission, unlike most other radio halos."
 The brighter halo region visible at high resolution (Fig., The brighter halo region visible at high resolution (Fig.
" 1) is in good agreement with the X-ray bimodal distribution, but the more extended low brightness halo emission, which is most clearly imaged at low resolution, is elongated in the E-W direction i.e. in the direction perpendicular to the merger."," 1) is in good agreement with the X-ray bimodal distribution, but the more extended low brightness halo emission, which is most clearly imaged at low resolution, is elongated in the E-W direction i.e. in the direction perpendicular to the merger."
 This morphology could be related to peculiar cluster conditions that give rise to these overluminous radio halos and needs to be studied in better detail with more sensitive X-ray and radio data and radio spectral information., This morphology could be related to peculiar cluster conditions that give rise to these overluminous radio halos and needs to be studied in better detail with more sensitive X-ray and radio data and radio spectral information.
"procedure of artilicially increasing (he positron capture rate. A,45A,4. which is likely an overestimate of (he protonization rate.","procedure of artificially increasing the positron capture rate, $\lambda_{e^+{\rm n}}\rightarrow 5\lambda_{e^+{\rm n}}$, which is likely an overestimate of the protonization rate."
" The increase in À,μονές in an electron Iraction of Y.20.166 near the event horizon."," The increase in $\lambda_{e^+{\rm n}}$ results in an electron fraction of $Y_e\approx
0.166$ near the event horizon."
 This is approximately higher than the electron fraction calculated by neglecting the influence of 7 capture. though sll equite neutron rich.," This is approximately higher than the electron fraction calculated by neglecting the influence of $\nu_e$ capture, though still quite neutron rich."
 To summarize. Y. in disks with highex viscosity. and modest accretion rates will not be allected. by neutrino capture simply because neutrinos are not trapped or because weak processes are (oo slow.," To summarize, $Y_e$ in disks with high viscosity and modest accretion rates will not be affected by neutrino capture simply because neutrinos are not trapped or because weak processes are too slow."
" The electron Iraction in disks with neutrino absorptive optical depths οἱ a few will increase somewhat but will remain neutron rich owing to the sharp rise in A,p with Y...", The electron fraction in disks with neutrino absorptive optical depths of a few will increase somewhat but will remain neutron rich owing to the sharp rise in $\lambda_{e^-{\rm p}}$ with $Y_e$.
 In order for a low electron fraction to have observable implications the electron fraction must not come to equilibrium at Y.=1/2 as the material travels oul of the plane of the disk., In order for a low electron fraction to have observable implications the electron fraction must not come to equilibrium at $Y_e=1/2$ as the material travels out of the plane of the disk.
" To estimate the evolution of the electron [raction in convective blobs moving out of the disk we parametrize the convective timescale by (he turbulent convection speed Piran.&Kamar2002) where a4,=a/0.1 and rz=r/10'cm.", To estimate the evolution of the electron fraction in convective blobs moving out of the disk we parametrize the convective timescale by the turbulent convection speed \citep{nar02} where $\alpha_{-1}=\alpha/0.1$ and $r_7=r/10^7 \cm$.
 This implies a (time (o go one pressure scale height We also assume that the convective blob expands adiabatieallv., This implies a time to go one pressure scale height We also assume that the convective blob expands adiabatically.
 An estimate for the entropy per barvon in the disk is given by Qian&Woosley(1000) Here Tij is the temperature in MeV and py is the density in units of LOMecm7., An estimate for the entropy per baryon in the disk is given by \citet{qia96}: Here $T_{\rm MeV}$ is the temperature in MeV and $\rho_{10}$ is the density in units of $10^{10} \gcc$.
 The first term on the right hand side of Eq., The first term on the right hand side of Eq.
 192 is the contribution to the entropy from relativistic light. particles (5/67). while the next (wo represent the contribution from [ree nucleons.," \ref{entropy} is the contribution to the entropy from relativistic light particles $\gamma/e^{\pm}$ ), while the next two represent the contribution from free nucleons."
 Eq., Eq.
 12 is not appropriate when electrons are degenerate., \ref{entropy} is not appropriate when electrons are degenerate.
 For degenerate electrons the contribution of thermal e= pairs is small and the coefficient. 0.052 should be closer to 0.02. representing just the entropy of the photons.," For degenerate electrons the contribution of thermal $e^{\pm}$ pairs is small and the coefficient 0.052 should be closer to 0.02, representing just the entropy of the photons."
 However. changing the coefficient to 0.02 makes little difference for our purposes.," However, changing the coefficient to 0.02 makes little difference for our purposes."
density aud pressure profiles which are related by The density profile is determined by solving the Lane-Eimden equation (SeeChandrasekhar1957).,density and pressure profiles which are related by The density profile is determined by solving the Lane-Emden equation \citep[See][]{cha57}.
. We adopt an ideal gas equation of state with adiabatic index 5=5/3., We adopt an ideal gas equation of state with adiabatic index $\gamma=5/3$.
 Note that for aun 9=3 polvtrope. of the total mass is contained within r=0.5R.," Note that for an $n=3$ polytrope, of the total mass is contained within $r\lesssim0.5R$."
 We define the dynamical time to be. where p ds the average density.," We define the dynamical time to be, where $\bar{\rho}$ is the average density."
 For the chosen parent stars. the dynamical time 1s approximately one physical hour.," For the chosen parent stars, the dynamical time is approximately one physical hour."
 The collision is simulated iu à box with 512«256 cells aud the orbital plane coimcides with the.4 plane., The collision is simulated in a box with $512\times512\times256$ cells and the orbital plane coincides with the $x-y$ plane.
 Initially. each pareut star has a radius of 96 eric cells.," Initially, each parent star has a radius of 96 grid cells."
 The stars are set up on zero-enerev parabolic orbits with a periceutre separation equal to 0.25R.," The stars are set up on zero-energy parabolic orbits with a pericentre separation equal to $0.25\,R$."
" The initial trajectories are calculated assuiiug poli masses,", The initial trajectories are calculated assuming point masses.
 Iu an Eulerian ΠΕΓΕ the vacuna came have zero deusitv.," In an Eulerian simulation, the vacuum cannot have zero density."
 We set the minima deusitv of tli cells to be LO* of the central deusity of the parci stars., We set the minimum density of the cells to be $10^{-8}$ of the central density of the parent stars.
 The lvdrodvuaimics is done iu a non-periodic box with vacunu boundary couditious., The hydrodynamics is done in a non-periodic box with vacuum boundary conditions.
 A mnonu-trivial test of a self-eravitating Eulerian livdro code is the advection of an object in lbydrostatic equilibriuu., A non-trivial test of a self-gravitating Eulerian hydro code is the advection of an object in hydrostatic equilibrium.
 The challenge is to maintain the equilibrium profile over a large umber of time steps., The challenge is to maintain the equilibrium profile over a large number of time steps.
 One of the parent stars is placed in a periodic box with 256? cells iid eiven some initial momentum., One of the parent stars is placed in a periodic box with $256^3$ cells and given some initial momentum.
 We make he test rigorous by having the polvtrope move in all three directions., We make the test rigorous by having the polytrope move in all three directions.
 In Figure 10 WO conipae the mass aud eutropv profiles of the initial aud advected polytrope., In Figure \ref{fig:poly} we compare the mass and entropy profiles of the initial and advected polytrope.
 The eutropie variable 44—P/p is used in place of the specific cutropy., The entropic variable $A\equiv P/\rho^\gamma$ is used in place of the specific entropy.
 The xuaneter ο. is defined to be the παπα cutropy of he parent polvtrope., The parameter $A_\circ$ is defined to be the minimum entropy of the parent polytrope.
 After 1000 tinesteps iu which the polvtrope has 110ved. 256 cells in each direction. the advected polvtrope has still retained its equilibrium profile.," After 1000 timesteps in which the polytrope has moved 256 cells in each direction, the advected polytrope has still retained its equilibrium profile."
 Shock heating cau occur iu the outer envelope as the polvtrope moves through the false vacuum., Shock heating can occur in the outer envelope as the polytrope moves through the false vacuum.
 However. by setting the density of the false vacuna to be 10* of the central density of the polvtrope. we can minimize the spurious VArock heating.," However, by setting the density of the false vacuum to be $10^{-8}$ of the central density of the polytrope, we can minimize the spurious shock heating."
 Iu Figure H1 we show four snapshots of the mereine process taken at tine f=0. 2. I and τμ.," In Figure \ref{fig:merge} we show four snapshots of the merging process taken at time $t=0$, 2, 4, and $8\,\tau_{dyn}$."
 The 2-D deusitv maps are created * averages over 1 planes taken about the orbital mid-plane., The 2-D density maps are created by averaging over 4 planes taken about the orbital mid-plane.
 The density contours are spaced logarithmically with 2 per decade coverme 3 decades down from the masini., The density contours are spaced logarithmically with 2 per decade and covering 3 decades down from the maximum.
 The parent stars are initially separated bv 3.75R ralaced ou zero-energv orbits with a periceutre separation ο: 0.25R.," The parent stars are initially separated by $3.75\,R$ and placed on zero-energy orbits with a pericentre separation of $0.25R$."
 During he collision process. the outer envelopes of tlhe pareu stars are shock heated and niateria gets ejected.," During the collision process, the outer envelopes of the parent stars are shock heated and material gets ejected."
" Iu less than 1074,, the morecr ποια! establishes hydrostatie equilibriui."," In less than $10\,\tau_{dyn}$, the merger remnant establishes hydrostatic equilibrium."
 The uerecr remnant is a rotating oblate with mass approximately of the combined mass of the parent stars., The merger remnant is a rotating oblate with mass approximately of the combined mass of the parent stars.
 A Luge fraction of the mass loss is due to the vacui boundary coucitious., A large fraction of the mass loss is due to the vacuum boundary conditions.
 Ejected material do not have the opportunity to fall back outo the merger remnant., Ejected material do not have the opportunity to fall back onto the merger remnant.
 However. the additional mass loss in the euvelope does not present a problem since we are interested iu the question of mixing in the interior of the star.," However, the additional mass loss in the envelope does not present a problem since we are interested in the question of mixing in the interior of the star."
 Tn Fiewre 12 we plot the thermodvuaimic profiles of the merecr remnant aud the parent stars., In Figure \ref{fig:profiles} we plot the thermodynamic profiles of the merger remnant and the parent stars.
 The central density aud pressure in the core of the mereer remmaut, The central density and pressure in the core of the merger remnant
(ii) Alaccler’s (1992) oxvgen vields are considered in tandem with the iron vields of Tsujimoto (1995) 7995|M927.,(iii) Maeder's (1992) oxygen yields are considered in tandem with the iron yields of Tsujimoto (1995) [`T95+M92'].
 Alaeder. along with Langer Llenkel (1995). represen he only published. eric of vields. incorporating mass-loss.," Maeder, along with Langer Henkel (1995), represent the only published grid of yields incorporating mass-loss."
 Alaccler USCS the Schwarzschild criterion for. convection. ike Tsujimoto but also includes some degree> of overshooting.," Maeder uses the Schwarzschild criterion for convection, like Tsujimoto, but also includes some degree of overshooting."
 Oxygen production is severely. hampered in moz30 AL. models with solar a result. tha vas profound implications for the Ένρο La versus Tvpoe LH ICM iron argument of Ishimaru Arimoto (1997)., Oxygen production is severely hampered in $m\simgt 30$ $_\odot$ models with solar a result that has profound implications for the Type Ia versus Type II ICM iron argument of Ishimaru Arimoto (1997).
 A direc mapping of Maeders oxvgen vields onto the Fsujimoto vields. is not optimal bv any means. but it does provide a tantalising clue to the importance of niass-lIoss consideration. (," A direct mapping of Maeder's oxygen yields onto the Tsujimoto yields, is not optimal by any means, but it does provide a tantalising clue to the importance of mass-loss consideration. ("
iv) Arnett’s (1996) oxvgen. magnesium. and neon vields have been coupled to his earlier iron predictions (Arnett 1991) ΑΟ].,"iv) Arnett's (1996) oxygen, magnesium, and neon yields have been coupled to his earlier iron predictions (Arnett 1991) [`A96']."
 This has been necessary as the 1996 models contain vields arising from hvedrostatic evolution only., This has been necessary as the 1996 models contain yields arising from hydrostatic evolution only.
 Explosive. nucleosvnthesis can modify the silicon. sulphur. and iron results substantially (Dazánn 1997. priv commi)," Explosive nucleosynthesis can modify the silicon, sulphur, and iron results substantially (Bazánn 1997, priv comm)."
 Arnett’s new ος of SN models avoids the use of mixing-length theory with semiconvection Woosley Weaver 1996). and assumes that convection is so ellicient that complete adiabaticity and chemical homogeneity are maintained.," Arnett's new grid of SN models avoids the use of mixing-length theory with semiconvection Woosley Weaver 1996), and assumes that convection is so efficient that complete adiabaticity and chemical homogeneity are maintained."
 Semiconvective regions are also assumed to homogeneous., Semiconvective regions are also assumed to be homogeneous.
 ὃν considering “Pype LE SN. vields [rom progenitors with uniform: metallicities. we have implicitly. ignored. t ellects. of galaxy evolution.," By considering Type II SN yields from progenitors with uniform metallicities, we have implicitly ignored the effects of galaxy evolution."
 In. principle. one ought couple models of galaxy formation ancl chemical evolution directly to the SNL explosion calculations to determine self-consistent integrated: nucleosvnthetie: vields.," In principle, one ought to couple models of galaxy formation and chemical evolution directly to the SNII explosion calculations to determine self-consistent integrated nucleosynthetic yields."
 These woulc o» superpositions of enrichment. from Tvpe IE. SNe with oogenitors of varving metallicity., These would be superpositions of enrichment from Type II SNe with progenitors of varying metallicity.
 By including both high and low WWΟΡ metalleities we do bracket the expectec range of average vields for that subset of our models. anc wovide some indication of the general cllects of varving the wogenitor abuncdances.," By including both high and low WW95 metallcities we do bracket the expected range of average yields for that subset of our models, and provide some indication of the general effects of varying the progenitor abundances."
 A full discussion of the input physies dilferences. arc heir respective implications. in cach of the above SNe models. is well bevond the scope of this paper.," A full discussion of the input physics differences, and their respective implications, in each of the above SNe models, is well beyond the scope of this paper."
 The reader is stronely urged to turn to Woosley Weaver (1995). Arnet (1996). anc," The reader is strongly urged to turn to Woosley Weaver (1995), Arnett (1996), and"
 The reader is stronely urged to turn to Woosley Weaver (1995). Arnet (1996). ancl," The reader is strongly urged to turn to Woosley Weaver (1995), Arnett (1996), and"
"Convection is taken to set in whenever The actual gradient V. is then caleulated in accordance with the mixing length recipe (?):: consider (he non-dimensional (inverse) convective efficiency. parameter where ση is Stefans constant: ( is (he mixing length. which we take to be a constant multiple (of order unitv) of the pressure scale height //.=ο. where v2=p/p is the squared thermal speed. and g=μή is the local acceleration of gravitv: —Jlnp(p.T.X)/OlnT: ep is the specific heat at constant pressure: and 7,=rapt.","Convection is taken to set in whenever The actual gradient $\nabla\,$ is then calculated in accordance with the mixing length recipe \citep{1978stat.book.....M}: consider the non-dimensional (inverse) convective efficiency parameter where $\sigma_{\rm R}$ is Stefan's constant; $\ell$ is the mixing length, which we take to be a constant multiple (of order unity) of the pressure scale height $H=v_0^2/g\,$, where $v_0^2=p/\rho$ is the squared thermal speed and $g=Gm/r^2$ is the local acceleration of gravity; $Q=-\partial\ln\rho(p,T,X)/\partial\ln T\,$ ; $c_{\rm P}$ is the specific heat at constant pressure; and $\tau_e=\kappa\rho\ell\,$."
 Let c be the root of the cubic equation where Then the actual gradient is given by It is readily seen that V4Và as P20. and VGVp as f—x.," Let $x$ be the root of the cubic equation where Then the actual gradient is given by It is readily seen that $\nabla\rightarrow\nabla_{\rm A}$ as $b'\rightarrow 0\,$, and $\nabla\rightarrow\nabla_{\rm R}$ as $b'\rightarrow\infty\,$."
 Convective mixing is taken {ο be due to diffusion in a gas of particlesrepresenting the convective elementismoving at the convective speed (?).. with the mean ου path (.," Convective mixing is taken to be due to diffusion in a gas of particles—representing the convective elements—moving at the convective speed \citep{1978stat.book.....M}, with the mean free path $\ell\,$."
" In such a gas the diffusion coellicient is ~o,f."," In such a gas the diffusion coefficient is $\sim v_c\ell\,$."
 Bul in eqs., But in eqs.
 the derivatives are wilh respect to mass. nol radius.," the derivatives are with respect to mass, not radius."
 We therelore set the convective dilfusion coefficients equal to the same for all species /.," We therefore set the convective diffusion coefficients equal to the same for all species $j\,$."
 The code sometimes runs into difficulties with the foregoing convective diffusion coefficients., The code sometimes runs into difficulties with the foregoing convective diffusion coefficients.
 We therefore retain an option whereby (he last formula is replaced by a much simpler one: where fy.< lis a numerical coellicient., We therefore retain an option whereby the last formula is replaced by a much simpler one: where $k_c < 1$ is a numerical coefficient.
 Its purpose is to ensure (hal convective mixing does not occur too suddenly., Its purpose is to ensure that convective mixing does not occur too suddenly.
 The value of fy is related tothe evolutionary time scale. and ranges [rom ~0.1 for low-mass stars to ~0.001 [or massive ones.," The value of $k_c$ is related tothe evolutionary time scale, and ranges from $\sim0.1$ for low-mass stars to $\sim0.001$ for massive ones."
We should note here that calculations preseuted in this section rely on our use of viscosity (9))-(10)) throughout the whole region of AY. phase space that we consider.,"We should note here that calculations presented in this section rely on our use of viscosity \ref{eq:opacity}) \ref{eq:dust_opacity}) ) throughout the whole region of $\dot M,\Omega$ phase space that we consider."
 Iu reality. at high AZ and © disk temperature should exceed 10? K at which poiut icv erains sublimate leaving metalsilicate eras as a source of opacity.," In reality, at high $\dot M$ and $\Omega$ disk temperature should exceed $10^2$ K at which point icy grains sublimate leaving metal-silicate grains as a source of opacity."
 This latter opacity source While still beiug in the form (9)). is characterized by smaller values of & at the same temperature aud >c1/2.," This latter opacity source while still being in the form \ref{eq:opacity}) ), is characterized by smaller values of $\kappa$ at the same temperature and $\beta\approx 1/2$."
 This is likely to quantitatively (out not qualitatively) affect results presented im Figures 1--3 atf laugh ÀJ aud O., This is likely to quantitatively (but not qualitatively) affect results presented in Figures \ref{fig:CaseA}- \ref{fig:CaseC} at high $\dot M$ and $\Omega$.
 To not complicate thines further here we do not attempt to self-cousisteutlv describe transitions between different opacity regiaues but rather displav a qualitative picture for a single opacity law., To not complicate things further here we do not attempt to self-consistently describe transitions between different opacity regimes but rather display a qualitative picture for a single opacity law.
 Our results cau be applied to understanding the xoperties of the outer. cold parts of realistic accretion disks.," Our results can be applied to understanding the properties of the outer, cold parts of realistic accretion disks."
 Tn particular. we address three iuportant isstes.," In particular, we address three important issues."
 Fist. a possibility of laut planet formation by GIi- xotoplanetary disks las been discussed since Camerou (1978).," First, a possibility of giant planet formation by GI in protoplanetary disks has been discussed since Cameron (1978)."
 Iu this context it is interesting to ask under which conditions a constaut AZ protoplanctary disk would Ὡς sone to fragimoeutation iuto gravitationally bouud. selt-eravitatine objects.," In this context it is interesting to ask under which conditions a constant $\dot M$ protoplanetary disk would be prone to fragmentation into gravitationally bound, self-gravitating objects."
 Our results described in &8L1 cau cirectlv address this issuc., Our results described in \ref{subsect:regimes} can directly address this issue.
 Indeed. conditions used iu xoducing Figure 1.. namely a=0.003 aud Tyz35 Is are quite typical for the outer regions of protoplauctary disks. bevoud ~100 AU from the central star.," Indeed, conditions used in producing Figure \ref{fig:CaseA}, namely $\alpha=0.003$ and $T_0\approx 35$ K are quite typical for the outer regions of protoplanetary disks, beyond $\sim 100$ AU from the central star."
" One oue hand.the disk surface deusity there is low enough (see below) for the cosmic rav loulzation to stimulate MRI operation which gives rise to a, at the level of ~107."," One one hand,the disk surface density there is low enough (see below) for the cosmic ray ionization to stimulate MRI operation which gives rise to $\alpha_\nu$ at the level of $\sim 10^{-3}-10^{-2}$."
 Ou the other haud. outer regions of protoplanctary disks are warmed up by radiation of either the parent star or the neighborime stars at the level of several tens of I. Thus. the situation represcuted in Fieure 1. can be directly used for wuderstanding the properties of external parts of protoplauctary disks.," On the other hand, outer regions of protoplanetary disks are warmed up by radiation of either the parent star or the neighboring stars at the level of several tens of K. Thus, the situation represented in Figure \ref{fig:CaseA} can be directly used for understanding the properties of external parts of protoplanetary disks."
" What is obvious from this Figure is that giant planet formation by gravitational instability iu constant AL disks can take place only bevoud 5120 AU which is the distance πο a 1 AL. star at which ο=Q9, releuber that in the optically gravitoturbulent disks fraginentation occurs at this specific value of O (Matzner Levin 2005). see equation (79))."," What is obvious from this Figure is that giant planet formation by gravitational instability in constant $\dot M$ disks can take place only beyond $\approx 120$ AU which is the distance from a $1$ $_\odot$ star at which $\Omega=\Omega_f$ – remember that in the optically gravitoturbulent disks fragmentation occurs at this specific value of $\Omega$ (Matzner Levin 2005), see equation \ref{eq:om_fr_thick}) )."
 Thus. planets produced by gravitational mstabilitv should be born far from their parent stars although one caunot exclude their subsequent iigration to shorter periods.," Thus, planets produced by gravitational instability should be born far from their parent stars although one cannot exclude their subsequent migration to shorter periods."
 Another obvious coustraint on planet formation that follows οι Figure 1l ds that AY must be pretty biel at the location where disk fragments aud. planets. form., Another obvious constraint on planet formation that follows from Figure \ref{fig:CaseA} is that $\dot M$ must be pretty high at the location where disk fragments and planets form.
 Iudeed. one can easily see that fragmentation is possible only if AZ locally exceeds 107 AL. vri.," Indeed, one can easily see that fragmentation is possible only if $\dot M$ locally exceeds $10^{-5}$ $_\odot$ $^{-1}$."
 At lower M disk mnaiutains itself ina eravitoturbuleut state (or even being kept gravitationallv stable by its own backerouud viscosity at very low M ) without fragmentation even very far frou the star., At lower $\dot M$ disk maintains itself in a gravitoturbulent state (or even being kept gravitationally stable by its own background viscosity at very low $\dot M$ ) without fragmentation even very far from the star.
 Aceretion rates in excess of 10.7 AL 1 bare atypical for mature T Tauri disks (Coulbring 1998)., Accretion rates in excess of $10^{-5}$ $_\odot$ $^{-1}$ are atypical for mature T Tauri disks (Gullbring 1998).
 Towever. they may have been present at the very earliest stages of star and disk formation when the material from collapsing protostellay envelope rains down outo the disk at a very Μο] rate. possibly exceeding 107 M. | in some locations.," However, they may have been present at the very earliest stages of star and disk formation when the material from collapsing protostellar envelope rains down onto the disk at a very high rate, possibly exceeding $10^{-5}$ $_\odot$ $^{-1}$ in some locations."
 Such disks are likely not to have AL constant through their whole extent but as we discussed in 83 our results are still even in this wore coniplicated case as long as AL is specified locally., Such disks are likely not to have $\dot M$ constant through their whole extent but as we discussed in \ref{sect:mdot} our results are still even in this more complicated case as long as $\dot M$ is specified locally.
 Second practical issue that we are goiug to address has to do with the feeding of supermassive black holes in ceuters of ealaxies., Second practical issue that we are going to address has to do with the feeding of supermassive black holes in centers of galaxies.
 It has been kuown for a long time that the outer parts of quasar disks must be gravitationally tustable which was always raising a question of how eas is transported to the black hole from lavge distances., It has been known for a long time that the outer parts of quasar disks must be gravitationally unstable which was always raising a question of how gas is transported to the black hole from large distances.
 Our results demoustrate that as long as M is uot very high the Gis not goiug to iupedoe mass transter through the disk since for low enough M. namely for AL(Dy3. see equation (82)). a eravitationally unstable<Aly diskΤΗ) cau persist iu a eravitoturbulent state at arbitrarily larec distances from the central object.," Our results demonstrate that as long as $\dot M$ is not very high the GI is not going to impede mass transfer through the disk since for low enough $\dot M$, namely for $\dot M\lesssim M_f(T_0/T_f)^{3/2}$, see equation \ref{eq:stable}) ), a gravitationally unstable disk can persist in a gravitoturbulent state at arbitrarily large distances from the central object."
 Wow high AL can be carried through a eravitoturbulent disk elobally thus depends only on the level of external irradiation., How high $\dot M$ can be carried through a gravitoturbulent disk globally thus depends only on the level of external irradiation.
" Raciation fields in galactic uuclei due to eircinnuclear stars are expected to be quite intense giving rise to Ty at the level of teus to hundreds of EK. Απο Jy=100 E (which is a radiation field «μον more intense than that expected in the Galactic Center) we find that exavitoturbuleut disk can transport mass from infinity to the black hole as loug as Af<Lear,zLo? AL. +.", Radiation fields in galactic nuclei due to circumnuclear stars are expected to be quite intense giving rise to $T_0$ at the level of tens to hundreds of K. Assuming $T_0=100$ K (which is a radiation field slightly more intense than that expected in the Galactic Center) we find that gravitoturbulent disk can transport mass from infinity to the black hole as long as $\dot M\lesssim 10^3\dot M_f\approx 10^{-2}$ $_\odot$ $^{-1}$ .
" This is about 104 of the Eddington rate (for radiative efficienev of 105€) for the £«109 AL. black hole in the ceuter of our Galaxy. which is quite siguificaut eiven that the Dondi accretion rate of this object is =10 OAL, VrE (Daganoff 2003)."," This is about $10\%$ of the Eddington rate (for radiative efficiency of $10\%$ ) for the $4\times 10^{6}$ $_\odot$ black hole in the center of our Galaxy, which is quite significant given that the Bondi accretion rate of this object is $\lesssim 10^{-5}$ $_\odot$ $^{-1}$ (Baganoff 2003)."
 Thus. irradiated eravitoturbuleut accretion disks provide a natural wav," Thus, irradiated gravitoturbulent accretion disks provide a natural way"
Tabs.,Tabs.
 Al - C2. contains the results of the Gaussian decompostion procedure that we have applied to the spectra., \ref{TabFitHCOp} - \ref{TabFitCN} contains the results of the Gaussian decompostion procedure that we have applied to the spectra.
" The column densities. given in the last columns. are derived assuming a single excitation temperature 7 for all the levels of a given molecule as where vo. 2,. 9; and A,,; are the rest frequency. the upper and lower level degeneracies and the Einstein's coetficients of theobserved transition. QUA.) is the partition funtion. and c is the speed of light."," The column densities, given in the last columns, are derived assuming a single excitation temperature $T_{\rm ex}$ for all the levels of a given molecule as where $\nu_0$, $g_u$, $g_l$ and $A_{ul}$ are the rest frequency, the upper and lower level degeneracies and the Einstein's coefficients of theobserved transition, $Q(T_{\rm ex})$ is the partition funtion, and $c$ is the speed of light."
 We also remind that for a Gaussian profile ofpeak opacity το and FWHM Av. the opacity integral is [rdv=1/2VgíIn204Av.," We also remind that for a Gaussian profile ofpeak opacity $\tau_0$ and FWHM $\Delta
\upsilon$, the opacity integral is $\int \tau \, d\upsilon = 1/2 \,
\sqrt{\pi/\ln{2}} \, \tau_0 \, \Delta \upsilon$."
 For anexcitation temperature of 2.73 K. Eq.," For anexcitation temperature of 2.73 K, Eq."
 Al becomes and using the HCO! /Z0— I. HNC/=0- I.HCN JF20.1- 1.2. and CN AFLF=0.1/2.3/3—1.1/2.3/2 transitions respectively.," \ref{EqDcol} becomes and using the $^{+}$ $J=0-1$ , HNC $J=0-1$ , HCN $J,F=0,1-1,2$ , and CN $J,F1,F=0,1/2,3/2-1,1/2,3/2$ transitions respectively."
 EI. E2. ΕΙ E2 El., \ref{FigChemistry0} \ref{FigChemistry} \ref{FigChemistry0} \ref{FigChemistry} \ref{TabChem}.
 EI. E2. ΕΙ E2 El.+, \ref{FigChemistry0} \ref{FigChemistry} \ref{FigChemistry0} \ref{FigChemistry} \ref{TabChem}.
= J2pt = ]2pt,= 12pt = 12pt
|b]>10 respectively.,$|b|>10^\circ$ respectively.
 In our simulation. we use energy Lux threshold. instead. of photon flux threshold.," In our simulation, we use energy flux threshold instead of photon flux threshold."
 For simplicity. we have assumed. photon index ~2 for all simulated sources.," For simplicity, we have assumed photon index $\sim 2$ for all simulated sources."
 We convert the photon flux thresholds suggested by Gonthier et. al. (, We convert the photon flux thresholds suggested by Gonthier et al. (
2002) to energy [ux threshold as ~↓⋅⋅↱≻↓∪⊔⋖⋅↓⋅⋏∙≟≼∼⊔↓−≱∖↓⇂∪↓⋅≱∖⋯⊔⋅≼∙∢⋅≱∖↓⋯∙⋜⋯⋅∠⇂⋜⊔(2 ⋅ |b«LO” and 6.8.10Hopgcmτν for sources Located at |b]>10 respectively.,"2002) to energy flux threshold as $\sim 1.5 \times 10^{-10}{\rm
erg~cm^{-2}~s^{-1}}$ for sources located at $|b|<10^\circ$ and $\sim 6.8 \times 10^{-11}{\rm erg~cm^{-2}~s^{-1}}$ for sources located at $|b|>10^\circ$ respectively."
 We carry out Monte Carlo simulation of the Galactic pulsars »»rn during the past 10. Myr., We carry out Monte Carlo simulation of the Galactic pulsars born during the past 10 Myr.
" We find a total of 76 5-ràv mature pulsars of ages larger than LO"" vears that could be detected by EGRET.", We find a total of 76 $\gamma$ -ray mature pulsars of ages larger than $10^5$ years that could be detected by EGRET.
 Out of this simulated. sample. 44 of hem lie in the Galactic plane (|p| 57) and 32 lie at ueher latitudes. (|| 57).," Out of this simulated sample, 44 of them lie in the Galactic plane $|b|\leq 5^\circ$ ) and 32 lie at higher latitudes $|b|> 5^\circ$ )."
 This current result. is. slightly different from the simulations presented. in. Cheng ct al. (, This current result is slightly different from the simulations presented in Cheng et al. (
2004a) because of the revised age restrictions here of taking only mature pulsars of 27107. vears.,2004a) because of the revised age restrictions here of taking only mature pulsars of $\geq 10^5$ years.
 Currently. four radio rulsars with age >107 ves are identified as >-ray pulsars. Le. Geminga. PSR D1055-52. PSR. D1951|32. PSR. JO218|42 Cl'hompson ct al.," Currently, four radio pulsars with age $>10^5$ yrs are identified as $\gamma$ -ray pulsars, i.e. Geminga, PSR B1055-52, PSR B1951+32, PSR J0218+42 (Thompson et al."
