source,target
 This determines the mean separation of superclusters across voids which is taken as the characteristic length of the model., This determines the mean separation of superclusters across voids which is taken as the characteristic length of the model.
 We generated ten models of box size TOO wwith 431 void centres. in which case the characteristic scale is 115Alpe.. a value observed. in our study of superclusters ancl voids in Paper Land in the study of the cluster correlation function in Paper 11.," We generated ten models of box size 700 with 431 void centres, in which case the characteristic scale is 115, a value observed in our study of superclusters and voids in Paper I, and in the study of the cluster correlation function in Paper II."
 Results for the correlation functions anc power spectra of random models are shown in Figure 2., Results for the correlation functions and power spectra of random models are shown in Figure 2.
 All random moclels have a correlation function with no sign of oscillations., All random models have a correlation function with no sign of oscillations.
 The correlation function of the random supercluster node approaches zero on large scales immediately after the initial maximum., The correlation function of the random supercluster model approaches zero on large scales immediately after the initial maximum.
 The correlation function of the Voronoi model is different., The correlation function of the Voronoi model is different.
 It has a minimum at a separation between 60 and ~100 aand one secondary maximum at ~140Mpc., It has a minimum at a separation between $\sim 60$ and $\sim 100$ and one secondary maximum at $\sim 140$.
 We discuss dillerences between the random supercluster aud Voronoi mioclels later., We discuss differences between the random supercluster and Voronoi models later.
 The analysis of the correlation function of real cluster samples has shown that it depends strongly on the richness of superclusters (see Paper LL)., The analysis of the correlation function of real cluster samples has shown that it depends strongly on the richness of superclusters (see Paper II).
 We have thus made separate analyses of the correlation function for our random mocels for clusters located in rich ancl poor superclusters., We have thus made separate analyses of the correlation function for our random models for clusters located in rich and poor superclusters.
 We shall discuss this problem in more detail below. (Section 7)., We shall discuss this problem in more detail below (Section 7).
 In these models clusters or superclusters are located. with a certain degree of fuzziness. on the corners or on the edges between corners (rods) of a regular rectangular three-dimensional grid.," In these models clusters or superclusters are located, with a certain degree of fuzziness, on the corners or on the edges between corners (rods) of a regular rectangular three-dimensional grid."
 The fuzziness of the model was realized by adding to positions of clusters or superclusters random shifts around the exact position on the corner or the edge of the grid., The fuzziness of the model was realized by adding to positions of clusters or superclusters random shifts around the exact position on the corner or the edge of the grid.
 Depending on thedegree of the fuzziness we, Depending on thedegree of the fuzziness we
"(c= 0.102), which is basically the same as that of Poznanskietal.","$\sigma=0.102$ ), which is basically the same as that of \citet{poznanski}."
"(2010).. Thus, our study fully confirms the results by Poznanskietal.(2010),, but extends the validity of the relation toward later phases."," Thus, our study fully confirms the results by \citet{poznanski}, but extends the validity of the relation toward later phases."
 Improving the accuracy of the velocity measurements has an important aspect in measuring extragalactic distances with SCM or EPM (cf., Improving the accuracy of the velocity measurements has an important aspect in measuring extragalactic distances with SCM or EPM (cf.
 81)., 1).
" Both SCM and EPM need velocities, thus, the results of this paper can be significant for both techniques."," Both SCM and EPM need velocities, thus, the results of this paper can be significant for both techniques."
 SCM was calibrated using ure on day +50., SCM was calibrated using $v_{Fe}$ on day +50.
" However, in many cases getting a spectrum at or around day +50 is not possible."," However, in many cases getting a spectrum at or around day +50 is not possible."
 In these cases Eq.(2)) can be used to estimate Ure(50d)., In these cases \ref{eq2}) ) can be used to estimate $v_{Fe}(50\rmn{d})$.
" We have improved the exponent in Eq.(2)) as —0.546+0.01, based on more data obtained on wider range of phase than previously."," We have improved the exponent in \ref{eq2}) ) as $-0.546 \pm 0.01$, based on more data obtained on wider range of phase than previously."
 The difference between our result and the previous curve (Nugentetal.2006) is the highest around day +20 (Fig.9))., The difference between our result and the previous curve \citep{nugent06} is the highest around day +20 \ref{nug}) ).
 The new curve may result in better constrained vre(50d) when only early-phase spectra obtained around day +20 are available., The new curve may result in better constrained $v_{Fe}(50\rmn{d})$ when only early-phase spectra obtained around day +20 are available.
" However, there are several drawbacks of SCM."," However, there are several drawbacks of SCM."
" For example, the uncertainty in the moment of explosion, i.e. in determining the phase of a particular spectrum can lead to significant error in the distance determination."," For example, the uncertainty in the moment of explosion, i.e. in determining the phase of a particular spectrum can lead to significant error in the distance determination."
" Moreover, as the example of SN 2005cs shows in Fig.9,, some Type II-P SNe can deviate significantly from the average, especially during early phases."," Moreover, as the example of SN 2005cs shows in \ref{nug}, some Type II-P SNe can deviate significantly from the average, especially during early phases."
" Thus, one should be careful when such kind of interpolation or extrapolation is to be applied."," Thus, one should be careful when such kind of interpolation or extrapolation is to be applied."
 The example of SN 2005cs suggests that multi-epoch spectroscopic observations should always be preferred against single-epoch spectra when distance determination is the aim., The example of SN 2005cs suggests that multi-epoch spectroscopic observations should always be preferred against single-epoch spectra when distance determination is the aim.
 The case of EPM is different., The case of EPM is different.
" Since this method does not require calibration, but needs multi-epoch data, deviations in the measured velocities have higher impact."," Since this method does not require calibration, but needs multi-epoch data, deviations in the measured velocities have higher impact."
" To show this, we calculated the EPM-distances of all 5 SNe via the method described in Vinkóetal.(2011).."," To show this, we calculated the EPM–distances of all 5 SNe via the method described in \citet{vinko11dh}."
" We used two sets of velocities for each SNe: i) from the absorption minimum of the Fe 45169 line, ii) Όπιοαει determined in Sec. ??.."," We used two sets of velocities for each SNe: $i)$ from the absorption minimum of the Fe $\lambda$ 5169 line, $ii)$ $v_{model}$ determined in Sec. \ref{sec_synow}."
 'The resulted distances are in Table 3.., The resulted distances are in Table \ref{epm}.
 The correction factors of D05 were applied for all SNe., The correction factors of \citeauthor{dessart2005a} were applied for all SNe.
 Usually the photometric data were interpolated to the epochs of the velocities., Usually the photometric data were interpolated to the epochs of the velocities.
" However, for SN 2004dj Eq."," However, for SN 2004dj Eq."
 2 and Eq., \ref{eq2} and Eq.
" 3 were used to extrapolate the velocity data to the photometric epochs, because of the low number of spectra taken before day 4-50, i.e. during the expansion of the photosphere."," \ref{eq3} were used to extrapolate the velocity data to the photometric epochs, because of the low number of spectra taken before day +50, i.e. during the expansion of the photosphere."
 Data on SN 1999em in NGC 1637 were used for distance determination with EPM several times., Data on SN 1999em in NGC 1637 were used for distance determination with EPM several times.
 Hamuyetal.(2001) used cross-correlation velocities (with the model spectra of E96 as the template set) and the correction factors of E96, \citet{hamuy2001} used cross-correlation velocities (with the model spectra of E96 as the template set) and the correction factors of E96
universe.,universe.
 Since thev become clilficult to observe. from the ground. as their (Mus redshifts oul of (he optical window and the terrestrial skv background grows verv bright. space based measurements are necessary.," Since they become difficult to observe from the ground as their flux redshifts out of the optical window and the terrestrial sky background grows very bright, space based measurements are necessary."
 Wide field instruments are needed to achieve sufficient numbers to study. and stringent. svstematics controlled experiments (o derive accurate results.," Wide field instruments are needed to achieve sufficient numbers to study, and stringent, systematics controlled experiments to derive accurate results."
 For example. ihe Supernova/Acceleration Probe (SNAP: Alderingetal.(2004))) is carefully desiened specifically to achieve high quality (in both statistics and svstematics). well characterized. photometric and spectroscopic observations of thousands of supernovae.," For example, the Supernova/Acceleration Probe (SNAP: \citet{aldering04}) ) is carefully designed specifically to achieve high quality (in both statistics and systematics), well characterized, photometric and spectroscopic observations of thousands of supernovae."
 Space extends the reach of a non-crvogenic telescope to μπα. bevond which thermal noise swamps the astronomical signal.," Space extends the reach of a non-cryogenic telescope to $\mu$ m, beyond which thermal noise swamps the astronomical signal."
 To this wavelength limit the Sill sspectral feature used for classification of Ἔνρο la supernovae (SNe Ia) can be observed to redshift 2=1.7., To this wavelength limit the SiII spectral feature used for classification of Type Ia supernovae (SNe Ia) can be observed to redshift $z=1.7$.
 This redshift limit matches extremely. well the optimum depth for dark energv investigations. bevond which the sensitivitv to the dark energv characteristics [ndes away (Linder&Ihuerer2003).," This redshift limit matches extremely well the optimum depth for dark energy investigations, beyond which the sensitivity to the dark energy characteristics fades away \citep{linhut03}."
. However. a 2-m class space telescope such as SNAP will observe large numbers of supernovae. both SNe Ia ancl other (vpes. at redshilts 2>1.7.," However, a 2-m class space telescope such as SNAP will observe large numbers of supernovae, both SNe Ia and other types, at redshifts $z>1.7$."
 For example. the visible flux could be followed out to zzz4 and the near UV down to (SNe la have almost no emission « 2500A)) out to z6.," For example, the visible flux could be followed out to $z\approx4$ and the near UV down to (SNe Ia have almost no emission $< 2500$ ) out to $z\approx6$."
 In this article we investigate (he usefuluess of space based. wide field observations of SNe bevond 2=1.1 lor cosmology and astrophysics.," In this article we investigate the usefulness of space based, wide field observations of SNe beyond $z=1.7$ for cosmology and astrophysics."
 Section 2. addresses (he cosmological impact of extending precision distance measurements to z>1.7. including gravitational lensing effects: this will be generally applicable to any standardized candle. not just supernovae.," Section \ref{sec:cos} addresses the cosmological impact of extending precision distance measurements to $z>1.7$, including gravitational lensing effects; this will be generally applicable to any standardized candle, not just supernovae."
 The rates ancl vield of supernovae of all tvpes are discussed in relsec:measure.. together with measurement issues such as light eurve fitting. redshift determination. Alalmequist bias. ancl supernova tvping.," The rates and yield of supernovae of all types are discussed in \\ref{sec:measure}, together with measurement issues such as light curve fitting, redshift determination, Malmquist bias, and supernova typing."
 Section 4 investigates what we can learn aboul progenitor age. metallicitv. aud dust properties. aud how (his impacts treatment of svstematic uncertainties of the ϱ1.7 sample.," Section \ref{sec:sys} investigates what we can learn about progenitor age, metallicity, and dust properties, and how this impacts treatment of systematic uncertainties of the $z<1.7$ sample."
 We summarize in relsec:concl (he. prospects for using verv high redshift SNe (obtained for “free”. ancl in conjunction wilh JWST or a TAIT) to advance a variety of astrophivsical fields.," We summarize in \\ref{sec:concl} the prospects for using very high redshift SNe (obtained for “free”, and in conjunction with JWST or a TMT) to advance a variety of astrophysical fields."
 The discovery of the recent acceleration of the cosmic expansion is a breakthrough in the quest to understuxd (he universe., The discovery of the recent acceleration of the cosmic expansion is a breakthrough in the quest to understand the universe.
 To reveal the nature of the dark energy responsible for (he acceleration requires accurate measurements throughout the accelerating epoch and back into the time of deceleration., To reveal the nature of the dark energy responsible for the acceleration requires accurate measurements throughout the accelerating epoch and back into the time of deceleration.
 However. indefinite extension through the matter dominated.," However, indefinite extension through the matter dominated,"
pores of (he same polarity.,pores of the same polarity.
 For example. in Panel (a). the rectangle outlines a region with [lux emergence. where (he negative flix is moving in the upper right direction into the negalive pores and (he positive flux bands are moving in the lower left direction into the positive pores.," For example, in Panel (a), the rectangle outlines a region with flux emergence, where the negative flux is moving in the upper right direction into the negative pores and the positive flux bands are moving in the lower left direction into the positive pores."
 The coalescence of the small-scale fIuxes into the major pores facilitates the accumulation of the magnetic flux on the surface and. therefore. the formation of the large pores shown in Panel (c) and (d).," The coalescence of the small-scale fluxes into the major pores facilitates the accumulation of the magnetic flux on the surface and, therefore, the formation of the large pores shown in Panel (c) and (d)."
 ? simulates the formation of an active region and finds that the counterstreaming motion of opposite polarities is driven bv the Lorentz force., \cite{cheung2010} simulates the formation of an active region and finds that the counterstreaming motion of opposite polarities is driven by the Lorentz force.
 The large pores of negative polarity show a coherent pattern of rotation at the photosphere alter (heir formation in Panel (a) of Figure 11.., The large pores of negative polarity show a coherent pattern of rotation at the photosphere after their formation in Panel (a) of Figure \ref{bzz=0}.
 The rotation of the pores persists during (he emergence aud (he increase of magnetic flux at the photosphere., The rotation of the pores persists during the emergence and the increase of magnetic flux at the photosphere.
 llowever. (he positive polarity on the left does not present a complete rotation pattern during the emerging phase. but the rotation is interrupted by (he horizontal motions of the convective flow.," However, the positive polarity on the left does not present a complete rotation pattern during the emerging phase, but the rotation is interrupted by the horizontal motions of the convective flow."
 The coherent rotation starts to develop on the positive pore alter 5.5 hrs. shown by Panel (e) and (1) in Figure 1H..," The coherent rotation starts to develop on the positive pore after 5.5 hrs, shown by Panel (e) and (f) in Figure \ref{bzz=0}."
 Figure 12. illustrates the evolution of 2. and the horizontal velocity fields at z=—3 Mm. in the convection zone.," Figure \ref{bzz=-3} illustrates the evolution of $B_{z}$ and the horizontal velocity fields at $z = -3$ Mm, in the convection zone."
 Here. we observe a coherent rotation at (his depth on the negative polarity as well.," Here, we observe a coherent rotation at this depth on the negative polarity as well."
 The question is (hen. to what depth does the rotation extend.," The question is then, to what depth does the rotation extend."
" Thus we examine the structure of 4, on the y=0 plane during the rising of the flix rope in the upper panels in Figure 13..", Thus we examine the structure of $u_{y}$ on the $y=0$ plane during the rising of the flux rope in the upper panels in Figure \ref{roty=0}.
" The reversal of the direction of uw, in the right side of the domain corresponds to theprojection of the rotation of the negalive polarity on the y=0 plane.", The reversal of the direction of $u_{y}$ in the right side of the domain corresponds to theprojection of the rotation of the negative polarity on the $y = 0$ plane.
 The coherent rotation starts to extend downward al |—4:00:00 and approaches the depth of -10 Mam in 21 mins. (, The coherent rotation starts to extend downward at $t = 4:00:00$ and approaches the depth of -10 Mm in 21 mins. (
see Panel (a)).,see Panel (a)).
 Panel (c) shows a very coherent. pattern of rotation on the negative polarity al /=5:13:00. while on the positive pore on the left. the rotation is not obvious.," Panel (c) shows a very coherent pattern of rotation on the negative polarity at $t = 5:13:00$, while on the positive pore on the left, the rotation is not obvious."
 Sunspol rotation has long been observed aud studied in detail and has been found in association wilh CMEs (??)..," Sunspot rotation has long been observed and studied in detail and has been found in association with CMEs \citep[]{brown2003,kazachenko2009}. ."
 The rotation mechanism for sunspots found at work, The rotation mechanism for sunspots found at work
From the above results it is clear that diffusive fluxes are much more important in alleviating catastrophic quenching when compared to the Vishniac Cho fluxes (in the form,From the above results it is clear that diffusive fluxes are much more important in alleviating catastrophic quenching when compared to the Vishniac Cho fluxes (in the form
Understanding the details of galaxy. formation remains an important challenge in cosmology.,Understanding the details of galaxy formation remains an important challenge in cosmology.
 As shown by numerical calculations. the first. generation of galaxies should. have formed at very. high redshifts. inside collapsing halos. starting at 265. corresponding to high peaks of the primordial dark matter (DAL) density Ποια (Naozctal. OG).," As shown by numerical calculations, the first generation of galaxies should have formed at very high redshifts inside collapsing halos, starting at $z \sim 65$, corresponding to high peaks of the primordial dark matter (DM) density field \citep{NNB}."
 Cosmic Microwave. Background. (CMD). radiation observations suggest that reionization began at high redshifts., Cosmic Microwave Background (CMB) radiation observations suggest that reionization began at high redshifts.
 This means that a high. abundance of luminous objects must have existed. at that time. since these first Iuminous objects are expected to have heated ancl reionized their surroundings (Barkana&Loeb2001:Wyithe2003:LIaiman&LlolclerCon 2003).," This means that a high abundance of luminous objects must have existed at that time, since these first luminous objects are expected to have heated and reionized their surroundings \citep{rev,WL03,HH03,Cen}."
. The formation of a uminous object inside a halo necessarily requires the existence of barvonie gas there., The formation of a luminous object inside a halo necessarily requires the existence of baryonic gas there.
 Even in halos that are too small for cooling via atomic hyedrogen. the gas content can have substantial. and observable. astrophysical effects.," Even in halos that are too small for cooling via atomic hydrogen, the gas content can have substantial, and observable, astrophysical effects."
 In addition to the possibility of hosting astrophysical sources. such as stars. small halos may produce a 2]-cm signature (Ixuhlenetal.2006:ShapiroNaoz&Barkana2008:FurlanettoOh 2006).. and can block ionizing radiation and. produce an overall delay in the global progress of reionization (Barkana&Loeb2002:etal.2003.2005:MeQOuinn 2007).," In addition to the possibility of hosting astrophysical sources, such as stars, small halos may produce a 21-cm signature \citep{Kuhlen,Shapiro06,NB08, Furlanetto06}, and can block ionizing radiation and produce an overall delay in the global progress of reionization \citep{bl02, iliev2, iss05, mcquinn07}."
. The evolution of the halo gas fraction at various epochs of the Universe is of prime importance. particularly in the carly Universe.," The evolution of the halo gas fraction at various epochs of the Universe is of prime importance, particularly in the early Universe."
 We evaluate here the possible inlluence of a primordial magnetic field on the halo gas fraction., We evaluate here the possible influence of a primordial magnetic field on the halo gas fraction.
 As noted by Cnedin(2000):Cinedin&LIui(1998).. both in the linear and non-linear regimes. the accretion of eas into DM halos is suppressed. below a characteristic mass scale called the filtering mass. Adp.," As noted by \citet{Gnedin2000a, Gnedin1997}, both in the linear and non-linear regimes, the accretion of gas into DM halos is suppressed below a characteristic mass scale called the filtering mass, $M_F$."
 This mass scale coincides with the Jeans mass. M. if the latter does not vary in time.," This mass scale coincides with the Jeans mass, $M_J$, if the latter does not vary in time."
 Otherwise. Mp is a time average of AZ;.," Otherwise, $M_F$ is a time average of $M_J$."
 Thus. an increase in the ambient. pressure in the past. causes an increase in Aly ancl suppresses the aceretion of barvons into DAL halos in a cumulative fashion. producing an increase in Alp.," Thus, an increase in the ambient pressure in the past, causes an increase in $M_J$ and suppresses the accretion of baryons into DM halos in a cumulative fashion, producing an increase in $M_F$."
 Until now. studies focused on the UV. heating of the neutral interstellar gas as the main source of pressure. for determining the filtering mass.," Until now, studies focused on the UV heating of the neutral interstellar gas as the main source of pressure, for determining the filtering mass."
 Phese results are widely used in many semi-analvtic models (e.g. Maccióetal. 2010)). particularly those designed to study the properties of small ealaxies (due to the high redshift. character of the UV. heating).," These results are widely used in many semi-analytic models (e.g. \citealt{Maccio2009}) ), particularly those designed to study the properties of small galaxies (due to the high redshift character of the UV heating)."
specifically we can reject the faint ancl red signature of SNe la al very. high redshifts.,specifically we can reject the faint and red signature of SNe Ia at very high redshifts.
 The discovery images for all four SNe are shown in Figure 3.. and the positional ancl photometric data are listed in Tables 3. ancl 4..," The discovery images for all four SNe are shown in Figure \ref{fig:fig3}, and the positional and photometric data are listed in Tables \ref{tab:tab1} and \ref{tab:tab2}."
 Three SNe were identified in the area of the UDFP field., Three SNe were identified in the area of the UDFP field.
 was discovered in (he GOODS [ollow-up images trom GO 9352. and not detected seven mouths later (to within 50) in the UDFP images.," was discovered in the GOODS follow-up images from GO 9352, and not detected seven months later (to within $\sigma$ ) in the UDFP images."
 The host of IX0302-001 was verv faint. with FGOOGITzz28 mag within a radius. and verv blue. virtually undetectable al F850LP>27.5 in the same aperture.," The host of K0302-001 was very faint, with $F606W\approx 28$ mag within a radius, and very blue, virtually undetectable at $F850LP\ge27.5$ in the same aperture."
 The galaxy could not be sufficiently detected in anv of the deep multi- eround-based data sample assembled for the GOODS (spanning U though A.- ancl was only identified in two ACS bands: F606V and £775.," The galaxy could not be sufficiently detected in any of the deep multi-wavelength ground-based data sample assembled for the GOODS (spanning $U$ though $K_s$ -bands), and was only identified in two ACS bands: $F606W$ and $F775$."
 The lack of photometric measurements of the host galaxy made it difficult to constrain its photometric redshift using the Bavesian Photometrie Redshilt (DPZ) method (Benitez2000).. The, The lack of photometric measurements of the host galaxy made it difficult to constrain its photometric redshift using the Bayesian Photometric Redshift (BPZ) method \citep{2000ApJ...536..571B}.
 phot-z estimate derived of the host of IX0302-001. lacks a significant peak and has a broad confidence interval of 1.03<2 2.22., The $z$ estimate derived of the host of K0302-001 lacks a significant peak and has a broad confidence interval of $1.03<z<2.22$ .
 However. the photometry of the SN is more illuminating.," However, the photometry of the SN is more illuminating."
 The magnitude and colors (specilically the red. FGOGI—F850LP color of 3.33 mag: see 2004a)) match those of the five SNe Ia measured by Riessetal.(20045). at or near maxinun at zδέ1.3., The magnitude and colors (specifically the red $F606W-F850LP$ color of 3.33 mag; see \citeauthor{Riess:2003gz}~ \citeyear{Riess:2003gz}) ) match those of the five SNe Ia measured by \citet{Riess:2004b} at or near maximum at $z\approx1.3$.
 Results from Riessetal.(2004a.b) demonstrate that ~ of SNe with these photometric characteristics are correctly identified as SNe la (with the other being SNe le or Ib).," Results from \citet{Riess:2003gz,Riess:2004b} demonstrate that $\sim$ of SNe with these photometric characteristics are correctly identified as SNe Ia (with the other being SNe Ic or Ib)."
 A firm conclusion we can make is that this SN is too bright and too blue to be a SN Ia (of any previously seen Iuminosity. and color) at 2>1.4., A firm conclusion we can make is that this SN is too bright and too blue to be a SN Ia (of any previously seen luminosity and color) at $z > 1.4$.
 SN 200310 was discovered in the first UDFP stack (mean. date 2003 Ang. 31). and undetected in the GOODS [follow-up comparison images.," SN 2003lt was discovered in the first UDFP stack (mean date 2003 Aug. 31), and undetected in the GOODS follow-up comparison images."
 It was also well detected in the second UDEP stack of mean date 2003 Sep. 12., It was also well detected in the second UDFP stack of mean date 2003 Sep. 12.
 The host galaxy. was well detected in several passbands. and (thus the phot-z lor the host was well constrained al z=1.0 (0.74<21.26 conlidence interval).," The host galaxy was well detected in several passbands, and thus the $z$ for the host was well constrained at $z=1.0$ $0.74<z<1.26$ confidence interval)."
 We find that the photometry and colors of this SN were consistent with those lor a SN Ia discovered ~80 days from maximum light al z=1.0. and inconsistent with tested SN Ia scenarios (varving age. light-curve shape. and extinction) at z>1.4.," We find that the photometry and colors of this SN were consistent with those for a SN Ia discovered $\sim 80$ days from maximum light at $z=1.0$, and inconsistent with tested SN Ia scenarios (varying age, light-curve shape, and extinction) at $z>1.4$."
 SN 2003lu was found in the second UDEP stack. and notdetected in the first UDFP stack.," SN 2003lu was found in the second UDFP stack, and notdetected in the first UDFP stack."
 The single F850£ P-band measurement alone does not allow for a restriction in SN ivpe and redshift space., The single $F850LP$ -band measurement alone does not allow for a restriction in SN type and redshift space.
 However. the phot-z for the bright and. well-detected host. was zo—O.11 (0.0 - 0.25 confidence interval). and therefore we canreject the possibility that this was à SN Ia al z> 1.4.," However, the $z$ for the bright and well-detected host was $z=0.11$ (0.0 - 0.25 confidence interval), and therefore we canreject the possibility that this was a SN Ia at $z>1.4$ ."
 The only SN detected in several epochs of the UDF target. [ield. observations was, The only SN detected in several epochs of the UDF target field observations was
positive flux of the active region is computed by adding the contribution of all the pixels whose flux is larger than -—30GG (before multiplying by the above factor).,positive flux of the active region is computed by adding the contribution of all the pixels whose flux is larger than $-30$ G (before multiplying by the above factor).
 Similarly. the negative flux of the active region is computed by adding all the pixels with fluxes below +30GG. By including pixels with fluxes in the range [-30.430]GG (which represents the peak-to-peak noise) in the computations. we ensure efficient noise cancellation.," Similarly, the negative flux of the active region is computed by adding all the pixels with fluxes below $+30$ G. By including pixels with fluxes in the range G (which represents the peak-to-peak noise) in the computations, we ensure efficient noise cancellation."
 The two polarities nicely coincide in magnitude and show a similar evolution., The two polarities nicely coincide in magnitude and show a similar evolution.
 À linear decay phase is observed during the first three days., A linear decay phase is observed during the first three days.
 The flux decay rate is 9.3xΙΟ MMx day! which is intermediate in the range of values mentioned above., The flux decay rate is $9.3 \times 10^{20}$ Mx $^{-1}$ which is intermediate in the range of values mentioned above.
 We do not persue in this work whether this could have potentially contributed to the formation of the flux rope., We do not persue in this work whether this could have potentially contributed to the formation of the flux rope.
 Magnetic field extrapolations of some form would be necessary to conduct such a study. and this is beyond the scope of this paper.," Magnetic field extrapolations of some form would be necessary to conduct such a study, and this is beyond the scope of this paper."
 After curves show a plateau region. where no more net losses or gains are seen., After curves show a plateau region where no more net losses or gains are seen.
 The fractional decrease is. of course. a lower limit since we do not observe the onset of the decay phase.," The fractional decrease is, of course, a lower limit since we do not observe the onset of the decay phase."
 This plateau region was also encountered by ?:: however. in their study. the amount of flux lost was found to be in the range of 50—70 the initial value.," This plateau region was also encountered by \citet{sainz08}; however, in their study, the amount of flux lost was found to be in the range of $50-70$ the initial value."
 The sliding door phenomenon was seen to occur on July 3rd., The sliding door phenomenon was seen to occur on July 3rd.
 This date sits in the linear decay phase of the AR., This date sits in the linear decay phase of the AR.
 However. this phase was already taking place before and no particular slope change is seen on July 3rd.," However, this phase was already taking place before and no particular slope change is seen on July 3rd."
 The appearance of the orphan penumbrae structures happens on July 4th and 5th. coinciding with the flat section of the flux curve.," The appearance of the orphan penumbrae structures happens on July 4th and 5th, coinciding with the flat section of the flux curve."
 Clearly. these processes (sliding door and orphan-penumbrae generation) cause a minimal impact on the flux curves.," Clearly, these processes (sliding door and orphan-penumbrae generation) cause a minimal impact on the flux curves."
 One way to explain this result would require that the amount of flux change involved in both processes were at. or below. the noise level of the data (20.3x10°! MMx).," One way to explain this result would require that the amount of flux change involved in both processes were at, or below, the noise level of the data $\pm 0.3 \times 10^{21}$ Mx)."
 The first set of spatial scans were taken on 2005 July 3rd. centered on the filament.," The first set of spatial scans were taken on 2005 July 3rd, centered on the filament."
" Two maps with a FOV of 36""x35”. which was unfortunately not large enough to cover the whole active region (see Fig. 3))."," Two maps with a FOV of $36\arcsec \times 35\arcsec$, which was unfortunately not large enough to cover the whole active region (see Fig. \ref{Fig:MDIevol}) ),"
 were acquired with TIP-II between 13:53 and 15:01 UT., were acquired with TIP-II between 13:53 and 15:01 UT.
 The filament is seen all along the vertical direction., The filament is seen all along the vertical direction.
 Slit-reconstructed maps at different wavelengths for one of the two data sets for this day are presented in the first column of Fig. 5.., Slit-reconstructed maps at different wavelengths for one of the two data sets for this day are presented in the first column of Fig. \ref{Fig:TIPmaps}.
 The frames in this figure are located at different positions to approximately represent the alignment of their respective FOVs., The frames in this figure are located at different positions to approximately represent the alignment of their respective FOVs.
 The panel shows a tight filament spine. inferred from the strong absorption. which extends along the vertical direction.," The panel shows a tight filament spine, inferred from the strong absorption, which extends along the vertical direction."
 There are no big pores. but only some small magnetic features (dark patches) seen among the granulation in the continuum image on the panel of the figure.," There are no big pores, but only some small magnetic features (dark patches) seen among the granulation in the continuum image on the panel of the figure."
 The line core image (in the middle row) shows dark areas with larger absorption in regions of weak longitudinal fielc (this line weakens in faculae. as do most photospheric lines).," The line core image (in the middle row) shows dark areas with larger absorption in regions of weak longitudinal field (this line weakens in faculae, as do most photospheric lines)."
 The second set of spectropolarimetric data was taken on July 5th between 7:36 and 14:51 UT. columns 2-4 in Fig. 5..," The second set of spectropolarimetric data was taken on July 5th between 7:36 and 14:51 UT, columns 2–4 in Fig. \ref{Fig:TIPmaps}."
 Each sean took around 20 minutes to complete., Each scan took around 20 minutes to complete.
 The acquired maps were centered at a highly 1teresting area with very tight opposite polarities that correspoded. in continuum image. to pores and orphan penumbrae. all located along the PIL.," The acquired maps were centered at a highly interesting area with very tight opposite polarities that corresponded, in continuum image, to pores and orphan penumbrae, all located along the PIL."
 Note that these maps overlap with the upper half of the former map from July 3rd (see black boxes in Fig., Note that these maps overlap with the upper half of the former map from July 3rd (see black boxes in Fig.
 3. to get a better notion of the FOV)., \ref{Fig:MDIevol} to get a better notion of the FOV).
 The red core intensity Images in the row of Fig., The red core intensity images in the row of Fig.
 5. still show the spine of the filament in the lower part., \ref{Fig:TIPmaps} still show the spine of the filament in the lower part.
 Moreover. the filamet in the upper part appears to be more diffused and extended.," Moreover, the filament in the upper part appears to be more diffused and extended."
 One can easily distinguish dark Helium threads formed on July Sth especially in the panel of Fig. 5.., One can easily distinguish dark Helium threads formed on July 5th especially in the panel of Fig. \ref{Fig:TIPmaps}. .
" Many authors have observed the presence of threads in filaments and prominences before (e.g..2291,"," Many authors have observed the presence of threads in filaments and prominences before \citep[e.g.,][]{menzel60,engvold76,lin05,lin08,okamoto07}."
 It is generally believed that dark thin features in the chromosphere near ARs trace magnetic field lines., It is generally believed that dark thin features in the chromosphere near ARs trace magnetic field lines.
 This idea ts particularly interesting when applied to threads seen in AR filaments. since it could explain the presence of magnetic dips where plasma is trapped.," This idea is particularly interesting when applied to threads seen in AR filaments, since it could explain the presence of magnetic dips where plasma is trapped."
 Nevertheless. care must be taken. since a recent paper by ? proved that chromospheric fibrils mostly. but not always. trace magnetic field lines.," Nevertheless, care must be taken, since a recent paper by \citet{jaime11} proved that chromospheric fibrils mostly, but not always, trace magnetic field lines."
 From our maps we see that the threads observed with TIP-II change only slightly in a time range of 5-6 hours., From our maps we see that the threads observed with TIP-II change only slightly in a time range of 5–6 hours.
This becomes apparent when closely comparing the Helium maps of columns 2 and 4 in Fig. 5..,This becomes apparent when closely comparing the Helium maps of columns 2 and 4 in Fig. \ref{Fig:TIPmaps}.
 The short white arrow in the panel of the last column points at one of these threads. and can be compared with the same position in the core and continuum images.," The short white arrow in the panel of the last column points at one of these threads, and can be compared with the same position in the core and continuum images."
 From these maps we see that the most prominent threads are located above pores or orphan penumbrae., From these maps we see that the most prominent threads are located above pores or orphan penumbrae.
 A more detailed study of the magnetic configuration of these threads is presented below in Sect. ?2.., A more detailed study of the magnetic configuration of these threads is presented below in Sect. \ref{Sect:threads}.
 Strong absorption in the line core is present below the spine of the filament on July Sth (see Fig. 5))., Strong absorption in the line core is present below the spine of the filament on July 5th (see Fig. \ref{Fig:TIPmaps}) ).
 It is remarkable that the axis of the filament seems to lay so low in the atmosphere that even the highest layers of the photospheric Silicon absorption line (at the core of the line) trace it., It is remarkable that the axis of the filament seems to lay so low in the atmosphere that even the highest layers of the photospheric Silicon absorption line (at the core of the line) trace it.
 High resolution (07007I/px) Πα images from the Dutch Open Telescope (DOT:?) for the morning of 2005 July Sth confirm the presence of the filament. which has an inverse S-like shape and a spine in its lower part.," High resolution 071/px) $\alpha$ images from the Dutch Open Telescope \citep[DOT;][]{DOT} for the morning of 2005 July 5th confirm the presence of the filament, which has an inverse S-like shape and a spine in its lower part."
 This is also confirmed by inspection of at 171 limages., This is also confirmed by inspection of at $171$ images.
 Such an inverse S-like shape is likely to be expected in the northern hemisphere (2).., Such an inverse S-like shape is likely to be expected in the northern hemisphere \citep{pevtsov01}.
 The panel of Fig., The panel of Fig.
 6 shows one image of the Ha data set taken by the DOT at 8:44 UT., \ref{Fig:DOT} shows one image of the $\alpha$ data set taken by the DOT at 8:44 UT.
 The filament is surrounded by a bright plage., The filament is surrounded by a bright plage.
 The image reveals small arch-like structures in the upper half of the filament that are almost perpendicular to its axis and. in the spine. then stretch along it towards its center.," The image reveals small arch-like structures in the upper half of the filament that are almost perpendicular to its axis and, in the spine, then stretch along it towards its center."
 These archs can be identified as the H« counterpart of the threads mentioned before., These archs can be identified as the $\alpha$ counterpart of the threads mentioned before.
 A continuumimage (with a, A continuumimage (with a
We uow compare our results for the weak-leusing dspectruni with numerical simulations.,We now compare our results for the weak-lensing bispectrum with numerical simulations.
 Iu addition. we also consider the predictions obtained from the following our simple models. which have been used iu some previous works.," In addition, we also consider the predictions obtained from the following four simple models, which have been used in some previous works."
" We first compute the results obtained from the owest-order (""trec-ordor prediction from standard erturbation theory for the )3D bispectimm (?).. (Aj. 2Pa(hy Prk hop)Pr(he) | eve. where pio»=(sy-ko)/(hyho) and :l25.1 Mas |v"," We first compute the results obtained from the lowest-order (“tree-order”) prediction from standard perturbation theory for the 3D bispectrum \citep{Bernardeau2002}, (k_1,k_2,k_3) = 2 P_L(k_1) P_L(k_2) + 2 where $\mu_{12}= (\vk_1\cdot\vk_2)/(k_1 k_2)$ and = + ) +."
"h Second. we consider a “trec-nonlincar” approximation where in Eq.(28)) we replace the linear 3D power Pp(h) by the nonlinear power ο) frou ?.. oakJu Ευ. Path Pshy) | 2 Third. we cousider the fitting formula frou ?.. Un:ho.ha) = 2 πα. | 2 where the kernel Foxp is an effective kernel that interpolates from the large-scale perturbative result (29)) to a suallseale ansatz where the angular depeudenuce Don, Avudishes."," Second, we consider a “tree-nonlinear” approximation where in \ref{B-treeL-def}) ) we replace the linear 3D power $P_L(k)$ by the nonlinear power $P_S(k)$ from \cite{Smith2003}, (k_1,k_2,k_3) = 2 P_S(k_1) P_S(k_2) + 2 Third, we consider the fitting formula from \cite{Scoccimarro2001a}, (k_1,k_2,k_3) = 2 P_S(k_1) P_S(k_2) + 2 where the kernel $F_{2,\rm NL}$ is an effective kernel that interpolates from the large-scale perturbative result \ref{F2-def}) ) to a small-scale ansatz where the angular dependence on $\mu_{12}$ vanishes."
 Tere we shall use the noulineax power spectitun Ps(h) from ? as well as the nonlinear power spectrin Prane(40) of our model. Eqxs(17))-(18)).," Here we shall use the nonlinear power spectrum $P_S(k)$ from \cite{Smith2003} as well as the nonlinear power spectrum $P_{\rm tang}(k)$ of our model, \ref{P-tang-1}) \ref{P-tang-2}) )."
" Four. we cousider the scale transformation studied Z1 following the spirit of the scale transformation FU,introduced iu ?. for the tvo-poiut correlation function aud next∙ in 7?↻∪↖↖↸↥↴∖↻∩↑⊔∐⊔⋅ for the (29)↴∖⊳⋅ DAbomkey) = lhe. imb ο”. Dy wm, 3e"," Four, we consider the scale transformation studied in \cite{Pan2007}, following the spirit of the scale transformation introduced in \cite{Hamilton1991}
 for the two-point correlation function and next in \cite{Peacock1996} for the power spectrum, (k_1,k_2,k_3) = _1) _2) _3) 2 _1) _2) + 2"
Planetary nebulae (PNe) are the ionised nebulae ejected by Ιow-intermediate[liat mass stars[ that |have undergoneunclere: extensive[ mass loss during the AGB phase.,Planetary nebulae (PNe) are the ionised nebulae ejected by low-intermediate mass stars that have undergone extensive mass loss during the AGB phase.
 The central stars. of planctary nebulae (CSPN) constitute a rich resource to study the [ate stages of binary stellar evolution., The central stars of planetary nebulae (CSPN) constitute a rich resource to study the late stages of binary stellar evolution.
 At least 40 ‘lose binary CSPN are known that have orbital periods less than ~1 day (Aliszalski ct al., At least 40 close binary CSPN are known that have orbital periods less than $\sim$ 1 day (Miszalski et al.
 2011a) and these make up at least 17dE5% of all CSPN (Miszalski et al., 2011a) and these make up at least $17\pm5$ of all CSPN (Miszalski et al.
 20092), 2009a).
 With their short-lived nebulae (~10 ves) close binary CSPN are assured. to have just. recently. passed. through the comumon-envelope (CL) phase (ben Livio. 1993)., With their short-lived nebulae $\sim$ $^4$ yrs) close binary CSPN are assured to have just recently passed through the common-envelope (CE) phase (Iben Livio 1993).
 With significantly. less time to undergo further. angular momentum. loss compared. to other more evolved: post-CI binaries (Schreiber Gannsicke 2003). the orbital periods of close binary CSPN reflect the true post-CL distribution.," With significantly less time to undergo further angular momentum loss compared to other more evolved post-CE binaries (Schreiber Gännsicke 2003), the orbital periods of close binary CSPN reflect the true post-CE distribution."
AX reliable: wav of establishing that the chosen partial coverage model can (or cannot) give rise to a detectable ADR for a given SNR combination is to perform a set of simulations. as explained in the next subsection.,"A reliable way of establishing that the chosen partial coverage model can (or cannot) give rise to a detectable ADR for a given –SNR combination is to perform a set of simulations, as explained in the next subsection."
 Once the detectabilitv. or not. of the ADR has been established. this can be compared. to. the.ασ situation in the observed spectrum.," Once the detectability, or not, of the ADR has been established, this can be compared to the situation in the observed spectrum."
 For each SNR combination there are four possibilities: Cases (ii) and (id) are useful lor estimating absorber sizes: dn case (di)partial coverage ds established and. herefore. the transverse size of the absorber must besmaller han the proper separation of the LOS at the absorbing redshift.," For each –SNR combination there are four possibilities: Cases (ii) and (iii) are useful for estimating absorber sizes: In case (ii) coverage is established and, therefore, the transverse size of the absorber must be than the proper separation of the LOS at the absorbing redshift."
 Conversely. in case (iii)/o/al coverage is established and the transverse size of the absorber must befarger than he proper separation of the LOS.," Conversely, in case (iii) coverage is established and the transverse size of the absorber must be than the proper separation of the LOS."
 Further. a maximum likelihood approach can be used ο estimate most probable absorber sizes from the number ob established. partial and total coverage cases.," Further, a maximum likelihood approach can be used to estimate most probable absorber sizes from the number of established partial and total coverage cases."
 Each of the 100 fitted ppairs mentioned above gives a single r value ai can be used to produce an artificial continuum normalize absorption profile. e..," Each of the 100 fitted pairs mentioned above gives a single $\tau$ value and can be used to produce an artificial continuum normalized absorption profile, $e^{-\tau}$."
 If one adds a term o=1.520 to each data point in this profile. one effectively. introduces excess Hux due to partial coverage from our chosen physical moce 5)).," If one adds a term $\alpha=1.520$ to each data point in this profile, one effectively introduces excess flux due to partial coverage from our chosen physical model )."
 Decause the SNR. varies considerably over the observe: spectrum from ~25 to ~120. for cach region containing a celoublet component an average SNR. value was cetermines by inspection of the spectrum using the task inLRAL.," Because the SNR varies considerably over the observed spectrum from $\sim 25$ to $\sim 120$, for each region containing a doublet component an average SNR value was determined by inspection of the spectrum using the task in."
 For cach Iv)). pair two artificial spectra were produced., For each ) pair two artificial spectra were produced.
 “Phe first spectrum contained 120 dedoublets with a profile e.., The first spectrum contained 120 doublets with a profile $e^{-\tau}$.
 The spacing of the lines was chosen empiricallv so that when subsequently the. lines would be fitted withvrrrr.. blending complications would be absent. ie. even the broadest Lines were well apart from each other.," The spacing of the lines was chosen empirically so that when subsequently the lines would be fitted with, blending complications would be absent, i.e. even the broadest lines were well apart from each other."
 The spectrum was resampled to the resolution of the observed spectrum (0.04 pper pixel) and smoothed to the instrumental resolution of 6.6 , The spectrum was resampled to the resolution of the observed spectrum (0.04 per pixel) and smoothed to the instrumental resolution of 6.6 .
Gaussian noise was added with o=ΒΛl to obtain the desirable final SNR. as measured beforehand for cach region.," Gaussian noise was added with $\sigma=\frac{1}{\rm SNR}$ to obtain the desirable final SNR, as measured beforehand for each region."
 The above process was repeated to produce another set of 120 simulations of the same line aiming to reproduce the ellects of excess Dux., The above process was repeated to produce another set of 120 simulations of the same line aiming to reproduce the effects of excess flux.
 This time gaussian noise with oa=SKHlon =vas added to the unit continuum spectrum and both data and continuum were then inereasecl by a., This time gaussian noise with $\sigma=\frac{1+\alpha}{\rm SNR}$ was added to the unit continuum spectrum and both data and continuum were then increased by $\alpha$.
 This ensured that 1. desired SNR was obtained in this case as well., This ensured that the desired SNR was obtained in this case as well.
 Next. wwas used to fit the artificial spectra.," Next, was used to fit the artificial spectra."
 Each of the 120 artificial doublets in the spectrum was fitted independently. so that 120 separate vvalues were obtained.," Each of the 120 artificial doublets in the spectrum was fitted independently, so that 120 separate values were obtained."
 The starting vyvalues for the iiterations were exactly the same as those used to make the simulated lines. so that one would expect to obtain a good fit. unless the elfects of excess [ux were significant.," The starting values for the iterations were exactly the same as those used to make the simulated lines, so that one would expect to obtain a good fit, unless the effects of excess flux were significant."
 wwas allowed: to fit only a single Voigt profile to each simulated. line., was allowed to fit only a single Voigt profile to each simulated line.
 Phe. option of automatically putting in acditional narrow lines to improve poor fits was not use since such lines were known to be spurious by construction., The option of automatically putting in additional narrow lines to improve poor fits was not used since such lines were known to be spurious by construction.
 The fitting region for each doublet component was centrec on the component aand extended ΣΕ where EWIIM=2Vln2b is the full width at half minimum.," The fitting region for each doublet component was centred on the component and extended over $3\times {\rm FWHM}$, where ${\rm FWHM}=2\sqrt{\ln 2} \ b$ is the full width at half minimum."
 This was done to avoic including too much continuum which can make a poor fi less pronounced., This was done to avoid including too much continuum which can make a poor fit less pronounced.
 If fora given ppair the higher continuum introduced an observable ADI. then. on average. the second set of 120 [its should be markedly poorer than the firstset.," If for a given pair the higher continuum introduced an observable ADR, then, on average, the second set of 120 fits should be markedly poorer than the firstset."
 Otherwise. the two," Otherwise, the two"
The study of magnetic eclueuts at very μπα scales Is One ¢ft the most iuportant topics in solar pliwvsics.,The study of magnetic elements at very small scales is one of the most important topics in solar physics.
 Magnetic Bright Poiuts (AIBPs) are ubiquitous iu the solar photosphere., Magnetic Bright Points (MBPs) are ubiquitous in the solar photosphere.
 They have suall dizuueters. typically less than 300 kni aud are fouid iu the iutererauuar lanes.," They have small diameters, typically less than 300 km, and are found in the intergranular lanes."
 MBPs correspond to areas of kilogauss fieds. are best observed in C-band disk eeitre Huages aud are nuinerous in active reelons Or car suspots.," MBPs correspond to areas of kilogauss fields, are best observed in G-band disk centre images and are numerous in active regions or near sunspots."
 They are formed. weal coniplex process involviug the interaction of he Πα field wih the couvectively wnstable hot rlasuua., They are formed by a complex process involving the interaction of the magnetic field with the convectively unstable hot plasma.
 T physical processes associated with their formalon been outlined iu Scehüssleretal.(2003):5iclvagο(2001):Carlssonetal.(200 1).. usiic forward node of radiative iiagneto-coivection iu he solar photosphere and upper convection zone.," The physical processes associated with their formation have been outlined in \citet{shelyagbp1,shelyagbp2,carlsson}, using forward modelling of radiative magneto-convection in the solar photosphere and upper convection zone."
 Despie the overal SILCCOSS M4 photospheric a sub-phnotosphnerie raciaive 1naegneOQ-convective models to reproduce imany of the observational properties solar radiation. we still «lo LO tly understaud 1ο physical processes invoved in t1ο stronely maguoetised photospheric plasma.," Despite the overall success of photospheric and sub-photospheric radiative magneto-convective models to reproduce many of the observational properties of solar radiation, we still do not fully understand the physical processes involved in the strongly magnetised photospheric plasma."
 I1 particular. it is difficult to use 1ο results of these simlations for studies of acoustic wave propagation through the solar amosphere aud interior.," In particular, it is difficult to use the results of these simulations for studies of acoustic wave propagation through the solar atmosphere and interior."
 Strong convective motions of the photospheric plaslia can hide the signatures of ACOsIc waves. nakius them. a dificult subject in oth παΊσα. aud observatioial investigatious.," Strong convective motions of the photospheric plasma can hide the signatures of acoustic waves, making them a difficult subject in both numerical and observational investigations."
 The developiieu of new inethods for inferring he xoperties of solar plasma using sound waves have becu ollowed. bv the successful modeling of the magioto-acoustic properties iu the solar atmosphere aud iuterior (ITasanetal..2005:ITanasogeal.2007:Παρα&vauSteiner.2009:Vieceshetal.. 2009)..," The development of new methods for inferring the properties of solar plasma using sound waves have been followed by the successful modelling of the magneto-acoustic properties in the solar atmosphere and interior \citep{hasan2, hanasoge, hasan1, fedun, khomenko2, parchevskii, shelyag4, 
steiner1,vigeesh1}."
 ITowever. duc to the 1oni-localitv of radiative processes in the solar atmosphere. a direct comparison of the plasina parameters at a certainyoomctrical depth in the computational box with the solar radiation paraincters at a eivenoptical depth may not be entirely correct.," However, due to the non-locality of radiative processes in the solar atmosphere, a direct comparison of the plasma parameters at a certain depth in the computational box with the solar radiation parameters at a given depth may not be entirely correct."
 The nou-localitv of radiative trausport iust be taken iuto account., The non-locality of radiative transport must be taken into account.
 Iliomoeuko&Collaos(2009) have recently sugeested that the changes in tje height of continuum formation with respect to the equipartition laver (the laver where the Alfvéóun speed is eqal to the sound speed. ey=ος). nav help to explain the appearance of the high-frequency acoustic haloes around suispots.," \citet{khomenkol2009} have recently suggested that the changes in the height of continuum formation with respect to the equipartition layer (the layer where the Alfvénn speed is equal to the sound speed, $v_A=c_s$ ), may help to explain the appearance of the high-frequency acoustic haloes around sunspots."
 παΊσαι siuulations of solu wave phenomena require a static magnetic configuration nioel which Incorporates as many physical properties of the real Sun as »ossible., Numerical simulations of solar wave phenomena require a static magnetic configuration model which incorporates as many physical properties of the real Sun as possible.
 In this paper we provide a recipe to create such a model. based ou the results of ummerical uodelliug of naenueo-convection in the photosphere.," In this paper we provide a recipe to create such a model, based on the results of numerical modelling of magneto-convection in the photosphere."
 We demonstrate hat the spectropoluinetrie properties of t10 Inaegnetic confietration we created successfully reproduces those of MDBPs., We demonstrate that the spectropolarimetric properties of the magnetic configuration we created successfully reproduces those of MBPs.
 Iu Section 2 we describe the tecinique used ο recumstruct the magnetic aud thermal parameters of he MBP model., In Section 2 we describe the technique used to reconstruct the magnetic and thermal parameters of the MBP model.
 The results of the spectro»olarimetric simulaions using the model are preseuted iu Section 3., The results of the spectropolarimetric simulations using the model are presented in Section 3.
 Iu Section Lowe show our preliminary results «n the wave uode couversion in the MDDP and discuss he possible observational signatures., In Section 4 we show our preliminary results on the wave mode conversion in the MBP and discuss the possible observational signatures.
 Our concluding remarks are xeseuted In Section 5., Our concluding remarks are presented in Section 5.
 We use a snapshot from tjo 7age magneto-convection siuulation of the solar photosphere undertaken with the MURAAM code (Voelereta2005) to produce the average MBP uxxdel.," We use a snapshot from the ""plage"" magneto-convection simulation of the solar photosphere undertaken with the MURaM code \citep{voegler1} to produce the average MBP model."
 Since the avecrage naenetic field flux in this sunapslio is relatively hiel (200 CO. a large ΠΠΡΟ of intereranular magnetic ficld coicentrations are generated.," Since the average magnetic field flux in this snapshot is relatively high $200~\mathrm{G}$ ), a large number of intergranular magnetic field concentrations are generated."
 The magnetic feld conceitrationus appear bright iu the cout m(A= 1300À).aIT 11 he € bid.," The magnetic field concentrations appear bright in the continuum $\lambda=4300\mathrm{\AA}$ ), and in the G band."
" This snapshot has been used to demonstrate 16 Inaenetic"" nature of the C-banud bight points (Schiissleretal.203:Shelvagal. 2001)."," This snapshot has been used to demonstrate the magnetic nature of the G-band bright points \citep{shelyagbp1,shelyagbp2}. ."
. To reveal the ]ose structure «ft the vertical component of the magnetic feld Dy. im the AIBPs. we average the depth depeucdices of the verical magnetic field strength over the brigif points. whichn are selected by their culauced C-band lutensity and naenetic field streneth.," To reveal the basic structure of the vertical component of the magnetic field $B_{0z}$ in the MBPs, we average the depth dependences of the vertical magnetic field strength over the bright points, which are selected by their enhanced G-band intensity and magnetic field strength."
 Fig., Fig.
 d shows D. as afunction ¢ot depth., \ref{fig1} shows $B_{0z}$ as afunction of depth.
 Note that 7=0 on the depth scaο COLTCSPOlleIs ο the average, Note that $z=0$ on the depth scale corresponds to the average
The parameter A is eliminated «quite easily.,The parameter $\lambda$ is eliminated quite easily.
" We first multiply each of the A equations by the corresponding 5; ancl then sum them up to eet: Changing the order of summation reduces the first term. after a simple manipulation. {ο simply Using the constraint reduces (he second term to A. and we finally get: and we can simply set A=—V,yy."," We first multiply each of the $K$ equations by the corresponding $b_k$ and then sum them up to get: Changing the order of summation reduces the first term, after a simple manipulation, to simply Using the constraint reduces the second term to $\lambda$, and we finally get: and we can simply set $\lambda = -N_{eff}$."
 The fy equations we are now left with are: We have a set of A non-linear equations in A variables - ὃς. An elegant reduction of the complexity of the problem can be achieved if we set A to AN. by assigning mj=yy lor h=1.....:V.," The $K$ equations we are now left with are: We have a set of $K$ non-linear equations in $K$ variables - $b_k$ 's. An elegant reduction of the complexity of the problem can be achieved if we set $K$ to $N$, by assigning $m_k \equiv y_k$ for $k = 1,\ldots,N$."
 Let us also denote (remember (hat now A= NJ): The NV equations now look like: which is a svstem of .N linear equations in the No variables f;., Let us also denote (remember that now $K=N$ ): The $N$ equations now look like: which is a system of $N$ linear equations in the $N$ variables $h_j$.
 We can easily solve [or them., We can easily solve for them.
 The problem is even more easily solved when we note that the matrix 1j is, The problem is even more easily solved when we note that the matrix $A_{jk}$ is
small but significant re-orientation of the magnetic field is expected. from the wy-plane into the z-direction.,"small but significant re-orientation of the magnetic field is expected, from the $xy$ -plane into the $z$ -direction."
 Plotting the evolution. of the magnetic energies in cach of the three directions however. shows that there is. in fact. no significant erowth in the z-direction (see figure 7)).," Plotting the evolution of the magnetic energies in each of the three directions however, shows that there is, in fact, no significant growth in the $z$ -direction (see figure \ref{hall_ideal_bxyz2}) )."
 This is in distinct opposition with the results (rom Paper L in which significant growth of the magnetic energy in the z-direction was observed for the same level o£ Llall resistivity.," This is in distinct opposition with the results from Paper I, in which significant growth of the magnetic energy in the $z$ -direction was observed for the same level of Hall resistivity."
 Lt is important to recall that the strength of the Hall ellect depends on the current in the svstem., It is important to recall that the strength of the Hall effect depends on the current in the system.
 The current. in urn. depends on the charge densities of the three charged uids.," The current, in turn, depends on the charge densities of the three charged fluids."
 Phe charge density of the dust &rain Duid is 6593τεSOPsatCem 7.," The charge density of the dust grain fluid is $\alpha_3 \rho_3 \approx -8 \times 10^{-18} \,\mbox{statC\,cm}^{-3}$ ."
 However. for the ion and. electron uids. the charge densities are much higher. approximately x5.10“statCem7.," However, for the ion and electron fluids, the charge densities are much higher, approximately $\pm 5 \times 10^{-15} \, \mbox{statC\,cm}^{-3}$."
 Therefore the current in the svsten. J=NM oipivisds primarily due to the velocity dillerence »etween the ion and electron IEuids.," Therefore the current in the system, $\mathbf{J} = \sum_{i} \alpha_i \rho_i \mathbf{v}_i$, is primarily due to the velocity difference between the ion and electron fluids."
 Therefore. while the decoupling of the dust grain [ui rom the magnetic field provides a high Llall resistivity. the strength ofthe Hall effect is in fact also critically dependen on the dvnamies of the ion Iuid relative to the electron [uid.," Therefore, while the decoupling of the dust grain fluid from the magnetic field provides a high Hall resistivity, the strength of the Hall effect is in fact also critically dependent on the dynamics of the ion fluid relative to the electron fluid."
" As the ion fluid. Hall parameter is much greater than 1i will be somewhat decoupled from the neutral Εις, insteac »ing more strongly tied to the magnetic field."," As the ion fluid Hall parameter is much greater than 1 it will be somewhat decoupled from the neutral fluid, instead being more strongly tied to the magnetic field."
 Vhis means hat the relative velocity between the ion and electron Iu will be rather small., This means that the relative velocity between the ion and electron fluid will be rather small.
 As a result. the majority of current in he svstem remains{οἱ to the magnetic field. and the strength ofthe Lall clleet. which is proportional to J.B. is very small.," As a result, the majority of current in the system remains to the magnetic field, and the strength of the Hall effect, which is proportional to $\mathbf{J} \times \mathbf{B}$, is very small."
 Vhis accounts for the growth of the magnetic ield in the z-direction being much less than would naively »f expected., This accounts for the growth of the magnetic field in the $z$ -direction being much less than would naively be expected.
 Put simply. the introduction. of ambipolar resistivity changes which fluids are coupled to which ancl. in doing so. inhibits the Hall elfect.," Put simply, the introduction of ambipolar resistivity changes which fluids are coupled to which and, in doing so, inhibits the Hall effect."
 On a side note. this can also occur in a system with only two charged fuids.," On a side note, this can also occur in a system with only two charged fluids."
 In this case. it is typically the ion luid that is the Larger contributor to both the Lall and aimbipolar conductivity.," In this case, it is typically the ion fluid that is the larger contributor to both the Hall and ambipolar conductivity."
 Phe decoupling of the ion [uid from he magnetic field leads to Llall resistivity. as anv velocity dillerence between the ion and electron Duid can give rise to a current with a component perpendicular to the magnetic ield.," The decoupling of the ion fluid from the magnetic field leads to Hall resistivity, as any velocity difference between the ion and electron fluid can give rise to a current with a component perpendicular to the magnetic field."
 Llowever. the ambipolar resistivity arises due to a low collision rate between the ion IHuid and the neutral uid.," However, the ambipolar resistivity arises due to a low collision rate between the ion fluid and the neutral fluid."
 As a result. the ions do not. in fact. behave in the same way as he neutrals.," As a result, the ions do not, in fact, behave in the same way as the neutrals."
 Their coupling with the magnetic field. though weak. is sullicient to ensure only a minimal relative velocity between the ions and. electrons.," Their coupling with the magnetic field, though weak, is sufficient to ensure only a minimal relative velocity between the ions and electrons."
 In this way. the impact of the Tall effect is similarly. reciucecd.," In this way, the impact of the Hall effect is similarly reduced."
 In a Hall-dominated How. we would expect to see not only a growth in magnetic field strength in the z-direction. but also a resulting growth of kinetic energv in the same irection. as the plasma is influenced to travel out of the gy-plane.," In a Hall-dominated flow, we would expect to see not only a growth in magnetic field strength in the $z$ -direction, but also a resulting growth of kinetic energy in the same direction, as the plasma is influenced to travel out of the $xy$ -plane."
 With even moderate Lall resistivity. this kinetic nergy in the z-direction can become comparable to that in je weclirection (see Paper D.," With even moderate Hall resistivity, this kinetic energy in the $z$ -direction can become comparable to that in the $x$ -direction (see Paper I)."
 However. in this multilluid ase. the magnetic field. experiences. only a minimal re-xientation into the z-direction. ane therefore only the Duids mt are tightly coupled to the magnetic field will experience nv noticeable dynamics in this direction.," However, in this multifluid case, the magnetic field experiences only a minimal re-orientation into the $z$ -direction, and therefore only the fluids that are tightly coupled to the magnetic field will experience any noticeable dynamics in this direction."
 Figure 8. shows jut the bulk [ow demonstrates negligible erowth of kinetic energy in the z-direction (upper panel). while the ion Duid. ing more Closely tied to the magnetic field. demonstrates a verv small. but. non-negligible. growth in this direction (lower panel).," Figure \ref{hall_ideal_kx_perturbB+kz_bz2} shows that the bulk flow demonstrates negligible growth of kinetic energy in the $z$ -direction (upper panel), while the ion fluid, being more closely tied to the magnetic field, demonstrates a very small, but non-negligible, growth in this direction (lower panel)."
 The WI instability is seen to undergo a very cillerent evolution in the presence of multilluid effects., The KH instability is seen to undergo a very different evolution in the presence of multifluid effects.
 La the ideal case. the initial wind-up of the velocity field has the elfect of also winding up the magnetic field. due to strong coupling between the two.," In the ideal case, the initial wind-up of the velocity field has the effect of also winding up the magnetic field, due to strong coupling between the two."
 As the KIL vortex is caused to stretch and expand by the amplified magnetic field. it reaches the periodic y-boundaries of the simulated grid.," As the KH vortex is caused to stretch and expand by the amplified magnetic field, it reaches the periodic $y$ -boundaries of the simulated grid."
 As the neighbouring vortices merge. numerical viscosity allows for magnetic reconnection. which results in the creation of," As the neighbouring vortices merge, numerical viscosity allows for magnetic reconnection, which results in the creation of"
Figure 9. shows the simulation results (relaxation timescales and conversion efficiency of the particle energy into the waves) for the different relative concentrations of the energetic electrons (p/n=107. 107. and 1) while the total plasma density is assumed to be constant (0.=2x10% em? that corresponds to w)/wy= 1077).,"Figure \ref{par_nb} shows the simulation results (relaxation timescales and conversion efficiency of the particle energy into the waves) for the different relative concentrations of the energetic electrons $n_{\mathrm{b}}/n=10^{-4}$, $10^{-2}$, and 1) while the total plasma density is assumed to be constant $n=2\times 10^7$ $\textrm{cm}^{-3}$ that corresponds to $\omega_{\mathrm{p}}/\omega_{\mathrm{B}}=10^{-2}$ )."
 The typical energy of the accelerated electrons £y and the loss-cone boundary a. equal 10 keV and 60°. respectively.," The typical energy of the accelerated electrons $E_{\mathrm{b}}$ and the loss-cone boundary $\alpha_{\mathrm{c}}$ equal 10 keV and $60^{\circ}$, respectively."
 One can see that the relaxation timescales are simply inversely proportional to the concentration of the energetic. particles., One can see that the relaxation timescales are simply inversely proportional to the concentration of the energetic particles.
 The conversion efficiency of the particle energy into the waves increases slightly with increasing 75/72 and varies from to13., The conversion efficiency of the particle energy into the waves increases slightly with increasing $n_{\mathrm{b}}/n$ and varies from to.
"6%.. Figure 10. shows the simulation results for the case when the concentration of the energetic particles is constant (ji=2x10° em?) while the total plasma density varies (which results in different ratios both of n,/n and c/c)."," Figure \ref{par_Y} shows the simulation results for the case when the concentration of the energetic particles is constant $n_{\mathrm{b}}=2\times 10^5$ $\textrm{cm}^{-3}$ ), while the total plasma density varies (which results in different ratios both of $n_{\mathrm{b}}/n$ and $\omega_{\mathrm{p}}/\omega_{\mathrm{B}}$ )."
 With increasing, With increasing
rend for the median velocity. dispersion when considering smaller host-groups distances.,trend for the median velocity dispersion when considering smaller host-groups distances.
 Top panel of figure 1. shows he above mentioned trend. for all svstems in our group sample.," Top panel of figure \ref{masa} shows the above mentioned trend, for all systems in our group sample."
 As we are considering host-group distances starting at 3Alpeh miscaleulation of group velocity. dispersion owing to hosts particles contamination. is not likely to happen.," As we are considering host-group distances starting at $3~Mpc ~h^{-1}$, miscalculation of group velocity dispersion owing to hosts particles contamination, is not likely to happen."
 Assuring that the observed. ellect is not. produced by high velocity host. particles misplaced in nearby groups., Assuring that the observed effect is not produced by high velocity host particles misplaced in nearby groups.
 As stated by Lemson Ixaulfmann (1999). there is a dependence of the halo mass function on the environment. which is skewed towards high mass objects in overdense regions.," As stated by Lemson Kauffmann (1999), there is a dependence of the halo mass function on the environment, which is skewed towards high mass objects in overdense regions."
 Hence. the rising of the velocity dispersion in denser environments. could be the result of a higher abundance of massive haloes.," Hence, the rising of the velocity dispersion in denser environments, could be the result of a higher abundance of massive haloes."
 In order to test this possibility. we compute the mass function in. 1.Mpeἡ thick spherical shells. centered on hosts for several radii (3.5. 9.5. 20.5 ancl 40.5 Alpeh 5).," In order to test this possibility, we compute the mass function in $1~Mpc~h^{-1}$ thick spherical shells, centered on hosts for several radii (3.5, 9.5, 20.5 and 40.5 $Mpc~h^{-1}$ )."
 phis allows us to quantify the dependence. of the mass function on the overdensity (6= 5.89. 1.00. 0.28. 0.05 respectively. for the above radii).," This allows us to quantify the dependence of the mass function on the overdensity $\delta$ = 5.89, 1.09, 0.28, 0.05 respectively, for the above radii)."
 Figure ὸ shows in dashed lines the mass function for the mentioned. racii multiplied by (1|9)t and labelled with the associated os: solid line. represents the total mass function.," Figure \ref{fm} shows in dashed lines the mass function for the mentioned radii multiplied by $(1+\delta)^{-1}$ and labelled with the associated $\delta 's$; solid line, represents the total mass function."
 Due to the overlapping. we shift the curves corresponding to the three highest overdensities by factors LO. 100. ancl 1000 respectively.," Due to the overlapping, we shift the curves corresponding to the three highest overdensities by factors 10, 100 and 1000 respectively."
 As can be seen. the mass function shape does not change for groups with masses 1.4197A.bt«AMx2LOMAL.fot (vertical dashed lines in ligure 2)).," As can be seen, the mass function shape does not change for groups with masses $1.4 \times 10^{12} M_{\odot} ~h^{-1} < M < 2\times 10^{13} M_{\odot} ~h^{-1}$ (vertical dashed lines in figure \ref{fm}) )."
 Llenee. the results obtained (rom this low mass sample will not be allected by the overabundance of massive haloes in high clonsity regions.," Hence, the results obtained from this low mass sample will not be affected by the overabundance of massive haloes in high density regions."
 Based on the previous analysis. we explore the observed velocity dispersion behaviour for groups according to their masses: considering masses greater and lower than 2.01077AL.b. I.," Based on the previous analysis, we explore the observed velocity dispersion behaviour for groups according to their masses; considering masses greater and lower than $2.0 \times 10^{13}~M_{\odot} ~h^{-1}$ ."
 Ns a result of this resampling we Lind that velocity dispersions of low mass groups are strongly alfected w the presence of host clusters (middle panel of figure 1)). whereas high mass groups do not show a significant variation of the median when approaching to their associated: hosts (lower panel of figure 1)).," As a result of this resampling we find that velocity dispersions of low mass groups are strongly affected by the presence of host clusters (middle panel of figure \ref{masa}) ), whereas high mass groups do not show a significant variation of the median when approaching to their associated hosts (lower panel of figure \ref{masa}) )."
 According to this. we focus the ollowing analysis on this low mass group sample.," According to this, we focus the following analysis on this low mass group sample."
 At first sight. the visine of the median velocity dispersion. could be a result of the gravitational influence of he host on its neighbourhood.," At first sight, the rising of the median velocity dispersion, could be a result of the gravitational influence of the host on its neighbourhood."
 This possibility encourages us to analyse the behaviour of the internal energy. ££. in the same way we did for the velocity. dispersion.," This possibility encourages us to analyse the behaviour of the internal energy, $E$, in the same way we did for the velocity dispersion."
" This quantity is estimated by: where the first and second. terms correspond to the kinetic ane potential energies respectively. @ is the 3D velocity dispersion. Agron, the group mass. m the particle mass. N the number of members of à group and ej, the group virial radius."," This quantity is estimated by: where the first and second terms correspond to the kinetic and potential energies respectively, $\sigma$ is the 3D velocity dispersion, $M_{group}$ the group mass, m the particle mass, N the number of members of a group and $R_{vir}$ the group virial radius."
 Top panel of figure 3. shows the, Top panel of figure \ref{sigE2} shows the
The halo model (see Coorav Sheth 2002 for a review) has become the preferred language in which to interpret measurements of galaxy clustering.,The halo model (see Cooray Sheth 2002 for a review) has become the preferred language in which to interpret measurements of galaxy clustering.
 Recently. Zehavi οἱ al. (," Recently, Zehavi et al. ("
2005) have expressed the luminosity dependence: of clustering in the Sloan Digital Sky Survey (SDSS. York et al.,"2005) have expressed the luminosity dependence of clustering in the Sloan Digital Sky Survey (SDSS, York et al."
 2000) Second Data Release (DID. Abazajian et al.," 2000) Second Data Release (DR2, Abazajian et al."
 2004) in terms of the halo mocdel., 2004) in terms of the halo model.
 Skibba et al. (, Skibba et al. (
2006) show that. if Zehavi et al,"2006) show that, if Zehavi et al."
s halo model decomposition is correct. then the luminosity of the central galaxy in a halo depends strongly on halo mass. whereas the luminositics of satellite &alaxies depend only weakly on the masses of their host haloes.,"'s halo model decomposition is correct, then the luminosity of the central galaxy in a halo depends strongly on halo mass, whereas the luminosities of satellite galaxies depend only weakly on the masses of their host haloes."
 The main goal of this paper is to test this prediction., The main goal of this paper is to test this prediction.
 We co this in Section 727. by studying the satellite population in the group catalog provided. by Derlind. ct al. (, We do this in Section \ref{testLsat} by studying the satellite population in the group catalog provided by Berlind et al. (
2006).,2006).
 Ehe abundance of groups decreases and the clustering strength increases with increasing richness. as expected. (Berlind et al.," The abundance of groups decreases and the clustering strength increases with increasing richness, as expected (Berlind et al."
 2007)., 2007).
 This suggests that the test we perform is unlikely to have been biased by incompleteness ellects in the catalog., This suggests that the test we perform is unlikely to have been biased by incompleteness effects in the catalog.
 As an additional check. we show that the satellite population in the group catalogs of Yang et al. (," As an additional check, we show that the satellite population in the group catalogs of Yang et al. ("
2005a) are similar to those from Derlind ct al.,2005a) are similar to those from Berlind et al.
 Dark matter haloes have substructure (e.g. Tormen 1997: Tormen. Diaferio Sver 1998: Gao et al.," Dark matter haloes have substructure (e.g. Tormen 1997; Tormen, Diaferio Syer 1998; Gao et al."
 2004a)., 2004a).
 If we identify subhaloes with satellite galaxies (e.g. Ixravtsov et al., If we identify subhaloes with satellite galaxies (e.g. Kravtsov et al.
 2004: Conroy et al., 2004; Conroy et al.
 2007). then the halo model makes," 2007), then the halo model makes"
left large ambiguity on the mix of emission mechanisms (Stephens&Badhwar1981).,left large ambiguity on the mix of emission mechanisms \citep{SB81}.
. The spatial distribution of (he enerev-integrated eamnima-ravy 1wensily. on the other hand. gave a higher statistical accuracy on which Maver-Ilasselwanderelal.(1982).. Strongetal.(1982). Bloemenetal. (1984).. Bloemenetal. (1985).. and ot1ος sel the path to the Galactic eamnia-ray astronomy.," The spatial distribution of the energy-integrated gamma-ray intensity, on the other hand, gave a higher statistical accuracy on which \citet{Hasselwander82}, , \citet{Strong82}, \citet{Bloemen84}, \citet{Bloemen85}, and others set the path to the Galactic gamma-ray astronomy."
 We refer to Murthy&Wolfendale(1993).. Sehoenlelder(2001). and schlickeiser(2002) [or general references on (he topics ο“(his work.," We refer to \citet{MurthyWolfendale93}, \citet{Schoenfelder01}, and \citet{Schlickeiser02} for general references on the topics of this work."
 When the much improved data obtained with EGRET (Thompsonetal.1993). were studied by Bertschetal.(1993). and IIunteretal.(1997). an excess of about. x(1.52) became apparent in the data in the GeV band relative to the Galactic gamma-ray. emission models cited above.," When the much improved data obtained with EGRET \citep{EGRET} were studied by \citet{Bertsch93} and \citet{Hunter97}, an excess of about $\times (1.5-2)$ became apparent in the data in the GeV band relative to the Galactic gamma-ray emission models cited above."
 This excess is visible along the entire Galactic plane (—10<b«10 deg., This excess is visible along the entire Galactic plane $-10<b<10$ deg.
 and —90«(+90 deg.), and $-90<\ell<+90$ deg.)
 but most pronounced in the central region of the plane (—40«€<440 deg.)., but most pronounced in the central region of the plane $-40<\ell<+40$ deg.).
 Here b and £ are the Galactic latitude aad longitude. respectively.," Here $b$ and $\ell$ are the Galactic latitude and longitude, respectively."
" In literature. the excess is referred (to as the ""GeV Excess”."," In literature, the excess is referred to as the “GeV Excess”."
 Mori(1997) studied the diffuse ΠΠ emission bv using Monte Carlo p-p interaction simulators devloped for accelerator experiments ancl confirmed (hat the EGRET spectrum can not be reproduced with the conventional cosmic proton spectrum., \citet{Mori97} studied the diffuse gamma-ray emission by using Monte Carlo $p$ $p$ interaction simulators devloped for accelerator experiments and confirmed that the EGRET spectrum can not be reproduced with the conventional cosmic proton spectrum.
 Strong and Moskalenko developed a computer program. GALPROP. where the cosmic rav propagation and interaction are numerically calculated in a model Galaxy to obtain the spatial distribution and spectrum. of secondary. particles including gamuna-ravs ancl radio isotopes (Strong&Moskalenko1997.2001)..," Strong and Moskalenko developed a computer program, GALPROP, where the cosmic ray propagation and interaction are numerically calculated in a model Galaxy to obtain the spatial distribution and spectrum of secondary particles including gamma-rays and radio isotopes \citep{Galprop1,Galprop2}."
 The diffuse Galactic σάςΤο spectra have been caleulated. separately for the QUx decay. bremsstralhlung. and inverse-Compton with various parameter settings of GALPROP by Strongetal.(2000).," The diffuse Galactic gamma-ray spectra have been calculated separately for the $\pi^0$ decay, bremsstrahlung, and inverse-Compton with various parameter settings of GALPROP by \citet{SMR00}."
. They noted that: a) the local interstellar spectra of electrons ancl protons (power-law index >2.5 above 10—20 GeV) do not reproduce (he gamma-ray spectrum along the Galactic plane observed by EGRET: b) a very hard electron spectrum (power-law index ~ 1.8) and a modified nucleon spectrum will be needed to minimize the difference between (he prediction and the data in the GeV band: and ο) the GeV excess in (he central Galactic ridge can not be reproduced within the constraint on the proton spectral index imposed by recent cosmic proton measurements and the limit on the electron spectral index (~ 1.9) [rom radio and local cosmic ταν observations., They noted that: a) the local interstellar spectra of electrons and protons (power-law index $\ge 2.5$ above $10-20$ GeV) do not reproduce the gamma-ray spectrum along the Galactic plane observed by EGRET; b) a very hard electron spectrum (power-law index $\sim 1.8$ ) and a modified nucleon spectrum will be needed to minimize the difference between the prediction and the data in the GeV band; and c) the GeV excess in the central Galactic ridge can not be reproduced within the constraint on the proton spectral index imposed by recent cosmic proton measurements and the limit on the electron spectral index $\sim 1.9$ ) from radio and local cosmic ray observations.
 They noted that the excess persists at higher Galactic latitude (|(|>5 deg)., They noted that the excess persists at higher Galactic latitude $|\ell|>5$ deg).
 Dueschingetal.(2001) have also noted that the EGRET spectrum is incompatible with the locally measured cosmic proton spectrum., \citet{Buesching01} have also noted that the EGRET spectrum is incompatible with the locally measured cosmic proton spectrum.
 The GeV Excess has led (o new optimizations of (he Galactic gamma-ray enmission models ancl speculations on possible new eamunma-rayv sources in (he Galaxy., The GeV Excess has led to new optimizations of the Galactic gamma-ray emission models and speculations on possible new gamma-ray sources in the Galaxy.
 One choice is lo assume a harder protonspectrum in the Galactic ridee region as has been noted by, One choice is to assume a harder protonspectrum in the Galactic ridge region as has been noted by
uodel cases shown iu Fie. L.,"model cases shown in Fig. \ref{acorr},"
 the Li abuudance derived roni this line shows very simular scusitivity to the new electron collision data., the Li abundance derived from this line shows very similar sensitivity to the new electron collision data.
 The effects of the new clectron collision data on the abundance measured from the 6101 line are considerable less iu the solar case: onlbv about of the difference shown bv the other two lines., The effects of the new electron collision data on the abundance measured from the 6104 line are considerably less in the solar case: only about of the difference shown by the other two lines.
 In the other cases the influcnee of the electron collision data on he abuudanee measured from the 6101 sxpectral line is again comparable to the ifuence on the 6TÜS and S126 lines., In the other cases the influence of the electron collision data on the abundance measured from the 6104 spectral line is again comparable to the influence on the 6708 and 8126 lines.
" 3 colon problem for calculating non-LTE. abundance Corrections is that they can be subject to enxve vot UWheertautics in the underlying atomic data,", A common problem for calculating non-LTE abundance corrections is that they can be subject to errors from uncertainties in the underlying atomic data.
 We have shown that clectrou collision data from a umber of different. calculations based ou quite different methods are in good or even excellent agrecuucut., We have shown that electron collision data from a number of different calculations based on quite different methods are in good or even excellent agreement.