 1996: Ixuiper et al., 1996; Kuiper et al.
 2000)., 2000).
 The predicted 5-rav pulsar numbers appear very much larger than the confirmed. ταν pulsars., The predicted $\gamma$ -ray pulsar numbers appear very much larger than the confirmed $\gamma$ -ray pulsars.
 We should. notice that. first. not all 76 predicted are radio-loud.," We should notice that first, not all 76 predicted are radio-loud."
 Ehe radio beaming factor is roughly 0.15 (Enmmerine and Chevalier 1989: ίσος 1990)., The radio beaming factor is roughly 0.15 (Emmering and Chevalier 1989; Biggs 1990).
 ‘Taking the radio beaming [factor into account. we preclict that ~12 EGRET Unidentified Sources will be identified in the radio band in future.," Taking the radio beaming factor into account, we predict that $\sim$ 12 EGRET Unidentified Sources will be identified in the radio band in future."
 In fact recently there are 20 known radio pulsars located within the error boxes of EGRET sources and many of them may be identified as raclio-loud + - pulsars (Manchester 2004)., In fact recently there are 20 known radio pulsars located within the error boxes of EGRET sources and many of them may be identified as radio-loud $\gamma$ -ray pulsars (Manchester 2004).
 Ht is very important to note hat ‘TeV -ravs from pulsar wind nebulae are isotropic and independent of radio-Ioud or radio-quiet οταν pulsars., It is very important to note that TeV $\gamma$ -rays from pulsar wind nebulae are isotropic and independent of radio-loud or radio-quiet $\gamma$ -ray pulsars.
 In Figure 1. we plot the distributions of the pulsar »eriod. (upper panel) and the magnetic field (bottoni panel) of our simulated. sample. for both sources in. the the ασ] latitudes of |b|]25° (solid histogram). and in the ow latitudes jbl<5° (dashed histogram).," In Figure 1, we plot the distributions of the pulsar period (upper panel) and the magnetic field (bottom panel) of our simulated sample, for both sources in the the high latitudes of $|b|>
5^\circ$ (solid histogram), and in the low latitudes $|b|\leq
5^\circ$ (dashed histogram)."
 The proper motion velocity (op panel) ancl distance (bottom. panel) distributions of our mature pulsar sample are presented in ligure 2., The proper motion velocity (top panel) and distance (bottom panel) distributions of our mature pulsar sample are presented in Figure 2.
 The average velocity of our sample is found to be ~350kms.I., The average velocity of our sample is found to be $\sim 350\ {\rm km\ s^{-1}}$.
 We have taken this value in equation (5) to estimate the termination radius (cf., We have taken this value in equation (5) to estimate the termination radius (cf.
 2.2)., 2.2).
 We show also in ligure 2 that the low and high latitude pulsar samples have cilferent. distance distributions., We show also in Figure 2 that the low and high latitude pulsar samples have different distance distributions.
 The average distance of the pulsars in the Galactic plane (θες ο} is determined to be «dc900 pe. while the average distance is «dox400 pe for the high latitude sample (Jb 57).," The average distance of the pulsars in the Galactic plane $|b|\leq 5^\circ$ ) is determined to be $<d>\simeq 900$ pc, while the average distance is $<d>\simeq 400$ pc for the high latitude sample $|b|> 5^\circ$ )."
 This suggests that many high latitude 7?-rav mature pulsars may lie in the Gould Belt., This suggests that many high latitude $\gamma$ -ray mature pulsars may lie in the Gould Belt.
 In Figure 3.2 we plot the 5-rav luminosity versus spin down power of our simulated 5-rav. pulsar sample.," In Figure 3, we plot the $\gamma$ -ray luminosity versus spin down power of our simulated $\gamma$ -ray pulsar sample."
" The spin down power are all found to be lower than 107""ergs which is consistent with our expectations."," The spin down power are all found to be lower than $10^{36}\ {\rm erg\ s^{-1}}$, which is consistent with our expectations."
 Many. of them in the Galactic plane may. be the Geminga-like. pulsars., Many of them in the Galactic plane may be the Geminga-like pulsars.
 owe fit the simulated relation of 5-rav. luminosity versus spin down power with single power law and it is consistent with the observed correlation of the known 5-rav. pulsars. LeooxLEP (Phompson 2001).," If we fit the simulated relation of $\gamma$ -ray luminosity versus spin down power with single power law and it is consistent with the observed correlation of the known $\gamma$ -ray pulsars, $L_{\gamma, \rm
GeV}\propto L_{\rm sd}^{0.5}$ (Thompson 2001)."
" Llowever. [rom Figure 3 there probably exist two populations of the relations: one »opulation follows ἐςxLov: another population emergesὃν as a branch for Loy7loESTergslosa""owih£.ox LU).ll."," However, from Figure 3 there probably exist two populations of the relations: one population follows $L_\gamma \propto L_{sd}$; another population emerges as a branch for $L_{sd} > 10^{34}{\rm erg\
s^{-1}}$, with $L_\gamma \propto L_{sd}^{1/4}$."
Zhang οἱ al. (, Zhang et al. (
2004) have provided a possible explanation for the nature of these two populations and they estimate the separation of the two populations should occur at 1.5«LOD!ores,2004) have provided a possible explanation for the nature of these two populations and they estimate the separation of the two populations should occur at $1.5\times 10^{34}{\rm P^{1/3} erg ~s^{-1}}$.
 Assuming that mature pulsars can form faint and compact nebulae. anc can produce Γον photons through LCS processes. the LOS flux from the pulsar nebulae can be calculated by Ag E... where LES—Lye|Lase (see 3). and £- is the threshold οποιον. taken to be 1 TeV. In order to calculate the Tey luminosity for cach of the simulated: pulsars.," Assuming that mature pulsars can form faint and compact nebulae, and can produce TeV photons through ICS processes, the ICS flux from the pulsar nebulae can be calculated by d^2 , where $L^{\rm ICS}\simeq
L_{\rm IC}+L_{\rm SSC}$ (see 3), and $E_\gamma$ is the threshold energy, taken to be 1 TeV. In order to calculate the TeV luminosity for each of the simulated pulsars."
" we have to choose some fixed. values for the pulsar wind parameters. Le. gee. p and 5,4. which are produced. in non-linear processes and. will certainly. vary from. pulsar to pulsar."," we have to choose some fixed values for the pulsar wind parameters, i.e. $\epsilon_e,
\epsilon_B$, p and $\gamma_w$, which are produced in non-linear processes and will certainly vary from pulsar to pulsar."
" We have assumed. a set of pulsar wind. nebula parameters. for all simulated: pulsars. with ο,~0.5 according to the energy equipartition assumption. cg0.01. p—2.3. 5,~10"". and the ISM. density n~1 cm7."," We have assumed a set of pulsar wind nebula parameters for all simulated pulsars, with $\epsilon_e\sim 0.5$ according to the energy equipartition assumption, $\epsilon_B\sim 0.01$, $p\sim 2.2$, $\gamma_w\sim 10^6$, and the ISM density $n\sim 1$ $^{-3}$."
 The choices of these owanmeters are consistent. with theoretical estimations., The choices of these parameters are consistent with theoretical estimations.
 In Figure 4. we plot the GeV 5-ray. photon flux from he pulsar outer gap versus the TeV photon flux from the oulsar wind. nebula.," In Figure 4, we plot the GeV $\gamma$ -ray photon flux from the pulsar outer gap versus the TeV photon flux from the pulsar wind nebula."
 There exists a correlation between the GeV and TeV Duxes because both quantities depend on the »ulsar spin clown power., There exists a correlation between the GeV and TeV fluxes because both quantities depend on the pulsar spin down power.
 This suggests that strong EGRET sources may be potential TeV sources to be detected. by present and future Ley telescopes., This suggests that strong EGRET sources may be potential TeV sources to be detected by present and future TeV telescopes.
 The ‘TeV flux distribution of the mature pulsars at high. latitudes. |b|25 (solid histogram) and on he Galactic plane. |b]<5 (dashed. bistogran) are oesented in Figure 5.," The TeV flux distribution of the mature pulsars at high latitudes, $|b|> 5^\circ$ (solid histogram) and on the Galactic plane, $|b|\leq 5^\circ$ (dashed histogram), are presented in Figure 5."
 The predicted. TeV fluxes of our ow latitude simulated. sample are all lower than 3107?photonem7s * whieh is also the upper Dux limit of all but two of the high latitude sample.," The predicted TeV fluxes of our low latitude simulated sample are all lower than $3\times 10^{-12}\ {\rm photon\ cm^{-2}\ s^{-1}}$ , which is also the upper flux limit of all but two of the high latitude sample."
 The predicted TeV lux from our sample is lower than the previous observational constraints mentioned earlier in the Introduction., The predicted TeV flux from our sample is lower than the previous observational constraints mentioned earlier in the Introduction.
 However. with the rapid advancements of the ground-based Toy elescopes. some of the unidentified ECGBIZE sources could xe identified as TeV sources in the future.," However, with the rapid advancements of the ground-based TeV telescopes, some of the unidentified EGRET sources could be identified as TeV sources in the future."
" We study the high energy. radiation. from mature pulsars with agesof ~10”10"" vears in the present paper.", We study the high energy radiation from mature pulsars with agesof $\sim 10^5-10^6$ years in the present paper.
 We consider LOO MeV. to GeV. 5-ravs generated. from. the, We consider 100 MeV to GeV $\gamma$ -rays generated from the
oh UT with a flare duration of about two hours.,5h UT with a flare duration of about two hours.
 Another feature we note in Figure 3 is a possible, Another feature we note in Figure 3 is a possible
The svstematic errors examined by ΗΛΙΟ and NEOA4 have already been discussed by us in the PDS analvsis of A2256 (Fusco-Femiano. Landi Orlandini 2005). but considering (heir importance in (he analvsis results we intend to report here again the main parts of the discussion.,"The systematic errors examined by RM04 and NE04 have already been discussed by us in the PDS analysis of A2256 (Fusco-Femiano, Landi Orlandini 2005), but considering their importance in the analysis results we intend to report here again the main parts of the discussion."
 rr ΗΛΙΟ claim the presence of an. Iistrumental background residual’ (see sect.," 1) RM04 claim the presence of an ""Instrumental background residual"" (see sect."
 2.1 of (heir paper) derived from the analysis of 15 blank fields. i.e. fields which do not contain sources showing significant emission in the PDS energv range.," 2.1 of their paper) derived from the analysis of 15 ""blank fields"", i.e. fields which do not contain sources showing significant emission in the PDS energy range."
 By sumnmüng the spectra from these observations they. [find Chat the spectrum differs from zero: the count rate is (1.4520.77)xLO7 in the 12-100 keV energy range.," By summing the spectra from these observations they find that the spectrum differs from zero: the count rate is $1.45\pm 0.77)\times
10^{-2}$ in the 12-100 keV energy range."
 This seems to indicate that the background in the ON position is larger Chan that in (he OFF positions producing an instrumental contribution not removed by (the background subtraction procedure., This seems to indicate that the background in the ON position is larger than that in the $\pm$ OFF positions producing an instrumental contribution not removed by the background subtraction procedure.
" This effect has been studied by Landi (2005) considering the complete sample of 868 PDS pointings with galactic latitude |b)>15°. and selecting the 15100 keV net count spectra for which there is source detection below lo (that is. ""blank fields"")."," This effect has been studied by Landi (2005) considering the complete sample of 868 PDS pointings with galactic latitude $|b|>15^\circ$, and selecting the 15–100 keV net count spectra for which there is source detection below $\sigma$ (that is, “blank fields”)."
 These spectra have been summed imposing a net exposure greater than 20 ksec., These spectra have been summed imposing a net exposure greater than 20 ksec.
 A net count rate of (1.67255.30)x10.* has been derived. consistent with the definition of “blank field”.," A net count rate of $(1.67\pm
5.30)\times 10^{-3}$ has been derived, consistent with the definition of “blank field”."
 Also ΝΕΟΙ do not report evidence for an instrumental residual., Also NE04 do not report evidence for an instrumental residual.
 2) The other effect evaluated by RAIO4 regards the svstematic differences between the backeround fields., 2) The other effect evaluated by RM04 regards the systematic differences between the background fields.
 Thev analvze a sample of 69 observations whose target is outsicle the ealactie plane and with a long exposure time (see Appendix of their paper)., They analyze a sample of 69 observations whose target is outside the galactic plane and with a long exposure time (see Appendix of their paper).
 RAIOS find that the mean value of the difference between ON and the (wo -OFF and +OFF sky positions is significantly different from zero ancl positive., RM04 find that the mean value of the difference between ON and the two -OFF and +OFF sky positions is significantly different from zero and positive.
 Also this elfect has been investigated by Landi (2005) on the sample of PDS observations., Also this effect has been investigated by Landi (2005) on the sample of PDS observations.
 The obtained value of (5.36.3)x10.7 is consistent with no contamination at all., The obtained value of $(5.3\pm 6.3)\times 10^{-3}$ is consistent with no contamination at all.
 We presume that the value found by ΗΛΙΟ could be due to the simall sample of observations they. considered., We presume that the value found by RM04 could be due to the small sample of observations they considered.
 NEOA. analvzing a larger sample of data wilh respect to that used by ΠΑΛΙΟ (164 PDS observations). found a svstematic difference between ON and the two offset pointings (hat cancels out in the standard usage of both offsets.," NE04, analyzing a larger sample of data with respect to that used by RM04 (164 PDS observations), found a systematic difference between ON and the two offset pointings that cancels out in the standard usage of both offsets."
 3) In addition. NEOL introduce a svstematic error in the net source count rates cue to unresolved and not significantly detected point sources present in the PDS field of view.," 3) In addition, NE04 introduce a systematic error in the net source count rates due to unresolved and not significantly detected point sources present in the PDS field of view."
 Thev find that an excess of 0.019 counts + has to be added to the net count rate spectra (no errors are eiven on (his measurement). when the standard method of background evaluation is used. and 0.027 counts | has to be added when the background is evaluated [rom only," They find that an excess of 0.019 counts $^{-1}$ has to be added to the net count rate spectra (no errors are given on this measurement), when the standard method of background evaluation is used, and 0.027 counts $^{-1}$ has to be added when the background is evaluated from only"
science goal.,science goal.
" It is necessary to clarify whether this means a galaxy identical to the MW placed at a cosmological distance corresponding to z=3, or rather a plausible MW progenitorat z=3."," It is necessary to clarify whether this means a galaxy identical to the MW placed at a cosmological distance corresponding to $z=3$, or rather a plausible MW progenitorat $z=3$."
" The former interpretation is more common, but we here adopt the latter for it is perhaps more sensible in a study ultimately dedicated to the understanding of our own origins."," The former interpretation is more common, but we here adopt the latter for it is perhaps more sensible in a study ultimately dedicated to the understanding of our own origins."
" Yet, this interpretation complicates the predictions as they require a model of the MW at a cosmic time corresponding to z= 3.1.6. 11 billion years back in time."," Yet, this interpretation complicates the predictions as they require a model of the MW at a cosmic time corresponding to $z=3$, i. e. 11 billion years back in time."
 Section ?? reviews thes, Section \ref{section_simulation} reviews the.
imulation!.. Section studies the cosmic evolution of MW-type galaxies in with a focus on the CO and lines at z=3., Section \ref{section_mw_evolution} studies the cosmic evolution of MW-type galaxies in with a focus on the CO and lines at $z=3$.
" Section ?? summarizes current specifications of ALMA and SKA, based on which Sections ?? and ?? predict the detectability of emission lines from MW-type galaxies at z=3 and arbitrary galaxies at z=3, respectively."," Section \ref{section_telescope_specifications} summarizes current specifications of ALMA and SKA, based on which Sections \ref{section_detections_mw} and \ref{section_detections_general} predict the detectability of emission lines from MW-type galaxies at $z=3$ and arbitrary galaxies at $z=3$, respectively."
 Section ?? concludes the paper., Section \ref{section_conclusion} concludes the paper.
" Our analysis relies on a computer model of neutral atomic(Obreschkow (HI)) andet al.|2009a),,molecular (H5)) hydrogen in galaxies”, which builds on the Millennium simulational."," Our analysis relies on, a computer model of neutral atomic ) and molecular ) hydrogen in $^2$, which builds on the Millennium simulation."
|2005).. The Millennium simulation is a gravitational N-bodyet (Springelsimulation of about 10!? dark matter particles in a cubic comoving volume of (500/hMpo)?.," The Millennium simulation is a gravitational $N$ -body simulation of about $10^{10}$ dark matter particles in a cubic comoving volume of $(500/h\rm\,Mpc)^3$."
" It models the formation of cosmic structure down to galaxy haloes as low in mass as those of the Small Magellanic Cloud (SMC), while tracking features as large as the Baryon Acoustic Oscillations (BAOs)."," It models the formation of cosmic structure down to galaxy haloes as low in mass as those of the Small Magellanic Cloud (SMC), while tracking features as large as the Baryon Acoustic Oscillations (BAOs)."
" The cosmological parameters of the Millennium simulation are h=0.73, where the Hubble constant Hy=1005kms""!Mpc!, Qmatter=0.25, 0.045, O4=0.75, eg=0.9."," The cosmological parameters of the Millennium simulation are $\h=0.73$, where the Hubble constant $H_0\equiv100\,h\rm\,km\,s^{-1}\,Mpc^{-1}$, $\Omega_{\rm matter}=0.25$, $\Omega_{\rm baryon}=0.045$ , $\Omega_\Lambda=0.75$, $\sigma_8=0.9$."
" Through a_ post-processing of the Millennium simulation, studied the evolution of idealized 2006)mainBodyCitationEnd796]DeLucia2007model-galaxies placed at the centers of the dark matter haloes."," Through a post-processing of the Millennium simulation, studied the evolution of idealized model-galaxies placed at the centers of the dark matter haloes."
" The properties, such as stellar mass, cold gas mass, and globalmorphology,galaxy were evolved according to discrete, simplistic rules."," The global galaxy properties, such as stellar mass, cold gas mass, and morphology, were evolved according to discrete, simplistic rules."
 This “semi-analytic” processing resulted in a catalog of evolving and merging galaxies., This “semi-analytic” processing resulted in a catalog of evolving and merging galaxies.
" The number of galaxies at a cosmological time of 13.7-10?yrs (i. e. today) is about 3- 107, and each of these galaxies has a well-defined history of growing and discretely merging progenitor galaxies that have been stored in 64 discrete cosmic time steps."," The number of galaxies at a cosmological time of $13.7\cdot10^9\rm~yrs$ (i. e. today) is about $3\cdot10^7$ , and each of these galaxies has a well-defined history of growing and discretely merging progenitor galaxies that have been stored in 64 discrete cosmic time steps."
" applied an additional post-processing to the galaxies (2009a)in the semi-analytic simulation in order to subdivide their bycold gas masses intoHL,Ho. and Helium."," applied an additional post-processing to the galaxies in the semi-analytic simulation by in order to subdivide their cold gas masses into, and Helium."
 They also assigned realistic radial distributions and velocity profiles to the and components., They also assigned realistic radial distributions and velocity profiles to the and components.
" Subsequently, introduced a model to CO line luminosities(2009b) to the molecular gas of assigneach galaxy."," Subsequently, introduced a model to assign approximate CO line luminosities to the molecular gas of each galaxy."
" approximateThis model relies on a single gas phase in thermal equilibrium with frequency-dependent optical depths, and it approximately accounts for the following mechanisms: (i) molecular gas is heated by starbursts, AGNs, and the redshift-dependent CMB; (ii) overlapping clouds in dense and inclined galaxies cause CO self-shielding; (iii) in compact galaxy cores molecular gas transits from a clumpy to a smooth distribution; (iv) CO-luminosities are metallicity dependent; (v) are always measured relative to the redshift- CMB."," This model relies on a single gas phase in thermal equilibrium with frequency-dependent optical depths, and it approximately accounts for the following mechanisms: (i) molecular gas is heated by starbursts, AGNs, and the redshift-dependent CMB; (ii) overlapping clouds in dense and inclined galaxies cause CO self-shielding; (iii) in compact galaxy cores molecular gas transits from a clumpy to a smooth distribution; (iv) CO-luminosities are metallicity dependent; (v) are always measured relative to the redshift-dependent CMB."
 The integrated CO and line luminosities were further expanded into frequency-dependent profiles -- typically double-horn profiles — by applying mass models and random galaxy-inclinations (sine-distribution)., The integrated CO and line luminosities were further expanded into frequency-dependent profiles -- typically double-horn profiles – by applying mass models and random galaxy-inclinations (sine-distribution).
" The semi-analytic galaxy model with our additional properties forHL,H2,, and CO is called -Box” as a reminder that the simulated evolving galaxies are contained within the cubic volume (box) of the Millennium simulation."," The semi-analytic galaxy model with our additional properties for, and CO is called -Box” as a reminder that the simulated evolving galaxies are contained within the cubic volume (box) of the Millennium simulation."
" Given S?-SAX--Box we then constructed a virtual sky by mapping the Cartesian coordinates (x, y, z) of the simulated galaxies onto apparent positions (RA, Dec, z), using the method of(2005)."," Given -Box we then constructed a virtual sky by mapping the Cartesian coordinates (x, y, z) of the simulated galaxies onto apparent positions (RA, Dec, $z$ ), using the method of."
". Alongside this mapping, the intrinsic CO and luminosities of each galaxy were transformed into observable line-fluxes."," Alongside this mapping, the intrinsic CO and luminosities of each galaxy were transformed into observable integrated line-fluxes."
" The resulting virtual sky simulation isintegrated called *S?-SAX--Sky"" in contrast to -Box.", The resulting virtual sky simulation is called -Sky” in contrast to -Box.
 The maximal field-of-view (FoV)) of S?-SAX--Sky depends on the selected maximal redshift z., The maximal field-of-view ) of -Sky depends on the selected maximal redshift $z$.
" At z=3 the is 37.2deg?, to the comoving surfaceapproximately area of (500/hMpc)?correspondingof the Millennium box, which is large enough to suppress significant effects of cosmic variance."," At $z=3$ the is approximately $37.2\rm\,deg^2$, corresponding to the comoving surface area of $(500/h\rm\,Mpc)^2$of the Millennium box, which is large enough to suppress significant effects of cosmic variance."
 In this paper we are using both S?-SAX--Box and SAX--Sky., In this paper we are using both -Box and -Sky.
" S?-SAX--Box contains the pointers needed to backtrack the cosmic evolution of MW-type galaxies to z=3 (Section ??)), while S?-SAX--Sky provides the apparent positions and line fluxes required to study the detectability of the simulated galaxies (Sections ?? and ??))."," -Box contains the pointers needed to backtrack the cosmic evolution of MW-type galaxies to $z=3$ (Section \ref{section_mw_evolution}) ), while -Sky provides the apparent positions and line fluxes required to study the detectability of the simulated galaxies (Sections \ref{section_detections_mw} and \ref{section_detections_general}) )."
" Throughout the whole paper, we assume that the continuum emission can be perfectly subtracted, such that the line emission can be studied independently."," Throughout the whole paper, we assume that the continuum emission can be perfectly subtracted, such that the line emission can be studied independently."
" For other assumptions, limitations, and uncertainties of the simulation, please refer to Section 6 in and Section 6.2 in⋅"," For other assumptions, limitations, and uncertainties of the simulation, please refer to Section 6 in and Section 6.2 in."
⋅ We shall now investigate the cosmic evolution of the CO and line signatures of the galaxies “like the MW” in the S?-SAX--Box simulation (see Section ??))., We shall now investigate the cosmic evolution of the CO and line signatures of the galaxies “like the MW” in the -Box simulation (see Section \ref{section_simulation}) ).
" By definition, we call a model galaxy at z=0 a type"", if its morphological type, derived from the bulge-to-disk ratio is Sc, and if it matches the stellar mass (ObreschkowetM,, al]the 20093),mass Myr, the mass My,, the half-mass radius ret and the half-mass radius ne of the MW, given in Tab. Hh"," By definition, we call a model galaxy at $z=0$ a ``MW-type'', if its morphological type, derived from the bulge-to-disk ratio, is Sb--Sc, and if it matches the stellar mass $\ms$, the mass $\mha$, the mass $\mhm$, the half-mass radius $\rhahalfmass$, and the half-mass radius $\rhmhalfmass$ of the MW, given in Tab. \ref{tab_mw_coldgas},"
 within a factor 1.3., within a factor 1.3.
 This factor approximately corresponds to the empirical uncertainties., This factor approximately corresponds to the empirical uncertainties.
" According to this definition, the SAX--Box simulation contains 1928 MW-type galaxies at 0."," According to this definition, the -Box simulation contains 1928 MW-type galaxies at $z=0$ ."
" A simulated galaxy at redshift z>0 is called a *MW-type"" galaxy or a *MW progenitor"", if, at its particular redshift, it is the most massive progenitor of a MW-type galaxy at z= 0. S"," A simulated galaxy at redshift $z>0$ is called a “MW-type” galaxy or a “MW progenitor”, if, at its particular redshift, it is the most massive progenitor of a MW-type galaxy at $z=0$ ."
?-SAX--Box consists of 64 discrete cosmic time steps (Section ??))., -Box consists of 64 discrete cosmic time steps (Section \ref{section_simulation}) ).
 The cosmic evolution of any galaxy through those time steps can be extracted using a system of galaxy, The cosmic evolution of any galaxy through those time steps can be extracted using a system of galaxy
tells that the maximum mass which a dark halo can acquire is a function of the local density.,tells that the maximum mass which a dark halo can acquire is a function of the local density.
 In low density regions massive halos simply cannot form by the present epoch., In low density regions massive halos simply cannot form by the present epoch.
 A similar observation can be made from the panel showing the velocity dispersion of dark halos (the left panel of the third row)., A similar observation can be made from the panel showing the velocity dispersion of dark halos (the left panel of the third row).
" The mean halo mass is relatively higher in low potential regions or in high shear ellipticity and prolateness regions, but its dependence on these parameters is weaker than that on local density."," The mean halo mass is relatively higher in low potential regions or in high shear ellipticity and prolateness regions, but its dependence on these parameters is weaker than that on local density."
 This dependence of halo mass on potential and shear is partly due to the correlation of potential and shear with local density., This dependence of halo mass on potential and shear is partly due to the correlation of potential and shear with local density.
 'The second row of Figure 9 shows dependence of the spin parameter A on the environmental parameters., The second row of Figure 9 shows dependence of the spin parameter $\lambda$ on the environmental parameters.
" The spin parameter is defined by (Peebles 1969, Gardner 2001, and for an alternative definition see, Bullock et al."," The spin parameter is defined by (Peebles 1969, Gardner 2001, and for an alternative definition see, Bullock et al."
" 2001, Shaw et al."," 2001, Shaw et al."
" 2006, Hetznecker Burkert 2006) where Myir,Jyiy and Ey, are the mass, total angular momentum and energy of a dark halo, respectively."," 2006, Hetznecker Burkert 2006) where $M_{\rm vir}, J_{\rm vir}$ and $E_{\rm vir}$ are the mass, total angular momentum and energy of a dark halo, respectively."
study by Wandel(2002) is a compilation of inhomogeneous data from the literature.,study by \citet{wandel02} is a compilation of inhomogeneous data from the literature.
 The bulge luminosities were primarily from MeLure&Dunlop(2001) and include measurements from ground-based photographic plates and CCD imagine. as well as saturated and unsaturatedHST imaging. all in various passbands.," The bulge luminosities were primarily from \citet{mclure01} and include measurements from ground-based photographic plates and CCD imaging, as well as saturated and unsaturated imaging, all in various passbands."
 Many of the studies included in the compilation did not use the same cosmologies and distances for the objects or the same analysis techniques in determining the black hole mass., Many of the studies included in the compilation did not use the same cosmologies and distances for the objects or the same analysis techniques in determining the black hole mass.
 All of the reverberation-based black hole masses have since been homogeneously analyzed and updated by Petersonetal.(2004).. and 221304099 which has an updated mass from the analysis of anew reverberation data set by Grieretal.(2008).," All of the reverberation-based black hole masses have since been homogeneously analyzed and updated by \citet{peterson04}, and 2130+099 which has an updated mass from the analysis of a new reverberation data set by \citet{grier08}."
. Figure 2 shows the black hole masses versus the host galaxy V-bard luminosities for the full sample of 26 objects included in this study., Figure 2 shows the black hole masses versus the host galaxy $V$ -band luminosities for the full sample of 26 objects included in this study.
 We employed two independent fitting routines in. our examination of the Myy— relationship: FITEXY (Pressetal. 1992). which estimates Los;the parameters of a straight-line fit through the data including errors in both coordinates; and BCES (Akritas&Bershady1996).. which accounts for the effects of errors on both coordinates in the fit using bivariate correlated errors and à component of intrinsic scatter.," We employed two independent fitting routines in our examination of the $M_{\rm BH} - L_{\rm bulge}$ relationship: FITEXY \citep{press92}, which estimates the parameters of a straight-line fit through the data including errors in both coordinates; and BCES \citep{akritas96}, which accounts for the effects of errors on both coordinates in the fit using bivariate correlated errors and a component of intrinsic scatter."
 FITEXY numerically solves for the minimum orthogonal v using an interative root-finding algorithm and is a “symmetric” algorithm in that it does not assume a dependent and independent variable., FITEXY numerically solves for the minimum orthogonal $\chi^2$ using an interative root-finding algorithm and is a “symmetric” algorithm in that it does not assume a dependent and independent variable.
 Following Tremaineetal.(2002). we include an estimate of the fractional scatter. in this case the fraction of the 434 measurement value (not the error value) that is added in quadrature to the error value to obtain a reduced 47 of 1.0.," Following \citet{tremaine02}, we include an estimate of the fractional scatter, in this case the fraction of the $M_{\rm BH}$ measurement value (not the error value) that is added in quadrature to the error value to obtain a reduced $\chi^2$ of 1.0."
 While BCES also accounts for intrinsic scatter. it does not provide a measure of it.," While BCES also accounts for intrinsic scatter, it does not provide a measure of it."
 We adopt the bootstrap of the BCES bisector value with N=1000 iterations., We adopt the bootstrap of the BCES bisector value with $N=1000$ iterations.
 Fits of the form were performed utilizing both the single-component bulge luminosities and the multiple-component bulge luminosities and are presented in Table 2., Fits of the form were performed utilizing both the single-component bulge luminosities and the multiple-component bulge luminosities and are presented in Table 2.
 The powerlaw slope ranges from 0.76£0.08 to 0.85+0.11 depending on the definition of the bulge luminosity and the specific fitting routine utilized., The powerlaw slope ranges from $0.76 \pm 0.08$ to $0.85 \pm 0.11$ depending on the definition of the bulge luminosity and the specific fitting routine utilized.
" We take the BCES fit nearest the middle of this range. with a slope of 0.80+0.09, as the ""best"" fit."," We take the BCES fit nearest the middle of this range, with a slope of $0.80 \pm 0.09$, as the “best” fit."
 For comparison. we fit the quiescent galaxy Mgg—Lou: relationship using the sample of nearby galaxies with dynamical black hole mass measurements (Ferrarese&Ford 2005: FFOS).," For comparison, we fit the quiescent galaxy $M_{\rm BH} - L_{\rm
bulge}$ relationship using the sample of nearby galaxies with dynamical black hole mass measurements \citealt{ferrarese05}; FF05)."
 We restricted the sample to ellipticals. both to circumvent the need for bulge-disk decompositions and because ellipticals are reported to show less scatter about the My—Louee relationship (cf. MeLure&Dunlop 200100.," We restricted the sample to ellipticals, both to circumvent the need for bulge–disk decompositions and because ellipticals are reported to show less scatter about the $M_{\rm BH} - L_{\rm bulge}$ relationship (cf. \citealt{mclure01}) )."
 Bulge magnitudes were converted to V-band using a typical elliptical galaxy color of 8—V=0.9., Bulge magnitudes were converted to $V$ -band using a typical elliptical galaxy color of $B-V=0.9$.
 The fitting results are presented in Table 2., The fitting results are presented in Table 2.
 We also fit the quiescent galaxy relationship excluding AA and 55845. both of which are known to deviate significantly (FFOS).," We also fit the quiescent galaxy relationship excluding A and 5845, both of which are known to deviate significantly (FF05)."
" Figure 3 shows the Mgy—ZLpuee relationship for the FFOS ellipticals compared to the ""best"" fit for the AGNs in this study.", Figure 3 shows the $M_{\rm BH} - L_{\rm bulge}$ relationship for the FF05 ellipticals compared to the “best” fit for the AGNs in this study.
 The slope of the quiescent galaxy relationship is steeper. although the severity of the discrepancy depends on the specifies of the fitting routine used. as the best-fit slope from BCES is à=1.4340.21 versus a=1.11£0.21 from FITEXY.," The slope of the quiescent galaxy relationship is steeper, although the severity of the discrepancy depends on the specifics of the fitting routine used, as the best-fit slope from BCES is $\alpha =
1.43 \pm 0.21$ versus $\alpha = 1.11 \pm 0.21$ from FITEXY."
 The fits presented here for the quiescent elliptical galaxies are slightly steeper than that reported by FFOS (a= 1.05+0.21) and are in reasonable agreement with the slope of, The fits presented here for the quiescent elliptical galaxies are slightly steeper than that reported by FF05 $\alpha = 1.05 \pm 0.21$ ) and are in reasonable agreement with the slope of
"perform:. model ruis in. the range of Dau10299 97 << Ny- x +1072""1212 οιP7.",perform model runs in the range of $10^{20.0}$ $^{-2}$ $\le$ $N_{\rm H}$ $\le$ $10^{22.0}$ $^{-2}$.
 For the dust-free models. we set the gas-phase elemental abundances to be the solu ones. which are taken fro1i Crevesse Anders (1989) with extensions by CGrevesse Nocls (1993).," For the dust-free models, we set the gas-phase elemental abundances to be the solar ones, which are taken from Grevesse Anders (1989) with extensions by Grevesse Noels (1993)."
" The adopted gas-phase elemental abundances are: IE: 1.00. Πο 1.0010. 3. Li: 20b 7. De: 2.689410 H, DB: 7.59410 19, οἱ 355410 b κ: 410 7. O: «10. 1 Ε 410 ὃν Ne: 410. |. Nus 2406410 9. Me: 380410 7. Ab 2.95410 9. Si 3.55410 7, P: 3.73410. 7. S: 410 7. Cl: slo ©, Ar δα 9. K: 135410 *2 Ca: 2.20410 9. Se: 1.58410 9. Ti: 410.7. V: «10 5. Cs: LSIAIO. *. Mu: 3.12<10 *.. L.10For 3.21.10 7. Co: 832410 7. Ni: 1.06.10 9. Cu: L8T410 5. aud Zu: 410 7."," The adopted gas-phase elemental abundances are: H: 1.00, He: $\times$ $^{-1}$, Li: $\times$ $^{-9}$, Be: $\times$ $^{-11}$, B: $\times$ $^{-10}$, C: $\times$ $^{-4}$, N: $\times$ $^{-5}$, O: $\times$ $^{-4}$, F: $\times$ $^{-8}$, Ne: $\times$ $^{-4}$, Na: $\times$ $^{-6}$, Mg: $\times$ $^{-5}$, Al: $\times$ $^{-6}$, Si: $\times$ $^{-5}$ , P: $\times$ $^{-7}$, S: $\times$ $^{-5}$, Cl: $\times$ $^{-7}$, Ar: $\times$ $^{-6}$, K: $\times$ $^{-7}$, Ca: $\times$ $^{-6}$, Sc: $\times$ $^{-9}$, Ti: $\times$ $^{-7}$, V: $\times$ $^{-8}$, Cr: $\times$ $^{-7}$, Mn: $\times$ $^{-7}$ , Fe: $\times$ $^{-5}$ , Co: $\times$ $^{-8}$ , Ni: $\times$ $^{-6}$ , Cu: $\times$ $^{-8}$ , and Zn: $\times$ $^{-8}$."
 For the dusty aodels. Orion-tvpe graphite and silicate grains (Baldwin ct al.," For the dusty models, Orion-type graphite and silicate grains (Baldwin et al."
 1991: see also Ferlaud 1997) are contained iu a gas cloud., 1991; see also Ferland 1997) are contained in a gas cloud.
" As a result of the moetal depletion outo dust erains. the eas-plase clementa abundances are altered to: II: 1.00. He: «10. 2. Li: ido H.Dis.90«10. HC: 00010. 2. N: τον 7.0: «10.5 Ne: G.00 7. Nas 3.0010 Me: 3.00.1 ο, Ak 2.00410""... Si «10 9. P: YF S: «10 . Ck E0010 *. Ar 00410 9. EK: 0. Ca 2.00410 ὃν Ti hadslo 19, V: q.00«.10 «1t19, Cr: 1.00410 95. Mu: 2.3010. 7, Fe: <1 ON: «10 ""Cu: 1.5010. ?. and Zu: 410. 5."," As a result of the metal depletion onto dust grains, the gas-phase elemental abundances are altered to: H: 1.00, He: $\times$ $^{-2}$, Li: $\times$ $^{-11}$, B: $\times$ $^{-11}$, C: $\times$ $^{-4}$, N: $\times$ $^{-5}$, O: $\times$ $^{-4}$, Ne: $\times$ $^{-5}$, Na: $\times$ $^{-7}$, Mg: $\times$ $^{-6}$, Al: $\times$ $^{-7}$, Si: $\times$ $^{-6}$, P: $\times$ $^{-7}$, S: $\times$ $^{-5}$, Cl: $\times$ $^{-7}$, Ar: $\times$ $^{-6}$, K: $\times$ $^{-8}$, Ca: $\times$ $^{-8}$, Ti: $\times$ $^{-10}$, V: $\times$ $^{-10}$, Cr: $\times$ $^{-8}$, Mn: $\times$ $^{-8}$, Fe: $\times$ $^{-6}$, Ni: $\times$ $^{-7}$, Cu: $\times$ $^{-9}$, and Zn: $\times$ $^{-8}$."
 T1ese depleted elemental alincdauaces ire based on results of seveqal studies of the Orion nebula (Baldwin et al., These depleted elemental abundances are based on results of several studies of the Orion nebula (Baldwin et al.
 1991: Rubin et al., 1991; Rubin et al.
 1991: Rubin. Dufour. Walter 19922: Rubin et al.," 1991; Rubin, Dufour, Walter 1992a; Rubin et al."
 1992b: Osterbrock. Tran. Veulleux 1992).," 1992b; Osterbrock, Tran, Veulleux 1992)."
 Note that bervlliun. fluorine. scanditun and cobalt are not included im the calculations for the dusty models.," Note that beryllium, fluorine, scandium and cobalt are not included in the calculations for the dusty models."
 See Ferland (1997) for details of the treatinents of elemental albtuclances and dust eraius., See Ferland (1997) for details of the treatments of elemental abundances and dust grains.
 Iu Figure 3. we show the depeudenuces of the fiux ra10 of [Fe A6087/[Ne v]A3126 0u the hydrogen density. he cohuun vii]density aud the ionization parameters of a clotd. and on the presence of dust eras. which are calculaed * our photoionization iodeIs with aud without dus erains.," In Figure 3, we show the dependences of the flux ratio of [Fe $\lambda$ 6087/[Ne $\lambda$ 3426 on the hydrogen density, the column density and the ionization parameters of a cloud, and on the presence of dust grains, which are calculated by our photoionization models with and without dust grains."
 The most striking cependeuce is that on the xesence of dust eraius., The most striking dependence is that on the presence of dust grains.
 The models without dust evans xedict larger ratios of |Fe AGOST/[Ne v]A3126 than the uodels with dust eraius by a factor of —10., The models without dust grains predict larger ratios of [Fe $\lambda$ 6087/[Ne $\lambda$ 3426 than the models with dust grains by a factor of $\sim$ 10.
 This factor corresponds to the depletion factor of wou., This factor corresponds to the depletion factor of iron.
 This implos hat the difference in the flix ratio between the nioels with and without eraius is niainly due to the depletion of ion outo dust eraius: i.e.. the effects of grains ou he thermal equilibrium aud ou the radiation transfer are weheibly small.," This implies that the difference in the flux ratio between the models with and without grains is mainly due to the depletion of iron onto dust grains; i.e., the effects of grains on the thermal equilibrium and on the radiation transfer are negligibly small."
 Tudeed the models without dust eraius mt with eas-phase clemental abundances of the dusty uodel xediet nearly the same flux ratios as those of the dusty models., Indeed the models without dust grains but with gas-phase elemental abundances of the dusty model predict nearly the same flux ratios as those of the dusty models.
 This also sugeests that the iron depletion is the main reason of the difference dn the flux ratio of Fe viiA6087/[Ne v]A3126 between the models with aud withou dust grains., This also suggests that the iron depletion is the main reason of the difference in the flux ratio of [Fe $\lambda$ 6087/[Ne $\lambda$ 3426 between the models with and without dust grains.
 The remaining dependences of the flux ralo are nof so luge., The remaining dependences of the flux ratio are not so large.
" As xesented in Figure 3. the flux ratio of Fe vul|A6087/Ne v[A3126 is almost independent of the ivdrosen deusitv in the ranee of 1097 cin ""n Ln cin?5m while it depends ou the* bvdrogen column density aud the ionizajon parameter."," As presented in Figure 3, the flux ratio of [Fe $\lambda$ 6087/[Ne $\lambda$ 3426 is almost independent of the hydrogen density in the range of $10^{6.5}$ $^{-3}$ $\leq$ $10^{7.5}$ $^{-3}$ while it depends on the hydrogen column density and the ionization parameter."
" Note that the mocels with U—102° mei uplausible for sas clouds in UINERs since those models predict significantly ualer ratios of [Fe AGOST/[O 1|ABOO T and [Ne v|A3126/ O ASQ07 (<0.01 and <0.1. respectively) than the observed values (see. οι, Muravana Taniguchi 19088: Nagao ct al."," Note that the models with $U = 10^{-2.5}$ are implausible for gas clouds in HINERs since those models predict significantly smaller ratios of [Fe $\lambda$ 6087/[O $\lambda$ 5007 and [Ne $\lambda$ 3426/[O $\lambda$ 5007 $< 0.01$ and $< 0.1$, respectively) than the observed values (see, e.g., Murayama Taniguchi 1998a; Nagao et al."
 2000b. 20015).," 2000b, 2001b)."
" Thus the dexudeuce of the flux ratio of [Fe AGUST /[Ne V|A3126 on the hydrogen colin density aud the ionization xwanmeter in the rauges ofE 10299P P3 Ny < 10??? ? aud 1029<7L? is not so lurge. Ίου, a actor of 2 - 5."," Thus the dependence of the flux ratio of [Fe $\lambda$ 6087/[Ne $\lambda$ 3426 on the hydrogen column density and the ionization parameter in the ranges of $10^{20.0}$ $^{-2}$ $\leq$ $N_{\rm H}$ $\leq$ $10^{22.0}$ $^{-2}$ and $10^{-2.0} \leq U \leq 10^{-1.5}$ is not so large, i.e., a factor of 2 - 5."
 This is cousistent with the remark by FereIso ct a. (, This is consistent with the remark by Ferguson et al. (
1997b) aud thus the exact determination of he gas-phase iron abundance seeuis to be difficult by simply using the flix ratio of [Fe AG0ST/[Ne VJA3 126.,1997b) and thus the exact determination of the gas-phase iron abundance seems to be difficult by simply using the flux ratio of [Fe $\lambda$ 6087/[Ne $\lambda$ 3426.
 This is nore clearly shown in Figure { in which the volume enissivities of the [Fe VvujAGOS87 and [Ne VJA3 126 cinission are plotted as functions of the depth into the nebula or the models with my=Loe! 5m with U=1027.11020lo aud with/witlott dust erains.," This is more clearly shown in Figure 4, in which the volume emissivities of the [Fe $\lambda$ 6087 and [Ne $\lambda$ 3426 emission are plotted as functions of the depth into the nebula for the models with $n_{\rm H} = 10^{7.0}$ $^{-3}$, with $U = 10^{-2.5}, 10^{-2.0}, 10^{-1.5}$, and with/without dust grains."
" The ratio of the enussivities for the two emission lines appareutv depends on the ionization parameΟΥ,", The ratio of the emissivities for the two emission lines apparently depends on the ionization parameter.
 Although the fiux ratio of |Fe AGOST/[Ne. v]A3126 Is luappropriae for the exact deteruumation of the eas-phase mon abuudaree. dt can be used to disciss the dust abundauces iu IHINERs.," Although the flux ratio of [Fe $\lambda$ 6087/[Ne $\lambda$ 3426 is inappropriate for the exact determination of the gas-phase iron abundance, it can be used to discuss the dust abundances in HINERs."
 This is beαπο the ranecs of the predicted raio of [Fe AGOST /Ne v|A3126 are well separated between the nodels wih and without dust erains., This is because the ranges of the predicted ratio of [Fe $\lambda$ 6087/[Ne $\lambda$ 3426 are well separated between the models with and without dust grains.
 The chist-free models: predi+t 0.05< Το vujAGOST) /F([NOe A3 126) <0.3 while tje dusty models predict 0.007< F([Fe AGOST) F([Ne ]A3126) <0.01., The dust-free models predict $0.05 \lesssim$ $F$ ([Fe $\lambda$ $F$ ([Ne $\lambda$ 3426) $\lesssim 0.3$ while the dusty models predict $0.007 \lesssim$ $F$ ([Fe $\lambda$ $F$ ([Ne $\lambda$ 3426) $\lesssim 0.04$.
 Tere we should reca] that the models witliU —102° are not taken iuto accotut since they are not dlausible models for clouds in HINERs., Here we should recall that the models with $U = 10^{-2.5}$ are not taken into account since they are not plausible models for clouds in HINERs.
 Usine his flux ratic» we discuss the dust abundances at IIINERs i the next section.," Using this flux ratio, we discuss the dust abundances at HINERs in the next section."
 Now we discuss our mail xobleni: are IHENERs dusty or uot?, Now we discuss our main problem; are HINERs dusty or not?
 The predicted range of the flux ratio of [Fe vii|AGOST/[Ne v|A3126 by both the dust-frce and the dusty models is παπαο han the observed range., The predicted range of the flux ratio of [Fe $\lambda$ 6087/[Ne $\lambda$ 3426 by both the dust-free and the dusty models is smaller than the observed range.
 This is because the colected data are not corrected for the extinction., This is because the collected data are not corrected for the extinction.
 Since a waveleugh difference between the two emission lines. [Fe viij AGOST and [Ne v]A3126. is arge. the effects of extiicfiou correction are not ποσο]e.," Since a wavelength difference between the two emission lines, [Fe $\lambda$ 6087 and [Ne $\lambda$ 3426, is large, the effects of extinction correction are not negligible."
 Adopting the extinction curve «escribed by Cardelli. Cavton. Mathis (1989). and Ry=AY:E(BVV)3.1. the correction factor for the dus extinction is 1.9L iu the ense Of Ay1 mae.," Adopting the extinction curve described by Cardelli, Clayton, Mathis (1989), and $R_V = A_V / E({\rm B - V}) = 3.1$, the correction factor for the dust extinction is 1.94 in the case of $A_V = 1$ mag."
" Therefore. the predicted ranges of the flux ratio of [Fo A6087/Ne v]A3126 whenthe extiicfioncorrection of0 magxze< Lamag istaken iuto account are0.05x F(|Fo vu|AG087) ΕΙ[Ne v]A3126) < 0.Gaxd 0,007x FYFe TAGOST) ΕΙΝNe vJA3126) x0.08 for the dust-free 110€els uid the dusty uodels. respectively."," Therefore, the predicted ranges of the flux ratio of [Fe $\lambda$ 6087/[Ne $\lambda$ 3426 whenthe extinctioncorrection of 0 mag$\leq A_V \leq$ 1 mag istaken into account are$0.05 \lesssim$ $F$ ([Fe $\lambda$$F$ ([Ne $\lambda$ 3426) $\lesssim 0.6$ and $0.007 \lesssim$ $F$ ([Fe $\lambda$ $F$ ([Ne $\lambda$ 3426) $\lesssim 0.08$ for the dust-free models and the dusty models, respectively."
 Note that the observed Bahuer cecrements sugeest the reddening amount o 0) nae xAy< Laimag for type 1 AGNs (e... Cobhenu 1983: NMiwavama 1995: Rodrteeuez-Ardila.ao Pastoriza. Donzelli 2000).," Note that the observed Balmer decrements suggest the reddening amount of 0 mag $\lesssim A_V \lesssim$ 1 mag for type 1 AGNs (e.g., Cohen 1983; Murayama 1995; guez-Ardila, Pastoriza, Donzelli 2000)."
 The range of the flux ratio predicted by the dist- models is roughly consisteut with the observed data while that predicted by the dusty models is far sialer han the observed data., The range of the flux ratio predicted by the dust-free models is roughly consistent with the observed data while that predicted by the dusty models is far smaller than the observed data.
 To explain the observed range of the flux ratio of Fe vu[AGOST/[Ne. v]A3126 bv the dusty models. dust extinction of 3 nag xA 10 mag is required.," To explain the observed range of the flux ratio of [Fe $\lambda$ 6087/[Ne $\lambda$ 3426 by the dusty models, dust extinction of 3 mag $\lesssim A_V \lesssim$ 10 mag is required."
 This, This
= 16x 10 7.,= 1.6 $\times$ $^{13}$ $^{-2}$.
 In Model D. NOIDO) is too low at 9.3 x 10? 7 to account [or the observations. but in Models Ci and D photodesorption can keep a much higher abundance of ΠΡΟ in the eas.," In Model B, N(HDO) is too low at 9.3 $\times$ $^9$ $^{-2}$ to account for the observations, but in Models C and D photodesorption can keep a much higher abundance of HDO in the gas."
 These models have N(IIDO) = 2.0 x 10! 7. somewhat higher than the observed value. but. demonstrating that photodesorption is an efficient means of returning IIDO (and other molecules) to the gas.," These models have N(HDO) = 2.0 $\times$ $^{14}$ $^{-2}$, somewhat higher than the observed value, but demonstrating that photodesorption is an efficient means of returning HDO (and other molecules) to the gas."
 ? also looked (he effects of photodesorption on water and ils isolopomers., \cite{dom05} also looked the effects of photodesorption on water and its isotopomers.
 Using a simplified model they. calculated the column density. ofΠ.Ο averaged. across a [ace on disk to be L.6 x LOY 7. in excellent agreement with our model.," Using a simplified model they calculated the column density of$_2$ O averaged across a face on disk to be 1.6 $\times$ $^{15}$ $^{-2}$, in excellent agreement with our model."
 Combining their model results with the observations of ?.. thev estimate IIDO/I1I4O ~ 0.01.," Combining their model results with the observations of \citet{cec05}, they estimate $_2$ O $\sim$ 0.01."
 Our models caleulate much hieher ratios with IIDO/IISO = 0.12 in Models C and D. These calculated ratios are also much higher (han are observed in Solar System objects and may point to deuteration on the erains being less efficient than assumed here., Our models calculate much higher ratios with $_2$ O = 0.13 in Models C and D. These calculated ratios are also much higher than are observed in Solar System objects and may point to deuteration on the grains being less efficient than assumed here.
 There is another reported detection of ILDO in a protostellar disk., There is another reported detection of HDO in a protostellar disk.
 ?./ observed IIDO in LkCal5 using the OVRO interferometer and found NUIDO) = 2) 7 x10! 7. with an intensity peak that was offset from the central star.," \cite{qi01} observed HDO in LkCa15 using the OVRO interferometer and found N(HDO) = 2 – 7 $^{14}$ $^{-2}$, with an intensity peak that was offset from the central star."
 As in DM Tan. models that include photodesorption give the best agreement with the observations.," As in DM Tau, models that include photodesorption give the best agreement with the observations."
 ? also observed DCN in LkCal5 with N(DCN) ~ LOM ? and DCN/IICN = 0.01., \cite{qi01} also observed DCN in LkCa15 with N(DCN) $\sim$ $^{13}$ $^{-2}$ and DCN/HCN = 0.01.
 Model B caleulates a low value of N(DCN) = 8.9 x105 7. but Models C and D have NODCN) = L2 x10P ? (DCN/IICN = 0.036). in good agreement with the observations.," Model B calculates a low value of N(DCN) = 8.9 $^{8}$ $^{-2}$, but Models C and D have N(DCN) = 1.2 $^{12}$ $^{-2}$ (DCN/HCN = 0.036), in good agreement with the observations."
 Il3D has been observed in DM. Tau (2). with a column density of 88 x10P em7. and a midplane fractional abundance Ρ ) = 3.4 I.," $_2$ $^+$ has been observed in DM Tau \citep{cec04}
 with a column density of 8.8 $^{12}$ $^{-2}$, and a midplane fractional abundance $x$ $_2$ $^+$ ) = 3.4 $^{-10}$."
 In all our models we find ΤΗ ) e few P in the midplane for 7 100 AU. and NOISD. ) ~ few x10! em7.," In all our models we find $x$ $_2$ $^+$ ) $\sim$ few $^{-12}$ in the midplane for $R$ $\geq$ 100 AU, and $_2$ $^+$ ) $\sim$ few $^{11}$ $^{-2}$."
 Our calculated N(IISD. ) is therefore a factor of 10 lower than observed and our midplane fractional abundance more than a factor of LOO lower., Our calculated $_2$ $^+$ ) is therefore a factor of 10 lower than observed and our midplane fractional abundance more than a factor of 100 lower.
 and have both been detected in (wo sources: DA Tau (DCO. and TW va (DCO/IICO=0.035:?).., $^+$ and $^+$ have both been detected in two sources: DM Tau \citep[DCO$^+$/HCO$^+$ = 4 \x 10$^{-3}$ and TW Hya \citep[DCO$^+$/HCO$^+$ = 0.035;][]{vd03}.
 The lormation of these molecular ions depends on the presence of CO in the gas., The formation of these molecular ions depends on the presence of CO in the gas.
 The column density of CO in DM Tau is 5.7 x10/5 7 (7) in good agreement with all our models., The column density of CO in DM Tau is 5.7 $^{16}$ $^{-2}$ \citep{dutrey97} in good agreement with all our models.
 2. do not give a column density for DCO. but in TW να ) = 3 x10! ? compared to the caleulated values of — 3.1 x10 in Models B and. C and 4.8 x10! in Model D. In the same source. } — 85 x10P7 em7? and the model values. which range [rom 2.8 - 3.3. 107 7. are in eood agreement with (his.," \cite{guilloteau06} do not give a column density for $^+$, but in TW Hya $^+$ ) = 3 $^{11}$ $^{-2}$ compared to the calculated values of $\sim$ 3.1 $^{12}$ in Models B and C and 4.8 $^{11}$ in Model D. In the same source, $^+$ ) = 8.5 $^{12}$ $^{-2}$ and the model values, which range from 2.8 - 3.3 $^{12}$ $^{-2}$ , are in good agreement with this."
 In our models the desorption process (hat affects the calculated ratios most is CRIT., In our models the desorption process that affects the calculated ratios most is CRH.
 This allows CO to be present in the cold midplane where deuteration is most efficient., This allows CO to be present in the cold midplane where deuteration is most efficient.
 When CRIT is included } is high and our calculated ~ | (Models D and C)., When CRH is included $^+$ ) is high and our calculated $^+$ $^+$ $\sim$ 1 (Models B and C).
 Without CRII (Model D) both ) and the ratio of 0.13 are, Without CRH (Model D) both $^+$ ) and the ratio of 0.18 are
due to the high background that dominates in this non-imaging instrument. in combination with spectral shape of Gemingas non-thermal emission. as will be discussed in the next secon.,"due to the high background that dominates in this non-imaging instrument, in combination with spectral shape of Geminga's non-thermal emission, as will be discussed in the next section."
 The FTOOLS/XSELECT software package was used (o prepare the ddata for spectral analvsis., The FTOOLS/XSELECT software package was used to prepare the data for spectral analysis.
 Source spectra were extracted [rom a circle 275 in radius for the SIS data. and 3/5 in radius lor the GIS data.," Source spectra were extracted from a circle $2.\!^{\prime}5$ in radius for the SIS data, and $3.\!^{\prime}5$ in radius for the GIS data."
 The source was at a suitable location [or backeround spectra to be extracted from anuuli concentric with (he source circle lor bot SIS and GIS., The source was at a suitable location for background spectra to be extracted from annuli concentric with the source circle for both SIS and GIS.
 It is important to choose an annulus close enough to the source circle to acquire a fair sample of the background sky at the point of the source. but not close enough to contain a significant number of source counts. which would oversubtract the source spectrum.," It is important to choose an annulus close enough to the source circle to acquire a fair sample of the background sky at the point of the source, but not close enough to contain a significant number of source counts, which would oversubtract the source spectrum."
 To obtain response matrices. the latest GIS “rm” files were downloaded and rebinned to match the reduced number of enerev channels in the data.," To obtain response matrices, the latest GIS “rmf” files were downloaded and rebinned to match the reduced number of energy channels in the data."
 The “sisrme” program was used to generate response matrices (rms) for the SIS spectral files., The “sisrmg” program was used to generate response matrices (rmfs) for the SIS spectral files.
" Ancillary response (auf) files were created from the rif files using the program ""asciuuf.", Ancillary response (arf) files were created from the rmf files using the program “ascaarf”.
" The spectral data were rebinned. using the program ""grppha so that there were 40 counts or more in each bin."," The spectral data were rebinned, using the program “grppha” so that there were 40 counts or more in each bin."
 This reduces (he noise. especially al higher energies where (he instrument has less sensitivity. ancl allows Gaussian statistics to be used in the evaluation of the fit.," This reduces the noise, especially at higher energies where the instrument has less sensitivity, and allows Gaussian statistics to be used in the evaluation of the fit."
 Guided by the combined rrestuts of Halpern&Wang(1997).. we fitted simple power-law models to each of the instruments using NSPEC.," Guided by the combined results of \cite{hw97}, we fitted simple power-law models to each of the instruments using XSPEC."
 The soft blackbody component that dominates the sspecirum does not contribute significantly in the bband. and was neglected.," The soft blackbody component that dominates the spectrum does not contribute significantly in the band, and was neglected."
" In this analvsis. (he intervening column clensity Vy, was held fixed ab the best fitted value of 1.07x10°"" given in Halpern&Wang(1997)."," In this analysis, the intervening column density $N_{\rm H}$ was held fixed at the best fitted value of $1.07\times 10^{20}$ given in \cite{hw97}."
". Uncertainties in this small Ay, do not affect the rresults.", Uncertainties in this small $N_{\rm H}$ do not affect the results.
 The energy limits of the fit for the SIS data were set at 0.7—10 keV for SISO. and 0.7—7.5 keV [or SIS] data because of its poorer signal-Lo-noise at higher energy.," The energy limits of the fit for the SIS data were set at $0.7-10$ keV for SIS0, and $0.7-7.5$ keV for SIS1 data because of its poorer signal-to-noise at higher energy."
 The GIS spectra were fitted from 0.3—10 keV to avoid calibration uncertainties at the lowest energies., The GIS spectra were fitted from $0.8-10$ keV to avoid calibration uncertainties at the lowest energies.
 In acldition to fits of the individual insiruments. combined fits were made.," In addition to fits of the individual instruments, combined fits were made."
 The combined SIS and GIS fits ave shown in Figures 5. and 6.., The combined SIS and GIS fits are shown in Figures \ref{sisspect} and \ref{gisspect}.
 Results of the fits are given in Table 3. for the combined SIS and GIS as well as [or all instruments combined., Results of the fits are given in Table \ref{tbl-3} for the combined SIS and GIS as well as for all instruments combined.
 All fits are acceptable. with 4?~1 per degree of [reedom.," All fits are acceptable, with $\chi^2\sim 1$ per degree of freedom."
Pulsars emit over a wide range of euergies [rou radio to 5-rav.,Pulsars emit over a wide range of energies from radio to $\gamma$ -ray.
" Recent observaious by theFermi CGamima-Ray Space Telescope of more than sixty pulsars (Abdoetal.2010) have revealed further details of the st""ucture of the emission region."," Recent observations by the Gamma-Ray Space Telescope of more than sixty pulsars \citep{Abcat, Pa10} have revealed further details of the structure of the emission region."
" Tje. dletectioi oL the emissious in the GeV euergy rauge from a ptlsar ruaguetospliere means that eectrons alle positrons"" are accelerated to more than > 10108T yw the electric field parallel to tje magnetic field. which arises iu a depleted region of the Coldreichi-Juliau charge ceusity 1969).."," The detection of the emissions in the GeV energy range from a pulsar magnetosphere means that electrons and positrons are accelerated to more than $\sim 10^{12}$ eV by the electric field parallel to the magnetic field, which arises in a depleted region of the Goldreich-Julian charge density \citep{GJ69}. ."
 The light curve in the 5-ray band is an ipotaut tool lorprobing tlie particle acceleration, The light curve in the $\gamma$ -ray band is an important tool forprobing the particle acceleration
 109 has been shown to exceed the asi mass of a stable neutron star (3AL... Ikalogera Bavin 1996). confirming the presence of black holes iu these systems: GRO J0122]|32 (Orosz Bailvu 1995. Filippeuko. Matheson. Πο 1995): A0620-OO (MeCliutock Remillard 1986): GRS 1009-5 (Filippeuko et 11999): NTE J1118|15 (MeCliutock ot 22001. Wagner et 22001): GS 1121-683 (Renullard. MeCliutock.. Bailwu 1992); IU 15L-17 (Orosz et 11998): NTE 41550-561 (Orosz ot 22002): GRO J1655-0 (Dailvu et 11995): CUN. 2339-1: (vues et 22003): II1705-250 (Remillard et 11996): SAN J1519.5-2525 (Οτο et 22001): NTE J1859|226 (Filippeuko Chornock 2001): CRS 1915|105 (Cixeiner. Cuby. AcCanghrean 2001): GS 2000125 (Casares. Charles. Marsh. 1995): GS 2023|338 (Casares. Charles. Navlor 1992): Cre X-1 (Cues Bolton 1986): LMC Νο (Cowley et 11983): LAIC X-1 (Hutchres et 11987).," $10^6$ has been shown to exceed the maximum mass of a stable neutron star $\approx 3\,M_{\odot}$, Kalogera Baym 1996), confirming the presence of black holes in these systems: GRO J0422+32 (Orosz Bailyn 1995, Filippenko, Matheson, Ho 1995); A0620-00 (McClintock Remillard 1986); GRS 1009-45 (Filippenko et 1999); XTE J1118+480 (McClintock et 2001, Wagner et 2001); GS 1124-683 (Remillard, McClintock, Bailyn 1992); 4U 1543-47 (Orosz et 1998); XTE J1550-564 (Orosz et 2002); GRO J1655-40 (Bailyn et 1995); GX 339-4 (Hynes et 2003); H1705-250 (Remillard et 1996); SAX J1819.3-2525 (Orosz et 2001); XTE J1859+226 (Filippenko Chornock 2001); GRS 1915+105 (Greiner, Cuby, McCaughrean 2001); GS 2000+25 (Casares, Charles, Marsh 1995); GS 2023+338 (Casares, Charles, Naylor 1992); Cyg X-1 (Gies Bolton 1986); LMC X-3 (Cowley et 1983); LMC X-1 (Hutchings et 1987)."