 Data calculate with advanced close-coupling tecliniques provides data in exccllent agreement. eiving rate cocfhiicicuts for excitation processes Within a factor of 2 for the temperatures of most interest in cool stellar atiuospheres. T—5000 S000 Ik. This. aud the good agreciment with experiuenta results where available (see7).. suggests the data have an uncertainty of simular maeuitucde.," Data calculated with advanced close-coupling techniques provides data in excellent agreement, giving rate coefficients for excitation processes within a factor of 2 for the temperatures of most interest in cool stellar atmospheres, $T \sim 5000$ – 8000 K. This, and the good agreement with experimental results where available \citep[see][]{CCC}, suggests the data have an uncertainty of similar magnitude."
 The seui-enmpirica, The semi-empirical
Iu order to münimuize conuumnication anions processors. we divide potential halos iuto two ists.,"In order to minimize communication among processors, we divide potential halos into two lists."
" For every poteutial laο, we compute the overdensity at the largest possible ou-processor radius."," For every potential halo, we compute the overdensity at the largest possible on-processor radius."
 If the next search radius is larger thaw lis. the halo is added to a list that ums be couinmnuicated.," If the next search radius is larger than this, the halo is added to a list that must be communicated."
 Thus. all ou-processor halos arc| processed. concurrentLy wih no communication.," Thus, all on-processor halos are processed concurrently with no communication."
 Since the volun! of colnnmnicatiou is very suniall. we seud all other ios to every processor.," Since the volume of communication is very small, we send all other halos to every processor."
" Iloπόνο, since this approach is not scalable te, very laree halo catalogs or uunibers of preycessors. We switch to a nnnffered. communication pattern if we cannot alocate a elobal halo catalog."," However, since this approach is not scalable to very large halo catalogs or numbers of processors, we switch to a buffered communication pattern if we cannot allocate a global halo catalog."
 In the butfered approach. halo lists are ouv conuumuicated to the nearest processors «mie at a time.," In the buffered approach, halo lists are only communicated to the nearest processors one at a time."
 The list is conmuumnicated uuib all blocks within the VOtune of the processors halos have been scareied., The list is communicated until all blocks within the volume of the processor's halos have been searched.
 While slower than the all-to-all approacl1. the amount of storage ICL DYOCCSSOL| yequired stavs fixed as the nuuber of processors aud umber of halos grow.," While slower than the all-to-all approach, the amount of storage per processor required stays fixed as the number of processors and number of halos grow."
 In eitLer Case. COMMCation COities unil all halos are fully searched.," In either case, communication continues until all halos are fully searched."
 For lis study. we will use the allto-all approach.," For this study, we will use the all-to-all approach."
 Figure 12(a) shows the strong scaling of the pSO halo finder as a fraction of the total wall clock time in a sing FLΑΡΗ time step., Figure \ref{fig:scaling} shows the strong scaling of the pSO halo finder as a fraction of the total wall clock time in a single FLASH time step.
 We show three ciffercut uuiform: problem sizes: 256°. 512°. and 10212 particles aud zones;," We show three different uniform problem sizes: $256^3$, $512^3$, and $1024^3$ particles and zones."
 We yostarted cach simulation at a represcutative recshift. 50.25. and rau for five time steps.," We restarted each simulation at a representative redshift, $z=0.25$, and ran for five time steps."
 These times do not iuclude optioual portions of the halo finder routine. suc jas writing the halo catalog to disk or tageine particles within halos.," These times do not include optional portions of the halo finder routine, such as writing the halo catalog to disk or tagging particles within halos."
 We performed these calculations on jaguar. a Crav NTS system at Oak Ridec National Laboratory.," We performed these calculations on jaguar, a Cray XT5 system at Oak Ridge National Laboratory."
 Jaguar consists of 16.688 dual six-core AMD Opteron nodes wit1 16 CD of memory per node and has a peak performance of 2.332 etaflops.," Jaguar consists of 16,688 dual six-core AMD Opteron nodes with 16 GB of memory per node and has a peak performance of 2.332 petaflops."
 Our approach offers good strong scaling behavior: we are able to beat or match the scaling performance «t ΕΤΑΡΗ at all problem sizes., Our approach offers good strong scaling behavior: we are able to beat or match the scaling performance of FLASH at all problem sizes.
 At larecr core counts. FLASII has difficulty scaling the Poissou ποvor. whereas the haQ finder maintains good scalability.," At larger core counts, FLASH has difficulty scaling the Poisson solver, whereas the halo finder maintains good scalability."
 However. we ca iiufer that we have poor weak scaling: the halk) fincling steps require ever larger wall clock time as the problem size erows.," However, we can infer that we have poor weak scaling: the halo finding steps require ever larger wall clock time as the problem size grows."
 The oor weak scaling is due to several factorbi., The poor weak scaling is due to several factors.
 First. since these are uniforiii exid. caleulations. at low redshift the varticl| cistribution among processors becomes vehly uubalanced.," First, since these are uniform grid calculations, at low redshift the particle distribution among processors becomes highly unbalanced."
 FLASID is block based and uses a Mortou curve m» lisribute these blocks amoug the processors., FLASH is block based and uses a Morton curve the distribute these blocks among the processors.
 Thus. while cach processor has roughly the same number of blocks. mwe blocks in highly dense regions will couaiu anv more particles than those iu voids.," Thus, while each processor has roughly the same number of blocks, those blocks in highly dense regions will contain many more particles than those in voids."
 Siice our halo fiuder scaus Im'Oug1 particles. there is a lack of concurrency (ue to this inbaliuce.," Since our halo finder scans through particles, there is a lack of concurrency due to this imbalance."
" At small probeni SIZCS, this is not an issue. but with 1tμι 12(b) 5)}."," At small problem sizes, this is not an issue, but with $1024^3$ \ref{fig:adjusted} \ref{fig:massFunc})"
" At small probeni SIZCS, this is not an issue. but with 1tμι 12(b) 5)}.Γ"," At small problem sizes, this is not an issue, but with $1024^3$ \ref{fig:adjusted} \ref{fig:massFunc})"
Au optical telescope cannot transmit spatial frequencies bevoud cj;=x253D/A. where D is the largest dimension of the telescope aperture aud A is the wavelength.,"An optical telescope cannot transmit spatial frequencies beyond $\pm k_{\rm max}=\pm 2\pi
D / \lambda$, where $D$ is the largest dimension of the telescope aperture and $\lambda$ is the wavelength."
 There is no aliasing if For D=2 meters. A=1pu. this samping corresponds to 07005 pixels.," There is no aliasing if For $D=2$ meters, $\lambda = 1\,\mu{\rm m}$, this sampling corresponds to 05 pixels."
 When the data have been sampled at Nyquist or ugher deusity. we cau produce shifted. rotated. or deconvolved versions of the image with no ambieutty (apart from noise).," When the data have been sampled at Nyquist or higher density, we can produce shifted, rotated, or deconvolved versions of the image with no ambiguity (apart from noise)."
 In the9/VAP mission. this will mean that subtraction of the host galaxy Irou supernova images will be essentially perfect. as loug as the template image is Nyquist-sampled.," In the mission, this will mean that subtraction of the host galaxy from supernova images will be essentially perfect, as long as the template image is Nyquist-sampled."
 This holds for other time-doimain signals. such as ticrolenusing. planetary tratsits. aud Ixuiper Bel surveys.," This holds for other time-domain signals, such as microlensing, planetary transits, and Kuiper Belt surveys."
 For weak leusing surveys. Ht means that the systematic ellipticities iiuposed ou galaxies by the PSF can. in theory. be removed nearly perfectly.," For weak lensing surveys, it means that the systematic ellipticities imposed on galaxies by the PSF can, in theory, be removed nearly perfectly."
 Nyquist sampling is thus highly. desirable., Nyquist sampling is thus highly desirable.
 By taking a series of exposures with poiutiugsdithered by a [ractional pixel aniounts. we cau sample the ePSF-couvolved scene imo'e deusely than the pixel eril.," By taking a series of exposures with pointings by a fractional pixel amounts, we can sample the ePSF-convolved scene more densely than the pixel grid."
 ]t is uuportant to realize that te two ellects of pixelization are in [act separable: the ePSF depeucds ou the size of the pixel through the PRE £2Gro): buta.," It is important to realize that the two effects of pixelization are in fact separable: the ePSF depends on the size of the pixel through the PRF $R(x,y)$; but."
 If we choose dither positions ou a grid af. then we elimiuate aliasing as long as μας€Na/a.," If we choose dither positions on a grid $a/N$, then we eliminate aliasing as long as $k_{\rm max} < N\pi / a$."
 We cau therefore obtain Nyquist-sampled data even with large pixels., We can therefore obtain Nyquist-sampled data even with large pixels.
 To first order this comes with uo noise penalty: if. we replace ≺↵⋜↕⊳∖↕∐∑≟↥≺↵≺↵⊸∖↥↽≻∩⊳∖⋯⋅↩∩↥∎⋃∐↩⊺∖∖↽∐∐⋜⊓∐↕∐≺↵↕⋅≺↵≺⇂ . . DO ⋅⋅ ∑⇁⋟⊔≺⇂∩⋀∖−≺↵⊸∖↥↽≻∪⊳∖⋯⋅↩⊳∖≺↵⋜↕∢∙∐∩↕⊔∐≺↵⊺↙∕∕≛∖−⋅↕∐≺↵∐↕∐≺↲↕ otal counts from the source are the same: the ↥∎⋯⋜↕⊔⋯⋜≹∑≟≺↵∐⋜↕⊳∖↕∐≺↵⊳∖⋜⋃∐≺↵⋯⊔↕∣⋈↵↕⋅∩↥∎↜∖ sv. photons per uiuit area (fewer per sample. but more samples per uuit area).," To first order this comes with no noise penalty: if we replace a single exposure of time $T$ with a dithered grid of $N^2$ exposures each of time $T/N^2$, then the total counts from the source are the same; the final image has the same number of sky photons per unit area (fewer per sample, but more samples per unit area)."
 There is. however. au increase in overliead aud read uoise from the extra exposures. aud the data rate must be higher.," There is, however, an increase in overhead and read noise from the extra exposures, and the data rate must be higher."
 What is the optimal ditier pattern?, What is the optimal dither pattern?
 L99a demonstrates that. for image reconstruction. a regularly. interlaced grid ollers the lowest noise.," L99a demonstrates that, for image reconstruction, a regularly interlaced grid offers the lowest noise."
 I lave not encouutered auy reason to execute ally other pattern., I have not encountered any reason to execute any other pattern.
 Iuterlaciug makes the analysis straightforward. and the L99a and tecliuiques can be reudered equivalent in this case.," Interlacing makes the analysis straightforward, and the L99a and techniques can be rendered equivalent in this case."
 Given that interlacing cau recover Nyquist sampling. the remaining drawback to larger pixels is the poorer resolution in the ePSF. which degrades the S/N for background-limited photometry aud [or centroid aud ellipticity ineasurements of mareinally resolved galaxies.," Given that interlacing can recover Nyquist sampling, the remaining drawback to larger pixels is the poorer resolution in the ePSF, which degrades the S/N for background-limited photometry and for centroid and ellipticity measurements of marginally resolved galaxies."
 E will quautify this below., I will quantify this below.
‘Table 6...,Table \ref{tab:summary}.
 Although the results broadly agree with selfsimilar predictions. the residual contamination tends to cause the scalings to appear too flat.," Although the results broadly agree with self--similar predictions, the residual contamination tends to cause the scalings to appear too flat."
 For instance. in the high signal to noise subsample where the effect of sources is clearest. the slope of the jyo/Lx. relation is found to be latter by 0.2 i a fit is attempted before source corrections are mace.," For instance, in the high signal to noise sub–sample where the effect of sources is clearest, the slope of the $y_0/L_\mathrm{X}$ relation is found to be flatter by 0.27 if a fit is attempted before source corrections are made."
 A similar result is found for the yofds scaling relation., A similar result is found for the $y_0/Y_{\mathrm{X}}$ scaling relation.
 We check the consisteney of the set of clusters with the more usual X.rav scaling relations between Lx and Zx. ὃν and Zx. and YS and Lx (e.g. ?)) in the same way as [or the SZ / NXray scaling relations (resultsalso summarised in Table 6)).," We check the consistency of the set of clusters with the more usual X–ray scaling relations between $L_{\mathrm{X}}$ and $T_{\mathrm{X}}$, $Y_{\mathrm{X}}$ and $T_{\mathrm{X}}$, and $Y_{\mathrm{X}}$ and $L_{\mathrm{X}}$ (e.g. \citealp{Morandi2007}) ) in the same way as for the SZ / X–ray scaling relations (resultsalso summarised in Table \ref{tab:summary}) )."
 The slopes that we measure. of 0.49+0.04. 2.19+0.16. and 1.24250.05. are consistent with the similarity expectations of 0.5. 2.5 and 1.25.," The slopes that we measure, of $0.49 \pm 0.04$, $2.19 \pm 0.16$, and $1.24 \pm 0.05$, are consistent with the similarity expectations of 0.5, 2.5 and 1.25."
 As the slight discrepaney for the correlation between Yx and YX is not of hish statistical significance. this study shows our sample to be representative of the population of hot. (£76 kkeV) clusters.," As the slight discrepancy for the correlation between $Y_{\mathrm{X}}$ and $T_{\mathrm{X}}$ is not of high statistical significance, this study shows our sample to be representative of the population of hot $T
\gtrsim 6$ keV) clusters."
 We have observed a complete sample of galaxy clusters using OCRAp. ancl studied the scaling. of the central Compton parameter. yo. with various X.ray quantities.," We have observed a complete sample of galaxy clusters using OCRA–p, and studied the scaling of the central Compton parameter, $y_0$, with various X–ray quantities."
 For each relation. we find. slopes in good. agreement with the predictions from self.similar models.," For each relation, we find slopes in good agreement with the predictions from self–similar models."
 Our study has similarities to that of ?.. and the two samples have 7 clusters in common. although we imposed stricter initial selection criteria.," Our study has similarities to that of \cite{Morandi2007}, and the two samples have 7 clusters in common, although we imposed stricter initial selection criteria."
 ? consider scalings with jo. so we are able to perform a direct comparison.," \citeauthor{Morandi2007} consider scalings with $y_0$ , so we are able to perform a direct comparison."
 Thev find that the go/Zx 7.2)). 2? 1.2)). 7)), They find that the $y_0/T_{\mathrm{X}}$ \ref{sec:scaling}) \cite{Bonamente2008} \ref{sec:scaling}) \citealp{Johansson2010})
 Thev find that the go/Zx 7.2)). 2? 1.2)). 7))., They find that the $y_0/T_{\mathrm{X}}$ \ref{sec:scaling}) \cite{Bonamente2008} \ref{sec:scaling}) \citealp{Johansson2010})
the most promising sources (see. c.e@.. Thorue Bragiusky 1976: Thorne 1995).,"the most promising sources (see, e.g., Thorne Braginsky 1976; Thorne 1995)."
" In particulary, LISA may be able to detect the collapse of a SMS to a SMDII."," In particular, LISA may be able to detect the collapse of a SMS to a SMBH."
 Even more pronisiug is the possible detection of the coalescence of two SMDIIS (LISA Pre-Phase A report 1995)., Even more promising is the possible detection of the coalescence of two SMBHs (LISA Pre-Phase A report 1995).
 The likelihood. of such an event. however. largely depends ou how SMDIIS form aud is therefore still uncertain.," The likelihood of such an event, however, largely depends on how SMBHs form and is therefore still uncertain."
 Tn a seres of papers we revisit the formation of SMBs via the collapse of SAISs. focussing ou the influence of rotation and eecneral relativity.," In a series of papers we revisit the formation of SMBHs via the collapse of SMSs, focussing on the influence of rotation and general relativity."
 We analyze the secular contraction of a uniforlv rotating equilibria configuration via thermal enüsson and mass loss., We analyze the secular contraction of a uniformly rotating equilibrium configuration via thermal emission and mass loss.
 We concentrate on a coufiguration rotating at the niasshedding luit., We concentrate on a configuration rotating at the mass-shedding limit.
 In Bammearte Shapiro (1999. hereafter Paper D. we have shown that the Iuninositv from such a star is considerable reduced below the value of a ronretating spherical star of the sanie mass.," In Baumgarte Shapiro (1999, hereafter Paper I), we have shown that the luminosity from such a star is considerably reduced below the value of a nonrotating spherical star of the same mass."
 Iu this paper. we analyze the structure and stability against collapse of fully relativistic. rotating n=3 xlvtropes in stationary equilibrium.," In this paper, we analyze the structure and stability against collapse of fully relativistic, rotating $n=3$ polytropes in stationary equilibrium."
 SAISs to which these calculations apply are radiation-doninated. iscutropic configurations of sufficient nass that ucither nuclear nurnnug nor electron-positrou pairs are important before he stars reaches the ouset of relativistic eravitational iustabilitv.," SMSs to which these calculations apply are radiation-dominated, isentropic configurations of sufficient mass that neither nuclear burning nor electron-positron pairs are important before the stars reaches the onset of relativistic gravitational instability."
" Stars with AJ>ΟΛΗ, fall in this category (Zeldovich Novvikkov 1971: Fuller. Woosley Weaver 1986)."," Stars with $M \gtrsim 10^6 M_{\odot}$ fall in this category (Zel'dovich kov 1971; Fuller, Woosley Weaver 1986)."
 Moreover. the evolutionary timescale due to cooling has to be longer than the livdrodyvnuauic timescale for the star to evolve iu a quasistationary fashion.," Moreover, the evolutionary timescale due to cooling has to be longer than the hydrodynamic timescale for the star to evolve in a quasistationary fashion."
 According to equations (9) and (10) below. we find that this coustraiut is satisfied for all inasses AL<<LOMAS...," According to equations (9) and (10) below, we find that this constraint is satisfied for all masses $M \lesssim 10^{13} M_{\odot}$."
 We track the quasistationary evolution of such stars to he poit of ouset of radial instability., We track the quasistationary evolution of such stars to the point of onset of radial instability.
 We first identity lis critical configuration analytically by micas of a post-Newtouian cucrey variational method., We first identify this critical configuration analytically by means of a post-Newtonian energy variational method.
 As pointed out by Bisnovatvi-lvogan. Zeldovvich Novvikkov (1967). determining the ousct of relativistic collapse in a rapidly rotating SMS requires asecond-order xost-Newtonian analysis. not a first-order. as in the case of a nonrotatiug star.," As pointed out by Bisnovatyi-Kogan, vich kov (1967), determining the onset of relativistic collapse in a rapidly rotating SMS requires a post-Newtonian analysis, not a first-order, as in the case of a nonrotating star."
 We provide au approximate. post-Newtoman analytic analysis (vigorizing and completing he qualitative argument of Disuovatvi-Ikogau. Zeldovvich Novvikkov (1967) and Zeldovich Novvikkov (1971). who oulv provide a dineusioual estimate of the second post-Newtoniui term).," We provide an approximate, post-Newtonian analytic analysis (rigorizing and completing the qualitative argument of Bisnovatyi-Kogan, vich kov (1967) and Zel'dovich kov (1971), who only provide a dimensional estimate of the second post-Newtonian term)."
 Then. to establish the result rigorously. we use a receut uunerical code (Cook. Shapiro Teukolsky 1992. 1991) to construct rotating equilibrium models in full general relativity.," Then, to establish the result rigorously, we use a recent numerical code (Cook, Shapiro Teukolsky 1992, 1994) to construct rotating equilibrium models in full general relativity."
 We show that the mass of the critical configuration is a unique function of the specific entropy., We show that the mass of the critical configuration is a unique function of the specific entropy.
" The values of R/M. T/[W aud J/AI? at the ousct of collapse are universal πανα, independent| of tle mass or prior evolution."," The values of $R/M$, $T/|W|$ and $J/M^2$ at the onset of collapse are universal numbers, independent of the mass or prior evolution."
 Were AZ is the mass. 7 the (polar) radius. J the angular momentum. £ the rotational and W the exavitatioual potential energy of the star.," Here $M$ is the mass, $R$ the (polar) radius, $J$ the angular momentum, $T$ the rotational and $W$ the gravitational potential energy of the star."
" We also speculate on the likely outcome of collapse for stars which do not disrupt due to thermomuclear explosions durius collapse: it is formed that stars with Af>ΤΟAZ, aud initial mctallicities Z<<0.005 do not explode (Fuller. Woosley Weaver 1986)."," We also speculate on the likely outcome of collapse for stars which do not disrupt due to thermonuclear explosions during collapse; it is found that stars with $M > 10^5 M_{\odot}$ and initial metallicities $Z < 0.005$ do not explode (Fuller, Woosley Weaver 1986)."
 Since these stars start collapsing from a universal critical configuration. the subsequeut. collapse is also uuiquelv. determined and should produce a inique eravitational waveform.," Since these stars start collapsing from a universal critical configuration, the subsequent collapse is also uniquely determined and should produce a unique gravitational waveform."
 We postpone a detailed discussion of this phase for a future paper in which we follow the dynamical collapse mmuerically in general relativity (Banmearte. Shapiro Shibata 1999).," We postpone a detailed discussion of this phase for a future paper in which we follow the dynamical collapse numerically in general relativity (Baumgarte, Shapiro Shibata 1999)."
" The key goals of our study are to decide whether a SMDII. can realle emerge frou, the collapse of a SMS aud to determine the hole parameters if indeed it can be formed this wav.", The key goals of our study are to decide whether a SMBH can really emerge from the collapse of a SMS and to determine the hole parameters if indeed it can be formed this way.
" Alternatively, a rotating supermassive cloud or star could collapse to a weakly relativistic disk (c.g. Wagoucr 1969: Loeb Rasio 1991)."," Alternatively, a rotating supermassive cloud or star could collapse to a weakly relativistic disk (e.g. Wagoner 1969; Loeb Rasio 1994)."
 If the collapsing imucrinost region euters the stroue-field domain. the aneular momentum of this matter must be below the maxiunun value of a Kerr hole (J/A/7=1) for black hole formation to occur eventually.," If the collapsing innermost region enters the strong-field domain, the angular momentum of this matter must be below the maximum value of a Kerr hole $J/M^2 = 1$ ) for black hole formation to occur eventually."
 What happens if the augular momentum exceeds this mit?, What happens if the angular momentum exceeds this limit?
 Does angular momentum dissipation by outflowing gas allow for black hole formation of the core?, Does angular momentum dissipation by outflowing gas allow for black hole formation of the core?
 Or. does gravitational radiation. following the formation of bars or axial currents carry away chough augular momentum to permit collapse?," Or, does gravitational radiation, following the formation of bars or axial currents carry away enough angular momentum to permit collapse?"
 Finally. ifa SAIBI can form by the collapse of a SAIS. what Is its nass and spin given the mass and spin of the SMS at the onset of collapse?," Finally, if a SMBH can form by the collapse of a SMS, what is its mass and spin given the mass and spin of the SMS at the onset of collapse?"
 Tn this paper we deal primarily with the structure. stability and carly secular evolution phases of the SAIS scenario.," In this paper we deal primarily with the structure, stability and early secular evolution phases of the SMS scenario."
 Our calculation. iu effect. sets up the initial data at the onset of collapse.," Our calculation, in effect, sets up the initial data at the onset of collapse."
 Tracking the subsequeut dynamical evolution of these imitial data will resolve the sey questions posed above. aud in this paper we will only speculate briefiv on the outcome of the dvuamical collapse.," Tracking the subsequent dynamical evolution of these initial data will resolve the key questions posed above, and in this paper we will only speculate briefly on the outcome of the dynamical collapse."
 This paper is organized as follows: In Section 2. we xovide a qualitative overview of the problem auc present our basic assunptions., This paper is organized as follows: In Section \ref{Sec2} we provide a qualitative overview of the problem and present our basic assumptions.
 In Section 3/— we diseuss the equilibrimn aud stability of rotating. relativistic SMSs.," In Section \ref{Sec3} we discuss the equilibrium and stability of rotating, relativistic SMSs."
 Iu articular. we determine the critical configuration at which an evolving SMS becomes dynamically uustable to racial serturbations.," In particular, we determine the critical configuration at which an evolving SMS becomes dynamically unstable to radial perturbations."
 We compare results from anu approximate analytical treatment (Section 3.2)) with those from a miuerical. fully relativistic calculation (Section 3.3)).," We compare results from an approximate analytical treatment (Section \ref{anal}) ) with those from a numerical, fully relativistic calculation (Section \ref{numerics}) )."
 ILwius identified the onset of instability. we then solve analytically for the evolution of SMSs during the secular contraction phase up to this critical configuration in Section ," Having identified the onset of instability, we then solve analytically for the evolution of SMSs during the secular contraction phase up to this critical configuration in Section \ref{Sec4}."
Iu Section 5 πο provide some qualitative argunients which sugeest that the direct formation of SMDIIs from the collapse of SMSs indeed may be possible., In Section \ref{coll} we provide some qualitative arguments which suggest that the direct formation of SMBHs from the collapse of SMSs indeed may be possible.
 We stumarize aud discuss our results iu Section 6.., We summarize and discuss our results in Section \ref{Summary}.
 Except where noted otherwise. we adopt gcometrized wits with οσlic throughout this paper.," Except where noted otherwise, we adopt geometrized units with $c \equiv 1 \equiv G$ throughout this paper."
 SAISs may form if collapsing primorcial gas builds up chough eutropy so that the radiation pressure can slow down the collapse (see. Begchuan Rees. 1978. for au alternative scenario).," SMSs may form if collapsing primordial gas builds up enough entropy so that the radiation pressure can slow down the collapse (see Begelman Rees, 1978, for an alternative scenario)."
 Further coutraction will then spin up the uewly formed SAIS to the mass-shedding unit. provided that the eas had some initial augular moment aud that viscosity maiutains uniform rotation.," Further contraction will then spin up the newly formed SMS to the mass-shedding limit, provided that the gas had some initial angular momentum and that viscosity maintains uniform rotation."
 The SAIS will then evolve secularly along the mass-shedding lait. siauultaneouslv enüttius radiation. matter and angular moment (see. e.c. Disuovatvi-kogau. Zeldovich vvikkov 1967: Zeldovich Novvikkov 1971).," The SMS will then evolve secularly along the mass-shedding limit, simultaneously emitting radiation, matter and angular momentum (see, e.g., Bisnovatyi-Kogan, Zel'dovich kov 1967; Zel'dovich kov 1971)."
 Onco it reaches the ouset of radial instability. the star collapses ou a dynauical timescale. auc may ultimately form à SMDIT.," Once it reaches the onset of radial instability, the star collapses on a dynamical timescale, and may ultimately form a SMBH."
 For sufficicutly massive objects (AL>109 A£.). the," For sufficiently massive objects $M \gtrsim 10^6 M_{\odot}$ ), the"
uuiuus the probability of a false For Ay=0. Equation 5. gives the probability of a false detection EEquation 1)) aud cousequeutly (0)x:a.,"minus the probability of a false For $\lamS=0$, Equation \ref{eq:beta} gives the probability of a false detection Equation \ref{eq:alpha}) ) and consequently, $\beta(0) \leq\alpha$."
 This reflecs the trade-off in anv detection algorithia: the colupronuse between nüninizius the nuniber of false detections against maximizing the nunuber of true detections., This reflects the trade-off in any detection algorithm: the compromise between minimizing the number of false detections against maximizing the number of true detections.
 That is. if the detection threshold is set low erough to detect weaker sources. the aleorithiu will also produce a larger nuuber of false positives that are actually backeround fluctuations.," That is, if the detection threshold is set low enough to detect weaker sources, the algorithm will also produce a larger number of false positives that are actually background fluctuations."
 Conversely. the more stringeut the criterion for detection. the smaller t1e probability of detecting a real source (this is illustrated by the location of the threshold S* that defines voth a aud. ο) in Figure 3)).," Conversely, the more stringent the criterion for detection, the smaller the probability of detecting a real source (this is illustrated by the location of the threshold $\thresh$ that defines both $\alpha$ and $\beta$ in Figure \ref{fig:alfabetillus}) )."
 Note that although our notation enpliasizes the dependence of the power ou As. it also depends on Ap. Ts. TR. and rr.," Note that although our notation emphasizes the dependence of the power on $\lamS$ , it also depends on $\lamB$, $\exptime$, $\exptimeB$, and $\rr$ ."
 The power calculation is shown for the simple Poissoji case in Figure L. where HAS) is plotted for different dustances of Ap aud for ciffereat levels of the detecion threshold S*.," The power calculation is shown for the simple Poisson case in Figure \ref{fig:power}, where $\beta(\lamS)$ is plotted for different instances of $\lamB$ and for different levels of the detection threshold $\thresh$."
 As expected. stronger sources are invariably detected.," As expected, stronger sources are invariably detected."
 For a eiven source intensity. an iucrease in the background or a larger detection threshold (ie. lower a) both cause tie detectionprobabilitv to decrease.," For a given source intensity, an increase in the background or a larger detection threshold (i.e., lower $\alpha$ ) both cause the detectionprobability to decrease."
 Iun a typical observation. the," In a typical observation, the"
and angular momentum are transferred. from their orbit to the envelope which is gradually ejected.,and angular momentum are transferred from their orbit to the envelope which is gradually ejected.
 As he cores get closer together their orbital period falls and. this sets up differential rotation within the Cl., As the cores get closer together their orbital period falls and this sets up differential rotation within the CE.
 By its giant nature the CIS is expected to be largely convective., By its giant nature the CE is expected to be largely convective.
 Dillerential rotation and convection are the kev ingredients ofa stellar magnetic dvnamo (Tout&Prinele 1992).., Differential rotation and convection are the key ingredients of a stellar magnetic dynamo \citep{tout1992}. .
 Reeds&Tout(1995). &o so [ar as to sav that this dynamo actually drives the transfer οf οποίον and angular momentum [rom the orbit to the envelope as well as he strong wind that expels the envelope., \citet{regos1995} go so far as to say that this dynamo actually drives the transfer of energy and angular momentum from the orbit to the envelope as well as the strong wind that expels the envelope.
 Irrespective of this. we expect that. at the end of the common envelope evolution. either when he spiralling cores coalcsce or when all the envelope is driven away. there is a very strong magnetic field in the vicinity of the hot degenerate. core.," Irrespective of this, we expect that, at the end of the common envelope evolution, either when the spiralling cores coalesce or when all the envelope is driven away, there is a very strong magnetic field in the vicinity of the hot degenerate core."
 This field can penetrate he nondegenerate surfac “eof the core and become frozen in as it later cools and contracts., This field can penetrate the nondegenerate surface of the core and become frozen in as it later cools and contracts.
 The closer tie cores at the end of CIS evolution the greater the dillerential rotation in the CE and so the stronger he expected frozen in magnetic field., The closer the cores at the end of CE evolution the greater the differential rotation in the CE and so the stronger the expected frozen in magnetic field.
 We then expec the strongest white dwarf magnetic fields to form in the cores of systems that merge curing CI evolution., We then expect the strongest white dwarf magnetic fields to form in the cores of systems that merge during CE evolution.
 A main-sequence companion is likely to cdisolve into the giant envelooc when it has spiralled in deep enough that its density is comparable with its surroundings., A main-sequence companion is likely to disolve into the giant envelope when it has spiralled in deep enough that its density is comparable with its surroundings.
 The spin angular momenunm remaining in the envelope depends on the details of tre CIS. process as well as the initial conditions of the svstem., The spin angular momentum remaining in the envelope depends on the details of the CE process as well as the initial conditions of the system.
 I£ we assume that the remaining envelope has the specilic angular momentum of the original orbit its spin period would have recluced [rom vears to davs., If we assume that the remaining envelope has the specific angular momentum of the original orbit its spin period would have reduced from years to days.
 The degenerate core therefore finds itself at thie' centre. of a rapidly spinning giant to which its spin is [ikelv to be coupled., The degenerate core therefore finds itself at the centre of a rapidly spinning giant to which its spin is likely to be coupled.
 Because of the small size of the core its moment of inertia is negligible compared with that of the Πο envelope., Because of the small size of the core its moment of inertia is negligible compared with that of the remaining envelope.
 Such a giant would itself eenerate a strong dynamo and spin down quite quickly. typically within 1Ho love (Tout&Pringle1992).," Such a giant would itself generate a strong dynamo and spin down quite quickly, typically within $10^4-10^5\,$ yr \citep{tout1992}."
. Thus. except in the rare| case that the envelope is almost completely ejected when the cores merge. we would not expect the HEMW to be rapidly spinning by the time they emerge from t1e Dsgiant envelope.," Thus, except in the rare case that the envelope is almost completely ejected when the cores merge, we would not expect the HFMWDs to be rapidly spinning by the time they emerge from the giant envelope."
 This is consistent with the tencdaney for LIEMVVDs to be extremely. slow rotators. some with spin periods up to 100vr (Wickramasinghe&Ferrario2000).," This is consistent with the tendancy for HFMWDs to be extremely slow rotators, some with spin periods up to $100\,$ yr \citep{wickramasinghe2000}."
. Then. from the COoninioln envelope πλσος that almost Merec. WὉ expect a range of relatively high magnetic field white dwarls in MC which emerge from the CL very close to interictine. the »olars and intermediate polars. with a corresponeing clearth of such fields amongst the single stars (IXoesteretal.2001).," Then, from the common envelope systems that almost merge, we expect a range of relatively high magnetic field white dwarfs in MCVs which emerge from the CE very close to interacting, the polars and intermediate polars, with a corresponding dearth of such fields amongst the single stars \citep{koester2001}."
. Systems which emerge with wider separations s1ould. tend o have much Lower fields., Systems which emerge with wider separations should tend to have much lower fields.
 We note at this point hat. while we do not understand. the precise mechanism «X common envelope evolution. we must expect à range of maenetic icles associated with any given final separation.," We note at this point that, while we do not understand the precise mechanism of common envelope evolution, we must expect a range of magnetic fields associated with any given final separation."
 Vhis is then consistent with the fact that the longest period|»olars tend o have high fields., This is then consistent with the fact that the longest period polars tend to have high fields.
 Indeed they must if the fie cis to be strong cnough to lock the white dwarf spin to t10 orbit atall., Indeed they must if the field is to be strong enough to lock the white dwarf spin to the orbit atall.
feasible.,feasible.
 We therefore developed an approximate procedure based ou the original grid spaciug. calibrated against the few higher resolution SCDNI projections.," We therefore developed an approximate procedure based on the original grid spacing, calibrated against the few higher resolution SCDM projections."
" In grid cells where the self-shieldiug corrected HI column is greater than a threshold value Nyy. we treat as fully neutral all gas particles hat contribute to that grid cell aud meet the following criteria: temperature Z7«30.000 αμα gas density pg>(1000/177)píi(Q5/18,,). where pij, is the virialization overdeusity described in 'e[ssecikdent.."," In grid cells where the self-shielding corrected HI column is greater than a threshold value $N_{{\rm HI},c}$, we treat as fully neutral all gas particles that contribute to that grid cell and meet the following criteria: temperature $T<30,000$ K and gas density $\rho_g > (1000/177) \rho_{vir} (\Omega_b/\Omega_m)$, where $\rho_{vir}$ is the virialization overdensity described in \\ref{ssec:ident}."
 For critical models. the density cut correspouds to 1000Q5.," For critical models, the density cut corresponds to $1000\ \Omega_b$."
" Iu subcritieal models. he deusity cut occurs at the same fraction of the critical deusity as in the ,,=I moclels."," In subcritical models, the density cut occurs at the same fraction of the critical density as in the $\Omega_m=1$ models."
" We ind that for loeSeVue=(20.1.20.7.20.7) at 2=(2.3.1) this procedure reproduces the SCDM high 'esolution values for λος aud 8,55; to within1051."," We find that for $\log N_{{\rm
HI},c} = (20.4, 20.7, 20.7)$ at $z=(2,3,4)$ this procedure reproduces the SCDM high resolution values for $\Omega_{ccg}$ and $\Omega_{obs}$ to within."
. It is possible that some Lyinau limit and/or aabsorption originates from regions other than galactic halos., It is possible that some Lyman limit and/or absorption originates from regions other than galactic halos.
 To investigate this alternative witlin our sitmulatious. we project the entire simulation volume aud compare the area of aand aabsorptiou to the stun of the absorption calculated by projecting each halo individually.," To investigate this alternative within our simulations, we project the entire simulation volume and compare the area of and absorption to the sum of the absorption calculated by projecting each halo individually."
 La the analysis presented here. we use all halos that have at least oue group ideutified by SIXID as described in relssecident at least one concentration of cold gas that is gravitationally bound). whether or uot the halo itself has AL>AM.," In the analysis presented here, we use all halos that have at least one group identified by SKID as described in \\ref{ssec:ident} at least one concentration of cold gas that is gravitationally bound), whether or not the halo itself has $M\geq M_{res}$."
 Above M=Alpes. of the dark matter halos harbor at least ¢ue SIlxID-identilied eroup.," Above $M=M_{res}$, of the dark matter halos harbor at least one SKID-identified group."
" We have removed ΤΟΝ from the analysis in this section due to the extreme paucity of S""ucture in the model.", We have removed TCDM from the analysis in this section due to the extreme paucity of structure in the model.
 For the remaliniug four models. we calculate the total area subteucdec by aabsorption i ie halos with SIXID-identilied groups.," For the remaining four models, we calculate the total area subtended by absorption in the halos with SKID-identified groups."
 Comparing this value to the total area subtended iu au entire volume projection of each simulation at redshifts z=2 aud z=L we fincl agreement within for all the models at both redshifts. aud to better than in five of the eight cases.," Comparing this value to the total area subtended in an entire volume projection of each simulation at redshifts $z=2$ and $z=4$, we find agreement within for all the models at both redshifts, and to better than in five of the eight cases."
 We attribute the remaining differences to having more than one absorber along a eiven line of sight., We attribute the remaining differences to having more than one absorber along a given line of sight.
 Hence. all aabsorptiou iu the simulation occurs within halos with at least oue concentration of cold. gas.," Hence, all absorption in the simulation occurs within halos with at least one concentration of cold, gravitationally-bound gas."
 In aabsorption. five of the eight outputs agree to better than when compared iu this manner.," In absorption, five of the eight outputs agree to better than when compared in this manner."
 However. at 2=lI the results of volume projection and halo projection differed. by and for SCDM. CCDM. and OCDNMI respectively.," However, at $z=4$ the results of volume projection and halo projection differed by, and for SCDM, CCDM, and OCDM respectively."
 We took the worst case. 2=1 CCDM. aud projected all the halos that contaiued at least 32 particles (gas + dark matter). whether or uot they coutained a SIKID-ideutified gas concentration.," We took the worst case, $z=4$ CCDM, and projected all the halos that contained at least 32 particles (gas $+$ dark matter), whether or not they contained a SKID-identified gas concentration."
 When we sium the area subtended by aabsorption in these halos. we find that it now accounts for all but of the," When we sum the area subtended by absorption in these halos, we find that it now accounts for all but of the"
Llurley et al. (,Hurley et al. (
"2004) where one model startec well within r, ane the other started with muss=nm.",2004) where one model started well within $r_{\rm t}$ and the other started with $r_{\rm max} = r_{\rm t}$.
 These are shown in Figure 2bb ancl we clearly distinguish path A ancl path D-like evolution before both clusters end at a similar point., These are shown in Figure \ref{f:fig2}b b and we clearly distinguish path A and path B-like evolution before both clusters end at a similar point.
 In reality we would expect most clusters to evolve between he two extremes of paths A and D as they head. towards 33. particularly curing violent relaxation where clusters will expand and can move along path ο to join D2.," In reality we would expect most clusters to evolve between the two extremes of paths A and B as they head towards B3, particularly during violent relaxation where clusters will expand and can move along path C1 to join B2."
 We see this Oo some extent when we look at the evolution of models d... N2 and N3 in Figure 2ec. Model N3 in particular first evolves across the phase space before starting down path D2.," We see this to some extent when we look at the evolution of models N1, N2 and N3 in Figure \ref{f:fig2}c c. Model N3 in particular first evolves across the phase space before starting down path B2."
" There is also a clear distinction between the evolution of the three models. residing at well separated rjr, values as they start to move down in {οfry."," There is also a clear distinction between the evolution of the three models, residing at well separated $r_{\rm h} / r_{\rm t}$ values as they start to move down in $r_{\rm c} / r_{\rm h}$."
 Of course. owing to the arge half-mass relaxation timescales. the models do not get he opportunity to evolve completely through the parameter space.," Of course, owing to the large half-mass relaxation timescales, the models do not get the opportunity to evolve completely through the parameter space."
 We have now seen that it is possible to reach large ry values for clusters evolving in a weak 6822-like tidal field and that quite distinct rj values can be obtained. by clusters with cülferent initial sizes.," We have now seen that it is possible to reach large $r_{\rm h}$ values for clusters evolving in a weak $\,6822$ -like tidal field and that quite distinct $r_{\rm h}$ values can be obtained by clusters with different initial sizes."
 But can clistinet rj values be obtained by other means?, But can distinct $r_{\rm h}$ values be obtained by other means?
 The first possibility we explore is the inclusion of a primordial binary population (Moclel N2b)., The first possibility we explore is the inclusion of a primordial binary population (Model N2b).
 Figure 3. compares the rj evolution of models N2 and N2b which are identical in setup except for a 5 per cent primordial binary population in the latter., Figure \ref{f:fig3} compares the $r_{\rm h}$ evolution of models N2 and N2b which are identical in setup except for a 5 per cent primordial binary population in the latter.
 We see that the ry evolution is indistinguishable., We see that the $r_{\rm h}$ evolution is indistinguishable.
 This is also true for the evolution of bound. cluster mass (see Table 2)) ancl other general quantities., This is also true for the evolution of bound cluster mass (see Table \ref{t:table2}) ) and other general quantities.
 We note that as an accuracy check models N2 and N2b were both performed twice with dillerent initial random number seeds and the variation between cdilferent realisations of the same model was less than the dillerence between the two model tvpes., We note that as an accuracy check models N2 and N2b were both performed twice with different initial random number seeds and the variation between different realisations of the same model was less than the difference between the two model types.
 For these extended: clusters it is not surprising that the addition of binaries makes little dillerence to the evolution., For these extended clusters it is not surprising that the addition of binaries makes little difference to the evolution.
 The lone relaxation times for Alodels N2 and N2b (see Tables 1. and 2)) mean that the collisional extraction of binding energy [rom the binary orbits will not be ellicient at heating the cluster., The long relaxation times for Models N2 and N2b (see Tables \ref{t:table1} and \ref{t:table2}) ) mean that the collisional extraction of binding energy from the binary orbits will not be efficient at heating the cluster.
" The second: possibility. for internal evolution creating ry, differences between models relates to the formation of tight. BH-BIT binaries which then act as a central energy source to heat the cluster.", The second possibility for internal evolution creating $r_{\rm h}$ differences between models relates to the formation of tight BH-BH binaries which then act as a central energy source to heat the cluster.
 Hurley (2007) showed that the formation of one such lone-lived 111-111 binary could double the rofry ratio compared to a similar model which did not form a DII-DIE binary., Hurley (2007) showed that the formation of one such long-lived BH-BH binary could double the $r_{\rm c} / r_{\rm h}$ ratio compared to a similar model which did not form a BH-BH binary.
" However. we compare the ry, evolution of these models. (IX100-00a. and. WLOO-00b from Llurley 2007) in Figure 3. (and in Tables 2)) and. we sec no clear clistinetion."," However, we compare the $r_{\rm h}$ evolution of these models (K100-00a and K100-00b from Hurley 2007) in Figure \ref{f:fig3} (and in Tables \ref{t:table2}) ) and we see no clear distinction."
 Alackey et al. (, Mackey et al. (
2008) took this further and contrasted. the evolution of clusters with no BII-BII rinaries to that of clusters which retained a [arge number of post-supernovac Bills (~ 200) that subsequently sank to he cluster centre and formed. DII-DIHE binaries (as many as ive such binaries present at any one time).,2008) took this further and contrasted the evolution of clusters with no BH-BH binaries to that of clusters which retained a large number of post-supernovae BHs $\sim 200$ ) that subsequently sank to the cluster centre and formed BH-BH binaries (as many as five such binaries present at any one time).
 The focus was on star clusters in the Large Alagellanic Cloud and as such a tical field the same as For our 6822 case was used (but with Aue= 6kpc rather than. 10κρο ," The focus was on star clusters in the Large Magellanic Cloud and as such a tidal field the same as for our $\,6822$ case was used (but with $R_{\rm gc} = 6\,$ kpc rather than $10\,$ kpc)."
They. found hat the inclusion. of the DII-DBII. binaries could. increase rh by as much as a factor of two bv the time that. the model with no DLII-DII binaries had. reached: core-collapse (compared to a corresponding factor of 20 increase in. re)., They found that the inclusion of the BH-BH binaries could increase $r_{\rm h}$ by as much as a factor of two by the time that the model with no BH-BH binaries had reached core-collapse (compared to a corresponding factor of 20 increase in $r_{\rm c}$ ).
 The rj behaviour first started to diverge after 1 (αντ of evolution. corresponding to roughly one half-mass relaxation ime. with the expansion driven on the shorter relaxation imescale of the centralised. BLL population.," The $r_{\rm h}$ behaviour first started to diverge after $1-2\,$ Gyr of evolution, corresponding to roughly one half-mass relaxation time, with the expansion driven on the shorter relaxation timescale of the centralised BH population."
 However. we note that the most extended. of these models. were in the advanced stages of dissolution at a Hubble time.," However, we note that the most extended of these models were in the advanced stages of dissolution at a Hubble time."
 Another xossibilitv is one that has gathered much attention of late. namely the question of whether or not some star clusters ibour intermecdiate-mass black holes (AAIBLIs).," Another possibility is one that has gathered much attention of late, namely the question of whether or not some star clusters harbour intermediate-mass black holes (IMBHs)."
 Call et al. (, Gill et al. (
2008) compare the rj evolution of models with and withou an IAIBIL and find no significant dillerence until well after core-collapse and even at very [ate times the dilference is still less than a factor of two.,2008) compare the $r_{\rm h}$ evolution of models with and without an IMBH and find no significant difference until well after core-collapse and even at very late times the difference is still less than a factor of two.
 Daumgardt. Makino Llu (2005) looked at the cllect of increasing LAIBIT mass an founcl an increase in 7j of 15 per cent at most.," Baumgardt, Makino Hut (2005) looked at the effect of increasing IMBH mass and found an increase in $r_{\rm h}$ of 15 per cent at most."
 IH should be notedl that the maximum black hole mass included in. the models to date is 1000. and that the heating produce bv significantly more massive LAIBIIs. if indeed they exist. is vet to be documented.," It should be noted that the maximum black hole mass included in the models to date is $1\,000 \, M_\odot$ and that the heating produced by significantly more massive IMBHs, if indeed they exist, is yet to be documented."
 We next look at the evolution of our models. MI ane AP which were evolved in the stronger M31-like tidal field., We next look at the evolution of our models M1 and M2 which were evolved in the stronger M31-like tidal field.
" These models started with dillerent. initial density. profiles so provide an opportunity to look at how the choice of a Plummer or Wing profile alfects the mm, evolution.", These models started with different initial density profiles so provide an opportunity to look at how the choice of a Plummer or King profile affects the $r_{\rm h}$ evolution.
 This is shown in Figure 3. (also in Figure 4)) and we see that at various stages in the evolution the difference can be up to 50 per cent., This is shown in Figure \ref{f:fig3} (also in Figure \ref{f:fig4}) ) and we see that at various stages in the evolution the difference can be up to 50 per cent.
 The radius evolution of models MI ane M2 is studied in more detail in Figure ει., The radius evolution of models M1 and M2 is studied in more detail in Figure \ref{f:fig4}.
 Comparing this to Figure Lo we clearly see that the stronger tidal field drives more rapid evolution for the M31 models relative to their 6822 counterparts.," Comparing this to Figure \ref{f:fig1} we clearly see that the stronger tidal field drives more rapid evolution for the M31 models relative to their $\,6822$ counterparts."
 Indeed. both MI and M2. reach core-collapse prior το 20€vr.," Indeed, both M1 and M2 reach core-collapse prior to $20\,$ Gyr."
 The model with the Wing density profile evolves more rapidly., The model with the King density profile evolves more rapidly.
 This is primarily owing to a greater central density of stars in the initial mioclel which led to a greater rate of dynamical interactions. more mass lost across the tical boundary in the carly stages. and consequently a reduced relaxation timescale.," This is primarily owing to a greater central density of stars in the initial model which led to a greater rate of dynamical interactions, more mass lost across the tidal boundary in the early stages, and consequently a reduced relaxation timescale."
 However. in the," However, in the"
of the so-called. “hot Jupiters”. with a period of 1.09 clays. corresponding to an orbital distance only 3 times the radius ofits host star.,"of the so-called “hot Jupiters”, with a period of 1.09 days, corresponding to an orbital distance only 3 times the radius of its host star."
 Moreover. WASP-I2b has an inflated radius. HcL.SIu. one of the most extreme examples of anomalous racii for hot Jupiters.," Moreover, WASP-12b has an inflated radius, $R\simeq1.8 {\rm \, R_J}$, one of the most extreme examples of anomalous radii for hot Jupiters."
 As a result. the planet fills about half of its Roche lobe (?)..," As a result, the planet fills about half of its Roche lobe \citep{Li2010}."
 With such a short. orbital distance. and large size. a gas giant planet is expected to undergo complete orbital svnchronisation and. circularisation on a short timescale. much. shorter than the age of a typical field main-sequence cool star.," With such a short orbital distance and large size, a gas giant planet is expected to undergo complete orbital synchronisation and circularisation on a short timescale, much shorter than the age of a typical field main-sequence cool star."
 Indeed. most planets. orbiting closer than 0.05 AU are observed to have circular orbits.," Indeed, most planets orbiting closer than 0.05 AU are observed to have circular orbits."
 Llowever. LOO determined. a value of ο=0.049+0.015 for the orbital eccentricity of WASP-12. a significant departure from circularity.," However, H09 determined a value of $e=0.049 \pm 0.015$ for the orbital eccentricity of WASP-12, a significant departure from circularity."
 “Phis would make the planet bv [ar the subject of the strongest. tical dissipation in any known planetary system., This would make the planet by far the subject of the strongest tidal dissipation in any known planetary system.
 The measured. eccentricity is based. on fitting a Ixeplerian orbital motion on the radial velocity measurements collected by 1009 with the SOPLILE spectrometer (7). together with transit photometry., The measured eccentricity is based on fitting a Keplerian orbital motion on the radial velocity measurements collected by H09 with the SOPHIE spectrometer \citep{Perruchot2008} together with transit photometry.
 7.— stuclied the case of WASDP-12 with that value of eccentricitv. ancl found. a large implied. mass loss and dissipation of tidal energy in the planet.," \cite{Li2010} studied the case of WASP-12 with that value of eccentricity, and found a large implied mass loss and dissipation of tidal energy in the planet."
 In a transiting svstem. the time lag between the ransit and the occultation has a strong dependence. on he projected orbital eccentricity (6cosz).," In a transiting system, the time lag between the transit and the occultation has a strong dependence on the projected orbital eccentricity $e \cos \omega$ )."
 Therefore. if the occultation can be detected with sullicient significance. this oovides a stringent test of the eccentricitv.," Therefore, if the occultation can be detected with sufficient significance, this provides a stringent test of the eccentricity."
 2.hereafterLOO have measured the occultation of WASP-12b from he ground with SPICam on the ARC telescope at Apache Point Observatory in the z/ band., \citet[hereafter L09]{Morales2009} have measured the occultation of WASP-12b from the ground with SPICam on the ARC telescope at Apache Point Observatory in the $z'$ band.
 Their best-fit. resul indicated a occultation with a significant time lag compare o the epoch expected. for a circular orbit. with a similar evel of significance to 1109.," Their best-fit result indicated a occultation with a significant time lag compared to the epoch expected for a circular orbit, with a similar level of significance to H09."
 Nevertheless. the presence of residual correlated: noise is apparent in the LOO data. (see Fie. 2)).," Nevertheless, the presence of residual correlated noise is apparent in the L09 data (see Fig. \ref{morales-transit}) ),"
 as expected. for grounc-basecl photometry at such a high accuracy - the depth of the occultation is only abou 0.08.02%., as expected for ground-based photometry at such a high accuracy - the depth of the occultation is only about $\pm$ 0.02.
. As a result. the issue remained inconclusive unti a space-based measurement of the occultation with the Spitzer Space Telescope (?.hereafterC10). unambiguously showed that the timing of the occultation was precisely tha expected for a circular orbit.," As a result, the issue remained inconclusive until a space-based measurement of the occultation with the Spitzer Space Telescope \citep[hereafter C10]{Campo2010} unambiguously showed that the timing of the occultation was precisely that expected for a circular orbit."
 Εις result suggested that the LOO time lag was probably due to instrumental svstematics. and that the orbit of WASP-12 was probably circular. since a fine-tuned alignment would be required to reconcile the Spitzer result with the LO09 value of the eccentricity.," This result suggested that the L09 time lag was probably due to instrumental systematics, and that the orbit of WASP-12 was probably circular, since a fine-tuned alignment would be required to reconcile the Spitzer result with the H09 value of the eccentricity."
 lt is interesting to note that there is an inherent uas in eccentricity measurements. from. radial. velocities. »ecause a [xeplerian orbit cannot get more circular than c—0.," It is interesting to note that there is an inherent bias in eccentricity measurements from radial velocities, because a Keplerian orbit cannot get more circular than $e=0$."
 Any noise applied to a circular orbit. will result. in an eccentric best-fit. orbit., Any noise applied to a circular orbit will result in an eccentric best-fit orbit.
 Uncderestimating the noise will ead to spurious detections of small eccentricities., Underestimating the noise will lead to spurious detections of small eccentricities.
 This was already. recognized in the context of stellar binaries by 2.., This was already recognized in the context of stellar binaries by \cite{Lucy1971}.
 These authors showed that spurious eccentricity. detections ended: to dominate for ο<0.1 for a typical precision at hat time and stellar binary amplitudes., These authors showed that spurious eccentricity detections tended to dominate for $e< 0.1$ for a typical precision at that time and stellar binary amplitudes.
 Four decades later. roth companion masses and RV accuracies having changed ov about three orders of magnitudes. and the same issue resurfaces for exoplanets.," Four decades later, both companion masses and RV accuracies having changed by about three orders of magnitudes, and the same issue resurfaces for exoplanets."
 WASP-14 is. after WASP-12. the known transiting λαοί having a reported. non-circular orbit with the scconc-shortest period (P=2.2 days).," WASP-14 is, after WASP-12, the known transiting planet having a reported non-circular orbit with the second-shortest period (P=2.2 days)."
 This makes it another test-case for tidal evolution of close-in gas elants., This makes it another test-case for tidal evolution of close-in gas giants.
 I£ dts orbital eccentricitv is indeed near 0.1. then his non-zero but. relatively low value — in the context. of he distribution of giant exoplanet eccentricities — makes it likely that this planet has undergone some degree. of orbital evolution. ancl is still subject to strong tidal forces a esent.," If its orbital eccentricity is indeed near 0.1, then this non-zero but relatively low value – in the context of the distribution of giant exoplanet eccentricities – makes it likely that this planet has undergone some degree of orbital evolution, and is still subject to strong tidal forces at present."
 “Therefore its presence may be useful to constrain he tidal svnchronisation timescale., Therefore its presence may be useful to constrain the tidal synchronisation timescale.
" Lt is also an importan object when studying the issue of the anomalous radius of 100 Jupiters because of its inflated size. with A,=1.28tj."," It is also an important object when studying the issue of the anomalous radius of hot Jupiters because of its inflated size, with $R_p=1.28 {\rm \, R_J}$."
 WASP-14 occupies a distinctive. position in the relevan »wanmeter space: irradiation. orbital distance. eccentricity ancl size.," WASP-14 occupies a distinctive position in the relevant parameter space: irradiation, orbital distance, eccentricity and size."
 We obtained 29 racial-velocitv. measurements for WASD-12 (16 during a single night. and. 13 at various values of orbital phase) ancl 11 for WASP-14. using the SOPLILE spectrograph installed on the 1.93-m telescope at OLLP (France).," We obtained 29 radial-velocity measurements for WASP-12 (16 during a single night, and 13 at various values of orbital phase) and 11 for WASP-14, using the SOPHIE spectrograph installed on the 1.93-m telescope at OHP (France)."
 The observations were gathered between 17 January 2009 and 27 March. 9010., The observations were gathered between 17 January 2009 and 27 March 2010.
 The 16. in-transit measurements for WASDP-12 were obtained with the objective of constraining the spin-orbit angle via the ltossiter-MeLaughlin elfect., The 16 in-transit measurements for WASP-12 were obtained with the objective of constraining the spin-orbit angle via the Rossiter-McLaughlin effect.
 SOPLILZ is a spectrograph optimized. for precise radial-velocity measurements and. has. participated. in the detection of numerous transiting exoplanets in the northern hemisphere. notably from the WASP and ColtoT. transit searches.," SOPHIE is a spectrograph optimized for precise radial-velocity measurements and has participated in the detection of numerous transiting exoplanets in the northern hemisphere, notably from the WASP and CoRoT transit searches."
 It reaches a stability of a few flor bright targets., It reaches a stability of a few for bright targets.
 WASP-12 and WASP-14. however. are near the faint end of the capacity of the 1.932m telescope. and were measured in the -clHligh LElliciencv mode of SOPLILE (See77)..," WASP-12 and WASP-14, however, are near the faint end of the capacity of the 1.93-m telescope, and were measured in the “High Efficiency” mode of SOPHIE \citep[See][]{Perruchot2008,Bouchy2009}."
" Ες mode has a higher throughput han the standard mode. the ""High Resolution” mode. thus allowing fainter targets to be measured. but is less optimized or racial velocity."," This mode has a higher throughput than the standard mode, the “High Resolution” mode, thus allowing fainter targets to be measured, but is less optimized for radial velocity."
 When considering the ensemble of data or known transiting planets obtained with SOPLILE. we aave found evidence for large excursions of the velocity point with time (to the level of several dozen lin some cases).," When considering the ensemble of data for known transiting planets obtained with SOPHIE, we have found evidence for large excursions of the velocity zero-point with time (to the level of several dozen in some cases)."
 As part of the constant. improvement of he SOPLILE reduction pipeline. this cllect is monitored. and corrected for as far as possible. but the presence of relatively arge instrumental svstematics in the High Elliciencey data is a possibility. especially with older data collected before we »ecamie aware of the issue.," As part of the constant improvement of the SOPHIE reduction pipeline, this effect is monitored and corrected for as far as possible, but the presence of relatively large instrumental systematics in the High Efficiency data is a possibility, especially with older data collected before we became aware of the issue."
 This must be remembered when »erforming an orbital analysis based on data from the Ligh Efficicney ποσο., This must be remembered when performing an orbital analysis based on data from the High Efficiency mode.
 The orbital parameters of the two transiting planets were calculated from. the racial velocity data. (together. with published. photometry data for the transit and occultation in the case of WASP-12). with a Marko. Chain Monte Carlo (AICAIC) method.," The orbital parameters of the two transiting planets were calculated from the radial velocity data, (together with published photometry data for the transit and occultation in the case of WASP-12), with a Marko Chain Monte Carlo (MCMC) method."
 Phe main advantage of the AICAIC method is that it allows a seamless combination of racial- data with light-curve data both for the transit and occultation. as well as information on the parent star.," The main advantage of the MCMC method is that it allows a seamless combination of radial-velocity data with light-curve data both for the transit and occultation, as well as information on the parent star."
 The, The
result in the lower spatial resolution study by Caselliοἱal.(2002¢).. where cores wilh stars show steep integrated intensity distribution.,"result in the lower spatial resolution study by \citet{cac02}, where cores with stars show steep integrated intensity distribution."
 There is a possibility that the shallow density prolile in cores with stars can be results of the core collapse (Foster&Chevalier1993) and/or core dispersal due to the molecular outflow., There is a possibility that the shallow density profile in cores with stars can be results of the core collapse \citep{fos93} and/or core dispersal due to the molecular outflow.
 The present observations are probably nol enough for disentangling these possibilities. and further observations (high-resolution dust continuum map. near-intrarecl color-excess map. higher resolution Noll imaging. etc) are clesirable.," The present observations are probably not enough for disentangling these possibilities, and further observations (high-resolution dust continuum map, near-infrared color-excess map, higher resolution $_2$ $^+$ imaging, etc) are desirable."
 On the basis of Noll observations toward Taurus. we have studied (he physical properties ol the molecular cloucl core.," On the basis of $_2$ $^+$ observations toward Taurus, we have studied the physical properties of the molecular cloud core."
 The core radius. linewidth. and intensity distribution do not much differ between starless cores and cores with stars.," The core radius, linewidth, and intensity distribution do not much differ between starless cores and cores with stars."
 This result is in contrast with that previously obtained in 0Ο ., This result is in contrast with that previously obtained in $^{13}$ $^+$.
 We suggest that depletion of LLCO causes this difference., We suggest that depletion of $^{13}$ $^+$ causes this difference.
 From the critical pressure analvsis for Taurus cores. there is no svstematic difference between starless cores and cores wilh stars.," From the critical pressure analysis for Taurus cores, there is no systematic difference between starless cores and cores with stars."
 Both are not far from the critical state for equilibrium., Both are not far from the critical state for equilibrium.
 We suggest (hat the starless cores which are almost. thermally. supported. evolve toward star formation bv keeping close to the critical state., We suggest that the starless cores which are almost thermally supported evolve toward star formation by keeping close to the critical state.
 This result is in contrast. wilh that obtained in the intermediate-mass star forming region OMC-2/3. where (he molecular cloud core evolves by dissipating turbulence lurgelv.," This result is in contrast with that obtained in the intermediate-mass star forming region OMC-2/3, where the molecular cloud core evolves by dissipating turbulence largely."
 The density profile is investigated Ilrom the integrated intensity distribution in the cores., The density profile is investigated from the integrated intensity distribution in the cores.
 Cores wilh stus show shallow density profiles. rI.N lo rL lx.," Cores with stars show shallow density profiles, $r^{-1.8}$ to $r^{-1.6}$."
 T. is grateful to Takenori Nakano for comments on the draft and (ο Jeong-Eun Lee for discussion., K. T. is grateful to Takenori Nakano for comments on the draft and to Jeong-Eun Lee for discussion.
we chose spherical regions.,we chose spherical regions.
" We used three levels of zoom, and ended with a spherical region of radius R4=8.56 Mpc, a mass resolution of m3,=3.01x107Mo,, mapw=1.42x105Mo,, and a force resolution &=6.25 kpc (comoving)."," We used three levels of zoom, and ended with a spherical region of radius $R_3 = 8.56$ Mpc, a mass resolution of $m_{3,\text{b}} = 3.01 \times
10^7 $, $m_{3,\text{DM}} = 1.42\times 10^8 $, and a force resolution $\eps = 6.25$ kpc (comoving)."
" These 1287/2 particles of mass mopw and moy at the level 0 give the same mass resolution as a simulation of 128?x10243/2 particles of mass m3pm51.42x105 and mx~3.01x107 Me,, but focused on a smaller volume of radius 8.56 Mpc at level 3."," These $128^3/2$ particles of mass $m_{0\text{DM}}$ and $m_{0\text b}$ at the level 0 give the same mass resolution as a simulation of $128^3\times 
8^3/2 = 1024^3/2$ particles of mass $m_{3\text{DM}} \simeq 1.42\times
10^{8}$ and $m_{3\text b} 
\simeq 3.01\times 10^{7}$ , but focused on a smaller volume of radius 8.56 Mpc at level 3."
" This technique enable us to simulate galaxies with a fairly high resolution starting with a reasonably sized cosmological box, at a smaller CPU cost."," This technique enable us to simulate galaxies with a fairly high resolution starting with a reasonably sized cosmological box, at a smaller CPU cost."
" One of the main characteristics of this technique is that, except at the zeroth level of zoom, the number of particles does not remain constant during the whole simulation."," One of the main characteristics of this technique is that, except at the zeroth level of zoom, the number of particles does not remain constant during the whole simulation."
" At higher levels of zoom, a particle at timestep i inside the level N box, but outside the level N+1 box, can indeed enter the level N+1 box at timestep i+1 and be split into eight high-resolution particles."," At higher levels of zoom, a particle at timestep $i$ inside the level $N$ box, but outside the level $N+1$ box, can indeed enter the level $N+1$ box at timestep $i+1$ and be split into eight high-resolution particles."
" Particles with unrecorded history the enter the box, and a special care must be taken when establishing particle identities."," Particles with unrecorded history the enter the box, and a special care must be taken when establishing particle identities."
" Because of this increasing number of particles, the third level of simulations could not be run further than 9.1 Gyr, or z=0.46, but lower levels of zoom reached z=0."," Because of this increasing number of particles, the third level of simulations could not be run further than $t=9.1$ Gyr, or $z =
0.46$, but lower levels of zoom reached $z= 0$."
" At the third level of zoom, we end up with 90 snapshots, sampled every 100 Myr from t=0.2 Gyr to t=9.1 Gyr, which enables us to build the merger tree of structures, while at the three lower levels of zoom we have 70 snapshots, sampled every 200 Myr from t=0.2 Gyr to t=14 Gyr."," At the third level of zoom, we end up with 90 snapshots, sampled every 100 Myr from $t=0.2$ Gyr to $t=9.1$ Gyr, which enables us to build the merger tree of structures, while at the three lower levels of zoom we have 70 snapshots, sampled every 200 Myr from $t=0.2$ Gyr to $t = 14$ Gyr."
 The latter can be used for a resolution study (see section 7.1))., The latter can be used for a resolution study (see section \ref{sect:resol}) ).
 The properties of each level of zoom are summed up in table 1.., The properties of each level of zoom are summed up in table \ref{tab:sim_zoom}.
" While collisionless particles, namely stars and dark matter, undergo only gravitational forces and are treated by a tree algorithm, gas dynamics is treated by smooth particle hydrodynamics (SPH)."," While collisionless particles, namely stars and dark matter, undergo only gravitational forces and are treated by a tree algorithm, gas dynamics is treated by smooth particle hydrodynamics (SPH)."
 Additional recipes are needed to mimic subgrid physics such as star formation and feedback., Additional recipes are needed to mimic subgrid physics such as star formation and feedback.
" Our physical treatment is described in ?,, The SPH gas is treated with the same equation of state and the same viscosity prescription."," Our physical treatment is described in \citet{2002A&A...388..826S}, The SPH gas is treated with the same equation of state and the same viscosity prescription."
" The range of temperatures is 800—2x10 K. Any dependance of cooling on metallicity is ignored, and only a primordial metallicity (10? Zo) is considered."," The range of temperatures is $800-2\times 10^6$ K. Any dependance of cooling on metallicity is ignored, and only a primordial metallicity $10^{-3}$ $_\odot$ ) is considered."
" A unique timestep per zoom level is adopted, which is respectively 20, 10, 5, and 2.5 Myr for levels 0 to 3."," A unique timestep per zoom level is adopted, which is respectively 20, 10, 5, and 2.5 Myr for levels 0 to 3."
" The softening length for gravity is respectively 50, 25, 12.5, and 6.25 kpc (comoving), and we checked that the SPH smoothing length is not far shorter than the softening length, as shown on the histogram of Fig."," The softening length for gravity is respectively 50, 25, 12.5, and 6.25 kpc (comoving), and we checked that the SPH smoothing length is not far shorter than the softening length, as shown on the histogram of Fig."
 | at t=9 Gyr in the level 3 zoom., \ref{fig:hist_h} at $t = 9$ Gyr in the level 3 zoom.
 The radiative cooling term A is taken from the normalised tables of ? modelling atomic absorption-line cooling from 10 K to 108° K. The background ultraviolet (UV) radiation field is modelled by a constant uniform heating [yy=10724 erg s! term., The radiative cooling term $\Lambda$ is taken from the normalised tables of \citet{1993ApJS...88..253S} modelling atomic absorption-line cooling from $10^4$ K to $10^{8.5}$ K. The background ultraviolet (UV) radiation field is modelled by a constant uniform heating $\Gamma_\text{UV} = 10^{-24}$ erg $^{-1}$ term.
 Star formation is modelled by a Schmidt law with a star formation rate of with n=1., Star formation is modelled by a Schmidt law with a star formation rate of with $n = 1$.
" It is applied to gas particles with densities higher than a density threshold of Gas particles form stars, and have a fraction of stars within them."," It is applied to gas particles with densities higher than a density threshold of Gas particles form stars, and have a fraction of stars within them."
" When this fraction reaches a given threshold (set to 20%)), we search among their neighbours to determine whether there is enough material to form a full star particle, whether the sum of the star fractions among the neighbouring gas"," When this fraction reaches a given threshold (set to ), we search among their neighbours to determine whether there is enough material to form a full star particle, whether the sum of the star fractions among the neighbouring gas"
The PDFs of pure & field. pure noise and & field added by noise are 2?(rr). P(&) and D?(5) respectivelv.,"The PDFs of pure $\kappa$ field, pure noise and $\kappa$ field added by noise are $P^S(\kappa)$, $P^N(\kappa)$ and $P^{S+N}(\kappa)$ respectively."
 The number of maps is V=40. ie. n=1.2..N.," The number of maps is $N=40$, i.e. $n=1,2,\cdots N$."
 Normally. PDFs are normalized to be unit. te. f.{σεραν=1.," Normally, PDFs are normalized to be unit, i.e. $\int^{+\infty}_{-\infty}P(\kappa)d\kappa=1$."
 From here on we ouly consider binned PDFs. choosing AL equally spaced. bins separated by An.," From here on we only consider binned PDFs, choosing $M$ equally spaced bins separated by $\Delta\kappa$."
 Our notation becomes s;=#+LN. mPens. and each PDF ean also carry an appropriate superscript.," Our notation becomes $\kappa_i =\kappa_-+i
\Delta\kappa$, $P_i \equiv P(\kappa_i) \Delta \kappa$, and each PDF can also carry an appropriate superscript."
 The nunber of bins for all PDFs is M= 19. ke. jj=1.2.M.," The number of bins for all PDFs is $M=19$ , i.e. $i,j=1,2, \cdots M$."
 In the form of matrix. C is the signal covariance and C* is a noise covariance.," In the form of matrix, $\mathbf{C}^S$ is the signal covariance and $\mathbf{C}^N$ is a noise covariance."
 The signal covariance is expressed as <> is the average over 40 maps. and I? (&)is the average value of the & field PDF for 40 maps.," The signal covariance is expressed as where $<>$ is the average over 40 maps, and $\bar{P}^S(\kappa)$ is the average value of the $\kappa$ field PDF for 40 maps."
 The noise PDF. which will also serve as (he noise convolution kernel q(&—s). is à Gaussian distribution where o« is the standard deviation of the noise after the wiener filter.," The noise PDF, which will also serve as the noise convolution kernel $g^N(\kappa-\kappa')$, is a Gaussian distribution where $\sigma_N$ is the standard deviation of the noise after the wiener filter."
 We can also think of this kernel as a noise matrix IN For a noisy # field. (he noise deviation of the PDF relative to an invertible convolution can be written as for each map where P (5;)is the PDF of & field with added noise.," We can also think of this kernel as a noise matrix $\mathbf{N}$ For a noisy $\kappa$ field, the noise deviation of the PDF relative to an invertible convolution can be written as for each map where $P^{S+N}(\kappa_i)$ is the PDF of $\kappa$ field with added noise."
 Thus we have thenoise covallance matrix Using the convolution theorem. we have," Thus we have thenoise covariance matrix Using the convolution theorem, we have"
A preliminary look at the distribution of dwarf nova white dwarf temperatures above the period gap. suggests that for orbital periods. P4. between 200 minutes and minutes and ου320 minutes. there may be a clustering of WD temperatures around 30.000Ix. These include U Gem. SS Aur. WW Ceti. BD Pav. RX And. UU Aq! and TU Men.,"A preliminary look at the distribution of dwarf nova white dwarf temperatures above the period gap, suggests that for orbital periods, $_{orb}$, between $\sim 200$ minutes and minutes and $\sim 320$ minutes, there may be a clustering of WD temperatures around 30,000K. These include U Gem, SS Aur, WW Ceti, BD Pav, RX And, UU Aql and TU Men."
 The WD in the long period SU UMa system TU Men has a temperature at the hot extreme of the WDs in the SU UMa systems below the period gap., The WD in the long period SU UMa system TU Men has a temperature at the hot extreme of the WDs in the SU UMa systems below the period gap.
" Above 380 minutes. there appears to be a considerable spread in the WD T,;; with all having T,jj; = 40.000Ix. or greater. typically hotter than the group between 200 minutes and 320 minutes."," Above 380 minutes, there appears to be a considerable spread in the WD $_{eff}$ with all having $_{eff}$ = 40,000K or greater, typically hotter than the group between 200 minutes and 320 minutes."
 This hotter group includes 55 (νο Z Cam. RU Peg. DV Cen and V442 Cen.," This hotter group includes SS Cyg, Z Cam, RU Peg, BV Cen and V442 Cen."
 Possible evidence of a classical nova shell has been advanced [or Z Cam by Shara et al. (, Possible evidence of a classical nova shell has been advanced for Z Cam by Shara et al. (
2007). who constrain the nova outburst to have occurred between 240 and 2400 vears ago.,"2007), who constrain the nova outburst to have occurred between 240 and 2400 years ago."
 If we take our derived temperatures at [ace value aud are mindful of the small nunber of svstems analvzed above the gap. then it is difllicult to convincinglv argue anv plwsical significance to the two groupings.," If we take our derived temperatures at face value and are mindful of the small number of systems analyzed above the gap, then it is difficult to convincingly argue any physical significance to the two groupings."
 However. it is tempting to speculate on several possibilities.," However, it is tempting to speculate on several possibilities."
" If CVs begin their lives at long periods and evolve to shorter periods as expected. then the larger spread of Tip, at the longer periods is possibly manifesting the fact that their long term core-envelope thermal coupling in response lo compressional heating by (üme-averaged accretion ((Sion1995:Towuslev&Bildsten 2003))) has not vel achieved equilibrium."," If CVs begin their lives at long periods and evolve to shorter periods as expected, then the larger spread of $T_{eff}$ at the longer periods is possibly manifesting the fact that their long term core-envelope thermal coupling in response to compressional heating by time-averaged accretion \citep{sio95a, tow03}) ) has not yet achieved equilibrium."
" The ereater spread with £7, mav also be due (ο WDs in CVs having a wider range of core temperatures al (he onset of CV evolution.", The greater spread with $P_{orb}$ may also be due to WDs in CVs having a wider range of core temperatures at the onset of CV evolution.
 That is. it may be possible that some clwarl novae began their mass (ransler while still quite hot.," That is, it may be possible that some dwarf novae began their mass transfer while still quite hot."
 Thev might have become CVs before their cores had cooled to 10*IK. On the other hand. their WDs may be less massive and hence cooler after (he same degree of long term accretion.," They might have become CVs before their cores had cooled to $10^{7}$ K. On the other hand, their WDs may be less massive and hence cooler after the same degree of long term accretion."
 It is also possible that svstems al very long periods wilh evolved secondaries have a different evolutionary history Caan shorter period dwarf novae., It is also possible that systems at very long periods with evolved secondaries have a different evolutionary history than shorter period dwarf novae.
 It is also not unexpected that the long term. time-averaged accretion rales are variable.," It is also not unexpected that the long term, time-averaged accretion rates are variable."
 There may be one important difference apparent between the ditributions of CY WD temperatures above the period gap versus below the period gap., There may be one important difference apparent between the ditributions of CV WD temperatures above the period gap versus below the period gap.
 Namely. the dispersion in CV WD temperatures above (he period eap appear to be substantially greater (han one fines below the period gap where there is a surprisingly narrow dispersion in teniperatures around. 15.000Ix. In order to better illustrate this difference. we have plotted in figure 6 the temperatures of the white dwarls in non-magnetic CVs during nova-like low states and clwarl novae quiescences (filled triangles) and magnetic CVs during polar low states (filled circles).," Namely, the dispersion in CV WD temperatures above the period gap appear to be substantially greater than one finds below the period gap where there is a surprisingly narrow dispersion in temperatures around 15,000K. In order to better illustrate this difference, we have plotted in figure 6 the temperatures of the white dwarfs in non-magnetic CVs during nova-like low states and dwarf novae quiescences (filled triangles) and magnetic CVs during polar low states (filled circles)."
 All of the temperatures except for seven non-magnetic CVs above the period gap are taken from the compilation in Table 7 of Aranjo-Betancor et al. (, All of the temperatures except for seven non-magnetic CVs above the period gap are taken from the compilation in Table 7 of Araujo-Betancor et al. (
2005).,2005).
 The three objects close to the 3 hour upper boundary of the period gap with WD temperatures above 40.000IN. are all VY Sculptoris nova-like variables. TT Ari. MV Lyra and DW UMa.," The three objects close to the 3 hour upper boundary of the period gap with WD temperatures above 40,000K are all VY Sculptoris nova-like variables, TT Ari, MV Lyra and DW UMa."
 While the difference, While the difference
simulations are usually performed with rigid boundary conditions.,simulations are usually performed with rigid boundary conditions.
 On the one hand flows implement rigid boundary conditions., On the one hand Couette-Taylor flows implement rigid boundary conditions.
 Although in real experiments. the vibrations of the boundary play some role in triggering (urbulent motions. there is little doubt that in (hese experiments. turbulence is sell-sustained.," Although in real experiments, the vibrations of the boundary play some role in triggering turbulent motions, there is little doubt that in these experiments, turbulence is self-sustained."
 On (he other haad. from the experiments ol DBidokhtiandTritton(1992) the rotating shear flows with [ree boundary. conditions are turbulent. although by construction no mean steady state can be reached in these svstems.," On the other hand, from the experiments of \citet{Bid92} the rotating shear flows with free boundary conditions are turbulent, although by construction no mean steady state can be reached in these systems."
 Therefore. it seems unlikely that boundary conditions play an important role in (he presence or absence of turbulence in numerical experiments.," Therefore, it seems unlikely that boundary conditions play an important role in the presence or absence of turbulence in numerical experiments."
 In the shearing sheet approximation. the mean shear is imposed by the tidal force term: in rotating Couette simulations. it results from the boundary conditions.," In the shearing sheet approximation, the mean shear is imposed by the tidal force term; in rotating Couette simulations, it results from the boundary conditions."
" In Couette-Tavlor flows. the boundary conditions do not only produce the shear. but also generate a mean radial pressure gradient,"," In Couette-Taylor flows, the boundary conditions do not only produce the shear, but also generate a mean radial pressure gradient."
 Note however that the term —d(DP)/dr/(p)+r(Q)? of Eq. (8))," Note however that the term $-d\langle P \rangle/dr/\langle\rho\rangle
+r\langle\Omega\rangle^2$ of Eq. \ref{NSCT}) )"
 is similar in function to the term 2gQ7r in Eq. (10))., is similar in function to the term $2q\Omega^2 x$ in Eq. \ref{NSSS}) ).
 Furthermore. the mean pressure gradient in Couette-Tavlor experiments is radial. whereas it is longitudinal (streamwise) in the rotating free shear laver experiments of BidokhtianclTritton(1992)..," Furthermore, the mean pressure gradient in Couette-Taylor experiments is radial, whereas it is longitudinal (streamwise) in the rotating free shear layer experiments of \citet{Bid92}."
 This suggests that neither large scale mean pressure gradients. nor tidal terms. make any significant difference on the «question of the onset of turbulence in the various [lows considered here. especially (hat. all eradient terms get out of the way in incompressible flows (they disappear Irom the vorticity equation).," This suggests that neither large scale mean pressure gradients, nor tidal terms, make any significant difference on the question of the onset of turbulence in the various flows considered here, especially that all gradient terms get out of the way in incompressible flows (they disappear from the vorticity equation)."
 Finally. D will show in the next section that the main ellect of the geometry. (which enters through the geometric terms in Couette-Tavlor flows) is to change the conditions of onset of turbulence. but this does not affect the occurrence of turbulence in itself.," Finally, I will show in the next section that the main effect of the geometry (which enters through the geometric terms in Couette-Taylor flows) is to change the conditions of onset of turbulence, but this does not affect the occurrence of turbulence in itself."
 Although such arguments do not exclude more complex possibilities (as. e.g.. that turbulence might be impedecd in shearing sheet [lows by a combination of these [actors instead ol only one of them). this strongly indicates that rotating Couette flows and shearing sheet ones should be turbulent. suggesting that the absence of turbulence in all the published simulations of this kind stems from limitations in (he munerics involved.," Although such arguments do not exclude more complex possibilities (as, e.g., that turbulence might be impeded in shearing sheet flows by a combination of these factors instead of only one of them), this strongly indicates that rotating Couette flows and shearing sheet ones should be turbulent, suggesting that the absence of turbulence in all the published simulations of this kind stems from limitations in the numerics involved."
 This last. point is addressed in the next section., This last point is addressed in the next section.
 The purpose of this section is to point out important features of turbulence in sheared flows. through a phenomenological model developed in section ??..," The purpose of this section is to point out important features of turbulence in sheared flows, through a phenomenological model developed in section \ref{turbord}."
 The consequences of (his model are used in section ?? to identify the potential limitations in the numerics just, The consequences of this model are used in section \ref{cor} to identify the potential limitations in the numerics just
A decade of extrasolar planet discoveries has shown that the process of planet formation is more complex than originally anticipated.,A decade of extrasolar planet discoveries has shown that the process of planet formation is more complex than originally anticipated.
 It leads to a remarkable diversity of planetary configurations. ranging from mierating hot Jupiters to eccentric giant planets. as well as our own “circular” Solar," It leads to a remarkable diversity of planetary configurations, ranging from migrating hot Jupiters to eccentric giant planets, as well as our own “circular” Solar"
followed up in photometry mode 5 sources detected in a shallow 850jm map of the Groth Strip. in an attempt to quantify the amount of Lux boosting present in the map.,"followed up in photometry mode 5 sources detected in a shallow $850\,\mathrm{\mu m}$ map of the Groth Strip, in an attempt to quantify the amount of flux boosting present in the map."
 To interpret the results we have developed a general method to assess the reliability of low SNR. sources., To interpret the results we have developed a general method to assess the reliability of low SNR sources.
 We apply these techniques to a particular SCUBA survey in the “Groth Strip., We apply these techniques to a particular SCUBA survey in the `Groth Strip'.
 The “Groth Strip Survey’ (GSS) is aTelescope (LIST) programme (ΤΟ 5090. PI: Groth) consisting of 28 overlappingLST Wide Field. Planetary. Camera 2 (WEDPC2) medium-deep images. covering an area of 1132aremin?. forming a long strip centred on16388... (12000). at a Galactic latitude of b=607.," The `Groth Strip Survey' (GSS) is a ) programme (GTO 5090, PI: Groth) consisting of 28 overlapping Wide Field Planetary Camera 2 (WFPC2) medium-deep images, covering an area of $113\,\mathrm{arcmin^{2}}$, forming a long strip centred on, (J2000), at a Galactic latitude of $b\simeq60^{\circ}$."
 The GSS was the deepestUST cosmological integration before the LDF. reaching a imiting Vega magnitude of ~27.5 28 in both the and bands (Grothetal.1994).," The GSS was the deepest cosmological integration before the HDF, reaching a limiting Vega magnitude of $\sim27.5$ –28 in both the and bands \citep{Groth}."
. The GSS has an enormous egacy value. since extensive multi-wavelength observations centred. on this region. have been conducted or are xanned.," The GSS has an enormous legacy value, since extensive multi-wavelength observations centred on this region have been conducted or are planned."
. Morphological ancl photometric information from. he WEPC2 images are provided. by the Medium: Deep Survey (AIDS) database (Ratnatunga.Criliths&Ostran-der1999). and the Deep Extragalactic Evolutionary Probe (DEEP) survey (Simardctal.2002)., Morphological and photometric information from the WFPC2 images are provided by the Medium Deep Survey (MDS) database \citep{Ratnatunga} and the Deep Extragalactic Evolutionary Probe ) survey \citep{Simard}.
. X-ray sources have also been identified in an SOksNALALNewtou observation of the GSS (Mivajictal.2004)...," X-ray sources have also been identified in an $80\,\mathrm{ks}$ observation of the GSS \citep{Miyaji}."
 The GSS is currently. part of the on-going survey anc is also targetted to be a major component of upcoming large surveys in the UV (using the Galaxy Evolution Explorer. GALEN?)). in the optical (as part of the Canaca-brance-Llawaii ‘Telescope Legacy Survey. CELETLS1). and in the LR (the Spitzer GLO IRAC Deep Survey).," The GSS is currently part of the on-going survey and is also targetted to be a major component of upcoming large surveys in the UV (using the Galaxy Evolution Explorer, ), in the optical (as part of the Canada-France-Hawaii Telescope Legacy Survey, ), and in the IR (the GTO IRAC Deep Survey)."
 In this paper. we present 850sam SCUBA observations of about 60 per cent of the original ΝΕΡΟ coverage of the GSS.," In this paper, we present $850\,\mathrm{\mu m}$ SCUBA observations of about 60 per cent of the original WFPC2 coverage of the GSS."
 We have also performed confirmation photometry on some of the sources., We have also performed confirmation photometry on some of the sources.
 Our goal is to make the S501 map ancl source list available to the community so that it may be correlated against existing and future data sets at other wavelengths.," Our goal is to make the $850\,\mathrm{\mu m}$ map and source list available to the community so that it may be correlated against existing and future data sets at other wavelengths."
 No claim is mace that this survey is cither the deepest or the most extensive performed. using SCUBA., No claim is made that this survey is either the deepest or the most extensive performed using SCUBA.
 Llowever. the observations cover enough integration time that we expect a handful of real sources to be detected. and our survey represents the best submillimetre data likely to be available in this field until the advent of SCUBA-2.," However, the observations cover enough integration time that we expect a handful of real sources to be detected, and our survey represents the best submillimetre data likely to be available in this field until the advent of SCUBA-2."
 A roughly TOzarcmin? portion of the Groth Strip (GSS) was observed. with a resolution of 14.7 arcsec and 7.5 aresec at S50 and 4504n. respectively. with the 152m. JCAL atop Alauna Wea in Hawaii in January 1999 ancl January 2000.," A roughly $70\,\mathrm{arcmin}^{2}$ portion of the Groth Strip (GSS) was observed with a resolution of 14.7 arcsec and 7.5 arcsec at 850 and $450\,\mathrm{\mu m}$, respectively, with the 15-m JCMT atop Mauna Kea in Hawaii in January 1999 and January 2000."
" The GSS SCUBA map is centred on RA=1216400"". Dee=52""L000"" (J2000)."," The GSS SCUBA map is centred on $\,{=}\,14^{\mathrm{h}}16^{\mathrm{m}}00^{\mathrm{s}}$, $\,{=}\,52^{\circ}10^\prime00^{\prime\prime}$ (J2000)."
 52 overlapping 64-point jiggle maps of the GSS were obtained. providing measurements of the continuum at both wavelengths simultaneously. with SCUBA (Holland.1999).. which has a field of view of 2.3 aremin.," 52 overlapping 64-point jiggle maps of the GSS were obtained, providing measurements of the continuum at both wavelengths simultaneously with SCUBA \citep{Holland}, which has a field of view of 2.3 arcmin."
 The atmospheric zenith opacity. at 225Cllz was monitored with the Caltech Submillimetre Observatory (CSO) tau (toso) monitor.," The atmospheric zenith opacity at $225\,\mathrm{GHz}$ was monitored with the Caltech Submillimetre Observatory (CSO) tau $\tau_{\mathrm{CSO}}$ ) monitor."
 The roso ranged from 0.08 to 0.09 in January 1999 and from 0.05 to 0.08 in January 2000., The $\tau_{\mathrm{CSO}}$ ranged from 0.03 to 0.09 in January 1999 and from 0.05 to 0.08 in January 2000.
 The weather was generally more stable for the latter set of data., The weather was generally more stable for the latter set of data.
 The secondary mirror was chopped. at ai stanclarc frequeney of 2SHz in azimuth to reduce the effect of rapic sky variations.," The secondary mirror was chopped at a standard frequency of $\simeq
8\,\mathrm{Hz}$ in azimuth to reduce the effect of rapid sky variations."
 Phe telescope was also ‘nodded’ on ancl off the source., The telescope was also `nodded' on and off the source.
 A 40 aresee chopthrow was used at à position angle of 54. almost parallel to the lengthwise orientation of the strip.," A 40 arcsec chop–throw was used at a position angle of $54^{\circ}$, almost parallel to the lengthwise orientation of the strip."
 Pointing checks were performed hourly on blazars ancl planets and varied by less than 3 aresec in azimuth anc by less than 2 aresec in elevation., Pointing checks were performed hourly on blazars and planets and varied by less than 3 arcsec in azimuth and by less than 2 arcsec in elevation.
 The overlapping jigele maps were co-added to produce a final map with a tota integration time of 18 hours and 50 minutes., The overlapping jiggle maps were co-added to produce a final map with a total integration time of 18 hours and 50 minutes.
 We used SURE (SCUBA User Recuetion Facility: Jenness&Lightfoot 1998)) scripts together with locally developed code (Borys2002) to reduce the data., We used SURF (SCUBA User Reduction Facility; \citealt{Jenness}) ) scripts together with locally developed code \citep{Borysthesis} to reduce the data.
 The SURE map and our map look similar., The SURF map and our map look similar.
 The benefit of using our own code to analyse the data is that it makes a map with minimally: correlated pixels ancl provides an estimate of the noise in each. pixel., The benefit of using our own code to analyse the data is that it makes a map with minimally correlated pixels and provides an estimate of the noise in each pixel.
 We chose 3 aresec pixels oriented. along ltA.Dec coordinates.," We chose 3 arcsec pixels oriented along RA,Dec coordinates."
 This pixel size is slightly too large for 450pim studies. but has proven to be adequate at. S50jum (sce Borysctal. 2003)).," This pixel size is slightly too large for $450\,\mathrm{\mu m}$ studies, but has proven to be adequate at $850\,\mathrm{\mu m}$ (see \citealt{Borys2003}) )."
 Calibration data were reduced in the same wav as the CSS ata., Calibration data were reduced in the same way as the GSS data.
 The Εις conversion factors (FCEs) over 3 of the 4 nights in January 1999 and all 3 nights in January 2000 agree with the monthly averages to within 10 per cent (see the ΑΟΛΕΤΕ calibration web-page)., The flux conversion factors (FCFs) over 3 of the 4 nights in January 1999 and all 3 nights in January 2000 agree with the monthly averages to within 10 per cent (see the JCMT calibration web-page).
 The PCE value for one night in January was 30 per cent higher than the monthly average and this could indicate that the sky was so variable that the zco was not accurately rellecting the opacity along 1e line of sight to the object., The FCF value for one night in January was 30 per cent higher than the monthly average and this could indicate that the sky was so variable that the $\tau_{\rm CSO}$ was not accurately reflecting the opacity along the line of sight to the object.
 The calibration uncertainty is omitted from our quoted error values since it is not a major contributor to the global uncertainty of our low SNR data and has no effect on our source detection method., The calibration uncertainty is omitted from our quoted error values since it is not a major contributor to the global uncertainty of our low SNR data and has no effect on our source detection method.
 The 8504n map has a mean consistent with zero. as expected. from dillerential measurements. and an rms of 3.5mJv.," The $850\,\mathrm{\mu m}$ map has a mean consistent with zero, as expected from differential measurements, and an rms of $3.5\,\mathrm{mJy}$."
 The final map is shown in Fig. L.., The final map is shown in Fig. \ref{fig:850map}.
 Phe 450ji map also has à mean consistent with zero and an rms of 50mv.," The $450\,\mathrm{\mu m}$ map also has a mean consistent with zero and an rms of $50\,\mathrm{mJy}$."
 Given the 14.7 aresee beam. a high-redshift galaxy wil be unresolved ancl will appear as a positive source Hanke bv 2 negative sources.," Given the 14.7 arcsec beam, a high-redshift galaxy will be unresolved and will appear as a positive source flanked by 2 negative sources."
 The source density at S50/m (see e.g. Scottetal.2002.. Borysοἱal. 2003.. Webbetal. 2003)) suggests that only a handful of sources will be recoverec in our map.," The source density at $850\,\mathrm{\mu m}$ (see e.g. \citealt{Scott}, \citealt{Borys2003}, \citealt{Webb}) ) suggests that only a handful of sources will be recovered in our map."
 Llenee we do not expect many overlapping sources. and therefore sources were extracted by fitting theraw rebinned map with a three-Iobed. PSE of an. isolate point-source with the same chop throw and position angle as the map data.," Hence we do not expect many overlapping sources, and therefore sources were extracted by fitting theraw rebinned map with a three-lobed PSF of an isolated point-source with the same chop throw and position angle as the map data."
 A fit to the PSE model centred on each, A fit to the PSF model centred on each
To reproduce algorithm & in ?.. let the initial guess for q' be Then iterate equation once. producing qo and po ave then given bv equations and(16c).. with this choice for q'.,"To reproduce algorithm 8 in \citet{Omelyan2006}, let the initial guess for $q'$ be Then iterate equation once, producing $q_2$ and $p_2$ are then given by equations and, with this choice for $q'$."
 This choice of initial guess and single iteration allows the algorithm to be written compositionally as This is exactly the sequence of operations in ?.. algorithun. 8: equation is the approximation derived in ? to the loree gradient recuired in the corresponding algoritlim of ?..," This choice of initial guess and single iteration allows the algorithm to be written compositionally as This is exactly the sequence of operations in \citet{Omelyan2006}, algorithm 8; equation is the approximation derived in \citet{Omelyan2006} to the force gradient required in the corresponding algorithm of \citet{Chin2003}."
 The algorithm needs four force evaluations lor a single step. but only tree in a simulation because the first force evaluation of a step occurs at the same position as the last force evaluation of the previous step.," The algorithm needs four force evaluations for a single step, but only three in a long-running simulation because the first force evaluation of a step occurs at the same position as the last force evaluation of the previous step."
 The algorithm exactly conserves pliase-space volume and momentum. but is only fourth-order svuiplectic (in 2»-dimensional pliase-spaces with nz» 1).," The algorithm exactly conserves phase-space volume and momentum, but is only fourth-order symplectic (in $2n$ -dimensional phase-spaces with $n
> 1$ )."
 As stated above. in practice we find that the energy. error [rom this algorithm in N-body simulations is significantly worse than that from the following algorithm.," As stated above, in practice we find that the energy error from this algorithm in $N$ -body simulations is significantly worse than that from the following algorithm."
 We compare (he energv error behavior of the aleorithms in Figure I.., We compare the energy error behavior of the algorithms in Figure \ref{OmelyanVsUs}.
 As we shall see in Section 5.. it is not. in general. possible to iterate equation in the presence of individual timesteps.," As we shall see in Section \ref{IndividualTimeSteps}, it is not, in general, possible to iterate equation in the presence of individual timesteps."
 Iterating equation for a particle corresponds (o, Iterating equation for a particle corresponds to
 Ina flat. matter-dominated universe. we would not expect to see an ISW effect as the large-scale gravitational potentials do not changetime.,"In a flat, matter-dominated universe, we would not expect to see an ISW effect as the large-scale gravitational potentials do not change."
 However. in a universe dominated by DE or curvature. we should detect a so called ISW elect. which provides a direct measure of these quantities at the redshift of the changing potentials. i.c.. the effect does not depend on the previous history of the erowth of structure.," However, in a universe dominated by DE or curvature, we should detect a so called ISW effect, which provides a direct measure of these quantities at the redshift of the changing potentials, i.e., the effect does not depend on the previous history of the growth of structure."
 The late-time ISW elfect introduces additional secondary anisotropies on top —of the primary— CALB Óluctuations and is therefore hard to detect directly., The late-time ISW effect introduces additional secondary anisotropies on top of the primary CMB fluctuations and is therefore hard to detect directly.
 However. the ISW ellect can be seen via the eross-correlation of the €MD with tracers in the large-scale structure of the universe as outlined by Crittenden&Turok(1996)...," However, the ISW effect can be seen via the cross-correlation of the CMB with tracers in the large-scale structure of the universe as outlined by \citet{1996PhRvL..76..575C}."
 This has now been achieved by a number of authors using a host of dillerent. galaxy datasets (Fosalba.Gaztanaga.&Cas-al.2008:Ciranett.Nevrinck.&Szapucdi 2008)..," This has now been achieved by a number of authors using a host of different galaxy datasets \citep{2003ApJ...597L..89F,
2003astro.ph..7335S,
2004Natur.427...45B,
2004ApJ...608...10N,
2004PhRvD..69h3524A, 
2004MNRAS.350L..37F,
2005PhRvD..72d3525P,
2006MNRAS.372L..23C, 
2006PhRvD..74f3520G,
2007MNRAS.377.1085R, 
2008PhRvD..78d3519H,
2008ApJ...683L..99G}."
 In this paper. we exploit the recent analysis of Ciannantonioetal.(2008) and focus on the subset of intermecdiate-redshift (2< 0.4) SDSS data they used.," In this paper, we exploit the recent analysis of \citet{2008PhRvD..77l3520G} and focus on the subset of intermediate-redshift $z<0.4$ ) SDSS data they used."
 Even this subset of cata shows a detection of the ISW elfect a the 36. level (Ciannantonio2008a).., Even this subset of data shows a detection of the ISW effect at the $3\sigma$ level \citep{giannantonio_private}.
 The contours for this new determination of the ISW οσο are plotted in. Figs. 4.. 5..," The contours for this new determination of the ISW effect are plotted in Figs. \ref{fig_sn_bao_qs_isw}, \ref{fig_sn_gs_isw_curvature},"
 and 6.., and \ref{fig_sdss_plus_gs_and_isw}.
 In Table 1.. we present the combination of this new ISW cllect measurement with our SDSS-II SN ane BAO data. using the same procedure as discussed in Section -5.1.1..," In Table \ref{table_w}, we present the combination of this new ISW effect measurement with our SDSS-II SN and BAO data, using the same procedure as discussed in Section \ref{section_gs_structure}."
 We provide in Table 1 measurements of w anc Quy [rom various combinations of the four data-sets considered herein (SN. BAO. RS. IS8W).," We provide in Table \ref{table_w} measurements of $w$ and $\Omega_M$ from various combinations of the four data-sets considered herein (SN, BAO, RS, ISW)."
" The most stringent constraint comes from the combination of all the probes giving w=OSL(15 and Oy,=0.22Qu which is competitive eiven the restricted. redshift range considered in this analvsis."," The most stringent constraint comes from the combination of all the probes giving $w=-0.81^{+0.16}_{-0.18}$ and $\Omega_M=0.22^{+0.09}_{-0.08}$, which is competitive given the restricted redshift range considered in this analysis."
 However. much of this constraint comes from the combination of just. the SDSS-LL SNe anc LSW measurements (See Table 1)).," However, much of this constraint comes from the combination of just the SDSS-II SNe and ISW measurements (See Table \ref{table_w}) )."
 Phe ISW contours already include correlations between different angular and recishift bins and cosmic variance. ancl could therefore be considered stable (see e.g. Giannantonioetal. 2008)).," The ISW contours already include correlations between different angular and redshift bins and cosmic variance, and could therefore be considered stable (see e.g. \citealt{2008PhRvD..77l3520G}) )."
 Similarly the contours we use for recdshift-space distortions include the cominant uncertainty coming from the galaxy bias (see the procedure laid. out. in Section 5.1.1))., Similarly the contours we use for redshift-space distortions include the dominant uncertainty coming from the galaxy bias (see the procedure laid out in Section \ref{section_gs_structure}) ).
 Percivalctal.(2009) has done several checks and found that their result is robust against variations in sample selection. number of redshift slices. calibration ancl other potential influences.," \cite{2009arXiv0907.1660P} has done several checks and found that their result is robust against variations in sample selection, number of redshift slices, calibration and other potential influences."
 Therefore. the results presented in. Table. 1 includes major uncertainties allecting the other probes but only the statistical uncertainties [from the SDSS-SN data on the measured. cosmological parameters.," Therefore, the results presented in Table 1 includes major uncertainties affecting the other probes but only the statistical uncertainties from the SDSS-SN data on the measured cosmological parameters."
 As discussed in IWwessleretal.(2009).. the SDSS-LL SN distances also depend on the detailed. choices and assumptions within the AILCS2k2 supernova light-curve fitting procedure. including dillerent training vectors. priors on ly and Ay. uncertainties in zero points and the filter systems. anc selection biases.," As discussed in \citet{kessler}, the SDSS-II SN distances also depend on the detailed choices and assumptions within the MLCS2k2 supernova light-curve fitting procedure, including different training vectors, priors on $A_V$ and $R_V$, uncertainties in zero points and the filter systems, and selection biases."
" To quantify, the systematic uncertainties associated with these parameter. choices. we repeat our analysis above for these cillerent choices and. following the procedure laid out in [xessleretal.(2009)... we calculate a variation of Aw=£0.15 with respect to the fiducial AILOS2k2 reduction presented in Table 1 in the case of combining all four constraints and slightly. larger. values for the other cases."," To quantify the systematic uncertainties associated with these parameter choices, we repeat our analysis above for these different choices and, following the procedure laid out in \citet{kessler}, we calculate a variation of $\Delta w=\pm 0.15$ with respect to the fiducial MLCS2k2 reduction presented in Table \ref{table_w} in the case of combining all four constraints and slightly larger values for the other cases."
 Our estimates of the systematic uncertainty for ALCS2k2 are [larger than the values caleulated in Kessleretal.(2009) because they use the BAO cl-parameter from Eisensteinetal.(2005)... ancl the added constraints on 1 ancl i derived from using the CAIB R-parameter (Ixomatsuetal.2008)...," Our estimates of the systematic uncertainty for MLCS2k2 are larger than the values calculated in \citet{kessler} because they use the BAO $A$ -parameter from \citet{2005ApJ...633..560E}, and the added constraints on $\Omega_M$ and $w$ derived from using the CMB $R$ -parameter \citep{2008arXiv0803.0547K}."
 We reproduce their values for the svstematic uncertainties on AILCS2k2 (Awzz0.1). if we include these constraints in our analvsis.," We reproduce their values for the systematic uncertainties on MLCS2k2 $\Delta w \approx 0.1$ ), if we include these constraints in our analysis."
 Llowever. in this paper. we restrict our analysis to intermediate-redshift probes and therefore do not include the CMD constraints. which results in larger uncertainties.," However, in this paper, we restrict our analysis to intermediate-redshift probes and therefore do not include the CMB constraints, which results in larger uncertainties."
 Our analvsis of the MLCS2k2 svstematic uncertainties discussed. above does not include the large shift in w discussed in Ixesslerctal.(2009) when the rest-frame C- band template is removed in the light-curve fitting., Our analysis of the MLCS2k2 systematic uncertainties discussed above does not include the large shift in $w$ discussed in \citet{kessler} when the rest-frame $U$ -band template is removed in the light-curve fitting.
 As seen in Fable 6 of Ixessleretal.(2009).. removing the rest.[rame Uband results ina 0.31 shift in e. while we find a shift of 0.48 if we remove this data.," As seen in Table 6 of \citet{kessler}, removing the rest–frame U–band results in a $-0.31$ shift in $w$, while we find a shift of $-0.43$ if we remove this data."
 This particular uncertainty would therefore give rise to a bimodal result either centered around dw2OS (with Uband included) or αν--12 (without. U-band). vet both consistent with w=1 within he errors.," This particular uncertainty would therefore give rise to a bimodal result either centered around $w\simeq-0.8$ (with U–band included) or $w=-1.2$ (without U-band), yet both consistent with $w=-1$ within the errors."
 We do not add the uncertainty due to excluding the rest[rame Uband to our svstematic errors. because we relieve it is incorrect to exclude this data from the lightcurve fitting., We do not add the uncertainty due to excluding the rest–frame U–band to our systematic errors because we believe it is incorrect to exclude this data from the light--curve fitting.
 Even though there is evidence for diversity in he UV spectra of SNe Ia (see. Ellis et al., Even though there is evidence for diversity in the UV spectra of SNe Ia (see Ellis et al.
 2008: Foley. et al., 2008; Foley et al.
 2008). the removal of the rest-frame Woband data from he SDSSonly analysis results in the light curve litter using only two filters at z«0.2 to constrain the colors of the SNe.," 2008), the removal of the rest-frame U–band data from the SDSS–only analysis results in the light curve fitter using only two filters at $z<0.2$ to constrain the colors of the SNe."
 This provides significant freedom to the MLECS2E?2 fitter and hen the priors on the fitted parameters become important., This provides significant freedom to the MLCS2k2 fitter and then the priors on the fitted parameters become important.
 We note that wis only shifted by 0.1 when using the SALT ight curve Litter (seeTableSinIxessleretal.2000). on the SDSSonly sample with the rest-frame Uband. excluded., We note that $w$ is only shifted by $-0.1$ when using the SALT light curve fitter \citep[see Table 8 in][]{kessler} on the SDSS–only sample with the rest-frame U–band excluded.
 ‘This is the only noticeable dillercnee between these two light curve fitting methodologies when considering the SDSSonly sample: namely the error on aw when the rest-frame Uoband is excluded., This is the only noticeable difference between these two light curve fitting methodologies when considering the SDSS–only sample; namely the error on $w$ when the rest-frame U–band is excluded.
 Finally. Ixessleretal.(2009). also sees a clear jump in the SDSS Llubble diagram at z20.2 when the rest-frame Woband is excluded from the AILCS2k2 analysis (see their Section 10.1.3 and Fig.," Finally, \citet{kessler} also sees a clear jump in the SDSS Hubble diagram at $z\simeq0.2$ when the rest-frame U–band is excluded from the MLCS2k2 analysis (see their Section 10.1.3 and Fig."
 30). indicating that a constant w model is not à good fit in this case.," 30), indicating that a constant $w$ model is not a good fit in this case."
" Me present an. analysis of the luminosity distances of Type la Supernovae from the Sloan Digital Sky Survey- (SDSS-1I) Supernova Survey in conjunction with other intermediate redshift ἐς< 0.4) cosmological measurements including redshift-space distortions from the 2dECIUS. the TSW. οσο, and the BAO. distance. scale from both the SDSS and δα."," We present an analysis of the luminosity distances of Type Ia Supernovae from the Sloan Digital Sky Survey-II (SDSS-II) Supernova Survey in conjunction with other intermediate redshift $z<0.4$ ) cosmological measurements including redshift-space distortions from the 2dFGRS, the ISW effect, and the BAO distance scale from both the SDSS and 2dFGRS."
 We have analyzed the SDSS-LL SN luminosity distances using several, We have analyzed the SDSS-II SN luminosity distances using several
the accretion rate. the midplane pressure (and therefore jet Iuminositv) declines xin.,"the accretion rate, the midplane pressure (and therefore jet luminosity) declines $\propto \dot m^{4/5}$."
 This break (ime is «quite late in the development of the flare for low-mass events. but when the black hole mass is relatively large. it could take place as early as c30/0.," This break time is quite late in the development of the flare for low-mass events, but when the black hole mass is relatively large, it could take place as early as $\simeq 30 t_0$."
 Although the theory of jet and clisk emission from tidal disruptions as we have presented it contains a large number of free parameters. in anv given event (here are also potentially a sizable number of observable properties (hat may be used (o constrain these parameters.," Although the theory of jet and disk emission from tidal disruptions as we have presented it contains a large number of free parameters, in any given event there are also potentially a sizable number of observable properties that may be used to constrain these parameters."
 In nearly every. event. il is possible to measure (he characteristic time /p.," In nearly every event, it is possible to measure the characteristic time $t_0$."
" Optical and/or ultraviolet observations often give an indicator of the peak thermal disk luminosity. Lug: we describe this as only an ""indicator"" because. as we discuss below. (here is likelv to be a sizableand uncertainbolometric correction."," Optical and/or ultraviolet observations often give an indicator of the peak thermal disk luminosity, $L_{d0}$; we describe this as only an “indicator"" because, as we discuss below, there is likely to be a sizable—and uncertain—bolometric correction."
" When there is hard X-ray enission. the peak jet luminosity Ljj can also be obtained: if an event can be followed long enough. it mav also be possible to measure (wo (mes related to (he transition from super- to sub-Eddington accretion: the (nme fj, al which the jet Iuninosity flattens. and the time lai 04 Which the disk luninositv begins (o diminish."," When there is hard X-ray emission, the peak jet luminosity $L_{j0}$ can also be obtained; if an event can be followed long enough, it may also be possible to measure two times related to the transition from super- to sub-Eddington accretion: the time $t_{\rm jet}$ at which the jet luminosity flattens, and the time $t_{\rm disk}$ at which the disk luminosity begins to diminish."
 In this section. we will lav out a eeneral formalism for using these observables as parameter constraints and then apply Chat method to a specilic example. Swill J2058.44-0516.," In this section, we will lay out a general formalism for using these observables as parameter constraints and then apply that method to a specific example, Swift J2058.4+0516."
 As shown by Lodatoetal. (2009).. the accretion rale peaks at a time Peg) past pericenter passage (see equ. 3)).," As shown by \cite{lkp09}, , the accretion rate peaks at a time $P_{\rm orb}(a_{\rm min})$ past pericenter passage (see eqn. \ref{eq:porb_min}) ),"
 and diminishes thereafter as a power-law in time., and diminishes thereafter as a power-law in time.
" If we identilv the time of peak flare Iuminosity. /j with that orbital period. we obtain the constraint where /,is measured in davs."," If we identify the time of peak flare luminosity $t_0$ with that orbital period, we obtain the constraint where $t_0$is measured in days."
magnifications is weaker at j/1. showing considerable scatter for all of the models.,"magnifications is weaker at $\mu > 1$, showing considerable scatter for all of the models."
 This can be understood in terms of the clustering of the caustie network in regions of high magnification which exhibits structure on quite small scales., This can be understood in terms of the clustering of the caustic network in regions of high magnification which exhibits structure on quite small scales.
 With this. the magnification of the continuum mirrors this small scale caustic structure. whereas the BLR is magnified by a weighted average of the larger scale caustic structure.," With this, the magnification of the continuum mirrors this small scale caustic structure, whereas the BLR is magnified by a weighted average of the larger scale caustic structure."
 Interestingly. for all the models. there is also a non-zero probability that while the continuum source is being strongly magnitied. the over all BLR region is undergoing demagnification.," Interestingly, for all the models, there is also a non-zero probability that while the continuum source is being strongly magnified, the over all BLR region is undergoing demagnification."
 The reverse of this. however. appears to be significantly rarer in most models.," The reverse of this, however, appears to be significantly rarer in most models."
 The situation is very similar for the larger BLR models (Figure 6)., The situation is very similar for the larger BLR models (Figure \ref{fig5}) ).
 As expected from Figure 3. the distributions of BLR magnification are somewhat narrower than the smaller BLR model.," As expected from Figure \ref{fig2}, the distributions of BLR magnification are somewhat narrower than the smaller BLR model."
 Again. no clear correlation of the continuum and BLR magnification is apparent with the continuum source undergoing significant magnitication while the BLR is relatively unmagnitied.," Again, no clear correlation of the continuum and BLR magnification is apparent with the continuum source undergoing significant magnification while the BLR is relatively unmagnified."
 It is also apparent that while there is the general correlation between the magnification of the two regions. there is still a significant range over which the continuum source can be substantially magnified while the BLR undergoes a magnification of ~1.," It is also apparent that while there is the general correlation between the magnification of the two regions, there is still a significant range over which the continuum source can be substantially magnified while the BLR undergoes a magnification of $\sim1$."
 Hence. a microlensing fluctuation observed in broadband photometric monitoring will not necessarily be an indicator of strong microlensing of the BLR.," Hence, a microlensing fluctuation observed in broadband photometric monitoring will not necessarily be an indicator of strong microlensing of the BLR."
 Rather than spectroscopic monitoring. however. broadband. monitoring. could be combined with observations obtained through a narrow band filter which covers a broad line in the quasar spectrum.," Rather than spectroscopic monitoring, however, broadband monitoring could be combined with observations obtained through a narrow band filter which covers a broad line in the quasar spectrum."
 With this. a plot similar to those presented in Figures 5. and 6. could be constructed and compared to simulations.," With this, a plot similar to those presented in Figures \ref{fig4} and \ref{fig5} could be constructed and compared to simulations."
 As well as the total magnification of the emission lines. it is important to characterize the moditication of the emission line orofile due to differential magnification effects.," As well as the total magnification of the emission lines, it is important to characterize the modification of the emission line profile due to differential magnification effects."
 This can be seen as a shift in the velocity centroid of the emission line., This can be seen as a shift in the velocity centroid of the emission line.
 In undertaking his. however. it is important to note the S'S and 1 models display surface brightness structure which is symmetrical in velocity. and any gravitational lensing magnification results in identical line oofile modification at positive and negative velocities. leading to a centroid shift of zero.," In undertaking this, however, it is important to note the $SS$ and $BS$ models display surface brightness structure which is symmetrical in velocity, and any gravitational lensing magnification results in identical line profile modification at positive and negative velocities, leading to a centroid shift of zero."
 Therefore. in the following study only the »ositive velocity component of the emission lines are considered or the SS’ and £5 models. whereas the positive velocity and the otal emission line profile are considered for the A21 and AA1 models.," Therefore, in the following study only the positive velocity component of the emission lines are considered for the $SS$ and $BS$ models, whereas the positive velocity and the total emission line profile are considered for the $KD1$ and $KM1$ models."
 Figure 7 presents the distribution of the measured centroid of he positive velocity component of the BLR emission line for euch of the models presented in this paper., Figure \ref{fig6} presents the distribution of the measured centroid of the positive velocity component of the BLR emission line for each of the models presented in this paper.
 The black line presents the distributions for the smaller BLR models for each lensed image. whereas the thicker. grey line represents the larger BLR models.," The black line presents the distributions for the smaller BLR models for each lensed image, whereas the thicker, grey line represents the larger BLR models."
 The vertical dot-dashed line running vertically through the panels, The vertical dot-dashed line running vertically through the panels
This is achieved withpreconditionzng.,This is achieved with.
 Instead of solving Eq., Instead of solving Eq.
 directly. one solves with the preconditioniug matrix B.," directly, one solves with the preconditioning matrix ${\cal B}$."
 Now the iterative solver deals with the matrix BY., Now the iterative solver deals with the matrix ${\cal B}\cal J$ .
 IE B is a good approximation to F+. then BF will be close to the identity matrix. the condition πο will be close to unity; aud the linear solver will converge quickly.," If ${\cal B}$ is a good approximation to ${\cal J}^{-1}$, then ${\cal B}{\cal J}$ will be close to the identity matrix, the condition number will be close to unity, and the linear solver will converge quickly."
 Ποιος the problem reduces to finding a matrix B that approximates JF+ sufficiently well and that cau be computed eficieutly., Hence the problem reduces to finding a matrix $\cal B$ that approximates ${\cal J}^{-1}$ sufficiently well and that can be computed efficiently.
 There exist may different approaches. most notably finite differcuce precouditioniug|?] aud finite clement preconditioniug|?|:: we will follow a two-stage process proposed by Orszag|?|..," There exist many different approaches, most notably finite difference \cite{Orszag:1980} and finite element \cite{Deville-Mund:1985}; ; we will follow a two-stage process proposed by \cite{Orszag:1980}."
 First. initialize a matrix Arp witha finite differcuce approximation of the Jacobian 7.," First, initialize a matrix ${\cal A}_{FD}$ with a finite difference approximation of the Jacobian $\cal J$."
 Second. approximately invert Arp to construct B. Iu one spatial dimension Arp is tridiagonal and direct inversion 5=App ls feasible.," Second, approximately invert ${\cal A}_{FD}$ to construct ${\cal B}$, In one spatial dimension ${\cal A}_{FD}$ is tridiagonal and direct inversion ${\cal B}\equiv{\cal A}_{FD}^{-1}$ is feasible."
 In two or more dimensions. direct inversion of Arp is too expensive: for problems iu one two-dimensional subdomain. hardcoded incomplete LU-factorizatious have been developed?|..," In two or more dimensions, direct inversion of ${\cal A}_{FD}$ is too expensive; for problems in one two-dimensional subdomain, hardcoded incomplete LU-factorizations have been \cite{Canuto-Hussaini}."
 Tn our case we lave to deal with the additional complexity that the Jacobian aud therefore Arp contains matching conditions., In our case we have to deal with the additional complexity that the Jacobian and therefore ${\cal A}_{FD}$ contains matching conditions.
 Since we choose the domain decomposition at xuutinc. nothing is known about the particular structure of the subdomains.," Since we choose the domain decomposition at runtime, nothing is known about the particular structure of the subdomains."
 We proceed as follows: We initialize App with the finite differeuce approximation of J., We proceed as follows: We initialize ${\cal A}_{FD}$ with the finite difference approximation of ${\cal J}$.
 It is sufficient to include those terms of the Jacobian in App that cause the condition number to Increase with the expansion order., It is sufficient to include those terms of the Jacobian in ${\cal A}_{FD}$ that cause the condition number to increase with the expansion order.
 These are the secoud spatial derivatives aud the first derivatives from matching conditions aud boundary conditions. Eqs.," These are the second spatial derivatives and the first derivatives from matching conditions and boundary conditions, Eqs."
 and(386)., and.
. Iucludiug the value matching conditions(38cd)..OSf).. in Arp inproves the ability of the precouditioncr to represent modes extending over several subdomains aud thus decreases the wuuber of iterations. too.," Including the value matching conditions, in ${\cal
 A}_{FD}$ improves the ability of the preconditioner to represent modes extending over several subdomains and thus decreases the number of iterations, too."
 In the first example iu section [1 we demonstrate that precoucditiouing is iudeed necessary. aud that one should precondition not only the ποσο order derivatives. but also the matching conditions.," In the first example in section \ref{sec:Example1} we demonstrate that preconditioning is indeed necessary, and that one should precondition not only the second order derivatives, but also the matching conditions."
 Some details about the finite difference approximations are eiven in appendix A.., Some details about the finite difference approximations are given in appendix \ref{sec:FD-details}.
 Taving set up Arp we theu use the software package ¢|?| for the approximate inversion of Eq., Having set up ${\cal A}_{FD}$ we then use the software package \cite{petsc-home-page} for the approximate inversion of Eq.
(17)... PETSc provides niuiv general purpose precouditiouers that pertorm the step either explicitly or müiplicitlv. most notable ILU aud the overlapping Sclavarz method.," PETSc provides many general purpose preconditioners that perform the step either explicitly or implicitly, most notably ILU and the overlapping Schwarz method."
 With PETSc we can explore these to find the most cficient onc., With PETSc we can explore these to find the most efficient one.
 We will describe our particular choices for preconditioning below for cach example., We will describe our particular choices for preconditioning below for each example.
 Ceneralizing S to multiple dimensions is conceptually straightforward. since Eqs.," Generalizing $\cal S$ to multiple dimensions is conceptually straightforward, since Eqs."
 generalize nicely to higher dimensions., generalize nicely to higher dimensions.
 In order to simplify the matching between touching subdomains. we require that ou a surface shared by touching subdomains. the collocation points are identical.," In order to simplify the matching between touching subdomains, we require that on a surface shared by touching subdomains, the collocation points are ."
 If for example. two three-cdimensioual rectangular blocks touch along the .c-axis. then both blocks must have ideutical lower and upper boundsof the blocks along the y and z axis aud both blocks unst use the same mappines and the same munberof collocation poiuts along the y- aud," If, for example, two three-dimensional rectangular blocks touch along the $x$ -axis, then both blocks must have identical lower and upper boundsof the blocks along the $y$ and $z$ axis and both blocks must use the same mappings and the same numberof collocation points along the $y$- and"
"birth is between 5 and 185 km s!, while the progenitor mass Mp; is between 1.25and 2.65 Mo, both with confidence.","birth is between 5 and 185 km $^{-1}$, while the progenitor mass $M_{2i}$ is between 1.25and 2.65 $_\sun$, both with confidence."
" Both polar and planar kicks are allowed, but planar kicks are more favorable than polar ones."," Both polar and planar kicks are allowed, but planar kicks are more favorable than polar ones."
 The spin tilt angle of NSI is smaller than 16.4? with confidence., The spin tilt angle of NS1 is smaller than $^\circ$ with confidence.
" At the current time and at the measured distance, PSR J1756-2251 has a total transverse velocity between 6.0 and 64.5 km s!, and a radial velocity between —110 and 98 km s, both with confidence."," At the current time and at the measured distance, PSR J1756-2251 has a total transverse velocity between 6.0 and 64.5 km $^{-1}$, and a radial velocity between $-110$ and 98 km $^{-1}$, both with confidence."
" Furthermore, this binary is equally likely to be moving towards us as away from us."," Furthermore, this binary is equally likely to be moving towards us as away from us."
 When comparing with Wang et al. (, When comparing with Wang et al. (
"2006), we have tighter constrained limits on V; and M);, due to the fact that we have the additional constraint on the proper motion JigA..","2006), we have tighter constrained limits on $V_k$ and $M_{2i}$, due to the fact that we have the additional constraint on the proper motion $\mu_{R.A.}$."
" The two neutron stars have masses of 1.62 and 1.11 Mo, where the more massive one is NS1."," The two neutron stars have masses of 1.62 and 1.11 $_\sun$, where the more massive one is NS1."
" However, each mass measurement has an uncertainty of ~0.5 Mo."," However, each mass measurement has an uncertainty of $\sim$ 0.5 $_\sun$."
 PSR J1811 has a characteristic age of 1830 Myr., PSR J1811 has a characteristic age of 1830 Myr.
" The neutron stars are in an orbit with a period of 18.8 days, and an eccentricity of 0.828."," The neutron stars are in an orbit with a period of 18.8 days, and an eccentricity of 0.828."
" At the current time, this binary is close to the galactic plane, at |=12.8? and b=0.44°, and at a distance of 6.0 kpc away from us."," At the current time, this binary is close to the galactic plane, at $l = 12.8^\circ$ and $b = 0.44^\circ$, and at a distance of 6.0 kpc away from us."
" Like PSR J1756-2251, there are currently no spin tilt nor proper motion measurements available."," Like PSR J1756-2251, there are currently no spin tilt nor proper motion measurements available."
 The results are displayed in Figures 13 and 14., The results are displayed in Figures 13 and 14.
" The 2D V;- Mp; joint distribution shows that the kick given to NS2 at birthprobability is less than 310 km s!, while the progenitor mass Mp; is between 1.11 and 8.0 Mo, both with confidence."," The 2D $V_k$ $M_{2i}$ joint probability distribution shows that the kick given to NS2 at birth is less than 310 km $^{-1}$, while the progenitor mass $M_{2i}$ is between 1.11 and 8.0 $_\sun$, both with confidence."
" Both polar and planar kicks are allowed, but the planar kicks are more favorable than the polar ones."," Both polar and planar kicks are allowed, but the planar kicks are more favorable than the polar ones."
" The spin tilt angle 0, is smaller than 57.6? with confidence.", The spin tilt angle $\theta_t$ is smaller than $^\circ$ with confidence.
" At the measured distance, the total transverse velocity of PSR J1811-1736 at the current epoch is between 4 and 202 km s, and the radial velocity between -90 and 210 km s! with confidence, which means this binary is likely moving away from us."," At the measured distance, the total transverse velocity of PSR J1811-1736 at the current epoch is between 4 and 202 km $^{-1}$, and the radial velocity between -90 and 210 km $^{-1}$ with confidence, which means this binary is likely moving away from us."
 Although our upper boundary of the confidence intervals of M»; is the same as the upper limit found by Wang et al. (, Although our upper boundary of the confidence intervals of $M_{2i}$ is the same as the upper limit found by Wang et al. (
"2006), the value of our lower boundary is less than their lower limit.","2006), the value of our lower boundary is less than their lower limit."
 This is because Wang et al. (, This is because Wang et al. (
"2006) put a conservative lower limit of 2.1 Mo on the progenitor mass of a neutron star, which we did not.","2006) put a conservative lower limit of 2.1 $_\sun$ on the progenitor mass of a neutron star, which we did not."
" On the other hand, our limits on V; are more constrained than those of Wang et al. ("," On the other hand, our limits on $V_k$ are more constrained than those of Wang et al. ("
"2006), as we compute confidence levels instead of allowed ranges of solution as Wang et al. (","2006), as we compute confidence levels instead of allowed ranges of solution as Wang et al. ("
2006).,2006).
" The two neutron stars of this binary have masses of 1.14 and 1.36 Mo, where the less massive one is NS1."," The two neutron stars of this binary have masses of 1.14 and 1.36 $_\sun$, where the less massive one is NS1."
" However, there is an uncertainty of ~0.5 Mo in the mass measurements."," However, there is an uncertainty of $\sim$ 0.5 $_\sun$ in the mass measurements."
 The characteristic age is 12.4 , The characteristic age is 12.4 Gyr.
"For the same reason as PSR J1518+4904, we set an the upper Gyr.limit of 10 Gyr on the age of this binary in our analysis."," For the same reason as PSR J1518+4904, we set an the upper limit of 10 Gyr on the age of this binary in our analysis."
" The neutron stars are orbiting each other with a period of 1.18 days, and an orbital eccentricity of 0.139."," The neutron stars are orbiting each other with a period of 1.18 days, and an orbital eccentricity of 0.139."
" At current time, this binary is out of the galactic plane, at |=53.3? and b=15.6°, and it is 1.2 kpc away from us."," At current time, this binary is out of the galactic plane, at $l = 53.3^\circ$ and $b = 15.6^\circ$, and it is 1.2 kpc away from us."
" Although there is no spin tilt nor proper motion measurements available at current time, Lorimer et al. ("," Although there is no spin tilt nor proper motion measurements available at current time, Lorimer et al. ("
2005) derived that the transverse velocity is smaller than 118 km κ”.,2005) derived that the transverse velocity is smaller than 118 km $^{-1}$.
 The results are shown in Figure 15., The results are shown in Figure 15.
" The Υι-Μοι joint probability distribution shows that the kick given to NS2 at birth is between 5 and 225 km s, while the progenitor mass Mp; is between 1.4 and 6.1 Mo with confidence."," The $V_k$ $M_{2i}$ joint probability distribution shows that the kick given to NS2 at birth is between 5 and 225 km $^{-1}$ , while the progenitor mass $M_{2i}$ is between 1.4 and 6.1 $_\sun$ with confidence."
" The PDFs of 6, and 6’ are similar to those of PSR J1756-2251.", The PDFs of $\theta_t$ and $\theta'$ are similar to those of PSR J1756-2251.
" Both polar and planar kicks are allowed, but planar kicks are"," Both polar and planar kicks are allowed, but planar kicks are"
(e.g. Shapley et al.,(e.g. Shapley et al.
 2003. Nagao et al.," 2003, Nagao et al."
 2008. di Serego Alighieri et al.," 2008, di Serego Alighieri et al."
 2008)., 2008).
 However. near-infrared spectroscopy of the sensitivity required to detect this line at 2>7 will certainly not be available until the (WSTY. and even then some theoretical predictions indicate that it is unlikely to be found in detectable objects (Salvaterra. Ferrara Dayal 2011. but see also Pawlik. Milosavljevie Bromm 2011).," However, near-infrared spectroscopy of the sensitivity required to detect this line at $z > 7$ will certainly not be available until the ), and even then some theoretical predictions indicate that it is unlikely to be found in detectable objects (Salvaterra, Ferrara Dayal 2011, but see also Pawlik, Milosavljevic Bromm 2011)."
 By necessity. therefore. recent attention has focussed on whether the broad-band near-infrared photometry which has now been successfully used to discover galaxies at. 20.58.5 (eg. Ίοιο et al.," By necessity, therefore, recent attention has focussed on whether the broad-band near-infrared photometry which has now been successfully used to discover galaxies at $z \simeq 6.5 - 8.5$ (e.g. McLure et al."
 2010: Oesch et al., 2010; Oesch et al.
 2010: Bouwens et al., 2010; Bouwens et al.
 2010a: Bunker et al., 2010a; Bunker et al.
 2010: Finkelstein et al., 2010; Finkelstein et al.
 2010: Vanzella et al., 2010; Vanzella et al.
 2011) can actually be used to establish the rest-frame continuum slopes of he highest redshift galaxies., 2011) can actually be used to establish the rest-frame continuum slopes of the highest redshift galaxies.
" Specifically. very young. metal-poor stellar populations are arguably expected to result in substantially pluer continuumslopes around À,,.;&1500À than have been detected to date in galaxies discovered at any lower redshift 2.«6.5 (e.g. Steidel et al."," Specifically, very young, metal-poor stellar populations are arguably expected to result in substantially bluer continuumslopes around $\lambda_{rest} \simeq 1500$ than have been detected to date in galaxies discovered at any lower redshift $z < 6.5$ (e.g. Steidel et al."
 1999: Meurer et al., 1999; Meurer et al.
 1999: Adelberger Steidel 2000: Ouchi et al., 1999; Adelberger Steidel 2000; Ouchi et al.
 2004: Stanway et al., 2004; Stanway et al.
 2005: Bouwens et al., 2005; Bouwens et al.
 2006: Hathi et al., 2006; Hathi et al.
 2008: Bouwens et al., 2008; Bouwens et al.
 2009: Erb et al., 2009; Erb et al.
 2010)., 2010).
 It has become the normal convention to parameterise the ultra-violet continuum slopes of galaxies in terms of a power-law index. 71. where fyxA (teg. Meurer et al.," It has become the normal convention to parameterise the ultra-violet continuum slopes of galaxies in terms of a power-law index, $\beta$, where $f_{\lambda} \propto
\lambda^{\beta}$ (e.g. Meurer et al."
 1999: thus. 7=2 corresponds to a source which has a flat spectrum in terms of fv. and hence has zero colour in the AB magnitude system).," 1999; thus, $\beta = -2$ corresponds to a source which has a flat spectrum in terms of $f_{\nu}$, and hence has zero colour in the AB magnitude system)."
 As discussed by several authors. while the bluest galaxies observed at 22:3 dthave 22 values as low (i.e. blue) as;=3 can in principle be produced by a young. low-metallicity stellar population (e.g. Bouwens et al.," As discussed by several authors, while the bluest galaxies observed at $z \simeq 3 - 4$ have $\beta \simeq -2$, values as low (i.e. blue) as $\beta = -3$ can in principle be produced by a young, low-metallicity stellar population (e.g. Bouwens et al."
 2010b: Schaerer 2002)., 2010b; Schaerer 2002).
 However. for this idealized prediction to actually be realized in practice. several conditions have to besatisfied simultaneously. namely i) the stellar population has to be very young (e.g. /.< 30MMyr for Zc10Z.. or!« 3MMvr for Z~10 7Z.). ii the starlight must obviously be completely free from any signiticant dust extinction. and iii) the starlight must also be significantly contaminated by (redder) nebular continuum (a condition which has important implications for UV photon escape fraction. and hence reionization — see. for example. Robertson et al.," However, for this idealized prediction to actually be realized in practice, several conditions have to besatisfied simultaneously, namely i) the stellar population has to be very young (e.g. $t < 30$ Myr for $Z \simeq 10^{-3}\,{\rm Z_{\odot}}$, or $t < 3$ Myr for $Z \simeq 10^{-2}\,{\rm Z_{\odot}}$ ), ii) the starlight must obviously be completely free from any significant dust extinction, and iii) the starlight must also be significantly contaminated by (redder) nebular continuum (a condition which has important implications for UV photon escape fraction, and hence reionization – see, for example, Robertson et al."
 2010)., 2010).
 For this reason. the recent report by Bouwens et al. (," For this reason, the recent report by Bouwens et al. ("
2010b) (supported to some extent by Finkelstein et al.,2010b) (supported to some extent by Finkelstein et al.
 2010) that the faintest galaxies detected at 2>>6.5 do indeed display an average value of 7)=3.00.2 is both exciting and arguably surprising enough to merit further detailed and independent investigation., 2010) that the faintest galaxies detected at $z > 6.5$ do indeed display an average value of $\langle \beta \rangle = -3.0 \pm 0.2$ is both exciting and arguably surprising enough to merit further detailed and independent investigation.
 This is especially the case because some authors are already beginning to assume that the existence of such extreme blue slopes is a robust result. already ripe for detailed theoretical interpretation (e.g. Taniguchi et al.," This is especially the case because some authors are already beginning to assume that the existence of such extreme blue slopes is a robust result, already ripe for detailed theoretical interpretation (e.g. Taniguchi et al."
 2010)., 2010).
 The aim of this paper is to carefully assess whether the currentHST WFC3 data do indeed provide clear evidence for such extremely blue slopes in faint galaxies at 2—7., The aim of this paper is to carefully assess whether the current WFC3 data do indeed provide clear evidence for such extremely blue slopes in faint galaxies at $z \simeq 7$.
 There are a number of potentially subtle biases which can affect the determination of UV continuum slopes from the WFC3/IR data. especially when. as is inevitably the case for the faintest objects. the results have to be based on the colours of galaxies whose individual 2 values have associated errors which can be as large as A—c1.5.," There are a number of potentially subtle biases which can affect the determination of UV continuum slopes from the WFC3/IR data, especially when, as is inevitably the case for the faintest objects, the results have to be based on the colours of galaxies whose individual $\beta$ values have associated errors which can be as large as $\Delta \beta \simeq \pm 1.5$."
 To check for. and attempt to quantify. the extent of any such biases we undertake two different approaches in this paper.," To check for, and attempt to quantify, the extent of any such biases we undertake two different approaches in this paper."
 First. we take advantage of the dynamic range offered by the available public WFC3/IR imaging to explore how derived values of 2 Gund average values (2322) depend on galaxy candidate robustness and signal:noise ratio as we approach the flux limit of a given survey.," First, we take advantage of the dynamic range offered by the available public WFC3/IR imaging to explore how derived values of $\beta$ (and average values $\langle \beta \rangle$ ) depend on galaxy candidate robustness and signal:noise ratio as we approach the flux limit of a given survey."
 Second. we undertake and analyse a set of fairly simple (but complete end-to-end) simulations to explore what apparent values of (and trends in) (2? would be deduced from the existing WFC3/IR data for different assumed input values of «7=—2.2.5.53 combined with realistic estimates of the faint-end slope of the 2=7 galaxy luminosity function.," Second, we undertake and analyse a set of fairly simple (but complete end-to-end) simulations to explore what apparent values of (and trends in) $\langle \beta \rangle$ would be deduced from the existing WFC3/IR data for different assumed input values of $\beta = -2, -2.5, -3$ combined with realistic estimates of the faint-end slope of the $z \simeq 7$ galaxy luminosity function."
 The layout of this paper is as follows., The layout of this paper is as follows.
 First. in Section 2 we briefly review how we have selected three new. high-redshift galaxy samples from the WFC3/IR+ACS+IRAC imaging of the Hubble Ultra Deep Field (HUDF). the HUDF Parallel Field 2 (HUDFO9-2j. and the Early Release Science imaging (ERS) of the northern portion of GOODS-South.," First, in Section 2 we briefly review how we have selected three new, high-redshift galaxy samples from the WFC3/IR+ACS+IRAC imaging of the Hubble Ultra Deep Field (HUDF), the HUDF Parallel Field 2 (HUDF09-2), and the Early Release Science imaging (ERS) of the northern portion of GOODS-South."
 The reduction of theAST data. the deconfusion of theSpizer TRAC data. and the extraction. analysis. classification and redshift estimation of the galaxies uncovered from this imaging are described in detail in MeLure et al. ," The reduction of the data, the deconfusion of the IRAC data, and the extraction, analysis, classification and redshift estimation of the galaxies uncovered from this imaging are described in detail in McLure et al. ("
2011). as this underpins the extraction of a new robust galaxy sample at 6<2«S87 which is the focus of the MeLure et al. (,"2011), as this underpins the extraction of a new robust galaxy sample at $6 < z < 8.7$ which is the focus of the McLure et al. ("
2011) study.,2011) study.
 In this study we retain not only the robust 2-6 sources detailed in MeLure et al. (, In this study we retain not only the robust $z > 6$ sources detailed in McLure et al. (
2011). but all galaxies from the larger parent sample with acceptable redshift solutions at 24.5. which are classified as either ROBUST or UNCLEAR.,"2011), but all galaxies from the larger parent sample with acceptable redshift solutions at $z > 4.5$, which are classified as either ROBUST or UNCLEAR."
 This allows us to explore trends in «ή over a reasonably wide range in redshift (5«z«tN and UVluminosity(. 22<Misig«LS) and also to explore potential biases introduced by the exclusion or inclusion of galaxies with less robust photometric redshifts.," This allows us to explore trends in $\beta$ over a reasonably wide range in redshift $5 < z < 8$ ) and UV luminosity $-22 < M_{UV,AB} < 18$ ), and also to explore potential biases introduced by the exclusion or inclusion of galaxies with less robust photometric redshifts."
 In Section 3 we explain how we determined the rest-frame UV continuum slope. «2. for the galaxies extracted from the different imaging datasets at different redshifts.," In Section 3 we explain how we determined the rest-frame UV continuum slope, $\beta$, for the galaxies extracted from the different imaging datasets at different redshifts."
 Then. in Section + we present and analyse our results. and demonstrate what level of data quality is actuallyrequired to achieve internally consistent results between the different galaxy samples uncovered from surveys of varying depths.," Then, in Section 4 we present and analyse our results, and demonstrate what level of data quality is actually to achieve internally consistent results between the different galaxy samples uncovered from surveys of varying depths."
 We move on to describe and analyse our simulations in Section 5 before discussing the implications of our findings in Section 6., We move on to describe and analyse our simulations in Section 5 before discussing the implications of our findings in Section 6.
 A summary of our conclusions is then presented in Section 7., A summary of our conclusions is then presented in Section 7.
" All magnitudes are quoted in the AB system (Oke Gunn 1983) and any cosmological calculations assume (3;=0.3. Oy—0.7. and ff,=τὸkms*\Ipei."," All magnitudes are quoted in the AB system (Oke Gunn 1983) and any cosmological calculations assume $\Omega_M = 0.3$, $\Omega_{\Lambda} = 0.7$, and $H_0 = 70\,{\rm kms^{-1}Mpc^{-1}}$."
 The candidate galaxies were all selected from our own reductions of the pubicly available near-infrared WFC3/IR imaging of the HUDF. ERS and HUDFO9-2? fields. as described in McLure et al. ," The candidate galaxies were all selected from our own reductions of the pubicly available near-infrared WFC3/IR imaging of the HUDF, ERS and HUDF09-2 fields, as described in McLure et al. ("
@OlL) Ove note that the HUDF WFC3/IR imaging is the same vear-l. 2009. imaging as utilised in MeLure et al.,"2011) (we note that the HUDF WFC3/IR imaging is the same year-1, 2009, imaging as utilised in McLure et al."
 2010)., 2010).
 In brief. candidate selection in all three fields was undertaken by first selecting sources with (Bertin Arnouts 1996) down to a deep signal:noise limit in each of the WFC3/IR YiosYoox. Jies and {του images. and then forming the superset of near-infrared selected sources by merging these catalogues.," In brief, candidate selection in all three fields was undertaken by first selecting sources with (Bertin Arnouts 1996) down to a deep signal:noise limit in each of the WFC3/IR $Y_{105}/Y_{098}$, $J_{125}$ and $H_{160}$ images, and then forming the superset of near-infrared selected sources by merging these catalogues."
 Then. as again detailed in MeLure et al. (," Then, as again detailed in McLure et al. ("
2011). photometric redshifts (with associated. probability distributions) were derived for all potential sources based on 0.6-aresee diameter flux-density measurements made on the available HS7 ACS optical imaging. the WFC3/IR imaging. and the Spifcer TRAC imaging (after deconfusion of the TRAC images based on the WFC3/IR {τω or {τος data).,"2011), photometric redshifts (with associated probability distributions) were derived for all potential sources based on 0.6-arcsec diameter flux-density measurements made on the available ACS optical imaging, the WFC3/IR imaging, and the IRAC imaging (after deconfusion of the IRAC images based on the WFC3/IR $H_{160}$ or $J_{125}$ data)."
 The samples were then culled to retain only sources with an acceptable solution at redshift 54.5 (ie. redshift solutions, The samples were then culled to retain only sources with an acceptable solution at redshift $z > 4.5$ (i.e. redshift solutions
Establishing a firm link between a galaxy’s morphology and its spectrum is advantageous for several reasons.,Establishing a firm link between a galaxy's morphology and its spectrum is advantageous for several reasons.
 For instance. galaxy spectra can be accurately determined to much greater redshifts and for fainter objects than morphologies.," For instance, galaxy spectra can be accurately determined to much greater redshifts and for fainter objects than morphologies."
 Also. most large redshift surveys currently taking place will contain many thousands of galaxy spectra but little information relating to the optical morphologies of those galaxies.," Also, most large redshift surveys currently taking place will contain many thousands of galaxy spectra but little information relating to the optical morphologies of those galaxies."
" In particular the separation of different morphological types of galaxies in these redshift surveys will be very useful as a means of separating objects for follow- observations to determine independent distance measurements using either D,—c or the Tully-Fisher relation.", In particular the separation of different morphological types of galaxies in these redshift surveys will be very useful as a means of separating objects for follow-up observations to determine independent distance measurements using either $D_n-\sigma$ or the Tully-Fisher relation.
 In this paper I have tried to quantify the link between galaxy spectra and morphology using several advanced statistical methods: namely. Fisher's linear discriminant and Artificial Neural Networks.," In this paper I have tried to quantify the link between galaxy spectra and morphology using several advanced statistical methods; namely, Fisher's linear discriminant and Artificial Neural Networks."
 The best results produced suggest that it is possible to use optical galaxy spectra to create galaxy samples containing of the Early type galaxies present and of the Late types respectively., The best results produced suggest that it is possible to use optical galaxy spectra to create galaxy samples containing of the Early type galaxies present and of the Late types respectively.
 The contamination between these samples depends on the morphological mix of the survey under consideration., The contamination between these samples depends on the morphological mix of the survey under consideration.
 In the case of the bj-selected 2?4FGRS the most significant contamination will be of mis-classified Late types in the Early type sample (~ contamination). in the case of a near-infrared selected sample this situation will be reversed.," In the case of the $\bj$ -selected 2dFGRS the most significant contamination will be of mis-classified Late types in the Early type sample $\sim40\%$ contamination), in the case of a near-infrared selected sample this situation will be reversed."
 Essentially the results obtained using more advanced statistical techniques (Sections 4 and 5) are comparable to those that could be obtained simply using the default 3HFGRS spectral classification η) (Madgwick 22002) which can be accessed from the 2UFGRSdatabase?., Essentially the results obtained using more advanced statistical techniques (Sections 4 and 5) are comparable to those that could be obtained simply using the default 2dFGRS spectral classification $\eta$ (Madgwick 2002) which can be accessed from the 2dFGRS.
. This is an interesting result and certainly adds significantly to the physical interpretation of this parameter., This is an interesting result and certainly adds significantly to the physical interpretation of this parameter.
 Another interesting aspect of this analysis is that the Fisher discriminant (Section 4) identified the bbreak to be the most essential element of a galaxy's spectrum for the purposes of estimating its morphology., Another interesting aspect of this analysis is that the Fisher discriminant (Section 4) identified the break to be the most essential element of a galaxy's spectrum for the purposes of estimating its morphology.
 This result is somewhat expected since the general correlation between galaxy morphology and colour is already well established., This result is somewhat expected since the general correlation between galaxy morphology and colour is already well established.
 However. it is intriguing to see this result derived in a quantitative manner from the observed spectra themselves.," However, it is intriguing to see this result derived in a quantitative manner from the observed spectra themselves."
 The results presented in this paper are essentially limited by the coarseness of the morphological classification adopted. which for practical reasons can only be divided into two separate types (rather than a more realistic sequence of types).," The results presented in this paper are essentially limited by the coarseness of the morphological classification adopted, which for practical reasons can only be divided into two separate types (rather than a more realistic sequence of types)."
 As larger samples of more accurately morphologically classitied galaxies become available it will be interesting to repeat the analysis presented here. in order to determine whether even more information can be recovered to link a galaxys morphology and spectrum.," As larger samples of more accurately morphologically classified galaxies become available it will be interesting to repeat the analysis presented here, in order to determine whether even more information can be recovered to link a galaxy's morphology and spectrum."
 I wish to thank Ofer Lahav for suggesting this project and providing plenty of invaluable advice and suggestions., I wish to thank Ofer Lahav for suggesting this project and providing plenty of invaluable advice and suggestions.
 Raven Kaldare and Andrew Firth were very helpful in explaining the intricacies of Artificial Neural Networks to me., Raven Kaldare and Andrew Firth were very helpful in explaining the intricacies of Artificial Neural Networks to me.
 I would also like to thank the anonymous referee for their helpful comments on the draft of this paper., I would also like to thank the anonymous referee for their helpful comments on the draft of this paper.
 The efforts of the 2dFGRS collaboration. in preparing and compiling the data used in this analysis. are greatly appreciated.," The efforts of the 2dFGRS collaboration, in preparing and compiling the data used in this analysis, are greatly appreciated."
 This work was supported by an Isaac Newton studentship from the Institute of Astronomy and Trinity College. Cambridge.," This work was supported by an Isaac Newton studentship from the Institute of Astronomy and Trinity College, Cambridge."
low-level of 5-rav. emission for this object which is stable over several vears and strongly constrains the blazar's VILE quicscent state (Aharonianetal.2010).. but whose origin is still unknown.,"low-level of $\gamma$ -ray emission for this object which is stable over several years and strongly constrains the blazar's VHE quiescent state \citep{prep}, but whose origin is still unknown."
 The low state of PINS 2155-304 (2= 0.116) has been studied recently in a multiwavelength campaign by HLIZS.S. and the LAT instrument. onboard Fermi (Abaronianοἱal. 2009).. with which the observations presented. here are simultaneous.," The low state of PKS 2155-304 $z = 0.116$ ) has been studied recently in a multiwavelength campaign by H.E.S.S. and the LAT instrument onboard Fermi \citep{b1c}, with which the observations presented here are simultaneous."
 The time-averaged SED of the source was moceled. as a single-zone svncehrotron-selt. Compton. (88C€) »ocess which fitted the entire profile., The time-averaged SED of the source was modeled as a single-zone synchrotron-self Compton (SSC) process which fitted the entire profile.
 Phe derived relations oetween the optical and VILE fluxes. suggest. that. the ormer provides the target photons for the inverse-C'ompton (1C) emission. but a detailed study of the energeties. of he model shows that a single-zone description cannot accommodate the entire multibanc temporal behaviour of he light-curve.," The derived relations between the optical and VHE fluxes suggest that the former provides the target photons for the inverse-Compton (IC) emission, but a detailed study of the energetics of the model shows that a single-zone description cannot accommodate the entire multiband temporal behaviour of the light-curve."
 Part of the aim of this paper is to exploit he contemporancity of our data to propose an explanation or the lack of temporal correlation observed between the optical and the high-encrey components of the SED. and o give further support to the proposal by Aharonianctal.(2009) that a multi-zone mocel is necessary to describe the cquiescent state emission of this DL Lac.," Part of the aim of this paper is to exploit the contemporaneity of our data to propose an explanation for the lack of temporal correlation observed between the optical and the high-energy components of the SED, and to give further support to the proposal by \cite{b1c} that a multi-zone model is necessary to describe the quiescent state emission of this BL Lac."
 PIS 2155-304 has been the target of several optical »obuimetrie campaigns which have probed its long aud short term behaviour., PKS 2155-304 has been the target of several optical polarimetric campaigns which have probed its long and short term behaviour.
 The polarisation degree is observed ο assume typical values between ~3-74.. with significant variability. registered. down to. sub-hour timescales (e.g. Aneruchowctal. 2005)).," The polarisation degree is observed to assume typical values between $\sim$, with significant variability registered down to sub-hour timescales (e.g. \citealt{micro}) )."
 The polarisation vector. shows evidence of preferential cürection within the range 100-140 (Tommasietaal.(2001). and references therein)., The polarisation vector shows evidence of a preferential direction within the range $^\circ$ \cite{tommasi} and references therein).
 Frequeney dependent polarisation (FDP) has also been detected. on several occasions (Smith&Sitko1991:Smithetal.1992:Allenetal.1993). ancl determined. to be intrinsic to the svnchrotron source.," Frequency dependent polarisation (FDP) has also been detected on several occasions \citep{b22a, b22c, allen} and determined to be intrinsic to the synchrotron source."
 In radio. the parsec-scale. jet. of. PINS 2155-304 was imaged twice at 15 €illz bv Piner&IEcwards(2004) and Pineretal.(2008).," In radio, the parsec-scale jet of PKS 2155-304 was imaged twice at 15 GHz by \cite{b20} and \cite{b21}."
. A single jet component is resolved downstream from the radio core. moving with a derived bulk Lorentz factor E 3.," A single jet component is resolved downstream from the radio core, moving with a derived bulk Lorentz factor $\Gamma \sim$ 3."
 Polarised radio Lux was detected in those images coming from the core component alone. and the polarisation vector (1317) was seen to be closely aligned with the jet-projectecl position angle (PLA.  10-1607).," Polarised radio flux was detected in those images coming from the core component alone, and the polarisation vector $131^\circ$ ) was seen to be closely aligned with the jet-projected position angle (P.A. $\sim$ $^\circ$ )."
 In the optically thin regime this is evidence [or the presence of a dominant. magnetic field. component transverse to the Dow., In the optically thin regime this is evidence for the presence of a dominant magnetic field component transverse to the flow.
 The polarisation degree of the core exhibited a spatial gracient. between that increased in the upstream direction., The polarisation degree of the core exhibited a spatial gradient between that increased in the upstream direction.
 The existence of a preferred. position angle in optical similar to that of the mme-wave core favours the presence of a dominant or large scale component with a regular magnetic ield which is associated with both emissions., The existence of a preferred position angle in optical similar to that of the mm-wave core favours the presence of a dominant or large scale component with a regular magnetic field which is associated with both emissions.
 Furthermore. similar values of the polarisation degree seen in both bands and. the lack of polarised emission [rom other parts of the jet in the VLBI images suggests the unresolved: polarised! optical emission originates in the pe-seale radio core.," Furthermore, similar values of the polarisation degree seen in both bands and the lack of polarised emission from other parts of the jet in the VLBI images suggests the unresolved polarised optical emission originates in the pc-scale radio core."
 “Phis ivpothesis will be adopted here. motivated as well by recent studies which usec VLBI maps to compare the optical »ó»Llarisation properties of the jet with the radio images. ancl associated the variable emission with the position of the 43 Gllz core (Lister 2006)..," This hypothesis will be adopted here, motivated as well by recent studies which used VLBI maps to compare the optical polarisation properties of the jet with the radio images, and associated the variable emission with the position of the 43 GHz core \citep{b15,
jorstad07, gabuzda}. ."
bv lower hybrid waves survive (bx equating the collisional equilibration rate with the wind expansion rale).,by lower hybrid waves survive (by equating the collisional equilibration rate with the wind expansion rate).
 Such densiües are only [ound at or bevond the radial position where ion charge states [reeze in. and so nonthermal electrons appear unlikely to produce a significant change (ο our charge state results. given the other current observational constraints.," Such densities are only found at or beyond the radial position where ion charge states freeze in, and so nonthermal electrons appear unlikely to produce a significant change to our charge state results, given the other current observational constraints."
 However lower hvbrid waves do appear to be a viable means for producing the electron distributions observed in the [ast solar wind., However lower hybrid waves do appear to be a viable means for producing the electron distributions observed in the fast solar wind.
 The determination that 5!=5;M;/wfq?(wfhv;yc0.5—1 is necessary to produce the observed charge states requires the existence of density gradients in the fast wind with scale lengths on the order of the a-particle gvroradius. which is about 0.1 km at 1.5 HR...," The determination that $\gamma ^{\prime}=
\gamma _iM_i/\omega Afq^2\left(\omega /kv_{iy}\right)^2\simeq 0.5-1$ is necessary to produce the observed charge states requires the existence of density gradients in the fast wind with scale lengths on the order of the $\alpha$ -particle gyroradius, which is about 0.1 km at 1.5 $R_{\sun}$."
 Badio scintillation observations demonstrating the existence of such size scales in the solar wind in the ecliptic plane have rather a long history (e.g.Coles&Harmon1939:Armstrong1990:Colesetal. 1991).," Radio scintillation observations demonstrating the existence of such size scales in the solar wind in the ecliptic plane have rather a long history \citep[e.g.][]{coles89,armstrong90,coles91}."
. These are found perpendicular to the magnetic field. with larger size scales (Uvpicallv a factor of LO within 6 A... becoming more isotropic al larger distances) inferred along the radial direction.," These are found perpendicular to the magnetic field, with larger size scales (typically a factor of 10 within 6 $R_{\sun}$, becoming more isotropic at larger distances) inferred along the radial direction."
 Colesοἱal.(1995) inferred. values of dn? in polar regions al solar mininmmn to be around 1/10 to 1/15 of that observed in equatorial regions. but due to a lack of knowledge of n. in polar regions. were unable to sav anvthing about the variation ol ón./n..," \citet{coles95}
 inferred values of $\delta n_e^2$ in polar regions at solar minimum to be around 1/10 to 1/15 of that observed in equatorial regions, but due to a lack of knowledge of $n_e$ in polar regions, were unable to say anything about the variation of $\delta n_e/n_e$."
" The density measurements reviewed in this paper indicate electron clensilies in polar regions a [actor of 1/2 to 1/3 of those in equatorial regions. making ο, in polar regions of similar order to. but still slightly smaller than that in equatorial regions."," The density measurements reviewed in this paper indicate electron densities in polar regions a factor of 1/2 to 1/3 of those in equatorial regions, making $\delta n_e/n_e$ in polar regions of similar order to, but still slightly smaller than that in equatorial regions."
" Absolute values of ón,./n. in coronal hole regions of interest here have been determined observalionally by Ofmanetal.(1997) to be from 0.1 (o a few times 0.1.", Absolute values of $\delta n_e/n_e$ in coronal hole regions of interest here have been determined observationally by \citet{ofman97} to be from 0.1 to a few times 0.1.
 This is smaller than the value ~1 tacitly assumed here. (he consequence of which is discussed further below.," This is smaller than the value $\sim 1$ tacitly assumed here, the consequence of which is discussed further below."
 Gralletal.(1997) present more data on the transition from anisotropy. inside 5-6 H. on scales of order 10 km to isotropy further out. concluding that à real change in the microstructure rather than in Alfvénn wave turbulence takes place. again with reference to (he eclipüe plane.," \citet{grall97} present more data on the transition from anisotropy inside 5-6 $R_{\sun}$ on scales of order 10 km to isotropy further out, concluding that a real change in the microstructure rather than in Alfvénn wave turbulence takes place, again with reference to the ecliptic plane."
" Feldmanetal.(1996) review these interplanetary scintillation observations together wilh Ulysses observations to constrain the high speed wind structure near ils coronal base. and argue that the plasma is ""sufficiently structured to relax through generation of a οκανε instability (hat results in electrostatic waves having A-vectors oriented perpendicular to BY. which is precisely the motivation for the current work."," \citet{feldman96} review these interplanetary scintillation observations together with Ulysses observations to constrain the high speed wind structure near its coronal base, and argue that the plasma is “sufficiently structured to relax through generation of a drift-wave instability that results in electrostatic waves having $k$ -vectors oriented perpendicular to B”, which is precisely the motivation for the current work."
" Grallοἱal.(1997). go further and show that within 6 A24. large scale turbulence is isotropic with a Ixolmogorov spectrum (structure function x scale""). while smaller scale turbulence shows anisotropy with higher structure functions (x scale) than Ixolmogorov turbulence would predict."," \citet{grall97}
 go further and show that within 6 $R_{\sun}$ large scale turbulence is isotropic with a Kolmogorov spectrum (structure function $\propto {\rm scale}^{5/3}$ ), while smaller scale turbulence shows anisotropy with higher structure functions $\propto $ scale) than Kolmogorov turbulence would predict."
 The scale at which, The scale at which
As far as infrared. data is available. 10/11 variable sources show evidence for the presence of a cireumstellar disk.,"As far as infrared data is available, 10/11 variable sources show evidence for the presence of a circumstellar disk."
 Since the disk fractions in the samples are high. this does not imply a statistically significant connection between variability and disk. but it gives several options to explain the nature of the variabilitv.," Since the disk fractions in the samples are high, this does not imply a statistically significant connection between variability and disk, but it gives several options to explain the nature of the variability."