 These sources open up the possiilitv of studyiug eeneral relativity in the strong field regiae., These sources open up the possibility of studying general relativity in the strong field regime.
" For exanple. the study of hieh frequeicy quasiperiodic oscillations in the N-rvayv light «""Uurves of certain NN 1μαν lead to a measurement «Xf black hole spin MMceClintock Remuillare 2001 aud cited references)."," For example, the study of high frequency quasiperiodic oscillations in the X-ray light curves of certain XN may lead to a measurement of black hole spin McClintock Remillard 2004 and cited references)."
 We must press hare to obtain further, We must press hard to obtain further
Preprint Starlight produced by the first galaxies is the leading candidate for ionizing the hydrogen as well as sinely ionizing the lielinm at 2~6., Starlight produced by the first galaxies is the leading candidate for ionizing the hydrogen as well as singly ionizing the helium at $z\sim 6$.
 It takes a harder source of racdiatiou to doubly ionize the helium. so the reionization of this species is likely deferred uutil +~3 when quasars produce a sufficient hard UV. backeround (Aladauctal.1999:Furlanctto&Oh2008:MeQuiunetal. 2009).," It takes a harder source of radiation to doubly ionize the helium, so the reionization of this species is likely deferred until $z\sim 3$ when quasars produce a sufficient hard UV background \citep{madau99, furlanetto08, mcquinn09}."
. ILlowever. the helimm could have been doubly ionized at nearly the same cosmic time that hydrogen was reionized if more exotic sources ionized the lvdrogen. such as the first generation of metal-free stars 2001:Venkatesanetal.2003:Tunulinson2001) or niüniquasus (Aladauctal.1999:Volouteri&Cunediu 2009).," However, the helium could have been doubly ionized at nearly the same cosmic time that hydrogen was reionized if more exotic sources ionized the hydrogen, such as the first generation of metal-free stars \citep{bromm01, venkatesan03, tumlinson04} or miniquasars \citep{madau99, volonteri09}."
. Iu a third poteutial scenario. early sources doubly ionized the helium and then shut off.," In a third potential scenario, early sources doubly ionized the helium and then shut off."
 Afterward. the ireconmibined such that quasars could again reionize it at Do3 (Wvithe&Loeb2003:Voukatesanetal.2003).," Afterward, the recombined such that quasars could again reionize it at $z\sim 3$ \citep{wyithe03, venkatesan03}."
. If irejonization were colpleting at 2—3. au epoch for which there are nunerous observations of the interealactic medimu (ICM. it should be an easier task to definitively detect this process compared to detecting 2 roionization processes.," If reionization were completing at $z \sim 3$, an epoch for which there are numerous observations of the intergalactic medium (IGM), it should be an easier task to definitively detect this process compared to detecting $z \gtrsim 6$ reionization processes."
 Furthermore. if irejonization26 were ending at i~3. it should have sieuificautlv affected the temperature of the intergalactic eas and the ultraviolet radiation. background.," Furthermore, if reionization were ending at $z \sim 3$, it should have significantly affected the temperature of the intergalactic gas and the ultraviolet radiation background."
 These motivations. along with recent additious to the IIubble Space Telescope (IIST). have iuspired a significant effort of late to understand the signatures and the detection prospects of rrejonization2009).," These motivations, along with recent additions to the Hubble Space Telescope (HST), have inspired a significant effort of late to understand the signatures and the detection prospects of reionization."
. Three separate observations of the 2~3 IGM sugecst that weionization was endings around this redshift: First. several studies have measured the temperature of the intergalactic gas from the widths of the narrowest lines in the LLwe forest. and the majority of these studies have found evidence for au increase in the ICAL temperature of ~10! IK between 2z Land iom3. before a decline o lower redshift (Schaveetal.2000:RicottiLidzctal. 2009).," Three separate observations of the $z\sim 3$ IGM suggest that reionization was ending around this redshift: First, several studies have measured the temperature of the intergalactic gas from the widths of the narrowest lines in the $\alpha$ forest, and the majority of these studies have found evidence for an increase in the IGM temperature of $\sim 10^4$ K between $z \approx 4$ and $z \approx 3$, before a decline to lower redshift \citep{schaye00, ricotti00, lidz09}."
. These trends have been attributed to he heating from eionization., These trends have been attributed to the heating from reionization.
 Second. observations of LLwe absorption from gas at 2.8<23.3) show eus of comoving AIpe (cMpc) regions with no detected rausinission (Reimersctal.1997:Heapet2000).. which may indicate that ircionization was not complete.," Second, observations of $\alpha$ absorption from gas at $2.8 < z < 3.3$ show tens of comoving Mpc (cMpc) regions with no detected transmission \citep{reimers97, heap00}, which may indicate that reionization was not complete."
 Thirdly. Songaila(1998) and Aeafonovactal.(2007) detected evolution in the cohuun density ratios of certain highly ionized metals at 2D. which they argued was due to a hardening in the ionizing background around 50 eV and. thus. the eud of rrelonizatiou.," Thirdly, \citet{songaila98} and \citet{agafonova07} detected evolution in the column density ratios of certain highly ionized metals at $z \approx 3$, which they argued was due to a hardening in the ionizing background around $50~$ eV and, thus, the end of reionization."
 However. the interpretations of all of these mdications for rroionization are controversial.," However, the interpretations of all of these indications for reionization are controversial."
 Temperature measurements of the ΤΝΤ are dithcult. and not all nieasurenmieuts detected the aforementioned trends.," Temperature measurements of the IGM are difficult, and not all measurements detected the aforementioned trends."
 It is often argued that Ίσα absorption saturates at fractious that are too small (~107 at the mean density) to study, It is often argued that $\alpha$ absorption saturates at fractions that are too small $\sim 10^{-3}$ at the mean density) to study
neighborhood are ~0.01 * in both cases (Durgasser(2007).. Metchevetal.(2008))). (he corresponding expectation numbers within this region are ~0.5 for both object tvpes.,"neighborhood are $\sim0.01$ $^{-3}$ in both cases \citet{bur07}, \citet{met08}) ), the corresponding expectation numbers within this region are $\sim0.5$ for both object types."
 This is consistent with estimates of the J<21 magnitude-Iimited sky density of T chwarls (Burgasseretal.2004) which would suggest ο”0.5-1.0 such objects in a region of this size., This is consistent with estimates of the $J<21$ magnitude-limited sky density of T dwarfs \citep{bur04} which would suggest $\sim0.5$ -1.0 such objects in a region of this size.
 We therefore conclude that the number of low-Zzr foreground objects in the “cloud” region is relatively small.," We therefore conclude that the number of $T_{\rm eff}$ foreground objects in the “cloud"" region is relatively small."
" We can oblain an upper limit to the number of extragalactic contaminants by. assuming that all of the inferred. cluster members in the ""exterior region are spurious."," We can obtain an upper limit to the number of extragalactic contaminants by assuming that all of the inferred cluster members in the “exterior"" region are spurious."
 We can then predict the imunber of contaminating sources in the “cloud” region by scaling Nex by the cloud:exterior background source countratio!.. equal to 1.32 from the background source counts estimated above.," We can then predict the number of contaminating sources in the “cloud"" region by scaling $N_{\rm ext}$ by the cloud:exterior background source count, equal to 1.32 from the background source counts estimated above."
 On this basis. an upper limit lor the number of non-cluster menibers included in μα Is 24. ie. of our 139 cluster member candidates. (he percentage ol contaminating sources is between 0 and11.," On this basis, an upper limit for the number of non-cluster members included in $N_{\rm cloud}$ is 24, i.e. of our 139 cluster member candidates, the percentage of contaminating sources is between 0 and."
.. A particularly interesting subset of the cluster member candidates in Figure 4 is the eroup of low-Zar objects (Zur<1800 IX). of which there are 11 in the “cloud” regionthese are most likely low-mass brown cdwarls.," A particularly interesting subset of the cluster member candidates in Figure \ref{fig4} is the group of $T_{\rm eff}$ objects $T_{\rm eff}<1800$ K), of which there are 11 in the “cloud"" region—these are most likely low-mass brown dwarfs."
" By contrast. there is only 1: such object in the ""exlerior region."," By contrast, there is only 1 such object in the “exterior"" region."
" The fact that the number of low-Zar objects decreases so sharply when eoing from ""cloud"" to ""exterior. supports their inferred cluster membership and argues strongly against their being extragalactic."," The fact that the number of $T_{\rm eff}$ objects decreases so sharply when going from “cloud"" to “exterior"" supports their inferred cluster membership and argues strongly against their being extragalactic."
 Even the 1 low-Zagy object in the “exterior” region could be a foreground T. dwarf based on the statistics quoted earlier.," Even the 1 $T_{\rm eff}$ object in the “exterior"" region could be a foreground T dwarf based on the statistics quoted earlier."
 We therefore consider, We therefore consider
A detailed: study. of the ionization history of the Universe is fundamentally important for our understanding of the ooperties of the structure and evolution of the Universe. yarticularly the large-scale structure and galaxy formation.,"A detailed study of the ionization history of the Universe is fundamentally important for our understanding of the properties of the structure and evolution of the Universe, particularly the large-scale structure and galaxy formation."
 Although the epoch of galaxy formation is often referred as he due to the dilliculty in direct observations. Ht is. nevertheless. feasible to investigate in details the ionization ustory of the Universe. through the cosmic microwave iickeround (CAIB) anisotropies and polarization.," Although the epoch of galaxy formation is often referred as the due to the difficulty in direct observations, it is, nevertheless, feasible to investigate in details the ionization history of the Universe through the cosmic microwave background (CMB) anisotropies and polarization."
 The recent CAIB experiments. such as theDOOALERANG (deDernardisetal. 2000)... (Llananyetal.2000).. (Alasonetal. 2002)... (Watsonetal.2002)..DAST (Llalversonetal.2002).. and its polarization data (Ixovacetal.2002:Leitehet2002) have shed light on probing the dark age of the Universe.," The recent CMB experiments, such as the \cite{boomerang}, , \cite{maxima}, \cite{cbi}, , \cite{vsa}, \cite{dasi}, and its polarization data \cite{dasipol1,dasipol2} have shed light on probing the dark age of the Universe."
 In. particular. the newly released temperature-polarization data (Llinshawetal.2003:etal.2003). provide a new wav for understanding of the very carly stages of galaxy and star formation.," In particular, the newly released temperature-polarization data \cite{wmapdata1,wmapdata2} provide a new way for understanding of the very early stages of galaxy and star formation."
 We expect to have the future polarization data. with unprecedented. accuracy., We expect to have the future polarization data with unprecedented accuracy.
 Ehe polarization power spectrum [ron these two missions will therefore. provide. us. the information about the kinetics of hydrogen recombination and allow us to determine the parameters of the. [ast scattering surlace ancl the ionization history of the cosmic rlasma at very high redshifts z107., The polarization power spectrum from these two missions will therefore provide us the information about the kinetics of hydrogen recombination and allow us to determine the parameters of the last scattering surface and the ionization history of the cosmic plasma at very high redshifts $z\sim 10^3$.
 In the framework of the modern theory of the primary CAB anisotropy and polarization formation. the theory of ivdrogen recombination are assumed to be a παπαο one.," In the framework of the modern theory of the primary CMB anisotropy and polarization formation, the theory of hydrogen recombination are assumed to be a `standard' one."
 The classical theory of hydrogen. recombination [or he pure barvonic cosmological model was developed: by oebles (1905)... Zelclovieh. Kurt and Sunvaev (LOGS)... and was generalized. for. non-barvonic dark matter by Zabotin and. Naselskv (1985)... Jones and Wvse (1985).. Seager. Sasselov and Sco (2000).. Peebles. Seager and Hu (2000)..," The classical theory of hydrogen recombination for the pure baryonic cosmological model was developed by Peebles \shortcite{peebles}, Zel'dovich, Kurt and Sunyaev \shortcite{zeldovich}, and was generalized for non-baryonic dark matter by Zabotin and Naselsky \shortcite{zabotin}, Jones and Wyse \shortcite{jones}, Seager, Sasselov and Scott \shortcite{recfast}, Peebles, Seager and Hu \shortcite{psh}."
" This standard model of recombination has been mocified in various Ways,", This standard model of recombination has been modified in various ways.
 First of all. there are some variants from the stancdauxl ivdrogen recombination model. namely. the celay and acceleration of recombination at the redshift zc10° due to energy injection from unstable massive particles (DoroshkevichandNaselskv2002) or due to the lumpy structure of the barvonic fraction of the matter at small scales. (NaselskvandNovikov2002). in which the vpical mass of the clouds is of the order.107LOPAL. (sce.Doroshkeviehal.2003. anc the references. therein)," First of all, there are some variants from the standard hydrogen recombination model, namely, the delay and acceleration of recombination at the redshift $\zrec\simeq 10^3$ due to energy injection from unstable massive particles \cite{dn} or due to the lumpy structure of the baryonic fraction of the matter at small scales \cite{nn}, in which the typical mass of the clouds is of the order$10^5-10^6 M_{\odot}$ (seeDoroshkevich2003 and the references therein)."
 Secondly.the most crucial part of the ionization history," Secondly,the most crucial part of the ionization history"
It is now well established that spiral galaxies lave universal rotation curves (URC) that can be characterized by one sinele free parameter. the huuinosity (0.8. Rubin et al.,"It is now well established that spiral galaxies have universal rotation curves (URC) that can be characterized by one single free parameter, the luminosity (e.g. Rubin et al."
" 1980: Persie Salneci,S: 1991. Persie. ∡Salnect &fStel 1996t al.(PSS))."," 1980; Persic Salucci, 1991, Persic, Salucci Stel 1996 (PSS))."
SS)). For Persicinstance.sti. low-huninosity-: spiralespirals show: ever-rotation ∙curves⋅↽↴≻∢ (RC) ⋅out to the optical radiusoni. :d in ⋅the same region. theya RC of high-huninosity ∙∙spirals∙ ↙∙↴↴⋅⋠⋅↴⋅⋝∙an iflat oraxing. even decreasine," For instance, low-luminosity spirals show ever-rising rotation curves (RC) out to the optical radius, while, in the same region, the RC of high-luminosity spirals are flat or even decreasing."
 results. has beenh demonstrated bv€b Porsic &€ (LOSSΟΣΟΝ articular. aud Brocils (1992) that. as the galaxy huuimositv COUR theο lightlieht isix progressivelyprooressively unable touu trace tlic. Feeukcatures of⋅⋅⋅ the⋅⋅ eravitating↥⋅↸∖↕↽⊳⊳≽∶↿∐⋅↽⋜∖↥⋅↽⊳↕↽⊳⋟∙↸∖⋪↧∪↽↜∪⋯⋯↸∖↥⋅≓ matter (secradial also tane lou Thiscd," It has been demonstrated by Persic Salucci (1988, 1990) and Broeils (1992) that, as the galaxy luminosity decreases, the light is progressively unable to trace the radial distribution of the gravitating matter (see also Salucci, 1997)."
"s discrepancydiscrepaney Is.Is, inH1 general,eeneral. Iinterpreted BLarsen “1999).hana signature of an invisible mass component (Rubin ⋅ ⋅ :I"," This discrepancy is, in general, interpreted as the signature of an invisible mass component (Rubin et.al."
"OS éaa HEAS ,7 nn H, EE ", 1980; Bosma 1981).
""" BH : ∙⋅∙ − ∐⋅≺∪∪↴∖↴↸∖≼↧⋪⋯↸∖∐∩∐⋅∐⋈↧↕∐⋅≺∏↕↸∖↑↕⊔↑↴∖↴⋯⊳↸⊳↸∖↴∖↴↴∖↴↕∏∐↖↽∏↑↑↸∖≼↧↑↕∐∖ ü⋯∐↖↽↸∖↥⋅↴∖↴⋜↧∐⋅↖↽∪↕↑∐↸∖↥⋅∪↑⋜↧⊓∪∐↸⊳↿∐⋅↖↽↸∖↴∖↴∙∐↕↸⊳∪∐∐⋝∐↕⋜↧⊓∪∐↖↖⇁↕↑∐ ] ⋅ ⋅ ⊔∪↥⋅∪⋪↧↕∪↕⊔⊳↿∐⋅↖↽↸∖↴∖↴∪≺∏∐⋅≺⋪∐⋅↽∐⊔↸∖↥⋅≺∪∐∐∐⋪⊓∖≺≺↖↖↽⋪∐⋅ ‘↑∐↸∖∐↕↖↽⋜∐⋅↕⋜⋯↑≼∐↴∖↴⊓⋅↕↴⋝∏⊓∪∐∪↕↑∐↸∖↕∏∐∐∐∪∏↴∖↴⋯⋜↧↑↑↸∖↥⋅∙⋯∏≻∐↸∖↴∖↴ 4ln distribution withealaxics πιο τν -an eeeuniversal dependentdarkscalingproperties."," As pointed out by PSS the universality of the rotation curves, in combination with the invariant distribution of the luminous matter, implies an universal dark matter distribution with luminosity-dependent scaling properties."
Pury m Ou recent — high-resolution puri tr ry)? shown that cold | dark matter halos achieve a specific equilibrimm density profile (Navarro. Frenk White 1996. NEW: Cole Lacey 1997: Füukushige Makino 1997: Moore et al.," On the theoretical side, recent high-resolution cosmological N-body simulations have shown that cold dark matter halos achieve a specific equilibrium density profile (Navarro, Frenk White 1996, NFW; Cole Lacey 1997; Fukushige Makino 1997; Moore et al."
 1998: INravtsov et al., 1998; Kravtsov et al.
 1998)., 1998).
 This cau be characterized by oue free piaraiaeter. e.g. Mogg. the dark mass euclosed within the radius inside which the average over-densitv is 200 times the critical deusitv of the Universe.," This can be characterized by one free parameter, e.g. $M_{200}$, the dark mass enclosed within the radius inside which the average over-density is 200 times the critical density of the Universe."
 Iu the iunneriiost regions the dark matter profiles show some scatter around an average profile which is characterized by a power-law cusppor5. ith—115 (NFW. Moore et al.," In the innermost regions the dark matter profiles show some scatter around an average profile which is characterized by a power-law cusp $\rho \sim r^{-\gamma} $, with $\gamma =1-1.5$ (NFW, Moore et al."
 1998. Dullock et al.," 1998, Bullock et al.,"
 1999)., 1999).
 Until recently. due to both the DIuited nuuber of suitable rotation curves aud a poor knowledge of the exact amount of luminous matter prescut in the mnernost regions of spirals. if las been dificult to investigate the internal structure of dark matter halos.," Until recently, due to both the limited number of suitable rotation curves and a poor knowledge of the exact amount of luminous matter present in the innermost regions of spirals, it has been difficult to investigate the internal structure of dark matter halos."
 The situation is iore favorable for (low surface brightuess) dwarf ealaxies. which. are strougly dark matter dominated. even small radi., The situation is more favorable for (low surface brightness) dwarf galaxies which are strongly dark matter dominated even at small radii.
 The ⋅⋅↴kinematics of⋅ these∙⋅↴⋅↜∙ svstenis slows rising universality --oflitt the ddark halo∙⋅⋅ deusitdeusitv profiles.Bless ..but.lt. iti while.⋅⋅ in disagreement with that predicted bx] CDL.⋅ in ὲave because: of the. existence of. dark. halo deusitv etTt ," The kinematics of these systems shows an universality of the dark halo density profiles, but, it results in disagreement with that predicted by CDM, in particular because of the existence of dark halo density cores. ("
Moore 1991:1990 Burkert(© 1995).,Moore 1994; Burkert 1995).
"1995 heTli Quomoriei ofwe thes⋅ --1990) is not vet understood (see e.g. Navarro. Eke & 1906: teBurkert distribution&toh) 1997.C CelioPU &f. .but it is likely that nit iuvolves more plivysics malice, 1906).L997). simple hierarchical asseniblw of cold structures."," The origin of these features is not yet understood (see e.g. Navarro, Eke Frenk 1996; Burkert Silk 1997, Gelato Sommer-Larsen 1999), but it is likely that it involves more physics than a simple hierarchical assembly of cold structures."
" as the ⋅ £C⋅⋅ ≱ ⋠⊺↕↕↕↺∖∖⊧↕≱↭∖⋯↕↕↺∖∖∐≚∖↴⋯↕↕⋔⋠↕⋯↕↾↴⋝∖↕⋟⊆⊆↾∐⋠ ⊺≺≻⋯↻↸∖↖∏↑∐↑↕⊔↴∖↴∪↴⋝↴∖↴↸∖↥⋅↖↽⋜↧⊓∪∐⋜↧↕↸∖↖⇁↕∩∖∐∩∖∙↕≽∏∏↘↽↸∖↥⋅↑∐⊳∪⋅⊐⋝ Ta J tlar]Ü‘ tor: dwart : . | ⋅of n doninated ⋅⋅⋅. ⋅ ⋅⋅⋅⋅⋅ ""miatter‘ where py and ry are free parameters which represeut the ceutral dark matter density aud the scale radius."," To cope with this observational evidence, Burkert (1995) proposed an empirical profile that successfully fitted the halo rotation curves of four dark matter dominated dwarf galaxies where $\rho_0$ and $r_0$ are free parameters which represent the central dark matter density and the scale radius."
 This sample has been extended. more receuth to 17 dwarf nireenlar aud low surface brightucss galaxies (INravtsov ct al.," This sample has been extended, more recently, to 17 dwarf irregular and low surface brightness galaxies (Kravtsov et al."
 1998. see however vau deu Bosch et al.," 1998, see however van den Bosch et al."
 1999) which all are found to confirma equation (1)., 1999) which all are found to confirm equation (1).
 Adopting spherical svuuuetry. the mass distribution of the Burkert halos is eiven by," Adopting spherical symmetry, the mass distribution of the Burkert halos is given by"
"The general stationary vacuum solution (the herr spacetime) of the Eiustein equations is specified uniquely by the eravitational mass AM. and the augular niomieutuui J (see, ce. Wald (198133).","The general stationary vacuum solution (the Kerr spacetime) of the Einstein equations is specified uniquely by the gravitational mass $M$ and the angular momentum $J$ (see, e.g., \citet{wald1984}) )."
 Th F<GAL?fe. we have a rotating black hole.," If $J \le GM^2/c$, we have a rotating black hole."
 However. if J>λα. the Ίνα spacetime would have a naked singularity without a horizon.," However, if $J > GM^2/c$, the Kerr spacetime would have a naked singularity without a horizon."
 One could then consider closed timelike curves and causality would be violated (Chaudrasekliar1983)., One could then consider closed timelike curves and causality would be violated \citep{chandra1983}.
 While its validitv las not vet been proven. the cosnic-censorship conjecture (Penrose1969) asserts that naked sineularitics cannot be formed via the eravitational collapse of a body.," While its validity has not yet been proven, the cosmic-censorship conjecture \citep{penrose1969} asserts that naked singularities cannot be formed via the gravitational collapse of a body."
 For this reason. it is believedthat astroplivsical black holes should satisfy the err bound j€ld where j=6J/GAM? is the dimensionless spin parameter.," For this reason, it is believedthat astrophysical black holes should satisfy the Kerr bound $j \le 1$, where $j = c J / G M^2$ is the dimensionless spin parameter."
 While the value of the spin paramcter j plavs a fundamental role iu black-hole physics. it appears that this is not the case for other stellar objects.," While the value of the spin parameter $j$ plays a fundamental role in black-hole physics, it appears that this is not the case for other stellar objects."
 Iu particular. there is no theoretical constraint on the value of j for stars.," In particular, there is no theoretical constraint on the value of $j$ for stars."
 It is known that the spin parameter of main stars depends scusitively ou the stellar mass and cau be much Luweer than unity (ντα1968.1970:Dicke1970:Crav 1982).," It is known that the spin parameter of main-sequence stars depends sensitively on the stellar mass and can be much larger than unity \citep{kraft1968,kraft1970,dicke1970,gray1982}."
. On the other haud. the spin piraueter of compact stars has not been studied in detail (see below).," On the other hand, the spin parameter of compact stars has not been studied in detail (see below)."
 As we shall discuss iu more detail in Section 3..3.. the spin parameter of conrpact stars ds interesting in its own right for two reasons. (," As we shall discuss in more detail in Section \ref{sec:astro}, the spin parameter of compact stars is interesting in its own right for two reasons. ("
1) It plavs a role in our understanding of the observed periodic oscillations (QPOs) in disk-accreting coumpact- systems. (,1) It plays a role in our understanding of the observed quasi-periodic oscillations (QPOs) in disk-accreting compact-star systems. (
2) It determines the final fate of the collapse of a rotating compact star.,2) It determines the final fate of the collapse of a rotating compact star.
 Ever since the seminal work of Ihbutle(1967) who considered the Bmnit of slow rotation. rotating compact stars have been studied extcusively in ecueral relativity.," Ever since the seminal work of \citet{hartle1967} who considered the limit of slow rotation, rotating compact stars have been studied extensively in general relativity."
 Iu the past two decades. various different iumuerical codes have been developed to construct rapidly rotating stellar models in ecneral relativity.," In the past two decades, various different numerical codes have been developed to construct rapidly rotating stellar models in general relativity."
 We refer the reader to Stergioulas(2003) for a review., We refer the reader to \citet{stergi2003} for a review.
 As the rotation frequency. fis a directly nicasurable quantity for pulsars. it is thus reasonable that the ιαπατα value for f (1.6.. the Keplerian frequency fig) has been oue of the most studied physical quantities for relativistic rotating stars (see. e.g. Cooketal.(1991):Tacusel(1995):Ixo-(2009))).," As the rotation frequency $f$ is a directly measurable quantity for pulsars, it is thus reasonable that the maximum value for $f$ (i.e., the Keplerian frequency $f_{\rm K}$ ) has been one of the most studied physical quantities for relativistic rotating stars (see, e.g., \citet{cook1994,haensel1995,koranda1997,benhar2005,haensel2009}) )."
 Tlowever. in contrast to these previous works. we shall focus extensively on the spin parameter.," However, in contrast to these previous works, we shall focus extensively on the spin parameter $j$."
 It has been kuown that the spin parameter for a nmiaxinmu-mass neutron star lies iu therange j~0.7 for most realistic equations of state (EOS: e.9.. Cooketal.(1991). aud Salgadoetal. (1991)}).," It has been known that the spin parameter for a maximum-mass neutron star lies in therange $j \sim 0.6-0.7$ for most realistic equations of state (EOS; e.g., \citet{cook1994} and \citet{salgado1994}) )."
 In this work. we first extend the previous works and show that the upper bound for the spin parameter μας~0.03 Is essentiallv independent of the mass of the neutron star if the exavitational mass of the star is larger than ~1AL...," In this work, we first extend the previous works and show that the upper bound for the spin parameter $j_{\rm max} \sim 0.7$ is essentially independent of the mass of the neutron star if the gravitational mass of the star is larger than $\sim 1\ M_\odot$."
 Next we study the spin parameter of selt-bound quar stars. Which was not considered previously iu Cook.otal.(1991) and Salgadoctal.(1991).," Next we study the spin parameter of self-bound quark stars, which was not considered previously in \citet{cook1994} and \citet{salgado1994}."
. We fud that the behavior of the spin parameters of neutron stars aud quark stars is very different., We find that the behavior of the spin parameters of neutron stars and quark stars is very different.
 Tn contrast to the case of neutron stars. the spin parameter of quark stars does not have a universal upper bound.," In contrast to the case of neutron stars, the spin parameter of quark stars does not have a universal upper bound."
 It also depeuds seusitivelv on the parameter of the quark matter EOS aud the mass of the star., It also depends sensitively on the parameter of the quark matter EOS and the mass of the star.
 Furthermore. the spin parameter of quark stars can be larger than unity.," Furthermore, the spin parameter of quark stars can be larger than unity."
 This leads us to propose that the spin parameter could be a useful iucdicator to identity rapidly rotating quark stars., This leads us to propose that the spin parameter could be a useful indicator to identify rapidly rotating quark stars.
 The plan of this paper is as follows., The plan of this paper is as follows.
 Section 2. presents the main nunuerical results of this work., Section \ref{sec:results} presents the main numerical results of this work.
 Iu Section 3.. we discuss the astrophysical implications of our results.," In Section \ref{sec:astro}, we discuss the astrophysical implications of our results."
 Our conclisionus are sununuauizediu Section L.., Our conclusions are summarized in Section \ref{sec:conclude}. .
 We make use of the nuuerical code from the C| LORENE to caleulate uniformly rotating colmpact star models in general relativitv., We make use of the numerical code from the C++ LORENE to calculate uniformly rotating compact star models in general relativity.
 The code uses a 1ulti-domaiu spectral method (Bonazzolactal.1998) to solve the LEiusteiu equations in a stationary and, The code uses a multi-domain spectral method \citep{bonazzola1998} to solve the Einstein equations in a stationary and
οσον 1994).,Czerny 1994).
 This Uuorescent line is linked to the Compton reflection feature. as they are both resulting from the irradiation of the disk surface by the hard. X-rays.," This fluorescent line is linked to the Compton reflection feature, as they are both resulting from the irradiation of the disk surface by the hard X-rays."
 “Pherefore. in the spectral analysis we used the mocel of the rellection hump plus the iron line (Zvvcki. Done Smith. 1997).," Therefore, in the spectral analysis we used the model of the reflection hump plus the iron line (Żyycki, Done Smith, 1997)."
 Both literature and archives (NED. LIEASARC) were searched to obtain a complete UV to hard-N-rav. continuum for each source.," Both literature and archives (NED, HEASARC) were searched to obtain a complete UV to hard-X-ray continuum for each source."
" Ehe bolometric luminosity £,,7 was estimated using the extrapolation of V magnitude to the 2"," The bolometric luminosity $L_{bol}$ was estimated using the extrapolation of V magnitude to the bandpass, with the assumption of the continuum slope of 0.5, and taking into account the X-ray luminosity $L_{2-10keV}$ derived from the spectral fits."
, Then we calculated the accretion rate assuming the accretion efficiency of 1/16 and the central black hole mass was estimated from the standard relation $F_{\nu} \sim \nu^{1/3}(M\dot M)^{2/3}$.
500, To calculate distances we assumed H=50 km $^{-1}$ $^{-1}$ and q=0.
AL2, The value of eigenvector 1 has been determined by Boroson Green for only one quasar PG1211+143.
ias cnCALA 11 7 I<B," For the other three objects we estimated this value by comparing the EV1 range of objects with similar values of FWHM $\beta$, $\beta$ and III] strength in the Boroson Green PG sample."
VI 11," In Table 2 we show the minimum and maximum values of eigenvector 1 corresponding to the quasars with similar properties to our objects (up to difference in FWHM $\beta$ ), and the mean value $<EV1>$, weighted by the two other crucial properties: $\beta$ and III]."
," The values of $\beta$ width, $\beta$ and $\beta$ were taken from Boller et al."
11 ," 1996 and Leighly 1999 The X-ray properties were examined by fitting simultaneously the ASCA and RXTE data, using the XSPEC ver."
, 10.0.
," We used the power law continuum model, corrected for the galactic absorption."
," Then we added the reflection component, which in most cases gave a significant improvement in the fit."
"O/2zlt,cosi"," This spectral feature is parameterized by the ionization parameter $\xi$, reflection amplitude $\Omega/2\pi$, inner disc radius $R_{in}$ and the disc inclination $\cos i$."
b, The incident hard X-ray flux was assumed to have a radial distribution fixed at $F_{irr} \sim r^{-3}$.
;y, In Table 3 we show the results of spectral fitting to the X-ray data.