 Without. disks. only two options remain. eclipses by a companion and chromospheric Πάνος.," Without disks, only two options remain, eclipses by a companion and chromospheric flares."
 Both are relatively short events on timescales of hours ancl thus unlikely to be detected: with only two epochs., Both are relatively short events on timescales of hours and thus unlikely to be detected with only two epochs.
 With an accretion disk. additional. explanations become viable: a) variations in the hot spots generated by an accretion shock. b) variable circumstellar extinction. c) variable emission [rom a cust disk. d) eclipses bv optically thick cireumstellar material (2)..," With an accretion disk, additional explanations become viable: a) variations in the hot spots generated by an accretion shock, b) variable circumstellar extinction, c) variable emission from a dusty disk, d) eclipses by optically thick circumstellar material \citep{2001AJ....121.3160C}."
 With two epochs it is not possible to unambiguously decide between these options. however. the colour of the variabilitv gives ao first hint.," With two epochs it is not possible to unambiguously decide between these options, however, the colour of the variability gives a first hint."
 Lot spots ancl extinction cause decreasing amplitudes: towards longer wavelengths. ie. αν<dJ or αν«dif.," Hot spots and extinction cause decreasing amplitudes towards longer wavelengths, i.e. $dK < dJ$ or $dK< dH$."
 The reverse is the case for variable clisk emission., The reverse is the case for variable disk emission.
 Eclipses would cause grey absorption. i.c. similar amplitudes in dilferent. bands.," Eclipses would cause grey absorption, i.e. similar amplitudes in different bands."
 As seen in Table 1.. 5/13 clearly fall in the first category. 2/13 in the second. and 6/13 in the third.," As seen in Table \ref{var}, 5/13 clearly fall in the first category, 2/13 in the second, and 6/13 in the third."
 With reddening laws for standard. dust properties. variable extinction. causes J-band. amplitudes that are 1.5 times larger than in H-band and 2.5 times larger than in the Ix-band (2)... ," With reddening laws for standard dust properties, variable extinction causes J-band amplitudes that are 1.5 times larger than in H-band and 2.5 times larger than in the K-band \citep{2009MNRAS.398..873S}. ."
3 objects from Table 1. fit these requirements (ISO-Oph-21. I5O-Oph-65. NMDBOJ6).," 3 objects from Table \ref{var} fit these requirements (ISO-Oph-21, ISO-Oph-65, MBO46)."
 The other two with decreasing amplitude towards longer wavelength are better explained. by variable hot spots. which causes less colour variations than extinction.," The other two with decreasing amplitude towards longer wavelength are better explained by variable hot spots, which causes less colour variations than extinction."
 For a delinite decision about the nature of. the variability. follow-up spectroscopy and further multi-baand monitoring is required.," For a definite decision about the nature of the variability, follow-up spectroscopy and further multi-band monitoring is required."
 As noted in Sect. 3..," As noted in Sect. \ref{s2},"
 the current sample might still be allectecd by erowcding. companions or other problems with the photometry.," the current sample might still be affected by crowding, companions or other problems with the photometry."
 Particularly the 6 objects with almost equal amplitudes in several bands seem highly interesting for follow-up. as they might contain equivalents to INKII5D (7). which could give detailed insights into the structure of the disk.," Particularly the 6 objects with almost equal amplitudes in several bands seem highly interesting for follow-up, as they might contain equivalents to KH15D \citep{2002PASP..114.1167H} which could give detailed insights into the structure of the disk."
 One other possible application for the results presented. in this paper is to derive constraints for scenarios of “cpisoclic accretion. Le. the hypothesis that a laree fraction of the stellar mass is accreted in short episodic bursts of accretion.," One other possible application for the results presented in this paper is to derive constraints for scenarios of 'episodic accretion', i.e. the hypothesis that a large fraction of the stellar mass is accreted in short episodic bursts of accretion."
 Episodic aceretion might be the explanation for the dramatic outbursts in FU Ori-type objects. and it could. also resolve the problem of the underluminosity of protostars (e.g.2)..," Episodic accretion might be the explanation for the dramatic outbursts in FU Ori-type objects, and it could also resolve the problem of the underluminosity of protostars \citep[e.g.][]{1996ARA&A..34..207H}."
 Based on Spitzer photometry. ? find that half the mass of LT ‘Tauri stars is accreted in only of the Class L lifetime. which is 0.5 MMvr.," Based on Spitzer photometry, \citet{2009ApJS..181..321E} find that half the mass of T Tauri stars is accreted in only of the Class I lifetime, which is $\sim 0.5$ Myr."
" Fhis implies that episodes with strong accretion of >10.7AZ. vr.to which last in total a few 107 vs are interspersed. with significantly longer quiescent phases with much lower accretion rates (<10""AZ. vr.+)."," This implies that episodes with strong accretion of $>10^{-5}\,M_{\odot}$ $^{-1}$ which last in total a few $10^5$ ys are interspersed with significantly longer quiescent phases with much lower accretion rates $<10^{-6}\,M_{\odot}$ $^{-1}$ )."
 ‘These numbers are supported bv the available submim data from embedded: protostars (7)., These numbers are supported by the available submm data from embedded protostars \citep{2009ApJ...692..973E}.
 There is strong interest in episodic accretion [roni jeoretical work on star and planet formation., There is strong interest in episodic accretion from theoretical work on star and planet formation.
 Numerical simulations of the gravitational cloud collapse (22). actually owediet/ episodic accretion to occur. with duty evcles ii are consistent with the current constraints by the bservations (e.g.. of protostars with accretion rates > ve1 ).," Numerical simulations of the gravitational cloud collapse \citep{2006ApJ...650..956V,2009ApJ...704..715V} actually predict episodic accretion to occur, with duty cycles that are consistent with the current constraints by the observations (e.g., of protostars with accretion rates $>10^{-5}\,M_{\odot}$ $^{-1}$ )."
 Models of ⋅⋠⋠episodic accretion. can reproduce 16 observed. luminosity spread. in LR diagrams. with uiescent phases of 107 to 10? ver (?)..," Models of episodic accretion can reproduce the observed luminosity spread in HR diagrams, with quiescent phases of $10^3$ to $10^4$ yr \citep{2009ApJ...702L..27B}."
 Phese Tull? allow for 1¢ formation of low-mass stars. brown cdwarls. and planets via disk fragmentation. and their curation may be critical or the frequency of these objects (?)..," These 'lulls' allow for the formation of low-mass stars, brown dwarfs, and planets via disk fragmentation, and their duration may be critical for the frequency of these objects \citep{2011ApJ...730...32S}."
 Episodic aceretion causes variability on very. long imescales of hundreds. of vears or more., Episodic accretion causes variability on very long timescales of hundreds of years or more.
 One wav of improving the constraint on the aforementioned. models is hus to monitor the brightness of large samples of accreting YSOs over long time windows. to identify possible outbursts and derive their frequency.," One way of improving the constraint on the aforementioned models is thus to monitor the brightness of large samples of accreting YSOs over long time windows, to identify possible outbursts and derive their frequency."
 Ehe increase in accretion rate should. be approximately proportional to the increase in bolometric luminosity. if the gravitational energv. of the accreted material is fully converted to radiation.," The increase in accretion rate should be approximately proportional to the increase in bolometric luminosity, if the gravitational energy of the accreted material is fully converted to radiation."
 Lt is dillicult to assess the effect of an accretion burst on the near-infrared) magnitudes ancl colours. without knowing the spectral energy. clistribution of theaccretion shockfront and the effects of increased. aceretion on the heating aud," It is difficult to assess the effect of an accretion burst on the near-infrared magnitudes and colours, without knowing the spectral energy distribution of theaccretion shockfront and the effects of increased accretion on the heating and"
"Then the force-free condition (43)) reads From this we find that and One can see that the spacial part of 7. which we will denote as J!=JT|UD. has the following components parallel and perpendicularto 2! The coellicient 77D, in Eq.760 can be expressed in terms of the electric and magnetic fields ancl their derivatives. making this equation an explicit) expression for ","Then the force-free condition \ref{FFC}) ) reads From this we find that and One can see that the spacial part of $I^\mu$, which we will denote as ${\cal J}^\mu={\cal J}^\mu_\parallel+ {\cal J}^\mu_\perp $, has the following components parallel and perpendicularto $B^\mu$ The coefficient $I^\nu B_\nu$ in \ref{Jpa} can be expressed in terms of the electric and magnetic fields and their derivatives, making this equation an explicit expression for ${\cal J}^\mu_\parallel$."
"Following Mcelxinney(2006) we first contract the Alaxwell-AmpeérreJy. law (8)) with D"" to find that where the comma indicates partial derivative.", Following \citet{M06} we first contract the Maxwell-Ampérre law \ref{Maxw2}) ) with $B^\mu$ to find that where the comma indicates partial derivative.
" Phen we contract the Maxwell-Faraday equation (7)) with D, to find that ‘Thus. where the semi-colon stands for covariant dillerentiation."," Then we contract the Maxwell-Faraday equation \ref{Maxw1}) ) with $D_\nu$ to find that Thus, where the semi-colon stands for covariant differentiation."
" The corresponding expression in Mcelxinney(2006) is a little bit cüllerent because it includes the term 2°D(nas,|nui). which equals to zero."," The corresponding expression in \citet{M06} is a little bit different because it includes the term $ B^\alpha D^\beta(n_{\beta;\alpha}+n_{\alpha;\beta})$, which equals to zero."
 Collecting all the results. we obtain lt is easy to verify that in the 311 notation I2q.NI is identical to τος. which does not include neither the lapse function nor the shift vector. nor the time derivatives of B and D.," Collecting all the results, we obtain It is easy to verify that in the 3+1 notation \ref{J} is identical to \ref{j}, which does not include neither the lapse function nor the shift vector, nor the time derivatives of $\bB$ and $\bD$ ."
 lt is a pleasure to thank Maximi Lyutikoy and. Jonathan Alclxinney for stimulating discussions., It is a pleasure to thank Maxim Lyutikov and Jonathan McKinney for stimulating discussions.
spatial extent. (~630 kpc) the LS diameter feld for the more distant. NGC 1399 is spatially equivalent to the 27-ciameter AIST field.,spatial extent $\sim\!630 \; \mbox{kpc}$ ) – the $1.8^\circ$ -diameter field for the more distant NGC 1399 is spatially equivalent to the $2^\circ$ -diameter M87 field.
" Within the magnitude range Mp,<10.5 we estimate. by adjusting for completeness ancl using Poisson statistics for uncertainty estimation. that AIST has 25+48 luminous CSSs. or half the number (47+ 12) estimated. for NGC 1399."," Within the magnitude range $M_{b_J}<-10.5$ we estimate, by adjusting for completeness and using Poisson statistics for uncertainty estimation, that M87 has $25\pm8$ luminous CSSs, or half the number $47\pm12$ ) estimated for NGC 1399."
" ""his finding contrasts sharply with the relative size of the innermost GC populations. usually expressed. as the Iuminositv-scaled specific [requencey Sx? (seereviewby ?).. "," This finding contrasts sharply with the relative size of the innermost GC populations, usually expressed as the luminosity-scaled specific frequency $S_N$ \citep[see review by][]{Elmegreen..1999}. ."
Dased on observations within 7aremin of AIST and NCC 1399. 7? caleulated Sy of G41 and 3.7+0.8. galaxy luminosities of V=8.54+0.01 and V=9.02+0.06. ancl total GC populations of 4700=400 and 2300300 respectively.," Based on observations within $7 \; \mbox{arcmin}$ of M87 and NGC 1399, \citet{Forte..2002} calculated $S_N$ of $6\pm1$ and $3.7\pm0.8$, galaxy luminosities of $V=8.54\pm0.01$ and $V=9.02\pm0.06$, and total GC populations of $4700\pm400$ and $2300\pm300$ respectively."
 LU luminous CSSs are simply an extension of the central giant clliptical galaxy GC population. we would expect the Virgo cluster core to have a luminous CSS population 4 times ereater than we have estimated. from. our redshift surveys.," If luminous CSSs are simply an extension of the central giant elliptical galaxy GC population, we would expect the Virgo cluster core to have a luminous CSS population $\sim4$ times greater than we have estimated from our redshift surveys."
 Even though the Sv estimates are not redshift confirmed we consider they are likely to be accurate within a factor of ~2. so our contrary estimates for the luminous CSS populations may be due either to a real dillerence with the GC populations or to uncertainties inpopulation estimates," Even though the $S_N$ estimates are not redshift confirmed we consider they are likely to be accurate within a factor of $\sim\!2$, so our contrary estimates for the luminous CSS populations may be due either to a real difference with the GC populations or to uncertainties inpopulation estimates"
1981).,.
 lt was known onlv as a y-ray source unül a promising candidate was detected in N-ravs by the Einstein Observatory (Dignami.Caraveo.&Lamb1933).. and associated with an optical counterpart (Dignamietal.1987:Halpern&Tytler1938:1983).," It was known only as a $\gamma$ -ray source until a promising candidate was detected in X-rays by the Einstein Observatory \citep{bi83}, and associated with an optical counterpart \citep{bi87,ht88,bi88}."
. Subsequently. Geminga was found to be a rotation-powered pulsar will a period of 237 ms in N-ravs by citephh92.. and in s-ravs by the Energetic Ganuna hay Experiment Telescope (EGRET) on theObservatory (Bertchetal.1992).," Subsequently, Geminga was found to be a rotation-powered pulsar with a period of 237 ms in X-rays by \\citep{hh92}, and in $\gamma$ -rays by the Energetic Gamma Ray Experiment Telescope (EGRET) on the \citep{be92}."
. Prior to the discovery of the 237 ms spin period of Genminga. claims had been made lor various periods in (he range 5960 s in 5-ravs and in N-ravs (Thompsonetal.1977:MasnouLOTT:Zvskin&Abukanov1983;Bienami.Caraveo.&Paul1984:Zvskin1988:lxaulοἱal. 1985)... but no such detections have been mace in hieh quality A-rayv and οταν observations during the past decade.," Prior to the discovery of the 237 ms spin period of Geminga, claims had been made for various periods in the range 59–60 s in $\gamma$ -rays and in X-rays \citep{th77,ma77,zm83,bi84,zy88,ka85}, but no such detections have been made in high quality X-ray and $\gamma$ -ray observations during the past decade."
 The optical spectrum of Genmünga is predominantly non-thermal. with possible ion ev¢lotvon features (Martin.Halpern.&Sehimninovich1998:Mignanm.Caraveo.Dienami 1993).," The optical spectrum of Geminga is predominantly non-thermal, with possible ion cyclotron features \citep{mhs98,mcb98}."
. Sheareretal.(1998) reported optical modulation from Genminga that resembles ils 5-rav light curve.," \cite{sh98}
 reported optical modulation from Geminga that resembles its $\gamma$ -ray light curve."
 Geminga is unusual as a rotation-powered pulsar because il is not a strong radio source., Geminga is unusual as a rotation-powered pulsar because it is not a strong radio source.
 In 1997. three groups (Malofeev&Malov1997;IxuzminLosovskii1997:Shitov&Pugachev1997) claimed detection of pulsed radio emission at 102 MIIz. but observations at other radio [requencies have so [ar been negative (Ramachandran.Lazio 1999)..," In 1997, three groups \citep{mm97,kl97,sp97} claimed detection of pulsed radio emission at 102 MHz, but observations at other radio frequencies have so far been negative \citep{rdi98,mcl99,bfb99,kl99}."
 A phase-connected ephemeris covering the first 27 vears of 5-ray observations of Geminga was presented and updated by Mattox. Halpern. Caraveo (1998. 2000).," A phase-connected ephemeris covering the first 27 years of $\gamma$ -ray observations of Geminga was presented and updated by Mattox, Halpern, Caraveo (1998, 2000)."
 In this paper we present the results of a long observation with the CASCA). which allows us to better constrain the hard X-ray spectrum of Geminga and perform pulse-phase spectroscopy.," In this paper we present the results of a long observation with the ), which allows us to better constrain the hard X-ray spectrum of Geminga and perform pulse-phase spectroscopy."
 X-ray. pulse (mes of arrival are compared with the latest ephemeris from EGRET., X-ray pulse times of arrival are compared with the latest ephemeris from EGRET.
" Additional constraints on the hard X-ray enussion are derived from an observation by (theExplorer Proportional Counter Arrav PCA),", Additional constraints on the hard X-ray emission are derived from an observation by the Proportional Counter Array PCA).
 A log of the observations used in this paper is given in Table 1.., A log of the observations used in this paper is given in Table \ref{tbl-1}.
 A six-day observation ol Geminga was obtained by iin 1999 October 511., A six-day observation of Geminga was obtained by in 1999 October 5–11.
 Observations by were made in 1996 April and May., Observations by were made in 1996 April and May.
 EGRET made many 5-rayv. observations of Geminga since 1991. until CGRO was de-orbited in 2000.," EGRET made many $\gamma$ -ray observations of Geminga since 1991, until was de-orbited in 2000."
(see.e.g..Milosavljevié&Nakar2006:Katzetal.2007).. in which case our analysis should be interpreted as applying to the highest energy accelerated particles. and to the magnetic field component. with its own characteristic correlation length Ager. that has the greatest influence on the dynamics of these particles.,"\citep[see, e.g.,][]{Milosavljevic:06,Katz:07}, in which case our analysis should be interpreted as applying to the highest energy accelerated particles, and to the magnetic field component, with its own characteristic correlation length $\lambda_{\rm def}$, that has the greatest influence on the dynamics of these particles."
 We also assume that the blastwave propagates into à quasi-homogeneous medium with average density p—yn., We also assume that the blastwave propagates into a quasi-homogeneous medium with average density $\bar \rho\sim m_{\rm p} n$.
 The highest energy protons can reach the farthest from the shock to a distance Asa)~RSI. where R is the radius of the blastwave. and the factor of one eighth is peculiar to adiabatie spherical ultrarelativistic blastwaves propagating into uniform density media (Blandford&McKee1976).," The highest energy protons can reach the farthest from the shock to a distance $\Delta_p(\gamma_{p,{\rm max}})\sim R/8\Gamma^2$, where $R$ is the radius of the blastwave, and the factor of one eighth is peculiar to adiabatic spherical ultrarelativistic blastwaves propagating into uniform density media \citep{Blandford:76}."
". Let LU’), denote the energy density in radiation at radius AR in the shock frame which is a fraction equ(απ)/Ew of the total isotropic equivalent energy of the blastwave £j.", Let $U_{\rm sh}$ denote the energy density in radiation at radius $R$ in the shock frame which is a fraction $\epsilon_{\rm rad}=(4\pi/3) R^3 U_{\rm sh}/E_{\rm tot}$ of the total isotropic equivalent energy of the blastwave $E_{\rm tot}$.
" Equating the inverse Compton power io,ecUn. where sesh~efT Is the electron Lorentz factor in the shock frame. σι is the Thompson cross section. and we neglected the Klein-Nishina effects (e.g..Li&Waxman2006).. to the energy gain ~Μος per DSA cycle of duration ~Ac/eDA,/c. we obtain the maximum Lorentz factor to which electrons can be accelerated. in spite of the cooling. as a function of the Lorentz factor to which the non-cooling protons can be accelerated . LIC.(1) which. as usual. is expressed in the rest frame of the shock upstream."," Equating the inverse Compton power $\frac{4}{3} \sigma_{\rm T} c \gamma_{e,{\rm sh}}^2 U_{\rm sh}$, where $\gamma_{e,{\rm sh}}\sim \gamma_e/\Gamma$ is the electron Lorentz factor in the shock frame, $\sigma_{\rm T}$ is the Thompson cross section, and we neglected the Klein-Nishina effects \citep[e.g.,][]{Li:06}, to the energy gain $\sim \gamma_{e,{\rm sh}} m_e c^2$ per DSA cycle of duration $\sim \Delta_{e,{\rm sh}}/c \sim \Gamma\Delta_e/c$, we obtain the maximum Lorentz factor to which electrons can be accelerated, in spite of the cooling, as a function of the Lorentz factor to which the non-cooling protons can be accelerated , , which, as usual, is expressed in the rest frame of the shock upstream."
 Here. we have eliminated the blastwave radius R via the relation R2CITE /88T7pc)? applicable to an adiabatic spherical blastwaves propagating into uniform density media (Blandford&McKee1976).," Here, we have eliminated the blastwave radius $R$ via the relation $R=(17 E_{\rm tot}/8\pi\Gamma^2 \bar\rho c^2)^{1/3}$ applicable to an adiabatic spherical blastwaves propagating into uniform density media \citep{Blandford:76}."
. The magnetic field length scale Ager (in the case of a tangled field) and strength squared do not appear in equation (1)) because they have been Biaexpressed in terms of the maximum proton Lorentz factor that can be accelerated by deflection in a field with these properties via By=[έςπρο”e)/T?|/CR/8T*) (coherent field) and Naotπμο87) (tangled field).," The magnetic field length scale $\lambda_{\rm def}$ (in the case of a tangled field) and strength squared $B_{\rm def}^2$ do not appear in equation \ref{eq:gamma_e_max}) ) because they have been expressed in terms of the maximum proton Lorentz factor that can be accelerated by deflection in a field with these properties via $B_{\rm def} =[(\gamma_{p,{\rm max}} m_p c^2 /e)/\Gamma^3]/(R/8\Gamma^2)$ (coherent field) and $\lambda_{\rm def} B_{\rm def}^2 =[(\gamma_{p,{\rm max}} m_p c^2 /e)^2/\Gamma^4]/(R/8\Gamma^2)$ (tangled field)."
 The nondimensional distance from the shock that the most energetic electrons can reach. relative to the distance that the protons can reach. can be expressed as (," The nondimensional distance from the shock that the most energetic electrons can reach, relative to the distance that the protons can reach, can be expressed as ."
"3) For typicalc values of ej4. Tmaxag£i. D. PEtand ‘iyη. thisoy becomes μα... which shows that for ~p.nax»109. regardless of the magnetic field geometry. the electrons are unable to travel as far from the shock as the protons and xo,«I in either case."," For typical values of $\epsilon_{\rm rad}$, $E_{\rm tot}$, $\Gamma$, and $n$, this becomes which shows that for $\gamma_{p,{\rm max}}\gg 10^3$, regardless of the magnetic field geometry, the electrons are unable to travel as far from the shock as the protons and $x_{\rm cool}\ll 1$ in either case."
 Note that for a coherent confining field STA 40 IT Πεἰά).. implying(GE? that(Gee if the confinement is dominated(7) by a pre- Microgauss upstream magnetic field we expect that v10°—105. while a larger value is expected if the shockpanas precursor generates a magnetic field in which the tangled component dominates particle deflection.," Note that for a coherent confining field 7 10^5 ) , implying that if the confinement is dominated by a pre-existing microgauss upstream magnetic field we expect that $\gamma_{p,{\rm max}} \sim 10^5-10^6$ , while a larger value is expected if the shock precursor generates a magnetic field in which the tangled component dominates particle deflection."
 Therefore we always expect that xo;«I., Therefore we always expect that $x_{\rm cool}\ll 1$.
 In what follows. we ignore the interior region A«A.Ceanay) populated by nonthermal particles of either sign and assume that the exterior region A>Ao contains only nonthermal ions. which we have assumed to be protons.," In what follows, we ignore the interior region $\Delta < \Delta_e(\gamma_{e,{\rm max}})$ populated by nonthermal particles of either sign and assume that the exterior region $\Delta > \Delta_e(\gamma_{e,{\rm max}})$ contains only nonthermal ions, which we have assumed to be protons."
 The nonthermal particle concentration at a given distance ahead of the shock will be dominated by the lowest energy particles that reach that distance., The nonthermal particle concentration at a given distance ahead of the shock will be dominated by the lowest energy particles that reach that distance.
" Thus. we can relate the nonthermal proton density 7, in the shock upstream to their energy distribution Nap)8) where Δημtup(5) 1s: the total number ofc nonthermal protons inη the shock upstream with Lorentz factors less than >."," Thus, we can relate the nonthermal proton density $n_{\rm ntp}$ in the shock upstream to their energy distribution ), where $N^{({\rm up})}_{\rm ntp}(\gamma)$ is the total number of nonthermal protons in the shock upstream with Lorentz factors less than $\gamma$ ."
 We assume that the accelerated particle spectrum in the shock downstream resulting from DSA contains equal energy on all energy scales. dNaariel)/dx57= (Lemoine:&Pel-letier2003:Ellison&Double2002.2004.cf. e.g.) this assumption is not critical as somewhat steeper spectra. expected when particle scattering in the shock downstream is not isotropic (e.g..Keshet&Waxman2005:Lemoine&Revenu 2006).. lead to similar conclusions.," We assume that the accelerated particle spectrum in the shock downstream resulting from DSA contains equal energy on all energy scales, $dN_{\rm ntp}^{({\rm down})}/d\gamma \propto \gamma^{-2}$ \citep[cf. e.g.,]{Lemoine:03,Ellison:02,Ellison:04}; this assumption is not critical as somewhat steeper spectra, expected when particle scattering in the shock downstream is not isotropic \citep[e.g.,][]{Keshet:05,Lemoine:06a}, lead to similar conclusions."
" Ignoring the energy in nonthermal protons located in the upstream. we may normalize the spectrum by requiring that ↷↴⋯∕↗∠⋅−↙⊽∕⊓⋯∠∣↷↴⋮←↽⋯∊⇂↭⇂∙≺⊖⋟ where ey, i5 the fraction of the total energy in the accelerated protons."," Ignoring the energy in nonthermal protons located in the upstream, we may normalize the spectrum by requiring that m_p c^2 =, where $\epsilon_{\rm nt}$ is the fraction of the total energy in the accelerated protons."
 The minimum Lorentz factor of the nonthermal particles. resulting from a single scattering across the shock is paninvI? (Gallant&Achterberg1999).. but the dependence ON >panin IS only logarithmic.," The minimum Lorentz factor of the nonthermal particles, resulting from a single scattering across the shock is $\gamma_{p,{\rm min}} \sim \Gamma^2$ \citep{Gallant:99}, but the dependence on $\gamma_{p,\rm min}$ is only logarithmic."
 To relate Nd to Nae”. let P~1 denote the probability that a particle in the shock upstream. upon returning to the shock. is scattered again into the shock upstream.," To relate $N^{({\rm up})}_{\rm ntp}$ to $N^{({\rm down})}_{\rm ntp}$, let $P\sim \frac{1}{2}$ denote the probability that a particle in the shock upstream, upon returning to the shock, is scattered again into the shock upstream."
 The downstreamthen contains theparticles that are not re- into the upstream. but areentrapped within and are advecting with the downstream.," The downstreamthen contains theparticles that are not re-scattered into the upstream, but areentrapped within and are advecting with the downstream."
 Conservation of nonthermal proton flux at the shock transitionthen, Conservation of nonthermal proton flux at the shock transitionthen
for the residuals and the whole procedure was repeated until no feature exceeding ANOVA value of 15 appeared.,for the residuals and the whole procedure was repeated until no feature exceeding ANOVA value of 15 appeared.
 Both methods yielded the same results within. statistical errors., Both methods yielded the same results within statistical errors.
 The only discrepancies appeared when a true frequency and its alias had similar amplitudes and the first method preferred one peak while the second method preferred the other., The only discrepancies appeared when a true frequency and its alias had similar amplitudes and the first method preferred one peak while the second method preferred the other.
 In such a cases we chose the frequency. which vielded a fit with lower c.," In such a cases we chose the frequency, which yielded a fit with lower $\sigma$."
 In the course of our analysis we identified many RR Lyr variables with secondary periodicities close to the primary (radial) pulsation frequency., In the course of our analysis we identified many RR Lyr variables with secondary periodicities close to the primary (radial) pulsation frequency.
 These objects. commonly referred to as Blazhko RR Lyr stars. are discussed elsewhere (Moskalik Olech 2008: 2009).," These objects, commonly referred to as Blazhko RR Lyr stars, are discussed elsewhere (Moskalik Olech 2008; 2009)."
 In six of the RRe variables we detected multiperiodicity of a different kind — a secondary mode appeared at a frequency much higher than the primary one., In six of the $c$ variables we detected multiperiodicity of a different kind – a secondary mode appeared at a frequency much higher than the primary one.
 These stars are listed in Table I., These stars are listed in Table 1.
 The most interesting case is variable VIO., The most interesting case is variable V10.
 Its primary period of δι=0.3749759 day and its light curve are typical for RRe pulsator., Its primary period of $P_1=0.3749759$ day and its light curve are typical for $c$ pulsator.
 Prewhitening led to discovery of the second frequency. corresponding to the period of P»=0.299176 day.," Prewhitening led to discovery of the second frequency, corresponding to the period of $P_2=0.299176$ day."
 The resulting period ratio of P2/P)=0.79785 is characteristic for simultaneous pulsation in the first and second overtone (FO/SO double mode variable)., The resulting period ratio of $P_2/P_1=0.79785$ is characteristic for simultaneous pulsation in the first and second overtone (FO/SO double mode variable).
 The light curve of VIO. its Fourier power spectrum and power spectrum of the prewitened light curve are shown in 1.," The light curve of V10, its Fourier power spectrum and power spectrum of the prewitened light curve are shown in 1."
 Both £ and the combination peak fj+f» ale clearly visible., Both $f_2$ and the combination peak $f_1+f_2$ ale clearly visible.
 We note. that the spectral window is not very good and it is possible that the true secondary frequency is at the 1-day alias of the highest peak.," We note, that the spectral window is not very good and it is possible that the true secondary frequency is at the 1-day alias of the highest peak."
" If this is the case. then P»= day. giving period ratio of P2/P,=0.61371."," If this is the case, then $P_2 =
0.230126$ day, giving period ratio of $P_2/P_1=0.61371$."
 This solutionis listed in the second line of Table 1., This solution is listed in the second line of Table 1.
 It yields higher dispersion of the least-square fit. but it cannot be definitely excluded.," It yields higher dispersion of the least-square fit, but it cannot be definitely excluded."
 Nevertheless. the most likely period ratio in VIO is ~0.80. which makes this star a strong candidate to be the first FO/SO double mode pulsator among RR Lyr variables.," Nevertheless, the most likely period ratio in V10 is $\sim\! 0.80$, which makes this star a strong candidate to be the first FO/SO double mode pulsator among RR Lyr variables."
 We found five more double mode pulsators with high frequency secondary modes., We found five more double mode pulsators with high frequency secondary modes.
 Their properties are summarized also in Table |., Their properties are summarized also in Table 1.
 In 2 we display light curves. original power spectra and power spectra of prewitened light curves of these stars.," In 2 we display light curves, original power spectra and power spectra of prewitened light curves of these stars."
 Judging from shapes of their light curves. there 1s no doubt that in all five stars the primary frequency corresponds to the first overtone.," Judging from shapes of their light curves, there is no doubt that in all five stars the primary frequency corresponds to the first overtone."
 There is also no doubt that secondary frequencies are real., There is also no doubt that secondary frequencies are real.
 The first three star. V350. V8] and V87. are similar to VIO: they display the period ratios of either ~0.80 or ~0.61. depending on the choice of an alias.," The first three star, V350, V81 and V87, are similar to V10: they display the period ratios of either $\sim\! 0.80$ or $\sim\! 0.61$, depending on the choice of an alias."
 This time. selecting the true alias is not possible. however. because both choices lead to least-square fits of the same quality.," This time, selecting the true alias is not possible, however, because both choices lead to least-square fits of the same quality."
 We were initially tempted to reject the period ratio of ~0.61 as unphysical., We were initially tempted to reject the period ratio of $\sim\! 0.61$ as unphysical.
 As it turned out. this would be unjustified.," As it turned out, this would be unjustified."
 The most surprising result was found for the other two double mode pulsators. V105 and V19.," The most surprising result was found for the other two double mode pulsators, V105 and V19."
 For these two variables, For these two variables
11998).,1998).
 These color features will be explored in a later paper., These color features will be explored in a later paper.
 This dataset is also sufficiently high in S/N to allow us to compare the color of individual pixels with the pixel's surface brightness., This dataset is also sufficiently high in S/N to allow us to compare the color of individual pixels with the pixel's surface brightness.
" This is accomplished by assigning to each pixel a mean B—V color and a surface brightness, based on its calibrated V flux divided by pixel area."," This is accomplished by assigning to each pixel a mean $B-V$ color and a surface brightness, based on its calibrated $V$ flux divided by pixel area."
" This plot, using 280,000 pixels above 25 V mag arcsecs? is shown in top panel of Figure 16."," This plot, using 280,000 pixels above 25 $V$ mag $^{-2}$, is shown in top panel of Figure 16."
 Each color-j/ data point is treated as a 2D gaussian with a standard deviation tied to the color and surface brightness error of the pixel., Each $\mu$ data point is treated as a 2D gaussian with a standard deviation tied to the color and surface brightness error of the pixel.
 All the pixels are summed and binned to produce the density diagrams in Figure 16., All the pixels are summed and binned to produce the density diagrams in Figure 16.
A full tutorial is available to new volunteers of the website to illustrate the different questions using real PTF data.,A full tutorial is available to new volunteers of the website to illustrate the different questions using real PTF data.
" Once a volunteer has examined a candidate, their response is converted into a score, S, as follows."," Once a volunteer has examined a candidate, their response is converted into a score, $S$, as follows."
constant.,constant.
 Accordingly. masses based on shear measurements are subject to a possible upward. correction arising from a ‘mass sheet degeneracy," Accordingly, masses based on shear measurements are subject to a possible upward correction arising from a `mass sheet degeneracy'."
 With sullicienthy wide-field data it is possible to make the assumption that the surface mass density will approach zero at large distances [rom the cluster., With sufficiently wide-field data it is possible to make the assumption that the surface mass density will approach zero at large distances from the cluster.
 However. with independent knowledge of the magnification of the lens. the mass-sheet degeneracy can be broken regardless of the field of view of the data.," However, with independent knowledge of the magnification of the lens, the mass-sheet degeneracy can be broken regardless of the field of view of the data."
 Pwo methods have been proposed. to make use of this magnification information and calibrate the absolute scale of the mass distribution. cither through the change of image size at fixed surface brightness (Bartelmann Naravan 1995) or source counts (Broadhurst. Taylor Peacock 1995).," Two methods have been proposed to make use of this magnification information and calibrate the absolute scale of the mass distribution, either through the change of image size at fixed surface brightness (Bartelmann Narayan 1995) or source counts (Broadhurst, Taylor Peacock 1995)."
" This paper is concerned with exploring the role that infrared imaging ollers in the gravitational depletion (or ""convergence) method for estimating the total masses of clusters.", This paper is concerned with exploring the role that infrared imaging offers in the gravitational depletion (or `convergence') method for estimating the total masses of clusters.
 The depletion method. was first. suggested: by Aroadhurst. “Taylor Peacock (1995) who predicted. the diminution in background galaxy. surface number density as a function of radius expected behind a lensing cluster.," The depletion method was first suggested by Broadhurst, Taylor Peacock (1995) who predicted the diminution in background galaxy surface number density as a function of radius expected behind a lensing cluster."
 Here we are concerned with extending the original test to near-infrared wavelengths where. in principle. there are significant advantages. namely the flatter number-count. slope and a more accurate colour discrimination between foreground and background. populations.," Here we are concerned with extending the original test to near-infrared wavelengths where, in principle, there are significant advantages, namely the flatter number-count slope and a more accurate colour discrimination between foreground and background populations."
 The unique wide-field capabilities of the panoramic near-infrared. Cambridge Infrared Survey lnstrument (CIRSL Beckett 1998) allow us to test the method on the rich cluster Abell 2219 2—0.22).," The unique wide-field capabilities of the panoramic near-infrared Cambridge Infrared Survey Instrument (CIRSI, Beckett 1998) allow us to test the method on the rich cluster Abell 2219 $z$ =0.22)."
 A plan of the paper follows., A plan of the paper follows.
 In 62 we review the eravitational depletion method. illustrating the cilliculties associated with its implementation at optical wavelengths and the potential gains of repeating the experiment at near-infrared wavelengths., In $\S$ 2 we review the gravitational depletion method illustrating the difficulties associated with its implementation at optical wavelengths and the potential gains of repeating the experiment at near-infrared wavelengths.
 In. §32 we present new observations of Abell 2219 made at the prime focus of the 4.2m. William Lerschel telescope and discuss the techniques used to reduce the data as well as the methods used to create a sample of background. galaxies., In $\S$ 3 we present new observations of Abell 2219 made at the prime focus of the 4.2m William Herschel telescope and discuss the techniques used to reduce the data as well as the methods used to create a sample of background galaxies.
 5&4 discusses the depletion signal observed in the context of various mass models and reviews the uncertainties involved., $\S$ 4 discusses the depletion signal observed in the context of various mass models and reviews the uncertainties involved.
 In §5 we discuss the prospects of routinely estimating cluster masses using this method both with CIRSL and with the upcoming suite of wide field infrared survey telescopes., In $\S$ 5 we discuss the prospects of routinely estimating cluster masses using this method both with CIRSI and with the upcoming suite of wide field infrared survey telescopes.
" The gravitational depletion or the ""convergence method of breaking the mass-sheet degeneracy (Broachurst. Taylor. Peacock 1995) relies on the change in the surface number density of background galaxies induced by the magnification elect. of à. gravitational lens."," The gravitational depletion or the `convergence' method of breaking the mass-sheet degeneracy (Broadhurst, Taylor, Peacock 1995) relies on the change in the surface number density of background galaxies induced by the magnification effect of a gravitational lens."
 Since only source counts are involved. exquisite image quality (essential for. shear measurements) is not. necessary.," Since only source counts are involved, exquisite image quality (essential for shear measurements) is not necessary."
 Furthermore. as the elect depends on the magnification (i. absolute mass estimates are possible if the redshift’ distribution of the background sources is reasonably well-understood.," Furthermore, as the effect depends on the magnification $\mu$, absolute mass estimates are possible if the redshift distribution of the background sources is reasonably well-understood."
 Theintrinsic (unlensed) counts my of galaxies brighter than some limiting magnitude m. are transformed. to the observed (lensed) counts 9 by where à is the logarithmic slope of the number counts. Two competing elfects serve to. change the. lensed surface number density of the background galaxies.," Theintrinsic (unlensed) counts $n_{0}$ of galaxies brighter than some limiting magnitude $m$ are transformed to the observed (lensed) counts $n$ by where $\alpha$ is the logarithmic slope of the number counts, Two competing effects serve to change the lensed surface number density of the background galaxies."
 Source magnification clearly increases the surface number density by magnifving galaxies that would otherwise be lainter than the limiting magnitude., Source magnification clearly increases the surface number density by magnifying galaxies that would otherwise be fainter than the limiting magnitude.
 Llowever. focusing within the beam. clilutes the overall surface number density.," However, focusing within the beam dilutes the overall surface number density."
 The net. effect depends on the value of a: for a0.4 there will be an overall increase in observed surface number density. while [or a«O04 a depletion is measured.," The net effect depends on the value of $\alpha$ : for $\alpha>0.4$ there will be an overall increase in observed surface number density, while for $\alpha<0.4$ a depletion is measured."
 Unfortunately. at the limits where a sizeable [raction of field. galaxies are expected to be behind an intermediate redshift’ cluster. the slope of the optical field. counts.OAL. produces only a weak effect.," Unfortunately, at the limits where a sizeable fraction of field galaxies are expected to be behind an intermediate redshift cluster, the slope of the optical field counts, produces only a weak effect."
 In. order. to demonstrate the elfect in one of the most massive clusters known. Abell 1689 (2—0.18). Tavlor (1998) restrict their analysis to à red subsample known from blank field studies to have a flatter slope (o« Q4).," In order to demonstrate the effect in one of the most massive clusters known, Abell 1689 $z$ =0.18), Taylor (1998) restrict their analysis to a red subsample known from blank field studies to have a flatter slope $\alpha<0.4$ )."
 ὃν colour-selecting sources redder than the sequence of cluster spheroidals. Tavlor simultaneously secure a background. population whose à. is sulliciently low or the depletion method. to work. and. with an unlensed surface number densitv of 12 7.," By colour-selecting sources redder than the sequence of cluster spheroidals, Taylor simultaneously secure a background population whose $\alpha$ is sufficiently low for the depletion method to work, and with an unlensed surface number density of 12 $^{-2}$."
 Fort. Mellier Dantel-Fort. (1997). also search for an optical depletion ellect behind the cluster CL0024|1654. by restricting their search to the magnitude ranges 26«D28 and I1κ26.5 where the slopes are found. to be and0.," Fort, Mellier Dantel-Fort (1997) also search for an optical depletion effect behind the cluster CL0024+1654, by restricting their search to the magnitude ranges $26<B<28$ and $24<I<26.5$ where the slopes are found to be and."
25... However. they apply no colour selection to remove faint cluster members in this magnitude range. and furthermore are left. with an extremely low number density of only a few galaxies per square arcmin.," However, they apply no colour selection to remove faint cluster members in this magnitude range, and furthermore are left with an extremely low number density of only a few galaxies per square arcmin."
 Similarly. Athreva (in. preparation) use photometric redshifts ο isolate a background. population for their weak lensing analysis of MS. 1005-1934. but ave hamperecl by a small iclel of view and background. clustering.," Similarly, Athreya (in preparation) use photometric redshifts to isolate a background population for their weak lensing analysis of MS 1008-1224, but are hampered by a small field of view and background clustering."
 Clearly. balancing accurate discrimination of the lensing foreground from the xickeround. population while maintaining both a Ilat slope and sullicicnt numbers of background. galaxies is of crucial importance. and it is for this reason that we turn to wicde- infrared observations.," Clearly, balancing accurate discrimination of the lensing foreground from the background population while maintaining both a flat slope and sufficient numbers of background galaxies is of crucial importance, and it is for this reason that we turn to wide-field infrared observations."
 llere we are concerned with extending the depletion method to near-infrared wavelengths. and we illustrate the ;xossible advantages via an initial application to the rich cluster Abell 2219.," Here we are concerned with extending the depletion method to near-infrared wavelengths, and we illustrate the possible advantages via an initial application to the rich cluster Abell 2219."
 The slope of the number counts IHattens at longer wavelengths. because of a reduced: sensitivity o intermecdiate-redshift star forming galaxies (Ellis. 19, The slope of the number counts flattens at longer wavelengths because of a reduced sensitivity to intermediate-redshift star forming galaxies (Ellis 1997).
 Aloreover. this Hlattening occurs at. progressively brighter apparent magnitudes. s," Moreover, this flattening occurs at progressively brighter apparent magnitudes. ,"
election. the slope of the countsat infrared. wavelengths is sub-critical with a~0.25 at a relatively bright magnitude of A7 I8.," the slope of the countsat infrared wavelengths is sub-critical with $\alpha
\sim 0.25$ at a relatively bright magnitude of $K\simeq 18$ ."
We used the ISIS package to combine [οw of the best-seeiug iunages in each band into a template image. and then subtracted the template from each individual image. alter convolving the template to the seeing iu each iuage.,"We used the ISIS package to combine four of the best-seeing images in each band into a template image, and then subtracted the template from each individual image, after convolving the template to the seeing in each image."
 The resiπιο subtracted images allowed us to measure all variable sources in tle observed field. including IRS165W.," The resulting subtracted images allowed us to measure all variable sources in the observed field, including IRS16SW."
 We photometrically calibraed the light οιrves by comparing the brightuess of IRSIGSW in the template image to the brighless 0[isolated stars in the frame., We photometrically calibrated the light curves by comparing the brightness of IRS16SW in the template image to the brightness of isolated stars in the frame.
 These stars varied by <0.5% over the course of tIe 2001 obse‘ving season: 11e brightuess of these stars were assumed to be the salue as reported by Blum.Sellgren.&DePoy(1996)., These stars varied by $\la 0.5\%$ over the course of the 2001 observing season; the brightness of these stars were assumed to be the same as reported by \citet{bsdp96}.
. Ilutercoimparisou of 10 of these stars suggests that the absolute caibration of the pleMometry is accurate to ~1056;, Intercomparison of 10 of these stars suggests that the absolute calibration of the photometry is accurate to $\sim10\%$.
 We note that find the mean Ix brightuess Gay) of IRSIGSW to be ~9.61 mag: we fiidly = 9.50.1 mag., We note that \citet{ott99} find the mean K brightness $m_{K}$ ) of IRS16SW to be $\sim$ 9.61 mag; we find $m_{K}$ $=$ $\pm$ 0.1 mag.
 The reatively Insignificait differeuce could be due to slight clilferences in the ellective waveleneth of the filers used in the tw«) data sets. since IRSIOSW is very red.," The relatively insignificant difference could be due to slight differences in the effective wavelength of the filters used in the two data sets, since IRS16SW is very red."
 Our ineastremenut is also cousistent with srevious high auglar resolution measurements of Ην (e.g. Simon e al., Our measurement is also consistent with previous high angular resolution measurements of $m_{K}$ (e.g. Simon et al.
 1990. Sunons. Hodapp. Becklin 1990. DePoy Sharp 1991. aud Blum. Selleren. DePoy 1996).," 1990, Simons, Hodapp, Becklin 1990, DePoy Sharp 1991, and Blum, Sellgren, DePoy 1996)."
 We find that the mean H—k color oL IRS168W is 2.620.125 imag., We find that the mean $-$ K color of IRS16SW is $\pm$ 0.15 mag.
 Previous determinations of the H-Jx color of IRSIGSW inclule QU-EO.0T mae (Blum.Sellgreu.&DePoy1996).. 2.05 mae (Rieke. Rieke. Paul 1989). 2.1-£0.3 1jag (Simous. Hodapp. aud Becklin 1990). 2.£ mae (Ixrabbe el al.," Previous determinations of the $-$ K color of IRS16SW include $\pm$ 0.07 mag \citep{bsdp96}, 2.05 mag (Rieke, Rieke, Paul 1989), $\pm$ 0.3 mag (Simons, Hodapp, and Becklin 1990), 2.4 mag (Krabbe et al."
 1995). and. 2.8+0.2 (DePoy 5iurp 1991).," 1995), and $\pm$ 0.2 (DePoy Sharp 1991)."
 Our measurement is generalv consistent. with these previous determiuations. althoug Lit ds somewhat redder than the most precise (e.g. Blum. Selleren. DePoy 1996).," Our measurement is generaly consistent with these previous determinations, although it is somewhat redder than the most precise (e.g. Blum, Sellgren, DePoy 1996)."
 The mareinaly significant (o) difference between our determination of the H—kx color of IRSIOSW aud tha oL Blum.Selleren.&DePoy(1996) suggests that our H- inaguitudes uay contaiu systematic uncertainties., The marginally significant $\sim$ $\sigma$ ) difference between our determination of the $-$ K color of IRS16SW and that of \citet{bsdp96} suggests that our H-band magnitudes may contain systematic uncertainties.
 Note that Blum.Selleren.&DePoy(1996) ujeasured the H—kx «‘olor ou a single nigit (13 July 1993). πο the variability of the color of IRSIGSW (see below) does not account for the cdiTerence.," Note that \citet{bsdp96} measured the $-$ K color on a single night (13 July 1993), so the variability of the color of IRS16SW (see below) does not account for the difference."
 We searched [or the periodic sigial in the H and Ek light. curves of IRSIGSW using the Multibarmonic Aialysis of Variances (ANOVA) period-search algoritlun desc‘ibecl by Cerny (1996)., We searched for the periodic signal in the H and K light curves of IRS16SW using the Multiharmonic Analysis of Variances (ANOVA) period-search algorithm described by \citet{sc96}.
.. We used a C-Iaunguage implementation based ou a program provided by Christophe Alarc for this anaysis., We used a C-language implementation based on a program provided by Christophe Alard for this analysis.
 Two harmonies were required to get a good periodogam fit. giving a period . variability of 9.7254 0.005 days. consistent with that reported by Ott.Eckwart.&Cenzel(1999).," Two harmonics were required to get a good periodogram fit, giving a period of variability of $\pm$ 0.005 days, consistent with that reported by \citet{ott99}."
. The period found or each of the Haud Ex lighteurves was consistent to within tlie stated Πο alid we see LO evicence for higher lrequency overtones., The period found for each of the H and K lightcurves was consistent to within the stated uncertainty and we see no evidence for higher frequency overtones.
 Figure 3 shows tlie pase-folded light curves a H and Is for IRSIGSW., Figure \ref{fig:f1} shows the phase-folded light curves at H and K for IRS16SW.
 We note tha the shape of the light curve is similar to that [otud by (1999)., We note that the shape of the light curve is similar to that found by \citet{ott99}.
. There are some cillerences. however.," There are some differences, however."
 La particular. our light curve shows more CoutintOUS Chanee in brightsess than that of Ott.Eckhart.&Cenzel(1999):: we see uo evidence of ay part X tlie light curve that remains constant for a substaital fraction of the phase.," In particular, our light curve shows more continuous change in brightness than that of \citet{ott99}; we see no evidence of any part of the light curve that remains constant for a substantial fraction of the phase."
 Also shown in Figure 3) is the color chauge iu IRSI68W over the period of variation., Also shown in Figure \ref{fig:f1} is the color change in IRS16SW over the period of variation.
 The H—N color of the source Changes by a total of 0.16250.02 mae (excusive of systematic calibration, The $H-K$ color of the source changes by a total of $\pm$ 0.03 mag (exclusive of systematic calibration
«mall. about 0.5 (vanPutten2004) up to ~2.5% (Guetta&DellaValle2007).,"small, about 0.5 \citep{van04} up to $\sim 2.5\%$ \citep{gue07}."
. It suggests the existence of many failed GRD-supernovae. notably supernovae with relativistic ejecta. supernovae with pronounced aspherical explosions and radio- loud supernovae (e.g. Valle(2010) ancl references therein).," It suggests the existence of many failed GRB-supernovae, notably supernovae with relativistic ejecta, supernovae with pronounced aspherical explosions and radio- loud supernovae (e.g. \cite{del10} and references therein)."
 Therefore. (he rate of events of interest to potential bursts in gravitational waves appears lo be 1-2 orders of magnitude larger than the event rate of successful GRB-supernovae.," Therefore, the rate of events of interest to potential bursts in gravitational waves appears to be 1-2 orders of magnitude larger than the event rate of successful GRB-supernovae."
 In. addition. also (wpe I1 SNe. whose event rate is 3-4 (times larger (han that of twpe Ib/c (Cappellaro.Evans&Turatto1999:Mannucciοἱal.2005 ).. mav explode and expand asvinmetrically (Ilóflich.Wheeler&Wane1999:Ishikawaοἱal. 1992).. suggesting a sienilicant additional potential for gravitational-waves burst production.," In addition, also type II SNe, whose event rate is 3-4 times larger than that of type Ib/c \citep{cap99,man05}, , may explode and expand asymmetrically \citep{hoe99,ish92}, suggesting a significant additional potential for gravitational-waves burst production."
 A blind rather than a triggered search for bursts events in the local Universe seems to be appropriate by taking advantage of the all-sky monitoring capability of (he detectors in view of a beaming [actor of gamma-ray bursts of /;«10 (0>25 deg) up to a lew hundred (8~4 deg. Frailetal.(2001):vanPutten&RegimbauDellaValle (2007))).," A blind rather than a triggered search for bursts events in the local Universe seems to be appropriate by taking advantage of the all-sky monitoring capability of the gravitational-wave detectors in view of a beaming factor of gamma-ray bursts of $f_b<10$ $(\theta>25$ deg) up to a few hundred $\theta\sim 4$ deg, \cite{fra01,van03,gue07}) )."
 A blind search is also expected to be competitive with current X/optical survevs for detecting the shock break-out associated with an emerging CC-SNe. as it lasts onlv a lew dozens or minutes up (o a few hours. and it naturally includes the possibilitv of long GRBs coming from merger events with no supernova. which may be exemplified by the long event GRDO60614 of duraton 102 s discovered by While (he energy output in long gravitational wave bursts (GWDs) produced by rapidly rotating black holes should be large. searching for these bursts by matched. filtering is challenging in view of anticipated phase-incoherence due to turbulent magnetohyvdrodsynamical motions in the inner disk or torus.," A blind search is also expected to be competitive with current X/optical surveys for detecting the shock break-out associated with an emerging CC-SNe, as it lasts only a few dozens or minutes up to a few hours, and it naturally includes the possibility of long GRBs coming from merger events with no supernova, which may be exemplified by the long event GRB060614 of duraton 102 s discovered by While the energy output in long gravitational wave bursts (GWBs) produced by rapidly rotating black holes should be large, searching for these bursts by matched filtering is challenging in view of anticipated phase-incoherence due to turbulent magnetohydrodynamical motions in the inner disk or torus."
 llere. we focus on the detection of a trajectory in (he time frequency. domain produced bv long GWDs. satisfving phDase-coherence on short up to intermediate timescales.," Here, we focus on the detection of a trajectory in the time frequency domain produced by long GWBs, satisfying phase-coherence on short up to intermediate timescales."
 This objective goes further (han the detection of a burst signal. with the aim to extract reasonably accurate information on the burst evolution.," This objective goes further than the detection of a burst signal, with the aim to extract reasonably accurate information on the burst evolution."
 Inevitably. the sensitivity distance lor extracting trajectories is considerably more conservative than the sensitivity clistance [or a detection per se.," Inevitably, the sensitivity distance for extracting trajectories is considerably more conservative than the sensitivity distance for a detection per se."
 We shall discuss a new matched filtering detection algorithm to detect. trajectories in the lime frequency domain for long GWDs with slowly varving frequencies lasting tens of seconds with intermittent phase coherence., We shall discuss a new matched filtering detection algorithm to detect trajectories in the time frequency domain for long GWBs with slowly varying frequencies lasting tens of seconds with intermittent phase coherence.
 For a burst lasting 50 s. for example. the algoritlàn searches by matched filtering using segmented templates on a time scale ol. e.g.. 1s. This procedure gives a compromise between optimal matched lillerine. applicable to phase-coherence extending over the entire burst duration as in binary coalescence of two black holes. and second order methods by correlation of independent detector signals in the time-domain.," For a burst lasting 50 s, for example, the algorithm searches by matched filtering using segmented templates on a time scale of, e.g., 1 s. This procedure gives a compromise between optimal matched filtering, applicable to phase-coherence extending over the entire burst duration as in binary coalescence of two black holes, and second order methods by correlation of independent detector signals in the time-domain."
 For our example. the compromise results in a sensitivity.distance below that," For our example, the compromise results in a sensitivitydistance below that"
reproduce multiplicity aud pseudo-rapidity distribution of particles. but simulations were done for differen values of menn transverse momenutun of particles in order to estimate the systematic uncertainties of ΠοΠΠ [2]..,"reproduce multiplicity and pseudo-rapidity distribution of particles, but simulations were done for different values of mean transverse momentum of particles in order to estimate the systematic uncertainties of measurements \cite{UA5diff}."
" Tu UCAS MC generator 0) the cross-section of sinele-diffraction dissociation as a functiou of diffracte «ποια niass Was parauetrized as follows: and masses were generated in the interval from 1.08 GeV (Sin, pony) to vO.05s (see [2]. and [3]. for more At fragmentation of a diffracted. system in siugle-diffractive interaction the distribution of particles is centered around yyclus/M) and covers he rapiditv region from ποAPP) ο ραmlutsfn).", In UA5 MC generator \cite{UA5gener} the cross-section of single-diffraction dissociation as a function of diffracted system mass was parametrized as follows: and masses were generated in the interval from 1.08 GeV $m_{\pi} + m_p$ ) to $\sqrt{0.05s}$ (see \cite{UA5diff} and \cite{UA5gener} for more At fragmentation of a diffracted system in single-diffractive interaction the distribution of particles is centered around $y_0\simeq\ln(\sqrt{s}/M)$ and covers the rapidity region from $y_{min} \simeq \ln(\sqrt{s}m_p/M^2)$ to $y_{max} \simeq \ln(\sqrt{s}/m_p)$.
 When the lass of the diffracted systel ds αιμα. then the particles are nally concentrated a the forward region., When the mass of the diffracted system is small then the particles are mainly concentrated at the forward region.
 Iucreasiug he amass of the diffracted system the distribution OVOY o»eudo)rapidities moves to nüd-rapidities and he spread of the distribution becomes wider., Increasing the mass of the diffracted system the distribution over (pseudo)rapidities moves to mid-rapidities and the spread of the distribution becomes wider.
 Thus acceptances of different trigecrs are sensitive to different imass regious of diffracted svsteni (at given center of mass energv)., Thus acceptances of different triggers are sensitive to different mass regions of diffracted system (at given center of mass energy).
 Iu particular. if the triggers are uot placed in very forward region then the particles produced frou low-mass diffracted system will not Lit the Tu Ref.," In particular, if the triggers are not placed in very forward region then the particles produced from low-mass diffracted system will not hit the In Ref."
 |2] UAS claims that masses below 2.5 fe? were alinost never scen by the detector., \cite{UA5diff} UA5 claims that masses below 2.5 $c^2$ were almost never seen by the detector.
 For this purpose they investigated Ώρος. «ποσολος chhaucing this low-mass region by 50% and studvius the consequences of this eliauge in their Iu Table 1. we present trieeer efficicucics for sinele-diffractive events as reporte by UA5 in Ref [2]., For this purpose they investigated trigger efficiencies enhancing this low-mass region by $\%$ and studying the consequences of this change in their In Table \ref{Tb:TriggEff} we present trigger efficiencies for single-diffractive events as reported by UA5 in Ref \cite{UA5diff}.
" Those marked with an asterisk were used for the cross-section calculations. while the others were used o calculate the systematic If the triegers of UAS detector were not sensitive o the masses bellow 2.5 οἱ then the triggering efficiency for the case wheu this mass region is enliauced wy HOM must be related with the trigecringOO efficiency uarked with an asterisk with the following relation: UsimgESI the"" oparanieterizatiowaleterization 5 (5)) ομοonc οἱui casils""asilv evaluate the factor in the denominator: Thus the “re-normalized” efficiencies will be: Comparing these uuubers with the corresponding iuubers in Table 1. we conclude that at Vs = 200 CoV the triggers saw some low-ass (AM< 2.5 /e3j sinele-difftactive eveuts but at Vs = 900 GeV hey did not."," Those marked with an asterisk were used for the cross-section calculations, while the others were used to calculate the systematic If the triggers of UA5 detector were not sensitive to the masses bellow 2.5 $c^2$ then the triggering efficiency for the case when this mass region is enhanced by $\%$ must be related with the triggering efficiency marked with an asterisk with the following relation: Using the parameterization \ref{Eq:SDvsM2}) ) one can easily evaluate the factor in the denominator: Thus the ""re-normalized"" efficiencies will be: Comparing these numbers with the corresponding numbers in Table \ref{Tb:TriggEff} we conclude that at $\sqrt{s}$ = 200 GeV the triggers saw some low-mass $M <$ 2.5 $c^2$ ) single-diffractive events but at $\sqrt{s}$ = 900 GeV they did not."
" This allows us to claim that at 900 GeV UAS performed modcldependent extrapolation o the low-anass region and the seen cross-section of sinele-diffraction dissociation. cll, has αμράσα, by .actor PED1.19 (=Iu(0.055/1.082)EwD/η2 I1n(0.055/2.57)) in: order o obtain the ""total sinele-diffraction cross-section."," This allows us to claim that at 900 GeV UA5 performed model-dependent extrapolation to the low-mass region and the seen cross-section of single-diffraction dissociation, $\sigma_{SD}^{HM}$, has multiplied by factor 1.19 $=\ln(0.05s/1.08^2)/\ln(0.05s/2.5^2)$ ) in order to obtain the ""total"" single-diffraction cross-section."
 Thus in Eq. CI) , Thus in Eq. \ref{Eq:RSdNsd}) )
as cross-section of sinele-diffraction dissociation must be understood the following quantity: Iu Ref., as cross-section of single-diffraction dissociation must be understood the following quantity: In Ref.
 |l] UAS reported the result of measurement of the ratio of the inelastic cross-sections at Vs= 200 aud 900 GeV: The first error is statistical aud the second error systematic which includes contributions of background corrections for lun aud 2-arià trigecrs. trieecr cticiencics ων sinele-diffractive and lon-sinele diffractive processes aud Iwnuinositv," \cite{UA5inelXS} UA5 reported the result of measurement of the ratio of the inelastic cross-sections at $\sqrt{s} =$ 200 and 900 GeV: The first error is statistical and the second error systematic which includes contributions of background corrections for 1-arm and 2-arm triggers, trigger efficiencies for single-diffractive and non-single diffractive processes and luminosity"
the svstem will be excited strongly by the lorcing compared to the case where the forcing frequency is not close to a natural one.,the system will be excited strongly by the forcing compared to the case where the forcing frequency is not close to a natural one.
 The purpose of this paper is to explore (he possibility of resonance in [Iux-transport dvnamos relevant to the solar cycle., The purpose of this paper is to explore the possibility of resonance in flux-transport dynamos relevant to the solar cycle.
 In flux transport dvnamos. (here are several physical properties that help determine the unforced [requencies of (he svstem.," In flux transport dynamos, there are several physical properties that help determine the unforced frequencies of the system."
 These include differential rotation. meridional circulation. the so-called a-effect. or kinetic helicity. ancl (urbulent magnetic diffusion.," These include differential rotation, meridional circulation, the so-called $\alpha$ -effect, or kinetic helicity, and turbulent magnetic diffusion."
" It is now well established (Dikpati and Charbonnean. 1999) that. unless the magnetic diffusivitv is very large. meridional flow at the bottom of the dynamo laver is primarily responsible for the real part of (he natural frequency of (he dynamo, which determines (he speed with which induced toroidal ancl poloidal fields near (he bottom migrate toward (he equator."," It is now well established (Dikpati and Charbonneau, 1999) that unless the magnetic diffusivity is very large, meridional flow at the bottom of the dynamo layer is primarily responsible for the real part of the natural frequency of the dynamo, which determines the speed with which induced toroidal and poloidal fields near the bottom migrate toward the equator."
 Therefore the closeness of the frequency of forcing at the top to the speed of the flow at the bottom could help determine how much cvuamo response there is., Therefore the closeness of the frequency of forcing at the top to the speed of the flow at the bottom could help determine how much dynamo response there is.
 since (he forcing al the top is created by emergence of concentrated magnetic Πας from ihe bottom. in the form of active regions. and the rate of movement of the zone where aclive regions are found moves toward the equator (not coincidentally) al a rate close to (he meridional flow speed near the bottom. we mieht expect the conditions for resonance to occur in the bottom laver to be favorable.," Since the forcing at the top is created by emergence of concentrated magnetic flux from the bottom, in the form of active regions, and the rate of movement of the zone where active regions are found moves toward the equator (not coincidentally) at a rate close to the meridional flow speed near the bottom, we might expect the conditions for resonance to occur in the bottom layer to be favorable."
 On the other hand. we know from observations (Ulrich. 2010 ancl references therein) that the meridional flow at the top of the convection zone is loward the poles. opposite to the propagation of the surface forcing as well as 5-10 times faster.," On the other hand, we know from observations (Ulrich, 2010 and references therein) that the meridional flow at the top of the convection zone is toward the poles, opposite to the propagation of the surface forcing as well as 5-10 times faster."
 Thus we should not expect resonance {ο occur near (he surface., Thus we should not expect resonance to occur near the surface.
 It is also well known (Ulrich 2010 and references therein) that the meridional circulation varies with (ime., It is also well known (Ulrich 2010 and references therein) that the meridional circulation varies with time.
 This time variation is now being incorporated into a f[Iux-irausport dvnamo used for prediction by Dikpati aud colleagues., This time variation is now being incorporated into a flux-transport dynamo used for prediction by Dikpati and colleagues.
 In the 2006 prediction. meridional circulation eenerallv was kept fixed in time.," In the 2006 prediction, meridional circulation generally was kept fixed in time."
 Dikpati et al (2006). Dikpati and Gilman (2006) recognized that such time variations could be important. but felt they Iacked sullicient knowledge of its variations to include them.," Dikpati et al (2006), Dikpati and Gilman (2006) recognized that such time variations could be important, but felt they lacked sufficient knowledge of its variations to include them."
 Thev adjusted the time-independent meridional flow aniplitucde lo give the average period of (he past solar evcles. ancl stretched or compressed all the surface forcing data to the same period. to avoid any artificial or non-phyvsical mismatches between the natural diamo period and (he period of the forcing.," They adjusted the time-independent meridional flow amplitude to give the average period of the past solar cycles, and stretched or compressed all the surface forcing data to the same period, to avoid any artificial or non-physical mismatches between the natural dynamo period and the period of the forcing."
 Bul there can also in principle in the Sun be real dillerences between (he period οἱ the top forcing that was created by the previous cvele. and the Ireqency of equatorwarel propagation associated with the meridional Low speed at the bottom.," But there can also in principle in the Sun be real differences between the period of the top forcing that was created by the previous cycle, and the freqency of equatorward propagation associated with the meridional flow speed at the bottom."
 In dvnamos forced al the top with a specilied period. (he amplitude of the induced fields within the dvnamo domain will be affected by (his frequency difference.," In dynamos forced at the top with a specified period, the amplitude of the induced fields within the dynamo domain will be affected by this frequency difference."
 The model we present here in ellect studies how this amplitude is affected. by treating the meridional flow at the bottom as a free parameter while keeping the Ireequency of the top forcing fixed.," The model we present here in effect studies how this amplitude is affected, by treating the meridional flow at the bottom as a free parameter while keeping the frequency of the top forcing fixed."
First. when the kinetic helicity increases. the number of bound magnetic eigenmocles increases significantly.,"First, when the kinetic helicity increases, the number of bound magnetic eigenmodes increases significantly."
 Their growth rates. À;. become strongly concentrated near the growth rate of the [astest unbouncl eigenmode. Ay. (," Their growth rates, $\lambda_n$, become strongly concentrated near the growth rate of the fastest unbound eigenmode, $\lambda_0$. ("
"This last result follows from a nearly uniform distribution of A,, on the logavitlimic-seale plots (A) and (C) in Figure I..)",This last result follows from a nearly uniform distribution of $\lambda_n$ on the logarithmic-scale plots (A) and (C) in Figure \ref{FIGURE_1}. .)
 second. on all plots in Fieure 1. the growth rate of the first bound. eigenmode. Ay. happens to be very close to Ay.," Second, on all plots in Figure \ref{FIGURE_1} the growth rate of the first bound eigenmode, $\lambda_1$, happens to be very close to $\lambda_0$."
 We found same result for all other high Revnolds number cases (hal we investigated (not reported here). with different acimissible values of the helicity parameter .," We found same result for all other high Reynolds number cases that we investigated (not reported here), with different admissible values of the helicity parameter $h$."
 Thus. we propose that for dvnanmo driven by high Revnolds number velocity field there alwavs exists a shallow bound eigenmode Ay. such (hat Aq4—Àj«Ap.," Thus, we propose that for dynamo driven by high Reynolds number Kolmogorov-type velocity field there always exists a shallow bound eigenmode $\lambda_1$, such that $\lambda_1-\lambda_0\ll\lambda_0$."
 This shallow mode grows faster than any of the unbound modes because Ay>Ap., This shallow mode grows faster than any of the unbound modes because $\lambda_1>\lambda_0$.
" ""Third. the spectra of the shallow bound eigenmode A4. shown by the dotted lines in Figures 2. and 3.. and (he spectra of the fastest erowing unbound eigenmode Aj. shown by the red jagged spiky lines. are close near (he magnetic energv containing large scales."," Third, the spectra of the shallow bound eigenmode $\lambda_1$, shown by the dotted lines in Figures \ref{FIGURE_2} and \ref{FIGURE_3}, and the spectra of the fastest growing unbound eigenmode $\lambda_0$ , shown by the red jagged spiky lines, are close near the magnetic energy containing large scales."
 structures of these modes are however different: the shallow eigenmocde has a relatively larger small-scales component.), (Small-scale structures of these modes are however different: the shallow eigenmode has a relatively larger small-scales component.)
 In practical applications. (he shallow mode grows faster (han the unbouncl modes and can dominate at large scales: however it cannot be described by the conventional a-moclel for large-scale dvnamo. since this model does not capture the bound mocles.," In practical applications, the shallow mode grows faster than the unbound modes and can dominate at large scales; however it cannot be described by the conventional $\alpha$ -model for large-scale dynamo, since this model does not capture the bound modes."
 Fourth. consider the spectra of eigenmodes Ay and Ay (the clotted lines and the red jagged spiky solid lines in Figures 2. and 3)).," Fourth, consider the spectra of eigenmodes $\lambda_0$ and $\lambda_1$ (the dotted lines and the red jagged spiky solid lines in Figures \ref{FIGURE_2} and \ref{FIGURE_3}) )."
 When (he value of the kinetic helicity crops by a factor of 10 (from fh=1 to h= 0.1). the location of the peaks of these spectra shifts to larger scales by (the same factor.," When the value of the kinetic helicity drops by a factor of $10$ (from $h=1$ to $h=0.1$ ), the location of the peaks of these spectra shifts to larger scales by the same factor."
 Thus. the characteristic scales of eigenmocles Ay aud Àj are both approximately equal to ~/j/h. so that both these modes peak at large scale when kinetic helicity is small.," Thus, the characteristic scales of eigenmodes $\lambda_0$ and $\lambda_1$ are both approximately equal to $\sim l_0/h$, so that both these modes peak at large scale when kinetic helicity is small."
 This result is consistent with general predictions of the a-model (Steenbeck.Krause&Radler1966)., This result is consistent with general predictions of the $\alpha$ -model \citep{skr}.
. We have presented the [ull numerical characterization of the kinematic dvnamo model in the case of the IXolmogorov sealing of the velocity field., We have presented the full numerical characterization of the kinematic Kazantsev-Kraichnan dynamo model in the case of the Kolmogorov scaling of the velocity field.
 Our main conclusion is that the structure and the characteristic correlation scalesof the magnetic, Our main conclusion is that the structure and the characteristic correlation scalesof the magnetic
been developed further.,been developed further.
 A later aleorithin. presented by ?.. works on a similar principle. ideutifviug “liked sequences” using the eigenvectors of the inertia tensor.," A later algorithm, presented by \citet{Dave97}, works on a similar principle, identifying “linked sequences” using the eigenvectors of the inertia tensor."
 The authors found that the algorithm was poor at discriminating between cosmological models using CLAl-like 1nock galaxy catalogs. but primarily because of the σα] umber of galaxies in the catalogs.," The authors found that the algorithm was poor at discriminating between cosmological models using CfA1-like mock galaxy catalogs, but primarily because of the small number of galaxies in the catalogs."
 Iu Paper 1. we used the distribution of the Ilessiau eieenvalues of the smoothed deusitv field (A-space) onu a gril to study three types of structure: clumps. filbuneuts. and walls.," In Paper $1$, we used the distribution of the Hessian eigenvalues of the smoothed density field $\lambda$ -space) on a grid to study three types of structure: clumps, filaments, and walls."
 Filaments were found in the A-space distributions at a variety of gioothing scales. ranging at least from 515Mpe.. in both N-body siuxilations and the ealaxy distribution measured by the Sloan Dieital Skv Survey (SDSS.7)..," Filaments were found in the $\lambda$ -space distributions at a variety of smoothing scales, ranging at least from $5-15$, in both N-body simulations and the galaxy distribution measured by the Sloan Digital Sky Survey \citep[SDSS,][]{SDSS}."
 Furthermore. filameuts were found to dominate the large-scale distribution of latter using snioothiugscales of 10155.AIpe.. giving wav to clumps with ~57 ssoothine.," Furthermore, filaments were found to dominate the large-scale distribution of matter using smoothingscales of $10-15$, giving way to clumps with $\sim 5$ smoothing."
 The fact that the eigenvalues of the IHTessiau can be used to discriminate different types of structure in a particle distribution is fundamental to a umber of structire-finding algorithms (e.g...2777).," The fact that the eigenvalues of the Hessian can be used to discriminate different types of structure in a particle distribution is fundamental to a number of structure-finding algorithms \citep[e.g.,][]{CPS00,Hahn07a,MMF,FR08}."
 Towever. the relationship between A-space and a particular structure is not always trivial.," However, the relationship between $\lambda$ -space and a particular structure is not always trivial."
 For example. oue night think that a filamentary erid cell would have two positive aud one uegative eieeuvalue.," For example, one might think that a filamentary grid cell would have two positive and one negative eigenvalue."
 This will be true near the centre of a filament connecting two overdense filament cuds. but in the vicinity of the overdeusities or in the case that the filament cuds at an uuderdeusty. all three cigeuvalucs will become negative.," This will be true near the centre of a filament connecting two overdense filament ends, but in the vicinity of the overdensities or in the case that the filament ends at an underdensity, all three eigenvalues will become negative."
 In addition. when working with a sinoothed deusity field. these criteria select regions that are near clumps and do not necessarily lie along the filament.," In addition, when working with a smoothed density field, these criteria select regions that are near clumps and do not necessarily lie along the filament."
 Finally. these criteria disregard the structures width — for example. the regions away from the centre of he filament may have positive values of A».," Finally, these criteria disregard the structure's width – for example, the regions away from the centre of the filament may have positive values of $\lambda_2$."
 Iu this paper. we will describe a procedure to identity filaments in the three-dimenusional galaxy distribution using au aleoritlin called the Smioothed Uessian Major Axis Filament Finder (SUAMLAFE). and compare their xoperties m cosmological N-body simulations to those i| the SDSS ealaxy redshift survey.," In this paper, we will describe a procedure to identify filaments in the three-dimensional galaxy distribution using an algorithm called the Smoothed Hessian Major Axis Filament Finder ), and compare their properties in cosmological N-body simulations to those in the SDSS galaxy redshift survey."
 Wo describe our iuethodolosgv. which uses the eigenvalues aud eieenvectors of the smoothed Iblessiu matrix (secjiereafter.Paper j.in 2..," We describe our methodology, which uses the eigenvalues and eigenvectors of the smoothed Hessian matrix \citep[see ][hereafter, Paper~$1$]{paper1}, in \ref{subsec:Method}."
 In 3.. we run the code with a rauge of possible iuput parameters aud justifv our choices for each.," In \ref{subsec:FilPars}, we run the code with a range of possible input parameters and justify our choices for each."
 We discuss the behavior of the algorithia when used on Gaussian random fields in 1. allowing us to distinguish those features of the larec-scale distribution of matter that are a direct consequence of the non-linear growth of structure.," We discuss the behavior of the algorithm when used on Gaussian random fields in \ref{subsec:FilGauss}, allowing us to distinguish those features of the large-scale distribution of matter that are a direct consequence of the non-linear growth of structure."
 In 8.5... we use mock galaxy catalogues to estimate the inconipleteuess and contamination rates of fllamcut samples aud tlen use these quantities to iuterpret the distribution of filaneuts found in the SDSS 6)).," In \ref{subsec:MockFils}, we use mock galaxy catalogues to estimate the incompleteness and contamination rates of filament samples and then use these quantities to interpret the distribution of filaments found in the SDSS \ref{subsec:FilData}) )."
 In 7 we sumuiuize our results aud discuss the implications of our fiudiues., In \ref{subsec:Results} we summarize our results and discuss the implications of our findings.
 Filkuneuts. clusters. aud walls all present sharp features in the density field along at least one of their principal axes.," Filaments, clusters, and walls all present sharp features in the density field along at least one of their principal axes."
 In Paper 1. we described a procedure to generate a matrix of Gaussian-smoothed second derivatives of the density feld (the DTlessian matrix) at cach erid cell. computing its cigeuvalues. A; (defined such that Ay<Az). and cigenvectors. A;.," In Paper 1, we described a procedure to generate a matrix of Gaussian-smoothed second derivatives of the density field (the Hessian matrix) at each grid cell, computing its eigenvalues, $\lambda_i$ (defined such that $\lambda_1<\lambda_2<\lambda_3$ ),and eigenvectors, $A_i$ ."
" For the testing and development of the algorithii we ran a seres of cosmiological N-body simiulatious. using a particle-mesh code with ©,,=0.29. Q,=0.71. σε=0.51. and 5=Ly/(100 lan 31 Atpe= 0.69 (see Paper l for details)."," For the testing and development of the algorithm, we ran a series of cosmological $N$ -body simulations, using a particle-mesh code with $\Omega_m = 0.29$, $\Omega_\Lambda = 0.71$, $\sigma_8 = 0.85$, and $h = H_0/(100 $ km $^{-1}$ $^{-1}$ $=0.69$ (see Paper 1 for details)."
 The simulation is performed within a 200 box with 512° particles. cach with mass. =LIT+410 b3 M...," The simulation is performed within a $200$ box with $512^3$ particles, each with mass, $m_p = 4.77 \times 10^9$ $h^{-1}$ $M_{\sun}$."
" m,Iu order to generate a three dimensional distribution of mock galaxies. we first identify dark matter halos within the particle distribution using the TOP aleorithim (7) aud then populate them using the halo occupatio- distribution and parametrization of 7.seePaper—fordetail."," In order to generate a three dimensional distribution of mock galaxies, we first identify dark matter halos within the particle distribution using the HOP algorithm \citep{HOP} and then populate them using the halo occupation distribution and parametrization of \citet[][see Paper~$1$ for details]{HODPars2}."
 The resulting mock galaxw distributioστσι is snoofhed using a Cus kernel and dts ποσο] derivatives. vieldiug a 128« erid with IHessiaτπτ eigenvalues and cigenvectors in each cell.," The resulting mock galaxy distribution is smoothed using a Gaussian kernel and its second derivatives, yielding a $128 \times 128 \times 128$ grid with Hessian eigenvalues and eigenvectors in each cell."
 In Fie. 1..," In Fig. \ref{fig:OneFil},"
 we plot a slice from the simulation 10 dee and 27.21 ou a side. chosen to euconipass a pronunent flamentary structure.," we plot a slice from the simulation $10$ deep and $27.21$ on a side, chosen to encompass a prominent filamentary structure."
 Shown are the galaxies (upper left). galaxy deusitv nap (upper right). aud Àj map (lower left and right). smoothed with a /2 kernel. to bring ont the filament.," Shown are the galaxies (upper left), galaxy density map (upper right), and $\lambda_1$ map (lower left and right), smoothed with a $l=2$ kernel to bring out the filament."
 The structure appears inmost clearly iu Ay. so we construct a list of exid cells. €. ordered by increasing value of Αι.," The structure appears most clearly in $\lambda_1$, so we construct a list of grid cells, G, ordered by increasing value of $\lambda_1$."
 Before marking the first flament. we remove from G all exid cells that satisfy auv of the following criteria. where pis the mean density of objects making up the density field.," Before marking the first filament, we remove from G all grid cells that satisfy any of the following criteria, where $\bar{\rho}$ is the mean density of objects making up the density field."
 The Ay and A» thresholds follow from he definition of a filament — the density feld must be concave down along at least two of the principal axes., The $\lambda_1$ and $\lambda_2$ thresholds follow from the definition of a filament – the density field must be concave down along at least two of the principal axes.
 The frst clement in € (the most negativo iu Ay) is uarked with a cross in the lower left panel of Fig. 1.., The first element in G (the most negative in $\lambda_1$ ) is marked with a cross in the lower left panel of Fig. \ref{fig:OneFil}.
 From this starting poiut. we trace out the filament in voth directions of the caxis of structure’ (parallel aud antiparallel to 3). taking steps equal to the erid scale of 1.5625AIpe.," From this starting point, we trace out the filament in both directions of the `axis of structure' (parallel and antiparallel to $A_3$ ), taking steps equal to the grid scale of $1.5625$."
. Subsequent filament elemieuts are iof constrained© to lie on the erid. so we use a third-order polynomial interpolation scheme ou the ericd o obtain the local Wessian parameters.," Subsequent filament elements are not constrained to lie on the grid, so we use a third-order polynomial interpolation scheme on the grid to obtain the local Hessian parameters."
 If. at amy poiut along the flament. the angular rate of chanee of the axis of structure excecds a threshold. C. we stop tracing and uark the point as a flament cud.," If, at any point along the filament, the angular rate of change of the axis of structure exceeds a threshold, $C$, we stop tracing and mark the point as a filament end."
 The stopping condition at step ut is given by. where A. the grid cell size. is also the size of each step.," The stopping condition at step m is given by, where $\Delta$, the grid cell size, is also the size of each step."
 The filament filucer will also stop and mark a flament end if it passes mto a cell that satisfies one or more of the criteria specified in Equation 1.., The filament finder will also stop and mark a filament end if it passes into a cell that satisfies one or more of the criteria specified in Equation \ref{eq:CellRemove}. .
 In the lower right panel of Fie. 1..," In the lower right panel of Fig. \ref{fig:OneFil},"
 we show the flamentsthat result frou a sunple run of SIIMIAFF ona 27<«10 5? ? slice from the dark matter particle distribution iu our cosinological simulation., we show the filamentsthat result from a sample run of SHMAFF on a $27 \times 27 \times 10$ $h^3$ $^{-3}$ slice from the dark matter particle distribution in our cosmological simulation.
 For cach step along a filament. all eid. cells within a removal width. W. of the most recently chosen filament clement. are removed frou G. where," For each step along a filament, all grid cells within a removal width, W, of the most recently chosen filament element, are removed from G, where"
Our results demonstrate the potential of the spacecraft for asteroseismology of sdB stars.,Our results demonstrate the potential of the spacecraft for asteroseismology of sdB stars.
 Continuous coverage and the unprecedented quality of the data allowed us to detect. at high S/N. stellar pulsations in stars which would not be easily studied from the ground.," Continuous coverage and the unprecedented quality of the data allowed us to detect, at high S/N, stellar pulsations in stars which would not be easily studied from the ground."
 The rich amplitude spectra of HHer class stars enables us to use the relation for period spacings to assign most of the detected peaks with » (relative) and / values (see Paper ΥΠΟ., The rich amplitude spectra of Her class stars enables us to use the relation for period spacings to assign most of the detected peaks with $n$ (relative) and $l$ values (see Paper VIII).
 With those determinations. along with the frequencies themselves. tight constraints can be placed on models of these stars. and therefore will expand our understanding of the formation. structure. and evolution of these highly evolved stars.," With those determinations, along with the frequencies themselves, tight constraints can be placed on models of these stars, and therefore will expand our understanding of the formation, structure, and evolution of these highly evolved stars."
 We anticipate that with much longer runs ofKepler data we can detect even more peaks with lower amplitudes making period spacing tool even more efficient., We anticipate that with much longer runs of data we can detect even more peaks with lower amplitudes making period spacing tool even more efficient.
 AB gratefully appreciates funding from Polish Ministry of Science and Higher Education under project No., AB gratefully appreciates funding from Polish Ministry of Science and Higher Education under project No.
 554/MOB/2009/0., 554/MOB/2009/0.
 MDR was partially funded by a Missouri State University Faculty Research Grant., MDR was partially funded by a Missouri State University Faculty Research Grant.
 ACQ is supported by the Missouri Space Grant Consortium. funded by NASA.," ACQ is supported by the Missouri Space Grant Consortium, funded by NASA."
 Funding for the Mission is provided by NASA's Science Mission Directorate., Funding for the Mission is provided by NASA's Science Mission Directorate.
 The authors gratefully acknowledge theKepler Science Team and all those who have contributed to making the Mission possible., The authors gratefully acknowledge the Science Team and all those who have contributed to making the Mission possible.
"is already falling in. then the added inwardly directed inertia of the shell raises the AZ, mass bv a factor of à few at most 77 and 8?77)).","is already falling in, then the added inwardly directed inertia of the shell raises the $M_\sigma$ mass by a factor of a few at most \ref{sec:underweight_fixed} and \ref{sec:critical_fixed}) )."
" The complications arising [rom a finite svsten size were recentlypointed out by Navakshinetal.(20095). who noted that dynamicaltime in the bulge. Z2,/o. where £2, is the scale racius of the bulge. plavs a key role in what happens."," The complications arising from a finite system size were recentlypointed out by \cite{NayakshinEtal09b} who noted that dynamicaltime in the bulge, $R_b/\sigma$, where $R_b$ is the scale radius of the bulge, plays a key role in what happens."
 Black holes growing at the Ecldineton rate. Mgqa. c-fold their mass on the Salpeter time. ἐν=AlbuAlpaa 191.," Black holes growing at the Eddington rate, $\dot M_{\rm
 Edd}$, $e$ -fold their mass on the Salpeter time, $t_{\rm S} = M_{\rm
 BH}/\dot M_{\rm Edd} \approx 4.5\times 10^7$ ."
" Observationallv. Thus ""Large"" bulges. ¢2200 km s. 1. have dvnanical"," Observationally, Thus “large” bulges, $\sigma \simgt 200$ km $^{-1}$ , have dynamical"
The elemental abundance ratio of [2C ΟΥ) in the local ISM is 60 (e.g. Langer Penzias (1993): Lucas Liszt (1998)).,The elemental abundance ratio of $^{12}$ $^{13}$ C] in the local ISM is 60 (e.g. Langer Penzias (1993); Lucas Liszt (1998)).
" The molecular abundance ratio of ""CN/MCN is often assumed to be the same as this elemental ratio.", The molecular abundance ratio of $^{12}$ $^{13}$ CX is often assumed to be the same as this elemental ratio.
 It has been reported. however. that," It has been reported, however, that"
are cescribect in detail in Poundsetal.(2001).,are described in detail in \cite{pounds01}.
. We have extracted all of the delata from the archive ancl produced 2.10 keV lightcurves in the same manner as we have describeL| for other AAGN monitoring programmes (e.g.seeAltardyctal.2004.for details).., We have extracted all of the data from the archive and produced 2–10 keV lightcurves in the same manner as we have described for other AGN monitoring programmes \citep[e.g. see][for details]{mch04}.
 For use in power spectral analysis we produce a long time-scale light curve. covering the full observing period with 4-day sampling. and an intermediate time-scale lighteurve. covering the one month period. of hour sampling.," For use in power spectral analysis we produce a long time-scale light curve, covering the full observing period with 4-day sampling, and an intermediate time-scale lightcurve, covering the one month period of 3-hour sampling."
 wwas monitored with between 2000 June 1. and July 5. producing a month-long ight curve.," was monitored with between 2000 June 1 and July 5, producing a month-long light curve."
 This observation was only interrupted. by the regular Earth occultations of the satellite on the orbital ime-scale of 5632s., This observation was only interrupted by the regular Earth occultations of the satellite on the orbital time-scale of 5632s.
" Binning the data in orbit-long bins owoduces an evenly sampled. light. curve. containing 551 »nts. Chat probes time-scales from a few times 10"" to 107 s. Additionally. each of the 551 individual orbits cover time-scales of 107 s. whose power spectra can be combined o produce a high quality high frequency PSD."," Binning the data in orbit-long bins produces an evenly sampled light curve, containing 551 points, that probes time-scales from a few times $10^6$ to $10^4$ s. Additionally, each of the 551 individual orbits cover time-scales of $10^3-10^2$ s, whose power spectra can be combined to produce a high quality high frequency PSD."
 We downloaded SIS data. from. the ΕλαΛι database in 0.62 and 210 keV. οποιον bands and oroduced background subtracted light curves. with average count rates of 2.7 and 0.6 c/s respectively.," We downloaded SIS data from the TARTARUS database in 0.6–2 and 2–10 keV energy bands and produced background subtracted light curves, with average count rates of 2.7 and 0.6 c/s respectively."
 Phe average οποίοι energies of these two bands are 1.18 and 3.2 keV respectively., The average photon energies of these two bands are 1.18 and 3.2 keV respectively.
 The lighteurves. PSD and other variability properties of this data set have been studied by c.g. (2007):Edelsonetal. (2002).," The lightcurves, PSD and other variability properties of this data set have been studied by e.g. \citet{papadakis07,edelson02}."
 wwas observed by [from 2005 January 5. 19:47. to 2005 January ο. 23:16.," was observed by from 2005 January 5, 19:47, to 2005 January 6, 23:16."
 The European Photon Imaging Cameras (EPIC) PN. MOSI and ALOS2 cameras were all operated in. small window moce using à medium filter. as described bv. Papadakiset.al. (2007).," The European Photon Imaging Cameras (EPIC) PN, MOS1 and MOS2 cameras were all operated in small window mode using a medium filter, as described by \cite{papadakis07}."
". The total exposures for the PN ancl MOS cameras were OS.S ks and 99.1 ks respectively,", The total exposures for the PN and MOS cameras were 98.8 ks and 99.1 ks respectively.
" For the PN camera. we extracted source photons from a ~2"".2” region and the background: was selected from a source-free. region of equal area on the same chip."," For the PN camera, we extracted source photons from a $\sim 2 \arcmin \times 2
\arcmin$ region and the background was selected from a source-free region of equal area on the same chip."
 Only single and double events. with quality Hag=0 were retained.," Only single and double events, with quality flag=0 were retained."
" For the MOSI and MOS2 cameras. source photons were extracted. [from a circular region of ~46"" in radius and single. double. triple and quaclruple events were used."," For the MOS1 and MOS2 cameras, source photons were extracted from a circular region of $\sim 46
\arcsec$ in radius and single, double, triple and quadruple events were used."
 The PN data was free of pile-up. but both MOS cameras sullered significant pile-up in the cores of the target PSES.," The PN data was free of pile-up, but both MOS cameras suffered significant pile-up in the cores of the target PSFs."
 Fherefore we discarded. data [rom thecentral 12” diameter of cach MOS exposure., Therefore we discarded data from thecentral $12\arcsec$ diameter of each MOS exposure.
 The average PN background-subtracted count rate in the 0.210 keV band was ~28 c/s. The background level was low and almost constant throughout the observation., The average PN background-subtracted count rate in the 0.2–10 keV band was $\sim 28$ c/s. The background level was low and almost constant throughout the observation.
 We produced. light curves in the 0.22 and 210 keV energy bands in 48 s bins. and combined. the light curves from the dilferent. detectors to. produce. weighted average light curves.," We produced light curves in the 0.2–2 and 2–10 keV energy bands in 48 s bins, and combined the light curves from the different detectors to produce weighted average light curves."
 The 0.210 keV lighteurve is shown in Fig 1. (seealsoPapadakisetal.2007)., The 0.2–10 keV lightcurve is shown in Fig \ref{fig:xmmlc} \citep[see also][]{papadakis07}.
. As the variability properties normally depend on energy band. we also constructed Ilieght. curves from the PN data alone in the 0.52 and 28.8 keV bands. to match the average energies of the flight curves.," As the variability properties normally depend on energy band, we also constructed light curves from the PN data alone in the 0.5–2 and 2–8.8 keV bands, to match the average energies of the light curves."
 We used these lighteurves in all quantitative analyses., We used these lightcurves in all quantitative analyses.
 The superposecl PSDs derived from the 2210 keV and 0.62 keV data are shown in Fig. 2.., The superposed PSDs derived from the 2–10 keV and 0.6–2 keV data are shown in Fig. \ref{fig:ascapsds}.
 Data xlow 10 2 result Crom the light curves binned on the orbital time-scale., Data below $10^{-4}$ Hz result from the light curves binned on the orbital time-scale.
" Data above LO?"" Lz are the sum of he PSDs derived from the many. short sub-orbital light curves.", Data above $10^{-3.5}$ Hz are the sum of the PSDs derived from the many short sub-orbital light curves.
 Note the frequeney gap that these data. co not cover., Note the frequency gap that these data do not cover.
 The Poisson noise level has been subtracted., The Poisson noise level has been subtracted.
 On ime-scales longer than the orbital time-scale. the low and uieh energy PSDs have a similar normalisation.," On time-scales longer than the orbital time-scale, the low and high energy PSDs have a similar normalisation."
 However on shorter time-scales the 210 keV. PSD lies above the 0.62 keV PSD. except perhaps at the very highest. frequencies (10 ΤΗ) where the two PSDs may be converging.," However on shorter time-scales the 2–10 keV PSD lies above the 0.6–2 keV PSD, except perhaps at the very highest frequencies $\sim 10^{-2}$ Hz) where the two PSDs may be converging."
 This requency dependent excess of the high energy PSD over the ow enerey PSD both below and above the high frequency weak (~10 2111. which is different from the behaviour of other well observed AGN. (e.g.Νέας51.M'LHardy 2004).. will be moclellecl properly in Section 5..," This frequency dependent excess of the high energy PSD over the low energy PSD both below and above the high frequency break $\sim
10^{-3}$ Hz), which is different from the behaviour of other well observed AGN, \citep[e.g. NGC4051,][]{mch04}, will be modelled properly in Section \ref{s_combinedpsd}. ."
 The flight curves were almost completely continuous except for 5 small gaps of duration. 20-30 secs each., The light curves were almost completely continuous except for 5 small gaps of duration 20-30 secs each.
 Following the procedure established. in. M'llardsetal.(2004) these, Following the procedure established in \cite{mch04} these
The standard thin accretion disc (Shakura&Sunvacy 1973)) has been extensively applied to a variety of astrophysical systems. such as active galactic nuclei. X-ray. binaries. and cataclysmic variable stars.,"The standard thin accretion disc \citealp{Shakura73}) ) has been extensively applied to a variety of astrophysical systems, such as active galactic nuclei, X-ray binaries, and cataclysmic variable stars."
 Phe theory of the standard thin disc. which is based on the à stress prescription. predicts that the disc will suller both thermal and viscous instability when the pressure is dominated by radiation pressure.," The theory of the standard thin disc, which is based on the $\alpha$ stress prescription, predicts that the disc will suffer both thermal and viscous instability when the pressure is dominated by radiation pressure."
 Llowever. observations of X-ray binaries show little evidence for such instabilities except lor GRS 1915]105 (hereafter GRS 1915).," However, observations of X-ray binaries show little evidence for such instabilities except for GRS 1915+105 (hereafter GRS 1915)."
 Since the stability is related to the description of stress. the standard @ stress prescription was moclified in some previous works to assure the disc to be stable no matter whether gas or radiation pressure dominates.," Since the stability is related to the description of stress, the standard $\alpha$ stress prescription was modified in some previous works to assure the disc to be stable no matter whether gas or radiation pressure dominates."
" For instance. Lightman&Eardley(1974). introduced a so-called } stress prescription. Ίου, the stress is proportional to the eas pressure rather than the sum of the eas and radiation pressure."," For instance, \citet{Lightman74} introduced a so-called $\beta$ stress prescription, i.e., the stress is proportional to the gas pressure rather than the sum of the gas and radiation pressure."
 With the 3 stress. the disc will remain stable even for the case that radiation. pressure cominates over gas pressure.," With the $\beta$ stress, the disc will remain stable even for the case that radiation pressure dominates over gas pressure."
 Furthermore. some other stress prescriptions were introduced by assuming that the stress is relevant to both the total pressure and the gas pressure (e.g... Ixatoetal. 2008.. p. 108).," Furthermore, some other stress prescriptions were introduced by assuming that the stress is relevant to both the total pressure and the gas pressure (e.g., \citealp{Kato08}, p. 108)."
 As pointed out by Cierliáski.&Done(2004).. however. the 3 stress would be in conflict with observations as follows.," As pointed out by \citet{Gierli04}, however, the $\beta$ stress would be in conflict with observations as follows."
 Observations show that the colour temperature correction remains stable for a wide range of luminosity. whereas disces with 3 stress should have a colour temperature correction that changes from 1.8 to ~2.7 as the accretion rate increases.," Observations show that the colour temperature correction remains stable for a wide range of luminosity, whereas discs with $\beta$ stress should have a colour temperature correction that changes from $\sim 1.8$ to $\sim 2.7$ as the accretion rate increases."
 Conversely. the standard a prescription may predict that the correction should remain stable at ~1.8 for varving accretion rates.," Conversely, the standard $\alpha$ prescription may predict that the correction should remain stable at $\sim 1.8$ for varying accretion rates."
 Moreover. some recent. simulations (c.g. Lliroseetal. 2000)) showed that the stress is roughly proportional to the sum of gas and radiation pressure.," Moreover, some recent simulations (e.g., \citealp{Hirose09}) ) showed that the stress is roughly proportional to the sum of gas and radiation pressure."
 Thus. the standard @ prescription seems to be more acceptable than other prescriptions such as the J stress.," Thus, the standard $\alpha$ prescription seems to be more acceptable than other prescriptions such as the $\beta$ stress."
 The slim cise model was introduced: by Xbramowiczal. (LOs8S8).. in which it was predicted that the thermal instability. of the racliation-pressurc-dominated thin. disc will trigger a limit evele behaviour between the thin disc and the slim cise.," The slim disc model was introduced by \citet{Abramowicz88}, in which it was predicted that the thermal instability of the radiation-pressure-dominated thin disc will trigger a limit cycle behaviour between the thin disc and the slim disc."
 Such a limit evele was confirmed. by time-dependent: numerical caleulations (e.g... Szuszkiewicz Aller POOL: Lietal. 20073).," Such a limit cycle was confirmed by time-dependent numerical calculations (e.g., Szuszkiewicz Miller 2001; \citealp{Li07}) )."
 On the other hand. 3ellonietal.(1997) applied. the limit evele theory to interpret the observational quasi-periodic variability of CIUS 1915.," On the other hand, \cite{Belloni97} applied the limit cycle theory to interpret the observational quasi-periodic variability of GRS 1915."
 Itecentlyv. such limit evele has also been applied to voung radio galaxies (o... Czernyctal.2009:\Wu 2009)).," Recently, such limit cycle has also been applied to young radio galaxies (e.g., \citealp{Czerny09,Wu09}) )."
 Comparing the numerical. results with the observationa ones. however. we can [ind the following inconsistency between the theory and the observation.," Comparing the numerical results with the observational ones, however, we can find the following inconsistency between the theory and the observation."
 The numerica results of Li et al. (, The numerical results of Li et al. (
2007) showed that the duration of the outburst. phase fuis is less than 5 percent of the duration of the quiescent. phase fy... and the luminosity of the outburs phase Luisn is around two orders of magnitude larger than that of the quicseent phase Lis: whereas observations of GAS 1915 showed that. fain is comparable to fie. and Luis is only 3-20 times larger than Lis (e.g. Yollonietal.LOOT:Wuetal. 20100).,"2007) showed that the duration of the outburst phase $t_{\rm high}$ is less than 5 percent of the duration of the quiescent phase $t_{\rm low}$, and the luminosity of the outburst phase $L_{\rm high}$ is around two orders of magnitude larger than that of the quiescent phase $L_{\rm low}$; whereas observations of GRS 1915 showed that, $t_{\rm high}$ is comparable to $t_{\rm low}$ and $L_{\rm high}$ is only 3-20 times larger than $L_{\rm low}$ (e.g., \citealp{Belloni97, Wu10}) )."
 Some cllorts have been made to improve he theory in order to explain observations either by some artifical viscosity. prescription (e.g.. Navakshinetal. 2000)) or by additional assumption of the energy exchange between he dise and corona (Janiuk et al.," Some efforts have been made to improve the theory in order to explain observations either by some artifical viscosity prescription (e.g., \citealp{Nayakshin00}) ) or by additional assumption of the energy exchange between the disc and corona (Janiuk et al."
 2002)., 2002).
 In the present paper. we will investigate this. issue hrough another way by taking the stress evolution process into account.," In the present paper, we will investigate this issue through another way by taking the stress evolution process into account."
 Our paper is organized as follows., Our paper is organized as follows.
 In Section 2. we describe the basic assumption for the stress evolution oocess.," In Section 2, we describe the basic assumption for the stress evolution process."
 “Phe time-dependent. equations and linear stability analvsis are presented in Sections 3 and 4. respectively.," The time-dependent equations and linear stability analysis are presented in Sections 3 and 4, respectively."
 Conclusions and discussion are mace in Section 5., Conclusions and discussion are made in Section 5.
Almost 40 vears ago. it was sugeested that the centres of galaxies host supermassive black holes and. further. that accretion onto those black holes powers active galactic nuclei (AGN: Salpeter 1964: Zeldovich 1964: Lyncden-Bell 1969).,"Almost 40 years ago, it was suggested that the centres of galaxies host supermassive black holes and, further, that accretion onto those black holes powers active galactic nuclei (AGN; Salpeter 1964; Zeldovich 1964; Lynden-Bell 1969)."
 Nowadays. the observational evidence in support of this picture is substantial.," Nowadays, the observational evidence in support of this picture is substantial."
" Proper motion studies of the stars in the centralmost regions of the Milky Way provide compelling evidence for the presence of a supermassive black hole with amass of about 8.10""M. (Eckart Genzel 1997: Chez el al.", Proper motion studies of the stars in the centralmost regions of the Milky Way provide compelling evidence for the presence of a supermassive black hole with a mass of about $3\times 10^6\Msun$ (Eckart Genzel 1997; Ghez et al.
 1998. 2000. 2003: Eckart el al.," 1998, 2000, 2003; Eckart et al."
 2002: Schóddel οἱ al., 2002; Schöddel et al.
 2002)., 2002).
 The kinematics of rotating central eas disks in several nearby low-Iuminosity AGN has also provided some of the most convincing evidence for supermassive black holes (for example. AIST: Ford et al.," The kinematics of rotating central gas disks in several nearby low-luminosity AGN has also provided some of the most convincing evidence for supermassive black holes (for example, M87: Ford et al."
 1994. Harms ct al.," 1994, Harms et al."
 1994: NGC 4258: Alivoshi ct al., 1994; NGC 4258: Miyoshi et al.
 1995: Greenhill et al..," 1995; Greenhill et al.,"
. 1995)., 1995).
 Finally. spectroscopic studies of stellar. kinematics reveal that almost all galaxies studied to date do indeed: possess a," Finally, spectroscopic studies of stellar kinematics reveal that almost all galaxies studied to date do indeed possess a"
Dises also show overall lower colour terms. regardless of the structure of interstellar dust.,"Discs also show overall lower colour terms, regardless of the structure of interstellar dust."
" The geometrical parameters derived from SExtractor (namely. the semimajor axis. e. and semiminor axis. b. of the largest ellipsoidal isophote encircling the galaxy) can be used to roughly estimate the inclination angle of the galaxy along the line of sight Gf the observed galaxy is approximated as a dise of radius /?—a. the inclination angle along the line of sight can be expressed as 0,,,=(90 /2x)acos(b/a))."," The geometrical parameters derived from SExtractor (namely, the semimajor axis, $a$, and semiminor axis, $b$, of the largest ellipsoidal isophote encircling the galaxy) can be used to roughly estimate the inclination angle of the galaxy along the line of sight (if the observed galaxy is approximated as a disc of radius $R=a$, the inclination angle along the line of sight can be expressed as $\theta_{\rmn{los}} = (90^{\circ}/2\pi)\rmn{acos}(b/a)$ )."
 We find that the very red galaxies all have inclination angles between 30° and 60°., We find that the very red galaxies all have inclination angles between $\degr$ and $\degr$.
 This suggests that these galaxies could appear reddened by superposition of a possibly thick dise over a relatively small bulge., This suggests that these galaxies could appear reddened by superposition of a possibly thick disc over a relatively small bulge.
 In this case. the expected attenuation coefficient is almos negligible in the near-IR. whieit can range from 0.2 to about 0.5 in the {2 band.," In this case, the expected attenuation coefficient is almost negligible in the near-IR, while it can range from 0.2 to about 0.5 in the $B$ band."
 We thus interpret the very red galaxies as dises with an overall evolved stellar populaion (i.e. belonging to the RS) and reatively low dust content. which are preferentially reddened because of their inclination.," We thus interpret the very red galaxies as discs with an overall evolved stellar population (i.e. belonging to the RS) and relatively low dust content, which are preferentially reddened because of their inclination."
 Following t1s. we stack the sub-mm maps on he combined catalogue of red and RS galaxies. considering them as a single population.," Following this, we stack the sub-mm maps on the combined catalogue of red and RS galaxies, considering them as a single population."
 We see that the addition of very red galaxies results in a mean SED consistent with that from RS galaxies., We see that the addition of very red galaxies results in a mean SED consistent with that from RS galaxies.
 Results of stacking are reported in Table 3., Results of stacking are reported in Table 3.
 To better characterize the nature of the optical counterparts to the bright BLAST sources. we investigate their location in the CM diagram and their optical colours.," To better characterize the nature of the optical counterparts to the bright BLAST sources, we investigate their location in the CM diagram and their optical colours."
 Fig., Fig.
 ?. shows the position in the CM diagram of the cluster members identified as BLAST counterparts., \ref{redseq} shows the position in the CM diagram of the cluster members identified as BLAST counterparts.
 These five galaxies all lie in a narrow region of the CM diagram. with a mean colour ΙΕ = 1.38 + 0.08 and magnitudes below (texeluding IRAS 03152-4427. which has a magnitude of order of A).," These five galaxies all lie in a narrow region of the CM diagram, with a mean colour $B-R$ ) = 1.38 $\pm$ 0.08 and magnitudes below (excluding IRAS 03152–4427, which has a magnitude of order of )."
 Several studies have revealed the presence of trends in the star-formation activity of cluster galaxies with respect to the cluster-centric radius., Several studies have revealed the presence of trends in the star-formation activity of cluster galaxies with respect to the cluster-centric radius.
 This is usually interpreted as a combination of environmental effects that trigger star-formation episodes in galaxies infalling on the cluster from the field., This is usually interpreted as a combination of environmental effects that trigger star-formation episodes in galaxies infalling on the cluster from the field.
 Investigating the radial distribution of sub-mm emission from cluster members can help in better understanding how the environment affects cluster galaxies and to what extent these effects are detected at FIR wavelengths., Investigating the radial distribution of sub-mm emission from cluster members can help in better understanding how the environment affects cluster galaxies and to what extent these effects are detected at FIR wavelengths.
 We thus divide our spectroscopic catalogue of 146 cluster members into radial bins centered on the BCG. whose position is coincident with the dynamical centre of the cluster.," We thus divide our spectroscopic catalogue of 146 cluster members into radial bins centered on the BCG, whose position is coincident with the dynamical centre of the cluster."
 We define the bins so that each contains similar numbers of objects to ensure homogeneous stacking statistics., We define the bins so that each contains similar numbers of objects to ensure homogeneous stacking statistics.
 We find that 25 galaxies per bin is a good compromise between number of bins (6) and S/N ratio., We find that 25 galaxies per bin is a good compromise between number of bins (6) and S/N ratio.
 The radial plot of the mean stacked flux density (see Fig. 62) , The radial plot of the mean stacked flux density (see Fig. \ref{stackrad}) )
shows two signiticant (~ 4c) peaks atmieron., shows two significant $\sim 4\sigma$ ) peaks at.
. The outermost of these peaks is detected at abou1L.5/?595.. Le. outside the gravitational radius of the cluster (this region is only covered by the shallower part ofthe BLAST map and thus the stacking results are quite noisy).," The outermost of these peaks is detected at about, i.e. outside the gravitational radius of the cluster (this region is only covered by the shallower part of the BLAST map and thus the stacking results are quite noisy)."
 This is expected. since a radii 2 the infall of galaxies from the field is expected to be most noticeable. and thus an increase in the mean SFR is expectec (e.g. 2).," This is expected, since at radii $\gtrsim$ the infall of galaxies from the field is expected to be most noticeable, and thus an increase in the mean SFR is expected (e.g. \citealt{Balogh99}) )."
 This signal drops at longer wavelengths., This signal drops at longer wavelengths.
 A second peak is detected closer to the cluster core. around0.," A second peak is detected closer to the cluster core, around."
6/?»05.. To investigate whether this peak is genuinely due to the presence of the cluster. we use the same method and stack the BLAST-BGS map (Devlin et al.," To investigate whether this peak is genuinely due to the presence of the cluster, we use the same method and stack the BLAST-BGS map (Devlin et al."
 2009) on simulated catalogues., 2009) on simulated catalogues.
 Since the BGS is a blank field. we can use it to assess the probability of random occurrence of a radial peak with the same Significance as detected in A3112.," Since the BGS is a blank field, we can use it to assess the probability of random occurrence of a radial peak with the same significance as detected in A3112."
 We thus generate 10000 sets of 146 positions. randomly distributed around a centre and on an area equivalent to the map of A3112. stack the BGS map on each. look for the presence of a radial peak and calculate its deviation from the mean of the radial profile.," We thus generate 10000 sets of 146 positions, randomly distributed around a centre and on an area equivalent to the map of A3112, stack the BGS map on each, look for the presence of a radial peak and calculate its deviation from the mean of the radial profile."
 To test if the presence of a cluster affects the outcome of the stacking analysis. we also simulate 10000 catalogues of 146 normally distributed positions over the same area (we use the value of found for A3112 as the standard deviation of the distribution. to roughly reproduce a density profile consistent with the presence of a cluster).," To test if the presence of a cluster affects the outcome of the stacking analysis, we also simulate 10000 catalogues of 146 normally distributed positions over the same area (we use the value of found for A3112 as the standard deviation of the distribution, to roughly reproduce a density profile consistent with the presence of a cluster)."
 We tind that the probability of random occurrence of a peak as significant as that detected in A3112 is less than LO7 in all cases., We find that the probability of random occurrence of a peak as significant as that detected in A3112 is less than $10^{-5}$ in all cases.
 Limiting this analvsis to the BGS-Deep or BGS-Wide maps also yields similar results., Limiting this analysis to the BGS-Deep or BGS-Wide maps also yields similar results.
 To eheck independently the significance of this peak. we also compare the stacked values with two radial profiles: a flat profile with value equal to the mean of the stacked values and a Gaussian- profile which we assume as a representation of the peak.," To check independently the significance of this peak, we also compare the stacked values with two radial profiles: a flat profile with value equal to the mean of the stacked values and a Gaussian-shaped profile which we assume as a representation of the peak."
 A Kolmogorov-Smirnov (KS) test shows that the flat profile is ruled out with a rejection probability of 0.9996. while a peaked profile is accepted with very high probability (rejection of 9«10.+).," A Kolmogorov–Smirnov (KS) test shows that the flat profile is ruled out with a rejection probability of 0.9996, while a peaked profile is accepted with very high probability (rejection of $9\times10^{-4}$ )."
 We also test the same profiles by stacking in smaller radial bins ¢12—20 objects per bin): although the data are noisier due to lower statistics. the flat profile is still ruled out while the peaked profile provides a good fit.," We also test the same profiles by stacking in smaller radial bins (12–20 objects per bin); although the data are noisier due to lower statistics, the flat profile is still ruled out while the peaked profile provides a good fit."
 We also notice that the cluster members matching the position of micron--detected sources mostly lie at the distance of the inner radial peak., We also notice that the cluster members matching the position of -detected sources mostly lie at the distance of the inner radial peak.
 These galaxies do not appear to be clustered among themselves. being instead randomly distributed azimuthally.," These galaxies do not appear to be clustered among themselves, being instead randomly distributed azimuthally."
 In order to evaluate whether the peak is entirely due to the presence of these galaxies. we stack our catalogue after removing them.," In order to evaluate whether the peak is entirely due to the presence of these galaxies, we stack our catalogue after removing them."
 Although the peak shows a lower deviation from the mean value (~ 20) a flat profile again has a low probability of being a good representation of the data (although with a lower rejection probability of 0.3).," Although the peak shows a lower deviation from the mean value $\sim 2\sigma$ ), a flat profile again has a low probability of being a good representation of the data (although with a lower rejection probability of 0.3)."
 A peaked profile has again a very low rejection probability (1.3.10. 2). thus providing a robust representation of the data.," A peaked profile has again a very low rejection probability $1.3\times10^{-3}$ ), thus providing a robust representation of the data."
 The same analysis on the 350 and data shows no significant peak at the same position. although cluster members from the innermost bin show on average a non-zero mean flux density.," The same analysis on the 350 and data shows no significant peak at the same position, although cluster members from the innermost bin show on average a non-zero mean flux density."
 The significance of this signal is nevertheless low (~ 1.57)., The significance of this signal is nevertheless low $\sim 1.5\sigma$ ).
 To ensure that no selection effect in the input catalogue is biasing this result. we also investigate the (5.77) colour of galaxies in each bin.," To ensure that no selection effect in the input catalogue is biasing this result, we also investigate the $(B-R)$ colour of galaxies in each bin."
 We find that all radial bins (but the innermost) are populated by a mix of red-sequence and blue galaxies. thus assuring that the peak is not due to undersampling of blue (i.e. galaxies at radii of the order ofooo.," We find that all radial bins (but the innermost) are populated by a mix of red-sequence and blue galaxies, thus assuring that the peak is not due to undersampling of blue (i.e. star-forming) galaxies at radii of the order of."
.. The number of blue galaxies is indeed the same (4—5) in all radial bins., The number of blue galaxies is indeed the same (4–5) in all radial bins.
 We can also stack maps on the spectroscopic catalogue of cluster members after dividing into bins of absolute magnitude. to study how the sub-mm BLAST flux is distributed across the cluster luminosity/mass function.," We can also stack maps on the spectroscopic catalogue of cluster members after dividing into bins of absolute magnitude, to study how the sub-mm BLAST flux is distributed across the cluster luminosity/mass function."
 Although the available data do not allow us to probe the dwarf population of cluster members. they cover three full magnitudes in the band. enough to reach intermediate-luminosity galaxies down to /Vz---2.," Although the available data do not allow us to probe the dwarf population of cluster members, they cover three full magnitudes in the band, enough to reach intermediate-luminosity galaxies down to +2."
 As in the case, As in the case
"case, the kinked part of the flux tube in black is submerged with two effects.","case, the kinked part of the flux tube in black is submerged with two effects."
 The submergence elongates the vertical thickness of the kinked part of the flux tube while the cross section of the tube becomes more narrow., The submergence elongates the vertical thickness of the kinked part of the flux tube while the cross section of the tube becomes more narrow.
 This elongation may be produced by a downward displacement that is larger at the bottom than at the top of the kinked part of the tube., This elongation may be produced by a downward displacement that is larger at the bottom than at the top of the kinked part of the tube.
 The three-dimensionality of our magnetostatic solution is essential., The three-dimensionality of our magnetostatic solution is essential.
" If the field does not vary in x, we would have a flux layer rather than a flux tube."," If the field does not vary in $x$, we would have a flux layer rather than a flux tube."
 The entire atmosphere lying above it is trapped and cannot fall through without breaking the layer with variation in x., The entire atmosphere lying above it is trapped and cannot fall through without breaking the layer with variation in $x$.
" In our case, we have a true flux tube with a finite cross-sectional area."," In our case, we have a true flux tube with a finite cross-sectional area."
" This means that the atmosphere external to the flux tube can yield and flow around a rising flux tube, for example."," This means that the atmosphere external to the flux tube can yield and flow around a rising flux tube, for example."
" Moreover, the narrowing of the cross section of the tube enhances the magnetic pressure in the tube, which naturally produces a siphon flow along the flux tube to drain fluid down the far arms of the tube (Pikel'Ner1971;Thomas1988).."," Moreover, the narrowing of the cross section of the tube enhances the magnetic pressure in the tube, which naturally produces a siphon flow along the flux tube to drain fluid down the far arms of the tube \citep{Pikelner1971, Thomas1988}."
 The reduced weight of the tops of the tube becomes more buoyant and rise to a greater height., The reduced weight of the tops of the tube becomes more buoyant and rise to a greater height.
 This brings about equilibrium with the external atmospheric pressure and a final balance between buoyancy and magnetic tension forces., This brings about equilibrium with the external atmospheric pressure and a final balance between buoyancy and magnetic tension forces.
" The dynamical process builds up stress that pushes the two far arms away from the origin while at the same time brings the two opposite-polarity elements on either sides of the origin closer together, in a manner similar to the observations reported in this paper."," The dynamical process builds up stress that pushes the two far arms away from the origin while at the same time brings the two opposite-polarity elements on either sides of the origin closer together, in a manner similar to the observations reported in this paper."
 In our observations the canceling opposite-polarity elements have fields that return to the photosphere at distances much larger than 10 hydrostatic scale heights from the canceling sites., In our observations the canceling opposite-polarity elements have fields that return to the photosphere at distances much larger than 10 hydrostatic scale heights from the canceling sites.
" We expect the buoyancy force to dominate in the atmospheric portion of the field, keeping the tops of these fields up in the chromosphere and above."," We expect the buoyancy force to dominate in the atmospheric portion of the field, keeping the tops of these fields up in the chromosphere and above."
 This simple theoretical analysis illustrates the interplay among the magnetic and hydrodynamic forces in the submergence of a field connection that happens to be located right at a subphotospheric convective downdraft., This simple theoretical analysis illustrates the interplay among the magnetic and hydrodynamic forces in the submergence of a field connection that happens to be located right at a subphotospheric convective downdraft.
 We of course need 3D time-dependent MHD simulations to examine the dynamics of this process to get a complete physical picture., We of course need 3D time-dependent MHD simulations to examine the dynamics of this process to get a complete physical picture.
"that line up in filaments, while smaller voids, such as the one at (x=77,yτὸ) Mpc/h have more spherical shapes and have more massive haloes around them.","that line up in filaments, while smaller voids, such as the one at $(x=77,y=73)$ $/h$ have more spherical shapes and have more massive haloes around them."
" Note that some numerical efforts in order to simulate the intergalactic voids are required: on one side large volumes need to be simulated in order to sample the void distribution at large sizes, on the other side relatively high resolution is mandatory."," Note that some numerical efforts in order to simulate the intergalactic voids are required: on one side large volumes need to be simulated in order to sample the void distribution at large sizes, on the other side relatively high resolution is mandatory."
" In fact, with poor resolution the denser regions at the edge of voids are not properly resolved and will result in a smaller amount of neutral hydrogen and thereby less absorption: this will cause an overestimate of the void sizes."," In fact, with poor resolution the denser regions at the edge of voids are not properly resolved and will result in a smaller amount of neutral hydrogen and thereby less absorption: this will cause an overestimate of the void sizes."
" The parameters chosen here, including the thermal history of the IGM, are in reasonably good agreement with observational constraints and with recent results from CMB data, weak lensing and other data sets obtained from the forest (e.g. ?,, ?))."," The parameters chosen here, including the thermal history of the IGM, are in reasonably good agreement with observational constraints and with recent results from CMB data, weak lensing and other data sets obtained from the forest (e.g. \citet{viel06}, \citet{lesg}) )."
" The mock QSO spectra extracted from the simulations have the same resolution and noise properties as the observed ones, even though this will not affect our results."," The mock QSO spectra extracted from the simulations have the same resolution and noise properties as the observed ones, even though this will not affect our results."
" Here, for two reasons we consideronly simulation snapshots at z~ 2."," Here, for two reasons we consideronly simulation snapshots at $z\sim 2$ ."
" First, the"," First, the"
available the g. 7 and / magnitudes. we cannot expect to reconstruct the spectrum using the four principal components tabulated bv MeGurketal.(2010). [rom only 2 measurements.,"available the $g$ , $r$ and $i$ magnitudes, we cannot expect to reconstruct the spectrum using the four principal components tabulated by \cite{mcgurk10} from only 3 measurements."
 As a consequence. we have (ο limit the reconstruction to only the average spectrum plus two principal components. leading to slightly larger errors.," As a consequence, we have to limit the reconstruction to only the average spectrum plus two principal components, leading to slightly larger errors."
 sunmmarizineg. fom (he knowledge of the svstem response at each waveleneth. the principal components associated to the g—r bin of the star and the g. r. and / magnitudes. one is able to reconstruct the stellar spectrum by solving the linear svstem of Eq. (16))," Summarizing, from the knowledge of the system response at each wavelength, the principal components associated to the $g-r$ bin of the star and the $g$, $r$, and $i$ magnitudes, one is able to reconstruct the stellar spectrum by solving the linear system of Eq. \ref{eq:linear_system_reconstruction}) )"
 and using the coefficients in the linear expansion given by Eq. (10))., and using the coefficients in the linear expansion given by Eq. \ref{eq:develop}) ).
 We carry out reconstructions using magnitudes svnthesized [rom observed spectra included in SDSS Data Release 7., We carry out reconstructions using magnitudes synthesized from observed spectra included in SDSS Data Release 7.
 The svnthetic magnitudes are obtained following Eq. (4)), The synthetic magnitudes are obtained following Eq. \ref{eq:magnitudes}) )
 for fillers g. r aud 7.," for filters $g$, $r$ and $i$."
 These could be taken directly. from the photometric observations iusteacl., These could be taken directly from the photometric observations instead.
 The sensing matrix is built using Eq. (8))., The sensing matrix is built using Eq. \ref{eq:sensing_matrix_final}) ).
 The spectrum of four representative stars from the sample are reconstructed. solving the linear svstem of Eq. (16))., The spectrum of four representative stars from the sample are reconstructed solving the linear system of Eq. \ref{eq:linear_system_reconstruction}) ).
 The success of the technique is shown in Fig. 2.., The success of the technique is shown in Fig. \ref{fig:reconstruction_example}.
 As stated before. to (his aim we make use only of the mean spectrum and two principal components.," As stated before, to this aim we make use only of the mean spectrum and two principal components."
 The original noisy spectrum is shown in black color., The original noisy spectrum is shown in black color.
 The projection of the observed spectrum on (he space spanned by (he first three principal components is shown in red color., The projection of the observed spectrum on the space spanned by the first three principal components is shown in red color.
 This constitutes the best possible reconstruction that we could achieve with the presented method., This constitutes the best possible reconstruction that we could achieve with the presented method.
 The spectrum reconstructed with our technique using the magnitude in the fillers gor. and 7 is shown in blue.," The spectrum reconstructed with our technique using the magnitude in the filters $g$, $r$, and $i$ is shown in blue."
 Note that the reconstruction Closely follows the red curve. indicating Chat a good reconstruction is possible and that the projection along the first three principal components can be obtained reliably from the linear measurements made with the SDSS filters.," Note that the reconstruction closely follows the red curve, indicating that a good reconstruction is possible and that the projection along the first three principal components can be obtained reliably from the linear measurements made with the SDSS filters."
 The fundamental characteristics of the spectra are reproduced with precision. making il possible to empirically infer spectroscopic quantities using photometric measurements.," The fundamental characteristics of the spectra are reproduced with precision, making it possible to empirically infer spectroscopic quantities using photometric measurements."
 Ai (he same time. thanks to the projection along the principal components. the spectrum reconstructed from gri magnitudes is automatically denoised (see.e.g..MartinezGonzálezelal.2008.forthedenoisingcapabilitiesof PCA)...," At the same time, thanks to the projection along the principal components, the spectrum reconstructed from $gri$ magnitudes is automatically denoised \citep[see, e.g.,][for the denoising capabilities of PCA]{marian_pcafilter08}."
 Particularly large residuals are visible at specific wavelengths in Fig. 2.., Particularly large residuals are visible at specific wavelengths in Fig. \ref{fig:reconstruction_example}.
 In. panel a) we can spot some issues wilh skv removal al the ereen [OI] line (5577 ) and in the IR end., In panel a) we can spot some issues with sky removal at the green [OI] line (5577 ) and in the IR end.
 In panels b). ο) and d) there are strong residuals around the transitions of the Balmer series and other strong features.," In panels b), c) and d) there are strong residuals around the transitions of the Balmer series and other strong features."
 These residuals change sien verv quickly around (he central wavelength. signaling a horizontal offset between the original and the reconstructed spectra. most likely relatedto the Dopper velocity shifts. which have not been corrected but happen to be small enough for (he star depicted in panel," These residuals change sign very quickly around the central wavelength, signaling a horizontal offset between the original and the reconstructed spectra, most likely relatedto the Dopper velocity shifts, which have not been corrected but happen to be small enough for the star depicted in panel"
evaporation model could explain (he existence of an inner disk al intermediate states.,evaporation model could explain the existence of an inner disk at intermediate states.
 The original disk evaporation model was proposed by Meyer \lever-Lolmeister (1994). where the magnetic field is not included since (he work aims a( explaining the UV lag observed in dwarf novae.," The original disk evaporation model was proposed by Meyer Meyer-Hofmeister (1994), where the magnetic field is not included since the work aims at explaining the UV lag observed in dwarf novae."
 Bul magnetic field has long been realized to plav an important role in aceretion disks (S873)., But magnetic field has long been realized to play an important role in accretion disks (SS73).
 Recently. observations also reveal the magnetic nature of disk accretion onto black holes (Miller et al.," Recently, observations also reveal the magnetic nature of disk accretion onto black holes (Miller et al."
 2006)., 2006).
 Meyer Mever-ILofmeister (2002) have included magnetic pressure in the disk evaporation model in order to explain (he clifferent iruncation radii of the outer thin disks between (the nuclei of elliptical galaxies and low huninosity AGN. which have similar Edclington-scaled accretion rate (normalized. by the Eddington accretion rate Mica=Lyaa/ij. where Ly is the Eddington luminosity. and η is (he efficiency of energy conversion).," Meyer Meyer-Hofmeister (2002) have included magnetic pressure in the disk evaporation model in order to explain the different truncation radii of the outer thin disks between the nuclei of elliptical galaxies and low luminosity AGN, which have similar Eddington-scaled accretion rate (normalized by the Eddington accretion rate $\dot{M}_{\rm Edd}=L_{\rm Edd}/\eta c^2$, where $L_{\rm Edd}$ is the Eddington luminosity, and $\eta$ is the efficiency of energy conversion)."
 One temperature model(hereafter 1-T. which means that the electrons and ions in the corona have the same temperature) was used in (his previous studs.," One temperature model(hereafter 1-T, which means that the electrons and ions in the corona have the same temperature) was used in this previous study."
 Besides the contribution of the magnetic pressure to the total pressure. magnetic field can also affect the heat conduction.," Besides the contribution of the magnetic pressure to the total pressure, magnetic field can also affect the heat conduction."
 Mever Mever-HofBneister (2006) already took Chis effect into account together with the irradiation/Comptoniz processes. and found (hat the variation of heat conduction can change the i»—7 relation significantlv.," Meyer Meyer-Hofmeister (2006) already took this effect into account together with the irradiation/Comptonization processes, and found that the variation of heat conduction can change the $\dot{m}-r$ relation significantly."
 In (his paper. we intend to investigate the influence of magnetic field on both the pressure and heat conduction in detail with a more realistic (wo temperature model (hereafter 2-T. which means that the electrons ancl ions in the corona have different temperatures. Liu et al.," In this paper, we intend to investigate the influence of magnetic field on both the pressure and heat conduction in detail with a more realistic two temperature model (hereafter 2-T, which means that the electrons and ions in the corona have different temperatures, Liu et al."
 20024)., 2002a).
 We present more detailed numerical results aud also give the fitting formula to (he numerical results. which enables the comparison of theory. and observations much easier.," We present more detailed numerical results and also give the fitting formula to the numerical results, which enables the comparison of theory and observations much easier."
 In 82 we briefly describe the model and basic equations: in 33 we present (he numerical results; in 84 our results are compared wilh observations: in 5 we discuss the mocel itself and present our conclusions in 86., In 2 we briefly describe the model and basic equations; in 3 we present the numerical results; in 4 our results are compared with observations; in 5 we discuss the model itself and present our conclusions in 6.
 Following previous works on disk evaporation (Meyer Mever-Ilofineister 1994: Liu. Alever Mever-IHofneister 1995: Mever et al 2000a; Lin et al.," Following previous works on disk evaporation (Meyer Meyer-Hofmeister 1994; Liu, Meyer Meyer-Hofmeister 1995; Meyer et al 2000a; Liu et al."
 2002a). we pav our main atlentions to the transition region between a SSD and a RIAF. which is characterized by a (hin disk sanclwiched by the corona flow.," 2002a), we pay our main attentions to the transition region between a SSD and a RIAF, which is characterized by a thin disk sandwiched by the corona flow."
 The viscous heat of ious is partially transferred io electrons by collisions and conducted down by electrons to the transition laver. which is cooler and denser.," The viscous heat of ions is partially transferred to electrons by collisions and conducted down by electrons to the transition layer, which is cooler and denser."
 Part of the cool matter in the transition laver is heated and evaporated into (he corona till an equilibrium density is reached., Part of the cool matter in the transition layer is heated and evaporated into the corona till an equilibrium density is reached.
 The gas in the corona carries similar, The gas in the corona carries similar
Our second result is that Uf this. as expected. will lead to an exceptionally extended [C/Fe] vs [N/Fe] anti-correlation. it would certainly be worthwhile to follow-up on M 15 with large samples of high-resolution spectra. to better study the presence of multiple populations also in the Na-O plane.,"Our second result is that If this, as expected, will lead to an exceptionally extended [C/Fe] vs [N/Fe] anti-correlation, it would certainly be worthwhile to follow-up on M 15 with large samples of high-resolution spectra, to better study the presence of multiple populations also in the Na-O plane."
 Given its peculiar properties (Sect. 5.11)).," Given its peculiar properties (Sect. \ref{sec-m15}) ),"
 M 15 could even belong to the group of massive clusters that have undergone more self-enrichment than usual. either because of their special properties or because they could be the remnants of accreted dwarf galaxies (such as ω Cen).," M 15 could even belong to the group of massive clusters that have undergone more self-enrichment than usual, either because of their special properties or because they could be the remnants of accreted dwarf galaxies (such as $\omega$ Cen)."
 Therefore. also further searches for variations in heavier species such as Ca. Fe. or Ba should be extremely interesting.," Therefore, also further searches for variations in heavier species such as Ca, Fe, or Ba should be extremely interesting."
 Our third result is that This challenges to some extent results by(2009a.b).. who find that the first or primordial (P) generation accounts for approximately 1/3 of the total cluster population. leaving space for a fraction for the second or intermediate (D) population.," Our third result is that This challenges to some extent results by, who find that the first or primordial (P) generation accounts for approximately 1/3 of the total cluster population, leaving space for a fraction for the second or intermediate (I) population."
 On the one hand the discrepancy is — at best — marginal. as discussed in Sect.," On the one hand the discrepancy is – at best – marginal, as discussed in Sect."
 6 and given the ample uncertainties involved: on the other hand. the discrepancy could be caused by the Na-O and the CH-CN anti-correlations sampling two sligthly different phenomena (as discussed in Sect. 4.1)).," \ref{sec-trends}
 and given the ample uncertainties involved; on the other hand, the discrepancy could be caused by the Na-O and the CH-CN anti-correlations sampling two sligthly different phenomena (as discussed in Sect. \ref{sec-bimo}) )."
 Certaintly more studies are required to shed more light on this issue. because these kind of discrepancies — if confirmed — could turn out into further clues on the formation and evolution of GGC.," Certaintly more studies are required to shed more light on this issue, because these kind of discrepancies – if confirmed – could turn out into further clues on the formation and evolution of GGC."
 Our fourth result is that While we must stress that the present study is limited to 12 clusters with spectra of modest S/N. the absence of strong corelations has one major implication in. thescenario: it would imply that the population ratio of the two (or more) stellar generations is only mildly Cf at all) influenced by the cluster properties.," Our fourth result is that While we must stress that the present study is limited to 12 clusters with spectra of modest S/N, the absence of strong corelations has one major implication in the: it would imply that the population ratio of the two (or more) stellar generations is only mildly (if at all) influenced by the cluster properties."
 In particular. clusters with larger present-day total masses (and therefore luminosities) could be able to form only sligthly higher fractions of second generation stars with respect to less massive clusters.," In particular, clusters with larger present-day total masses (and therefore luminosities) could be able to form only sligthly higher fractions of second generation stars with respect to less massive clusters."
 Similarly. the relations with cluster orbital parameters could hint that environment has some (minor) rólle in determining the size of the second stellar generation.," Similarly, the relations with cluster orbital parameters could hint that environment has some (minor) rôlle in determining the size of the second stellar generation."
 In summary. the use of low-resolution spectra to study CH and CN bands in GGC stars provides a useful complement to the high-resolution studies. needing less observing time and data analysis effort.," In summary, the use of low-resolution spectra to study CH and CN bands in GGC stars provides a useful complement to the high-resolution studies, needing less observing time and data analysis effort."
 In particular. the use of stars.," In particular, the use of stars."
 Le.. stars that have not undergone first dredge-up mixing. and of two elements such as C and N that (unlikely Na and O) are strictly produced in the same nuclear reaction chains and at the same temperature. can give additional constraints to studies based on red giants only.," i.e., stars that have not undergone first dredge-up mixing, and of two elements such as C and N that (unlikely Na and O) are strictly produced in the same nuclear reaction chains and at the same temperature, can give additional constraints to studies based on red giants only."
2010).,.
. For the ddata of676... we find an e-folding time of ~192=10 clays (see Section ?2?)).," For the data of, we find an e-folding time of $\sim192\pm10$ days (see Section \ref{subsec:decay}) )."
 These decay times provide a measure of the thermal relaxation time of the neutron star crust. which depends on the composition and structure of the lattice. the distribution of heating sources and the thickness of the crust2009).," These decay times provide a measure of the thermal relaxation time of the neutron star crust, which depends on the composition and structure of the lattice, the distribution of heating sources and the thickness of the crust."
. and calculate theoretical cooling curves for.260.. assuming cdillerent. physics for the crust ancl core.," and calculate theoretical cooling curves for, assuming different physics for the crust and core."
 These authors present simulations for both an amorphous crust and an ordered crvstalline lattice., These authors present simulations for both an amorphous crust and an ordered crystalline lattice.
 For the latter. the spread of nuclide charge numbers (Z) in the crust matter is small. which is referred to as a low level of impurities ancl results ina highly conductive crust.," For the latter, the spread of nuclide charge numbers $Z$ ) in the crust matter is small, which is referred to as a low level of impurities and results in a highly conductive crust."
 A large number of impurities gives an amorphous structure. which alfects the thermal properties of the crust ancl results in a low conductivity.," A large number of impurities gives an amorphous structure, which affects the thermal properties of the crust and results in a low conductivity."
 1n addition. explore standard (ie. slow) and enhanced neutrino cooling mechanisms. vielding different core temperatures.," In addition, explore standard (i.e., slow) and enhanced neutrino cooling mechanisms, yielding different core temperatures."
 Coniparing our results on wwith the decav shapes resulting from those calculations suggests that the neutron star has a highly conductive crust. similar to what has been inferred for the other three sources2010).," Comparing our results on with the decay shapes resulting from those calculations suggests that the neutron star has a highly conductive crust, similar to what has been inferred for the other three sources."
. The fact that the decay curve of iis rather shallow may be explained in terms of a relatively small temperature. gradient. and. thus lower thermal [lux across the core-crust boundary., The fact that the decay curve of is rather shallow may be explained in terms of a relatively small temperature gradient and thus lower thermal flux across the core-crust boundary.
2002).. This can be due to a combination of a warm neutron star core and a relatively low mass-accretion rate curing outburst., This can be due to a combination of a warm neutron star core and a relatively low mass-accretion rate during outburst.
 The exponential decay fit to the delata of indicates that the neutron star crust might already be close to restoring equilibrium with the core., The exponential decay fit to the data of indicates that the neutron star crust might already be close to restoring equilibrium with the core.
 The fit results in a quiescent base level of 107.9+0.2 eV. while we found a temperature of 108.631.1 eV for the observation performed in 2010 April.," The fit results in a quiescent base level of $107.9\pm0.2$ eV, while we found a temperature of $108.6\pm1.1$ eV for the observation performed in 2010 April."
 Prior to its last outburst. wavas observed in quiescence with the oobservatory. displaying a 0.510 keV unabsorbed Εαν of S4D210PDereem.7«11999)..," Prior to its last outburst, was observed in quiescence with the observatory, displaying a 0.5–10 keV unabsorbed flux of $8.4^{+4.2}_{-1.7} \times 10^{-13}~\flux$."
 Our oobservations of 2010 April detected aab a 0.5LO keV unabsorbed Dux of (7.7x0.2)10Dergem7s+ (see Table 2))., Our observations of 2010 April detected at a 0.5–10 keV unabsorbed flux of $(7.7\pm0.2) \times 10^{-13}~\flux$ (see Table \ref{tab:spec}) ).
 Assuming that the cleletection caught aab its quiescent base level. this supports the idea that the crust has nearly. cooled. down.," Assuming that the detection caught at its quiescent base level, this supports the idea that the crust has nearly cooled down."
 This would imply that the neutron star core in iis relatively hot.2009).. suggesting that either standard cooling mechanisms are operating and that the neutron star is not very massive. or that the time-averaged mass-accretion rate of the svstem is very high due to a short recurrence time (see below).," This would imply that the neutron star core in is relatively hot, suggesting that either standard cooling mechanisms are operating and that the neutron star is not very massive, or that the time-averaged mass-accretion rate of the system is very high due to a short recurrence time (see below)."
 The energv deposited. curing outburst is. given by Law0AlQuisfin2001).. Llere., The energy deposited during outburst is given by $L_{\mathrm{nuc}} \sim \langle \dot{M} \rangle Q_{\mathrm{nuc}}/m_{\mathrm{u}}$.
 Qune~2 MeV isthe nuclear energy deposited per accreted barvon2008).. nu is the atomic mass unit and £25 is the time-averaged rate of the system.," Here, $Q_{\mathrm{nuc}}\sim2$ MeV isthe nuclear energy deposited per accreted baryon, $m_{\mathrm{u}}$ is the atomic mass unit and $\langle \dot{M} \rangle$ is the time-averaged accretion rate of the system."
" The latter can be expressed as accretion(A)=(Man fonfbyoo. Where (AL is the average aceretion rate during outburst episodes. £3, is the"," The latter can be expressed as $\langle \dot{M} \rangle = \langle \dot{M}_{\mathrm{ob}} \rangle \times t_{\mathrm{ob}} / t_{\mathrm{rec}}$ , where $\langle \dot{M}_{\mathrm{ob}} \rangle$ is the average accretion rate during outburst episodes, $t_{\mathrm{ob}}$ is the"
ionising field is more likely to come from some other source given the relatively high metallicity and zero redshift.,ionising field is more likely to come from some other source given the relatively high metallicity and zero redshift.
 For example that knot is old enough that there could be an accreting black hole or neutron star present producing harder radiation., For example that knot is old enough that there could be an accreting black hole or neutron star present producing harder radiation.
 We have not yet attempted to include such emission in our models yet., We have not yet attempted to include such emission in our models yet.
 Therefore we have calculated the EW of the Hell line of Tol A ignoring the A4 knot., Therefore we have calculated the EW of the HeII line of Tol A ignoring the A4 knot.
 We plot our model line strengths against age in Figure 5 compared to the observed EW of features in the Tol A B regions.," We plot our model line strengths against age in Figure \ref{final7b}
 compared to the observed EW of features in the Tol A B regions."
 We find that single star and binary models are both able to reproduce the observed EW in these features simultaneously at around 109? years., We find that single star and binary models are both able to reproduce the observed EW in these features simultaneously at around $10^{6.5}$ years.
 We also show how show how the H-8 EW varies with age in Figure 6.., We also show how show how the $\beta$ EW varies with age in Figure \ref{final5}.
 While we find that the EW broadly agrees with those observed for Tol A B we do not use them to derive the ages of the stellar population., While we find that the EW broadly agrees with those observed for Tol A B we do not use them to derive the ages of the stellar population.
 The best fit metallicity is an LMC-like metallicity of 0.470.," The best fit metallicity is an LMC-like metallicity of $0.4{\rm
 Z}_{\odot}$."
 The age of Tol A is constrained to be from 109? and 1097 years., The age of Tol A is constrained to be from $10^{6.5}$ and $10^{6.7}$ years.
" At ages outside this range the stellar features are too weak to agree with the observed values, or for the binary models, too strong."," At ages outside this range the stellar features are too weak to agree with the observed values, or for the binary models, too strong."
 For Tol B the age is constrained to be less than 1094 years., For Tol B the age is constrained to be less than $10^{6.4}$ years.
" To verify the best fit ages and metallicities we show a more detailed comparison between these models and the observed spectra for Tol A and B in Figures 7 and 8 respectively, considering the three key WR diagnostic features and also the ultraviolet CIV absorption/emission feature at1550À,, which is sensitive to the presence of massive stars and in particular winds driven from O-stars."," To verify the best fit ages and metallicities we show a more detailed comparison between these models and the observed spectra for Tol A and B in Figures \ref{final8a} and \ref{final8b} respectively, considering the three key WR diagnostic features and also the ultraviolet CIV absorption/emission feature at, which is sensitive to the presence of massive stars and in particular winds driven from O-stars."
" For Tol A, we find reasonable visual fits between 109? and 109-9 years at both SMC (0.279) and LMC metallicities."," For Tol A, we find reasonable visual fits between $10^{6.5}$ and $10^{6.6}$ years at both SMC $0.2{\rm Z}_{\odot}$ ) and LMC metallicities."
 The CIV line requires younger ages for the system than the WR features provide., The CIV line requires younger ages for the system than the WR features provide.
 For Tol B we find any model with negligible Hell emission provides a reasonable fit to the data., For Tol B we find any model with negligible HeII emission provides a reasonable fit to the data.
 However models with ages of 10°* years and older tend to overpredict the CIV emission line relative the observed spectrum., However models with ages of $10^{6.4}$ years and older tend to overpredict the CIV emission line relative the observed spectrum.
 Also for the blue and red bumps there are no distinctive broad emission lines and the spectrum is dominated by narrow emission lines., Also for the blue and red bumps there are no distinctive broad emission lines and the spectrum is dominated by narrow emission lines.
 This again suggests a young population., This again suggests a young population.
" Our derived ages, both from matching the spectra by eye and from the line equivalent widths, are 4 Myrs for Tol A and < 2.5Myrs for Tol B. These agree with the ages of(2006).."," Our derived ages, both from matching the spectra by eye and from the line equivalent widths, are 4 Myrs for Tol A and $<2.5$ Myrs for Tol B. These agree with the ages of."
 However our ages are on the young side of the ages they derived., However our ages are on the young side of the ages they derived.
" By eye the model agreement is good, especially in light of the general models employed, which are not fine-tuned to any great degree."," By eye the model agreement is good, especially in light of the general models employed, which are not fine-tuned to any great degree."
 The line profiles and strengths of ultraviolet spectral features are generally less well fit than the optical features., The line profiles and strengths of ultraviolet spectral features are generally less well fit than the optical features.
 There are several ways in which our models might be fine tuned to fit the observational data in this case., There are several ways in which our models might be fine tuned to fit the observational data in this case.
" Firstly, it may be possible to refine our model for"," Firstly, it may be possible to refine our model for"
very close to the semi-regulars. which are on their way to become Mira variables.,"very close to the semi-regulars, which are on their way to become Mira variables."
 Hence. these periodic variations could well be intrinsic.," Hence, these periodic variations could well be intrinsic."
 From the analysis of the correlation between radial velocity amplitude and surface gravity we have evidence for the presence of both intrinsic. variability and companions in at least a fraction of the K giant stars with periodic radial velocity variations., From the analysis of the correlation between radial velocity amplitude and surface gravity we have evidence for the presence of both intrinsic variability and companions in at least a fraction of the K giant stars with periodic radial velocity variations.
 In order to study the characteristics of these companions. we take the hypothesis that the periodic radial velocity variations detected in 43 of our K giant stars. excluding binaries. are caused by sub-stellar companions.," In order to study the characteristics of these companions, we take the hypothesis that the periodic radial velocity variations detected in 43 of our K giant stars, excluding binaries, are caused by sub-stellar companions."
 Under this hypothesis. we investigate the statistical properties of the orbital parameters of the sample and compare these with the statistical properties of companions orbiting F. G and K dwarfs.," Under this hypothesis, we investigate the statistical properties of the orbital parameters of the sample and compare these with the statistical properties of companions orbiting F, G and K dwarfs."
 According to our analysis. 55 stars in the sample would have a single companion. and 11 stars multiple companions.," According to our analysis, 55 stars in the sample would have a single companion, and 11 stars multiple companions."
" Twenty-three (22 single and | in a multiple system) of these companions have asini larger than 100 Mj, and should be interpreted as stellar binaries.", Twenty-three (22 single and 1 in a multiple system) of these companions have $m\sin i$ larger than 100 $_{\rm Jup}$ and should be interpreted as stellar binaries.
 By advancing the multiple sub-stellar systems forward in time via a Runga-Kutta integration. we investigated the stability of the systems. taking into account the mutual interactions of the companions.," By advancing the multiple sub-stellar systems forward in time via a Runga-Kutta integration, we investigated the stability of the systems, taking into account the mutual interactions of the companions."
" With the orbital parameters that minimise y taken at face value. we found that most of the inferred sub-stellar multiple systems would be ‘likely unstable’. with a change in semi-major axis >1% and <10%. or ""unstable"" with a change in semi-major axis >10% on a time scale of 100 years due to companion-companion interaction."," With the orbital parameters that minimise $\chi^2$ taken at face value, we found that most of the inferred sub-stellar multiple systems would be 'likely unstable', with a change in semi-major axis $>
1\%$ and $<10\%$, or 'unstable' with a change in semi-major axis $>10\%$ on a time scale of 100 years due to companion-companion interaction."
 However. the inferred stability depends on the starting epoch of the computations. as well as on the orbital parameters. which might change with an increasing number of observations.," However, the inferred stability depends on the starting epoch of the computations, as well as on the orbital parameters, which might change with an increasing number of observations."
 Furthermore. there is no guarantee that the obtained y minimum is a global minimum.," Furthermore, there is no guarantee that the obtained $\chi^{2}$ minimum is a global minimum."
 Therefore. stars with multiple inferred sub-stellar companions that seem to be unstable. might also have stable solutions.," Therefore, stars with multiple inferred sub-stellar companions that seem to be unstable, might also have stable solutions."
 One could also use the equations for dynamical stability described by ? and ο., One could also use the equations for dynamical stability described by \citet{gladman1993} and \citet{marcy2001}.
 ? also notes that the Hill stability eriteria for companions in initially eccentric orbits may not be met. but that the systems may still be found to be empirically quite stable for a long period of time.," \citet{gladman1993} also notes that the Hill stability criteria for companions in initially eccentric orbits may not be met, but that the systems may still be found to be empirically quite stable for a long period of time."
 In order to draw a firm conclusion on the stability of a particular system. a more thorough investigation is needed. as well as data with a longer time base. which is beyond the scope of this paper.," In order to draw a firm conclusion on the stability of a particular system, a more thorough investigation is needed, as well as data with a longer time base, which is beyond the scope of this paper."
 For all stars with periodic radial velocity variations. we checked the Hipparcos (?) photometry.," For all stars with periodic radial velocity variations, we checked the Hipparcos \citep{esa1997} photometry."
 We checked periodograms for significant frequencies close to the obtained radial velocity period. and plotted the photometric values phased with the radial velocity period.," We checked periodograms for significant frequencies close to the obtained radial velocity period, and plotted the photometric values phased with the radial velocity period."
" None of the stars show photometric variations related to the observed radial velocity variations,", None of the stars show photometric variations related to the observed radial velocity variations.
 The mass distribution of our K giant sample is not known very well., The mass distribution of our K giant sample is not known very well.
 The stellar masses are typically between | and 4 Ma., The stellar masses are typically between 1 and 4 $_{\sun}$.
 Hence most of their main sequence progenitors should have been of A or F spectral class., Hence most of their main sequence progenitors should have been of A or F spectral class.
 The distribution of orbital parameters of sub-stellar companions orbiting A and F main sequence stars is still unknown., The distribution of orbital parameters of sub-stellar companions orbiting A and F main sequence stars is still unknown.
 The core accretion model predicts more giant planets around more massive stars. so that the distribution of orbital parameters of sub-stellar companions orbiting F. G and K main-sequence stars probably cannot serve as à proxy.," The core accretion model predicts more giant planets around more massive stars, so that the distribution of orbital parameters of sub-stellar companions orbiting F, G and K main-sequence stars probably cannot serve as a proxy."
 However. it should be instructive to compare the two distributions.," However, it should be instructive to compare the two distributions."
 Since the data presented here span ~2500 days. radial velocity variations with longer periods are uncertain. and. therefore. not taken into consideration.," Since the data presented here span $\sim 2500$ days, radial velocity variations with longer periods are uncertain, and, therefore, not taken into consideration."
 Companions with, Companions with
"Castellani (1993) who named these peculiar stellar objects ""red giant. stragelers.”",Castellani (1993) who named these peculiar stellar objects “red giant stragglers.”
 Stars that ignite helium on the white dwarf cooling sequence have a much less efficient II-burning shell. and will undergo extensive mixing between the He-core and the LHe-rich envelope (Cassisi et al.," Stars that ignite helium on the white dwarf cooling sequence have a much less efficient H-burning shell, and will undergo extensive mixing between the He-core and the H-rich envelope (Cassisi et al."
 2003)., 2003).
 This makes the progeny of hot-Hashers hotter and fainter than genuine IB stars (ie. stars that ignite He along the RGB). describing a kind of hook in UV CALDs that gives the name to this class of objects.," This makes the progeny of hot-flashers hotter and fainter than genuine HB stars (i.e. stars that ignite He along the RGB), describing a kind of hook in UV CMDs that gives the name to this class of objects."
 The presence of such peculiar sources in. NGC 2808 has been already noted by pure UV analvsis by Brown et al. (, The presence of such peculiar sources in NGC 2808 has been already noted by pure UV analysis by Brown et al. (
2001) ancl Dieball et al. (,2001) and Dieball et al. (
2005).,2005).
 As shown in Figure &.. he location of BLUk stars is inceccl reproduced by a hot-Lasher model (dashed-dotted line) from. Cassisi et al. (," As shown in Figure \ref{teo5}, the location of BHk stars is indeed reproduced by a hot-flasher model (dashed-dotted line) from Cassisi et al. ("
2003) for a mass Al=O.4S9A/..° The use of hot-Hasher models with cilferent total mass would not greatly modify the outlined: scenario since. all hot-IHasher models tend to cluster in a very narrow region of the CAID. regardless of their total mass (Brown οἱ al.,"2003) for a mass $M=0.489
M_{\odot}$ The use of hot-flasher models with different total mass would not greatly modify the outlined scenario since all hot-flasher models tend to cluster in a very narrow region of the CMD, regardless of their total mass (Brown et al."
 2001: see also Miller. Bertolami ct al., 2001; see also Miller Bertolami et al.
 2008)., 2008).
 Also. the ellect of the initial chemical composition on the location in d; is minor. at least at subsolar metallicities (see Miller. Bertolami et al.," Also, the effect of the initial chemical composition on the location in $T_{\rm eff}$ is minor, at least at subsolar metallicities (see Miller Bertolami et al."
 2008)., 2008).
 As a consequence it is not trivial to understand which Y sub-population produces the DIlks., As a consequence it is not trivial to understand which $Y$ sub-population produces the BHks.
 Potentially star counts derived from AIS analysis might shed light on this point., Potentially star counts derived from MS analysis might shed light on this point.
 IIvpothesizing three dilferent ogenitors for Bllks we obtain (NeueμηNeap)on.=1.9+ 01. (NeueVpypBHkJoba0.0+01 aud (Nnun/NEannui).=2.2£04.," Hypothesizing three different progenitors for BHks we obtain $(N_{\rm RHB+BHk}/N_{\rm BHB})_{\rm obs}=1.3 \pm 0.1$ , $(N_{\rm RHB}/N_{\rm BHB+BHk})_{\rm obs}=0.9 \pm 0.1$ and $(N_{\rm
 RHB}/N_{\rm EHB+BHk})_{\rm obs}=2.2 \pm 0.4$."
 In alb cases adding he BLIIK stars to a given HB sub-populations makes the disagreement with the ratios expected [rom Piotto et al. (, In all cases adding the BHk stars to a given HB sub-populations makes the disagreement with the ratios expected from Piotto et al. (
2007) worse.,2007) worse.
 Bailvn (1995) has suggested that hot IIB stars in a number of clusters have a binary origin., Bailyn (1995) has suggested that hot HB stars in a number of clusters have a binary origin.
 On the other hand a recent spectroscopic analvsis (Moni Didin ct al., On the other hand a recent spectroscopic analysis (Moni Bidin et al.
 2006) of a sample of hot HB stars in NGC 6752 found. no close binaries., 2006) of a sample of hot HB stars in NGC 6752 found no close binaries.
 Neither of these studies have direct application to the case of NGC 2808., Neither of these studies have direct application to the case of NGC 2808.
 Dailvn's arguments apply to scD stars which are probably ΙΕ stars (Dorman et al., Bailyn's arguments apply to sdB stars which are probably EHB stars (Dorman et al.
 1993)., 1993).
 Our preliminary results indicate that NGC 6752 has no DII stars. so the Moni Didin result. also applies to ELLD stars.," Our preliminary results indicate that NGC 6752 has no BHk stars, so the Moni Bidin result also applies to EHB stars."
 Our results here clearly show that EMB anc DBLIEK stars are not the same thing., Our results here clearly show that EHB and BHk stars are not the same thing.
 One must be quite precise in defining these hot populations., One must be quite precise in defining these hot populations.
 Specifically in NGC' 2808. Piotto et al.," Specifically in NGC 2808, Piotto et al."
 2007 tentatively suggest that their observed binary sequence might be connected. with the BILk stars. and they note that the binary fraction ancl BIIk fraction are similar.," 2007 tentatively suggest that their observed binary sequence might be connected with the BHk stars, and they note that the binary fraction and BHk fraction are similar."
 Most GC's have binary stars. and most of these contain exotic populations like BSS which are produced by binary evolution.," Most GCs have binary stars, and most of these contain exotic populations like BSS which are produced by binary evolution."
 On the other hand. BIIk stars are found in only a very lew GCs.," On the other hand, BHk stars are found in only a very few GCs."
 ΤΕ binaries are producing BILk stars. they should be found in most CC's.," If binaries are producing BHk stars, they should be found in most GCs."
 So [ar genuine BILk stars have been found only in the most. massive clusters most of which have multiple populations., So far genuine BHk stars have been found only in the most massive clusters most of which have multiple populations.
 This must be telling us something about their origin., This must be telling us something about their origin.
X-ray threshold could still have L4>10? ergs s! (see below).,X-ray threshold could still have $L_{\rm x} > 10^{42}$ ergs $^{-1}$ (see below).
Radio-quiet AGN were also selected by considering sources with R<1.4 and X-ray detections with 1043 ergs s-!., Radio-quiet AGN were also selected by considering sources with $R < 1.4$ and X-ray detections with $L_{\rm x} > 10^{42}$ ergs $^{-1}$.
 We did not apply any cut in radio power since the objects with P.>1034 W Hz-! are all at relatively high redshifts ((z)~ 2) and are therefore expected to have relatively large luminosities even if radio-quiet , We did not apply any cut in radio power since the objects with $P_{\rm r} > 10^{24}$ W $^{-1}$ are all at relatively high redshifts $\langle z \rangle \sim 2$ ) and are therefore expected to have relatively large luminosities even if radio-quiet (see \ref{properties}) ).
Table 2 and (seeFig., Table \ref{tab_counts_z} and Fig.
" 6 ??)).present the Euclidean normalized number counts for the total redshift sub-sample and also for SFG and AGN, derived as described in Paper IL AGN make up of sub-mJy sources with redshift information but 41596their number drops towards lower flux densities, going from at ~10 mJy down to 34% at the survey limit."," \ref{counts_z} present the Euclidean normalized number counts for the total redshift sub-sample and also for SFG and AGN, derived as described in Paper I. AGN make up $41^{+7}_{-6}\%$ of sub-mJy sources with redshift information but their number drops towards lower flux densities, going from at $\sim 10$ mJy down to $34\%$ at the survey limit."
" SFG, on the other hand, constitute 59*1996 of the sub-mJy sample having measured redshifts."," SFG, on the other hand, constitute $59^{+10}_{-9}\%$ of the sub-mJy sample having measured redshifts."
" SFG are missing at high flux densities but become the dominant population below ~0.1 mJy, reaching 66% at the survey limit."," SFG are missing at high flux densities but become the dominant population below $\approx 0.1$ mJy, reaching $66\%$ at the survey limit."
" Radio-quiet AGN represent 2378% (or ~56% of all AGN) of sub-mJy sources but their fraction appears to increase at lower flux densities, where they make up 81% of all AGN at the survey limit."," Radio-quiet AGN represent $23^{+6}_{-5}\%$ (or $\sim 56\%$ of all AGN) of sub-mJy sources but their fraction appears to increase at lower flux densities, where they make up $81\%$ of all AGN at the survey limit."
" We caution that the real uncertainties on the radio-quiet AGN counts are larger than indicated owing to two effects, which go in opposite directions: 1) ~60% of our putative radio-quiet AGN have elliptical or undefined morphology, which means their optical fluxes have been K-corrected assuming an elliptical spectrum."," We caution that the real uncertainties on the radio-quiet AGN counts are larger than indicated owing to two effects, which go in opposite directions: 1) $\sim 60\%$ of our putative radio-quiet AGN have elliptical or undefined morphology, which means their optical fluxes have been K-corrected assuming an elliptical spectrum."
" This could result in an artificial lowering of R if the AGN component is non negligible in the optical band, translating in turn in an overestimation of their number (as we selected sources with R< 1.4)."," This could result in an artificial lowering of $R$ if the AGN component is non negligible in the optical band, translating in turn in an overestimation of their number (as we selected sources with $R < 1.4$ )."