9r Concl," The model ingredients for PKS 0558-504, IRAS 13349+243 and ARK 564 are: galactic absorption, power law and reflected component with iron line."
usions/L.," The model ingredients for PG 1211+143 are: galactic absorption, comptonized black body, power law and reflected component with iron line Preliminary results showed that Narrow Line Seyfert 1 galaxies have high $L/L_{Edd}$ ratios and relatively small black hole masses when compared to normal Seyfert 1 galaxies."
l, The mass determination by means of the power density spectra (Czerny et al.
ogM," 2001) indicates, that in case of Seyfert 1 galaxies $log M_{BH}$ is $\sim 7.5$, while luminosity is only about of the Eddington luminosity."
pu- 7 5logMpg~65.S2L , For NLS1 the corresponding values are $log M_{BH} \sim 6.5 - 8.2$ and $L\sim 20-40\% L_{Edd}$ .
Li La, Since NLS1 have small eigenvector 1 values this finding points to $L/L_{Edd}$ ratio (or accretion rate) as the primary driver of eigenvector 1 (see also Boroson 2001).
LLu Lf, This also points to $L/L_{Edd}$ as the main physical parameter responsible for the extreme properties of the Narrow Line Seyfert 1 galaxies.
"Lati,"," For larger $L/L_{Edd}$ the matter of the accretion disk is more ionized, having an impact on the reflected spectrum shape."
, In our sample for only PKS 0558-504 the neutral reflection was acceptable at
"Figure 3 gives a good overview of the results for the two available plasma - kinetic neutral models BM and Hee, and the three multi-fluid models Flo, Mue, and Sch.","Figure \ref{figninout} gives a good overview of the results for the two available plasma - kinetic neutral models BM and Hee, and the three multi-fluid models Flo, Mue, and Sch."
" The left panel shows the plasma density profiles for upwind (solid), crosswind (dotted), and downwind (dashed) directions, and the right panel displays the information for total neutral density in the same format."," The left panel shows the plasma density profiles for upwind (solid), crosswind (dotted), and downwind (dashed) directions, and the right panel displays the information for total neutral density in the same format."
 The plasma results exhibit a level of similarity to each other that is comparable or slightly better than the level of similarity of the plasma results in the previous section reffigsnoverv))., The plasma results exhibit a level of similarity to each other that is comparable or slightly better than the level of similarity of the plasma results in the previous section \\ref{figsnoverv}) ).
" In particular, the upwind HP location nearly coincides in all five models."," In particular, the upwind HP location nearly coincides in all five models."
 The first four entries of Table 4 contain the key locations of the heliosphere for the full models., The first four entries of Table \ref{resfull} contain the key locations of the heliosphere for the full models.
" Again, the standard deviations in the last column express the range of the results against a simple arithmetic mean of the values in each row."," Again, the standard deviations in the last column express the range of the results against a simple arithmetic mean of the values in each row."
" It can be seen that also the upwind TS locations agree to within7%,, and only BS and downwind TS disagree (up to each)."," It can be seen that also the upwind TS locations agree to within, and only BS and downwind TS disagree (up to each)."
" While this type of disagreement was also found in the plasma-only cases of section 2, it tends to now be larger, especially for the bow shock."," While this type of disagreement was also found in the plasma-only cases of section 2, it tends to now be larger, especially for the bow shock."
 We note in passing the dramatic effect on the heliosphere boundary locations that the inclusion of neutrals has., We note in passing the dramatic effect on the heliosphere boundary locations that the inclusion of neutrals has.
 The results of Table 2 are significantly larger than those of Table 4 even though the boundary parameters of the plasma-only case are identical to those of the plasma/neutral case., The results of Table \ref{resplas} are significantly larger than those of Table \ref{resfull} even though the boundary parameters of the plasma-only case are identical to those of the plasma/neutral case.
" In the neutral H density reffigninout,, right) all models exhibit an overdensity (hydrogen wall) downstream of the bow shock, and a subsequent rapid drop in the density approaching the heliopause and further inside."," In the neutral H density \\ref{figninout}, right) all models exhibit an overdensity (hydrogen wall) downstream of the bow shock, and a subsequent rapid drop in the density approaching the heliopause and further inside."
" For this and similar diagnostics, the neutral multi-fluid results are summed (averaged) into a single total neutral hydrogen quantity, in the simplest manner as nio;=D>;ni for total density, Vtot=ng:Do;niv for velocity, and T=nj-0,nT; for temperature."," For this and similar diagnostics, the neutral multi-fluid results are summed (averaged) into a single total neutral hydrogen quantity, in the simplest manner as $n_{tot} = \sum_i n_i$ for total density, $v_{tot} = n_{tot}^{-1}
\cdot \sum_i n_i v_i$ for velocity, and $T = n_{tot}^{-1} \cdot
\sum_i n_i T_i$ for temperature."
" The two fluid models with less than four neutral fluids (Mue, Sch) almost agree in the sharpness and the peak height of the hydrogen wall."," The two fluid models with less than four neutral fluids (Mue, Sch) almost agree in the sharpness and the peak height of the hydrogen wall."
" As in previous findings (Baranovetal.(1998);; Figure 2 by McNutt(2004);; AI05; HFZ06), the hydrogen wall is quite a bit higher for these two fluid models compared to the kinetic models BM and Hee."," As in previous findings \citet{Baranov98}; Figure 2 by \citet{McNutt04}; AI05; HFZ06), the hydrogen wall is quite a bit higher for these two fluid models compared to the kinetic models BM and Hee."
 The two latter models match each other well in neutral hydrogen., The two latter models match each other well in neutral hydrogen.
" The hydrogen wall of five-fluid model Flo is higher than the kinetic ones, but closer to those than to the other multi-fluid models."," The hydrogen wall of five-fluid model Flo is higher than the kinetic ones, but closer to those than to the other multi-fluid models."
 The peak densities in the hydrogen wall are listed in Table 4.., The peak densities in the hydrogen wall are listed in Table \ref{resfull}.
" The hydrogen wall profiles fit the general trend displayed in Figure 3 of AI05: There, the one-fluid model (most similar to the Sch model) resulted in the highest-peaked hydrogen wall, the three-fluid model (most similar to the Mue model) exhibited a somewhat smaller hydrogen wall with a very sharp rise on the interstellar side, and the BM model had a small peak, with a smooth H density rise and fall, that was relatively closely matched by a four-fluid model (most similar to the Flo model)."," The hydrogen wall profiles fit the general trend displayed in Figure 3 of AI05: There, the one-fluid model (most similar to the Sch model) resulted in the highest-peaked hydrogen wall, the three-fluid model (most similar to the Mue model) exhibited a somewhat smaller hydrogen wall with a very sharp rise on the interstellar side, and the BM model had a small peak, with a smooth H density rise and fall, that was relatively closely matched by a four-fluid model (most similar to the Flo model)."
" Note that the neutral H column density through the upwind direction is basically constant; the displayed different hydrogen walls are either tall and narrow, or smaller and broad."," Note that the neutral H column density through the upwind direction is basically constant; the displayed different hydrogen walls are either tall and narrow, or smaller and broad."
" The largest contributor to the differences between the simulated hydrogen walls is the distribution of plasma velocities, notably the component parallel to the ISM flow."," The largest contributor to the differences between the simulated hydrogen walls is the distribution of plasma velocities, notably the component parallel to the ISM flow."
" Figure 4 shows an overview of the radial velocity component as a function of heliocentric distance in the left panel, and the right panel zooms in around the"," Figure \ref{figvr} shows an overview of the radial velocity component as a function of heliocentric distance in the left panel, and the right panel zooms in around the"
The current most widely used. P-L relation is based ou the Large Magellanic Cloud (LAIC} Cepheicds.,The current most widely used P-L relation is based on the Large Magellanic Cloud (LMC) Cepheids.
 This is primarily because there are many Cepheids discovered in the LMC., This is primarily because there are many Cepheids discovered in the LMC.
 The LAIC P-L relation has been assunied. and believed. to be linear in logCP?)o for a longo time. where P is the pulsation period in days.," The LMC P-L relation has been assumed, and believed, to be linear in $\log(P)$ for a long time, where $P$ is the pulsation period in days."
 ∐∪↖↖↽↸∖↖⇁↸∖↥⋅↑∐↕↴∖↴⋜↧↴∖↴↴∖↴∏∐∏≻↑↕∪∐↕↴∖↴∏∐⋅↥⋅↸∖↓↑↕⋅↖⇁∏∐≼∐∖↥⋅↸⊳∐⋜↧∐↸∖∐∶↴⋁↸∖↕⋟↥⋅∪⋯↴∖↴↸∖↖↽↸∖↥⋅⋜↧↕↥⋅↸∖↸⊳↸∖∐↑↻⋜∏⋉∖↥⋅↴∖↴≺⊺⋜∐⊔⋯⋜⋯∐∙∖," However this assumption is currently under challenge from several recent papers \citep{tam02,kan04,kan06,san04,nge05,nge06}."
↽↕⊰↸∖↕∐≼⇂⊔∩∩⊇∶ ↕↘⊽⋜⋯↴∏∐⋅∙∖↽⋀∖⊽∶↴∙⊾↸∖∪↖↖↽⊇∩∩↓∙⊇∩∩⊓∶≋⋜↧∐≼↧⋜↧∶↴∙⊾↸∖↸∖↑⋜↧↕∙⊇∩∩↓∶⋀∖⊽∶↴∙⊾↸∖∪↖↖↽↸∖↑⋜↧↕∙⊇∩∩⋅↱≻∶⋀∖⊽∶↴∙⊾↸∖∪↖↖↽∙∖↽↕↘⊽⋜⋯↴∏∐⋅⊇∩⋈∏⋝⋟∙⋅⊺↕∐∖↴∖↴↸∖↴∖↴↑⊓∐↸∖↴∖↴ present strong evidence that the LAIC P-L relation may not be linear. and further. that the relation can be broken into two relations with a discoutiuuitv at (or around) LO days.," These studies present strong evidence that the LMC P-L relation may not be linear, and further, that the relation can be broken into two relations with a discontinuity at (or around) 10 days."
 In particular. a rigorous statistical test (the F-test) for analyzing the noulinearitv of the LAIC P-L relation. using the W-baud data from both of the OGLE (Optical Gravitational Leusiug Experiment) aud the NACTIO (Massive Compact Halo Object) saluples has returned a significaut result: this is reported in IWanbur&Necow(2001.2006) aud (2005).. respectively.," In particular, a rigorous statistical test (the $F$ -test) for analyzing the nonlinearity of the LMC P-L relation, using the $V$ -band data from both of the OGLE (Optical Gravitational Lensing Experiment) and the MACHO (Massive Compact Halo Object) samples has returned a significant result: this is reported in \citet{kan04,kan06} and \citet{nge05}, respectively."
 The fact that the statistical test returus a significaut result frou two totally samples strongly indicates that the nonlinear LMC P-L relation is veal and not due to artifacts such as photometric reductions aud observational strategies., The fact that the statistical test returns a significant result from two totally samples strongly indicates that the nonlinear LMC P-L relation is real and not due to artifacts such as photometric reductions and observational strategies.
 Despite this. the evidence of the nonlinear LMC P-L relation is still a controversial issuc and draws uuch skepticisii within the astronomical commumity.," Despite this, the evidence of the nonlinear LMC P-L relation is still a controversial issue and draws much skepticism within the astronomical community."
 However this does not rule out the possible existeuce of au intrinsic. but harcd-to-cetect nonlinear P-L relation.," However this does not rule out the possible existence of an intrinsic, but hard-to-detect nonlinear P-L relation."
 The purpose of this paper is to examine some of the wis-conceptions aud clarify some of the issues regarding the detection of a nonlinear LAIC P-L relation., The purpose of this paper is to examine some of the mis-conceptions and clarify some of the issues regarding the detection of a nonlinear LMC P-L relation.
 Iu his paper the nonlinear P-L relation discussed is defined as two P-L relations with a discontinuity at/avound a period of 10 davs that separate the short aud long period Cepheids., In this paper the nonlinear P-L relation discussed is defined as two P-L relations with a discontinuity at/around a period of 10 days that separate the short and long period Cepheids.
 Heuce short aud long period Cepheids are those with period less and ereater than 10 davs. respectively.," Hence short and long period Cepheids are those with period less and greater than 10 days, respectively."
 Justifications of the choice of a fiducial xeak period at 10 davs are eiven in Raubur&Necow(2001).. Sandageetal. (2001)... and Necow&Πατ(2006b).. and will not be repeated here.," Justifications of the choice of a fiducial break period at 10 days are given in \citet{kan04}, \citet{san04}, \citet{nge05} and \citet{nge06}, and will not be repeated here."
 We note that Necowetal.(2005) also estimated this break period from the data., We note that \citet{nge05} also estimated this break period from the data.
 Other forms of the nonlinear P-L relation can be found in (2005).. however the study from Necow&Ixaubur(20060) sugeested the two-lnes relation 1s more appropriate to represcut the uoulinearity.," Other forms of the nonlinear P-L relation can be found in \citet{nge05}, however the study from \citet{nge06} suggested the two-lines relation is more appropriate to represent the nonlinearity."
 The confirmation of the break period at 10 days aud the true form. of the nonlinear P-L relation is difficult to verify with the observed data. due to the intrinsic dispersion of the P-L relation. aud has to wait for more pulsational modeling.," The confirmation of the break period at 10 days and the true form of the nonlinear P-L relation is difficult to verify with the observed data, due to the intrinsic dispersion of the P-L relation, and has to wait for more pulsational modeling."
 Some carly attempts to explain theoretically and model the nonluear P-L relation cau be found in Ίνα&Necow(2006) and Marconietal.(2005)., Some early attempts to explain theoretically and model the nonlinear P-L relation can be found in \citet{kan06} and \citet{mar05}.
. One of the arguments against the idea of a nonlinear P-L relation is that the P-L relation plotted from observed data looks linear by human eve. therefore the relation should be linear.," One of the arguments against the idea of a nonlinear P-L relation is that the P-L relation plotted from observed data looks linear by human eye, therefore the relation should be linear."
 However.linear.," However,."
 Wo demonstrate that it is dificult to distinguish these two P-L relations by eve with a simple experiment., We demonstrate that it is difficult to distinguish these two P-L relations by eye with a simple experiment.
" We generate (1.6. simulation) two ""fake"" P-L relations to mimic the distribution of real Cepheidsalong tle P-L regression: one is iutrinsically linear aud another one is dutrinsically nonlinear."," We generate (i.e., simulation) two “fake” P-L relations to mimic the distribution of real Cepheidsalong the P-L regression: one is intrinsically linear and another one is intrinsically nonlinear."
 For demonstration purposes. we use the V-banud P-L relations given iu Saudageetal. (2001)..," For demonstration purposes, we use the $V$ -band P-L relations given in \citet{san04}. ."
 The near version of the P-L relation is: aud the nonlinear version of the P-L relations are:, The linear version of the P-L relation is: and the nonlinear version of the P-L relations are:
Despite some disparity of the data on a whole. the good N-rav/TeV-5-rav. correlation strengthens (he case for leptonic svuchrotron-Compton models.,"Despite some disparity of the data on a whole, the good $\gamma$ -ray correlation strengthens the case for leptonic synchrotron-Compton models."
 In this paper. we focus the discussion on the X-ray ancl TeV-5-rax. emission trom BL Lac tvpe objects.," In this paper, we focus the discussion on the X-ray and $\gamma$ -ray emission from BL Lac type objects."
 In Section 4.. we will briefly outline the relevance of the model for quasars.," In Section \ref{discussion}, we will briefly outline the relevance of the model for quasars."
 We use (he term reference model [ον the following combination of model components., We use the term “reference model” for the following combination of model components.
 The accretion svstem launches a Poyntüng flux dominated jet and as the outflow propagates. the flow transforms into a particle dominated outflow.," The accretion system launches a Poynting flux dominated jet and as the outflow propagates, the flow transforms into a particle dominated outflow."
 Shocks within the jet transfer a fraction of the jets bulk kinetic energy (o a few hieh-enerev particles (hat emit svnchrotron and Inverse Compton enission., Shocks within the jet transfer a fraction of the jet's bulk kinetic energy to a few high-energy particles that emit synchrotron and Inverse Compton emission.
 The reference model sullers from a munber of weak links., The reference model suffers from a number of weak links.
 No simple mechanism has vet been suggested to convert the Povuting flux dominated outflow into a particle dominated outflow., No simple mechanism has yet been suggested to convert the Poynting flux dominated outflow into a particle dominated outflow.
 Furthermore. the hypothesis of shock acceleration of electrons lo ~TeV energies is observationallv very poorly supported.," Furthermore, the hypothesis of shock acceleration of electrons to $\sim$ TeV energies is observationally very poorly supported."
 The modeling of the SEDs of some BL Lacs require “non-standard” electron energy spectra., The modeling of the SEDs of some BL Lacs require “non-standard” electron energy spectra.
" Models of Mrk 501 and Mrk 421 data require a minimum Lorentz lactor of accelerated particles syn. on the order of 10"" in the jet reference [rame citealtPianl998.lrawczvuski2002)). or non-power-aw distributions with very high characteristic Lorentz factors citeali*Sauge2004.Ixatarzviski2006.Giebels2006))."," Models of Mrk 501 and Mrk 421 data require a minimum Lorentz factor of accelerated particles $\gamma_{\rm min}$ on the order of $10^5$ in the jet reference frame \\citealt*{Pian1998,Krawczynski2002}) ), or non-power-law distributions with very high characteristic Lorentz factors \\citealt*{Sauge2004,Katarzynski2006,Giebels2006}) )."
" I the shocks are internal to the jet and the jet medium is mace of cold protons. simple arguments lead (o ,,4-values close to the proton-to-electron mass ratio μην mg/mp/= 1836."," If the shocks are internal to the jet and the jet medium is made of cold protons, simple arguments lead to $\gamma_{\rm min}$ -values close to the proton-to-electron mass ratio $\gamma_{\rm min}\,\approx$ $m_{\rm p} / m_{\rm e}\,=$ 1836."
" If the shocks are external and (he jet medium runs into a much slower target medium. the 545;,-values could be higher by a factor of P."," If the shocks are external and the jet medium runs into a much slower target medium, the $\gamma_{\rm min}$ -values could be higher by a factor of $\Gamma$ ."
" A modification of the reference model might be able to account for the high 5,44,-values and for (he non-standard electron spectral indices even in the internal shock model.", A modification of the reference model might be able to account for the high $\gamma_{\rm min}$ -values and for the non-standard electron spectral indices even in the internal shock model.
" Bykov&(1996) point out that statistical acceleration bv relativisiicmagnetohydrodyvnamic fluctuations in flow collision regions of jets might give rise to hard electron energy. spectra and (o 5,44,2values on the order of 10”.", \citet{Bykov1996} point out that statistical acceleration by relativisticmagnetohydrodynamic fluctuations in flow collision regions of jets might give rise to hard electron energy spectra and to $\gamma_{\min}$ -values on the order of $^5$.
 As mentioned above. the (theory of shock acceleration predicts that the X-ray and TeV οταν spectra of [lares are soft during (he early rising phases of fares.," As mentioned above, the theory of shock acceleration predicts that the X-ray and TeV $\gamma$ -ray spectra of flares are soft during the early rising phases of flares."
 The beautiful Mik 421 observations taken in 2001 with the show both. soft and hard energy. spectra during the early rising phases of flares (Fossati 2004.. and Fossati and Ducklev. private communication. 2006).," The beautiful Mrk 421 observations taken in 2001 with the show both, soft and hard energy spectra during the early rising phases of flares \citealt*{Fossati2004}, , and Fossati and Buckley, private communication, 2006)."
 This negative result can, This negative result can
 Monitor (ASAT) on theExplorer (ENTE) frour 210 keV. (Levine 1996).. the Gas Slit Camera (CSC) on theDhinage (ALANT) frou 1.5 keV (Matsuokaetal.2009).. aud the Durst Alert Telescope (BAT) on from 1550 keV (Ciolrelsctal. 2001).. there has not been an allskv monitor in the low energy gamma-ray region suce the Burst and Trausieut Source Experiment (BATSE) iustrumneut on the Observatory (CGRO). which wasscusitive from 201800keV (Fishinanetal. 1989)..," Monitor (ASM) on the ) from 2–10 keV \citep{Levine1996}, the Gas Slit Camera (GSC) on the ) from 1.5--20 keV \citep{Matsuoka2009}, and the Burst Alert Telescope (BAT) on from 15–50 keV \citep{Gehrels2004}, , there has not been an all-sky monitor in the low energy gamma-ray region since the Burst and Transient Source Experiment (BATSE) instrument on the ), which wassensitive from 20–1800keV \citep{Fishman1989}. ."
as ΕΠΗ sources.,as FRIIb sources.
 The sources and their properties are listed in Table 1., The sources and their properties are listed in Table 1.
 The source redshifts range [rom 0.056 to 1.79. and the hot spot to hot spot source sizes range from about 100 kpe to over GOO kpe (O'Dea οἱ al.," The source redshifts range from 0.056 to 1.79, and the hot spot to hot spot source sizes range from about 100 kpc to over 600 kpc (O'Dea et al."
 2003)., 2008).
 The black hole mass for Cvgnus A (3C 405) is obtained [from Taclhunter et al. (, The black hole mass for Cygnus A (3C 405) is obtained from Tadhunter et al. (
2003): those lor the next four sources are obtained [rom MeLive et al. (,2003); those for the next four sources are obtained from McLure et al. (
2004). ancl those for (he remaining 14 sources are obtained using equation (3) of McLure et al. (,"2004), and those for the remaining 14 sources are obtained using equation (3) of McLure et al. ("
"2006) where the values of M, were provided by MeLure (ΑΙπο. private communication 2003).","2006) where the values of $M_{sph}$ were provided by McLure (McLure, private communication 2008)."
 The total energies are obtained from Wan. Dalv. Guerra (2000). Guerra. Daly. Wan (2000). and ODea et al. (," The total energies are obtained from Wan, Daly, Guerra (2000), Guerra, Daly, Wan (2000), and O'Dea et al. ("
2008) and converted to the cosmological moclel adopted here.,2008) and converted to the cosmological model adopted here.
" The enerey [rom the two sides of each source are combined (to obtain the total outflow enerev £,. which is taken to be twice the weighted mean of the outflow energies [rom each side of the source."," The energy from the two sides of each source are combined to obtain the total outflow energy $E_*$, which is taken to be twice the weighted mean of the outflow energies from each side of the source."
 Deviations of the magnetic field strength of the extenclecd radio source [rom the minimum energy value only enter ZZ through the normalization of this quantity. as discussed in detail by O'Dea et al. (," Deviations of the magnetic field strength of the extended radio source from the minimum energy value only enter $E_*$ through the normalization of this quantity, as discussed in detail by O'Dea et al. ("
2003).,2008).
 The lobes of Cvgnus A are used to normalize the sources. ancl an offset of 0.25 of magnetic field strength from the minimum energv value. appropriate for Cvenus A (Carilli et al.," The lobes of Cygnus A are used to normalize the sources, and an offset of 0.25 of magnetic field strength from the minimum energy value, appropriate for Cygnus A (Carilli et al."
 1991: Wellman. Daly. Wan 1997) has been adopted.," 1991; Wellman, Daly, Wan 1997) has been adopted."
" Note that if there is no offset [rom minimum energy conditions in Cygnus A. the empirically determined values of E, ancl r decreases by about a [actor of 5 (O'Dea et al."," Note that if there is no offset from minimum energy conditions in Cygnus A, the empirically determined values of $E_*$ and $r$ decreases by about a factor of 5 (O'Dea et al."
 2008). so the values of j decrease by about V5 from those discussed below.," 2008), so the values of $j$ decrease by about $\sqrt{5}$ from those discussed below."
" The dimensionless ratio of outflow energy to black hole mass. r=E,/(cM). is obtained for each source and substituted into eq. ("," The dimensionless ratio of outflow energy to black hole mass, $r\equiv E_*/(c^2M)$, is obtained for each source and substituted into eq. ("
1) to obtain the spin parameter j. and the values are listed in Table 1.,"1) to obtain the spin parameter $j$, and the values are listed in Table 1."
 The sources have very similar values of r and j. wilh no dependence of either parameter on source size or redshift.," The sources have very similar values of $r$ and $j$, with no dependence of either parameter on source size or redshift."
 The weighted mean values of r and j [for these 19 sources are (1.62:0.3)x10.* and 0.12£0.01. respectively.," The weighted mean values of $r$ and $j$ for these 19 sources are $(1.6 \pm 0.3)\times 10^{-3}$ and $0.12 \pm 0.01$, respectively."
 Interestingly. within the nmeasurenient error. (he values of r and j for each source are consistent will the mean value ol the 19 sources.," Interestingly, within the measurement error, the values of $r$ and $j$ for each source are consistent with the mean value of the 19 sources."
 The values of j are shown as a histogram in Figure | and as a function of black hole mass in Figure 2., The values of $j$ are shown as a histogram in Figure 1 and as a function of black hole mass in Figure 2.
 Figure 3 shows the total outflow energv as a [function of black hole mass., Figure 3 shows the total outflow energy as a function of black hole mass.
 It would appear that the values of r and j for these FRITb sources is constant. suggesting that the physical state of the svstem at the time the outflow is generated is very similar in each of (he sources studied.," It would appear that the values of $r$ and $j$ for these FRIIb sources is constant, suggesting that the physical state of the system at the time the outflow is generated is very similar in each of the sources studied."
 This could indicate Chat the outflow is triggered when a particular threshold. given by r22oE10.7. is reached.," This could indicate that the outflow is triggered when a particular threshold, given by $r \approx 10^{-3}$, is reached."
" A model that includes a threshold of this tvpe is discussed by Meier (1999),", A model that includes a threshold of this type is discussed by Meier (1999).
 A threshold for the onset of the outflow is also indicated. by a comparison of individual source properties wilh (he properties of the full population of sources (e.g. Dalv Guerra 2002: Daly et al., A threshold for the onset of the outflow is also indicated by a comparison of individual source properties with the properties of the full population of sources (e.g. Daly Guerra 2002; Daly et al.
 2003)., 2008).
"Hs EW. and the (NelII continuum. corrected). D,,4000 from Kauffmannetal.(2003b).. who. for the latter. have adopted a modified version of the original detinition (Bruzual1983). of the D,, 4000 introduced by Baloghetal.(1999).","$_\delta$ EW, and the (NeIII continuum corrected) $_n$ 4000 from \citet{kauff03b}, who, for the latter, have adopted a modified version of the original definition \citep{bruzual83} of the $_n$ 4000 introduced by \citet{balogh99}."
". A stronger D,, 4000 is an indicator of a metal-rich inter-stellar medium. which. together with the Hs EW. indicates whether the galaxy has been forming stars continuously Gintermediate/high D,,4000 plus low Hs EW) or in bursts (low D,,4000 plus high Hs EW) over the past 1-2 Gyr (Kauffmannetal.2003b)."," A stronger $_n$ 4000 is an indicator of a metal-rich inter-stellar medium, which, together with the $_\delta$ EW, indicates whether the galaxy has been forming stars continuously (intermediate/high $_n$ 4000 plus low $_\delta$ EW) or in bursts (low $_n$ 4000 plus high $_\delta$ EW) over the past 1-2 Gyr \citep{kauff03b}."
". We note that the observational error in D,, 4000 index is very small. typically ~0.02. but the same is not true for the Hs EW. which has an uncertainty of 1-2 in measurement (Kauffmannetal.2003b)."," We note that the observational error in $_n$ 4000 index is very small, typically $\sim$ 0.02, but the same is not true for the $_\delta$ EW, which has an uncertainty of 1-2 in measurement \citep{kauff03b}."
. Kauffmannetal.(2003b) discuss the physical constraints leading to these uncertainties. and show that the Hs index can assume only a selected range of values for all possible star formation histories.," \citet{kauff03b} discuss the physical constraints leading to these uncertainties, and show that the $_\delta$ index can assume only a selected range of values for all possible star formation histories."
 The large observational errors on the Hs EW imply that the estimated value of this index is constrained by the parameter space spanned by the acceptable models., The large observational errors on the $_\delta$ EW imply that the estimated value of this index is constrained by the parameter space spanned by the acceptable models.
" The red sequence galaxies in our sample show Hs in emission. and yield large values for the D,, 4000. contirming the fact that their main ingredient is a population of old. passively evolving stars. which determines the overall galaxy colours and dominates the spectra."," The red sequence galaxies in our sample show $_\delta$ in emission, and yield large values for the $_n$ 4000, confirming the fact that their main ingredient is a population of old, passively evolving stars, which determines the overall galaxy colours and dominates the spectra."
 The high observational uncertainty in the EW(CH;) implies that it is hard to determine whether Hs is actually occurring in emission. or the negative EWs are a result of a high correction factor in individual galaxies.," The high observational uncertainty in the $_\delta$ ) implies that it is hard to determine whether $_\delta$ is actually occurring in emission, or the negative EWs are a result of a high correction factor in individual galaxies."
 This is a common problem with the use of Hs index in individual systems. but this might not be an important issue for this statistical study.," This is a common problem with the use of $_\delta$ index in individual systems, but this might not be an important issue for this statistical study."
" The blue star-forming galaxies. in sharp contrast. yield small values for the D,,4000 and strong H5 in absorption."," The blue star-forming galaxies, in sharp contrast, yield small values for the $_n$ 4000 and strong $_\delta$ in absorption."
" The blue passive galaxies follow the blue star-forming galaxies. with the mean value for the D,, 4000 systematically higher by ~0.2. but with a very broad distribution of Hs EW. revealing a mix of galaxies with a large scatter in he ages of their youngest stellar populations."," The blue passive galaxies follow the blue star-forming galaxies, with the mean value for the $_n$ 4000 systematically higher by $\sim0.2$, but with a very broad distribution of $_\delta$ EW, revealing a mix of galaxies with a large scatter in the ages of their youngest stellar populations."
" In red star-forming galaxies. the distributions of Hs EW as well as the D,,4000 are bimodal."," In red star-forming galaxies, the distributions of $_\delta$ EW as well as the $_n$ 4000 are bimodal."
" The KMM test prefers a 2-mode tit over a |-mode fit with ikelihood ratios of 78 and 84. for Hs EW and D,,4000 respectively. with zero probability for the null hypothesis in both cases."," The KMM test prefers a 2-mode fit over a 1-mode fit with likelihood ratios of 78 and 84, for $_\delta$ EW and $_n$ 4000 respectively, with zero probability for the null hypothesis in both cases."
 We also check whether this bimodality is a result of the hreshold chosen to define whether a galaxy is star-forming or not., We also check whether this bimodality is a result of the threshold chosen to define whether a galaxy is star-forming or not.
" As for the internal extinction. the KMM test results remain statistically significant. for both Hs EW and the D,, 4000. when he red star-forming galaxies are selected with an even higher SSFR threshold (log SFR/M* = —10 yr . showing that these results are not sensitive to how the four categories are chosen. within reasonable limits."," As for the internal extinction, the KMM test results remain statistically significant, for both $_\delta$ EW and the $_n$ 4000, when the red star-forming galaxies are selected with an even higher SSFR threshold (log $^*$ = –10 $^{-1}$ ), showing that these results are not sensitive to how the four categories are chosen, within reasonable limits."
" The above results become even more convincing when we plot the four different galaxy populations on the plane defined by the two indices D,, 4000 and EW(H;) (Fig. 7). Kauf", The above results become even more convincing when we plot the four different galaxy populations on the plane defined by the two indices $_n$ 4000 and $_\delta$ ) (Fig. \ref{hd-d4}) ).
fmannetal.(20038). have shown that these two indices taken together can very effectively determine the star formation history of a galaxy., \citet{kauff03a} have shown that these two indices taken together can very effectively determine the star formation history of a galaxy.
 As shown in Fig. 7.. ," As shown in Fig. \ref{hd-d4}, ,"
this indeed seem to be the case., this indeed seem to be the case.
 The blue star-forming and the passive. red sequence galaxies occupy the opposite ends of the space.," The blue star-forming and the passive, red sequence galaxies occupy the opposite ends of the space."