" Our selection criteria could also include some radio galaxies, although their number is expected to be small; 2) the inclusion of X-ray detections only could underestimate the number of radio-quiet AGN, as some sources with upper limits on their X-ray power above 1043 ergs s! could still have intrinsic powers above this limit."," Our selection criteria could also include some radio galaxies, although their number is expected to be small; 2) the inclusion of X-ray detections only could underestimate the number of radio-quiet AGN, as some sources with upper limits on their X-ray power above $10^{42}$ ergs $^{-1}$ could still have intrinsic powers above this limit."
 To assess the dependence of our results on our selection criteria we show in Table 3 how the fraction of sub- SFG changes with different parameters., To assess the dependence of our results on our selection criteria we show in Table \ref{perturb} how the fraction of sub-mJy SFG changes with different parameters.
" Namely, we"," Namely, we"
"In the limit of zero stratification. Pyle) constant. abr] constantf US. garg. t hp=p at qOb,t(13) In Paper L we analvze the (ime dependence of the shwave amplitudes [or both an unstratified equilibritun and a radiallv-stratified ecquilibrium.","In the limit of zero stratification, P_0(x) constant, _0(x) constant, _0 x, q, and _x k_x + k_y t. In Paper I, we analyze the time dependence of the shwave amplitudes for both an unstratified equilibrium and a radially-stratified equilibrium."
" As cliseussecl in more detail in Paper L appling the shwave formalism to a radiallv-stratified shearing sheet effectively uses a short-wavelength WIXD approximation. and is therefore only valid in the limit 4,£>>1. where the background. varies on a scale L~H<BR."," As discussed in more detail in Paper I, applying the shwave formalism to a radially-stratified shearing sheet effectively uses a short-wavelength WKB approximation, and is therefore only valid in the limit $k_y L \gg 1$, where the background varies on a scale $L \sim H \ll R$."
 The disk scale height 77=cO. where C.202—VffsD0/fw—0-," The disk scale height $H \equiv c_s \Omega$, where $c_s = \sqrt{\gamma P_0/\Sigma_0}$."
 There are three nontrivial shwave solutions in the unstratified shearing sheet. two nonvortieal and one vorlical.," There are three nontrivial shwave solutions in the unstratified shearing sheet, two nonvortical and one vortical."
 The radial stratification gives rise to an additional vortical shwave., The radial stratification gives rise to an additional vortical shwave.
" In the limit of tightly-wound. shwaves (||29 f). the nonvortical and vortical shwaves are compressive and incompressive. respectively,"," In the limit of tightly-wound shwaves $|k_x| \gg k_y$ ), the nonvortical and vortical shwaves are compressive and incompressive, respectively."
" The former are the extension of acoustic modes to nonaxisvymmetry, and to leading order in (&,L).+ they are the same both with and without stratification."," The former are the extension of acoustic modes to nonaxisymmetry, and to leading order in $(k_y L)^{-1}$ they are the same both with and without stratification."
 Since the focus of our investigation is on convective instability and the generation of vorlicilv. we repeat here onlv (he solutions for the incompressive vorlical shwaves and refer the reader to Paper I for further details on (he nonvortical shwaves.," Since the focus of our investigation is on convective instability and the generation of vorticity, we repeat here only the solutions for the incompressive vortical shwaves and refer the reader to Paper I for further details on the nonvortical shwaves."
or slighth negative.,or slightly negative.
 Note that the dependence depends on the definition of the virial radius and with a cillerent definition there would be a cillerent O dependence., Note that the $\Omega$ dependence depends on the definition of the virial radius and with a different definition there would be a different $\Omega$ dependence.
 Although ο and 3 vary with all of the other cosmological parameters. it is more instructive to present its variation with the ellective power law index of the linear power spectrum at the non-linear scale. where AG(hs)=1 defines the non-linear. scale.," Although $c_0$ and $\beta$ vary with all of the other cosmological parameters, it is more instructive to present its variation with the effective power law index of the linear power spectrum at the non-linear scale, where $\Delta^2_{\rm lin}(k_*)=1$ defines the non-linear scale."
 The reason is that the slope of the linear power spectrum. determines the epoch of formation of small haloes that merge into the larger halo., The reason is that the slope of the linear power spectrum determines the epoch of formation of small haloes that merge into the larger halo.
 For lower ellective slope mar these haloes formect later. when the density of the universe was smaller. and the final halo concentration of the larger halo is also lower.," For lower effective slope $n_{\rm eff}$ these haloes formed later, when the density of the universe was smaller, and the final halo concentration of the larger halo is also lower."
 This is depicted with solid lines in Figure 4.., This is depicted with solid lines in Figure \ref{fig:neff}. .
 Our fiducial cosmology has np7LT., Our fiducial cosmology has $n_{\rm eff} \approx -1.7$.
 Varving Oy has no ellect on mar., Varying $\Omega_0$ has no effect on $n_{\rm eff}$ .
" When varving z. a portion ofthe variation of e, and 3 should be due to the change in £3(z)"," When varying $z$, a portion ofthe variation of $c_0$ and $\beta$ should be due to the change in $\Omega(z)$."
 The variation of ej with nar is consistent with while μας large errors. but ids typically slightly negative.," The variation of $c_0$ with $n_{\rm eff}$ is consistent with while $\beta$ has large errors, but is typically slightly negative."
 We now compare our results to the models of ? and. ?.., We now compare our results to the models of \citet{2001ApJ...554..114E} and \citet{2001MNRAS.321..559B}.
 ‘These are designed to reproduce the concentrations of halocs found. in IN-body simulations., These are designed to reproduce the concentrations of haloes found in $N$ -body simulations.
 Throughout we translate to our virial convention., Throughout we translate to our virial convention.
 We begin by considering concentration as a function of halo mass for the fiducial ACDAL cosmology defined in refsubsec:ltesults.., We begin by considering concentration as a function of halo mass for the fiducial $\Lambda$ CDM cosmology defined in \\ref{subsec:Results}.
 This is plotted in Figure οι., This is plotted in Figure \ref{fig:c(M)}.
 Ht is clear that our results are in agreement with those from direct halo structure analvsis., It is clear that our results are in agreement with those from direct halo structure analysis.
 However. most of the information in our model comes [rom the haloes with masses between 1012 and 107htML. because haloes smaller than this dominate at scales smaller than the range we considered for our fit.," However, most of the information in our model comes from the haloes with masses between $10^{13}$ and $10^{14}\ h^{-1}\ M_{\sun}$, because haloes smaller than this dominate at scales smaller than the range we considered for our fit."
 This means we have a relatively short lever arm with which to determine the mass concentration relation and consequently we are unable to strongly. constrain the slope 2., This means we have a relatively short lever arm with which to determine the mass concentration relation and consequently we are unable to strongly constrain the slope $\beta$.
 In direct analysis of haloes. concentration is a decreasing function of miss. so 3«Q0.," In direct analysis of haloes, concentration is a decreasing function of mass, so $\beta<0$."
 Our best fitted values for 7 are also typically negative. although the errors are large ancl positive values also cannot be excluded.," Our best fitted values for $\beta$ are also typically negative, although the errors are large and positive values also cannot be excluded."
 The strongest confirmation of this prediction comes from the analysis of scale-free models in previous section. where 7 is negative for p=1.5.," The strongest confirmation of this prediction comes from the analysis of scale-free models in previous section, where $\beta$ is negative for $n=-1.5$."
 Ht is clear that measuring the mass-concentration directly is a better wav to determine the mass dependence of concentration rather than using the power spectrum. particularly at lower κ...," It is clear that measuring the mass-concentration directly is a better way to determine the mass dependence of concentration rather than using the power spectrum, particularly at lower masses."
 Since determining mass depencence of concentration from the power spectrum does not appear promisinglet us ask the opposite question: how well can we predict the power spectrum using the mass concentration relations measured directive. from. the analysis of individual. haloes in the simulations?, Since determining mass dependence of concentration from the power spectrum does not appear promisinglet us ask the opposite question: how well can we predict the power spectrum using the mass concentration relations measured directly from the analysis of individual haloes in the simulations?
 Figure 6 shows the power spectra calculated. with power law approximations to the ο) functionsshown in Figure 5. as well as the 7 power spectrum.," Figure \ref{fig:Delta2} shows the power spectra calculated with power law approximations to the $c(M)$ functionsshown in Figure\ref{fig:c(M)}, , as well as the \citet{2002astro.ph..7664S} power spectrum."
 While there is £ood. agrement between them [or k«40h the halo models always predicts less," While there is good agrement between them for $k<40h$ $^{-1}$ , the halo models always predicts less"
‘This fact has suggested that V407 ονο could belong to the same class of recurrent novae. although its outburst was the first recorded nova event for this svstem.,"This fact has suggested that V407 Cyg could belong to the same class of recurrent novae, although its outburst was the first recorded nova event for this system."
 On the other hand. as discussed ον ο the historical lighteurve of V407 Cye is characterized by many gaps ancl it is possible that outbursts similar to that observed in 2010 were missed.," On the other hand, as discussed by \cite{2011A&A...527A..98S}
 the historical lightcurve of V407 Cyg is characterized by many gaps and it is possible that outbursts similar to that observed in 2010 were missed."
 Munari ct al (1990) estimated. an aceretion rate of ~I0“AL. ve3 for a WD mass of Ayo~LAL..," Munari et al (1990) estimated an accretion rate of $\sim 10^{-8}
M_\odot$ $^{-1}$ for a WD mass of $M\rs{WD}\sim 1\,M\rs{\odot}$."
. UW this accreted mass were ejected in the nova event. our estimate of the ejecta mass for the CDE case implies a recurrence time for nova events of 20 vears or so.," If this accreted mass were ejected in the nova event, our estimate of the ejecta mass for the CDE case implies a recurrence time for nova events of 20 years or so."
 For this accretion rate. the recurrence timescale is consistent with higher mass white dwarfs (c.g. Mp~1.25M .: eg. 7)).," For this accretion rate, the recurrence timescale is consistent with higher mass white dwarfs (e.g. $M\rs{WD}\sim
1.25\,M\rs{\odot}$ ; e.g. \citealt{1995ApJ...445..789P}) )."
 Within the fairly large uncertainties of accretion rate and ejecta mass estimates. this is consistent with either a scenario in which one or more outbursts have been missed. or with a recurrence timescale of the order of 100 vears.," Within the fairly large uncertainties of accretion rate and ejecta mass estimates, this is consistent with either a scenario in which one or more outbursts have been missed, or with a recurrence timescale of the order of 100 years."
 For a low mass WD the recurrence timescale is two orders of magnitude longer., For a low mass WD the recurrence timescale is two orders of magnitude longer.
 1n the light of the above considerations. and the results of numerical models showing that gas does accumulate in the orbital plane of οbinarv?.. we suggest that the model best describing the 2010 outburst of V407 νο is tha assuming the presence of a CDE and. predicting outburs enerev and mass of cjecta similar to those estimated: for RS Oph (run 3D-I544.35-NW7- CDEG.3).," In the light of the above considerations, and the results of numerical models showing that gas does accumulate in the orbital plane of a symbiotic, we suggest that the model best describing the 2010 outburst of V407 Cyg is that assuming the presence of a CDE and predicting outburst energy and mass of ejecta similar to those estimated for RS Oph (run 3D-E44.3-NW7- CDE6.3)."
 Finally. the N-ray structure predicted by our. moce has interesting implications for the Line profiles expectec to be observed. during the outburst.," Finally, the X-ray structure predicted by our model has interesting implications for the line profiles expected to be observed during the outburst."
 Simulations of the 2006 outburst. of RS Oph. that occurred. close to orbita quacdrature. have shown that most of the X-ray emission arises [rom a compact source propagating perpendicular o the line of sight. which is similar to that found. here.," Simulations of the 2006 outburst of RS Oph, that occurred close to orbital quadrature, have shown that most of the X-ray emission arises from a compact source propagating perpendicular to the line of sight, which is similar to that found here."
 This source produced asymmetric anc slightly bIuc-shifted ine profiles due to substantial A-ray absorption of red-shifted emission. by shocked. material (2))., This source produced asymmetric and slightly blue-shifted line profiles due to substantial X-ray absorption of red-shifted emission by shocked material \citealt{2009A&A...493.1049O}) ).
 These. moclel oedicetions were in nice agreement with the findings of ? who reported similar asvmumetric line. profiles from. the analysis of AMEPCG observations of RS Oph., These model predictions were in nice agreement with the findings of \citet{2009ApJ...691..418D} who reported similar asymmetric line profiles from the analysis of /HETG observations of RS Oph.
 In the ight of the above results. we expect therefore that even in he case of V407 νο the line profiles should be asvnimetric ancl blue-shifted: due to A-ray absorption of red-shiftec emission. by shocked material.," In the light of the above results, we expect therefore that even in the case of V407 Cyg the line profiles should be asymmetric and blue-shifted due to X-ray absorption of red-shifted emission by shocked material."
 Interestingly. 2 reporte asvnunetric line. profiles with extended blue. wings during the 2010 outburst of V407 Cye.," Interestingly, \citet{2011A&A...527A..98S}
 reported asymmetric line profiles with extended blue wings during the 2010 outburst of V407 Cyg."
 These authors suggestec that the emission and the asymmetric line profiles coulc originate in the wake produced. by the convergent: shock on the rear side of the companion star., These authors suggested that the emission and the asymmetric line profiles could originate in the wake produced by the convergent shock on the rear side of the companion star.
 We note that the scenario proposed by 2 , We note that the scenario proposed by \citet{2011A&A...527A..98S} 
that lis not associated withG42.8+0.6.. or that iis significantly older than its spin-down age would imply — are consistent wilh our data.,"that is not associated with, or that is significantly older than its spin-down age would imply – are consistent with our data."
 Our X-aaxy spectral observations find the source initially in a state of enhanced. X-ray Iuninosity relative to the quiescent-state observations of Woodsetal.(10004) and. etal.(2001)., Our X-ray spectral observations find the source initially in a state of enhanced X-ray luminosity relative to the quiescent-state observations of \citet{wkp+99a} and \citet{wkg+01}.
. These past observations lound (he source al an unabsorbed 210 keV [Iux of c|x10 oon two occasions. 1997 May. and 2000 March.," These past observations found the source at an unabsorbed 2–10 keV flux of $\approx 1\times 10^{-11}$ on two occasions, 1997 May and 2000 March."
 Our first observation finds the source αἱ ereater flux. while the Εικ at the second observation is consistent with the quiescent value (Table 1)).," Our first observation finds the source at greater flux, while the flux at the second observation is consistent with the quiescent value (Table \ref{tab:spec}) )."
 The fading nature of this excess emission is confirmed by reports of oobservalions al earlier times (Ferociοἱal.2001)., The fading nature of this excess emission is confirmed by reports of observations at earlier times \citep{mf+01}.
. Spectral parameters for the thermal component in the spectrum are consistent with values reported for the source in quiescence (Woodsetal.1999a.2001:Pernaοἱ2001).. and despite the decline in total X-ray flux between our (wo observations. fitted blackbody parameters show no sienilicant. variation indicating that the variations in source [lux are produced solely by (he power-law component in (he spectrum.," Spectral parameters for the thermal component in the spectrum are consistent with values reported for the source in quiescence \citep{wkp+99a,wkg+01,phh+01}, and despite the decline in total X-ray flux between our two observations, fitted blackbody parameters show no significant variation – indicating that the variations in source flux are produced solely by the power-law component in the spectrum."
 Similar fading of the power-law component alone was observed in the wake of the August. 1998. eiant. flare of the source (Woodsetal.1999a)., Similar fading of the power-law component alone was observed in the wake of the August 1998 giant flare of the source \citep{wkp+99a}.
. This stability of the blackbody component of hhas been cited as evidence in favor of the magnetar model for SGRs. with the blackbody produced by surface thermal emission and the power law produced in (he magnetosphere by. ee. inverse Compton effects (Woodsetal.1999a).," This stability of the blackbody component of has been cited as evidence in favor of the magnetar model for SGRs, with the blackbody produced by surface thermal emission and the power law produced in the magnetosphere by, e.g., inverse Compton effects \citep{wkp+99a}."
. This interpretation must be further strengthened by the observations reported here. as the stability of the blackbody component of hhas now withstood (wo giant flares as well as substantial excursions in X-ray (lus.," This interpretation must be further strengthened by the observations reported here, as the stability of the blackbody component of has now withstood two giant flares as well as substantial excursions in X-ray flux."
 The X-rav spectrum of (thus provides an interesting link between the SGR population and the related population of anomalous x-ray pulsars (ANPs)., The X-ray spectrum of thus provides an interesting link between the SGR population and the related population of anomalous x-ray pulsars (AXPs).
 The AXPs (see Mereghetti 2000)) are a group of sources that emit steady. pulsed. X-ray emission (Ly~109ergs 1) with periods and spin-down rates similar to those of the SGRs: indeed. Thompson&Duncan(1996) used spin properties to argue that the SGRs and ANPs were related.," The AXPs (see \citealt{m99}) ) are a group of sources that emit steady, pulsed X-ray emission $L_{X} \sim 10^{35}\mbox{ erg
s}^{-1}$ ) with periods and spin-down rates similar to those of the SGRs; indeed, \citet{td96} used spin properties to argue that the SGRs and AXPs were related."
 However. these spin properties are also shared bv a growing class of long-period radio pulsars (Ixaspietal.1999) which seem otherwise unrelated to both the ANPs showing no persistent bright X-ray emission and the SGRs /— showing no bursting behavior.," However, these spin properties are also shared by a growing class of long-period radio pulsars \citep{kcl+99} which seem otherwise unrelated to both the AXPs – showing no persistent bright X-ray emission \citep{pkc+00} – and the SGRs – showing no bursting behavior."
 We must therefore require more evidence than similar spin properties to relate the SGRs and AXPs., We must therefore require more evidence than similar spin properties to relate the SGRs and AXPs.
 For some time the X-ray spectra of the (wo eroups appeared to have important differences: the SGRs had relatively hard power-law spectra with photon indices D~2 and negligible, For some time the X-ray spectra of the two groups appeared to have important differences: the SGRs had relatively hard power-law spectra with photon indices $\Gamma \sim 2$ and negligible
is only an approximation to the classical atmosphere and standard LTE analysis techniques used to derive the abundances.,is only an approximation to the classical atmosphere and standard LTE analysis techniques used to derive the abundances.
 The line profiles require macroturbulent velocities that are supersonic., The line profiles require macroturbulent velocities that are supersonic.
 Strong lines suggest by the presence of blue asymmetries that a wind is driven off the star., Strong lines suggest by the presence of blue asymmetries that a wind is driven off the star.
 Refinement of the abundance analysis may primarily depend on developing an improved understanding of the physics of these dilute extended stellar photospheres., Refinement of the abundance analysis may primarily depend on developing an improved understanding of the physics of these dilute extended stellar photospheres.
 This research has been supported in part by the grant F-634 to DLL from the Robert A. Welch Foundation of Houston. Texas.," This research has been supported in part by the grant F-634 to DLL from the Robert A. Welch Foundation of Houston, Texas."
 VGK NST acknowledge support from the Russian Foundation for Basic Research (project aa)., VGK NST acknowledge support from the Russian Foundation for Basic Research (project a).
in Fig.,in Fig.
" 3 originate in one physical environment with a more homogeneous metallicity distribution, while the blue metal-poor absorber in the blue region with low W;?""986and mmay be the ‘classical’ DLAs where the sight-line is probing the ISM of small galaxies."," \ref{fig:gradient} originate in one physical environment with a more homogeneous metallicity distribution, while the blue metal-poor absorber in the blue region with low and may be the `classical' DLAs where the sight-line is probing the ISM of small galaxies."
 These two hypothesis are illustrated with Fig. 4.., These two hypothesis are illustrated with Fig. \ref{fig:model}.
" Since our recent results (Bouchéetal.2006,2007) favor the outflow scenario for II--selected absorbers, we postulate that the homogeneous metallicity distribution originates from the metal-rich material being driven out of sub-L* galaxies."," Since our recent results \citep{BoucheN_06c,BoucheN_07a} favor the outflow scenario for -selected absorbers, we postulate that the homogeneous metallicity distribution originates from the metal-rich material being driven out of $^*$ galaxies."
" Indeed, several studies (Bouchéetal.2007;Oppenheimer&Davé2008) have shown that galaxies with L«1/3L"" dominate the metal budget in the intergalactic medium, i.e. the metals outside the ISM of galaxies."," Indeed, several studies \citep{BoucheN_06b,OppenheimerB_08a} have shown that galaxies with $L<1/3L^*$ dominate the metal budget in the intergalactic medium, i.e. the metals outside the ISM of galaxies."
" This material is either directly entrained by ram pressure from the hot outflow, or traces cooling material (where the metallicity is higher and the cooling time is shorter) (MallerBullock 2004).."," This material is either directly entrained by ram pressure from the hot outflow, or traces cooling material (where the metallicity is higher and the cooling time is shorter) \citep{MallerA_04a}."
 Either way it may very well return to the ISM of the galaxy as recent wind models suggest (Oppenheimer 2008).., Either way it may very well return to the ISM of the galaxy as recent wind models suggest \citep{OppenheimerB_08a}.
" This picture outlined in Fig. 4,,"," This picture outlined in Fig. \ref{fig:model},"
" which may still be somewhat over simplified, naturally explains many other observables of intervening absorbers."," which may still be somewhat over simplified, naturally explains many other observables of intervening absorbers."
" For instance, as pointed out in the previous section, a sample of DLAs will be made of a mix of the two types of absorbers."," For instance, as pointed out in the previous section, a sample of DLAs will be made of a mix of the two types of absorbers."
" Interestingly, Wolfeetal.(2008) reported evidence for a bimodality in DLAs using [C II] 158um cooling rates, /.."," Interestingly, \citet{WolfeA_08a} reported evidence for a bimodality in DLAs using [C II] $\mu$ m cooling rates, $l_c$."
" The ‘low-cool’ DLAs have lower velocity widths, lower metallicity and lower dust-to-gas ratios than the *high-cool’ DLAs which have larger velocity widths and higher metallicities."," The `low-cool' DLAs have lower velocity widths, lower metallicity and lower dust-to-gas ratios than the 'high-cool' DLAs which have larger velocity widths and higher metallicities."
 Fig., Fig.
" 3 naturally shows that DLAs with large velocity dispersions (as measured by W?2796)) would be more metal rich, than those with low velocity widths."," \ref{fig:gradient} naturally shows that DLAs with large velocity dispersions (as measured by ) would be more metal rich, than those with low velocity widths."
" Furthermore, the UDF results of Wolfe&Chen imply that in situ star formation can be the dominant heating mechanism for the ‘low-cool’ population only, consistent with our interpretation shown in Fig. 4.."," Furthermore, the UDF results of \citet{WolfeA_06a} imply that in situ star formation can be the dominant heating mechanism for the `low-cool' population only, consistent with our interpretation shown in Fig. \ref{fig:model}."
 We have shown that the DLA bimodality originates from the biased selection at constantΝμι., We have shown that the DLA bimodality originates from the biased selection at constant.
. The picture outlined in Fig., The picture outlined in Fig.
 4 predicts an increasing reddening E(B—V) (owing to the iincrease) with equivalent width aas reported by Yorketal.(2006) (seealsoMénardetal.2008) assuming a constant dust-to-gas ratio for aabsorbers since globally aand aare Nyycorrelated.," \ref{fig:model} predicts an increasing reddening $E(B-V)$ (owing to the increase) with equivalent width as reported by \citet{YorkD_06a} \citep[see also][]{MenardB_08a}
 assuming a constant dust-to-gas ratio for absorbers since globally and are correlated."
 This assumption may be the case under the common physical nature (out-flowing material) of strong, This assumption may be the case under the common physical nature (out-flowing material) of strong
eenussion derived [rom numerical models of collapse have been shown to be a good indicator ol underlying infalland rotational velocity fields (NaravananandWalker(1993).. hereafter AW).,"emission derived from numerical models of collapse have been shown to be a good indicator of underlying infall rotational velocity fields \citet{nar98}, hereafter NW)."
 In the model isovelocity maps of NW. the rotational velocity Ποια imposes a eraclient ol blueshifted (ο redshiftecd velocities. with the sense of the gradient being orthogonal to the rotational axis.," In the model isovelocity maps of NW, the rotational velocity field imposes a gradient of blueshifted to redshifted velocities, with the sense of the gradient being orthogonal to the rotational axis."
 When infall clominates in (he central regions. the line profiles in the central region become blue asymmetric. and hence there is a preponderance of blue-shifted velocities in the central regions of the isovelocitv maps. giving rise to the so-called. signature.," When infall dominates in the central regions, the line profiles in the central region become blue asymmetric, and hence there is a preponderance of blue-shifted velocities in the central regions of the isovelocity maps, giving rise to the so-called ``blue-bulge'' signature."
" NW also showed that if the angular momentum content in a given cloud is low. or if the infalling cloud core is observed with low angular resolution. then the blue-bulge signature is ""washed-out. (hat is the central regions of the isovelocity maps just consist of blue-shifted velocities."," NW also showed that if the angular momentum content in a given cloud is low, or if the infalling cloud core is observed with low angular resolution, then the blue-bulge signature is “washed-out”, that is the central regions of the isovelocity maps just consist of blue-shifted velocities."
 The first detection of the predicted blue-bulge signature was reported towards IRAS 16293 (Naravananοἱal.1993)., The first detection of the predicted blue-bulge signature was reported towards IRAS 16293 \citep{nwb98}.
. In Figure 6.. we present the centroid velocity maps of the observed and CS transilions towards SMMA.," In Figure \ref{centall}, we present the centroid velocity maps of the observed and CS transitions towards SMM4."
 The centroid velocities are expressed with respect to the νεο of the source. ie.. we have subtracted the vpgp (8 |) from the centroid velocities. making neealive velocities (shown with dashed lines) blueshiltecl. aud positive velocities (shown with solid lines) redshifted.," The centroid velocities are expressed with respect to the $_{LSR}$ of the source, i.e., we have subtracted the $_{LSR}$ (8 $^{-1}$ ) from the centroid velocities, making negative velocities (shown with dashed lines) blueshifted, and positive velocities (shown with solid lines) redshifted."
 In an effort to separate out the effect of outflow velocity fields from the denamies of the cloud core. the velocity centroids were computed over velocities.," In an effort to separate out the effect of outflow velocity fields from the dynamics of the cloud core, the velocity centroids were computed over velocities."
 As shown in refheoint.. linecore emission. especially of the submillimeter transitions. is mostly distinct from effects of molecular outflow.," As shown in \\ref{hcoint}, linecore emission, especially of the submillimeter transitions, is mostly distinct from effects of molecular outflow."
 All four maps shown in Figure 6 show an increasing gradient in centroid velocity [rom ihe northwest to the southeast., All four maps shown in Figure \ref{centall} show an increasing gradient in centroid velocity from the northwest to the southeast.
 The contours are seen (o be more or less parallel. ancl is approximately orthogonal to the major axis of (he ellipse of Ilimecore emission.," The contours are seen to be more or less parallel, and is approximately orthogonal to the major axis of the ellipse of linecore emission."
 The gradient is more ordered aud pronounced in the submillimeter transitions., The gradient is more ordered and pronounced in the submillimeter transitions.
 The blueshifted emission in all four centroid velocity maps are seen lo encroach well south of (he rotational axis and the central source al (0.0). pushing redshifted velocities to the extreme southeastern edge of the map.," The blueshifted emission in all four centroid velocity maps are seen to encroach well south of the rotational axis and the central source at (0,0), pushing redshifted velocities to the extreme southeastern edge of the map."
" In Figure 6.. (he submillimeter maps of andJ=133.. probably because of the higher angular resolution and respectively). show the blue-bulge signature more clearly,"," In Figure \ref{centall}, the submillimeter maps of and, probably because of the higher angular resolution and respectively), show the blue-bulge signature more clearly."
 The millimeter maps of CS and (bottom panels of Figure 6)) are at lower angular resolution and respectively). and as predicted by theory. (NaravananandWalker1998).. al lower angular resolution the bulge signature appears washed out. so that only blueshifted. velocities are seen.," The millimeter maps of CS and (bottom panels of Figure \ref{centall}) ) are at lower angular resolution and respectively), and as predicted by theory \citep{nar98}, at lower angular resolution the blue-bulge signature appears washed out, so that only blueshifted velocities are seen."
 As was discussed: above. even the linecore emission of millimeter is affected. by outflow.," As was discussed above, even the linecore emission of millimeter is affected by outflow."
 llowever. (he gradient seen in the bottom panels of Figure 6 is not north to south or to south-west. as might be expected if the millimeter lincore emission was only purely tracing the outflow.," However, the gradient seen in the bottom panels of Figure \ref{centall} is not north to south or north-east to south-west, as might be expected if the millimeter lincore emission was only purely tracing the outflow."
 The eradient is norüliwest-soutlheast which is approximately orthogonal, The gradient is northwest-southeast which is approximately orthogonal
"slit (the continua is taken around Az100 45 only the ceutral part ofthe profiles. rx12"". is shown.","slit (the continuum is taken around $\lambda \approx 4400\,\AA$ ); only the central part of the profiles, $r \le 12\arcsec$, is shown."
 Both the mealindes profiles exhibit naxiina shiftes o the south-west with respect to the. «ΟΠΗ naxiumi., Both the metal-index profiles exhibit maxima shifted to the south-west with respect to the continuum maximum.
" The continuum peak marks he position of he brighter nuceus, P1. which is not the isophote center ror the dvnanucal ceuter."," The continuum peak marks the position of the brighter nucleus, P1, which is not the isophote center nor the dynamical center."
 The coutiuuuu profile looks asvuuuetrce. and a Cass analysis reveals a pPESCIICC O wo components. a point-like one at 7=0 aud a1 extende oue (FWIIIA_=| TU) at KocQ'L.," The continuum profile looks asymmetric, and a Gauss analysis reveals a presence of two components, a point-like one at $r=0$ and an extended one $FWHM=7\arcsec$ ) at $r=-0\farcs4$."
 It is he latter. he southerucwesteru component that nist οςntam the second. fainter nucleus of31.. P2. which correponds to he photometric aud the dynamical ceuters of he galaxy (Lauerοal. 1993)).," It is the latter, the southern-western component that must contain the second, fainter nucleus of, P2, which corresponds to the photometric and the dynamical centers of the galaxy \cite{letal93}) )."
" Therefore we conclude tha P2 is the chemicaIv and age decoupled nucleus of (though due to the flatuess of the Baluer line iudex muna mede krc5"" we may suspect that f1ο nuclear disk inenutioued bv IKormeudyv (1988)) has alsο a luetal abundauce enhancement)", Therefore we conclude that P2 is the chemically and age decoupled nucleus of (though due to the flatness of the Balmer line index minima inside $r < 5\arcsec$ we may suspect that the nuclear disk mentioned by Kormendy \cite{k88}) ) has also a metal abundance enhancement).
 Let us remüud tlji P2 ls dynamically decoupled Usormendy 1988))., Let us remind that P2 is dynamically decoupled (Kormendy \cite{k88}) ).
" Tus result. though impressive, was not unexpected."," This result, though impressive, was not unexpected."
 Iiπο ot al. (1995)), King et al. \cite{ksc95}) )
 obtained an nuage of at A=17504: they iad found that P2 is brighter iun the ultraviolet tha1 Pl. in contrast to the visible.," obtained an image of at $\lambda = 1750\,\AA$; they had found that P2 is brighter in the ultraviolet than P1, in contrast to the visible."
 They have immediately interpreted his fact as an evideuce for P2 metallicity overalnndauce vecatise there exists a correlation between UV excess ancl uctallicity in elliptical ealaxics., They have immediately interpreted this fact as an evidence for P2 metallicity overabundance because there exists a correlation between UV excess and metallicity in elliptical galaxies.
 owever. we unst note hat Davidee et al. (1997))," However, we must note that Davidge et al. \cite{detal97}) )"
 have found that P1 aud P2 ave roughly equal colours {4Is: mt the formal error estimates. 0.10.2 mae. can hide a metallicity difference as large as a factor 10 (Worthey. 199 ).," have found that P1 and P2 have roughly equal colours $H-K$; but the formal error estimates, 0.1–0.2 mag, can hide a metallicity difference as large as a factor 10 (Worthey \cite{w94}) )."
 We have used CCD images of the central part of obtained frou he La Palma Archive to analyze the two-dimensional surface brightuess distribution., We have used CCD images of the central part of obtained from the La Palma Archive to analyze the two-dimensional surface brightness distribution.
 The ealaxy was observed on November |7T. 1990. at the Tun Jacobus Isaptevu Telescope through our filters. BVRI. bv a 512 pixel RCA CCD. with a sceing quality of 175.," The galaxy was observed on November 17, 1990, at the m Jacobus Kapteyn Telescope through four filters, $BVRI$, by a $320 \times 512$ pixel RCA CCD, with a seeing quality of $1\farcs5$."
 After bias subtraction aud divisioi by flat fields. the isophotes of the images were approxinated by cllipses.," After bias subtraction and division by flat fields, the isophotes of the images were approximated by ellipses."
 Figure 6 preseuts the radial variations of the major axis position aueles. cllipticitics. aud fourlh Fourier coefficieuts a) fa.," Figure \ref{isopar} presents the radial variations of the major axis position angles, ellipticities, and fourth Fourier coefficients $a_4/a$ ."
(X0.05 (=100 G2>10° cm?) Millar 11997).,$\le\!0.05$ $\gtrsim100$ $n\gtrsim\!10^6$ $^{-3}$ Millar 1997).
 Thus. hot cores are supposed to be radiatively heated and originate in the innermost parts of the condensation where the massive star is being formed.," Thus, hot cores are supposed to be radiatively heated and originate in the innermost parts of the condensation where the massive star is being formed."
 However. the radiative heating mechanism is questioned. as some observations suggest that the COM emission could be associated with shocks as well (Liu 22002: Chandler 22005: Goicoechea 22006: Goddi 2201Ia: Favre 220]Ia; Zapata 22011).," However, the radiative heating mechanism is questioned, as some observations suggest that the COM emission could be associated with shocks as well (Liu 2002; Chandler 2005; Goicoechea 2006; Goddi 2011a; Favre 2011a; Zapata 2011)."
 This question cannot be easily answered because most of the hot cores known to date (~ 100) are associated with high-mass protostars. and are on average located at distances >2 kpe (studied typically at spatial scales 4000 AU). while in the low-mass case (studied at scales AU. BBisschop 22008). there are very few clear cases (the so-called hot corinos: CCeccarelli 2004; Bottinelli 22007).," This question cannot be easily answered because most of the hot cores known to date $\sim100$ ) are associated with high-mass protostars, and are on average located at distances $> 2$ kpc (studied typically at spatial scales $\gtrsim4000$ AU), while in the low-mass case (studied at scales 500--1000 AU, Bisschop 2008), there are very few clear cases (the so-called hot corinos: Ceccarelli 2004; Bottinelli 2007)."
 Concerning the intermediate-mass regime. the only well-known cases are 77129 (Fuente 22005). 11396N (Fuente 22009). and 22219846336 (Sánnchez-Monge 22010). and still the presence of COMs is not clear in all the cases. questioning the true nature of these objects as hot cores.," Concerning the intermediate-mass regime, the only well-known cases are 7129 (Fuente 2005), 1396N (Fuente 2009), and 22198+6336 (Sánnchez-Monge 2010), and still the presence of COMs is not clear in all the cases, questioning the true nature of these objects as hot cores."
 Thus. à detailed high spatial resolution (~500 AU) study of true hot cores wwith complex organic chemistry) is lacking.," Thus, a detailed high spatial resolution $\sim500$ AU) study of true hot cores with complex organic chemistry) is lacking."
 In this letter. we present new subaresecond interferometric observations of COMs towards two intermediate-mass star- regions contaming hot core candidates.," In this letter, we present new subarcsecond interferometric observations of COMs towards two intermediate-mass star-forming regions containing hot core candidates."
 The two, The two
ice: methyl formate was therefore released to the gas-phase after sublimation of these icy samples.,ice: methyl formate was therefore released to the gas-phase after sublimation of these icy samples.
 In the present work. we include the Modica Palumbo (2010) experiments in our chemical model CCLISM Viti et al. (," In the present work, we include the Modica Palumbo (2010) experiments in our chemical model CHEM Viti et al. ("
2004a). by extrapolating from the experiments a new rate coellicient. for the methyl formate formation on grains.,"2004a), by extrapolating from the experiments a new rate coefficient for the methyl formate formation on grains."
 Our purpose is to investigate whether surface reactions during the cold phase afore can account for the observed: abundanaces of methyl formate in massive star-forming regions ancl around low-mass stars., Our purpose is to investigate whether surface reactions during the cold phase $alone$ can account for the observed abundances of methyl formate in massive star-forming regions and around low-mass stars.
 In Section 2 we cleseribe the experimental procedure: physical and chemical details of the chemical model are summarised in Section 3., In Section 2 we describe the experimental procedure; physical and chemical details of the chemical model are summarised in Section 3.
 In Section 4 we qualitatively model four different sources. ane present our findings.," In Section 4 we qualitatively model four different sources, and present our findings."
 Experiments have been performed in. the Laboratory. of Experimental Astrophysics in Catania (Italy)., Experiments have been performed in the Laboratory of Experimental Astrophysics in Catania (Italy).
 Solid samples were prepared and irradiated in a stainless stecl vacuum chamber where pressure is kept below mbar., Solid samples were prepared and irradiated in a stainless steel vacuum chamber where pressure is kept below $^{-7}$ mbar.
 The gas mixture to be investigated. was injected into the chamber through a needle valve where it froze onto the substrate (Si or WBr) placed in thermal contact with the tail section of a crvostat. (10-300. IW)., The gas mixture to be investigated was injected into the chamber through a needle valve where it froze onto the substrate (Si or KBr) placed in thermal contact with the tail section of a cryostat (10-300 K).
 After eposition the samples. were bombarclecdl by 200 keV. I1. ions., After deposition the samples were bombarded by 200 keV $^+$ ions.
 Ίος are obtained [rom an ion implanter interfaced with the vacuum chamber., Ions are obtained from an ion implanter interfaced with the vacuum chamber.
 The beam used. produces current densities in the range from 0.1 to a few pA in order to avoid macroscopic heating of the target., The beam used produces current densities in the range from 0.1 to a few $\mu$ A $^{-2}$ in order to avoid macroscopic heating of the target.
 Infrared7 transmittance spectra of the samples were obtained before ancl after cach step of irradiation by a FTIR spectrometer (4400-400 ta)97-35 jum)., Infrared transmittance spectra of the samples were obtained before and after each step of irradiation by a FTIR spectrometer (4400-400 $^{-1}$ =2.27-25 $\mu$ m).
 More details on the experimental procedure. can. be found. in Palumbo et al. (, More details on the experimental procedure can be found in Palumbo et al. (
2004) and in Modica Palumbo (2010).,2004) and in Modica Palumbo (2010).
 Pure ΟΙ and α ο.οἱ mixture were irradiated at 16 Ix. with. 200 keV ions., Pure $_3$ OH and a $_3$ OH mixture were irradiated at 16 K with 200 keV $^+$ ions.
 ln both cases. after irradiation. the HU spectra show several absorption bands which testify for the formation of new molecules not present in the original sample.," In both cases, after irradiation, the IR spectra show several absorption bands which testify for the formation of new molecules not present in the original sample."
" Among these. two bands due to CIL, appear at 3010 + and 1304 em+ (Palumbo et al."," Among these, two bands due to $_4$ appear at 3010 $^{-1}$ and 1304 $^{-1}$ (Palumbo et al."
 1999): COs bands appear at 2344 and 660 1 (C04) and 2278 + (COs): LeCO is detected at 1720 em! (Lludson Moore. 2000); Coll (OLD). (ethylene. elyveol) is observed at 1090 5 (Hudson Moore 2000)., 1999); $_2$ bands appear at 2344 and 660 $^{-1}$ $^{12}$ $_2$ ) and 2278 $^{-1}$ $^{13}$ $_2$ ); $_2$ CO is detected at 1720 $^{-1}$ (Hudson Moore 2000); $_2$ $_4$ $_2$ (ethylene glycol) is observed at 1090 $^{-1}$ (Hudson Moore 2000).
 Moreover a band is observed. near 1100  and. is attributed. to methyl formate (HLCOOCII) and a band near 1067 em+ is assigned. to elveolaledehyvde ΟΙ) (Alodica Palumbo 2010)., Moreover a band is observed near 1160 $^{-1}$ and is attributed to methyl formate $_3$ ) and a band near 1067 $^{-1}$ is assigned to glycolaldehyde $_2$ OH) (Modica Palumbo 2010).
" Figure 1 shows the ratio between the column density of methyl formate and methanol. N(LICOOCIL) /N(CLL,OLD. as a function of ion [Luence (ions 7). measured after cach step of irraciation."," Figure 1 shows the ratio between the column density of methyl formate and methanol, $_3$ $_3$ OH), as a function of ion fluence (ions $^{-2}$ ), measured after each step of irradiation."
 The experimental data have been fitted with an exponential curve where X is the asymptotic value. 0 is the cross section (cm) and «d is the ion [luence (ions 7).," The experimental data have been fitted with an exponential curve where A is the asymptotic value, $\sigma$ is the cross section $^2$ ) and $\Phi$ is the ion fluence (ions $^{-2}$ )."
 The1o fittingBitting procedure gives givesX—0.0042 A=0.0042and a=s.6.- 7 àcmo., The fitting procedure gives A=0.0042 and $\sigma$ $\times$ $^{-15}$ $^2$.
 To apply the laboratory results to the interstellar medium conditions we assume a standard. ionisation rate (ὁ 2 3-10 I !) and derive the [lux Fysyy;=0.5 ions 7 5 of cosmic ions in the approximation of elfective monoencrectic 1. MeV. protons (see Mennella ct al. (, To apply the laboratory results to the interstellar medium conditions we assume a standard ionisation rate $\zeta$ = $\times$ $^{-17}$ $^{-1}$ ) and derive the flux $_{ISM}$ =0.5 ions $^{-2}$ $^{-1}$ of cosmic ions in the approximation of effective monoenergetic 1 MeV protons (see Mennella et al. (
20033).,2003)).
 Pysay must be regarded as an effective quantity., $_{ISM}$ must be regarded as an effective quantity.
 I represents the equivalent [ux of 1. MeV. protons. which gives rise to the ionisation rate produced. by the cosmic-ray spectrum if 1 MeV. protons were the only source. for ionisation.," It represents the equivalent flux of 1 MeV protons, which gives rise to the ionisation rate produced by the cosmic-ray spectrum if 1 MeV protons were the only source for ionisation."
 Furthermore we assume that the cross section scales with the stopping power (S. energv loss per unit path length) of impinging ions.," Furthermore we assume that the cross section scales with the stopping power (S, energy loss per unit path length) of impinging ions."
 According to SRIAL code (Ziegler οἱ al., According to SRIM code (Ziegler et al.
 2008). in the case of protons impinging on a CO:CIE;OLL mixture S(200keV. SC(LAleY protons).," 2008), in the case of protons impinging on a $_3$ OH mixture S(200keV $\times$ S(1MeV protons)."
 We defined σι ως 0/2.9 eng. where the product m ds the initial slope of eq. (," We defined $\sigma_{ISM}$ = $\times \sigma$ /2.9 $^2$, where the product $\times \sigma$ is the initial slope of eq. ("
1).,1).
 The formation rate of methyl formate is given by 1 “)= 2 aysas(eme™) © bysayfem73 1 ) Using aysay and γω às estimated. above we obtain 10Ps 4 , The formation rate of methyl formate is given by $^{-1}$ )= $\sigma_{ISM}$ $^2$ ) $\times$ $_{ISM}$ $^{-2}$ $^{-1}$ ) Using $\sigma_{ISM}$ and $_{ISM}$ as estimated above we obtain $\times$ $^{-18}$ $^{-1}$.
The chemical model is οΠΜ. developed by. Viti Williams (1999) and. Viti et al. (," The chemical model is CHEM, developed by Viti Williams (1999) and Viti et al. ("
20048).,2004a).
 οςΗΝ is à ime and depth dependent. gas-grain chemical model which estimates the fractional abuncances (with respect to the otal number of hydrogen nuclei) of gas and surface species in every environment where molecules are present., CHEM is a time and depth dependent gas-grain chemical model which estimates the fractional abundances (with respect to the total number of hydrogen nuclei) of gas and surface species in every environment where molecules are present.
 For this »urpose it was adapted: to model low and. high-mass star orming regions., For this purpose it was adapted to model low and high-mass star forming regions.
 The model performs a two-step calculation: hase LE starts from a fairly cülfuse medium in atomic form and undergoes a free-fall collapse until densities tvpical of he eas that will form hot cores and hot corinos are reachec (10° cni and 10 respectively)., The model performs a two-step calculation: Phase I starts from a fairly diffuse medium in atomic form and undergoes a free-fall collapse until densities typical of the gas that will form hot cores and hot corinos are reached $^{7}$ $^{-3}$ and $^{8}$ $^{-3}$ respectively).
 During this time atoms ancl molecules are depleted onto grain surfaces anc hey hydrogenate when possible., During this time atoms and molecules are depleted onto grain surfaces and they hydrogenate when possible.
 The depletion ellicieney. is determined. by the fraction of the gas-phase material tha is frozen onto the erains., The depletion efficiency is determined by the fraction of the gas-phase material that is frozen onto the grains.
 This approach allows a derivation of the ice composition by a time-dependent computation of, This approach allows a derivation of the ice composition by a time-dependent computation of
Asstuning isotropy G.c. all directions to be equivalent). the right hand side of Eq.0))) depends solely on |r”|. and we can write: Tere P is defined by the right haud side of Eq.(3)).,"Assuming isotropy (i.e. all directions to be equivalent), the right hand side of \ref{n4}) ) depends solely on $\| {\bf r}'' \|$, and we can write: Here $\Gamma $ is defined by the right hand side of \ref{n4}) )."
 As it has been shown by Pietroucro (LOST). Dir) is the physically significaut expression. rather than €(1).," As it has been shown by Pietronero (1987), $\Gamma (r)$ is the physically significant expression, rather than $\xi (r) $."
 If we can assume vit) — const.," If we can assume $n^{(1)}$ = const.,"
 then we can write a relation between £6r) aud Pre): Just as in Eq.(2)). we can write for T. It was poiuted out by Thieberger et al. (," then we can write a relation between $\xi (r)$ and $\Gamma (r)$ : Just as in \ref{n3}) ), we can write for $\Gamma$, It was pointed out by Thieberger et al. ("
1990) that the analvsis of data does not necessarily eive the same value for 5 and sp.,1990) that the analysis of data does not necessarily give the same value for $\gamma$ and $\gamma_{\Gamma}$.
 Taking a set of poiuts from a known fractal and performing these calculations showed that the theoretical value corresponds to that obtained from r., Taking a set of points from a known fractal and performing these calculations showed that the theoretical value corresponds to that obtained from $\gamma_{\Gamma}$.
 To reduce the problem caused by finite data sets. a method of coarse eraiminme has been introduced. with the integrated conditional density D (Coleman andl Pictronero. 1992): It produces au artificial smoothing of rapidly varving fluctuations. but correctly reproduces global properties.," To reduce the problem caused by finite data sets, a method of coarse graining has been introduced, with the integrated conditional density $\Gamma^*$ (Coleman and Pietronero, 1992): It produces an artificial smoothing of rapidly varying fluctuations, but correctly reproduces global properties."
 The iutegral over D ds stronely related to the correlation iutegral (Cirassberger and Procaccia. 1983). OQ is the IIeaviside function.," The integral over $\Gamma$ is strongly related to the correlation integral (Grassberger and Procaccia, 1983), $\Theta$ is the Heaviside function."
 The immer sumunation is over the whole set of NL galaxies with coordinates Xj. jxἐν and the outer sumunation is over a subset of NY’ ealaxies. taken as centers. with coordinates X;.," The inner summation is over the whole set of $N-1$ galaxies with coordinates ${\bf X}_j$, $j\ne i$, and the outer summation is over a subset of $N^{\prime}$ galaxies, taken as centers, with coordinates ${\bf X}_i$."
 By takine ouly the inner [N ealaxies as ceuters we allow for the effect of the finiteness of the sample. (sec c.g. Svlos Labini et al..," By taking only the inner $N^{\prime}$ galaxies as centers we allow for the effect of the finiteness of the sample, (see e.g. Sylos Labini et al.,"
 1998)., 1998).
 This procedure is also widely used iu astrononiv (Proveuzale. 1991).," This procedure is also widely used in astronomy (Provenzale, 1991)."
 As Ribeiro (1992. 1995: hereafter refered tfo as R92 aud R95) aud other authors cited therein quite rightly pointed out. galaxy observations are carried out along our past lieht cone.," As Ribeiro (1992, 1995; hereafter refered to as R92 and R95) and other authors cited therein quite rightly pointed out, galaxy observations are carried out along our past light cone."
 Iu a homogeneous ΕΙΝ cosmological model. the proper density is constaut onu hwpersurfaces of constant proper time.," In a homogeneous FLRW cosmological model, the proper density is constant on hypersurfaces of constant proper time."
 Therefore. ax oue looks back to hieher aud higher redshifted galaxies. the crossing of the uull ecocdesics through hvpersurfaces of coustaut proper time and deusitv miplies changes in the observed density and an apparent inhomogcucity can be measured.," Therefore, as one looks back to higher and higher redshifted galaxies, the crossing of the null geodesics through hypersurfaces of constant proper time and density implies changes in the observed density and an apparent inhomogeneity can be measured."
 One can thus wonder whether the imbomoegceucous pattern ideutified. v the fractal analysis of galaxy counts is a more artefact of this liebt cone effect., One can thus wonder whether the inhomogeneous pattern identified by the fractal analysis of galaxy counts is a mere artefact of this light cone effect.
 Iu R95. the uaecuitude of this effect iu an Eiustein«de Sitter universe is examined.," In R95, the magnitude of this effect in an Einstein-de Sitter universe is examined."
 The conclusion is hat “even accepting au error marem of in the measurcucuts of the global deusitv. a redshift equal to 0.1 is approximately the deepest scale where we could observe a hiomogeuceous distribution of dust in an Eiusteia-de Sitter model”. uinpaired by he light cone effect.," The conclusion is that “even accepting an error margin of in the measurements of the global density, a redshift equal to 0.1 is approximately the deepest scale where we could observe a homogeneous distribution of dust in an Einstein-de Sitter model”, unimpaired by the light cone effect."
 Now. such a redshift corresponds to a luminosity distance of about £10. Mpe for a value of the IIubble coustaut My=75 Win ! | and 310 Mpe for Hj=100 Kin | |l," Now, such a redshift corresponds to a luminosity distance of about 410 Mpc for a value of the Hubble constant $H_0=75$ Km $^{-1}$ $^{-1}$ and 310 Mpc for $H_0=100$ Km $^{-1}$ $^{-1}$."
 This is actually less than the depth reached by the ESO Slice Project galaxy survey (Vettolani ct al..," This is actually less than the depth reached by the ESO Slice Project galaxy survey (Vettolani et al.,"
 1997. 1998). which recently fueled the coutroversy about the trausitiou towards hoimogenucitv of the Iuninous matter distribution (Scaramella et al..," 1997, 1998), which recently fueled the controversy about the transition towards homogeneity of the luminous matter distribution (Scaramella et al.,"
. 1998: Jovee et ab.," 1998; Joyce et al.,"
 1999)., 1999).
 Other surveys aed at goiug bevoud this limut are curreutly uuder wav., Other surveys aimed at going beyond this limit are currently under way.
 Ribeivo’s aremmentoO is based on the analysis of the scusitivity of the integrated couditional density D Eq.(7)}). relative to the redshift.," Ribeiro's argument is based on the analysis of the sensitivity of the integrated conditional density $\Gamma^*$, \ref{gamstarl}) ), relative to the redshift."
 We show. in the preseut section. that the expression retained bw Ribeiro for D has to be modified which results in D? being less sensitive to the redshif value than claimed iu R95. thus Παρατις its conclusions.," We show, in the present section, that the expression retained by Ribeiro for $\Gamma^*$ has to be modified, which results in $\Gamma^*$ being less sensitive to the redshift value than claimed in R95, thus impairing its conclusions."
4. Tn R92. the author establishes expressious for some observational quautities. m an Eiustein-de Sitter space-time. as a function of the radial comoving coordinate r. chosen as a paraueter along the null ecodesics.," In R92, the author establishes expressions for some observational quantities, in an Einstein-de Sitter space-time, as a function of the radial comoving coordinate $r$, chosen as a parameter along the null geodesics."
 We list below. aud give in R95 units. the quautities relevant for our purpose.," We list below, and give in R95 units, the quantities relevant for our purpose."
 The cumulative iuuber count νι) is the umber of sources Which lie at radial coordinate distances less than reas seen by the observer at ¢=0.," The cumulative number count $N_c(r)$ is the number of sources which lie at radial coordinate distances less than $r$, as seen by the observer at $r=0$."
 In R95. it is written as where Me; is the average ealactic rest mass.," In R95, it is written as where $M_G$ is the average galactic rest mass."
 The Iuuiuositv distance d; of a source is the clistance ποια which the radiatiug body. if motionless iu an Euclidean space.would produce au cuerey flux equal to the one measured by the observer.," The luminosity distance $d_l$ of a source is the distance from which the radiating body, if motionless in an Euclidean space,would produce an energy flux equal to the one measured by the observer."
 It thus verifies L being the absolute huuüunositv. ic. the luminosity in the rest frame of the source. and f the measured," It thus verifies $L$ being the absolute luminosity, i.e. the luminosity in the rest frame of the source, and $f$ the measured"
is max[οἱ=552.0.,"is $ \max \, \vert \phi \vert \, = \, 552.0 $."
 The diffe'ence [rom the exact solution is typically as large as [.No|=0.1 à he region covered with the erid of f=).," The difference from the exact solution is typically as large as $ \vert \Delta \phi \vert \, = \, 0.1 $ in the region covered with the grid of $ \ell \, = \, 5 $."
 The difference from the ajalytie solution is less than Ae]«0.016 iu the region covered wi hie eril of f3 as shown in Figure Lb.," The difference from the analytic solution is less than $ \vert \Delta \phi \vert \, < \, 0.016 $ in the region covered with the grid of $ \ell \, = \, 3 $ as shown in Figure \ref{error4.eps}{."
 The differeuce is relatively large uear the grid. lev )OlLidary between {=3 auc I.," The difference is relatively large near the grid level boundary between $ \ell \, = \, 3 $ and 4."
 This is mos likely cue to the evaluation of the gravity at eyoyid level boundary., This is most likely due to the evaluation of the gravity at the grid level boundary.
 Our numerical scheme is the secoucd order accurate except at the erid le )OlLidaries since we employ tle center diffe'eice., Our numerical scheme is the second order accurate except at the grid level boundaries since we employ the center difference.
 The gravity at the grid level boundary. is ο hie first o«der accurate [see Eqs. (19)), The gravity at the grid level boundary is only the first order accurate [see Eqs. \ref{interpolation1}) )
 and »η., and \ref{interpolation2}) )].
 Ou the erid of f1. the error is global: ]Ü is 1egative iu the left (Gr<0) and positive iu le ish GrV 0).," On the grid of $ \ell \, = \, 1 $, the error is global; it is negative in the left $ x \, < \, 0 $ ) and positive in the right $ x \, > \, 0 $ )."
 This error comes frou the boundary condition., This error comes from the boundary condition.
 We applied the Neumaun coutjon [9] ‘the ouer boundary., We applied the Neumann condition for the outer boundary.
 The gravity at the »ouncda'vN ds evaluated by the inulti-pole expansion iu ich we ake account of the clipoe. quadruple. ard octuple iomuents as well as the total mass.," The gravity at the boundary is evaluated by the multi-pole expansion in which we take account of the dipole, quadruple, and octuple moments as well as the total mass."
 ese hiejer order morlets ald Olal mass are evaluated [rom the deusity distribution on the arse grid of €1.," These higher order moments and total mass are evaluated from the density distribution on the coarse grid of $ \ell \, = \, 1 $."
 Thus ever the dipole motet is seriously tucderestimatec in this example., Thus even the dipole moment is seriously underestimated in this example.
 is uude‘estniatlon is cloimiual ti ithe error o ithe coarse erid /=1.," This underestimation is dominant in the error on the coarse grid $ \ell \, = \, 1 $."
 The quadruple and octuple o»neuts are practically 100 take niilo account on {1e bouudary in the example., The quadruple and octuple moments are practically not taken into account on the boundary in the example.
 Lowe apply a better er boudary COLdition. the er “will be reduced.," If we apply a better outer boundary condition, the error will be reduced."
" we examine the accturey of the [n]e'avity at the cell center. g;j,. defined by Equation we 9"," Next we examine the accuracy of the gravity at the cell center, $ \mbox{\boldmath$ $} _{i,j,k} $ , defined by Equation \ref{c-center-g}) )."
" is the same as FieΘ 1 but fo riherelative error. |g — σαςjσι. wrere g., denotes e exact gravilv οplained aialytically."," Figure \ref{error-g.eps} is the same as Figure \ref{error4.eps} but for the relative error, $ \vert \mbox{\boldmath$ $} \, - \, \mbox{\boldmath$ $} _{\rm ex} 
\vert / \vert \mbox{\boldmath$ $} _{\rm ex} $, where $ \mbox{\boldmath$ $} _{\rm ex} $ denotes the exact gravity obtained analytically."
 The 'eative error is large (~0.1) iu the cells located on e sturlaces of the spheres., The relative error is large $ \sim 0.1 $ ) in the cells located on the surfaces of the spheres.
 I Is wich less than 10- o.jn most cells., It is much less than $ 10 ^{-2} $ in most cells.
" This"" small e‘ror ensures hat w scheue reprocdiCes not o the 1/r potenial but also the quacdruple momert of the binary.", This small error ensures hat our scheme reproduces not only the $ 1/r $ potential but also the quadruple moment of the binary.
 le er‘or is moclerately large ).02) in the cells adjaceut to the grid leve boundary., The error is moderately large $ \sim 0.02 $ ) in the cells adjacent to the grid level boundary.
 [t is fairly SLiall except in the cells locaed ou the surfaces of the spheres., It is fairly small except in the cells located on the surfaces of the spheres.
 The large eTOF OL ile surfaces of ile spleres are due to the [ac| that ever the finest grkl is too coarse to resove the surlace sharply aud not serious in practical tne., The large error on the surfaces of the spheres are due to the fact that even the finest grid is too coarse to resolve the surface sharply and not serious in practical use.
 Iu most hydrodysaiunical simulations. a sel-gravialing gas has a luore or less shrooth cleusity distributjon in the finest eric.," In most hydrodynamical simulations, a self-gravitating gas has a more or less smooth density distribution in the finest grid."
" 'To evaluae the relative error i1 the eravily |iantitatively. we measured the siiiple average. the root mean square ave""age. ALLE Ιe Inaxiuunm value."," To evaluate the relative error in the gravity quantitatively, we measured the simple average, the root mean square average, and the maximum value."
 Figure 6 show them as a fuction of ΑΝ., Figure \ref{norm.eps} show them as a function of $ N $.
 The average axl ναLD are couputed se)aratev lor cells adjacent to the grid level boundary ancl for the rest cells., The average and maximum are computed separately for cells adjacent to the grid level boundary and for the rest cells.
 Each curve ¢enoes the valte al the grkl of each level., Each curve denotes the value at the grid of each level.
" Panesh.d. αμαf are for the cels adjacent o the erie evel bounca""v whie panels«e.c. aud are lor he rest cells."," Panels, and are for the cells adjacent to the grid level boundary while panels, and are for the rest cells."
 Panels aud show the siuiple average., Panels and show the simple average.
 Panels ca1d dslow the root mean square average., Panels and show the root mean square average.
 Panels andf show the maxiumuu., Panels and show the maximum.
" The sjallower clashec lines deuote |g — gosj Geox)=10""N! for comparison between panes."," The shallower dashed lines denote $ \vert \mbox{\boldmath$ $} \, - \,
\mbox{\boldmath$ $} _{\rm ex} \vert / \vert 
\mbox{\boldmath$ $} _{\rm ex} \vert \; = \; 
10 ^{-0.5} \, N ^{-1} $ for comparison between panels."
 The steeper dashed lijes deLote |g — Josj σας)LON7 ," The steeper dashed lines denote $ \vert \mbox{\boldmath$ $} \, - \,
\mbox{\boldmath$ $} _{\rm ex} \vert / \vert 
\mbox{\boldmath$ $} _{\rm ex} \vert \; = \; 
10 \, N^{-2} $."
Iu the cells not adjacent to the grid level bouiclary. the simple average and root mean square average of the relative error iu the gravity are proportion alto N-97.The root mean square average are nearly. as large as the simple average.," In the cells not adjacent to the grid level boundary, the simple average and root mean square average of the relative error in the gravity are proportional to $ N ^{-2} $.The root mean square average are nearly as large as the simple average."
 The maxiuinun value is ouly three times larger than the, The maximum value is only three times larger than the
a change of the nou-thermal compoucut caunot explain the observed variation. a thermal variation can do it (Fieure 7-Sd)).,"a change of the non-thermal component cannot explain the observed variation, a thermal variation can do it (Figure \ref{fig88d}) )."
 However. the changes in Z aud υπ should be luwger in V than in RH.," However, the changes in $T$ and $n_T$ should be larger in $V$ than in $R$."
" In V. the temperature would have chiauged ~2000 1 with πι, (at. while in & the chauge would be of only —1200 K aud HT,00.92."," In $V$ the temperature would have changed $\sim 2~000$ K with $n_{T_{t_2}} \sim 0.87$ , while in $R$ the change would be of only $\sim 1~200$ K and $n_{T_{t_2}} \sim 0.92$."
 According to the changes of brightuess iu the V baud. the rate of the change would be of ~GOO IK hr3.," According to the changes of brightness in the $V$ band, the rate of the change would be of $\sim 600$ K $hr^{-1}$."
" The observations between R8 aud DB bauds were obtaiuce with a difference of ~& uinutes: then. the temperature difference would vo ~SO Ty. Considering the first aud the second data sets: Spe,=1.12 aud Sys,1.26."," The observations between $R$ and $B$ bands were obtained with a difference of $\sim 8$ minutes; then, the temperature difference would be $\sim 80$ K. Considering the first and the second data sets: $S_{Rt_0}=1.12$ and $S_{Rt_1}=1.26$."
 In such a case. the temperature ciscrepancy would )»c explained.," In such a case, the temperature discrepancy would be explained."
"The simultanecitycriterion indicates hat observations were not performed at the same evel of bxielituess (considering the first aud last data sets: Sp=0.05. Sy=(0,53 aud Sp= 0.96). )ecause the variation in Rods very quick. leading ο. a spurious spectral variation.","The simultaneitycriterion indicates that observations were not performed at the same level of brightness (considering the first and last data sets: $S_B=0.05$, $S_V=0.53$ and $S_R=0.96$ ), because the variation in $R$ is very quick, leading to a spurious spectral variation."
 In spite of this ack of simultaucity. the spectral microvariation yossesses thermal characteristics.," In spite of this lack of simultaneity, the spectral microvariation possesses thermal characteristics."
 This is evicleut aking iuto accom that the Band V. hands data conplies with the simultancity criterion., This is evident taking into account that the $B$ and $V$ bands data complies with the simultaneity criterion.
 This «nuasar showed variations iu hnree cifferent nichts., This quasar showed variations in three different nights.
 Its brightness was similar diving the three nigits (nac~ 17.6). and near o the brightuess reted by Stepanianctal.(2001). Gay.=17.29d 0.03) aud by Chavushyvan TEE 17.62).," Its brightness was similar during the three nights $m_V \sim 17.6$ ), and near to the brightness reported by \citet{Stepanian01} $m_V=17.29 \pm 0.03$ ) and by \citet{Chavu95} $m_V=17.62$ )."
 A unique conrponeut marginalvfits to the data of this object (Figures 7-9a.. T-10a.. 7-11a)).," A unique component marginallyfits to the data of this object (Figures \ref{fig89a}, , \ref{fig810a}, , \ref{fig811a}) )."
 Although a thermal componentcan be added with Z~10.000 Ix.contrary to the case of 1628.5|3808. the," Although a thermal componentcan be added with $T\sim 10,000$ K,contrary to the case of 1628.5+3808, the"
"seen, which is similar to that of the Lorenz system with R— (Figure 4)).","seen, which is similar to that of the Lorenz system with $R = 500$ (Figure \ref{svdlor}) )."
 This indicates that the observed oscillation is of a limit cycle origin., This indicates that the observed oscillation is of a limit cycle origin.
 Note that the surrogate data which has the same power spectrum and distribution has a different SVD reconstruction (Figure 9))., Note that the surrogate data which has the same power spectrum and distribution has a different SVD reconstruction (Figure \ref{GRS_rho_svd}) ).
" The power spectra and flux distribution for two other class of GRS 1915-105, y and x, are shown in Figure 10.."," The power spectra and flux distribution for two other class of GRS 1915+105, $\gamma$ and $\chi$, are shown in Figure \ref{GRS_chi_pow}."
 A low frequency QPO with harmonics similar to that seen in the p class is detected for the  class., A low frequency QPO with harmonics similar to that seen in the $\rho$ class is detected for the $\gamma$ class.
 During the x class no such QPO is detected., During the $\chi$ class no such QPO is detected.
" However, for both these classes, the SVD reconstruction of the dynamics does not show any qualitative features (Figure 11))."," However, for both these classes, the SVD reconstruction of the dynamics does not show any qualitative features (Figure \ref{GRS_chi_svd}) )."
 Such space filling SVD reconstructions are characteristics of systems with uncorrelated stochastic noise., Such space filling SVD reconstructions are characteristics of systems with uncorrelated stochastic noise.
" In agreement with this, the D;(M) values are ~M and show no saturation, for these two states (Figure 11)). Moreover, the D5(M) are consistent with those obtained from corresponding surrogate data."," In agreement with this, the $D_2 (M)$ values are $\approx M$ and show no saturation, for these two states (Figure \ref{GRS_chi_svd}) ).Moreover, the $D_2(M)$ are consistent with those obtained from corresponding surrogate data."
 Data from the @ and 6 classes show similar behavior and are not shown., Data from the $\phi$ and $\delta$ classes show similar behavior and are not shown.
" These resultsimply that the variability of these classes are of stochastic nature, in contrast to that of the p class."," These resultsimply that the variability of these classes are of stochastic nature, in contrast to that of the $\rho$ class."
" In particular, the observed low frequency QPO in the p and x class have a different origin."," In particular, the observed low frequency QPO in the $\rho$ and $\chi$ class have a different origin."
 The behavior of the rest of the classes is more complex., The behavior of the rest of the classes is more complex.
" For example, the power spectra for A, 0, κ. and D class do not show any low frequency (Figure 12)), while the flux strongdistribution is typically periodicitynon-Gaussian (Figure 13))."," For example, the power spectra for $\lambda$, $\theta$, $\kappa$ and $\beta$ class do not show any strong low frequency periodicity (Figure \ref{GRS_beta_pow}) ), while the flux distribution is typically non-Gaussian (Figure \ref{GRS_beta_dist}) )."
 The SVD reconstruction of these data (Figure 14)) show structure which qualitatively maybe similar to that of a chaotic with noise (Figure 5)) and are somewhat different than the systemSVD reconstruction of the corresponding surrogate data (Figure 15))., The SVD reconstruction of these data (Figure \ref{GRS_beta_svd}) ) show structure which qualitatively maybe similar to that of a chaotic system with noise (Figure \ref{svd_noise}) ) and are somewhat different than the SVD reconstruction of the corresponding surrogate data (Figure \ref{GRS_beta_svd_surgg}) ).
 More evidence is provided by the D2(M) values for these data sets (Figure 16)) which show saturation and are different from the values computed from corresponding surrogate data., More evidence is provided by the $D_2 (M)$ values for these data sets (Figure \ref{GRS_beta_d2}) ) which show saturation and are different from the values computed from corresponding surrogate data.
" Using non-linear time series analysis techniques, evidence has been provided that the black hole system GRS 19154105 exhibits stochastic variability when it is in xy, y, @ and 6 classes."," Using non-linear time series analysis techniques, evidence has been provided that the black hole system GRS 1915+105 exhibits stochastic variability when it is in $\chi$ , $\gamma$ , $\phi$ and $\delta$ classes."
" In the p class, the low frequency QPO detected in the power spectrum can be attributed to a non-linear limit cycle"," In the $\rho$ class, the low frequency QPO detected in the power spectrum can be attributed to a non-linear limit cycle"
Mg 15.2.,$M_B \sim $ –18.2.
 Corrected for the maguificatiou factor of 1.5 mae obtained from the lensing model by Suaith et ((2002). this vields an absolute maecuitude of only Mg~ 16.1.," Corrected for the magnification factor of 1.8 mag obtained from the lensing model by Smith et (2002), this yields an absolute magnitude of only $M_B \sim$ –16.4."
 Even taking the appareutly hieh extinction iuto account bbelow) this still corresponds to Mp~ Ls., Even taking the apparently high extinction into account below) this still corresponds to $M_B \sim$ --18.
 to 18.8., to –18.8.
 To the best of our knowledge. this males it the faintest starformineg source at intermediate redshift for which spectroscopic data have been obtained.," To the best of our knowledge, this makes it the faintest starforming source at intermediate redshift for which spectroscopic data have been obtained."
 We now discuss the possible nature of this faint galaxy., We now discuss the possible nature of this faint galaxy.
 The observed line ratio ADOOT  5.9 is of moderate to Ligh excitation typical of relatively metal-poor eealaxies whose emission lines are predominantly powered by star formation., The observed line ratio $\lambda$ $\sim$ 5.9 is of moderate to high excitation typical of relatively metal-poor galaxies whose emission lines are predominantly powered by star formation.
 The emission lines are unresolved. aud thus we can exclude a Sevfert 1 galaxy. but iun principle uot a Sevfert 2.," The emission lines are unresolved, and thus we can exclude a Seyfert 1 galaxy, but in principle not a Seyfert 2."
 However. the #22582 object is fainter than most Sev 2 IIo et 11997) even if corrected for extinction.," However, the 2582 object is fainter than most Sey 2 Ho et 1997) even if corrected for extinction."
 With au absolute magnitude of Mg~ -16.1 (or Isto 15.5 after extinction correction) this galaxy is fainter than Lyman break galaxies at +~3 by at least 3 ainae. but similar to the compact narrow cussion line ealaxies (CNELG) at 2< L1 of Guzman ct ((1997).," With an absolute magnitude of $M_B \sim$ -16.4 (or $\sim$ –18 to –18.8 after extinction correction) this galaxy is fainter than Lyman break galaxies at $z \sim 3$ by at least 3 mag, but similar to the compact narrow emission line galaxies (CNELG) at $z <$ 1.4 of Guzman et (1997)."
 The Thuninositv (L(IL7)~1.2x.10H cre lj ids also coniparable to that of CNELG. aud to the bright cud of OOeenlaxies in the local Universe.," The luminosity $L(\hb) \sim 1.2 \times 10^{41}$ erg $^{-1}$ ) is also comparable to that of CNELG, and to the bright end of galaxies in the local Universe."
 Tl‘he observedl emission lines coutributetril tto ~ 56 of he observed απ flux within the slit., The observed emission lines contribute to $\sim$ 56 of the observed $J$ -band flux within the slit.
 Assumiug Case D recombination and zero Gy~ L8 mag) extinction a ower lauit to the contribution of Ta to the ILE-baud is estimated ο  lr (30)., Assuming Case B recombination and zero $A_V \sim$ 1.8 mag) extinction a lower limit to the contribution of $\alpha$ to the H-band is estimated to $\sim$ 17 (30).
. We do not expect significant contanination from other emission lines ou the remainiug filters., We do not expect significant contamination from other emission lines on the remaining filters.
 After correction of he observed broad baud flix or the eumission lines. the ollowing estimate is obtained or the rest-fiune eequivaleu width: HW(OL)~ 139AL.," After correction of the observed broad band flux for the emission lines, the following estimate is obtained for the rest-frame equivalent width: $W(\hb)_{\rm rest} \sim$ 139."
 Whereas smaller equivalent widths are typically observed in large starburst ealaxies and in some CNELG. such values are fairly conmauon in low metallicity eealaxies SStasizkka Izotov 2003).," Whereas smaller equivalent widths are typically observed in large starburst galaxies and in some CNELG, such values are fairly common in low metallicity galaxies Stasiśkka Izotov 2003)."
 The broad-baud SED plotted iu rofüe.cdprocidesfurtherinforimationonthepropertiesofthisobjcct.," The broad-band SED plotted in \\ref{fig_sed}
 provides further information on the properties of this object."
 VT, Basically such a SED can only be reconciled with a population showing a strong Balmer break and little extinction or a younger stellar population strongly extinguished in the rest-frame UV.
 hisisquantitativelgconfivrincdbgS EDfitsofuuim," This is quantitatively confirmed by SED fits of numerous templates using the code of Bolzonella et (2000), including spectra from the 2001 version of Bruzual Charlot (1993) models, Starburst99 (Leitherer et 1999), and observed galaxy templates from Coleman et (1980) and Kinney et (1996)."
cvous 360510 Myr aud little or no extinction. or bursts of ages ~ 69 Myr with Ay~ 1.2LS mag depeudiug ou the adopted extinction law.," The best fits correspond to burst models with ages $\sim$ 360–510 Myr and little or no extinction, or bursts of ages $\sim$ 6–9 Myr with $A_V \sim$ 1.2–1.8 mag depending on the adopted extinction law."
 The former explanation is excluded. as populations of such age are uot compatible with the presence of enmuüssion lines indicative of vouug CS 10 My) massive stars., The former explanation is excluded as populations of such age are not compatible with the presence of emission lines indicative of young $\la$ 10 Myr) massive stars.
 Furthermore. if preseut (iu quantities sufficient to explain tthe observed flux) the vouug population will dominate the rest-frame UVoptical spectrum.," Furthermore, if present (in quantities sufficient to explain the observed flux) the young population will dominate the rest-frame UV–optical spectrum."
 We therefore conclude that the oulv consistent explanation for the observed SED of i£22582 is that it isdominated by a vouug (~ 69 My) population which sitters from a strong extinction., We therefore conclude that the only consistent explanation for the observed SED of 2582 is that it isdominated by a young $\sim$ 6–9 Myr) population which suffers from a strong extinction.
 This best fit reproduces the observed SED to within ~ | 20. as shown in ousingtwod:f fercutcrtinetionlaws Calzcttictal. (2000) forstarbursts. withAy ~ 1.6l.5 mag. aud the Seaton (1979) Milkv Way extinction law with Ay~ L2Ll image.," This best fit reproduces the observed SED to within $\sim$ 1–2 $\sigma$, as shown in \\ref{fig_sed}, using two different extinction laws: Calzetti et (2000) for starbursts, with $A_V
\sim$ 1.6--1.8 mag, and the Seaton (1979) Milky Way extinction law with $A_V \sim$ 1.2–1.4 mag."
" The later produces a strong ""absorption bump at ~ 5900À.", The later produces a strong “absorption bump” at $\sim$ 5900.
. Thus. we are probally dealing with a low-inctallicity :id dusty vouug starburst.," Thus, we are probably dealing with a low-metallicity and dusty young starburst."
 The best cousisteney checks of our explanation ou the nature of this source will probably be through sspectroscopy. in order to coufirin the large extinction aud to exclude the Sev 2 possibility.," The best consistency checks of our explanation on the nature of this source will probably be through spectroscopy, in order to confirm the large extinction and to exclude the Sey 2 possibility."
 Deeper optical imagine. including the Z-baud. will inuprove the constraints on the overall SED.," Deeper optical imaging, including the $Z$ -band, will improve the constraints on the overall SED."
 Measurements of other cussion lines such Us A3T27.. I8.G58L.. and," Measurements of other emission lines such as , , and"
should be present in the projected svstemi in our search reeine.,should be present in the projected system in our search regime.
 The differences in the x aud y aud z positious for the group members was selected within oof cach other., The differences in the x and y and z positions for the group members was selected within of each other.
 Out of the 1000 simulations that we performed. 892 of these παΊος found all group members iud no ake interlopers.," Out of the 1000 simulations that we performed, 892 of these simulations found all group members and no fake interlopers."
 All real eroup members were recovered as well as the inclusion of fakea. members in 103 of he simulations., All real group members were recovered as well as the inclusion of fake members in 103 of the simulations.
 In 2 of the simulations. some of the real group menibers were found with fake member interlopers. and in 3 of the simulations some of the group nembers were found with uo fake interlopers detected.," In 2 of the simulations, some of the real group members were found with fake member interlopers, and in 3 of the simulations some of the group members were found with no fake interlopers detected."
 We therefore cousider our detection method to be very successful as iu more than 289% of cases. we were able o find our exact sinulation group xvsteni and 10.354 of the time. we also found all group mcmbers however with iuterlopers.," We therefore consider our detection method to be very successful as in more than $>89\%$ of cases, we were able to find our exact simulation group system and $10.3\%$ of the time, we also found all group members however with interlopers."
 When iuterlopers were present in the detected subgroups. 96.2% of these occeurrances had oulv l iuterloper. while 2 iuterlopers were detected in the remmaming cases.," When interlopers were present in the detected subgroups, $96.2\%$ of these occurrances had only 1 interloper, while 2 interlopers were detected in the remaining cases."
 These results strougly sugecst that at least some of our observationallv detected suberoups are real and they cannot all siuultaneouslv be false detections., These results strongly suggest that at least some of our observationally detected subgroups are real and they cannot all simultaneously be false detections.
 Lastly. we test whether our candidate subgroups might ο snialler ones overlapped bw projection purely by chance.," Lastly, we test whether our candidate subgroups might be smaller ones overlapped by projection purely by chance."
 To the simulated GC system as a whole. we add random subgroups cousisting of 1-6 members whose nembers are confined within a iregion.," To the simulated GC system as a whole, we add random subgroups consisting of 4-6 members whose members are confined within a region."
 These subgroups were randomly placed in the ealaxy between obefore being deprojected iuto 2-dimensional space., These subgroups were randomly placed in the galaxy between before being deprojected into 2-dimensional space.
 Two eroups were considered to overlap if aux one of their ucnibers were within a snall designated distauce from any nienuber of another eroup., Two groups were considered to overlap if any one of their members were within a small designated distance from any member of another group.
 The distance chosen did not significantly change our findings (cousicerine differences between 0.1. 244). so we selected0.," The distance chosen did not significantly change our findings (considering differences between $0.1-2$ ), so we selected."
5/.. We performed 7 simulations. cach consisting of a different πανα of suberoups placed in the galaxy. which increased linearly from 2 subgroups up to 8 suberoups.," We performed 7 simulations, each consisting of a different number of subgroups placed in the galaxy, which increased linearly from 2 subgroups up to 8 subgroups."
 For each of these simulations. we examined. over 1000 trials. how many times these subgroups overlapped.," For each of these simulations, we examined, over 1000 trials, how many times these subgroups overlapped."
" The nmuuber of overlaps ranged frou, no overlapping suberoups up to 5 overlapping suberoups.", The number of overlaps ranged from no overlapping subgroups up to 5 overlapping subgroups.
 We did nof find auy simulation which had more than 5 overlapping eroups., We did not find any simulation which had more than 5 overlapping groups.
 As would be expected. the higher the uuuber of suberoups present. the hieher the uuuber of overlapping suberoups are found as a result.," As would be expected, the higher the number of subgroups present, the higher the number of overlapping subgroups are found as a result."
 These probabilities of having random overlapping eroups are listed in Table £.., These probabilities of having random overlapping groups are listed in Table \ref{tab:overlap}.
 We fud that the probability of having two subgroups randomly overlap is ~άν, We find that the probability of having two subgroups randomly overlap is $\sim4\%$.
 If all & subgroups in NGC 5128 (1 GCs and. { PNe) are real groups. then the probability that 3 sets of suberoups randomly overlap is found to be ~7%.," If all 8 subgroups in NGC 5128 (4 GCs and 4 PNe) are real groups, then the probability that 3 sets of subgroups randomly overlap is found to be $\sim7\%$."
 Exluding Croup 2. whose subgroups have very different average velocities. our results sugecstfelon] there may be 2 sets of overlapping subgroups. Cirot Land Groups.," Exluding Group 2, whose subgroups have very different average velocities, our results suggest there may be 2 sets of overlapping subgroups, Group 1 and Group3."
 The proubiltv of 2 sets of suCLO. raudomly overlaping witji 8 subgroups present is 23!, The probabilty of 2 sets of subgroups randomly overlaping with 8 subgroups present is $23\%$.
 It is therefore not clear if these overlapping surou found in Croups 1 aud 3 are real., It is therefore not clear if these overlapping subgroups found in Groups 1 and 3 are real.
 Work bv Pengetal.(2002) shows a complex but fait shell structure threading the iuner aud imid-halo regions of NGC 5128., Work by \cite{peng02} shows a complex but faint shell structure threading the inner and mid-halo regions of NGC 5128.
 These shells have been attributed to the phase-wrapping of stars from accreted satellites., These shells have been attributed to the phase-wrapping of stars from accreted satellites.
" Ouc particular blue elliptical arc was found to be associated with a voune star clusters (2350 Myr). but aside from this one example. no stellar streams have been associated with GCs or Όλο,"," One particular blue elliptical arc was found to be associated with a young star clusters $\simeq350$ Myr), but aside from this one example, no stellar streams have been associated with GCs or PNe."
 We have begun a search for evidence of stellar streams in NGC 5128 by probing the objects within the galaxy that iav trace the stream., We have begun a search for evidence of stellar streams in NGC 5128 by probing the objects within the galaxy that may trace the stream.
 We use the available data for the CCs and the PNo. which may be stripped along with the stellar stream material during galaxy mteractions.," We use the available data for the GCs and the PNe, which may be stripped along with the stellar stream material during galaxy interactions."
 If these objects are located. they can be used to ideutity the possible orbits of accreted satellites.," If these objects are located, they can be used to identify the possible orbits of accreted satellites."
 To do this. we use a fricudless algorithm (Mexrettetal.2003). and search for evidence of stellar streams using the GCs and PNe separately in the analysis below.," To do this, we use a friendless algorithm \citep{merrett03} and search for evidence of stellar streams using the GCs and PNe separately in the analysis below."
 For cach object in our saunple with a measured radial velocity and a velocity uncertainty less than 50 lau | (totalling [11 GCs aud 780 PNo). we have found its ΑΔ rearest neighbours.," For each object in our sample with a measured radial velocity and a velocity uncertainty less than 50 km $^{-1}$ (totalling 411 GCs and 780 PNe), we have found its $N$ nearest neighbours."
" For those No ucighbours. we have calculated their mean velocity Cec,v 2d their velocity dispersion. ay."," For those $N$ neighbours, we have calculated their mean velocity $v_{mean,N}$ and their velocity dispersion, $\sigma_N$ ."
 We have classified the central object as ilendless if its velocity is more than à«oy from eeu.vN-," We have classified the central object as friendless if its velocity is more than $n\times\sigma_N$ from $v_{mean,N}$."
 Varviug the No parameter does not see to siguificautlv alter the results., Varying the $N$ parameter does not seem to significantly alter the results.
 We do fud varving the ay parameter roni 3 to [| changes the mmuber of fieudless objects by a few. while varving oy from 2 to 3 does change the iuuber of objects significautly.," We do find varying the $\sigma_N$ parameter from 3 to 4 changes the number of friendless objects by a few, while varying $\sigma_N$ from 2 to 3 does change the number of objects significantly."
 Taking a conservative approach aud using ay=L. we find no frieudless GCs when No=30. 1 when N=20 (C0258). aud. 1 when /N=10 (CCO57s8).," Taking a conservative approach and using $\sigma_N=4$, we find no friendless GCs when $N=30$ , 1 when $N=20$ (GC0258), and 1 when $N=10$ (GC0578)."
 CGC(258 will not be considered further as it was classified as a resolved GC in Uarrisetal.(2006) while à recent radial velocity measurement indicates this object may be a star (Woodleyetal.2010b).. and it is because of this low radial velocity measurement that this object is identified.," GC0258 will not be considered further as it was classified as a resolved GC in \cite{harris06} while a recent radial velocity measurement indicates this object may be a star \citep{woodley10b}, and it is because of this low radial velocity measurement that this object is identified."
 GCOSTS may indeed be fricudless. but it is not possible to use one GC to mdicate evidence for a stellar stream.," GC0578 may indeed be friendless, but it is not possible to use one GC to indicate evidence for a stellar stream."
" Using No=10 and ay=3 vields 7 fricucless GCs (CGCO216. GC0219. CC0325. CGCO0506. CGCO577. CCOSTS, CCO5SU)."," Using $N=10$ and $\sigma_N=3$ yields 7 friendless GCs (GC0216, GC0249, GC0325, GC0506, GC0577, GC0578, GC0580)."
 We conduct the same analysis with the PNe dataset using gy= Land fud no frieudless objects when N—30. l wheu NV=20 (f05p02). and 6 when NV=10 (1012. 1285. 5602. f05p02. flsp2s. fI2p10).," We conduct the same analysis with the PNe dataset using $\sigma_N=4$ and find no friendless objects when $N=30$, 1 when $N=20$ (f05p02), and 6 when $N=10$ (4012, 4285, 5602, f05p02, f18p28, f42p10)."
 Using No=10 and oy=3 vields 20 fricudless PNe (1012. 1128. 1285. I117. 1511. 5203. 5601. 5602. 5617. GLOL. fOlpl. O5p02. füsp50—23002.. £LEpOTG. flaps. flSspG65— ‘Lsp67=1023. flSps3. £12p10. mosNEpu," Using $N=10$ and $\sigma_N=3$ yields 20 friendless PNe (4012, 4128, 4285, 4417, 4511, 5203, 5601, 5602, 5617, 6104, f04p1, f05p02, f08p50=3002, f14p016, f18p28, f18p65=1208, f18p67=4023, f18p83, f42p10, mosNEpn4)."
 The locations1208. of the inner ~15 of these are shown in 1).Figure 1.., The locations of the inner $\sim 15$ of these are shown in Figure \ref{fig:subgroups_all}.
 The friendless objects that are located at the argest distances from the ealaxws ceuter are likely rot indicators of streams., The friendless objects that are located at the largest distances from the galaxy's center are likely not indicators of streams.
 Rather. there are very few icielhibours as the incompleteness of plauctary nebulae and CC's is quite high bevoud ((see the radial distribition as a function of azimuth for he GCs in Figure 8 of Woodleyetal.(2010) aud the distribution of the PN i1 Figure 2 of Pengetal.(200 139).," Rather, there are very few neighbours as the incompleteness of planetary nebulae and GCs is quite high beyond (see the radial distribution as a function of azimuth for the GCs in Figure 8 of \cite{woodley10b} and the distribution of the PN in Figure 2 of \cite{peng04a}) )."
 This leaves oulv the inir wwhich can beexplored for fieudless objects. of which there are few (again. de»udiue onu the parameters clioseu in the fricudless algorilun).," This leaves only the inner which can beexplored for friendless objects, of which there are few (again, depending on the parameters chosen in the friendless algorithm)."
 We listthese objects with, We listthese objects with
For our reference simulation. we have chosen a size for the launching region of ten times (he gravitational softening radius: 2) 1θσσ=LAU.,"For our reference simulation, we have chosen a size for the launching region of ten times the gravitational softening radius: $\varpi_0=10 \varpi_g
=1\AU$."
" Inside z,. the dimensionless injection parameter is set (o V;—2. so that the injected material can escape without the help from the magnetocentrifugal effect."," Inside $\varpi_g$, the dimensionless injection parameter is set to $V_i=2$, so that the injected material can escape without the help from the magnetocentrifugal effect."
" For the launching region that rotates in a Ixeplerian [ashion (between ze, and zy). we let V,=0.01. so that the injection speed is much less than the local Keplerian speed (but still greater than the sound speed. which is set (o an arbitrarily small value)."," For the launching region that rotates in a Keplerian fashion (between $\varpi_g$ and $\varpi_0$ ), we let $V_o
=0.01$, so that the injection speed is much less than the local Keplerian speed (but still greater than the sound speed, which is set to an arbitrarily small value)."
" For the density distribution at the base of the wind. we set a,,=2. which is the same as (hat adopted by Dlandford&Payne(1982) for their sell-similar solutions. aud we choose D,=0.1."," For the density distribution at the base of the wind, we set $\alpha_m=2$, which is the same as that adopted by \citet{bp82}
 for their self-similar solutions, and we choose $D_0=0.1$."
" To specify the wind-launching magnetic field. we adopt a vertical field strength at a, of By=19.2G and an exponent for field distribution. ay=5/4."," To specify the wind-launching magnetic field, we adopt a vertical field strength at $\varpi_g$ of $B_0=19.2\gauss$ and an exponent for field distribution, $\alpha_B=5/4$."
 The latter is again (he Dlandford-Pavne scaling., The latter is again the Blandford-Payne scaling.
" The adopted field strength leads (o a wind mass loss rate of M,=10M.vr| from each side of the disk.", The adopted field strength leads to a wind mass loss rate of $\dot{M}_{w}=10^{-8}\solarmassyear$ from each side of the disk.
" The corresponding scale [or mass density al c,"" is 2.07x10.LiI5eem.I or. assumingS pure hydrogenS Seas. a number density scale of 1.23xLOMem. ."," The corresponding scale for mass density at $\varpi_g$ is $2.07\times 10^{-14}\massden$, or, assuming pure hydrogen gas, a number density scale of $1.23\times10^{10}\numden$ ."
 For other choices of By. the mass flux and density scale vary as D.," For other choices of $B_0$, the mass flux and density scale vary as $B_0^2$ ."
 Figure 1. shows the prescribed launching conditions for our reference simulation., Figure \ref{fig:f1} shows the prescribed launching conditions for our reference simulation.
" Note that the axial injection region within c,=0.1AU contains about of the cumulative mass [lux from the disk in our simulation.", Note that the axial injection region within $\varpi_g=0.1\AU$ contains about of the cumulative mass flux from the disk in our simulation.
 This fraction ean be made smaller by reclicing {he injection density. but it would take longer lor the wind to reach a steady state because ol a more stringent Courant condition.," This fraction can be made smaller by reducing the injection density, but it would take longer for the wind to reach a steady state because of a more stringent Courant condition."
 NLBO3 investigated the effects of the axial injection and concluded (hat the structure aud dvnamics of the magnetocentrifugal part of the wind remained largely unchanged for differing mass fluxes in the axial region., KLB03 investigated the effects of the axial injection and concluded that the structure and dynamics of the magnetocentrifugal part of the wind remained largely unchanged for differing mass fluxes in the axial region.
 We confirmed this result with a new set of simulations., We confirmed this result with a new set of simulations.
 Conmputatonalh. we have used a eril with 256 ac(üve zones in both the = aud z directions.," Computationally, we have used a grid with 256 active zones in both the $\varpi$ and $z$ directions."
 On both axes the grid spacing is linear for 0.<zzx12AU with 76 zones. and logarithmic lor 1.2<z.:I00AU with 180 zones.," On both axes the grid spacing is linear for $0\leq\varpi,z\leq1.2\AU$ with 76 zones, and logarithmic for $1.2
\leq\varpi,z\leq100\AU$ with 180 zones."
 This arrangement allows us to extend our simulation to large distances from the origin while still retaining good resolution of the launching region., This arrangement allows us to extend our simulation to large distances from the origin while still retaining good resolution of the launching region.
 The results of our reference simulation are shown in Figures 2- 4.., The results of our reference simulation are shown in Figures \ref{fig:f2}- \ref{fig:f4}.
 In reffig:[2.. we plot the steady-state solution on two scales.," In \\ref{fig:f2}, we plot the steady-state solution on two scales."
 On the smaller. 10AU scale. we find (hat most of the space is filled with magnetocentrifugallv accelerated wind material from the Keplerian part of the launching surface between 0.1 and 1AU.," On the smaller, $10\AU$ scale, we find that most of the space is filled with magnetocentrifugally accelerated wind material from the Keplerian part of the launching surface between $0.1$ and $1\AU$."
 The [ast injection part of the wind. enclosed within (he streamline closest to the axis. occupies a relatively small fraction of the space.," The fast injection part of the wind, enclosed within the streamline closest to the axis, occupies a relatively small fraction of the space."
 The fraction decreases on (he larger scale. as shown in (he bottom panel.," The fraction decreases on the larger scale, as shown in the bottom panel."
 There is some residual nonsteadiness in (he fast injection region. which has little effect on ihemagnetocentrifugal part of the wind.," There is some residual nonsteadiness in the fast injection region, which has little effect on themagnetocentrifugal part of the wind."
 In both panels.gradual collimation is evident in," In both panels,gradual collimation is evident in"
 ~—ray (6>| (Hartiuauelal.1999)., $\gamma-$ $b\ga 10^{\circ}$ \citep{h99}.
. (6x107). “the of the brightest sources have already been identified)., $b\la 10^{\circ}$ of the brightest sources have already been identified).
 There js ab excess of sourfes αἱ inid-latitudes (107ESbz«o30°).20()ye makiugal up a second component. which has been steeested to be associated wih[un the Gould Belt (Cirenier1993).. with some 1ication of an acditioual component associa with the Calac.ic halo.," There is an excess of sources at mid-latitudes $10^{\circ}\la b \la 30^{\circ}$ ), making up a second component, which has been suggested to be associated with the Gould Belt \citep{gr98}, with some indication of an additional component associated with the Galactic halo."
 Finally. there is a IOdulation which is highly coucentrated aloug ile Galactic plane. aud is our main Concern here.," Finally, there is a population which is highly concentrated along the Galactic plane, and is our main concern here."
 Spectral studies (Merckοἱal.1996) suggest a need for additional source classes., Spectral studies \citep{me96} suggest a need for additional source classes.
 In particular. there are many sources witl steeper spectra (photon ixlex [>2.3 beween LOO MeV aud 1CeV hau is expectec [or either a pulsar or a blazar.," In particular, there are many sources with steeper spectra (photon index $\Gamma\ga 2.2$ ) between 100 MeV and 1GeV than is expected for either a pulsar or a blazar."
 Iu. addition. variability studies (McLaughinetal.1996:Tompkins1999) iucicate ali excess οἱ variable. soIces al low Caactic latitudes.," In addition, variability studies \citep{m96,t99} indicate an excess of variable sources at low Galactic latitudes."
 Since pulsa ‘sare uot thought to be variable. this would Sugeest an additional Class of Galactic sowces.," Since pulsars are not thought to be variable, this would suggest an additional class of Galactic sources."
 However. fo Daly dclividua source tO 'Cpresent a Lew source Class. it would first have to be demonstrated lia it is not a blaza which are |iehly. variable.," However, for any individual source to represent a new source class, it would first have to be demonstrated that it is not a blazar, which are highly variable."
 The main obstacle to ideutilica101 has been the arge positioal uncertalnties of the sources., The main obstacle to identification has been the large positional uncertainties of the sources.
Lowcouning rates ¢Οιinedwith a broad. energy-deyenclent poii{-syreac,"Lowcounting rates combinedwith a broad, energy-dependent point-spread"
Lowcouning rates ¢Οιinedwith a broad. energy-deyenclent poii{-syreacl,"Lowcounting rates combinedwith a broad, energy-dependent point-spread"
J=VxBfppo.,$\vec j = \nabla \times \vec B / \mu_0$.
 Note that we ignore gas pressure in Eq.(1) as a simplifving assumption., Note that we ignore gas pressure in Eq.(1) as a simplifying assumption.
" Iu the simplest. possible case. whilst retaining essential plivsics. we assume that the radial velocity of the galactic matter is zero. V,=0. aud the only compouent of the velocity is azimuthal."," In the simplest possible case, whilst retaining essential physics, we assume that the radial velocity of the galactic matter is zero, $V_r=0$, and the only component of the velocity is azimuthal."
 Thus. we end up with the ouly 7-compouent of the MHD equation of motion Eq.(1): The latter quadratic equation cau be solved to vield Here V(r) is the azimuthal velocity in the rotating [rame.," Thus, we end up with the only $r$ -component of the MHD equation of motion Eq.(1): The latter quadratic equation can be solved to yield Here $V_{\phi}(r)$ is the azimuthal velocity in the rotating frame."
 It is related to the rotational (azimuthal) velocity in the laboratory frame. V(r). via As expected. we could have arrived at the same result by writing the MHD equation of motion in the non-inertial frame rotating with the galaxy as MOND aud MSTC models do.," It is related to the rotational (azimuthal) velocity in the laboratory frame, $\tilde V_{\phi}(r)$, via As expected, we could have arrived at the same result by writing the MHD equation of motion in the non-inertial frame rotating with the galaxy as MOND and MSTG models do."
 Note that + sigus refer to the galactic rotational curves lor the either side ofthe galactic centre on a giveu azimuth direction., Note that $\pm$ signs refer to the galactic rotational curves for the either side of the galactic centre on a given azimuth direction.
 Naturally. one could perform a study that would include inauy galaxies.," Naturally, one could perform a study that would include many galaxies."
 However. our aim here is to demonstrate the principle.," However, our aim here is to demonstrate the principle."
 Thus. our case study will be the galaxy auc iu what follows we fix |=uw atu22/(250x109365.2521x60GO) rad to as we know that the galaxy rotates ouce in 250 uilliou years.," Thus, our case study will be the galaxy and in what follows we fix $|\vec \omega| = \omega$ at $\omega= 2 \pi/(250 \times 10^6\times 365.25\times 24 \times 60 \times 60)$ rad $^{-1}$, as we know that the galaxy rotates once in 250 million years."
 As [ar as the distribution of ordinary. baryonic matter is concerned. we use observationally constrained model presented iu (Browustein Mollat 2006).," As far as the distribution of ordinary, baryonic matter is concerned, we use observationally constrained model presented in (Brownstein Moffat 2006)."
 La particular. they used a simple inodel for AZ(r) with the best fit parameters for the galaxy being SeAd=9.12xLOM ALL and ο=1.01 kpc.," In particular, they used a simple model for $M(r)$ with the best fit parameters for the galaxy being $M=9.12\times10^{10}$ $M_{\sun}$ and $ r_c = 1.04$ kpc."
 The density prescribed by the same model (Browustein MolIat 2006). is The key ingredient of our model is the magnetic fiekl. which manifests itself in the rotational curve via additional force jxBiplr)=VxBxB/ftptryn) in Ec.(1).," The density prescribed by the same model (Brownstein Moffat 2006), is The key ingredient of our model is the magnetic field, which manifests itself in the rotational curve via additional force ${\vec j \times \vec B}/ {\rho(r)}= {\nabla \times \vec B \times \vec B} /({\rho(r)} \mu_0 )$ in Eq.(4)."
 There is a body of work, There is a body of work
"Bautista&Pradhan(1996) and Osterbrock&Fer-land (2006), respectively, and found these to be 1-3 orders of magnitude smaller than πο.","\citet{bp:96} and \citet{osterbrock:06}, respectively, and found these to be 1-3 orders of magnitude smaller than $n_e$."
" On this basis, we deem an LTE treatment to be valid."," On this basis, we deem an LTE treatment to be valid."
" Using the line intensities in Table 4,, we derive masses using the upper excited state populations of the ions and find 3.7x1073 Mo, 1x107?Mo, and 2.2x10-?Mo for stable (Ni°,Ni+), Ar*, and Ne* respectively, for an electron temperature of KK. Note that the result is insensitive to temperature: a +1000KK change in temperature, changes the mass estimates by $15%.."," Using the line intensities in Table \ref{tab:intensities}, we derive masses using the upper excited state populations of the ions and find $\times 10^{-3}\,M_\odot$ , $\times 10^{-3}\,M_\odot$, and $\times 10^{-3}\,M_\odot$ for stable $^0$ $^+$ ), $^+$, and $^+$ respectively, for an electron temperature of K. Note that the result is insensitive to temperature: a $\pm$ K change in temperature, changes the mass estimates by $\lesssim$."
" The partition functions are from Halenkaetal.(2001) for Ni, and Irwin(1981) for Ar and Ne."," The partition functions are from \citet{halenka:01} for Ni, and \citet{irwin:81} for Ar and Ne."
" Assuming a uniform distribution of stable Ni, we find that the Sobolev optical depths of all detected Ni lines are less than 0.06."," Assuming a uniform distribution of stable Ni, we find that the Sobolev optical depths of all detected Ni lines are less than 0.06."
" Strong transitions of [NilII] jm and [NiIV] um lie within the wavelength region covered, but these lines are not detected at either epoch."," Strong transitions of [NiIII] $\mu$ m and [NiIV] $\mu$ m lie within the wavelength region covered, but these lines are not detected at either epoch."
 We conclude that the Ni is predominantly in the neutral and singly-ionised state., We conclude that the Ni is predominantly in the neutral and singly-ionised state.
" Thus, assuming insignificant clumping, the value we derive above is probably close to the total stable Ni mass."," Thus, assuming insignificant clumping, the value we derive above is probably close to the total stable Ni mass."
" The predicted mass of stable Ni is sensitive to the progenitor mass, although this relation is not monotonic, and depends sensitively on the explosion mechanism, multi-dimensional effects and, in spherical models, on the mass cut, which is a free parameter."," The predicted mass of stable Ni is sensitive to the progenitor mass, although this relation is not monotonic, and depends sensitively on the explosion mechanism, multi-dimensional effects and, in spherical models, on the mass cut, which is a free parameter."
" Thielemann predict stable Ni masses in the range for progenitors in the range Mo, and a much 0.01-0.014Μαlower value of Mo for a Μο star."," \citet{thielemann:96} predict stable Ni masses in the range $\,M_\odot$ for progenitors in the range $\,M_\odot$, and a much lower value of $\,M_\odot$ for a $\,M_\odot$ star."
" Other authors (e.g.Chieffi&Limongi2004;WoosleyWeaver1995;Nomotoetal.2006) derive comparable values, though detailed intercomparisons are difficult due to different parametrizations of physical processes."," Other authors \citep[e.g.][]{cl:04,ww:95,nomoto:06}
 derive comparable values, though detailed intercomparisons are difficult due to different parametrizations of physical processes."
 Chieffi&Limongi(2004) provide explosive yields as a function of metallicity based on parameters which have been calibrated to fit observed properties of massive stars., \citet{cl:04} provide explosive yields as a function of metallicity based on parameters which have been calibrated to fit observed properties of massive stars.
 The value for the stable Ni mass that we derive is closest to their progenitor models of Μο with metallicities of a third to a twentieth of the solar value., The value for the stable Ni mass that we derive is closest to their progenitor models of $M_\odot$ with metallicities of a third to a twentieth of the solar value.
" Although we can definitively rule out higher mass progenitors at even lower metallicities, we current cannot exclude a Mo progenitor at solar metallicity."," Although we can definitively rule out higher mass progenitors at even lower metallicities, we current cannot exclude a $M_\odot$ progenitor at solar metallicity."
" Further, planned, late-time spectroscopy should provide tighter constraints."," Further, planned, late-time spectroscopy should provide tighter constraints."
" Given the high energy required to ionise neutral Ne and Ar (15.8eV) we conclude that, given the low (21.6eV)ionisation conditions indicated by Ni, the bulk of the Ne and Ar lies in the neutral state."," Given the high energy required to ionise neutral Ne (21.6eV) and Ar (15.8eV) we conclude that, given the low ionisation conditions indicated by Ni, the bulk of the Ne and Ar lies in the neutral state."
" However, no strong transitions of or lie in our wavelength range."," However, no strong transitions of [NeI] or [ArI] lie in our wavelength range."
" Consequently, the [Nel]masses [A:I]derived here for the first ionisation state represent lower limits only."," Consequently, the masses derived here for the first ionisation state represent lower limits only."
" For SN 1987A at 260 days, using the [Coll] um line, Rocheetal.(1993) derivea value for Mg,+ of 4.6x107?Mo."," For SN 1987A at 260 days, using the [CoII] $\mu$ m line, \citet{roche:93} derivea value for $M_{\mathrm{Co}^{+}}$ of $4.6\times10^{-3}\,M_\odot$."
 Using our day 214 intensity for this line in SN 2005af we obtain Ma = 2.4x107?Mo.," Using our day 214 intensity for this line in SN 2005af we obtain $M_{\mathrm{Co}^{+}}$ = $2.4\times10^{-3}\,M_\odot$."
" Allowing for the different epochs for the two SNe, this implies that a ?6Ni mass of M; was ejected by SN 2005af."," Allowing for the different epochs for the two SNe, this implies that a $^{56}$ Ni mass of $M_\odot$ was ejected by SN 2005af."
" This estimate falls in the expected range for normal Type II SNe (e.g.,Hamuy2003)."," This estimate falls in the expected range for normal Type II SNe \citep[e.g.,][]{hamuy:03}."
. Although we have a clear detection of the SN 2005af spectrum between jum (Fig. 1)) —, Although we have a clear detection of the SN 2005af spectrum between $\mu$ m (Fig. \ref{fig:irsboth}) ) –
" the first, for any SN at this early epoch — we do not see any significant spectral features."," the first, for any SN at this early epoch – we do not see any significant spectral features."
" This is not surprising, given its youth."," This is not surprising, given its youth."
" In SN19874, lines of [FeII] in this spectral region were only detected after ~400dd (Haas 1990).."," In SN1987A, lines of [FeII] in this spectral region were only detected after $\sim$ d \citep{haas:90}. ."
 In Fig., In Fig.
" 3 we compare roughly coeval mid-IR spectra of SN 2005af with that of SN 1987A (IIpec) at 60 dd, and"," \ref{fig:compare} we compare roughly coeval mid-IR spectra of SN 2005af with that of SN 1987A (IIpec) at $\sim$ d, and"
Type Ic supernova (SN) 2002ap has attracted particular attention since its discovery by Y. Hirose in January 2002. because of its relatively close distance (about D= 7.3 Mpe. Sharma. Karachentsev. Tikhonov 1996; Sohn Davidge 1996) and its broad-line spectral features (Kinugasa et al.,"Type Ic supernova (SN) 2002ap has attracted particular attention since its discovery by Y. Hirose in January 2002, because of its relatively close distance (about $D = $ 7.3 Mpc, Sharina, Karachentsev, Tikhonov 1996; Sohn Davidge 1996) and its broad-line spectral features (Kinugasa et al."
 2002) that are considered as a signature of very energetic supernovae., 2002) that are considered as a signature of very energetic supernovae.
 Such a supernova population. often called as hypernovae whose prototype is the famous type Ic SN 1998bw. have explosion energy more than 10 times larger than the standard energy (~ 10°'erg) when spherical symmetry is assumed (Iwamoto et al.," Such a supernova population, often called as hypernovae whose prototype is the famous type Ic SN 1998bw, have explosion energy more than 10 times larger than the standard energy $\sim 10^{51} \rm erg$ ) when spherical symmetry is assumed (Iwamoto et al."
 1998: Woosley et al., 1998; Woosley et al.
 1999: see also Hófflich. Wheeler. Wang 1999 for asymmetric modeling of these events with less extreme explosion energies).," 1999; see also Höfflich, Wheeler, Wang 1999 for asymmetric modeling of these events with less extreme explosion energies)."
 The apparent association of a gamma-ray burst (GRB) 980425 with SN 1998bw makes these mysterious events even more interesting in the context of the possible SN/GRB Mazzali et al. (, The apparent association of a gamma-ray burst (GRB) 980425 with SN 1998bw makes these mysterious events even more interesting in the context of the possible SN/GRB Mazzali et al. (
2002) presented photometric and spectroscopic modeling of SN 2002ap assuming a spherical explosion. and indicated that the explosion occurred at Jan 28-£0.5 UT. with a kinetic energy of about «10°! erg and the progenitor is a C+O star whose main sequence mass Is ~ 20-25M...,"2002) presented photometric and spectroscopic modeling of SN 2002ap assuming a spherical explosion, and indicated that the explosion occurred at Jan $\pm$ 0.5 UT, with a kinetic energy of about $\times 10^{51}$ erg and the progenitor is a C+O star whose main sequence mass is $\sim 20$ $M_\odot$."
 It seems that an interacting binary is more likely for a star of this mass scale to lose its hydrogen and helium envelope. but theoretical and metallicity uncertainties do not reject a single Wolf-Rayet (WR) star as another possible progenitor (Smartt et al.," It seems that an interacting binary is more likely for a star of this mass scale to lose its hydrogen and helium envelope, but theoretical and metallicity uncertainties do not reject a single Wolf-Rayet (WR) star as another possible progenitor (Smartt et al."
 2002)., 2002).
 In contrast to SN 1998bw / GRB980425. SN 2002ap was not associated with a GRB to the sensitivity of IPN (Hurley et al.," In contrast to SN 1998bw / GRB980425, SN 2002ap was not associated with a GRB to the sensitivity of IPN (Hurley et al."
 2002: but see also Gal-Yam et al., 2002; but see also Gal-Yam et al.
 2002)., 2002).
 On the other hand. spectropolarimetric observations of SN 2002ap (Kawabata et al.," On the other hand, spectropolarimetric observations of SN 2002ap (Kawabata et al."
 2002: Leonard et al., 2002; Leonard et al.
 2002: Wang et al., 2002; Wang et al.
 2002) give an interesting hint for hidden energetic ejecta., 2002) give an interesting hint for hidden energetic ejecta.
 Kawabata et al. (, Kawabata et al. (
2002) noticed that the spectral shape of polarized continuum observed by Subaru around 10 Feb (re. ~13 days after the explosion) apparently looks like the original unpolarized spectrum. but redshifted by z=0.3 (ΑνναA=1 +5) and the ratio of the polarized to unpolarized flux is fp=0.0018 (in fA).,"2002) noticed that the spectral shape of polarized continuum observed by Subaru around 10 Feb (i.e., $\sim$ 13 days after the explosion) apparently looks like the original unpolarized spectrum, but redshifted by $z = 0.3$ $\lambda_{\rm
redshifted}/\lambda = 1 + z$ ) and the ratio of the polarized to unpolarized flux is $f_P = 0.0018$ (in $f_\lambda$ )."
 The polarization angle (PA) is different from line polarization at this epoch or PA in their second observation in March (40 days after the explosion)., The polarization angle (PA) is different from line polarization at this epoch or PA in their second observation in March (40 days after the explosion).
 Interestingly. they got a consistent PA and wavelength-independent polarization from February to March. that can be explained simply by an asymmetric photosphere as often seen in supernova spectra. after they subtracted the redshifted polarized continuum in February observation.," Interestingly, they got a consistent PA and wavelength-independent polarization from February to March, that can be explained simply by an asymmetric photosphere as often seen in supernova spectra, after they subtracted the redshifted polarized continuum in February observation."
 If it is not a chance coincidence. this result can be explained by an asymmetric supernova photospheread a jet moving at a much higher speed (~cz 0.90) than the supernova photosphere (Kawabata et al.," If it is not a chance coincidence, this result can be explained by an asymmetric supernova photosphere a jet moving at a much higher speed $\sim cz \sim 0.3c$ ) than the supernova photosphere (Kawabata et al."
 2002)., 2002).
 Following this suggestion. Leonard et al. (," Following this suggestion, Leonard et al. ("
2002) confirmed the resemblance between polarized and redshifted spectrum. by an independent data taken by Keck. although statistical significance of this resemblance ts difficult,"2002) confirmed the resemblance between polarized and redshifted spectrum, by an independent data taken by Keck, although statistical significance of this resemblance is difficult"
is no appreciable screening of the optical star by the disk.,is no appreciable screening of the optical star by the disk.
 Such an extension of the disk would mean that the binary system is on the common envelope evolutionary stage. aud so the narrow absorption lines from the optical star surface could not be observed.," Such an extension of the disk would mean that the binary system is on the common envelope evolutionary stage, and so the narrow absorption lines from the optical star surface could not be observed."
 The orbital period stability over 30 vears of observations also suggests against tle presence of a common euvelope in SS 133., The orbital period stability over 30 years of observations also suggests against the presence of a common envelope in SS 433.
 The results of our analvsis can be sununarized as ‘ollows., The results of our analysis can be summarized as follows.
 l., 1.
 Long uarrow jets (rp<<bj a) outfiowiug from he ceutral object can be ouly partially screened by the disk diving its eclipse and precession., Long narrow jets $r_j \ll b_j\sim a$ ) outflowing from the central object can be only partially screened by the disk during its eclipse and precession.
" Neither the observed eclipse depth nor the precession auiplitudoe <A, cal )e Explained by this model. (", Neither the observed eclipse depth nor the precession amplitude $A_{pr}\sim 4$ can be explained by this model. (
See Fig. 8)).,See Fig. \ref{fig:jthin_l}) ).
 2., 2.
 Short narrow jets (rj)«bj a) where b; is ound frou the condition that the precession variability auplitude is νοb, Short narrow jets $r_j\ll b_j \ll a$ ) where $b_j$ is found from the condition that the precession variability amplitude is $A_{pr}=4$.
 The theoretical eclipse light curves or this model for different mass ratios q are displaved in Fig. 9.., The theoretical eclipse light curves for this model for different mass ratios $q$ are displayed in Fig. \ref{fig:jthin_s}.
 For auv 4 this model is inconsistent with the observed 18-60 keV. X-ray eclipse shape., For any $q$ this model is inconsistent with the observed 18-60 keV X-ray eclipse shape.
 3., 3.
" An extended corona (rj> 0j) gives the best fit for the observed lard X-ray precession amplitude (el,~1 j and the observed eclipse shape (Fig. 103).", An extended corona $r_j > b_j$ ) gives the best fit for the observed hard X-ray precession amplitude $A_{pr}\sim 4$ ) and the observed eclipse shape (Fig. \ref{fig:jthick})).
 ΑΠ residuals iu this model are attained for the mass ratio q—anyf£myc0.2 (Fie. 11).," Minimum residuals in this model are attained for the mass ratio $q=m_x/m_v \approx 0.2$ (Fig. \ref{fig:chi2}) ),"
 which is close to that derived from fitting the aud observations with a narrow jet model (sawai ct al., which is close to that derived from fitting the and observations with a narrow jet model (Kawai et al.
 1989. Notani ct al.," 1989, Kotani et al."
 1996)., 1996).
 If we take iuto account only the upper euvelope of the ascending X-ray eclipse. branch (see above). the fit with q220.3 ποσο] to be acceptable as well (Fig.," If we take into account only the upper envelope of the ascending X-ray eclipse branch (see above), the fit with $q \approx 0.3$ seems to be acceptable as well (Fig."
 10. aud 11))., \ref{fig:jthick} and \ref{fig:chi2}) ).
 The parameters δ and w appear to be related aud cannot be determined- separately., The parameters $b_j$ and $\omega$ appear to be related and cannot be determined separately.
" Formal 47.D decreases as wo907. without any essential change of q for w~ SO""."," Formal $\chi^2$ decreases as $\omega\rightarrow 90^\circ$, without any essential change of $q$ for $\omega\grsim 80^\circ$ ."
 Obviously. the solution with w=90° (planar disk with zero thickness) could not provide any precessional," Obviously, the solution with $\omega=90^\circ$ (planar disk with zero thickness) could not provide any precessional"
,\begin{document}
"For example, the TP-AGB phase is more prominent in the Maraston(2005) models than in Bruzual&Char-lot(2003).","For example, the TP-AGB phase is more prominent in the \cite{ma05} models than in \cite{bc03}."
". Therefore, stellar masses derived using the Bruzual&Charlot(2003) models are generally higher than stellar masses derived using the Maraston(2005) SPS models (e.g.,Wuytsetal.2007;Muzzin2009;Kannappan&Gawiser2007;vanderWeletal. 2006)."," Therefore, stellar masses derived using the \cite{bc03}
 models are generally higher than stellar masses derived using the \cite{ma05} SPS models \citep[e.g.,][]{wu07,mu09,kg07,we06}."
". Several studies use galaxy spectral energy distributions (SEDs) to assess the different SPS models, and resolve the discrepancies Marastonetal.2006;Eminianetal."," Several studies use galaxy spectral energy distributions (SEDs) to assess the different SPS models, and resolve the discrepancies \citep[e.g,][]{ma06,em08}."
" This(e.g, exercise is complicated due to the large 2008).variety of possible stellar populations and the degeneracies between the star formation timescale, age, metallicity, and dust."," This exercise is complicated due to the large variety of possible stellar populations and the degeneracies between the star formation timescale, age, metallicity, and dust."
" However, specific galaxy populations can be used to constrain certain stellar evolution phases."," However, specific galaxy populations can be used to constrain certain stellar evolution phases."
" For example, Conroy&Gunn(2010) use post-starburst galaxies in the Sloan Digital Sky Survey to assess the treatment of the TP-AGB phase of (SDSS)different SPS models, as TP-AGB stars dominate the near-infrared luminosity during this phase."," For example, \cite{cg10} use post-starburst galaxies in the Sloan Digital Sky Survey (SDSS) to assess the treatment of the TP-AGB phase of different SPS models, as TP-AGB stars dominate the near-infrared luminosity during this phase."
" They find that the models by Bruzual&Charlot and Conroyetal. can reproduce the optical (2003)and near-infrared colors of (2009)post-starburst galaxies, while the Maraston(2005) models cannot."," They find that the models by \cite{bc03} and \cite{co09} can reproduce the optical and near-infrared colors of post-starburst galaxies, while the \cite{ma05} models cannot."
" In this Letter, we take a similar approach as Conroy&Gunn(2010) and use a post-starburst galaxy population in the NEWFIRM medium-band survey (NMBS;vanDokkumetal.2009) to test different SPS models, and obtain new constraints on the SED shape during the time that the TP-AGB stars are thought to be most dominant."," In this Letter, we take a similar approach as \cite{cg10} and use a post-starburst galaxy population in the NEWFIRM medium-band survey \citep[NMBS;][]{vd09a} to test different SPS models, and obtain new constraints on the SED shape during the time that the TP-AGB stars are thought to be most dominant."
" The NMBS allows us to photometrically select a large and clean sample of post-starburst galaxies, and to construct a composite SED which is more thoroughly sampled than in Conroy&Gunn(2010)."," The NMBS allows us to photometrically select a large and clean sample of post-starburst galaxies, and to construct a composite SED which is more thoroughly sampled than in \cite{cg10}."
". Throughout the Letter, we assume a ACDM cosmology with Q4,= 0.3, Q4=0.7, and Πο=70 km s! Mpc!."," Throughout the Letter, we assume a $\Lambda$ CDM cosmology with $\Omega_{\rm m}=0.3$ , $\Omega_{\rm\Lambda}=0.7$, and $H_{\rm
 0}=70$ km $^{-1}$ $^{-1}$."
 The NMBS uses five custom near-infrared medium-band filters and covers a total area of 0.4 deg? in the COSMOS (Scovilleetal.2007) and AEGIS (Davisetal.2007) fields., The NMBS uses five custom near-infrared medium-band filters and covers a total area of 0.4 $^2$ in the COSMOS \citep{sc07} and AEGIS \citep{da07} fields.
" The medium-band filter set, in combination with deep optical medium and broadband photometry and IRAC imaging, provides accurate photometric redshifts and stellar population properties (e.g.,Brammeretal.2009;vanDokkumal.2010;Whitak"," The medium-band filter set, in combination with deep optical medium and broadband photometry and IRAC imaging, provides accurate photometric redshifts and stellar population properties \citep[e.g.,][]{br09,vd10,wh10}."
eret A full overview of this survey is given in K. E. 2010)..Whitaker et al. (, A full overview of this survey is given in K. E. Whitaker et al. (
"2010, in preparation).","2010, in preparation)."
" The photometric redshifts and stellar population properties are derived using EAZY (Brammeretal. and FAST (Krieketal.2009b),, respectively."," The photometric redshifts and stellar population properties are derived using EAZY \citep{br08} and FAST \citep{kr09a}, respectively."
 Our 2008)post-starburst galaxy sample is selected using three optimized synthetic rest-frame filters of intermediate (see Figure 1))., Our post-starburst galaxy sample is selected using three optimized synthetic rest-frame filters of intermediate (see Figure \ref{fig:ill}) ).
" The Um and D, filters isolate the Balmer break, while mmeasures the slope of the SED just redwards of the Balmer break."," The $U_{\rm m}$ and $B_{\rm m}$ filters isolate the Balmer break, while measures the slope of the SED just redwards of the Balmer break."
" The location of the V4, filter is a trade-off between being red enough to constrain the SED slope and blue enough not to enter the regime where the stellar evolution models and spectral libraries start to deviate (seealsoMarastonetal.2009).", The location of the $V_{\rm m}$ filter is a trade-off between being red enough to constrain the SED slope and blue enough not to enter the regime where the stellar evolution models and spectral libraries start to deviate \citep[see also][]{m09}.
". Post-starburst galaxies have strong Balmer breaks, characterized by red ccolors and blue ccolors, and thus are expected to lie in the black selection box in Figure 2.."," Post-starburst galaxies have strong Balmer breaks, characterized by red colors and blue colors, and thus are expected to lie in the black selection box in Figure \ref{fig:sel}."
 The boundaries of the selection box are a trade-off between minimizing contamination by dusty star-forming galaxies (estimated to be ~1%)) and obtaining a large enough sample., The boundaries of the selection box are a trade-off between minimizing contamination by dusty star-forming galaxies (estimated to be $\sim$ ) and obtaining a large enough sample.
" As indicated by the orange SED in Figure 1,, dusty star-forming galaxies with the same ccolor as post-starburst galaxies will have redder ccolors."," As indicated by the orange SED in Figure \ref{fig:ill}, dusty star-forming galaxies with the same color as post-starburst galaxies will have redder colors."
" In order to solely include high-quality SEDs with rest-frame UV-to-NIR wavelength coverage, werequire a redshift of z>0.5 and a K-band signal-to-noise ratio (S/N) of 25."," In order to solely include high-quality SEDs with rest-frame UV-to-NIR wavelength coverage, werequire a redshift of $z>0.5$ and a $K$ -band signal-to-noise ratio (S/N) of 25."
" We also exclude galaxies for which the IRAC fluxes are strongly contaminated by nearby sources, and thus cannot properly be deblended (Labbéetal.2005)."," We also exclude galaxies for which the IRAC fluxes are strongly contaminated by nearby sources, and thus cannot properly be deblended \citep{la05}."
". The final selection consists of 62 galaxies at 0.695< 2.028, with a median redshift of z—1.56."," The final selection consists of 62 galaxies at $0.695<z<2.028$ , with a median redshift of $z=1.56$."
" Six targets have spectroscopic redshifts, yielding a median photometric redshift uncertainty of Az/(1+2)— 0.005."," Six targets have spectroscopic redshifts, yielding a median photometric redshift uncertainty of $\Delta
z/(1+z)=0.005$ ."
 We have inspected the SEDs of all targets by eye and none haveobvious problems., We have inspected the SEDs of all targets by eye and none haveobvious problems.
" Furthermore, for none of the selected galaxies there are indications that the rest-frame UV-to-NIR continuum is dominated by dusty star formation (Figure 2))."," Furthermore, for none of the selected galaxies there are indications that the rest-frame UV-to-NIR continuum is dominated by dusty star formation (Figure \ref{fig:sel}) )."
 Similar to spectroscopic, Similar to spectroscopic
(Pilbrattctal.2010) (Alolinavietal.2010)— fa (6OLyan). (Churchlwellctal.2009) (Careyetal.2000). 14an. (amoLOmm). spatial scales down to ~LO” and over a large fraction of the ealactic plane.,"\citep{pilbratt2010} \citep{molinari2010} $\mu$ $a\sim0.1\,\mu$ \citep{churchwell2009} \citep{carey2009} $\mu$ $\la 10\,$ spatial scales down to $\sim40\arcsec$ and over a large fraction of the galactic plane."
" At 70 and 160,040 many of the observed. structures show a close spatial correlation with some of the classical infrared tracers ofsiiall dust particles. like the emission nieasured at 8 and 21,4424. aud therefore. oue expects a partially similar origin and/or a similar cdepeucdence to ISM physical properties."," At 70 and $\mu$ m many of the observed structures show a close spatial correlation with some of the classical infrared tracers ofsmall dust particles, like the emission measured at 8 and $\mu$ m, and therefore, one expects a partially similar origin and/or a similar dependence to ISM physical properties."
 To properly uuderstaud the origin of this emission is the first step of the data analysis., To properly understand the origin of this emission is the first step of the data analysis.
 Dust is heated by stella. ultraviolet(UV)-visible photons and re-radiate the absorbed energv iu the infrared., Dust is heated by stellar ultraviolet(UV)-visible photons and re-radiate the absorbed energy in the infrared.
 Asstuing some dust properties. this dust Cluission is widely used to trace crucial quantities like cloud masses or star forming activity.," Assuming some dust properties, this dust emission is widely used to trace crucial quantities like cloud masses or star forming activity."
 However. to derive accurately these quautities requires to take iuto account je dust properties evolution. how it affects its oenission md how it reflects the ISM. properties.," However, to derive accurately these quantities requires to take into account the dust properties evolution, how it affects its emission and how it reflects the ISM properties."
 Ou the other rand. dust plavs a crucial role for the ISAL plivsics aud ahonüstry.," On the other hand, dust plays a crucial role for the ISM physics and chemistry."
 Since dust aud the rest of ISM. are tightly uterlock. chanecs on the dust propertics affect those of je gas phase.," Since dust and the rest of ISM are tightly interlock, changes on the dust properties affect those of the gas phase."
 It is then necessary to characterize the physical processes responsible for the dust evolution to assess their role within the ISM lifecycle aud to be able ο use dust as a reliable tracer of the ISAL, It is then necessary to characterize the physical processes responsible for the dust evolution to assess their role within the ISM lifecycle and to be able to use dust as a reliable tracer of the ISM.
 Accessing he full dust SED over a laree fraction of the sv allows o follow the behavior of every dust component over a xoad rauge of physical conditions which is au invaluable information for the study of the dust evolution., Accessing the full dust SED over a large fraction of the sky allows to follow the behavior of every dust component over a broad range of physical conditions which is an invaluable information for the study of the dust evolution.
 Tu this paper. we present the first analysis of the ΤΗ-(ναι data combined with that of GLIMIPSE aud MIPSGAL to obtain the full dust SED from 8 to gu. In the refsect:obs.. we describe the observations aud the fitting," In this paper, we present the first analysis of the Hi-Gal data combined with that of GLIMPSE and MIPSGAL to obtain the full dust SED from 8 to $\mu$ m. In the \\ref{sect:obs},, we describe the observations and the fitting"
The time periods evaluated in figure 6 are those which do not have a well-defined rise and decay. but do exhibit variable flix.,"The time periods evaluated in figure 6 are those which do not have a well-defined rise and decay, but do exhibit variable flux."
 Region E exhibits a [ast decay. but there were no observations during (he rise of the flare.," Region E exhibits a fast decay, but there were no observations during the rise of the flare."
 The HID exhibits a soltening spectra with the decrease in flux., The HID exhibits a softening spectra with the decrease in flux.
 Region F is characterized bv a long rise in [lux over a lime period of >2 weeks. but there are no observations during the decay of flux.," Region F is characterized by a long rise in flux over a time period of $>$ 2 weeks, but there are no observations during the decay of flux."
 This IUD diagram exhibits an overall hardening of the spectrum as the fIux increases. but there is some scatter in the data points.," This HID diagram exhibits an overall hardening of the spectrum as the flux increases, but there is some scatter in the data points."
 Ivsteresis properties cannot be determined due to the lack of data during the xesumed decay of the flux., Hysteresis properties cannot be determined due to the lack of data during the presumed decay of the flux.
 Regione G is similar to regione F in that it is a longe rise of flux over a period of 2 weeks. but it does turn over and begin to decay in the last. (wo clays.," Region G is similar to region F in that it is a long rise of flux over a period of $\sim$ 2 weeks, but it does turn over and begin to decay in the last two days."
 This IND exhibits spectral hardening with increased (lux., This HID exhibits spectral hardening with increased flux.
 An overall clockwise hvsteresis appears (ο be evident lor region G. however Chis is not well determined due to two factors: the complete long-timescale fux variation is not observed throughout (he entire decay. ancl the short-timescale flux. variations make it difficult (ο evaluate the characteristics of the longer üimescale variabilitv.," An overall clockwise hysteresis appears to be evident for region G, however this is not well determined due to two factors; the complete long-timescale flux variation is not observed throughout the entire decay, and the short-timescale flux variations make it difficult to evaluate the characteristics of the longer timescale variability."
 The two smaller IUD loops associated with regions C and D flaring can also be seen in (his HID., The two smaller HID loops associated with regions C and D flaring can also be seen in this HID.
 The effect of relatively short term variability combined with long-term variability is evident in the IIID diagram lor region G., The effect of relatively short term variability combined with long-term variability is evident in the HID diagram for region G.
The mass density can be found integrating the distribution function. f(r.e) over the velocity. obtaining an explicit relation for p as a function of the potential ο where (=(04+C)/o? is the dimensionless potential. πιαο(207)*? and pis the dimensionless clensitv. which explicitely depends only on Ü.Once assigned initial conditions for the potential e and its derivative ο in r=0. the Poisson equation can be rewritten in terms of the dimensionless potential. in (he form: where p(0)=οἱ) and P—r/rz; being the Ning radius.,"The mass density can be found integrating the distribution function $f(r,v)$ over the velocity, obtaining an explicit relation for $\rho$ as a function of the potential $\psi$: where $U\equiv(\psi+C)/\sigma^2$ is the dimensionless potential, $k=4\pi m\alpha e^{C/\sigma^2}(2\sigma^2)^{3/2}$ and $\tilde\rho$ is the dimensionless density, which explicitely depends only on $U$.Once assigned initial conditions for the potential $\psi$ and its derivative $\psi'$ in $r=0$, the Poisson equation can be rewritten in terms of the dimensionless potential, in the form: where $\rho(0)=\rho(U_0)$ and $\tilde r= r/r_{core}$ being the King radius."
" Once assigned as initial parameters Cj. U. the Poisson equation can be integrated. obtaining the dimensionless potential ('(*). the dimensionless mass clensitv p(r) and the lidal radius 5; being P,=rifrüa4; WILL ro; vet not determined."," Once assigned as initial parameters $U_0$, $U'_0$, the Poisson equation can be integrated, obtaining the dimensionless potential $U(\tilde r)$, the dimensionless mass density $\tilde\rho(\tilde r)$ and the tidal radius $\tilde r_t$ , being $\tilde r_t=r_t/r_{core}$ with $r_{core}$ yet not determined."
 To determine the core, To determine the core
parallax measurement feasible.,parallax measurement feasible.
 During outbursts. the radio cluission is often resolved at the high augular resolutious required for precision astronmietry. makiug it difeult to determine the true location of the biuuw system from epoch to epoch.," During outbursts, the radio emission is often resolved at the high angular resolutions required for precision astrometry, making it difficult to determine the true location of the binary system from epoch to epoch."
 Lastly. many black hole N-vav binaries are located d or close to the Calactic Plane. such that the scatter-broadeniug aloug the Lue of sieht makes ligh-precision astromctry mipossible in the centimeter wavebaud where current VLBI arravs have the highest sensitivity.," Lastly, many black hole X-ray binaries are located in or close to the Galactic Plane, such that the scatter-broadening along the line of sight makes high-precision astrometry impossible in the centimeter waveband where current VLBI arrays have the highest sensitivity."
 lere we present Πο Sensitivity Array (IISA) observations of VlOl Cre. the most. huninous kuow- black hole X-rav binary in quiescence.," Here we present High Sensitivity Array (HSA) observations of V404 Cyg, the most luminous known black hole X-ray binary in quiescence."
" With a lias:μα function of 6.08+0.0637, (Casares&Charles1991).. the compact object is a clvnamically-confirmed black hole. acerecting matter from a WO subeiaunt companion star (Casaresetal.1993)."," With a mass function of $6.08\pm0.06M_{\odot}$ \citep{Cas94}, the compact object is a dynamically-confirmed black hole, accreting matter from a K0 subgiant companion star \citep{Cas93}."
. The svstei las a quiesceut radio flux density of nuns. with a flat spectra indicative of a self-absorbed compact jet (Calloetal. 2005).. although the jets are not resolved at the angular resolution of the TSA (AGiller-Jonesetal.2008).," The system has a quiescent radio flux density of mJy, with a flat spectrum indicative of a self-absorbed compact jet \citep{Gal05}, although the jets are not resolved at the angular resolution of the HSA \citep{Mil08}."
. The persistent. uuresolved radio emission makes this source a οσους target for astrometric observations to measure its parallax.," The persistent, unresolved radio emission makes this source a good target for astrometric observations to measure its parallax."
 We observed V101 Cye every 3 months over the course of one vear. using the TSA.," We observed V404 Cyg every 3 months over the course of one year, using the HSA."
 Two of the observations were made at the times of παπα parallactic displacement πι Rieht Ascension (R.À.). since the ssignal is larger. aud. owing to the ereater size of the array in the castavest dimension. las smaller error bars than that iu Declination.," Two of the observations were made at the times of maximum parallactic displacement in Right Ascension (R.A.), since the signal is larger, and, owing to the greater size of the array in the east-west dimension, has smaller error bars than that in Declination."
 We observed at a frequency of LOGI2. iu dual circular polarization. with an observing bandwidth of GIMMIIZ per polarization.," We observed at a frequency of GHz, in dual circular polarization, with an observing bandwidth of MHz per polarization."
 To these four TSA observations we added three archival datasets; two of which have already been reported (Miller-Jonesetal.2008. 2009).. aud one in which the source was previously uot sienificautly detected (Mioduszewskietal.2008).. but kuowiug the astrometric parameters of the source. we were able to detect it at the 5o level.," To these four HSA observations we added three archival datasets, two of which have already been reported \citep{Mil08,Mil09}, and one in which the source was previously not significantly detected \citep{Mio08}, but knowing the astrometric parameters of the source, we were able to detect it at the $5\sigma$ level."
 À fourth archival epoch did not detect the source to a 36 limit of |., A fourth archival epoch did not detect the source to a $3\sigma$ limit of $^{-1}$.
 A παν of the observatious is listed in Table 2.. and shows the exteut of the source variability.," A summary of the observations is listed in Table \ref{tab:obs}, and shows the extent of the source variability."
 In ouly one of the epochs was the source brighter than the 30 upper lt of this archival dataset Gn which none of the huge dishes of the TSA were available). malsing the non-detection consistent with the expected source flux deusity.," In only one of the epochs was the source brighter than the $3\sigma$ upper limit of this archival dataset (in which none of the large dishes of the HSA were available), making the non-detection consistent with the expected source flux density."
 Iu all cases. the observations were pliase-refercuced to a bright. nearby calibrator from the Intemational Celestial Reference Frame ICRE) source list. 22025|3313 (Alaetal. 1998).. located oulv 16.6 from the target. source.," In all cases, the observations were phase-referenced to a bright, nearby calibrator from the International Celestial Reference Frame (ICRF) source list, 2025+3343 \citep{Ma98}, located only $^{\prime}$ from the target source."
 This implics that our systematic errors. wdüch scale with distance from the phase reference source. should )o relatively small (~30 pias: see below).," This implies that our systematic errors, which scale with distance from the phase reference source, should be relatively small $\sim30$ $\mu$ as; see below)."
 We observed iu Samim cvcles. spending Luunin on the phase reference source and 2inmun on the target in cach cvele.," We observed in 3-min cycles, spending min on the phase reference source and min on the target in each cycle."
 To naxiuize astrometric accuracy. alb data below 23° elevation were discarded.," To maximize astrometric accuracy, all data below $23^{\circ}$ elevation were discarded."
 We also discarded data taken during the short timescale flares seen in a nunber of he observations (e...Miller-Jonesetal.2008).. in case he assumed variations iu the jet power respousible for he flaring events trauslated iuto positional offsets.," We also discarded data taken during the short timescale flares seen in a number of the observations \citep[e.g.,][]{Mil08}, in case the assumed variations in the jet power responsible for the flaring events translated into positional offsets."
 To enable us to estimate the svstematic errors affecting the astronietry. we substituted every seveuth scan on the areet source with au observation of a check source. the ICRF calibrator J2023|3153. located 17.57 away frou he phase reference source.," To enable us to estimate the systematic errors affecting the astrometry, we substituted every seventh scan on the target source with an observation of a check source, the ICRF calibrator J2023+3153, located $1^{\circ}.87$ away from the phase reference source."
 Data were reduced according o standard procedures within AIPS (Creiseun2003). and the source position at each epoch was determined w fitting an elliptical. Gaussian to the source.," Data were reduced according to standard procedures within AIPS \citep{Gre03}, and the source position at each epoch was determined by fitting an elliptical Gaussian to the source."
 Iu no case did the source appear to be resolved., In no case did the source appear to be resolved.
 Since the first epoch of archival data assunaied a differeut position or the phase reference source. we corrected. all epochs oa coumnon calibrator position of 201010sJ21056. 33°pr007.2111316 22000) before fitting for the proper notion aud parallax of VOL Οτο," Since the first epoch of archival data assumed a different position for the phase reference source, we corrected all epochs to a common calibrator position of $20^{\rm h}25^{\rm m}10^{\rm
s}.8421056$ , $33^{\circ}43^{\prime}00^{\prime\prime}.2144316$ 2000) before fitting for the proper motion and parallax of V404 Cyg."
 The measured »ositious are shown in Figure 1.. together with the best-fit parallax aud proper motion.," The measured positions are shown in Figure \ref{fig:sky_positions}, together with the best-fit parallax and proper motion."
 Pradeletal.(2006)— used. simulations to derive au approxinate formula for the svstematic errors affecting various VLBI arrays., \citet{Pra06} used simulations to derive an approximate formula for the systematic errors affecting various VLBI arrays.
 For our calibrator-target separation aud source declination. the estimated svstematic errors (for a inean value of the wet zenith path delav) are pas in aand pas in Dec. The fitted positious of the check source show an rms scatter of 1343s in aad µας iu Dec. Since the check source is seven times further away from the plase reference source tla the target. this provides a rigorous upper huit on the systematic errors in position.," For our calibrator-target separation and source declination, the estimated systematic errors (for a mean value of the wet zenith path delay) are $\mu$ as in and $\mu$ as in Dec. The fitted positions of the check source show an rms scatter of $\mu$ as in and $\mu$ as in Dec. Since the check source is seven times further away from the phase reference source than the target, this provides a rigorous upper limit on the systematic errors in position."
 As seen from Table 2.. our astrometric accuracy is limited by signal-to-nolse rather than systematic errors.," As seen from Table \ref{tab:obs}, our astrometric accuracy is limited by signal-to-noise rather than systematic errors."
 Nevertheless. the systematic errors estimated from Pradeletal.(2006) were added to the statistical errors iu quadrature before using the siugular value decomposition (SVD) method (asdetailed to fit for a reference position and proper motion in aand Dec.. and for the source parallax.," Nevertheless, the systematic errors estimated from \citet{Pra06} were added to the statistical errors in quadrature before using the singular value decomposition (SVD) method \citep[as detailed in][]{Loi07} to fit for a reference position and proper motion in and Dec., and for the source parallax."
 The best-fitting astrometric parameters. talking the mid-poiutof the observations. 551322. as the reference date.were:," The best-fitting astrometric parameters, taking the mid-pointof the observations, 54322, as the reference date,were:"
overall L3CO 393—20» emission of all observed sources in Serpens(Iburt&Barsony1996).,overall $_2$ CO $3_{03}\rightarrow 2_{02}$ emission of all observed sources in \citep{hurt96}.
. We mapped the CS (transition. aud three dilferent transitions of enussion al four different angular resolutions to constrain the infall parameters of this source.," We mapped the CS transition, and three different transitions of emission at four different angular resolutions to constrain the infall parameters of this source."
 We also mapped a x rregion around SMAI4 in CO ito determine the orientation and effect. of outflows., We also mapped a $\times$ region around SMM4 in CO to determine the orientation and effect of outflows.
 In addition. we constrained. the infall parameters of 5MMA using three-dimensional collapse models based on (he (Terebev.Shu.&Cassen1984.hereafterTSC) solutions for protostellar collapse.," In addition, we constrained the infall parameters of SMM4 using three-dimensional collapse models based on the \citep*[hereafter TSC]{tsc84} solutions for protostellar collapse."
 In. 822. we describe our observations. and in 833 we present our results.," In 2 we describe our observations, and in 3 we present our results."
 A summary of all the observations obtained is shown in Table L.., A summary of all the observations obtained is shown in Table \ref{tbl-1}.
 Observations at the Five College Radio Astronomy (FCRAQO) LEm telescope were performed in December. L998 using the SEQUOLA 16-beam array receiver (Erickson.Grosslein.&Erickson 1999).. and the FAAS backend consisting of 16 autocorrelation spectrometers.," Observations at the Five College Radio Astronomy (FCRAO) 14 m telescope were performed in December, 1998 using the SEQUOIA 16-beam array receiver \citep*{erick99}, and the FAAS backend consisting of 16 autocorrelation spectrometers."
 The effective resolution obtained wilh each transition 15 summarized in Table 1., The effective resolution obtained with each transition is summarized in Table 1.
 The Cs and their isotopic counterpart (ransilions were observed using the [requency-swilched mode and. alter folding. third order baselines were subtracted.," The, CS and their isotopic counterpart transitions were observed using the frequency-switched mode and, after folding, third order baselines were subtracted."
" ""CO and its raver isotopes were observed using position-switched mode. ancl first order baselines were removed."," $^{12}$ CO and its rarer isotopes were observed using position-switched mode, and first order baselines were removed."
 Pointing and focus were checked every few hours on nearby. SiO maser sources., Pointing and focus were checked every few hours on nearby SiO maser sources.
" A x rregion centered on SMALL (a (1950) = 1827""247. 6 (1950) = 11/107)) was mapped with hall-beanm sampling in all transitions."," A $\times$ region centered on SMM4 $\alpha$ (1950) = $18^h27^m24.7^s$, $\delta$ (1950) = ) was mapped with half-beam sampling in all transitions."
 In the CO (transition. a larger region x 12/)) was mapped at full beam sampling.," In the CO transition, a larger region $\times$ ) was mapped at full beam sampling."
matter halos.,matter halos.
 Iu this paper. we alternatively adopt a Moute Carlo iethod. proposed by WWO6. to eencrate Lye forestnainBodyCitationEud spectra for a large ΙΠΠΜΟΟΙL661] of LOSs.," In this paper, we alternatively adopt a Monte Carlo method, proposed by , to generate $\alpha$ forest spectra for a large number of LOSs."
 This Moute-Carlo nethod has heen demoustratc«] to ο able to reproucὉ the Ίνα forest spectra of QSOs simular to observexd ones aud be useful ia micasurne he UVB through t16 QSO proximity effect2008)., This Monte-Carlo method has been demonstrated to be able to reproduce the $\alpha$ forest spectra of QSOs similar to observed ones and be useful in measuring the UVB through the QSO proximity effect.
. Wit1 detailed. statistical considerati1i oli different factors flat may affect the proximity effect of he feQSOs. incluliιο the QSO age. the anisotropic UV radiation aud he desity euliaucemenut. ete; (," With detailed statistical consideration on different factors that may affect the proximity effect of the fgQSOs, including the QSO age, the anisotropic UV radiation and the density enhancement, etc. ("
as cdseussed iu Section ?7)). we smulate both the LOSPE ux TPE or a large umber of feQSOs.,"as discussed in Section \ref{sec:Geom}) ), we simulate both the LOSPE and TPE for a large number of fgQSOs."
" The procedare adopted to generate the mock QSO Lyra Orest spectra is based on the observations that cach Lya absorption line with Voig profile can be described by the III column desity Nyy and the Doppler parameter b of its corresponding absorpion gas aud that the comoving uuuber deusitv of the absorption lines per uit :. ANYIl- aud b. denoted by »(:Viz.0). can be well described by the foowing three distritions: The coluuu deusities of the simulated absorbers aro Πίος, to |IO wit-lin. the range E10?Douw<ltο? and the Doppler paramcters within jns|oxob<l00kms+."," The procedure adopted to generate the mock QSO $\alpha$ forest spectra is based on the observations that each $\alpha$ absorption line with Voigt profile can be described by the HI column density $N_{\rm HI}$ and the Doppler parameter $b$ of its corresponding absorption gas and that the comoving number density of the absorption lines per unit $z$, $N_{\rm HI}$, and $b$, denoted by $n(z,N_{\rm HI},b)$, can be well described by the following three distributions: The column densities of the simulated absorbers are limited to be within the range $10^{12}{\rm cm}^{-2}<N_{\rm HI}<10^{18}{\rm cm}^{-2}$ and the Doppler parameters within $10\kms<b<100\kms$."
 Those three distrilntious are asstuned to be independent one another., Those three distributions are assumed to be independent one another.
 For the murpose of this paper. we populate absorbers iu eac1 liue of sight according to the above distributions aud generate nock samples of the Lya forest spectra.," For the purpose of this paper, we populate absorbers in each line of sight according to the above distributions and generate mock samples of the $\alpha$ forest spectra."
 GatESSET roise is added to the simulated Lya forest spectre vnnd he spectral resolution is also considered in ordor to natch the signal-to-noise level of those observed sauples discussed in Section 1., Gaussian noise is added to the simulated $\alpha$ forest spectra and the spectral resolution is also considered in order to match the signal-to-noise level of those observed samples discussed in Section 4.
 For simplicity. t16 endsson lines are not added to the spectra of mock ¢YSOs.," For simplicity, the emission lines are not added to the spectra of mock QSOs."
 Note that he adopted Monte-Carlo method naturally includes the Poisson variance of the nmuber of absortion lines iu t1C rear zone of feOSOs2008)., Note that the adopted Monte-Carlo method naturally includes the Poisson variance of the number of absorption lines in the near zone of fgQSOs.
. Iu the QSO near zones. the mass density nav be sigUficautly cuhanuced relative to the COSLLUC avierage densiνι be. (ACR)—(pLRy)fp> Lowrere (ACR)» ancl (UR) is the mass overdensity aud the mass deusitv at a ctsance R from central QSOs averaged over a Large sample of QSOs with similar properties. respectively.axd pis 16 cosmic average deusitv.," In the QSO near zones, the mass density may be significantly enhanced relative to the cosmic average density, i.e., $\left<\Delta(R)\right>\equiv
\left<\rho(R)\right>/\bar{\rho}>1$, where $\left<\Delta(R)\right>$ and $\left<\rho(R)\right>$ is the mass overdensity and the mass density at a distance $R$ from central QSOs averaged over a large sample of QSOs with similar properties, respectively,and $\bar{\rho}$ is the cosmic average density."
 A simple photoionization equiibriuni model can eive the neutral lvdrogen density of an absorber nIllXà?Urn where ó is the Lass OVCLCeusitv of the absorber à and 470.62 is the index of the vower-law tempcrature-deusity relation for the low- ICAL1997)..," A simple photoionization equilibrium model can give the neutral hydrogen density of an absorber $n_{\rm HI} \propto \delta^{2-0.7\eta}$, where $\delta$ is the mass overdensity of the absorber $\delta$ and $\eta\sim 0.62$ is the index of the power-law temperature-density relation for the low-temperature IGM."
 Asstmine that the coluun density distribution of Lye absorbers in the QSO near zones (with mean density culrancelent factor ο also follows a power law xNap with the same slope ο) as that for the cosimic average (item 2 Listed above). the column density of cach absorber generated roni the above distribution (item 2) should then be replaced by Nyy(ACY?ELTEul). considering )oth the effects of the enhanced deusitv and UV ionizi dux in QSO near zones2008b).," Assuming that the column density distribution of $\alpha$ absorbers in the QSO near zones (with mean density enhancement factor $\left<\Delta(R)\right>$ ) also follows a power law $\propto
N_{\rm HI}^{-\beta}$ with the same slope $\beta$ as that for the cosmic average (item 2 listed above), the column density of each absorber generated from the above distribution (item 2) should then be replaced by $N_{\rm HI}\left<\Delta(R)\right>^{2-0.7\eta}/(1+\omega)$, considering of both the effects of the enhanced density and UV ionizing flux in QSO near zones."
. Note that the effect. of that replacement is equivalent to the effect of increasing t ΠΙΟ of absorbers proportionally., Note that the effect of that replacement is equivalent to the effect of increasing the number of absorbers proportionally.
 As illustrated in Figure 1.. differeut choices of the (0S0 age. the half opening angle ©;» sud the offset angle Wy of the torus associated with the feQSO will affect the proximity region that the feQSO| can iluninate.," As illustrated in Figure \ref{fig:f1}, different choices of the fgQSO age, the half opening angle $\Theta_0$, and the offset angle $\Psi_0$ of the torus associated with the fgQSO will affect the proximity region that the fgQSO can illuminate."
 In our simulations. we se seven different values for the lifetime of QSOs τι. aud the QSO age το is either fixed or randomly chosen over he range (0.7).," In our simulations, we set seven different values for the lifetime of QSOs $\tau_{\rm lt}$, and the QSO age $\tauq$ is either fixed or randomly chosen over the range $(0,\tau_{\rm lt})$."
 We choose six sets of values for the opemine anele of the torus. Lo.. Oy=07.307.157.607.727. and 89°.," We choose six sets of values for the opening angle of the torus, i.e., $\Theta_0=0\degr, 30\degr, 45\degr, 60\degr,
72\degr$ , and $89\degr$."
" The Oy=07 correspouds to the cases of no ionizaion PE from the central QSOs. and the Oy=897 coresaids closely to no obscuration to the UV radiation from he feQSOs,"," The $\Theta_0=0\degr$ corresponds to the cases of no ionization PE from the central QSOs, and the $\Theta_0=89\degr$ corresponds closely to no obscuration to the UV radiation from the fgQSOs."
" The other specific values of Oy. ie. 307. Uroi"". GOP. aud 727 are chosen as their corresponding abundance ratios of type 2 to type 1 QSOs (6.5. 2.1. 1. aud V.1 respectively) are roughly in the range estimated by oservatious2010)."," The other specific values of $\Theta_0$ , i.e., $30\degr$, $45\degr$, $60\degr$, and $72\degr$, are chosen as their corresponding abundance ratios of type 2 to type 1 QSOs (6.5, 2.4, 1, and 0.4, respectively) are roughly in the range estimated by observations."
. We also raudonlv cnoose Wy within the raiege οι Oy to 1807.Oy for type 2 QSOs. aud other raiege for tvpe 1 QSOs.," We also randomly choose $\Psi_0$ within the range from $\Theta_0$ to $180\degr-\Theta_0$ for type 2 QSOs, and other range for type 1 QSOs."
 Accordiug to the above setines. we first simulate he Lya forest spectra of OSOs affected by its own UV radiation to account for the LOSPE.," According to the above settings, we first simulate the $\alpha$ forest spectra of QSOs affected by its own UV radiation to account for the LOSPE."
" In order to compare with the observational resuls on the LOSPE (aud he TPE later) bv (hereafter I&TOS) obtained from a siuye of 130 QSO pairs. the observational redslüft of the eO0SOso aud its Iuninosities at the Lyman lait frequency in our simulation are sot to be te.=2 and L,,hlPorex|IzἘ, which are roughly the mean recshift and luminosity of the sample in WT0s."," In order to compare with the observational results on the LOSPE (and the TPE later) by (hereafter KT08) obtained from a sample of 130 QSO pairs, the observational redshift of the fgQSOs and its luminosities at the Lyman limit frequency in our simulation are set to be $z_{\rm fg}=2$ and $L_{\nu_0}=5\times 10^{30}\ergshz$, which are roughly the mean redshift and luminosity of the sample in KT08."
 Note that most of he QSOs in ITUS sample are in the redshift range :—LS2.6. and the redshift dependence of the optica depth has been corrected im KTos.," Note that most of the QSOs in KT08 sample are in the redshift range $z\sim 1.8-2.6$, and the redshift dependence of the optical depth has been corrected in KT08."
 As the actual halos rosting these feQsOs aud the overdensity distribution surmronuudiie them are nof well known. we only consider the average effects. of the σαuple in this paper. not going to the detailed redshift aud luminosity distributions o: QSOs as shown in the ITOS sample.," As the actual halos hosting these fgQSOs and the overdensity distribution surrounding them are not well known, we only consider the average effects of the sample in this paper, not going to the detailed redshift and luminosity distributions of QSOs as shown in the KT08 sample."
 We first create 110 roalizatious of 130 independent svuthetic spectra to cjeck whether the saluple variance could be significant in fhe interpretatiou of the observational results., We first create 100 realizations of 130 independent synthetic spectra to check whether the sample variance could be significant in the interpretation of the observational results.
 Aud theji we also create larger miock samples with 500 iudepeud:ut svuthetic Lya forest spectra to check whether the QSO properties can be extracted effectively from a sample with 500 spectra or nore., And then we also create larger mock samples with 500 independent synthetic $\alpha$ forest spectra to check whether the QSO properties can be extracted effectively from a sample with 500 spectra or more.
 Simiar to KTOs. the amount of absorption in cach spectrum of the mock samses is quantified by DA—1 FC. where F is the flux aud € is the continu level. aud a uuiforiu fitx decrement due to the ietalabsorption Dol=0.0255 ijsalso added to cach spectrum at wavelcneth hieliY than the Τὰ cluission line.," Similar to KT08, the amount of absorption in each spectrum of the mock samples is quantified by $DA\equiv1-F/C$ where $F$ is the flux and $C$ is the continuum level, and a uniform flux decrement due to the metalabsorption $DA_{\rm metal}=0.025$ isalso added to each spectrum at wavelength higher than the $\alpha$ emission line."
 We also simulate the a forest spectra, We also simulate the $\alpha$ forest spectra
future (?).,future .
. We preseuted a study of the dynamical evolutiou of ealactic satellites using self-consisteut hieli-esolutiou sinulatious of three MW-sized halos., We presented a study of the dynamical evolution of galactic satellites using self-consistent high-resolution cosmological simulations of three MW-sized halos.
 Our main results aud conclusions are as follows., Our main results and conclusions are as follows.
 We would like to thank Nick Cuedin for providing us with the results of his filtering mass calculation iu muucrical form and for his hospitality at the Cuiversity of Colorado at Boulder where this paper was completed., We would like to thank Nick Gnedin for providing us with the results of his filtering mass calculation in numerical form and for his hospitality at the University of Colorado at Boulder where this paper was completed.
 We are also eratefil to Andrew Zeutuer for useful couments and Stelios Iazautzidis for conmuuuuicating results of his calculations prior to publication., We are also grateful to Andrew Zentner for useful comments and Stelios Kazantzidis for communicating results of his calculations prior to publication.
 The simulations preseuted here were performed ou the Oriein2000 at the National Center for Supercomputing Applications (NCSA)., The simulations presented here were performed on the Origin2000 at the National Center for Supercomputing Applications (NCSA).
 This work was supporte by the National Scicuce Foundation wader eraut No., This work was supported by the National Science Foundation under grant No.
 AST-0206216 and AST-0239759 to the University of Chicago., AST-0206216 and AST-0239759 to the University of Chicago.
 OY is supported by the STScI Fellowship., OYG is supported by the STScI Fellowship.
 Tn our analysis we use the external tidal force experienced. cosmologicaby‘thernetion. cach satellite halo to estimate the streneth of tidal , In our analysis we use the external tidal force experienced by each satellite halo to estimate the strength of tidal interaction.
We calculate the force both directly from the eravitational potential computed in the simulation aud musing an analytical approximation for the ucighbor halos., We calculate the force both directly from the gravitational potential computed in the simulation and using an analytical approximation for the neighbor halos.
 To compute the tidal force wmucerically from the local potential &. we estimate its secoud spatial derivative at the center-ofinass of the satellite: where rois the radius-vector m the satellite reference fraane and Ris the racius-vector in the perturber refercuce faune.," To compute the tidal force numerically from the local potential $\Phi$, we estimate its second spatial derivative at the center-of-mass of the satellite: where $\rr$ is the radius-vector in the satellite reference frame and $\RR$ is the radius-vector in the perturber reference frame."
 The potential ® is calculated ou the original refinement exid using the ART eravity solver., The potential $\Phi$ is calculated on the original refinement grid using the ART gravity solver.
 In the calculation of the potential. we subtract the self contribution of the halo aud consider oulv the external tidal poteutial.," In the calculation of the potential, we subtract the self contribution of the halo and consider only the external tidal potential."
 Tn a study of galaxy interactions in clusters of galaxies. used the Savitzkv-Colay smoothing filter to interpolate the potential ou a plane aud calculate its derivatives from a smooth polynomial function.," In a study of galaxy interactions in clusters of galaxies, used the Savitzky-Golay smoothing filter to interpolate the potential on a plane and calculate its derivatives from a smooth polynomial function."