" But whilst the blue passive galaxies seem to follow the blue star-forming galaxies. although withsomewhat lower EW(H;) and higher D, 4000. the red"," But whilst the blue passive galaxies seem to follow the blue star-forming galaxies, although withsomewhat lower $_\delta$ ) and higher $_n$ 4000, the red"
free-free continuum emission.,free-free continuum emission.
" In terms of mass, these two YSOs represent only the tip of the iceberg, because the total mass of the associated cluster is dominated by (undetected) low-mass stars."," In terms of mass, these two YSOs represent only the tip of the iceberg, because the total mass of the associated cluster is dominated by (undetected) low-mass stars."
" Assuming e.g. a Miller Scalo (1979)) mass function, one can estimate the cluster mass from that of the most massive star."," Assuming e.g. a Miller Scalo \cite{milsc}) ) mass function, one can estimate the cluster mass from that of the most massive star."
 For this we can use the value of 20-25 ccomputed by Osorio et al. (2009)), For this we can use the value of 20–25 computed by Osorio et al. \cite{osor}) )
 from their model fit and obtain a total mass of the cluster of ~10?Μο., from their model fit and obtain a total mass of the cluster of $\sim10^3$.
. The same result is obtained by fixing the total luminosity of the cluster to the value of 2x10°Lo quoted by Osorio et al. (2009))., The same result is obtained by fixing the total luminosity of the cluster to the value of $2\times10^5~\Lsun$ quoted by Osorio et al. \cite{osor}) ).
" In all likelihood ~10? iis an upper limit to the real stellar mass, because the cluster mass function may be highly incomplete in such a small region."," In all likelihood $\sim10^3$ is an upper limit to the real stellar mass, because the cluster mass function may be highly incomplete in such a small region."
" However, this estimate indicates that the dynamical mass of ~330 Mo,, obtained from the fit in Fig. 13,,"," However, this estimate indicates that the dynamical mass of $\sim$ 330 obtained from the fit in Fig. \ref{fpvfit},"
" is probably dominated by the stellar mass, which would lend support to the application of Bertin Lodato (1999)) model to the case of G31.41."," is probably dominated by the stellar mass, which would lend support to the application of Bertin Lodato \cite{belo}) ) model to the case of G31.41."
" Finally, we note that the toroid interpretation is compatible with the hourglass-shaped morphology of the magnetic field (see Girart et al. 2009)),"," Finally, we note that the toroid interpretation is compatible with the hourglass-shaped morphology of the magnetic field (see Girart et al. \cite{gira}) ),"
 whose symmetry axis is directed SE- because the latter coincides with the rotation axis of the toroid.," whose symmetry axis is directed SE--NW, because the latter coincides with the rotation axis of the toroid."
" However, a caveat is in order."," However, a caveat is in order."
 Girart et al. (2009)), Girart et al. \cite{gira}) )
" find a significant correlation between rotation velocity and radius in the core, using different tracers."," find a significant correlation between rotation velocity and radius in the core, using different tracers."
" In particular, they conclude that in the region sampled by their observations (lying between —0755 and 1766), velocity increases with distance from the HMC center (see their Fig."," In particular, they conclude that in the region sampled by their observations (lying between $\sim$ 5 and 6), velocity increases with distance from the HMC center (see their Fig."
 4)., 4).
" This result seems inconsistent with our hypothesis that the core is undergoing pseudo-Keplerian rotation, because in this case the rotation velocity should decrease with radius."," This result seems inconsistent with our hypothesis that the core is undergoing pseudo-Keplerian rotation, because in this case the rotation velocity should decrease with radius."
 Perhaps this discrepancy can be explained by the presence of the magnetic field., Perhaps this discrepancy can be explained by the presence of the magnetic field.
" Higher angular resolution observations are needed to sample the velocity field inside the core and thus obtain a reliable, direct measurement of the rotation curve."," Higher angular resolution observations are needed to sample the velocity field inside the core and thus obtain a reliable, direct measurement of the rotation curve."
" The last aspect we will discuss in the context of the outflow/toroid controversy, is the double-peaked, *8-shaped"" structure observed in the K= 2mapatthesystemicvelocity(seeFig. 3))."," The last aspect we will discuss in the context of the outflow/toroid controversy, is the double-peaked, “8-shaped” structure observed in the $K$ =2 map at the systemic velocity (see Fig. \ref{fmapsd}) )."
"T he samemorpholog Was eepinlécanthelarga pla i.e.uptoexcitationenergiesof ~300 K, whereas the K=8 map (energy of 513 K) presents a single peak at the HMC center (Fig. 3))."," The same morphology is seen in all components up to $K$ =6, i.e. up to excitation energies of $\sim$ 300 K, whereas the $K$ =8 map (energy of 513 K) presents a single peak at the HMC center (Fig. \ref{fmapsd}) )."
 In Sect., In Sect.
 3.1 we interpreted these facts in terms of opacity and temperature gradients., \ref{score} we interpreted these facts in terms of opacity and temperature gradients.
" Indeed, BELOS found that the rrotational temperature peaks toward the HMC center and from the ratio between our aand ((12-11) K=2 data we calculate an optical depth at the peak of the line in the range 8-77 across the HMC."," Indeed, BEL05 found that the rotational temperature peaks toward the HMC center and from the ratio between our and (12–11) $K$ =2 data we calculate an optical depth at the peak of the line in the range 8–77 across the HMC."
" The interplay between opacity and temperature can explain the existence of a dip at the HMC center, but does not justify the lack of circular symmetry in the low-K maps."," The interplay between opacity and temperature can explain the existence of a dip at the HMC center, but does not justify the lack of circular symmetry in the $K$ maps."
" Here, we wish to find an explanation for the “8-shaped” feature and check whether this can better fit into the outflow or toroid model."," Here, we wish to find an explanation for the “8-shaped” feature and check whether this can better fit into the outflow or toroid model."
" As a basis for our discussion, in Fig."," As a basis for our discussion, in Fig."
 14 we present an overlay of the blue- and red-shifted K= 4emissiononthebulkemis sioninthe sameline., \ref{fhmc} we present an overlay of the blue- and red-shifted $K$ =4 emission on the bulk emission in the same line.
"Inthisway, oneiscompar withthelow— velocityemission."," In this way, one is comparing the high- with the low-velocity emission."
" In the outflow scenario, a naivve interpretation of this figure is that the high-velocity gas is leaking from the HMC through the axis of a “donut-like” structure seen edge-on, corresponding to the “8-shaped” feature in the map."," In the outflow scenario, a ve interpretation of this figure is that the high-velocity gas is leaking from the HMC through the axis of a “donut-like” structure seen edge-on, corresponding to the “8-shaped” feature in the map."
" In this case, the two peaks would coincide with the maxima of column density across the “donut”."," In this case, the two peaks would coincide with the maxima of column density across the “donut”."
" Albeit plausible, this interpretation o"," Albeit plausible, this interpretation has a problem."
"opacity should prevent the KCNdetection of two distinct peaks, because the line brightness is independent of column density."," The large opacity should prevent the detection of two distinct peaks, because the line brightness is independent of column density."
" Therefore, instead of the 8-shaped feature, one should see an elongated structure perpendicular to the bipolar outflow and peaking of it (1.e. at the HMC center)."," Therefore, instead of the 8-shaped feature, one should see an elongated structure perpendicular to the bipolar outflow and peaking of it (i.e. at the HMC center)."
 Explaining the presence of the 8-shaped structure appears to be a problem also in the toroid scenario., Explaining the presence of the 8-shaped structure appears to be a problem also in the toroid scenario.
" In fact, if the toroid is seen edge-on, the emission at the systemic velocity should peak in between the blue- and red-shifted emission."," In fact, if the toroid is seen edge-on, the emission at the systemic velocity should peak in between the blue- and red-shifted emission."
" However, if the toroid is inclined with respect to the line of sight, the nearest and farthest sides of it are seen displaced from one another on the plane of the sky,symmetrically displaced with respect to the center."," However, if the toroid is inclined with respect to the line of sight, the nearest and farthest sides of it are seen displaced from one another on the plane of the sky,symmetrically displaced with respect to the center."
" This is indeed what we see in Fig. 14,,"," This is indeed what we see in Fig. \ref{fhmc}, ,"
 where the, where the
It is not easy to compare our spectra of the INO with previous X-ray. spectral studies of (he nucleus NGC 3628. using theOSAT PSPC (Dahlem.Heckman&1995) or (Yaqoobetal.1995).. given the significant. variability of the INO and the much poorer spatial resolution of the earlier observations (TheROSAL PSPC spectrum covers a region 2'=5.8 kpe in radius. and the spectra a region 3’=8.7 kpe in radius).,"It is not easy to compare our spectra of the IXO with previous X-ray spectral studies of the nucleus NGC 3628, using the PSPC \citep{dahlem95} or \citep{yaqoob95}, given the significant variability of the IXO and the much poorer spatial resolution of the earlier observations (The PSPC spectrum covers a region $2\arcmin = 5.8$ kpc in radius, and the spectra a region $3\arcmin = 8.7$ kpc in radius)."
 The most detailed existing spectral study is that of Dahlem.Weaver&Heckman(1995).. who performed a joint spectral fit of the PSPC and spectra. taking into account the variability between (he two observations.," The most detailed existing spectral study is that of \citet{dwh98}, who performed a joint spectral fit of the PSPC and spectra, taking into account the variability between the two observations."
 This joint spectrum is best characterized by. two soft thermal components aud a hard absorbed power law., This joint spectrum is best characterized by two soft thermal components and a hard absorbed power law.
" The photon index and hydrogen column derived. for: the power law component (P=1.63wy0,53 and Ni-=92ix109emDa?) agree well with the Chandra-based power law fit to the emission from the INO.", The photon index and hydrogen column derived for the power law component $\Gamma = 1.63^{+0.14}_{-0.17}$ and $\nH = 9\pm{2} \times 10^{21} \pcmsq$ ) agree well with the -based power law fit to the emission from the IXO.
 The close agreement between tlie power law slopes may be fortuitous. as most of the haud X-ray counts in the ASCA spectrum must have been [rom other point sources in NGC 3628 and not from the INO itself," The close agreement between the power law slopes may be fortuitous, as most of the hard X-ray counts in the ASCA spectrum must have been from other point sources in NGC 3628 and not from the IXO itself."
 Even in its present state. which is several times more Iuminous than it was during the 1993 ASCA observations (see 5)). hard X-ray emission from sourcesother than the INO still provide a signilicant fraction (e33%)) of the 2.0 5.0 keV count rate in the central region of NGC: 3628.," Even in its present state, which is several times more luminous than it was during the 1993 ASCA observations (see \ref{sec:results:variability}) ), hard X-ray emission from sourcesother than the IXO still provide a significant fraction $\sim 33$ ) of the 2.0 – 8.0 keV count rate in the central region of NGC 3628."
 Within a 3’ radius region. theChandra observations reveal al least 33 other point-like X-ray sources. in addition to the diffuse thermal emission associated with the starburst.," Within a $3\arcmin$ radius region, the observations reveal at least 33 other point-like X-ray sources, in addition to the diffuse thermal emission associated with the starburst."
" We find that the INO only provides ~35% of the ACIS-S3 0.3. 8.0 keV οποιον band count rate within a radius of 3’ from the source,", We find that the IXO only provides $\sim35$ of the ACIS-S3 0.3 – 8.0 keV energy band count rate within a radius of $3\arcmin$ from the source.
 In the 2.0. 8.0 keV οποίον band the INO is more dominant. providing of the ACIS-53 counts.," In the 2.0 – 8.0 keV energy band the IXO is more dominant, providing of the ACIS-S3 counts,."
"significant, We estimate Chat these other point sources. along with the diffuse emission. account [or ~80430% of the total count rate (the main uncertainty is the uncertainty in ihe count rate (Yaqoobetal. 1995)))."," We estimate that these other point sources, along with the diffuse emission, account for $\sim 80\pm{30}$ of the total count rate (the main uncertainty is the uncertainty in the count rate \citep{yaqoob95}) )."
 As the INO. at the luminosity observed in December 2000. would produce ~90% of the total count rate itself. the INO must have been less luminous in 1993 than it is now.," As the IXO, at the luminosity observed in December 2000, would produce $\sim90$ of the total count rate itself, the IXO must have been less luminous in 1993 than it is now."
 The shape of the hard spectral component in (he jointROSAT PSPC and spectral fit was therefore lareely determined by the 30 or so other hard. X-ray point sources within the central 3’ of NGC 3623., The shape of the hard spectral component in the joint PSPC and spectral fit was therefore largely determined by the 30 or so other hard X-ray point sources within the central $3\arcmin$ of NGC 3628.
 It is worth noting that provides — (he same can not be so easily said for spectra of INOs. which are (vpically ol a region a few arceminutes in radius.," It is worth noting that provides — the same can not be so easily said for spectra of IXOs, which are typically of a region a few arcminutes in radius."
 The luninosity of these objects is very similar (ο that of the rest of the normal spiral or starburst galaxies they. inhabit., The luminosity of these objects is very similar to that of the rest of the normal spiral or starburst galaxies they inhabit.
 That contaminationof the spectra by unrelated. binary and diffuse N-rav. emission may bebiasing, That contaminationof the spectra by unrelated binary and diffuse X-ray emission may bebiasing
 For this reason. the observed. spectra. and. the pulse profiles of the Vela pulsar have been studied: extensively. before. the of Ferm? (Romani. 1996: Dyks. Harding Rudak. 2004: ‘Takata. Chang Shibata 2008).," For this reason, the observed spectra and the pulse profiles of the Vela pulsar have been studied extensively before the of $Fermi$ (Romani, 1996; Dyks, Harding Rudak, 2004; Takata, Chang Shibata 2008)."
 ‘Takata. Chang Shibata (2008) proposed that the component around 100MeV of the Vela pulsar. as well as Geminga (Takata Chang. 2009). is due to the svnchrotron radiation of the incoming particles in the outer gap.," Takata, Chang Shibata (2008) proposed that the component around 100MeV of the Vela pulsar, as well as Geminga (Takata Chang, 2009), is due to the synchrotron radiation of the incoming particles in the outer gap."
 By solving the evolution of the Lorentz factor and the piteh angle in the two-dimensional electrodynamices model (Takata. Shibata Llirotani. 2004). they found that the svnchrotron radiation of the incoming particles dominates the radiation arounc LO MeV. to LOOAIEY and the curvature radiation of the outgoing particles dominates the radiation around 16eV. Zhang Cheng (1997) proposed. a scll-sustained thick outer gap model of >-ray emission from the rotation-powered pulsar.p," By solving the evolution of the Lorentz factor and the pitch angle in the two-dimensional electrodynamics model (Takata, Shibata Hirotani, 2004), they found that the synchrotron radiation of the incoming particles dominates the radiation around 10 MeV to 100MeV and the curvature radiation of the outgoing particles dominates the radiation around 1GeV. Zhang Cheng (1997) proposed a self-sustained thick outer gap model of $\gamma$ -ray emission from the rotation-powered pulsar.,"
ulsars. inclucing Cieminga-like and. Vela-like pulsars., including Geminga-like and Vela-like pulsars.
 Also based on this clistribution of primary pairs. Zhang Cheng (2001) applied a three-dimensional pulsar magnetosphere model to explain the high-cnerey emission from the Cieminga. pulsar with a thick outer gap.," Also based on this distribution of primary pairs, Zhang Cheng (2001) applied a three-dimensional pulsar magnetosphere model to explain the high-energy emission from the Geminga pulsar with a thick outer gap."
 In this caleulation. the high-energv *- are produced by the accelerated particles with a power- enerey distribution via curvature radiation insidethe outer gap.," In this calculation, the high-energy $\gamma$ -rays are produced by the accelerated particles with a power-law energy distribution via curvature radiation insidethe outer gap."
 After the launch of Fermi LAT. the bottleneck of the research of high energv radiation from pulsar is broken.," After the launch of $Fermi$ LAT, the bottleneck of the research of high energy radiation from pulsar is broken."
 Just in one vear. this high-quality 5-ray. telescope has measured 46 *5-rav pulsars CXbdo et al.," Just in one year, this high-quality $\gamma$ -ray telescope has measured 46 $\gamma$ -ray pulsars (Abdo et al."
 20102)., 2010a).
 We developed a two-[aver model (Wang et al..," We developed a two-layer model (Wang et al.,"
 2010) to study the phase averaged spectra of the mature pulsars. including the Vela pulsar. in the first catalogue of ~-ray pulsars of Fermi.," 2010) to study the phase averaged spectra of the mature pulsars, including the Vela pulsar, in the first catalogue of $\gamma$ -ray pulsars of $Fermi$ ."
 In this simple two-dimensional model. the outer gap extending outwards," In this simple two-dimensional model, the outer gap extending outwards"
"As shown by the left two columns in Figure 5,, the profile of the WMAP55 ACL,(v) function is consistent with that expected for apositive-fwr.. In particular, both Δία and Δία, rebinned for FWHM=1°28 and 1°70, demonstrate consistent features with the solid lines shown in Figure 1 for far=+150.","As shown by the left two columns in Figure \ref{fig_dske_KQ75}, the profile of the 5 $\Delta \mathcal{L}_{a}(\nu)$ function is consistent with that expected for a. In particular, both $\Delta
\mathcal{L}_{d}$ and $\Delta \mathcal{L}_{a}$ , rebinned for $\rm{FWHM}=1\fdg28$ and $1\fdg70$, demonstrate consistent features with the solid lines shown in Figure \ref{fig_ske_fnl} for $f_{\rm
NL}= +150$."
" However, the troughs in the v>1 region (hot region) seem relatively less depressed."," However, the troughs in the $\nu>1$ region (hot region) seem relatively less depressed."
 It is likely that the point sources and foreground components contribute to this asymmetry between the two troughs., It is likely that the point sources and foreground components contribute to this asymmetry between the two troughs.
 The results from the median-filtered map yield insights implications into this issue., The results from the median-filtered map yield insights implications into this issue.
" We computed the x? values of AL, for both the observed and the simulated samples.", We computed the $\chi^2$ values of $\Delta \mathcal{L}_{a}$ for both the observed and the simulated samples.
 We list the fraction of the simulations with a x? values less extreme than the observed one in Table 3.., We list the fraction of the simulations with a $\chi^2$ values less extreme than the observed one in Table \ref{tab_Gfreq}.
 The corresponding WMAP11 results are also listed (Table 3 in Eriksenetal. (2004)))., The corresponding 1 results are also listed (Table 3 in \citet{Eriksen_etal_2004}) ).
" Generally speaking, there is no qualitative difference between the five-year and one-year results."," Generally speaking, there is no qualitative difference between the five-year and one-year results."
 But our results show a unimodal dependence on the smoothing scales., But our results show a unimodal dependence on the smoothing scales.
" The fu--signal seems more significant around the angular scales FWHM=1°28, 1°70 and 2°13."," The -signal seems more significant around the angular scales $\rm{FWHM}=1\fdg28$, $1\fdg70$ and $2\fdg13$."
 We applied the one-year KpOB mask used in Eriksenetal.(2004) in our analysis with all other operations remaining unchanged., We applied the one-year Kp0B mask used in \citet{Eriksen_etal_2004} in our analysis with all other operations remaining unchanged.
 We also create a new base-mask called ‘KQhybrid’ which excludes the same Galactic plane with KQ75B but handles the six extended sources (Figure 3)) identically to Kp0B. The KQhybrid mask is then included in the data processing too as an independent test., We also create a new base-mask called `KQhybrid' which excludes the same Galactic plane with KQ75B but handles the six extended sources (Figure \ref{fig_base_mask}) ) identically to Kp0B. The KQhybrid mask is then included in the data processing too as an independent test.
 Some of the results are shown in Figure 6 and the right column of Figure 7.., Some of the results are shown in Figure \ref{fig_dske_KPQ0} and the right column of Figure \ref{fig_syseff}.
" In general, the AL. profiles of the Kp0B processing are generally consistent with the previous WMAP11 results, although the peak-trough structure is not identical in detail."," In general, the $\Delta \mathcal{L}_{a}$ profiles of the Kp0B processing are generally consistent with the previous 1 results, although the peak-trough structure is not identical in detail."
 The KQhybrid mask yields a consistent set of results with those of KQ75B as shown in Figure 6.., The KQhybrid mask yields a consistent set of results with those of KQ75B as shown in Figure \ref{fig_dske_KPQ0}.
" Moreover, we have applied the KQ75B mask to the WMAP11 data and found that the results (dashed grey line in the left column of Figure 7)) show a similar discrepancy from the Kp0B processed ones and consistency with results from our 5-year VW data processing."," Moreover, we have applied the KQ75B mask to the 1 data and found that the results (dashed grey line in the left column of Figure \ref{fig_syseff}) ) show a similar discrepancy from the Kp0B processed ones and consistency with results from our 5-year VW data processing."
 This indicates that modifications of the mask do significantly affect the skeleton estimation in the WMAP11 analysis., This indicates that modifications of the mask do significantly affect the skeleton estimation in the 1 analysis.
" Although the reason can be easily found by examining the area ratio of the dark-grey regions in Figure 3,, it is important to make a separate investigation on the impact of residual Galactic foreground and extragalactic sources since aanalysis exhibits different responses to different types of foreground contamination (Cabellaetal.2010)."," Although the reason can be easily found by examining the area ratio of the dark-grey regions in Figure \ref{fig_base_mask}, it is important to make a separate investigation on the impact of residual Galactic foreground and extragalactic sources since analysis exhibits different responses to different types of foreground contamination \citep{Cabella_etal_2010}."
. This separate analysis motivates future skeleton studies on the effects of different Galactic foreground templates., This separate analysis motivates future skeleton studies on the effects of different Galactic foreground templates.
It is noteworthy that the skeleton discrepancies caused by base-mask selection indicate that residual Galactic foregrounds bias the non-Gaussian analyses for WMAP11,It is noteworthy that the skeleton discrepancies caused by base-mask selection indicate that residual Galactic foregrounds bias the non-Gaussian analyses for 1
"Maps are obtained from the timelines for each AOR via the HCSS ‘photProject’ projection algorithm, which is equivalent to a simplified version of the ‘drizzle’ method (Fruchter Hook 2002).","Maps are obtained from the timelines for each AOR via the HCSS `photProject' projection algorithm, which is equivalent to a simplified version of the `drizzle' method (Fruchter Hook \cite{fruchter02}) )."
" Given the high data redundancy in the deep fields, PSF widths and noise correlation in the final map can be reduced choosing smaller projection drops than the physical PACS pixel size."," Given the high data redundancy in the deep fields, PSF widths and noise correlation in the final map can be reduced choosing smaller projection drops than the physical PACS pixel size."
" Drop sizes between 1/8 and 1/4 of the physical PACS pixel size were used, depending on redundancy of the individual maps for each field."," Drop sizes between 1/8 and 1/4 of the physical PACS pixel size were used, depending on redundancy of the individual maps for each field."
 Weights of the different detectors in the projection consider the inverse variance derived from the noise in the dataset itself., Weights of the different detectors in the projection consider the inverse variance derived from the noise in the dataset itself.
" Maps from each AOR were coadded into final maps, weighting the indivudal maps by the effective exposure of each pixel."," Maps from each AOR were coadded into final maps, weighting the indivudal maps by the effective exposure of each pixel."
 The final error map was computed as the standard deviation of the weighted mean., The final error map was computed as the standard deviation of the weighted mean.
 PSF fitting using the methods described in Sect., PSF fitting using the methods described in Sect.
 4.2 assumes errors that are uncorrelated neighbouring pixels., \ref{sect:extract} assumes errors that are uncorrelated between neighbouring pixels.
" In practice, correlations exist due 19 between and due fo to the correlations that are caused by residual Projection1/f noise in the filtered timelines, in particular along the scan direction."," In practice, correlations exist due to projection and due to to the correlations that are caused by residual 1/f noise in the filtered timelines, in particular along the scan direction."
" We have verified that, because of the high redundancy of the data, these correlations are close to uniform across the final map, with less than variation on the correction factor that is derived below."," We have verified that, because of the high redundancy of the data, these correlations are close to uniform across the final map, with less than variation on the correction factor that is derived below."
 Thus we derived from PSF shape and correlation information a mean correlation Correction factor which was then for in the errorson the extracted fluxes., Thus we derived from PSF shape and correlation information a mean correlation correction factor which was then accounted for in the errors on the extracted fluxes.
" A correlation map is accountedconstructed, starting"," A correlation map is constructed, starting"
Iu Figure { we report the results.,In Figure \ref{fig:CRbound} we report the results.
 It is evident how the variance of cach cocficicut flattens to the CR lit as the umber of iterations of the adaptive aleorithii increases., It is evident how the variance of each coefficient flattens to the CR limit as the number of iterations of the adaptive algorithm increases.
 After one minute of data input. the variance of the coeficicuts has already reached the CR bound.," After one minute of data input, the variance of the coefficients has already reached the CR bound."
 Therefore we couchide that the LSL estimator is an cficicnt onc., Therefore we conclude that the LSL estimator is an efficient one.
 We have shown that if is possible to model a noise spectrum with complex features like those relevant for the VIRGO experiment by parameterizing it iu ternis of a siuall uunuboer of parameters., We have shown that it is possible to model a noise spectrum with complex features like those relevant for the VIRGO experiment by parameterizing it in terms of a small number of parameters.
 We have tested some adaptive aleorithius which are able to ft ou liue the parameters of an autorceressive represeutation of the WEIRGO-like spectrum., We have tested some adaptive algorithms which are able to fit on line the parameters of an autoregressive representation of the -like spectrum.
to (hat of a rigid rotor.,to that of a rigid rotor.
 The shear is maximized near r0.342A4. as opposed to the true Keplerian case where (he shear remains unbounded as (he origin is approached.," The shear is maximized near $r\simeq 0.342 R_0$, as opposed to the true Keplerian case where the shear remains unbounded as the origin is approached."
 The density is taken to be constant (we shall examine the effects of varving clensity beow)., The density is taken to be constant (we shall examine the effects of varying density below).
 We normalize frequencies to the central rotation Irequency. Q9. and lengths to the fidi‘dal radius 1).," We normalize frequencies to the central rotation frequency $\Omega_0$, and lengths to the fiducial radius $R_0$."
" The density and magnetic field are normalized such that DV=O, lor οί jormalized)-1.", The density and magnetic field are normalized such that $v_A R_0^{-1}= \Omega_0$ for $v_A$ (normalized)=1.
 The effective potential for this profile is shown in Figure 3. [or ἰhree values of the erowlh rate 5. and for κ.=1l.ey.25.," The effective potential for this profile is shown in Figure \ref{effpotkep1} for three values of the growth rate $\gamma$, and for $k_z = 1,\ v_A = .25$."
 Modes with more rapid radial oscillation have smaller growth rates this corresponds to a deeper potential well., Modes with more rapid radial oscillation have smaller growth rates– this corresponds to a deeper potential well.
 When the well is very deep. the racial wavelength is small. and a local treatment becomes valid. but only near the bottom of the well.," When the well is very deep, the radial wavelength is small, and a local treatment becomes valid, but only near the bottom of the well."
 The most unstable mode has no nodes (η=0)., The most unstable mode has no nodes $n=0$ ).
 Although the local criterion for instability can be satisfied al some radii lor larger growth rales. no elgenmocles exist with these larger growth rates which satisfy the evanescent boundary conditions.," Although the local criterion for instability can be satisfied at some radii for larger growth rates, no eigenmodes exist with these larger growth rates which satisfy the evanescent boundary conditions."
"even for the extreme (and very artificial) cases of the time profiles c (gradual rise over 2/444. sharp decay) and d (sharp rise. gradual decay over 2/4,) illustrated here.","even for the extreme (and very artificial) cases of the time profiles c (gradual rise over $2 \, t_{\rm dyn}$, sharp decay) and d (sharp rise, gradual decay over $2 \, t_{\rm dyn}$ ) illustrated here."
 Its influence is basically restricted to the fIux-rise portion of the HID track and to photon energies below the svuchrotron eut-off. where the local spectra tend to be harder for Gime profiles with maxima closer to the onset of the flare.," Its influence is basically restricted to the flux-rise portion of the HID track and to photon energies below the synchrotron cut-off, where the local spectra tend to be harder for time profiles with maxima closer to the onset of the flare."
 The HID (racks for all our test cases show almost identical spectral inclices at the time of maximum flux., The HID tracks for all our test cases show almost identical spectral indices at the time of maximum flux.
 At the low-energy end of the electron spectra. particles cooling down from higher energies will either accumulate and build up a.7 power-law spectrum αἱ energies below 4. or escape. depending on the value of the escape time scale parameter jj.," At the low-energy end of the electron spectra, particles cooling down from higher energies will either accumulate and build up a $\gamma^{-2}$ power-law spectrum at energies below $\gamma_1$, or escape, depending on the value of the escape time scale parameter $\eta$."
 We can define a critical escape parameter for which the escape time scale for electrons al energy 24 equals the svnchrotron cooling lime scale., We can define a critical escape parameter for which the escape time scale for electrons at energy $\gamma_1$ equals the synchrotron cooling time scale.
 For op<a. the electron distribution will maintain a sharp low-energy cutoff al 1. while for 2»na. a -2 low-energy power law will develop.," For $\eta \le \eta_{\rm cr}$, the electron distribution will maintain a sharp low-energy cutoff at $\gamma_1$, while for $\eta \gg \eta_{\rm cr}$, a -2 low-energy power law will develop."
 In order to investigate whether our choice of —10 has a significant impact on our results. we have done test simulations with jj=3 and η=30. respectively.," In order to investigate whether our choice of $\eta = 10$ has a significant impact on our results, we have done test simulations with $\eta = 3$ and $\eta = 30$, respectively."
 We find all relevant aspects the time-averaged spectra. the monoenereelic lisht curves. aud the spectral hysteresis curves — (o be virtually independent of η within reasonable bounds.," We find all relevant aspects — the time-averaged spectra, the monoenergetic light curves, and the spectral hysteresis curves — to be virtually independent of $\eta$ within reasonable bounds."
 In the previous subsections. we have discussed the impact of various parameters on the broadband SED and the X-ray. variability characteristics of models for intermeciate and peaked BL Lac objects.," In the previous subsections, we have discussed the impact of various parameters on the broadband SED and the X-ray variability characteristics of models for intermediate and low-frequency peaked BL Lac objects."
 There are still a few more parameters left which we have fixecl in our suite of test simulations., There are still a few more parameters left which we have fixed in our suite of test simulations.
" In particular. the choice of the eutolls of the electron distribution. 54 and 55. the magnetic-lield equiparliGon parameter eg. the Doppler factor D. aud the size of the emitüng region. /2,. may have an impact on (he spectral variability characteristics."," In particular, the choice of the cutoffs of the electron distribution, $\gamma_1$ and $\gamma_2$ the magnetic-field equipartition parameter $\epsilon_B$, the Doppler factor $D$, and the size of the emitting region, $R_b$, may have an impact on the spectral variability characteristics."
 Llowever. (hose parameters can generally be constrained rather well through (he observed overall spectral characteristics. and through variability (nme scale considerations (see. e.g..Tavecchio.Maraschi.&Ghisellini(1998):Costamante (2002))).," However, those parameters can generally be constrained rather well through the observed overall spectral characteristics, and through variability time scale considerations (see, e.g.,\cite{tmg98,cg02}) )."
 The, The
"Consolidating the dependence of NV, on the various parameters. we finally arrive at. where dy = d,(Lo.dy.η. 0).","Consolidating the dependence of $N_{p}$ on the various parameters, we finally arrive at, where $d_0$ = $d_{max}(L_{0},R_{0},a_{0},r_{0},0)$ ."
 That is. dy is the clistance out to which a planet-star svslem wilh ¢=90° and the fiducial parameters Lo.Ry.dy.ry can just barely be detected al the S/N threshold.," That is, $d_{0}$ is the distance out to which a planet-star system with $i = 90^{\circ}$ and the fiducial parameters $L_{0}, R_{0}, a_{0}, r_{0}$ can just barely be detected at the S/N threshold."
" We now seek to simply equation (6)) bx integrating over the local stellar population ad fixecl absolute magnitude. M.and so we replace the three independent variables (η.R.L) by the single variable ή,"," We now seek to simplify equation \ref{equfin}) ) by integrating over the local stellar population at fixed absolute magnitude, $M_V$,and so we replace the three independent variables $(n,R,L)$ by the single variable $M_V$."
 We consider (wo regimes AM:>6 and M:x6 (with one overlapping bin at AA=6. whieh we will use later to check [or consistency).," We consider two regimes $M_V \geq 6$ and $M_V \leq 6$ (with one overlapping bin at $M_V = 6$, which we will use later to check for consistency)."
 We first treat the fainter regime., We first treat the fainter regime.
 Here. (he main sequence is relatively narrow.," Here, the main sequence is relatively narrow."
 Hence. Ho maw be regarded. as a funcüon of L. (ancl so. therefore. of Ady). while » is simply the number density of stars in a given magnitude bin.," Hence, $R$ may be regarded as a function of $L$ (and so, therefore, of $M_V$ ), while $n$ is simply the number density of stars in a given magnitude bin."
 Hence. the “integration” amounts (o a simple multiplication of factors.," Hence, the “integration” amounts to a simple multiplication of factors."
 We adapt the number density of stars » [rom the empirically determined local stellar luminosity function (LE): for the range (9 < Ady; x 18) we use the LE reported in (2001).. and for the range (6 < M: <8) we use the LF of Bessell&Stringfellow(1993).," We adapt the number density of stars $n$ from the empirically determined local stellar luminosity function (LF): for the range (9 $\leq$ $M_{V}$ $\leq$ 18) we use the LF reported in \citet{zheng01}, , and for the range (6 $\leq$ $M_{V}$ $\leq$ 8) we use the LF of \citet{bessell93}."
. To estimate stellar radii. we combine the linear color-magnitude relation. I1)2-2.89 from Reid (1991).. a color/surlace-brightness relation )—0.2ÀA4.. based on the data of vanBelle(1999).. and V£A. color-color relations for cbwarls fromBessell&Brett(1955).," To estimate stellar radii, we combine the linear color-magnitude relation, $M_{V} = 3.37(V - I) + 2.89$ from \citet{reid91}, , a color/surface-brightness relation $\log (R/R_{\odot}) = 0.69 \, + \, 0.2226(V-K) - 0.2M_{V}$ , based on the data of \citet{belle99}, and $VIK$ color-color relations for dwarfs from\citet{bessell88}."
 We can therefore calculate the relative number of svstems with a [fixed à and ras afunction of My. which we designate where ny.Lo. and fy are the normalizations chosen below.," We can therefore calculate the relative number of systems with a fixed $a$ and $r$ as afunction of $M_{V}$, which we designate where $n_{0}, L_{0},$ and $R_{0}$ are the normalizations chosen below."
 For the upper main sequence. M:x6. we evaluate F(M4) directly using theHipparcos catalog (ESA 1997)..," For the upper main sequence, $M_V \leq 6$, we evaluate $F(M_V)$ directly using theHipparcos catalog \citep{hip97}. ."
 For example. the LF for Mq=4 would be computed by summing So[(4/3)7D4)! over all stars within theHipparcos completeness limit. V.< 7.3. having 3.5<My 4.5. and ης within 50 pe.," For example, the LF for $M_V=4$ would be computed by summing $\sum_i [(4/3) \pi D_i^3]^{-1}$ over all stars within theHipparcos completeness limit, $V < 7.3$ , having $3.5 <M_V <4.5$ , and lying within 50 pc."
 The distance D; is theminimum of 50 pc and, The distance $D_i$ is theminimum of 50 pc and
The data were analysed using the analysis package XMMSAS version 8.0.0.,The data were analysed using the analysis package XMMSAS version 8.0.0.
 After removal of intervals with high background activity. we obtained a net exposure time of 17.3 ks (EPIC-PN).," After removal of intervals with high background activity, we obtained a net exposure time of 17.3 ks (EPIC-PN)."
" For morphology studies in comparisor with continuum and optical images EEPIC images were produced in the standard energy bands 0.2-0.5 keV. 0.5-1.0 keV. 1.0-2.0 keV and 2.0—4.5 keV. The images show faint diffuse emission at the position of the SNR and a point-like source near its centre at RA(2000)2528|7.9*. ((statistical error1"".. systematic uncertainty ))."," For morphology studies in comparison with radio-continuum and optical images EPIC images were produced in the standard energy bands $-$ 0.5 keV, $-$ 1.0 keV, $-$ 2.0 keV and $-$ 4.5 keV. The images show faint diffuse emission at the position of the SNR and a point-like source near its centre at $^h$ $^m$ $^s$, (statistical error, systematic uncertainty )."
 To investigate 1f the point-like source ts related to the SNR we extracted spectra for both sources separately., To investigate if the point-like source is related to the SNR we extracted spectra for both sources separately.
 For the like source we used a circular extraction region with rradius., For the point-like source we used a circular extraction region with radius.
" For the SNR the outer radius of the extraction region (centre at RA(J2000)=5""28"" 19.8"". 114/21) was100"".. excluding a circle around the point- source with radius25""."," For the SNR the outer radius of the extraction region (centre at $^h$ $^m$ $^s$, ) was, excluding a circle around the point-like source with radius."
. EPIC X-ray spectra were extracted for PN (single + double pixel events. corresponding to a PATTERN 0-4 selection) and MOS (PATTERN 0-12). excluding bad CCD pixels and columns (FLAG 0).," EPIC X-ray spectra were extracted for PN (single + double pixel events, corresponding to a PATTERN $-$ 4 selection) and MOS (PATTERN $-$ 12), excluding bad CCD pixels and columns (FLAG 0)."
 We used version 12.5.1 for spectral modelling., We used version 12.5.1 for spectral modelling.
 were fitted simultaneously. allowing only a renormalisation factor to account for cross-calibratior uncertainties. between the instruments and area losses for the MOS extraction as the region covered by the SNR is near the edge of the inner MOS CCD in both cameras.," were fitted simultaneously, allowing only a renormalisation factor to account for cross-calibration uncertainties between the instruments and area losses for the MOS extraction as the region covered by the SNR is near the edge of the inner MOS CCD in both cameras."
 To account for photo-electric absorption by interstellar gas. two hydrogen column densities were used.," To account for photo-electric absorption by interstellar gas, two hydrogen column densities were used."
 The first represents the foreground absorption in the Milky Way. fixed at assuming elemental abundances of ?..," The first represents the foreground absorption in the Milky Way, fixed at assuming elemental abundances of \citet{2000ApJ...542..914W}."
 The second considers the absorption in the LMC (withmetalabundancessetto0.5solarastypicaloftheLMC: ?).., The second considers the absorption in the LMC \citep[with metal abundances set to 0.5 solar as typical of the LMC; ][]{1992ApJ...384..508R}.
 The statistical quality of the spectra was sufficient to fit one-component thermal plasma emission models., The statistical quality of the spectra was sufficient to fit one-component thermal plasma emission models.
 For the supernova remnant we used a single-temperature non-equilibrium ionisation collisional plasma (NEI) model (inXSPEC.see?.andreferencestherein) with metal abundances fixed to 0.5 solar. yielding acceptable y values.," For the supernova remnant we used a single-temperature non-equilibrium ionisation collisional plasma (NEI) model \citep[in XSPEC, see][and references therein]{2001ApJ...548..820B} with metal abundances fixed to 0.5 solar, yielding acceptable $\chi^2$ values."
 Results from similar modelling of X-ray spectra from SNRs in the SMC were published by ? and ?.. allowing direct comparison.," Results from similar modelling of X-ray spectra from SNRs in the SMC were published by \citet{2004A&A...421.1031V} and \citet{2008A&A...485...63F}, allowing direct comparison."
 The Magellanic Cloud Emission Line Survey (MCELS) was carried out from the 0.6 m University of Michigan/CTIO Curtis Schmidt telescope. equipped with a SITE 2048x CCCD. which gave a field of aat à scale of .ppixel!.," The Magellanic Cloud Emission Line Survey (MCELS) was carried out from the 0.6 m University of Michigan/CTIO Curtis Schmidt telescope, equipped with a SITE $2048 \times 2048$ CCD, which gave a field of at a scale of $^{-1}$."
 Both the LMC and SMC were mapped in narrow bands corresponding toHa... (6125007 AA)). and ((126716. AA)). plus matched red and green continuum bands that are used primarily to subtract most of the stars from the images to reveal the full extent of the faint diffuse emission.," Both the LMC and SMC were mapped in narrow bands corresponding to, $\lambda$ ), and $\lambda$ ), plus matched red and green continuum bands that are used primarily to subtract most of the stars from the images to reveal the full extent of the faint diffuse emission."
 All the data have been flux-calibrated and assembled into mosaic images. a small section of which is shown in Fig. 5..," All the data have been flux-calibrated and assembled into mosaic images, a small section of which is shown in Fig. \ref{fig-opt}."
 Further details regarding the MCELS are given by ?.. Winkler et al. (," Further details regarding the MCELS are given by \citet{2006NOAONL.85..6S}, Winkler et al. ("
"in preparation) and at http://www.ctio.noao.edu/meels/. Additional observations were attempted on 25"""" September 2009. using the 1.9-meter telescope and Cassegrain spectrograph at the South African Astronomical Observatory (SAAO) in Sutherland.","in preparation) and at http://www.ctio.noao.edu/mcels/. Additional observations were attempted on $^\mathrm{th}$ September 2009, using the 1.9-meter telescope and Cassegrain spectrograph at the South African Astronomical Observatory (SAAO) in Sutherland."
 While the observing conditions were good. we did not detect any emission fromJ0528-6714.," While the observing conditions were good, we did not detect any emission from."
". The remnant has a cieular appearance centered at RA(Q2000)25""28""18.5*. wwith a diameter of 216745” ((52.441.0 pe)."," The remnant has a circular appearance centered at $^h$ $^m$ $^s$, with a diameter of $\pm$ $\pm$ 1.0 pc)."
 This is reasonably consistent with its X-ray extent as indicated in Fig., This is reasonably consistent with its X-ray extent as indicated in Fig.
 4 where the 30 radio-continuum contour is drawn on an X-ray image., \ref{fig-xray-radio} where the $\sigma$ radio-continuum contour is drawn on an X-ray image.
 The point-like ray source is located very close to the centre of the radio emission while the X-ray emission is brighter on the south-eastern side., The point-like X-ray source is located very close to the centre of the radio emission while the X-ray emission is brighter on the south-eastern side.
 A flux density measurement was made at 6 em. resulting in a value of 69+5 mJy (Table 1)).," A flux density measurement was made at 6 cm, resulting in a value of $69\pm5$ mJy (Table \ref{tab-flux}) )."
 Using the 20cem mosaic image described in ?.. we made a new estimate of the flux density ofJ0528-6714.. with a value of 122+5 mly.," Using the cm mosaic image described in \citet{2007MNRAS.382..543H}, we made a new estimate of the flux density of, with a value of $122\pm5$ mJy."
" A spectral index (defined as $o v"") using the flux densities in Table | is estimated to @=—0.3640.09 (Fig. 2))."," A spectral index (defined as $S\propto\nu^\alpha$ ) using the flux densities in Table \ref{tab-flux} is estimated to $\alpha$ $\pm$ 0.09 (Fig. \ref{fig-radspec}) ),"
 which is indicative of older SNRs (?).., which is indicative of older SNRs \citep{1998A&AS..130..421F}.
 We note that the 36cem and 6cem observations are only interferometer measurements. whereas the cem observations consist of both single dish and interferometer measurements.," We note that the cm and cm observations are only interferometer measurements, whereas the cm observations consist of both single dish and interferometer measurements."
 This could lead to a flux density underestimate at these two wavelengths., This could lead to a flux density underestimate at these two wavelengths.
 Previous spectral index estimates were based solely on single dish data. (αξ--0.7920.15:; ?).," Previous spectral index estimates were based solely on single dish data, \citep[\protect{$\alpha$=--0.79$\pm$0.15}; ."
 We note that this is a highly confused region. and that as our new estimate uses higher resolution data than ?.. we have been able to exclude the confusing sources from the spectral index estimate.," We note that this is a highly confused region, and that as our new estimate uses higher resolution data than \citet{1998A&AS..130..421F}, we have been able to exclude the confusing sources from the spectral index estimate."
 Linear polarization images at 6cem were created using stokes and parameters., Linear polarization images at cm were created using stokes and parameters.
 This image reveals regions of moderate and somewhat irregular polarisation within the SNR., This image reveals regions of moderate and somewhat irregular polarisation within the SNR.
 Without reliable polarisation measurements at a second, Without reliable polarisation measurements at a second
Tn all the previous cases equation (15) gives us a uonlinear I order differential equation for the $-depeudeut paraueter. with the initial conditious eiven bw the equation (11).,"In all the previous cases equation (15) gives us a nonlinear I order differential equation for the $\Phi$ -dependent parameter, with the initial conditions given by the equation (14)."
 We consider always Ar=10041. aud Afp=04M. since the depeudeuce on these parameters is negligible., We consider always $M_U=100M_{\odot}$ and $M_L=0.1M_{\odot}$ since the dependence on these parameters is negligible.
 The function M(d) in the first case considered is shown in Fie., The function $M(\Phi)$ in the first case considered is shown in Fig.
 3., 3.
 At the initia time ($= 0) the mass AM increases by increasing the slope at low mass cud., At the initial time $\Phi=0$ ) the mass $M$ increases by increasing the slope at low mass end.
 Iu particular when wy0.2 A/(0)~LOOAL..=Mr and therefore there is no solution for 4 exeater than 0.2., In particular when $x_1=0.2$ $M(0)\simeq 100M_{\odot}=M_U$ and therefore there is no solution for $x_1$ greater than $0.2$.
 Fie., Fig.
 E shows the slope at the low mass end (ry (903) for values of M in the range 2LOAL..., 4 shows the slope at the low mass end $x_1(\Phi)$ ) for values of $M$ in the range $2-10 M_{\odot}$.
 The initial values of wy are always negative aud moreover they merease bv increasing AL. as expected.," The initial values of $x_1$ are always negative and moreover they increase by increasing $M$, as expected."
 Finally Fig., Finally Fig.
 5 shows the results for the third case considered., 5 shows the results for the third case considered.
 Tere the mass AL is chosen in order to reproduce a final slope 1.2=1.35., Here the mass $M$ is chosen in order to reproduce a final slope $x_2=1.35$.
 Both the proposed IMES cau reproduce the observed C-dwarf distribution aud therefore we want to test the validity of the inferred IME by using nuuerncal models of galactic chemical evolution., Both the proposed IMFs can reproduce the observed G-dwarf distribution and therefore we want to test the validity of the inferred IMF by using numerical models of galactic chemical evolution.
 This can be done by studving the effect of the above IMEs ou the chemical evolution of the solar ucighbourhood., This can be done by studying the effect of the above IMFs on the chemical evolution of the solar neighbourhood.
 The model used is that of Matteucci and Francois (1989) where a detailed description can be found., The model used is that of Matteucci and Francois (1989) where a detailed description can be found.
 The main difference with that model is that we assmne here a very rapid formation of cither the halo aud the disk thus simulating a closed, The main difference with that model is that we assume here a very rapid formation of either the halo and the disk thus simulating a closed
For a non-evolving population. virtually. all the radio sources lic above our optical limit at 2<0.35.,"For a non-evolving population, virtually all the radio sources lie above our optical limit at $z\leq 0.35$."
 In other words. if we regard. our sample as a purely racio flux limited sample. then we can be confident of very high completeness to the radio tux limit.," In other words, if we regard our sample as a purely radio flux limited sample, then we can be confident of very high completeness to the radio flux limit."
 Rowan-Robinson demonstrated that luminosity evolution of the same strength as required for LAS galaxies Lí(=L(2OL|zy was sullicient to explain the sub-m.Jy. radio counts., Rowan-Robinson demonstrated that luminosity evolution of the same strength as required for IRAS galaxies $L(z)=L(z=0)(1+z)^{3.1}$ was sufficient to explain the sub-mJy radio counts.
 Such a pure luminosity evolution is equivalent to a large negative radio A-correction term. and the corrected. positions in Figure 2. also demonstrate a high completeness.," Such a pure luminosity evolution is equivalent to a large negative radio $K$ -correction term, and the corrected positions in Figure \ref{fig:optrad} also demonstrate a high completeness."
 We can quantify this by using the racio-optical correlation to estimate the incompleteness as a function of redshift. then use the observed recshilt clistribution to get a first-order estimate of the overall incompleteness: where f is the completeness. INGthe size of the star-burst sample. & is 1 over the fraction of the racdio-optical correlation above the optical Dux απ! as a function of redshift and. luminositv.. Lui; is the faintest raclio luminosity observable at rectshilt cy. and the sum ds performed. over the star-burst sample.," We can quantify this by using the radio-optical correlation to estimate the incompleteness as a function of redshift, then use the observed redshift distribution to get a first-order estimate of the overall incompleteness: where $f$ is the completeness, $N_{\rm obs}$the size of the star-burst sample, $k$ is $1$ over the fraction of the radio-optical correlation above the optical flux limit as a function of redshift and luminosity, $L_{{\rm min},i}$ is the faintest radio luminosity observable at redshift $z_i$, and the sum is performed over the star-burst sample."
 Phe D93 sample does appear to have a slightly larger. dispersion in the radio-optical plane han the local sample. but this larger scatter still vields 96.7*4 completeness.," The B93 sample does appear to have a slightly larger dispersion in the radio-optical plane than the local sample, but this larger scatter still yields $96.7\%$ completeness."
 We conservatively assume no passive stellar evolution. the effect of which would » to increase our completeness. further. still," We conservatively assume no passive stellar evolution, the effect of which would be to increase our completeness further still."
" Ν.Ο. js measure of 7completeness"" is not the same as wt described in Equation 4..", N.B. this measure of “completeness” is not the same as that described in Equation \ref{eqn:compl}.
 Phe assertion that the ptical selection does not have a significant additional impact on the radio selection is consistant with 1e findings from deep optical observations of the p»larano Field (Ciruppioni in preparation) that 1e faintest optical identifications of Μαιν racio sources do not appear to be star-burst galaxies., The assertion that the optical selection does not have a significant additional impact on the radio selection is consistant with the findings from deep optical observations of the Marano Field (Gruppioni in preparation) that the faintest optical identifications of sub-mJy radio sources do not appear to be star-burst galaxies.
 The luminosity function is plotted in Figure 3.. which agrees with the calculation in ltowan-lItobinson ct al. (," The luminosity function is plotted in Figure \ref{fig:radlf}, which agrees with the calculation in Rowan-Robinson et al. ("
1993).,1993).
 It is clear from Figure 3. that the faint end of the luminosity function is not well-constrained by this sample., It is clear from Figure \ref{fig:radlf} that the faint end of the luminosity function is not well-constrained by this sample.
 This is due to the small volume at low recshilt of this sample., This is due to the small volume at low redshift of this sample.
" For z«0.05 (where the limiting radio luminosity is £=l.lLethFW+ the BOS sample covers only 2700-47Mpc"". and using the 890 ""warm"" Luminosity Function we would only expect 1.75 galaxies within this volume."," For $z<0.05$ (where the limiting radio luminosity is $L=1.1\times 10^{21} h_{50}^{-2}{\rm WHz}^{-1}$ the B93 sample covers only $2700 h_{50}^{-3}Mpc^{3}$, and using the S90 “warm” luminosity function we would only expect 1.75 galaxies within this volume."
 This small volume at low redshifts is also very susceptible to large scale structure variations., This small volume at low redshifts is also very susceptible to large scale structure variations.
 Assuming the power spectrum of Peacock and. Dodds (1994) we would expect IMS density. Duetuations of around 60 to 60 per cent over such a volume (allowing for the survey being spilt into three)., Assuming the power spectrum of Peacock and Dodds (1994) we would expect RMS density fluctuations of around 60 to 60 per cent over such a volume (allowing for the survey being spilt into three).
 The co-moving number densities are consistent with the single. starburst at 2<0.35. detected in the Hubble. Deep Field. Richards et al., The co-moving number densities are consistent with the single star-burst at $z<0.35$ detected in the Hubble Deep Field (Richards et al.
 1998). as well as with the luminosity function. from the <0.35 Marano star-bursts (Gruppiont ct al 1998. in preparation).," 1998), as well as with the luminosity function from the $z<0.35$ Marano star-bursts (Gruppioni et al 1998, in preparation)."
 This data is however in strong disagreement with the verv high. star-burst. density claimed. in the mücro-Jansky radio population by Windhorst et al. (, This data is however in strong disagreement with the very high star-burst density claimed in the micro-Jansky radio population by Windhorst et al. (
1995),1995).
 Figure5 3. 1plots the z«0.35 Windhorst et al., Figure \ref{fig:radlf} plots the $z<0.35$ Windhorst et al.
 star-bursts. which have an order of magnitude higher space density than our estimate.," star-bursts, which have an order of magnitude higher space density than our estimate."
 The nature of the (Jy. population is controversial however. with Hammer et al. (," The nature of the $\mu$ Jy population is controversial however, with Hammer et al. ("
1995) claiming the population is dominated by weak AGN. albeit in a sky area which may be biased by the presence of a cluster.,"1995) claiming the population is dominated by weak AGN, albeit in a sky area which may be biased by the presence of a cluster."
 Part of the cliscrepaney may. also be due to high frequeney (58.5 111) selection in both the Hammer and Windhorst samples. where the radio spectral index may not be steep due to the flat-spectrum contributions from. Hail regions and. possibly ACN.," Part of the discrepancy may also be due to high frequency $5-8.5$ GHz) selection in both the Hammer and Windhorst samples, where the radio spectral index may not be steep due to the flat-spectrum contributions from regions and possibly AGN."
 The high-frequency selected μν population may therefore. be being samplecd higher. up the, The high-frequency selected $\mu$ Jy population may therefore be being sampled higher up the
is reported in Table 2 (P. Kretschmar S. Martinez NutikzmarkmainBodyEnd1008maimBodyStartl009neez priv.,"is reported in Table \ref{tab:sysjemx}
 (P. Kretschmar S. nez N\'u\\tikzmark{mainBodyEnd1008}\~\tikzmark{mainBodyStart1009}neez priv."
 comm.)., comm.).
 The IBIS/ISGRI data were reduced using version 4.1 of the OSA software., The IBIS/ISGRI data were reduced using version 4.1 of the OSA software.
 The data reduction procedure is identical to the one described in Paper |. ie. for each revolution we first ran the software up to the production of images and mosaics in the 20-40 and 40-80 keV energy ranges.," The data reduction procedure is identical to the one described in Paper 1, i.e. for each revolution we first ran the software up to the production of images and mosaics in the 20–40 and 40–80 keV energy ranges."
 The software was here free to find the most significant sources in the mages., The software was here free to find the most significant sources in the images.
 We then created a catalogue containing only the 9 brightest sources of the field (either detected in some of the revolutions or in all. and re-ran the software forcing the extraction of the count-rate of those sources.," We then created a catalogue containing only the 9 brightest sources of the field (either detected in some of the revolutions or in all), and re-ran the software forcing the extraction of the count-rate of those sources."
 The data products obtained through the ISGRI pipeline therefore include 20-40 keV and 40-80 keV light curves (Fig. 1)).," The data products obtained through the ISGRI pipeline therefore include 20–40 keV and 40–80 keV light curves (Fig. \ref{fig:lc}) ),"
 with a time bin about 2200s (typical length of a SCW)., with a time bin about 2200s (typical length of a SCW).
 Rather than using the standard spectral extraction. we extracted spectra from images/mosaics accumulated at different times.," Rather than using the standard spectral extraction, we extracted spectra from images/mosaics accumulated at different times."
 This non-standard method and its validity is described in Appendix First of all we restricted the spectral analysis to the times when the source was both in the IBIS and JEM-X FOV. revolutions 48. 57. 59. 62. 67. 68. 69 and 70.," This non-standard method and its validity is described in Appendix First of all we restricted the spectral analysis to the times when the source was both in the IBIS and JEM-X FOV, revolutions 48, 57, 59, 62, 67, 68, 69 and 70."
 The distinction of the different times was defined from the 20-40 keV light curve (Fig. 1).," The distinction of the different times was defined from the 20–40 keV light curve (Fig. \ref{fig:lc}) ),"
 ona SCW basis in a way similar to what is presented in Paper 1., on a SCW basis in a way similar to what is presented in Paper 1.
 The distinction of different times to accumulate the data from is solely based on the level of luminosity of the source during a SCW., The distinction of different times to accumulate the data from is solely based on the level of luminosity of the source during a SCW.
 Although the level on which the distinction is made is rather arbitrary. our approach allows us to try to understand the origin of the variability on the time scale of à SCW by accumulating spectra of similar (hard) luminosity.," Although the level on which the distinction is made is rather arbitrary, our approach allows us to try to understand the origin of the variability on the time scale of a SCW by accumulating spectra of similar (hard) luminosity."
 Although this approach can hide and completely miss the spectral variations on smaller time scales. it is dictated by the need to accumulate a large number of JEM-X and IBIS spectra to obtain good constraints on the spectral parameters (e.g. Paper 1).," Although this approach can hide and completely miss the spectral variations on smaller time scales, it is dictated by the need to accumulate a large number of JEM-X and IBIS spectra to obtain good constraints on the spectral parameters (e.g. Paper 1)."
 Our PCA analysis (Sec., Our PCA analysis (Sec.
 3.2) shows that although the source can be variable on short time scales. the fitting of the average spectrum leads to a rather good representation of the physics underlying the source emission.," 3.2) shows that although the source can be variable on short time scales, the fitting of the average spectrum leads to a rather good representation of the physics underlying the source emission."
" Here due to a larger sampling of the source as compared to Paper 1. 1t was possible to define more ""states"" to accumulate the spectra from. m order to understand better the origin of the variations and try to avoid possible mixture of different states together."," Here due to a larger sampling of the source as compared to Paper 1, it was possible to define more “states” to accumulate the spectra from, in order to understand better the origin of the variations and try to avoid possible mixture of different states together."
" We define here: We caution the reader that these definition of ""states"" have nothing to do with the standard definition. of spectral states usually employed in studies of X-ray Binaries (e.g. Tanaka Shibazaki 1996). and that they refer to luminosity in. the hard X-rays."," We define here: We caution the reader that these definition of “states” have nothing to do with the standard definition of spectral states usually employed in studies of X-ray Binaries (e.g. Tanaka Shibazaki 1996), and that they refer to luminosity in the hard X-rays."
 We thus extracted the source count rate and error from 20 bin mosaics accumulated during these four intervals as described in Appendix 1., We thus extracted the source count rate and error from 20 bin mosaics accumulated during these four intervals as described in Appendix 1.
 systematics have been added to all spectral channels., systematics have been added to all spectral channels.
 The JEM-X individual spectra were averaged together following the same time We also tentatively extracted SPI spectra following the standard method., The JEM-X individual spectra were averaged together following the same time We also tentatively extracted SPI spectra following the standard method.
" However. the SPI angular resolution is about 2*, which renders the analysis of delicate given the proximity to GRS 19154105. which is much brighter (Hannikainen et al."," However, the SPI angular resolution is about $^\circ$, which renders the analysis of delicate given the proximity to GRS 1915+105, which is much brighter (Hannikainen et al."
 2004b. Rodriguez et al.," 2004b, Rodriguez et al."
 20042)., 2004a).
 In fact. an analysis of the SPI spectra showed that the parameters were consistent with those of GRS 19154105.," In fact, an analysis of the SPI spectra showed that the parameters were consistent with those of GRS 1915+105."
 We therefore did not include the SPI data in our The JEM-X ISGRI spectra were then fitted in. XSPEC νυν... with latest rmf file for JEM-X (jmx2_rmf_grp_0021.fits). and the OSA 390 ISGRI matrices for IBIS rsp.8884.fits).," We therefore did not include the SPI data in our The JEM-X ISGRI spectra were then fitted in XSPEC v11.3.1, with latest rmf file for JEM-X ), and the OSA 3.0 ISGRI matrices for IBIS )."
 We retained the energy channels between 4 and 25 keV for JEM-X and those between 20 and 150 keV for ISGRI., We retained the energy channels between 4 and 25 keV for JEM-X and those between 20 and 150 keV for ISGRI.
 Further rebinning of the JEM-X data was applied so that both ISGRI and JEM-X data give similar weight to the y statistics in the spectral fittings., Further rebinning of the JEM-X data was applied so that both ISGRI and JEM-X data give similar weight to the $\chi^2$ statistics in the spectral fittings.
 The field of has been observed 3 times with during pointed observations. the journal of which is summarised in Table 3..," The field of has been observed 3 times with during pointed observations, the journal of which is summarised in Table \ref{tab:log2}."
 Two observations were truly dedicated to IGR J19140+0951. a public ToO. and an observation that is part of an on-going monitoring programme of the source.," Two observations were truly dedicated to IGR J19140+0951, a public ToO, and an observation that is part of an on-going monitoring programme of the source."
 The third and oldest observation was dedicated to EXO 1912097., The third and oldest observation was dedicated to EXO 1912+097.
 Whether or not and theEXOSAT source are the same is beyond the scope of this paper. given that the best position of (Cabanae et al.," Whether or not and the source are the same is beyond the scope of this paper, given that the best position of (Cabanac et al."
 2004) is still consistent with theEXOSAT position of EXO 19124097 (Lu et al., 2004) is still consistent with the position of EXO 1912+097 (Lu et al.
 1996)., 1996).
 We assume in the following that the sources are the TheRXTE data have been reduced with theLHEASOFT package v5.3.1. following the standard procedures for both (PCA. Jahoda et al.," We assume in the following that the sources are the The data have been reduced with the package v5.3.1, following the standard procedures for both (PCA, Jahoda et al."
 1996). andExperiment (ΠΕΝΤΕ. Rothschild et al.," 1996), and (HEXTE, Rothschild et al."
 1998) data., 1998) data.
 See e.g. Rodriguez et al. (, See e.g. Rodriguez et al. (
2003a. 2004b) for the procedure of spectral extraction. and 2-40 keV (channel 5-92) high time resolution light curves.,"2003a, 2004b) for the procedure of spectral extraction, and 2–40 keV (channel 5--92) high time resolution light curves."
" In addition. and since the source is quite weak. we further rejected times of high electron background in the PCA (r.e. times when the electron ratio in Proportional Counter Unit (PCU) #2 is greater than 0.1). and time during the passage through the South Atlantic Anomaly (re. we retained the times since SAA>30 or «0 minutes) to define the ""good time intervals”. and used the latest background files available for faint sources."," In addition, and since the source is quite weak, we further rejected times of high electron background in the PCA (i.e. times when the electron ratio in Proportional Counter Unit (PCU) $\#2$ is greater than 0.1), and time during the passage through the South Atlantic Anomaly (i.e. we retained the times since $> 30$ or $< 0$ minutes) to define the “good time intervals”, and used the latest background files available for faint sources."
 The spectra were extracted from the top layer of all PCUs turned on during each observation., The spectra were extracted from the top layer of all PCUs turned on during each observation.
 In order to account for uncertainties in the, In order to account for uncertainties in the
where 9=/ v/e. 0 is the anglee between the jets axis and the observer's line-of-sight.ex and Γη]--3) ?(eeg.Scheuere Readhead 1979).,"where $\beta \equiv v/c$ , $\theta$ is the angle between the jet's axis and the observer's line-of-sight, and $\Gamma \equiv (1-\beta^2)^{-1/2}$ (e.g., Scheuer Readhead 1979)."
" The observed flux. ο.Hh. is related to the emitted flix. 5,,Hh. via 5,4,Hh.=9""""5,,. where n=2 for a continuous jet but 7=3 for a discrete ""plasmokl or shocked emitting region (as the VLBI components are usually treated). aud a is the spectral index. defined by 5,αν[."," The observed flux, $S_{\nu,o}$, is related to the emitted flux, $S_{\nu,e}$ via $S_{\nu,o} = \delta^{n-\alpha} S_{\nu,e}$, where $n = 2$ for a continuous jet but $n = 3$ for a discrete “plasmoid” or shocked emitting region (as the VLBI components are usually treated), and $\alpha$ is the spectral index, defined by $S_{\nu} \propto \nu^{+\alpha}$."
 For simplicity. we will assume a=0 for the VLBI knots. aud will ignore the cosmological effects implemented through [actors of (1+2).," For simplicity, we will assume $\alpha = 0$ for the VLBI knots, and will ignore the cosmological effects implemented through factors of $(1+z)$."
 We will hurther ignore5 anv possible distinction between a bulk velocity and a pattern speed: none of these simplifications affects our qualitative argument., We will further ignore any possible distinction between a bulk velocity and a pattern speed; none of these simplifications affects our qualitative argument.
 The apparent transverse velocity of a knot in the jet is and the maximum value of vappras=[c when 0=1/TI., The apparent transverse velocity of a knot in the jet is and the maximum value of $v^{max}_{app} = \Gamma c$ when $\theta = 1/\Gamma$.
" Since the (typical values of 0,5, are under 10e. (he usual statistical studies of VLBI component velocities seem to imply that the dominant bulk (or pattern) Lorentz [actors are also <10 (e.g.. Vermeulen Cohen 1994: Ixellermann et 22004)."," Since the typical values of $v_{app}$ are under $c$, the usual statistical studies of VLBI component velocities seem to imply that the dominant bulk (or pattern) Lorentz factors are also $< 10$ (e.g., Vermeulen Cohen 1994; Kellermann et 2004)."
 Bul if the jet has a finite opening angle. w. corresponding to a solid augle. £2. as opposed (o an infinitesimal opening angle. (hen each small element of the jet cross-section is boosted by a dillerent amount because of having a different misalignment from the Ime-ol-sight. even if all elements have exactly the same bulk velocity. as we shall assume here.," But if the jet has a finite opening angle, $\omega$, corresponding to a solid angle, $\Omega$, as opposed to an infinitesimal opening angle, then each small element of the jet cross-section is boosted by a different amount because of having a different misalignment from the line-of-sight, even if all elements have exactly the same bulk velocity, as we shall assume here."
 Hence. we must integrate over the solid angle of the jet to obtain the boosting-weighted values of the kev observed quantiGes.," Hence, we must integrate over the solid angle of the jet to obtain the boosting-weighted values of the key observed quantities."
 The weighted fIux is where we have suppressed the subscript ». ancl in the second equality explicitly taken 5. (o be independent of O/. and defined the mean amplifieation factor. A(9).," The weighted flux is where we have suppressed the subscript $\nu$, and in the second equality explicitly taken $S_{e}$ to be independent of $\Omega^{\prime}$, and defined the mean amplification factor, $A(\theta)$."
 We then perform an integration of the (boosted) flux weighted apparent velocity over the jel cross-section to obtain the weighted observed value of theapparent velocity of the jet. Note that the resultant vector is along the line joining the directions of the blazar nucleus," We then perform an integration of the (boosted) flux weighted apparent velocity over the jet cross-section to obtain the weighted observed value of theapparent velocity of the jet, Note that the resultant vector is along the line joining the directions of the blazar nucleus"
Valenti&Fischer(2005): in addition. TO of the 147 stars in our comparison sample have vsini values listed. in their study.,"\citet{vf05}; in addition, 70 of the 147 stars in our comparison sample have vsini values listed in their study."
 We define a new zMindex that. includes the vsini term: We show the Li abundance cillerences calculated using the AA; index in Figure 5: the pattern apparent in the previous figures is still present., We define a new $\Delta$ -index that includes the vsini term: We show the Li abundance differences calculated using the $\Delta_3$ index in Figure 5; the pattern apparent in the previous figures is still present.
 Phe average Li abundance dilference for SWPs with 5800« Tar5950 Ix is. 0.3140.10 (s.c.m.), The average Li abundance difference for SWPs with $5800 < $ $_{\rm eff} < 5950$ K is $-0.31 \pm 0.10$ (s.e.m.)
 dex: SWPs with Tr5t50 Ix have an average Li abundance dillerence of 0.1540.05 (s.e.m.), dex; SWPs with $_{\rm eff} > 5950$ K have an average Li abundance difference of $0.15 \pm 0.05$ (s.e.m.)
 dex., dex.
 We repeated the calculations using an index with the vini term three times the weight of that in the A. index., We repeated the calculations using an index with the vsini term three times the weight of that in the $\Delta_3$ index.
 The resulting Li abundance cillerences are very similar to those in Figure 5., The resulting Li abundance differences are very similar to those in Figure 5.
 We summarize. the properties of the SWI and comparison stars plotted in Figures 3 to 5 in Table I., We summarize the properties of the SWP and comparison stars plotted in Figures 3 to 5 in Table 1.
 We confirm recent claims that the Li abundances of SWDPs with Tr near 5800 IX tend to be lower than those of stars without detected: planets., We confirm recent claims that the Li abundances of SWPs with $_{\rm eff}$ near 5800 K tend to be lower than those of stars without detected planets.
 We also find. for the first time. evidence that ολλον hotter than about 5900 Ix. have excess Li.," We also find, for the first time, evidence that SWPs hotter than about 5900 K have excess Li."
 Phe magnitudes of the average the Li abundance cillerenees for the cool ancl hot ολλΟν are larecr than the typical measurement errors., The magnitudes of the average the Li abundance differences for the cool and hot SWPs are larger than the typical measurement errors.
 We cannot reach any firm conclusions regarding SWI's cooler than 5800 Ix. given the paucity of such stars with detectable Li in our sample.," We cannot reach any firm conclusions regarding SWPs cooler than 5800 K, given the paucity of such stars with detectable Li in our sample."
 While our method of analysis does not rely on stellar evolutionary models. it does permit us to minimize the ellects of dillerences in age and mass in our analysis of the Li abundances of the SWP and comparison star seunples.," While our method of analysis does not rely on stellar evolutionary models, it does permit us to minimize the effects of differences in age and mass in our analysis of the Li abundances of the SWP and comparison star samples."
 La addition. the trends apparent in Figures 3 and 4 persisted even after correcting for dilferences in vsini.," In addition, the trends apparent in Figures 3 and 4 persisted even after correcting for differences in vsini."
 Inclusion. of vsini as a parameter reduced the magnitude of the average Li abundance deficit among the cool οΟν only by 0.07 dex., Inclusion of vsini as a parameter reduced the magnitude of the average Li abundance deficit among the cool SWPs only by 0.07 dex.
 Although the effect is small. vsini apparently does have an elfect on the Li abundances of SWI's.," Although the effect is small, vsini apparently does have an effect on the Li abundances of SWPs."
 To further explore, To further explore
we choose to display our results as plots of the a-effect needed for resonance as a function of the other parameters.,we choose to display our results as plots of the $\alpha$ -effect needed for resonance as a function of the other parameters.
" Figure 2 displays αι needed for resonance as a function of the magnetic diffusivity of the lower layer, for a solar differential rotation (s— 70) and a selection of lower layer thicknesses (the upper layer thickness is held fixed at 20%(Dy=0.2) of the total thickness)."," Figure 2 displays $\alpha_L$ needed for resonance as a function of the magnetic diffusivity of the lower layer, for a solar differential rotation $s=70$ ) and a selection of lower layer thicknesses (the upper layer thickness is held fixed at $20\% (D_U=0.2)$ of the total thickness)."
" Since the y-axis is logarithmic, we have reversed the sign of all the negative a, values."," Since the y-axis is logarithmic, we have reversed the sign of all the negative $\alpha_L$ values."
" Viewed from the left hand y-axis, the positive a, values are the upper family of curves, while the negative ar, values are the lower family."," Viewed from the left hand $y$ -axis, the positive $\alpha_L$ values are the upper family of curves, while the negative $\alpha_L$ values are the lower family."
" The negative values are all asymptotic to zero with decreasing P,,, while the positive values are all asymptotic to constant nonzero values, consistent with the analytical limits shown in section 6.1."," The negative values are all asymptotic to zero with decreasing $P_{\eta L}$, while the positive values are all asymptotic to constant nonzero values, consistent with the analytical limits shown in section 6.1."
" For increasing values of P, the positive and negative az values for the same lower layer thickness are asymptotic", For increasing values of $P_{\eta L}$ the positive and negative $\alpha_L$ values for the same lower layer thickness are asymptotic
The foregoing analysis gives us thousands of stepwise field changes to consider.,The foregoing analysis gives us thousands of stepwise field changes to consider.
 Field changes were observed in all 77 flares., Field changes were observed in all 77 flares.
 In order to characterize the field changes we followed SH05 in selecting a few representative pixels from each of 77 data sets., In order to characterize the field changes we followed SH05 in selecting a few representative pixels from each of 77 data sets.
" While two good data sets were available for each of six of the flares, we used only one data set per flare in this analysis."," While two good data sets were available for each of six of the flares, we used only one data set per flare in this analysis."
 SH05 selected representative pixels by examining by eye over 8000 mosaic plots like, SH05 selected representative pixels by examining by eye over 8000 mosaic plots like
δα=7/3.,$\delta/\alpha =7/3$.
 The principal numerical fact to note is thal 9/6 is greater than or less (han 2 depending on whether e is less than or greater (han 4., The principal numerical fact to note is that $\delta/\alpha$ is greater than or less than 2 depending on whether $a$ is less than or greater than 4.
 The reason for the numerical discussion of the preceding paragraph is that the value δα=2 is highly significant in spherical models of dark matter halo erowth (see e.g. llenriksen&Widrow(1999). [or a summary)., The reason for the numerical discussion of the preceding paragraph is that the value $\delta/\alpha=2$ is highly significant in spherical models of dark matter halo growth (see e.g. \citet{hen99} for a summary).
 In these models (his ratio is given in terms of the power law index —e of the initial cosmological density perturbation by Consequently we can infer from equations (28..29)) that the imitial cosmological overdensity had the power —e where If finally we relate e to the power spectrum index » of the primordial density through (he rms profile of such perturbations (other choices are possible. e.g. (1985).. but similar results are found). then Consequently we arrive at a direct link between e and (he primordial power spectrum index on the scale of galaxy halos as Thus under our interpretation of the black hole mass-velocitv-dispersion correlation we are led to conclude (that the primordial power spectrum on the scale of galaxies has the index m of equation (32)).," In these models this ratio is given in terms of the power law index $-\epsilon$ of the initial cosmological density perturbation by Consequently we can infer from equations \ref{eq:DA}, \ref{eq:SSclass}) ) that the initial cosmological overdensity had the power $-\epsilon$ where If finally we relate $\epsilon$ to the power spectrum index $n$ of the primordial density through the rms profile of such perturbations (other choices are possible, e.g. \citet{hof85}, but similar results are found), then Consequently we arrive at a direct link between $a$ and the primordial power spectrum index on the scale of galaxy halos as Thus under our interpretation of the black hole mass-velocity-dispersion correlation we are led to conclude that the primordial power spectrum on the scale of galaxies has the index $n$ of equation \ref{eq:Pindex}) )."
 For α=4 this vields n=—2. while a=15/4 and α=9/2 vield n=—]11/5 and»=—5/3 respectively.," For $a=4$ this yields $n=-2$, while $a=15/4$ and $a=9/2$ yield $n=-11/5$ and $n=-5/3$ respectively."
 These values for » on the scale of galaxies are all in good agreement with observation. which favours a value near 7=—2.," These values for $n$ on the scale of galaxies are all in good agreement with observation, which favours a value near $n=-2$."
 We conclude that our interpretation of the mass-velocity-cispersion relation as originating in the primordial density profile is consistent with cosmological evidence., We conclude that our interpretation of the mass-velocity-dispersion relation as originating in the primordial density profile is consistent with cosmological evidence.
 In (his paper we have explored (he implications of growing a black hole in various dark malter halo distribution functions., In this paper we have explored the implications of growing a black hole in various dark matter halo distribution functions.
 Our principal approach was to assume that the black, Our principal approach was to assume that the black
"We have perlormed maximum likelihood analysis assuming that. in addition to the central point sources and diffuse backgrounds (Strong.Moskalenko&Reimeretal.2009. 2010d).. there is a Chird component. namely. (he halo component. whose spatial extent is given by the Gaussian distribution: where 8 is the angle from the map center. and 97), is (he mean of 6? over this distribution function. 67,=(67).","We have performed maximum likelihood analysis assuming that, in addition to the central point sources and diffuse backgrounds \citep*{Strong2004,GB,EGB}, there is a third component, namely, the halo component, whose spatial extent is given by the Gaussian distribution: where $\theta$ is the angle from the map center, and $\theta_{\rm
halo}^2$ is the mean of $\theta^2$ over this distribution function, $\theta_{\rm halo}^2 \equiv \langle \theta^2 \rangle$."
 We fit the histogram of photon counts as a function of 6? read from (he maps bv minimizing where Nu. ο: and £y ave treated as free parameters.," We fit the histogram of photon counts as a function of $\theta^2$ read from the maps by minimizing where $N_{\rm psf}$, $N_{\rm halo}$ , and $\theta_{\rm halo}$ are treated as free parameters."
 The index 7 refers to the i-th bin. Vj; is the total mnunber of events in this bin. P4 is the normalized PSF. and ων is the events due to diffuse backerounds.," The index $i$ refers to the $i$ -th bin, $N_i$ is the total number of events in this bin, $P_{\rm psf}$ is the normalized PSF, and $N_{{\rm
bg},i}$ is the events due to diffuse backgrounds."
 We fix the backerounds to the values at 0?=2.025 2.25 deg? and 0.2330.25 deg? for 3.10 GeV and 10.100 GeV. respectively. in the simulated maps. assuming that they are homogeneous.," We fix the backgrounds to the values at $\theta^2 = 2.025$ –2.25 $^2$ and 0.233–0.25 $^2$ for 3–10 GeV and 10–100 GeV, respectively, in the simulated maps, assuming that they are homogeneous."
" Thus. Vy. and Naa are the total numbers of photons in the map attributed to the point source and the halo. respectively. aud Aa), Is (he apparent angular extent of the halo component."," Thus, $N_{\rm psf}$ and $N_{\rm halo}$ are the total numbers of photons in the map attributed to the point source and the halo, respectively, and $\theta_{\rm halo}$ is the apparent angular extent of the halo component."
 The inclusion of the halo component improves the fit significantly at high energies., The inclusion of the halo component improves the fit significantly at high energies.
 The minimum X? over degree of freedom (7) is μμΗν=18.8/19 and 13.3/12 for 310 GeV and 10100 GeV. respectivelv.," The minimum $\chi^2$ over degree of freedom $\nu$ ) is $\chi_{\rm
min}^2/\nu = 18.8 / 19$ and $13.3/12$ for 3–10 GeV and 10–100 GeV, respectively."
" In contrast. the ""best-Dlit point-source model. where Nj and the background amplitude are treated as [ree parameters. gives N25,/7&66/20 and 62/13 for 310 GeV and 10.100 GeV. respectively."," In contrast, the “best-fit” point-source model, where $N_{\rm psf}$ and the background amplitude are treated as free parameters, gives $\chi_{\rm min}^2 / \nu \simeq 66 / 20$ and $62 / 13$ for 3–10 GeV and 10–100 GeV, respectively."
 This clearly shows that. even though we stack many AGN. this simple Gaussian halo model gives a very good fit to the data.," This clearly shows that, even though we stack many AGN, this simple Gaussian halo model gives a very good fit to the data."
 The surface brightness profiles d.N/d0? of the best-fit halo model are juxtaposed with the data points in Fig. 2.., The surface brightness profiles $dN/d\theta^2$ of the best-fit halo model are juxtaposed with the data points in Fig. \ref{fig:bestfit}.
 In Fig. 5a.," In Fig. \ref{fig:contour}{,"
 we show the allowed regions of θι and Sha al and confidence levels., we show the allowed regions of $\theta_{\rm halo}$ and $f_{\rm halo}$ at and confidence levels.
" Here. fi, is the fraction of the halo photons. 1e... fna;=Nuuo/CVpa+Nia)."," Here $f_{\rm halo}$ is the fraction of the halo photons, i.e., $f_{\rm
halo} \equiv N_{\rm halo} / (N_{\rm psf} + N_{\rm halo})$."
" The best-fil values and lo statistical errors for these parameters are Ppa,=0.49c0.037.and fuo=0.097&0.014 for 310 GeV. and £4,=0.2620.01 and fg)=0.20&0.02 for 10100 GeV. For the lowest energv band. 13 GeV. only an upper limit on fia, is obtained. which is fia,<0.046 at confidence level."," The best-fit values and $1\sigma$ statistical errors for these parameters are $\theta_{\rm halo} = 0.49\pm 0.03\degr$and $f_{\rm halo}
= 0.097 \pm 0.014$ for 3–10 GeV, and $\theta_{\rm halo} =
0.26 \pm 0.01\degr$ and $f_{\rm halo} = 0.20 \pm 0.02$ for 10–100 GeV. For the lowest energy band, 1–3 GeV, only an upper limit on $f_{\rm
halo}$ is obtained, which is $f_{\rm halo} < 0.046$ at confidence level."
"erowth iu iuteractious of differiug mass ratio is likely a consequence of the efficiency of dynamical heating aud bulee formation during hose eucounters,",growth in interactions of differing mass ratio is likely a consequence of the efficiency of dynamical heating and bulge formation during those encounters.
" Qualitativelv. iu a ininor merecr. the first passage induces a bar. eas infow andl if it is an interpenctrating encounter violently relaxing approxinuiaely M, of he disk stars. which together formu a bugework."," Qualitatively, in a minor merger, the first passage induces a bar, gas inflow and – if it is an interpenetrating encounter – violently relaxing approximately $M_s$ of the disk stars, which together form a bulge."
.. I also teuds to put the secondary on a iostly racial orbi. and strip a significant raction of its mass prior to final coaescence.," It also tends to put the secondary on a mostly radial orbit, and strip a significant fraction of its mass prior to final coalescence."
 A low auguluw momentum final orbit. couple with a coeutral mass concentration will end to damp ou further wardriven eas inflows.," A low angular momentum final orbit, coupled with a central mass concentration will tend to damp out further bar–driven gas inflows."
 This. in combination with less dvnamical heating owine o the lower enerseties of the interaction. suppresses urther bulee erowth. aud wih it the final o»urst of SMEBII activity seen im major mnoergers.," This, in combination with less dynamical heating owing to the lower energetics of the interaction, suppresses further bulge growth, and with it the final burst of SMBH activity seen in major mergers."
 Iu Figure L.. we examine the effect of orbital iuclilation prograde coplanar (/= 07) to retrograde colamar (7= Lsorj on both miner (left panel) and niajor (right panel) merecrs.," In Figure \ref{fig:minor_grow_inc}, we examine the effect of orbital inclination – prograde coplanar $i=0^\circ$ ) to retrograde coplanar $i=180^\circ$ ) – on both minor (left panel) and major (right panel) mergers."
 In geucra. compared to retrograde interactions. prograde encounters produce sronger tidal responses in the disk that mduce bars aud drive t10 gus inflows that fuel lee formatio rand SMDII erowth?).," In general, compared to retrograde interactions, prograde encounters produce stronger tidal responses in the disk that induce bars and drive the gas inflows that fuel bulge formation and SMBH growth."
. We see his effect in our simulatiois: while the effect is more drauatic for major iiergers. for the liuitius case of a coplanar interaction. retrograde ordts result iu a siguificautlv less massive SAIBUs than clo prograce.," We see this effect in our simulations: while the effect is more dramatic for major mergers, for the limiting case of a coplanar interaction, retrograde orbits result in a significantly less massive SMBHs than do prograde."
 ILlowever. when he spins of the two galaxies are not aligned. the resulting SMDIT is lareely incependent of orbital inclination.," However, when the spins of the two galaxies are not aligned, the resulting SMBH is largely independent of orbital inclination."
 These trends with mass fraction and orbital imcelination qualitatively inoivate the aiu of this work: given a particular encounter. what mechanism sets the funal SAIBI imiass?," These trends with mass fraction and orbital inclination qualitatively motivate the aim of this work: given a particular encounter, what mechanism sets the final SMBH mass?"
 The simulations in the uustable disk series evolve variants of the same disk τιjiodels iu isolation. the paralucters of wÜüch are sununarized in Table 3..," The simulations in the unstable disk series evolve variants of the same disk models in isolation, the parameters of which are summarized in Table \ref{tab:unstable_sims}."
 The mass resolution and softening leneths of the particles were kept the same as with the mass ratio series. aud the particle comm sare summarized in Table L.," The mass resolution and softening lengths of the particles were kept the same as with the mass ratio series, and the particle counts are summarized in Table \ref{tab:unstable_resolution}."
 The disk lnass fraction Is increased while holding the total mass fixed. which sees elobal instabilities bv increasing the selferavity of the disk relative to its kinetic energy from rotation??).," The disk mass fraction is increased while holding the total mass fixed, which seeds global instabilities by increasing the self–gravity of the disk relative to its kinetic energy from rotation."
". For three iuitial disk models and SD). we consider wo disk dass fractious (40,—0.08 and 0.10). aud three eas fractious (fy=0.10.6. and 0.5),"," For three initial disk models and ), we consider two disk mass fractions $m_d = 0.08$ and $0.10$ ), and three gas fractions $f_g = 0.4,0.6,$ and $0.8$ )."
" For a subset of tjese simulations. we cousider three different seed black hole masses Aipap;=Lol,10. ancl Loo aud wo differcut equations of state ui2005.bournagd208501Bbdttlista200"," For a subset of these simulations, we consider three different seed black hole masses – $M_{BH,i} = 10^4, 10^5$, and $10^6$ – and two different equations of state – $q_{EOS} = 0.5$, 1.0."
6 Stellar bars are found ecuerically i nunucerical simulations of isolated disk galaxies(2).. aud represent a elobal instability iu which rotating disks swineality spiral density wave perturbations(27).," Stellar bars are found generically in numerical simulations of isolated disk galaxies, and represent a global instability in which rotating disks swing–amplify spiral density wave perturbations."
. They have Όσοι shown enmpiicalle to develop when the selferavitv of he disk is comparable to its kinetic energy. of rotation)., They have been shown empirically to develop when the self–gravity of the disk is comparable to its kinetic energy of rotation.
. Most. disk ealaxies in the local universe lave ars?7). and — despiteOS conflicting observationa results dt secs clear that a substantial fraction of Hel redshift— 2~1 disks also show bar featuresTTLh.," Most disk galaxies in the local universe have bars, and – despite conflicting observational results – it seems clear that a substantial fraction of high redshift $z\sim 1$ disks also show bar features."
 These bars have been shown both theoretically and observationallv to drive eas inflows auc wiclear starbursts(227277)., These bars have been shown both theoretically and observationally to drive gas inflows and nuclear starbursts.
 As a result. they represeut a xotentiallv pronusing mechanism for fucling the erowth of nuclear SMDIIS. which las at fines been invoked iu senanalytic models as their dominant mode of erowth.," As a result, they represent a potentially promising mechanism for fueling the growth of nuclear SMBHs, which has at times been invoked in semi–analytic models as their dominant mode of growth."
 Since the onset of the 1stability is a collisiouless process77). dt dewlops first in the stellar distribution.," Since the onset of the instability is a collisionless process, it develops first in the stellar distribution."
" The stellar bar then drains the eas within a critical radius of its angular uonmentuinm(δν, driving it inwards fueliug a nuclear starburst: a process analogous Oo mergerdriven eas inflows iu which the bar is induced o» the timeevolution of tie tidal field duriug close λεσασος7)."," The stellar bar then drains the gas within a critical radius of its angular momentum, driving it inwards fueling a nuclear starburst; a process analogous to merger–driven gas inflows in which the bar is induced by the time–evolution of the tidal field during close passages."
 This nucear starburst concentrates sole of the mass oft1e initial disk at its center. forming a pseudobulge and eveutually cading to the destiction of the bar over a relatively short timescale as the ceutra πι concentration danips out the spiral density wave(9dTTTT).," This nuclear starburst concentrates some of the mass of the initial disk at its center, forming a pseudobulge and eventually leading to the destruction of the bar over a relatively short timescale as the central mass concentration damps out the spiral density waves."
. Because there is no interperctration by a satellite. there Is correspondingly uo violoiwt relaxation of the stellar disk and as a result he pseudobulee is almost eutirolv doninated by stars formed curing the simulation.," Because there is no interpenetration by a satellite, there is correspondingly no violent relaxation of the stellar disk and as a result the pseudobulge is almost entirely dominated by stars formed during the simulation."
"comparison from the instant labelled with number (2) in this ligure. which corresponds to f°=2055,44.","comparison from the instant labelled with number $(2)$ in this figure, which corresponds to $t^*=20t_{drag}$."
 We see that the asvmptotic behavior of the magnetic field. (labels (3). and (4) in the figure) calculated from these two methods is the same., We see that the asymptotic behavior of the magnetic field (labels (3) and (4) in the figure) calculated from these two methods is the same.
" With the purpose of characterizing this asymptotic behavior analvticallv. we construct an analytic ""box-tvpe solution of the form with where the magnetic [lux is b=D.(GX12.4(0)). and fUrp) is given by For the instants (3) and (4) in Fig. 2.."," With the purpose of characterizing this asymptotic behavior analytically, we construct an analytic “box”-type solution of the form with where the magnetic flux is $\Phi=B_s(t)(1-2x_1(t))$, and $t(x_1)$ is given by For the instants (3) and (4) in Fig. \ref{g2},"
 we show a full line that represents the solution given by Eq. (29))., we show a full line that represents the solution given by Eq. \ref{explicit-step}) ).
 We see that this analvtical characterization works well., We see that this analytical characterization works well.
 ln Fig. 3..," In Fig. \ref{g3},"
 we show the evolution of a harmonic initial magnetic field profile In this figure. we compare the evolution of this profile given bv Eq. (23))," we show the evolution of a harmonic initial magnetic field profile In this figure, we compare the evolution of this profile given by Eq. \ref{magn-equati1-nodime}) )"
 with that given by the full system of coupled eqs. (1)). (2)).," with that given by the full system of coupled Eqs. \ref{bz}) ), \ref{nB}) ),"
 ancl (3))., and \ref{nc}) ).
 For the latter. the initial conditions for the particle density. perturbations are OneGr.O)=δη0)0.," For the latter, the initial conditions for the particle density perturbations are $\delta n_B(x,0)=\delta n_c(x,0)=0$."
" At the instant labelled: with number (2). =10/575,,. this initial profile has evolved to be consistent with the dillusive equilibrium. therefore. (rom this"," At the instant labelled with number (2), $t^*=10t_{drag}$, this initial profile has evolved to be consistent with the diffusive equilibrium, therefore, from this"
Fourier transform JF. we can recover g exactly in the absence of noise by because (νο)=FhFy.,"Fourier transform $\cF$, we can recover $g$ exactly in the absence of noise by because $\cF(K g) = \cF k \,\cF g$."
 While the inverse exists in (he absence of noise. the clecay of Fh al high frequencies can produce catastrophically high variances in (he presence of noise. which produces nontrivial and random contribution at high Irequencies (so (he numerator is non-zero but the denominator goes (ο zero).," While the inverse exists in the absence of noise, the decay of $\cF k$ at high frequencies can produce catastrophically high variances in the presence of noise, which produces nontrivial and random contribution at high frequencies (so the numerator is non-zero but the denominator goes to zero)."
 Figure 1. demonstrates this effect in a l-dimensional analog of the problem. comparing noise free reconstruction via equation (2)) with reconstruction under noise with a 10e9:1 signal-to-noise ratio (SNR).," Figure \ref{fig:FourierInvOperator} demonstrates this effect in a 1-dimensional analog of the problem, comparing noise free reconstruction via equation \ref{eq:FourierInvOperator}) ) with reconstruction under noise with a 10e9:1 signal-to-noise ratio (SNR)."
 The estimate in the latter case is wholly untenable., The estimate in the latter case is wholly untenable.
 We asstune that each observation is drawn from a distribution with mean Decause the observation process in the telescope involves counting photons. the distribution of 3; 1s well modeled by a Poisson distribution (Iu2007:Scully1969).," We assume that each observation is drawn from a distribution with mean Because the observation process in the telescope involves counting photons, the distribution of $Y_{ij}$ is well modeled by a Poisson distribution \citep{Hu2007,Scully1969}."
. Thus. we assume that the ης are independent Poisson(£;;) random variables.," Thus, we assume that the $Y_{ij}$ 's are independent $\langle\theta_{ij}\rangle$ random variables."
 If the mean counts 0;; are large enough. the Gaussian approximation to (the Poisson distribution is accurate. and we can model the Y;;'s asindependent Normal(£;;.θε) random variables.," If the mean counts $\theta_{ij}$ are large enough, the Gaussian approximation to the Poisson distribution is accurate, and we can model the $Y_{ij}$ 's asindependent $\langle\theta_{ij},\theta_{ij}\rangle$ random variables."
 The statistical problem is to form an estimator g of g given observations τι, The statistical problem is to form an estimator $\hat g$ of $g$ given observations $Y_{ij}$.
 In the present context. g is the template or coadd we are attempting to create.," In the present context, $\hat g$ is the template or coadd we are attempting to create."
 For each g we need wavs (o measure its misfit relative to the true scene g., For each $\hat g$ we need ways to measure its misfit relative to the true scene $g$ .
 In this paper we consider (wo., In this paper we consider two.
 The, The
"in previous papers (see,e.g.,discussionofsimilaritysolutionparametersin ?), so here we focus on the relationships and degeneracies specific to the turbulent linewidth.","in previous papers \citep[see, e.g., discussion of
similarity solution parameters in][]{and09a}, so here we focus on the relationships and degeneracies specific to the turbulent linewidth."
" There are four main categories of line broadening in circumstellar disks that are relevant to our investigation: rotational, thermal, turbulent, and optical depth."," There are four main categories of line broadening in circumstellar disks that are relevant to our investigation: rotational, thermal, turbulent, and optical depth."
" These types of line broadening are all incorporated in detail into the ray-tracing portion of the RATRAN radiative transfer code, and will be handled appropriately for a given disk structure."," These types of line broadening are all incorporated in detail into the ray-tracing portion of the RATRAN radiative transfer code, and will be handled appropriately for a given disk structure."
 The goal is to understand how to distinguish the distinct contributions of each of these different sources of line broadening and their relationships to the parameters of our disk structure models., The goal is to understand how to distinguish the distinct contributions of each of these different sources of line broadening and their relationships to the parameters of our disk structure models.
" As discussed above, a detailed characterization of the multi-dimensional parameter space is prohibitively computationally expensive."," As discussed above, a detailed characterization of the multi-dimensional parameter space is prohibitively computationally expensive."
 We therefore investigate parameter relationships by letting the two-dimensional x? values generated in Section 4.2 guide an investigation using a toy model of an optically thick spectral line profile to highlight the distinct contribution of each related parameter to the observable properties., We therefore investigate parameter relationships by letting the two-dimensional $\chi^2$ values generated in Section \ref{sec:procedure} guide an investigation using a toy model of an optically thick spectral line profile to highlight the distinct contribution of each related parameter to the observable properties.
" The x? values indicate that for the similarity solution models, the parameters that are most strongly degenerate with the turbulent linewidth are the temperature (Tioo and q) and inclination (i)."," The $\chi^2$ values indicate that for the similarity solution models, the parameters that are most strongly degenerate with the turbulent linewidth are the temperature $T_{100}$ and $q$ ) and inclination $i$ )."