 We eniploy: a simular scheme but with the adaptive -th order interpolating polynomials in cach of the three orthogonal planes around the satellite center of nass: aud the same for the cz and y2 planes., We employ a similar scheme but with the adaptive 4-th order interpolating polynomials in each of the three orthogonal planes around the satellite center of mass: and the same for the $xz$ and $yz$ planes.
 The |-th order expansion eusures a smooth second derivative of the potential., The 4-th order expansion ensures a smooth second derivative of the potential.
 Iu each of the planes we extract an sà» suberid centered ou the original evid poiut. ucarest to the satellite center.," In each of the planes we extract a $n \times n$ subgrid centered on the original grid point, nearest to the satellite center."
 Iu order to obtain à ποτ accuracy of the tidal force for satellites of ditfereut sizes. we choose the size of the subexid cells to be closest to 1/1 of the satellites tidal radius.," In order to obtain a uniform accuracy of the tidal force for satellites of different sizes, we choose the size of the subgrid cells to be closest to 1/4 of the satellite's tidal radius."
" The coefficients ej are calculated by imiuinizine (? deviation using the CERN Program Library routineMINUIT"".", The coefficients $c_{kl}$ are calculated by minimizing $\chi^2$ deviation using the CERN Program Library routine.
.. We have experimented with η=16. 32. aud 61 aud found that »=61 provides the most accurate derivatives. as tested on the analytical NEW. inodels.," We have experimented with $n=16$, 32, and 64 and found that $n=64$ provides the most accurate derivatives, as tested on the analytical NFW models."
" The tidal tensor components £,; are then calculated by analytical differcutiation of equation CÀ2)).", The tidal tensor components $F_{\alpha\beta}$ are then calculated by analytical differentiation of equation \ref{eq:p4}) ).
 We compare the real tidal force due to the overall mass distribution iu the simulation with the coutributious of all icieliboriug halos. incbludiug the host halo.," We compare the real tidal force due to the overall mass distribution in the simulation with the contributions of all neighboring halos, including the host halo."
 We model the iios with au NEW density profile aud take their mass Mya aud virial radius rey directly from the halo catalogs eenerated by the halo finder (see 23)).," We model the halos with an NFW density profile and take their mass $M_{\rm vir}$ and virial radius $r_{\rm
vir}$ directly from the halo catalogs generated by the halo finder (see \ref{sec:haloid}) )."
 We determine he scale radius of the NEW iodel for the satellite halos roni the position of the παπακαπ circular velocity. Ες=Muax/ 2.16.," We determine the scale radius of the NFW model for the satellite halos from the position of the maximum circular velocity, $r_s = r_{\rm max}/2.16$ ."
 For the host halo. we use the parametrization Cub=Εκ16077. which is a best fit to the density motile of the analyzed host halos.," For the host halo, we use the parametrization $c_{\rm nfw} \equiv r_{\rm vir}/r_s = 16 \,
a^{3/2}$, which is a best fit to the density profile of the analyzed host halos."
 The analytical tidal orce in the reference frame of the satellite is then readily calculated using eq. (, The analytical tidal force in the reference frame of the satellite is then readily calculated using eq. (
5) of ?::,5) of :
he changeC» i niass-Ioss ra hat is accompanied bv the change iun ea.,the change in mass-loss rate that is accompanied by the change in $\vinf$.
 The concept of à bi-stabilitv jump was first described w Pauldrach Puls (1990) oereconnection to their model calculations of the wind of the Luninous Blue Variable (LBV) star P Cveui (Tigg= 19.3 KIN)., The concept of a bi-stability jump was first described by Pauldrach Puls (1990) in connection to their model calculations of the wind of the Luminous Blue Variable (LBV) star P Cygni = 19.3 kK).
 Their models showed iat αμα perturbations in the basic parameters of this y.ar can either result iu a wind with a relatively high nass loss. but low τοπια] velocity.or in a wind with relatively lowAV. but hieh.," Their models showed that small perturbations in the basic parameters of this star can either result in a wind with a relatively high mass loss, but low terminal velocity, in a wind with relatively low, but high."
. Their sugecstion was that 1ο niechauisi is related to the behaviour of the Lyman ontimmuu., Their suggestion was that the mechanism is related to the behaviour of the Lyman continuum.
 Tf the Lyman coutinmum exceeds a certain yptical depth. then as a consequence. the ionization of 1e 1netals shifts to a lower stage.," If the Lyman continuum exceeds a certain optical depth, then as a consequence, the ionization of the metals shifts to a lower stage."
 This causes a larger line cceleration gp aud finally vields ajmp in WM., This causes a larger line acceleration $g_{\rm L}$ and finally yields a jump in $\mdot$.
 The models of Pauldvach Puls (1990) for P. Cveni show tha the wind miomentite loss ver second. Mes; ds about constant on both sides of the jump (see Lamers Pauldrach[um 1991).," The models of Pauldrach Puls (1990) for P Cygni show that the wind momentum loss per second, $\mdot \vinf$, is about constant on both sides of the jump (see Lamers Pauldrach 1991)."
 So Lamers et al. (, So Lamers et al. (
1995) put forward the idea that the mass-loss rate or normal stars could increase by about a factor of wo. if ος decreases by a factor of two. so tha Alen is coustaut on both sides of he jump.,"1995) put forward the idea that the mass-loss rate for normal stars could increase by about a factor of two, if $\vinf$ decreases by a factor of two, so that $\mdot \vinf$ is constant on both sides of the jump."
 Whether this is indeed the case. js still nuknuow.," Whether this is indeed the case, is still unknown."
 To investigate the behaviour of the nass loss af the bi-stability jump. we will derive mass-loss rates for a erid of wind amocdels over a range inμ," To investigate the behaviour of the mass loss at the bi-stability jump, we will derive mass-loss rates for a grid of wind models over a range in."
ι The main goal of the paper is to uuderstaud the processes that cause the bi-stability jump., The main goal of the paper is to understand the processes that cause the bi-stability jump.
 Although our results are based on conrplex nunierieal simulations. we have attempted to provide a simple picture of the relevant plivsies.," Although our results are based on complex numerical simulations, we have attempted to provide a simple picture of the relevant physics."
 We focus ou the observed bi-stability jump for normal supergiauts., We focus on the observed bi-stability jump for normal supergiants.
 Nevertheless. these results nav also provide valuable insight into the possible jd-stable winds of LDVs.," Nevertheless, these results may also provide valuable insight into the possible bi-stable winds of LBVs."
 It is worth mentioning that Lamers Pauldrach (1991) aud Lamers et al. (, It is worth mentioning that Lamers Pauldrach (1991) and Lamers et al. (
1999) sugeested that he bi-stability mnechanisi may be responsible for the outfowine disks around rapidly-rotating Blc| stars.,1999) suggested that the bi-stability mechanism may be responsible for the outflowing disks around rapidly-rotating B[e] stars.
 Therefore our results mia also provide information about the formation of rotation imduced bi-stable disks., Therefore our results may also provide information about the formation of rotation induced bi-stable disks.
 The paper is organized in the following wax., The paper is organized in the following way.
 In Sect., In Sect.
 2 we describe the basic stellar wind theory., \ref{sec:simple} we describe the basic stellar wind theory.
 Iu. particular we concentrate on the question: “what determines send 77., In particular we concentrate on the question: “what determines and ?”.
 We show that lis deteruiued by the radiative acceleration in the reeion., We show that is determined by the radiative acceleration in the region.
 Iu Sect., In Sect.
 3. we explain the method that we use to calculate the radiative acceleration with a Monte Carlo technique aud the imass-loss rates of a eric of stellar paraiucters., \ref{sec:method} we explain the method that we use to calculate the radiative acceleration with a Monte Carlo technique and the mass-loss rates of a grid of stellar parameters.
 Sect., Sect.
 b describes the properties of the models for which we predictAT., \ref{sec:isa} describes the properties of the models for which we predict.
. In. Sect., In Sect.
 5Γ our predicted bi-stability jump in mass loss will be presented., \ref{sec:predictions} our predicted bi-stability jump in mass loss will be presented.
 Then. iu Sect.," Then, in Sect."
 6 we discuss the origin of this jump aud show that it is duc to a shift in the ionization balance of Fe to FeI., \ref{sec:origin} we discuss the origin of this jump and show that it is due to a shift in the ionization balance of Fe to Fe.
 Then. we discuss the possible role of the bi-stability jump in oon the variability of LBV stars in Sect. TS," Then, we discuss the possible role of the bi-stability jump in on the variability of LBV stars in Sect. \ref{sec:lbv}."
 Finally. in Sect. &..," Finally, in Sect. \ref{sec:concl},"
 the study will be sumunarized au discussed., the study will be summarized and discussed.
 Mass loss from carly-type stars is due to radiation pressure in dines and iu the contimuuni (imanlv by electron scattering)., Mass loss from early-type stars is due to radiation pressure in lines and in the continuum (mainly by electron scattering).
 Since the radiative acceleratiou bv liue processes is the lominant contributor. hne winds aro “line-cdviven”. ie. the momentum of the radiation is trausterred to the ious by line scattering or line absorption.," Since the radiative acceleration by line processes is the dominant contributor, the winds are “line-driven”, i.e. the momentum of the radiation is transferred to the ions by line scattering or line absorption."
 Liuc-scatteriug aud line absorption occur at all distances in the wind. from the photosphere up to distances of τοις of stellar radii.," Line-scattering and line absorption occur at all distances in the wind, from the photosphere up to distances of tens of stellar radii."
 So the radiative acceleration of the wind covers a large range in distance., So the radiative acceleration of the wind covers a large range in distance.
 The equation of motion of a stationary stellar wind is where goa Is the radiative acceleration., The equation of motion of a stationary stellar wind is where $g_{\rm rad}$ is the radiative acceleration.
 Together with the mass continuitv equation aud the expression for the gas pressure p=RpT/i. where Ris the gas constant and µ is the 100201 mass per free particle iu units of i75. we find the equation of motion where e is the isothermal speed ofsound.," Together with the mass continuity equation and the expression for the gas pressure $p= \cal{R}\rho T/ \mu$, where $\cal{R}$ is the gas constant and $\mu$ is the mean mass per free particle in units of $m_H$, we find the equation of motion where $a$ is the isothermal speed of sound."
 For simplicity we have assuned that the atmosphere is isothermal., For simplicity we have assumed that the atmosphere is isothermal.
 Iu this expression the effective mass Mog=ALCLTT.) is corrected for the radiation pressure x electron scatteriug., In this expression the effective mass $M_{\rm eff}=M_*(1-\Gamma_e)$ is corrected for the radiation pressure by electron scattering.
 gi is the line acceleration., $g_{\rm L}$ is the line acceleration.
 The equation las a sineularity at the poiut where ο)=e. this critical point is the sonic point.," The equation has a singularity at the point where $v(r)=a$, this critical point is the sonic point."
 Ifthe line acceleration gi(7) is known as a fiction of r. the equation can be solved ammerically.," If the line acceleration $g_{\rm L}(r)$ is known as a function of $r$, the equation can be solved numerically."
 A sinoothlily accelerating wind solution requires that the nuuerator of Eq., A smoothly accelerating wind solution requires that the numerator of Eq.
" 3 reaches zero exactly at the sonic poiut where the denominator vanishes,", \ref{eq:vdvdr1} reaches zero exactly at the sonic point where the denominator vanishes.
" It should be stated that critical )oiut (sonic pout) atr,z1.025R. aud ce.z 20 kn 1 isnof the same as the CAIs critical point.", It should be stated that critical point (sonic point) at $r_c \simeq 1.025 R_*$ and $v_c \simeq$ 20 km $^{-1}$ is the same as the CAK critical point.
" The CAI critical point is located iuch further out iu the wind at r,~L5R and about c,&O.5e..", The CAK critical point is located much further out in the wind at $r_c \simeq 1.5 R_*$ and about $v_c \simeq 0.5 \vinf$.
 Tf the ne acceleration. gp in Eq., If the line acceleration $g_{\rm L}$ in Eq.
 3 were to be rewritten as a function of velocity eracient instead of radius. then one would fiud the CÀK critical point.," \ref{eq:vdvdr1} were to be rewritten as a function of velocity gradient instead of radius, then one would find the CAK critical point."
 Pauldrach et al. (, Pauldrach et al. (
"1986) showed that if the finite disk correction to the CAIN theory is applied. then the Modified Αν critical point moves imward and is located at r,zLOLR and at e,22LOO kii lo","1986) showed that if the finite disk correction to the CAK theory is applied, then the Modified CAK critical point moves inward and is located at $r_c \simeq 1.04 R_*$ and at $v_c \simeq 100$ km $^{-1}$."
'Dhds ds much closer to the souic poiut!, This is much closer to the sonic point!
 Although the (Modified) CAI critical solution may well provide the correct mass- rate aud terminal velocity.there is concern about its plivsical reality (see e.g. Lucy 1998 aud Lamers Cassinelli 1999 for a thorough discussion).," Although the (Modified) CAK critical solution may well provide the correct mass-loss rate and terminal velocity,there is concern about its physical reality (see e.g. Lucy 1998 and Lamers Cassinelli 1999 for a thorough discussion)."
 Lucy (1998) lias, Lucy (1998) has
the wire is therefore where d is the perpendicular vector from the particle to the wire. d—|d|. and G is the eravitational constant.,"the wire is therefore where $\mathbf{d}$ is the perpendicular vector from the particle to the wire, $d = |\mathbf{d}|$ , and $G$ is the gravitational constant."
" As depicted in Figure 10.. the vertical distance from the particle to the wire at fixed longitude is where .N(a1)=al— a,1,."," As depicted in Figure \ref{c_proj}, the vertical distance from the particle to the wire at fixed longitude is where $\Delta(aI) = aI - a_p I_p$ ."
 Dorderies et ((1983b) assumeAtal)zaM. which is equivalent to ANa/a«/NLIT; since we have derived inclination proliles in lor which their assumption is not valid. we keep our more accurate expression.," Borderies et (1983b) assume$\Delta(aI) \approx a\Delta I$, which is equivalent to $\Delta a/a \ll \Delta I/I$; since we have derived inclination profiles in \\ref{inca} for which their assumption is not valid, we keep our more accurate expression."
" lelerring again to Figure 10.. we note that since O(a)=O(I). Furthermore. The changes in 7, and Q, due to F are given to leading order by (see. e.g.. Murray Dermott 1999) n, is the particles mean motion. Ε.=F22Cpd./d?~2GpAXz/d? is the vertical component of the perturbing force. and we have neglected. terms oforder 2."," Referring again to Figure \ref{c_proj}, , we note that since $\mathcal{O}(\alpha) = \mathcal{O}(I)$, Furthermore, The changes in $I_p$ and $\Omega_p$ due to $\mathbf{F}$ are given to leading order by (see, e.g., Murray Dermott 1999) $n_p$ is the particle's mean motion, $F_z \equiv \mathbf{F} \cdot \mathbf{\hat{z}} = 2G\rho d_z/d^2 \simeq 2G\rho
\Delta z / d^2$ is the vertical component of the perturbing force, and we have neglected terms oforder $I^2$."
 Substituting ((1G)). (17)). (18)). and (20)) into (21a)) and (21b)) vields," Substituting \ref{c_rho})), \ref{c_g}) ), \ref{c_deltaz}) ), and \ref{simplegeo}) ) into \ref{c_dodt}) ) and \ref{c_didt}) ) yields"
momentum in the disk which is due to the warp is The mass distribution of the disk is taken fron: Dehnen&Binney(1998).,momentum in the disk which is due to the warp is The mass distribution of the disk is taken from \citet{dehnen and binney98}.
". The disk surface density for a given component in these moclels is given by where X, is (he normalization. AH, is the scale leneth of the component. and £2, is introduced to allow the ISM to have a centraldepression!."," The disk surface density for a given component in these models is given by where $\Sigma_d$ is the normalization, $R_d$ is the scale length of the component, and $R_m$ is introduced to allow the ISM to have a central."
". 2,,=4 kpe for the gas disk and Ry=0 for the stellar disk.", $R_m=4$ kpc for the gas disk and $R_m=0$ for the stellar disk.
 The relative contributions to the surface density al the solar circle X are 0.25 for the ISM and 0.75 for the stars., The relative contributions to the surface density at the solar circle $\Sigma_0$ are 0.25 for the ISM and 0.75 for the stars.
 Dehnen&Binney(1993). distinguish between thin and thick disk components of the stellar disk. but because these only ciller in vertical scale height. whieh does not affect the angular momentum. I treat them as a sinele component.," \citet{dehnen and binney98} distinguish between thin and thick disk components of the stellar disk, but because these only differ in vertical scale height, which does not affect the angular momentum, I treat them as a single component."
 Their models 14. which dilfer primarily in disk scale length. Ry. are all acceptable fits to the observations. ancl therefore provide a reasonable range of mass distributions with which to estimate the angular momentum.," Their models 1–4, which differ primarily in disk scale length, $R_d$, are all acceptable fits to the observations, and therefore provide a reasonable range of mass distributions with which to estimate the angular momentum."
 Table 3. gives the essential parameters for the four mocels.," Table \ref{disk table}
 gives the essential parameters for the four models."
 The circular velocity. ος. of the disk [rom 3 kpc to the solar circle is zz200kms.| 1992).," The circular velocity, $v_c$, of the disk from 3 kpc to the solar circle is $\approx 200~\mathrm{km~s^{-1}}$ \citep[e.g.,][]{merrifield92}."
". While most measurements at /2>f£, show a rising rotation curve. argue that a constant rotation curve is consistent with the data when the correlations between errors ave taken into account."," While most measurements at $R>R_0$ show a rising rotation curve, \citet{binney and dehnen97} argue that a constant rotation curve is consistent with the data when the correlations between errors are taken into account."
 I adopt c.=200kms| at all radii., I adopt $v_c=200~\mathrm{km~s^{-1}}$ at all radii.
 The uncertainty in the angular momentum due to uncertainties in the mass models dominates over anv error in the circular velocity., The uncertainty in the angular momentum due to uncertainties in the mass models dominates over any error in the circular velocity.
" The height of the warp above the plane as a function of radius. (1), appears to differ for the stars ancl for the gas."," The height of the warp above the plane as a function of radius, $h(R)$, appears to differ for the stars and for the gas."
" Drinuneletal.(2000) fit Hipparcos measurements of OD stars and find with (he warp starting al 2,=6.5 kpe and scaled by Hj=15 kpc."," \citet{drimmal et al00}
 fit Hipparcos measurements of OB stars and find with the warp starting at $R_w=6.5$ kpc and scaled by $R_h=15$ kpc."
 approximate (he i»=1 mode of the ISM warp as, \citet{BM} approximate the $m=1$ mode of the ISM warp as
 (Per, \citep{MA:98}.
rymanetal.1997) (Kovalevskyetal.1997), \citep{PERRYMAN:97} \citep{KOVAL:97} \cite{LPJPRTRG:99}.
 yr! —1 ~10 ~50," $^{-1}$ $\sim$ $\sim$ \citep{CBSU:99} $\sim$ \citep{JWFD:85, JDG:03}."
 , 
Suppose the neural network produces (soft) discriminant function outputs g;(c) lor each of the known classes j=1......V.,"Suppose the neural network produces (soft) discriminant function outputs $g_j(\underline{x})$ for each of the known classes $j=1,\ldots,N_{c}$ ."
" Let g(a)=sete)gilr)minimin,gle)grG"," Let $\tilde{g}_j(\underline{x}) =
\frac{g_j(\underline{x}) - \min_l g_l(\underline{x})}{\sum\limits_k
g_k(\underline{x}) - \min_l g_l(\underline{x})}$."
rWith this choice. we have 0Xgv)€ Land Soοσα)=1. ie. g;Gr) is a probability mass function delined on the known classes.," With this choice, we have $0 \leq \tilde{g}_j(\underline{x}) \leq 1$ and $\sum\limits_j
\tilde{g}_j(\underline{x}) = 1$, i.e. $\tilde{g}_j(\underline{x})$ is a probability mass function defined on the known classes."
 One principled measure of uncertainty in (hese soft decisions is (he Shannon entropy Hf=—3°g;(x)logg;Ge).," One principled measure of uncertainty in these soft decisions is the Shannon entropy $H = - \sum\limits_j \tilde{g}_j(\underline{x} ) \log
\tilde{g}_j(\underline{x})$."
 If H is greater than a preset threshold. we can declare that the sample 2 does not convincingly belong to anv of the known classes. ie. it is declared an unknown class sample.," If $H$ is greater than a preset threshold, we can declare that the sample $\underline{x}$ does not convincingly belong to any of the known classes, i.e. it is declared an unknown class sample."
 This approach. based on a measure of the classifiers degree of inclecision. is (he one we have taken in imparting the neural network with some class discovery inlerence capability.," This approach, based on a measure of the classifier's degree of indecision, is the one we have taken in imparting the neural network with some class discovery inference capability."
 Other measures of the classifiers degree of indecision are also possible., Other measures of the classifier's degree of indecision are also possible.
 There are three error measures which we have used (o evaluate the class discovery approaches., There are three error measures which we have used to evaluate the class discovery approaches.
 Thev are defined as follows:hypotheses.., They are defined as follows:.
 This criterion was evaluated for both the mixture model and neural network approaches., This criterion was evaluated for both the mixture model and neural network approaches.
 For the mixture model. the classification decisions were made using a maximumposteriori probability rule. based on (3)).," For the mixture model, the classification decisions were made using a maximum probability rule, based on \ref{inf2}) )."
 For the neural network. the decisions were made based on thresholding of the neural networks entropy. measure. as discussed earlier.," For the neural network, the decisions were made based on thresholding of the neural network's entropy measure, as discussed earlier."
 The error rate was measured over the unlabeled portion of the data set. (which consisted of both known and unknown class data). ie. il was estimated as tlie fraction of unlabeled samples that were misclassified.," The error rate was measured over the unlabeled portion of the data set (which consisted of both known and unknown class data), i.e. it was estimated as the fraction of unlabeled samples that were misclassified."
 The first criterion simply measures how effective an algorithm is at identilving the subset of (unlabeled) samples that come from new. i.e. unknown classes.," The first criterion simply measures how effective an algorithm is at identifying the subset of (unlabeled) samples that come from new, i.e. unknown classes."
 If (here is a single unknown class present in (he data. (hen (his is all (hat is required.," If there is a single unknown class present in the data, then this is all that is required."
 However. suppose that there are multiple unknown classes present.," However, suppose that there are multiple unknown classes present."
 Then. in addition to identilving the subset of samples from unknown classes. one would also like to identify the the individual classes which comprise {his unknown class subset.," Then, in addition to identifying the subset of samples from unknown classes, one would also like to identify the the individual classes which comprise this unknown class subset."
 In other words. one would like to identilv the underlying cluster (group) structure within the unknown class data.," In other words, one would like to identify the underlying cluster (group) structure within the unknown class data."
 The mixture modeling approach directly models (the unknown ancl. separately. (he known class data by a mixture of components (clusters).," The mixture modeling approach directly models the unknown and, separately, the known class data by a mixture of components (clusters)."
 Each such cluster can be viewed as aputative unknown class., Each such cluster can be viewed as aputative unknown class.
 A measure of the, A measure of the
vears. a lot of evidence has been collected linking GRBs to the core collapse of massive stars (Woosley 1993: Paczviisski 1998).,"years, a lot of evidence has been collected linking GRBs to the core collapse of massive stars (Woosley 1993; Paczyńsski 1998)."
 The most important evidence came from the cirect association between GRB 030329 and the supernova SN 2002dh (Stanek et al., The most important evidence came from the direct association between GRB $030329$ and the supernova SN $2003$ dh (Stanek et al.
 2003: Hjorth οι al., 2003; Hjorth et al.
 2003). as well as the previous tentative association between GRB 980425 and $ 1993bw (Ixulkarni et al.," 2003), as well as the previous tentative association between GRB $980425$ and SN $1998$ bw (Kulkarni et al."
 1998: Galama οἱ al., 1998; Galama et al.
 1998)., 1998).
 These associated supernovae have been confirmed to be tvpe Ib/c SNe., These associated supernovae have been confirmed to be type Ib/c SNe.
 The progenitors of type Ib/c SNe are commonly recognized as massive Woll-Havet stars., The progenitors of type Ib/c SNe are commonly recognized as massive Wolf-Rayet stars.
 During their whole life. the massive progenitors eject (heir envelope material into (their surroundings through line pressure and (hus the stellar wind environments are formed.," During their whole life, the massive progenitors eject their envelope material into their surroundings through line pressure and thus the stellar wind environments are formed."
 This means that the circum-biurst mediiun for GRB alterglows mav be (he stellar wind (Dai Lu 1998:Mészüros.. Rees. Wijers 1993: Chevalier Li 1999. 2000: Panaitesen Kamar 2000).," This means that the circum-burst medium for GRB afterglows may be the stellar wind (Dai Lu 1998;, Rees, Wijers 1998; Chevalier Li 1999, 2000; Panaitescu Kumar 2000)."
 In this paper. we study the afterglow properties of realistic GRB shocks. considering the effect of energy losses.," In this paper, we study the afterglow properties of realistic GRB shocks, considering the effect of energy losses."
 The circum-burst environment is assumed to be either the ISM-tvpe or the stellar wind (wpe., The circum-burst environment is assumed to be either the ISM-type or the stellar wind type.
 We present an analytical solution for the realistic blast wave during the [ast-cooling phase of GRB alterglows in 2.., We present an analytical solution for the realistic blast wave during the fast-cooling phase of GRB afterglows in \ref{sec:fastcooling}.
 This semi-racdiative hvdrodynanmies is applied to the late slow-cooling phase with quite reasonable argument in §3.., This semi-radiative hydrodynamics is applied to the late slow-cooling phase with quite reasonable argument in \ref{sec:slowcooling}.
 Constraints on the IC components in the soft. X-ray alterglows are given in both sections., Constraints on the IC components in the soft X-ray afterglows are given in both sections.
 In 84. we illustrate (vpical analvlical light. curves for the realistic model in detail., In \ref{sec:lightcurves} we illustrate typical analytical light curves for the realistic model in detail.
 Conclusions and cliscussion are presented in 5.., Conclusions and discussion are presented in \ref{sec:conclusion}.
 The realistic model for GRB remnants has been extensively investigated in the past [ew vears (IInang. Dai. Lu 1999: IIuang et al.," The realistic model for GRB remnants has been extensively investigated in the past few years (Huang, Dai, Lu 1999; Huang et al."
 2000)., 2000).
 It has been shown that this model is correct. lor both acliabalic ancl radiative fireballs. and in both ultra-relativistic aud non-relativistic phases.," It has been shown that this model is correct for both adiabatic and radiative fireballs, and in both ultra-relativistic and non-relativistic phases."
 The basic hydrocwuamic equation of this model can be derived as lollows., The basic hydrodynamic equation of this model can be derived as follows.
" In the [fixed frame. which is rest to the cireum-burst environment. the total kinetic energy of the fireball is Ey=(5—DOM+Αλ(0€)5U. where 5 is the Lorentz factor of the blast wave. Mj is the initial mass of the blast wave ejected [rom the central engine. M, is the mass of the swept-up ambient medium. e is the speed of light. and εἰς the total radiation elliciency (IIuang et al."," In the fixed frame, which is rest to the circum-burst environment, the total kinetic energy of the fireball is $E_{\rm{K}}=(\gamma-1)(M_{\rm{ej}}+M_{\rm{sw}})c^{2}+(1-\epsilon)\gamma
U$, where $\gamma$ is the Lorentz factor of the blast wave, $M_{\rm{ej}}$ is the initial mass of the blast wave ejected from the central engine, $M_{\rm{sw}}$ is the mass of the swept-up ambient medium, $c$ is the speed of light, and $\epsilon$ is the total radiation efficiency (Huang et al."
 1999)., 1999).
 In the comoving frame of the blast wave. the total internal energy instantaneously heated by the shock is U=(5Αν. which is implied from the relativistic jump conditions (Blauclford Alelee 1976).," In the comoving frame of the blast wave, the total internal energy instantaneously heated by the shock is $U=(\gamma-1)M_{\rm{sw}}c^2$, which is implied from the relativistic jump conditions (Blandford McKee 1976)."
 The differential loss of the kinetic, The differential loss of the kinetic
substructure.,substructure.
 Belletal.(2008). find that about of stars in the inner halo are substructured. even if the only prominent stream in their data is the well known Sagittarius stream. while Starkenburgetal.(2009) find that around of the stars in the Spaghetti survey are more clustered than expected from a random distribution.," \cite{bell08}
 find that about of stars in the inner halo are substructured, even if the only prominent stream in their data is the well known Sagittarius stream, while \cite{starkenburg09} find that around of the stars in the Spaghetti survey are more clustered than expected from a random distribution."
 We apply the 4-distance method used by Starkenburgetal.(2009) to our data in Figure 5., We apply the 4-distance method used by \cite{starkenburg09} to our data in Figure 5.
 This is essentially a version of the correlation function for 4-dimensional data. computing the excess number of stellar pairs in position and velocity compared to à random sample (realized by scrambling the velocities but not the positions of the stars in the data) as a function of distance in +-dimensional space.," This is essentially a version of the correlation function for 4-dimensional data, computing the excess number of stellar pairs in position and velocity compared to a random sample (realized by scrambling the velocities but not the positions of the stars in the data) as a function of distance in 4-dimensional space."
 The angular. spatial and velocity separations are scaled by the range in these quantities covered by the data.," The angular, spatial and velocity separations are scaled by the range in these quantities covered by the data."
 Ata 5c level we find that at least of our stars are more paired than random., At a $\sigma$ level we find that at least of our stars are more paired than random.
 This agrees. broadly. with the estimates by Belletal.(2008) for the inner halo and Starkenburget(2009) for the outer halo.," This agrees, broadly, with the estimates by \cite{bell08} for the inner halo and \cite{starkenburg09} for the outer halo."
 In addition we detect a decrease in the correlation strength at small 4-distance., In addition we detect a decrease in the correlation strength at small 4-distance.
 This ts expected if the outer halo is dynamically young and suggests the presence of numerous streamlets and à complex structure. too weak to be resolved by our data.," This is expected if the outer halo is dynamically young and suggests the presence of numerous streamlets and a complex structure, too weak to be resolved by our data."
 We present further evidence to this effect from an analysis of halo kinematics., We present further evidence to this effect from an analysis of halo kinematics.
 The kinematics of metal-poor stars in the halo vielc information on the earliest phases of galaxy formation (Eggeretal.1962) and the shape of the Galactic potential., The kinematics of metal-poor stars in the halo yield information on the earliest phases of galaxy formation \citep{eggen62} and the shape of the Galactic potential.
 Until recently. known samples of halo stars were small. especially at large galactocentrie distances.," Until recently, known samples of halo stars were small, especially at large galactocentric distances."
 Battagliaetal.(2005) used a heterogeneous sample of red giants. BHB stars. globular clusters and dwarf galaxies to trace the velocity disperstot profile of the Galaxy out to ~100 kpe. finding a mildly declining profile.," \cite{battaglia05} used a heterogeneous sample of red giants, BHB stars, globular clusters and dwarf galaxies to trace the velocity dispersion profile of the Galaxy out to $\sim 100$ kpc, finding a mildly declining profile."
 Using BHB stars in SDSS Xueetal. found a flat or mildly declining profile out to 60 kpe anc therefore inferred a large mass of the Milky Way., Using BHB stars in SDSS \cite{xue08} found a flat or mildly declining profile out to 60 kpc and therefore inferred a large mass of the Milky Way.
 Brownetal.(2010) also derive a mildly declining profile out to 75 kpe using BHB stars in the Hypervelocity Star Survey., \cite{brown10} also derive a mildly declining profile out to 75 kpc using BHB stars in the Hypervelocity Star Survey.
 In all these cases. the fits depends strongly on the accuracy of the last (most distant) data points. which generally contain fewer objects.," In all these cases, the fits depends strongly on the accuracy of the last (most distant) data points, which generally contain fewer objects."
 We use our data to derive the velocity dispersion profile in both Northern and Southern samples separately., We use our data to derive the velocity dispersion profile in both Northern and Southern samples separately.
 We use bins containing equal numbers of stars and calculate the velocity dispersion and its error following a maximum likelihood approach (Walkeretal.2006)., We use bins containing equal numbers of stars and calculate the velocity dispersion and its error following a maximum likelihood approach \citep{walker06}.
. Figure 6(a.b) plots our results.," Figure 6(a,b) plots our results."
 While we are in reasonable agreement with previous work over the range where we overlap. we find evidence of a rising velocity dispersion at large radit. in both fields we study.," While we are in reasonable agreement with previous work over the range where we overlap, we find evidence of a rising velocity dispersion at large radii, in both fields we study."
 This is unlike the results of Battagliaetal.(2005) and Brownetal. (2010).. although we reach farther into the distant halo than they do.," This is unlike the results of \cite{battaglia05} and \cite{brown10}, although we reach farther into the distant halo than they do."
 In the former case. the heterogeneous sample and its relatively small size may cause part of the difference. as It Is known that different tracers have different kinematics (e.g.. Kinmanetal. 2007)).," In the former case, the heterogeneous sample and its relatively small size may cause part of the difference, as it is known that different tracers have different kinematics (e.g., \citealt{kinman07}) )."
 In the latter case. we and Brownetal.(2010) use the same tracers. but while our stars are concentrated in two narrow strips. Brownetal.(2010) uses a wide region selected from the SDSS.," In the latter case, we and \cite{brown10} use the same tracers, but while our stars are concentrated in two narrow strips, \cite{brown10} uses a wide region selected from the SDSS."
 We have more stars (by a factor of about 3) than they do at large (2>50 kpe) distances., We have more stars (by a factor of about 3) than they do at large $R > 50$ kpc) distances.
 One possibility is that we sample this regime more densely. especially 1f the halo is as inhomogeneous as theory suggests and as the evidence from Fig.," One possibility is that we sample this regime more densely, especially if the halo is as inhomogeneous as theory suggests and as the evidence from Fig."
 5 also argues., 5 also argues.
 Is it possible that our result may be affected by contamination from blue straggler stars., Is it possible that our result may be affected by contamination from blue straggler stars.
 Since these objects are 2 to 3 magnitudes fainter than BHB stars. blue stragglers will contaminate the bins at Re;e>LO kpe with objects that," Since these objects are 2 to 3 magnitudes fainter than BHB stars, blue stragglers will contaminate the bins at $R_{GC} 
> 40$ kpc with objects that"
"«mall velocity normal to the shock front. ie. 1/2M02<ώς, can be reflected from the shock front to the shock upstream. where o, is (he electrostatic shock Iront potential induced by the inerlia difference between ions aud electrons.","small velocity normal to the shock front, i.e., $1/2 M v_x^2 < e \phi_s$, can be reflected from the shock front to the shock upstream, where $\phi_s$ is the electrostatic shock front potential induced by the inertia difference between ions and electrons."
 During the gvro-2mnotion in upstream. ions gain their energy [rom the motional electric field. parallel to the shock Iront.," During the gyro-motion in upstream, ions gain their energy from the motional electric field parallel to the shock front."
 Η the width of the shock front potential ὡς is thin. the electric force can overcome the Lorentz force. ancl then (he multiple reflection can occurs.," If the width of the shock front potential $\phi_s$ is thin, the electric force can overcome the Lorentz force, and then the multiple reflection can occurs."
 Ii a e(quasi-perpendiceular shock. OlisawaandSakai(1937) studied the nonlinear steepening of magnetosonic waves. and showed that 1a fw<1. the thickness of the shock front. potential &; becomes of the order of the electron inertia scale Cope.," In a quasi-perpendicular shock, \citet{Osh87} studied the nonlinear steepening of magnetosonic waves, and showed that if $\omega_{pe}/\omega_{ce} < 1$, the thickness of the shock front potential $\phi_s$ becomes of the order of the electron inertia scale $c/\omega_{pe}$."
 They then demonstrated by using a particle simulation the strong resonant interaction of the reflected ions with the motional electric fields., They then demonstrated by using a particle simulation the strong resonant interaction of the reflected ions with the motional electric fields.
" What we discuss here is (he ""electron"" shock surfing acceleration (Iloshino2001:Mc-Clementsetal. 2001)."," What we discuss here is the “electron” shock surfing acceleration \citep{Hos01,McC01}."
". The above ""standard shock surfing acceleration cannol apply for the electron. acceleration. because the electron cannot be reflected [rom the shock front by the shock front potential ὦ,."," The above “standard” shock surfing acceleration cannot apply for the electron acceleration, because the electron cannot be reflected from the shock front by the shock front potential $\phi_s$."
" We propose a new scheme of ""electron"" shock surfing acceleration under the action of ESW.", We propose a new scheme of “electron” shock surfing acceleration under the action of ESW.
" Since (he electron hole is a positively charged. structure. and an electron can be trapped if m,02/2«eos. where ou; is the scalar potential for the electrostatic solitary wave (ESW). ("," Since the electron hole is a positively charged structure, and an electron can be trapped if $m_e v_x^2/2 < e \phi_{\rm esw}$, where $\phi_{\rm esw}$ is the scalar potential for the electrostatic solitary wave (ESW). ("
Note that the Lorentz force is also an important agent for the particle trapping. but we will discuss (his point later.),"Note that the Lorentz force is also an important agent for the particle trapping, but we will discuss this point later.)"
 Furthermore. the propagation velocily of ESW differs [rom the plasma bulk velocity. and ESW together with the trapped electrons can stav longer time in the shock transition region.," Furthermore, the propagation velocity of ESW differs from the plasma bulk velocity, and ESW together with the trapped electrons can stay longer time in the shock transition region."
 Namely. in the [rame moving with ESW. the convection electric field is not zero.," Namely, in the frame moving with ESW, the convection electric field is not zero."
" Therefore. we think that the so called ""shock surfing mechanism is occurring for electrons."," Therefore, we think that the so called “shock surfing” mechanism is occurring for electrons."
 Figure 6 summarizes our idea of the electron shock surfing mechanism., Figure 6 summarizes our idea of the electron shock surfing mechanism.
 Top panel shows an eleciron's trajectory in the «—y plane., Top panel shows an electron's trajectory in the $x-y$ plane.
 The magnetic field is polarized perpendicular to the ww—y plane. and the plasmas are convecting towards positive i.," The magnetic field is polarized perpendicular to the $x-y$ plane, and the plasmas are convecting towards positive $x$."
 The shock upstream is (he left-hand side. while the downstream is the right-hand side.," The shock upstream is the left-hand side, while the downstream is the right-hand side."
" Bottom panel shows the electric field E, along (her axis. and ESW in association with ils electron hole in phase space is depicted in the center."," Bottom panel shows the electric field $E_x$ along the $x$ axis, and ESW in association with its electron hole in phase space is depicted in the center."
 Due to the nature of the electron hole. (he electron charge density is slightly lower than the ion one. aud ESW has a bipolar signature with diverging electric field.," Due to the nature of the electron hole, the electron charge density is slightly lower than the ion one, and ESW has a bipolar signature with diverging electric field."
" If an electron convecting towards the ESW structure is reflected by both the Lorentz orce and the electric field E, and is trapped inside (he ESW structure. it is successively accelerated towards the negative E, direction."," If an electron convecting towards the ESW structure is reflected by both the Lorentz force and the electric field $E_x$ and is trapped inside the ESW structure, it is successively accelerated towards the negative $E_y$ direction."
" As increasing the electron’s velocity e, by the shock surfing/surfatron acceleration. it can be de-trapped from ESW when the Lorentz force ev,B./e becomes larger than the electric force €£,. and then it is convecting towards downstream and becomes quickly an isotropic. evrolvopic distribution."," As increasing the electron's velocity $v_y$ by the shock surfing/surfatron acceleration, it can be de-trapped from ESW when the Lorentz force $e v_y B_z/c$ becomes larger than the electric force $e E_x$, and then it is convecting towards downstream and becomes quickly an isotropic, gyrotropic distribution."
 The (ime variable nature of the ESW evolution may be the other important [actor to control the de-trappiug process., The time variable nature of the ESW evolution may be the other important factor to control the de-trapping process.
in hot subedwarf stars as a function of temperature and composition: they argued. that the atmospheres of rich κ) stars should be convective. whilst those of helium-poor sdOs and sdD stars ave mostly radiative (see also Leber 2009].,"in hot subdwarf stars as a function of temperature and composition; they argued that the atmospheres of helium-rich sdO stars should be convective, whilst those of helium-poor sdOs and sdB stars are mostly radiative (see also Heber [2009])."
 Llence. gravitational settling can operate in most sdD stars — producing Lle-poor photospheres — but not in Lle-scdOs., Hence gravitational settling can operate in most sdB stars – producing He-poor photospheres – but not in He-sdOs.
 The effective temperatures of the merger products thereby determine which remain He-rich: the cooler merger products experience settling., The effective temperatures of the merger products thereby determine which remain He-rich; the cooler merger products experience settling.
 The majority. of He-WD mergers simulated in Han et ((2002) are significantly cooler than the merger products in Fig. 4..," The majority of He-WD mergers simulated in Han et (2002) are significantly cooler than the merger products in Fig. \ref{fig:BPS},"
 consistent with he He-W mergers producing H-rich sdBs and the merger channnel proposedD. in this work producing He-sdOs., consistent with the He-WD mergers producing H-rich sdBs and the merger channnel proposed in this work producing He-sdOs.
 Llowever. if that explanation is correct. then the rotter He-WD. mergers may also contribute to the He-sdO »opulation.," However, if that explanation is correct then the hotter He-WD mergers may also contribute to the He-sdO population."
 In. addition. note that the boundary. between he atmospheric regimes found by Croth ct iis more complex than simply a division between sdO and sdB stars: in particular. their calculations found that the temperature roundary which allows a convective atmosphere becomes cooler at lower surface llence we should also expect some οκ stars to be xoduced by Lle-rich merger products which have convective atmospheres but are cool enough to be sd DocThis would be helpful to our mocoel. since it seems D.that our P.merger ooducts. are too hot to explain Lle-sclB stars.," In addition, note that the boundary between the atmospheric regimes found by Groth et is more complex than simply a division between sdO and sdB stars; in particular, their calculations found that the temperature boundary which allows a convective atmosphere becomes cooler at lower surface Hence we should also expect some He-sdB stars to be produced by He-rich merger products which have convective atmospheres but are cool enough to be sdB This would be helpful to our model, since it seems that our merger products are too hot to explain He-sdB stars."
 Naslim et ((2010) have stressed. that it is logical to consider the evolutionary status of ος] and. He-dO stars together: Our merger scenario seenis to require à second. population to explain the Le-sdBs: potentially some Le-WD mergers account for the Le-dDs as well as for the some of the Le-, Naslim et (2010) have stressed that it is logical to consider the evolutionary status of He-sdB and He-sdO stars together; our merger scenario seems to require a second population to explain the He-sdBs: potentially some He-WD mergers account for the He-sdBs as well as for the some of the He-sdOs.
 One outstanding and. as vet. unexplained piece. of evidence is the observation that. Lle-sdOs come in. both nitrogen-rich ancl carbon-rich classes. with a further subset enhanced in both € and N. whilst He-poor sdOs are not € or N rich (Stroeer ct 22007).," One outstanding and, as yet, unexplained piece of evidence is the observation that He-sdOs come in both nitrogen-rich and carbon-rich classes, with a further subset enhanced in both C and N, whilst He-poor sdOs are not C or N rich (Stroeer et 2007)."
 LE some IHe-WD. mergers produce Lle-sdOs (perhaps. e.g. the more massive Lle-WD mergers) then they might. conceivably produce. one composition subclass whilst the Lle-WD|post-sdB mergers produce another subclass.," If some He-WD mergers produce He-sdOs (perhaps, e.g., the more massive He-WD mergers) then they might conceivably produce one composition subclass whilst the He-WD+post-sdB mergers produce another subclass."
 Saio Jellery. (2000) argue that the outcome of their double Le-WD merger model could have CNO-processecl material al vw surface (Le. N-rich). whilst Saio Jellery (2002) produce a C-rich star from their He-WD|CO-WD merger à Our merger model is somewhere between those examples: it is not clear which range of surface abundances our merger scenario might produce.," Saio Jeffery (2000) argue that the outcome of their double He-WD merger model could have CNO-processed material at the surface (i.e. N-rich), whilst Saio Jeffery (2002) produce a C-rich star from their He-WD+CO-WD merger a Our merger model is somewhere between those examples; it is not clear which range of surface abundances our merger scenario might produce."
 The phase of accretion and ignition seems Likely to be important. for imprinting the surface carbon and nitrogen abundances of Le-sdOs: we encourage future work to investigate this detail., The phase of accretion and ignition seems likely to be important for imprinting the surface carbon and nitrogen abundances of He-sdOs; we encourage future work to investigate this detail.
 The model described. by this paper so far can explain the population of observed single LHe-rich sdO stars quite well., The model described by this paper so far can explain the population of observed single He-rich sdO stars quite well.
 Llowever. there are two known He-rich hot subdwarl stars. Le. binaries where both components are Πο or Lo-sdB stars.," However, there are two known He-rich hot subdwarf stars, i.e. binaries where both components are He-sdO or He-sdB stars."
 Interestingly. both of these svstems contain two hot subchwarls that appear to be Lle-rich.," Interestingly, both of these systems contain two hot subdwarfs that appear to be He-rich."
 The best. published. example of such a system is PG 1544)48s (Αίας οἱ 22004). which contains two Lle-rich hot subewarl stars.," The best published example of such a system is PG 1544+488 (Ahmad et 2004), which contains two He-rich hot subdwarf stars."
 The published mass ratio for that system is 1.730.2. though recent data may bring this value closer to 1 (Simon Jeffery. cecomm.).," The published mass ratio for that system is $1.7\pm0.2$, though recent data may bring this value closer to 1 (Simon Jeffery, comm.)."
" The orbital period is O48 d. Lisker et ((2004) also report the existence of a system containing two ""very similar He-rich sdO stars (115 (0301-3039: see also Strocer et al 2007).", The orbital period is 0.48 d. Lisker et (2004) also report the existence of a system containing two `very similar' He-rich sdO stars (HE 0301-3039; see also Stroeer et al 2007).
 A second. formation channel is needed to explain these systems: we sugeest that these systems are the products of a double-core common-envelope (CE) phase (e.g. Brown 1995: Xlezvnski Ixalogera 2001: Dewi. Podsiadlowski Sena 2006).," A second formation channel is needed to explain these systems: we suggest that these systems are the products of a double-core common-envelope (CE) phase (e.g. Brown 1995; Belczynski Kalogera 2001; Dewi, Podsiadlowski Sena 2006)."
 Double-core CL evolution is à special case of common-envelope evolution where the envelopes. of stars. in a binary are simultaneously ejectecl as both stellar. cores spiral inwards inside an envelope produced by the union of their envelopes., Double-core CE evolution is a special case of common-envelope evolution where the envelopes of stars in a binary are simultaneously ejected as both stellar cores spiral inwards inside an envelope produced by the union of their envelopes.
 This produces a close binary containing the exposed. cores of both original stars (see Fig. 6))., This produces a close binary containing the exposed cores of both original stars (see Fig. \ref{fig:double_core_schematic}) ).
"preferentially spherical. low anisotropy svstems by investigating the location of our axisvnuuelric merger remnants with IL,,/IL..Uus>0.9 in Fig.","preferentially spherical, low anisotropy systems by investigating the location of our axisymmetric merger remnants with $\Pi_{yy}/\Pi_{xx} \geq 0.9$ in Fig."
 2., 2.
 Their distribution turns out not to be different compared with the complete sample. ruling out such a solution.," Their distribution turns out not to be different compared with the complete sample, ruling out such a solution."
 ? emphasised (he importance of gaseous energv dissipation during galaxy mergers., \citet{2006MNRAS.372..839N} emphasised the importance of gaseous energy dissipation during galaxy mergers.
 They studied a set of disk mergers with mass ratios 1:1 and 3:1. including gas with a mass fraction of 10 per cent of the total disk mass.," They studied a set of disk mergers with mass ratios 1:1 and 3:1, including gas with a mass fraction of 10 per cent of the total disk mass."
 The gas dvnamics was followed during (he merging process. adopting an isothermal equation of state.," The gas dynamics was followed during the merging process, adopting an isothermal equation of state."
 Star formation and stellar feedback was neglected., Star formation and stellar feedback was neglected.
 Despite this simplification. ? showed that a clissipative eas component. settling into the ealactic center through its gravitational force has a strong effect. on the orbital structure ol the merger remnant. leading to asvimmetries of the line-o[-sight. velocity distribution of rotating ellipticals Chat are in much better agreement. wilh observations than collisionless merger remnanis (see also ?)).," Despite this simplification, \citet{2006MNRAS.372..839N} showed that a dissipative gas component, settling into the galactic center through its gravitational force has a strong effect on the orbital structure of the merger remnant, leading to asymmetries of the line-of-sight velocity distribution of rotating ellipticals that are in much better agreement with observations than collisionless merger remnants (see also \citealp{2006MNRAS.372L..78G}) )."
 The anisotropy. and ellipticity of (he 1:1 and 3:1 merger remnants with gas however turns out to be very similar to the distribution of the collisionless merger sample., The anisotropy and ellipticity of the 1:1 and 3:1 merger remnants with gas however turns out to be very similar to the distribution of the collisionless merger sample.
 Clearly. a gas action as expected in evolved disk galaxies does not solve the problem either.," Clearly, a gas fraction as expected in evolved disk galaxies does not solve the problem either."
 Ellipticals are in general old svstems (hat formed at a time when disk galaxies were still quite gas-rieh., Ellipticals are in general old systems that formed at a time when disk galaxies were still quite gas-rich.
 Star formation and stellar as well as central black hole feedback therelore is expected to have plaved an important role during galaxy mergers (?7?)..," Star formation and stellar as well as central black hole feedback therefore is expected to have played an important role during galaxy mergers \citep{2007arXiv0706.1246H,2007arXiv0706.1243H}."
 In order to investigate (his question we have started a new series of gas-rich (>20% eas) disk mergers. using GADGET? and taking into account star formation as well as stellar and black hole feedback as described by ?./— and ?..," In order to investigate this question we have started a new series of gas-rich $\geq 20 \%$ gas) disk mergers, using GADGET2 and taking into account star formation as well as stellar and black hole feedback as described by \citet{2003MNRAS.339..289S} and \citet{2005ApJ...620L..79S}."
 A detailed analvsis of these simulations will be presented in a subsequent. paper (Johansson et al.," A detailed analysis of these simulations will be presented in a subsequent paper (Johansson et al.,"
 in preparation)., in preparation).
 The triangles in Fig., The triangles in Fig.
 3 show how star formation ancl energetic feedback affects (he anisotropy. and. ellipticity of the merger remnants., 3 show how star formation and energetic feedback affects the anisotropy and ellipticity of the merger remnants.
 Large triangles correspond to simulations. including black hole accretion. merging and black hole feedback.," Large triangles correspond to simulations, including black hole accretion, merging and black hole feedback."
 Five simulations have been repeated. without taking into account black holes., Five simulations have been repeated without taking into account black holes.
 They are represented in Fig., They are represented in Fig.
 3 bx the smaller triangles., 3 by the smaller triangles.
 For a more detailed investigation of how star formation. energetic feedback and black hole physics affects the final structure of the merger remnants. table | compares the anisotropies and ellipticities of the collisionless merger simulations (columns 2 and 3) with those. starting with the same initial geometries and mass ratios. however now including of gas. star formation as well as stellar and black hole feedback (columns 4 and 5).," For a more detailed investigation of how star formation, energetic feedback and black hole physics affects the final structure of the merger remnants, table 1 compares the anisotropies and ellipticities of the collisionless merger simulations (columns 2 and 3) with those, starting with the same initial geometries and mass ratios, however now including of gas, star formation as well as stellar and black hole feedback (columns 4 and 5)."
 The columns 6 and 7 finally show the results for the simulations where black hole accretion and feedback has been neglected., The columns 6 and 7 finally show the results for the simulations where black hole accretion and feedback has been neglected.
 The initial conditions are shown in the first column of table 1: and are defined in table 1 of ?.., The initial conditions are shown in the first column of table 1 and are defined in table 1 of \citet{2003ApJ...597..893N}.
 Fig., Fig.
e 3 and table 1 show. that star formation and stellar energetice feedback has a stronge effect on (he anisotropy aud ellipticity of merger remnants.," 3 and table 1 show, that star formation and stellar energetic feedback has a strong effect on the anisotropy and ellipticity of merger remnants."
 We still find a trend of decreasing rotational support. i.e. decreasing W/o with decreasing mass ratio of the progenitor disks.," We still find a trend of decreasing rotational support, i.e. decreasing $V/\sigma$ with decreasing mass ratio of the progenitor disks."
 In, In
1) with a magnitude of Ks=16.74+0.05. though we cannot propose this as the counterpart with any certainty given the lack of colour information and weak positional agreement.,"1) with a magnitude of $K_S = 16.74 \pm 0.05$, though we cannot propose this as the counterpart with any certainty given the lack of colour information and weak positional agreement."
 Neither can we compare the colour of this source to other sources in the field to demonstrate that it has similar properties and ts thus likely to be a field source. unrelated to the suggested pulsar.," Neither can we compare the colour of this source to other sources in the field to demonstrate that it has similar properties and is thus likely to be a field source, unrelated to the suggested pulsar."
 There is also a bright 2MASS source (16320846—4749005) to the West (source 2). though it 1s at a distance of ~3.507 so is even less likely related to the high energy source.," There is also a bright 2MASS source $-$ 4749005) to the West (source 2), though it is at a distance of $\sim 3.5\sigma$ so is even less likely related to the high energy source."
 First reported by Molkovetal.(2004).. is à PWN (e.g.. Rattietal. 2010)) with a confirmed mms pulsar (Gotthelfetal..2011)..," First reported by \cite{Molkov2004:AstL.30}, is a PWN (e.g., \citealt{Ratti2010:MNRAS.408}) ) with a confirmed ms pulsar \citep{Gotthelf2011:ApJ729}."
 Rattietal. also suggest a nIR counterpart of magnitude Ky;=16.4+40.1 at RA. Dee = 18:49:01.563. —00:01:17.35 (£0.17) but find no evidence of any nIR extension as one might expect for à PWN.," \citeauthor{Ratti2010:MNRAS.408} also suggest a nIR counterpart of magnitude $K_S = 16.4 \pm 0.1$ at RA, Dec = 18:49:01.563, $-$ 00:01:17.35 $\pm 0.1$ ) but find no evidence of any nIR extension as one might expect for a PWN."
" Within the eerror circle ofJ18490—0000.. we confirm the proposed nIR counterpart of Rattietal.(2010) at a consistent magnitude of K,=17.2+0.4 (source 1)."," Within the error circle of, we confirm the proposed nIR counterpart of \cite{Ratti2010:MNRAS.408} at a consistent magnitude of $K_s = 17.2 \pm 0.4$ (source 1)."
" We also note. as those authors did. that the object is heavily blended with a nearby source of magnitude K,=15.58+0.05 (source 2)."," We also note, as those authors did, that the object is heavily blended with a nearby source of magnitude $K_s = 15.58 \pm 0.05$ (source 2)."
 Due to the lack of colour information for the proposed counterpart we are unable to gain any information regarding its equivalent spectral classification. or to compare it to other field sources to demonstrate that it has different properties that may indicate it is associated with the pulsar.," Due to the lack of colour information for the proposed counterpart we are unable to gain any information regarding its equivalent spectral classification, or to compare it to other field sources to demonstrate that it has different properties that may indicate it is associated with the pulsar."
 The lack of detected compact counterparts for aandJ1632-478.. particularly in the optical. is not surprising given the high levels of Galactic. extinction (Schlegeletal..1998) towards the sources: Ep=3.83 (Ag~L3. Av~12: Cardellietal. 1989)) and Eg=11.18 (Ag~3.9) respectively.," The lack of detected compact counterparts for and, particularly in the optical, is not surprising given the high levels of Galactic extinction \citep{schlegel1998:ApJ500} towards the sources: $E_{B-V} = 3.83$ $A_K \sim 1.3$, $A_V \sim 12$; \citealt{cardelli1989:ApJ345}) ) and $E_{B-V} = 11.18$ $A_K \sim 3.9$ ) respectively."
 Likewise ssuffers significant extinction of Eg=6.62 (Ας~2.3)., Likewise suffers significant extinction of $E_{B-V} = 6.62$ $A_K \sim 2.3$ ).
 Note that all these extinctions should be treated with caution as estimates so close to the Galactic plane (<5deg) are unreliable., Note that all these extinctions should be treated with caution as estimates so close to the Galactic plane $<5\deg$ ) are unreliable.
 The magnitude limits of the non-detections are consistent with the V band detections of other isolated neutron stars (Mignant. 2011):: excluding the Crab at V=16.6. these range from 22 to 28 magnitudes (corresponding to Κ.Σ18.6 fora spectral index of —1). at low optical extinctions (Eg.y€ 0.2) in the nearby Galaxy (x.Ikpe for most).," The magnitude limits of the non-detections are consistent with the $V$ band detections of other isolated neutron stars \citep{Mignani2011:AdSpR.47}; ; excluding the Crab at $V=16.6$, these range from 22 to 28 magnitudes (corresponding to $K_s \gtrsim 18.6$ for a spectral index of $-1$ ), at low optical extinctions $E_{B-V} \lesssim 0.2$ ) in the nearby Galaxy $\lesssim 1$ kpc for most)."
" On the other hand. the detection of a proposed counterpart to aat K,~17 is significantly brighter than any other optical identification of an isolated neutron star. except for the Crab: it should also be noted that the proposed counterpart is significantly brighter than a simple power-law extrapolation of the X-ray spectra (Gotthelfetal..2011) which implies a magnitude of K,~23 (uncorrected for Galactic extinction)."," On the other hand, the detection of a proposed counterpart to at $K_s \sim 17$ is significantly brighter than any other optical identification of an isolated neutron star, except for the Crab; it should also be noted that the proposed counterpart is significantly brighter than a simple power-law extrapolation of the X-ray spectra \citep{Gotthelf2011:ApJ729} which implies a magnitude of $K_s \sim 23$ (uncorrected for Galactic extinction)."
" While the power-law extrapolation of the X-ray spectra of (Balboetal.2010) is not constraining. that of citepRenaud2010:ApJ.716 implies that a counterpart should be much dimmer than the observed optical limit. at approximately K,~22."," While the power-law extrapolation of the X-ray spectra of \citep{Balbo2010:A&A.520} is not constraining, that of \\citep{Renaud2010:ApJ.716} implies that a counterpart should be much dimmer than the observed optical limit, at approximately $K_s \sim 22$."
 The extrapolations should however be treated with caution as the extracted X-ray spectra themselves may suffer from contamination from the surrounding PWN= and thus inaccurate spectral slopes and fluxes., The extrapolations should however be treated with caution as the extracted X-ray spectra themselves may suffer from contamination from the surrounding PWN and thus inaccurate spectral slopes and fluxes.
 By using a simple power-law extrapolation. we have assumed that the spectra do not evolve between the X-ray and nIR regimes. while it quite possibly breaks to a shallower spectral index or. alternatively. may be described by thermal emission which naturally turns over at lower frequencies.," By using a simple power-law extrapolation, we have assumed that the spectra do not evolve between the X-ray and nIR regimes, while it quite possibly breaks to a shallower spectral index or, alternatively, may be described by thermal emission which naturally turns over at lower frequencies."
 We have also implicitly assumed that the nIR emission originates from the same emission region as the X-ray spectra. which is not necessarily true. but assuming that it is. the above approximations can be treated as lower magnitude limitson how bright we might expect a nIR counterpart to be. before correction for Galactic extinction.," We have also implicitly assumed that the nIR emission originates from the same emission region as the X-ray spectra, which is not necessarily true, but assuming that it is, the above approximations can be treated as lower magnitude limitson how bright we might expect a nIR counterpart to be, before correction for Galactic extinction."
The goal of this paper is to outline some siimiple network tools to enliance the retrieval of astronomical data [rom local machines or data archive websites.,The goal of this paper is to outline some simple network tools to enhance the retrieval of astronomical data from local machines or data archive websites.
 Hopefully. these scripts improve the efficiency of a researchers to find and acquire the information they ueed to address their science questions.," Hopefully, these scripts improve the efficiency of a researchers to find and acquire the information they need to address their science questions."
 Less time spent managing files aud directories means more tine spent on analysis aud uniderstaudiug., Less time spent managing files and directories means more time spent on analysis and understanding.
 Some examples of uses for these scripts are: The reader is invited to moclily or add to the network Library., Some examples of uses for these scripts are: The reader is invited to modify or add to the network library.
 Simply seud your comments ancl scripts to jschombeeuoregon.edu aud we will post them ou the growing website., Simply send your comments and scripts to jschombeuoregon.edu and we will post them on the growing website.
(F< 13.5) aud an associated flag is set in the catalog see 855).,$I < 13.5$ ) and an associated flag is set in the catalog — see 5).
 There are 1095 stars that are affected by his correction., There are 1095 stars that are affected by this correction.
 We also see the asvuuuctry in residuals at faint magnitudes. however this time the tail is toward ooxitive residuals.," We also see the asymmetry in residuals at faint magnitudes, however this time the tail is toward positive residuals."
 Comparing coloranagnuitude diagrams Or stars with Am>0.3 we find that the sequences appear iehter using the OGLE photometry (Figure 13))., Comparing color-magnitude diagrams for stars with $\Delta m > 0.3$ we find that the sequences appear tighter using the OGLE photometry (Figure \ref{oglefaint}) ).
 We conclude that the OGLE photometry is superior at the zduter maguitude levels., We conclude that the OGLE photometry is superior at the fainter magnitude levels.
 Nevertheless. the uncertainties in the MCPS catalog do include anu approximation of he photometric uncertainties due to crowding.," Nevertheless, the uncertainties in the MCPS catalog do include an approximation of the photometric uncertainties due to crowding."
 The Ai» distribution for the faiuter stars is consistent. with the exception of a low-level tail toward positive residuals. with a Gaussian of unit dispersion aud the additional scatter due to subscan-to-sibscan photometric variations discussed carlicr.," The $\Delta m$ distribution for the fainter stars is consistent, with the exception of a low-level tail toward positive residuals, with a Gaussian of unit dispersion and the additional scatter due to subscan-to-subscan photometric variations discussed earlier."
 Although the measurement uucertainties do reflect the crowding problems. auv analysis that is sensitive to the details of the these errors should use artificial star tests (see Tlarris&Zaritslky(2001) for a discussion of those tests).," Although the measurement uncertainties do reflect the crowding problems, any analysis that is sensitive to the details of the these errors should use artificial star tests (see \cite{hz01} for a discussion of those tests)."
 Using the matched stars. we examine whether there are color-term variatious between the two studies.," Using the matched stars, we examine whether there are color-term variations between the two studies."
 Frou Figure lL. we conclude that the V. and. 7 plotometiv have no residual color-terii dependences.," From Figure \ref{oglecolor}, , we conclude that the $V$ and $I$ photometry have no residual color-term dependences."
 Iu contrast. the D photomoetry appears to have a systematic residual at red colors.," In contrast, the $B$ photometry appears to have a systematic residual at red colors."
 Limiting the comparison to bright P maeuitucdes. to avoid including many stars with laree photometric residuals due to crowding. we still Bud the svstematic color-dependent residual.," Limiting the comparison to bright $B$ magnitudes, to avoid including many stars with large photometric residuals due to crowding, we still find the systematic color-dependent residual."
 Such a color-terià is feasible because there are few standard stars at these extreme colors (Figure 1))., Such a color-term is feasible because there are few standard stars at these extreme colors (Figure \ref{stands}) ).
 However. the comparison to \Lassev's catalog does not show such a problem (Figure 10)).," However, the comparison to Massey's catalog does not show such a problem (Figure \ref{masseycolor}) )."
 Iun that conrparisou. there is a photometry difference at BoV— 1.2. but by B.V=1.5 the B photometry betweeu the two studies agrees well Gchile the AICPS and OGLE photometrydisagree by 0.1 mag at BW= 1.5).," In that comparison, there is a photometry difference at $B-V \sim 1.2$ , but by $B-V = 1.5$ the $B$ photometry between the two studies agrees well (while the MCPS and OGLE photometry disagree by 0.1 mag at $B-V = 1.5$ )."
 Because the comparison of the MCTS with these two surveys is inconclusive. and we have no further reason to suspect our photometry. we do uot correct for the color terii but caution that for the reddest stars there may be a B-hanucd systematic error of ~0.1 mae in either our data or the OGLE data.," Because the comparison of the MCPS with these two surveys is inconclusive, and we have no further reason to suspect our photometry, we do not correct for the color term but caution that for the reddest stars there may be a $B$ -band systematic error of $\sim 0.1$ mag in either our data or the OGLE data."
 Similar to our comparison to Massey catalog. we plot the distribution of maguitude differencess for matched stars du units of magnitudes and staudard deviations (Figure 15)) for stars with astrometric differences « 0.7 arcsec. DB and V»13.5. B aud V«15. aud 7«16.," Similar to our comparison to Massey's catalog, we plot the distribution of magnitude differences for matched stars in units of magnitudes and standard deviations (Figure \ref{oglehist}) ) for stars with astrometric differences $<$ 0.7 arcsec, $B$ and $V > 13.5$, $B$ and $V < 15$, and $I < 16$."
 A Gaussian of width corresponding to the propagated uucertainties with an additional random photometric zoropoiut uucertaimtyv of 0.03 magnitudes aerees well with the distributions iu all three bands., A Gaussian of width corresponding to the propagated uncertainties with an additional random photometric zeropoint uncertainty of 0.03 magnitudes agrees well with the distributions in all three bands.
" We conclude that the error estimates, with this small additional termi due to uucertainties iu the scan photometric zeropoiuts. describes the total uncertainties well at maguitudes where crowding does not plav a role."," We conclude that the error estimates, with this small additional term due to uncertainties in the scan photometric zeropoints, describes the total uncertainties well at magnitudes where crowding does not play a role."
 The large sample of stars iu common between MCTPS and OCLE enables us to compare the photometry spatially over the area in common. and so determine whether there are problems on the scale of an individual scan or subscan (either in the AICPS or OGLE).," The large sample of stars in common between MCPS and OGLE enables us to compare the photometry spatially over the area in common, and so determine whether there are problems on the scale of an individual scan or subscan (either in the MCPS or OGLE)."
" In Figure 16 we present maps of the photometric offsets (nediau magnitude differences within square ""pixels for the matched stars used earlier to study global differeuces) for D. V. aud f."," In Figure \ref{oglemos} we present maps of the photometric offsets (median magnitude differences within square “pixels"" for the matched stars used earlier to study global differences) for $B$, $V$, and $I$."
 Two types of spatial patterus are visible., Two types of spatial patterns are visible.
 The first consists either of vertical or horizontal stripine., The first consists either of vertical or horizontal striping.
 This striping is due to photometric errors in scans (MCTPS js horizoutal scaus in this orientation. OGLE has vertical scans).," This striping is due to photometric errors in scans (MCPS has horizontal scans in this orientation, OGLE has vertical scans)."
 Because different. AICPS scans. even in the same filters. πας come from runs separated by several vears. it becomes difficult to obtain photometry that agrees to setter than the iuterual calibration errors (typically ~0.03 uag)," Because different MCPS scans, even in the same filters, may come from runs separated by several years, it becomes difficult to obtain photometry that agrees to better than the internal calibration errors (typically $\sim 0.03$ mag)."
 A horizoutal οσο is visible iu the Z-band. near ie middle left of the nuage.," A horizontal edge is visible in the $I$ -band, near the middle left of the image."
 Vertical edges are visible in the right half of the /-baud panel., Vertical edges are visible in the right half of the $I$ -band panel.
 The difference cross these edges is 0.05 mag from the mean for the uost noticeable edges., The difference across these edges is $\pm 0.05$ mag from the mean for the most noticeable edges.
 The second spatial pattern is the oewcreasing discrepancy (especially in the V. baud) toward ιο SMC center., The second spatial pattern is the increasing discrepancy (especially in the $V$ band) toward the SMC center.
 This is almost certainly the effect of oecreasing crowding., This is almost certainly the effect of increasing crowding.
" At its worst. this offset appears to 90 0,08 nag."," At its worst, this offset appears to be 0.08 mag."
 As the crowding increases bevond the ability of the ata and software to discntanele. it becomes increasingly ikelv that fainter stars will contaminate the photometrv of brighter stars (and that au increasing fraction of fainter stars will be lost).," As the crowding increases beyond the ability of the data and software to disentangle, it becomes increasingly likely that fainter stars will contaminate the photometry of brighter stars (and that an increasing fraction of fainter stars will be lost)."
 Therefore. the detected stars will ecole Increasinely brighter Gvhich is what is observed when comparing MCPS data to OGLE data in the crowded regions}.," Therefore, the detected stars will become increasingly brighter (which is what is observed when comparing MCPS data to OGLE data in the crowded regions)."
 OGLE is superior in this respect for several reasons: 1) their template images are taken iu secius as good as 0.8 arcsec. 2) their pixel scale (0.117. arcsec pixel 1) is inch. better suited to the best secine episodes than ours. aud 3) they use repeat observations to cull uurchable plotometiry.," OGLE is superior in this respect for several reasons: 1) their template images are taken in seeing as good as 0.8 arcsec, 2) their pixel scale (0.417 arcsec $^{-1}$ ) is much better suited to the best seeing episodes than ours, and 3) they use repeat observations to cull unreliable photometry."
 In particular. our V scan of the central region is not optinuu.," In particular, our $V$ scan of the central region is not optimum."
 Obvioush. higher quality data is desirable. but for some applications (such as the eoneration of svuthetic color-imacuitude diagranis) this effect can be inchided in the simulations aud results ouly iu a loss of information. not du a systematic error.," Obviously, higher quality data is desirable, but for some applications (such as the generation of synthetic color-magnitude diagrams) this effect can be included in the simulations and results only in a loss of information, not in a systematic error."
 Alternativelv. investigators interested in the deusest regions of the SAIC may want to coustruct a hivbrid catalog that uses OGLE data along the SMC ridge and AICPS data bevoud the ridge.," Alternatively, investigators interested in the densest regions of the SMC may want to construct a hybrid catalog that uses OGLE data along the SMC ridge and MCPS data beyond the ridge."
 Users of the MCPS should be aware that there is a bias toward measuring a brighter magnitude for a star as one approaches the more heavily crowded fields., Users of the MCPS should be aware that there is a bias toward measuring a brighter magnitude for a star as one approaches the more heavily crowded fields.
" Finally, we compare our £-baud photometry to that in the DENIS catalog."," Finally, we compare our $I$ -band photometry to that in the DENIS catalog."
 Although the DENIS catalog is primarily an IR catalog. it contains an J baud chanel aud Cionietal.(2000). have extracted poiut-source catalogs in the regions of the Magellanic Clouds.," Although the DENIS catalog is primarily an IR catalog, it contains an $I$ band channel and \cite{c00} have extracted point-source catalogs in the regions of the Magellanic Clouds."
 We produce a similar comparison as to the Massey. aud OGLE catalogs. using a search aperture of 3.5 arcsec for matches.," We produce a similar comparison as to the Massey and OGLE catalogs, using a search aperture of 3.5 arcsec for matches."
 The distribution of astrometric aud photometric differences for matched stars are plotted iu Figure 17.., The distribution of astrometric and photometric differences for matched stars are plotted in Figure \ref{deniscomp}.
 Iu agreement with our previous results. we find thatthe astrometric accuracy is subpixel for the majority of the matches.," In agreement with our previous results, we find thatthe astrometric accuracy is subpixel for the majority of the matches."
 The mean difference is 0.9 arcsec. but the mode is ~0.3 arcsec.," The mean difference is 0.9 arcsec, but the mode is $\sim 0.3$ arcsec."
 Using ouly matched stars with positional offsets « 1 pixel. the zeropoiut differcuce between the two," Using only matched stars with positional offsets $<$ 1 pixel, the zeropoint difference between the two"
SAX J2103.5--4545 (2).. which are other types of XBPs with low luminosity (Ly<107 erg ! ) and long pulse period (P> 100 s).,"SAX J2103.5+4545 \citep{Inam+04}, which are other types of XBPs with low luminosity $L_{\rm X}\le10^{35}$ erg $^{-1}$ ) and long pulse period $P >$ 100 s)."
 Moreover. recently the same type of excess has been detected also in the three Supergiant Fast. X-ray Transients (SFXTs) IGR J11215-5292 (?).. IGR J08408-4503 (2) and XTE J1739-302 (?). only the first of which is a confirmed pulsar (P = 187 s).," Moreover, recently the same type of excess has been detected also in the three Supergiant Fast X–ray Transients (SFXTs) IGR J11215-5292 \citep{Sidoli+07}, IGR J08408-4503 \citep{Sidoli+09} and XTE J1739-302 \citep{Bozzo+10}, only the first of which is a confirmed pulsar $P$ = 187 s)."
 Finally. very recently a hot excess has been detected also in the SMC binary pulsar SXP 1062. a possible new persistent Be X-ray binary (?)..," Finally, very recently a hot excess has been detected also in the SMC binary pulsar SXP 1062, a possible new persistent Be X–ray binary \citep{Henault-Brunet+11}."
 In Fig., In Fig.
 5. we report the best-fit radius and temperature for the component of these sources. together with lines showing four different levels of the blackbody luminosity; for some source more than one set of values is shown. corresponding to different observations or flux levels.," \ref{BBparameters} we report the best–fit radius and temperature for the component of these sources, together with lines showing four different levels of the blackbody luminosity; for some source more than one set of values is shown, corresponding to different observations or flux levels."
 In most cases the spectral parameters are within a narrow range of values. Le. ATp~ 2 keV and Πω< 200 m: we emphasize that. in all these cases. the estimated total source X-ray luminosity is ~10°! erg with a 20-40 contribution of the blackbody component.," In most cases the spectral parameters are within a narrow range of values, i.e. $kT_{\rm BB} \sim$ 1--2 keV and $R_{\rm BB} <$ 200 m: we emphasize that, in all these cases, the estimated total source X–ray luminosity is $\sim 10^{34}$ erg $^{-1}$, with a 20–40 contribution of the blackbody component."
" For tthe radius ts slightly higher (py,~ 270 m). in agreement with the fact that its total X-ray luminosity is also higher (Lx~ὃς10? eres 19: when observed at high (Le. Ly~10° ere 1) luminosity level. also RX J1037.5-5647 (point 2). 4U 03524309 (point 4). SAX J2103.544545 (point 10) and IGR J11215-5292 (point 11) show large values of temperature and/or radius."," For the radius is slightly higher $R_{\rm BB} \sim$ 270 m), in agreement with the fact that its total X–ray luminosity is also higher $L_{\rm X} \sim 8\times10^{34}$ erg $^{-1}$ ): when observed at high (i.e. $L_{\rm X} \sim 10^{35}$ erg $^{-1}$ ) luminosity level, also RX J1037.5-5647 (point 2), 4U 0352+309 (point 4), SAX J2103.5+4545 (point 10) and IGR J11215-5292 (point 11) show large values of temperature and/or radius."
 In contrast to this sample of sources. several. XBPs are characterized by a excess. since the fit of this component with a thermal emission model provides low temperatures (KT.< 0.5 keV) and large emitting regions > 100 km).," In contrast to this sample of sources, several XBPs are characterized by a excess, since the fit of this component with a thermal emission model provides low temperatures $kT <$ 0.5 keV) and large emitting regions $>$ 100 km)."
 In Fig., In Fig.
 6 we report the luminosity and pulse period of both types of XBPs: the and the ones are reported as andcircles.. respectively.," \ref{luminosity_period} we report the luminosity and pulse period of both types of XBPs: the and the ones are reported as and, respectively."
 Based on their distribution in the PLx diagram. these pulsars are divided into two distinct groups: the sources in the first group are characterized by high luminosity (Lx.2107* ere 1) and short pulse period 100 s). and in most cases they are in close binary systems with an accretion disk: those i the second group have low luminosities (Lxx107 eres. +) and long pulse periods > 100 s). since they have wide orbits and are wind-fed systems.," Based on their distribution in the $P - L_{\rm X}$ diagram, these pulsars are divided into two distinct groups: the sources in the first group are characterized by high luminosity $L_{\rm X}\ge10^{37}$ erg $^{-1}$ ) and short pulse period $<$ 100 s), and in most cases they are in close binary systems with an accretion disk; those in the second group have low luminosities $L_{\rm X}\le10^{36}$ erg $^{-1}$ ) and long pulse periods $>$ 100 s), since they have wide orbits and are wind–fed systems."
 While all the pulsars in the first group are characterized by aexcess.. both types of pulsars are present in the second group.," While all the pulsars in the first group are characterized by a, both types of pulsars are present in the second group."
 In this case. the pulsars are the ones that. on the average. are characterized by the lowest luminosities and the longest periods.," In this case, the pulsars are the ones that, on the average, are characterized by the lowest luminosities and the longest periods."
 This suggests that the spectral component is à common feature of the low-luminosity and long-period XBPs., This suggests that the spectral component is a common feature of the low–luminosity and long–period XBPs.
 However. in the second group of sources there is no clear separation between the two types of pulsars.," However, in the second group of sources there is no clear separation between the two types of pulsars,"
"as Ti,/g, we obtain This is only a scaling law and not a detailed description, but it is very useful to estimate the luminosity-mass ratio for a large number of red-giant stars exhibiting oscillations (and with a known Τεῃ).","as $T_{\rm eff}^4/g$, we obtain This is only a scaling law and not a detailed description, but it is very useful to estimate the luminosity-mass ratio for a large number of red-giant stars exhibiting oscillations (and with a known $T_{\rm eff}$ )."
 Most of the red-giant stars that we investigated in this paper have been recently identified as belonging to the red clump (?).., Most of the red-giant stars that we investigated in this paper have been recently identified as belonging to the red clump \citep{Miglio09}.
" More precisely, these stars are post-flash helium-core burning stars."," More precisely, these stars are post-flash helium-core burning stars."
" They are characterized by a Vmax ranging from 20 to 50 uHz, by masses between approximately 0.8 and 2 Mo, and by luminosities centered around log(L/Lo)~1.75."," They are characterized by a $\nu_{\rm max}$ ranging from $20$ to $50 \, \mu$ Hz, by masses between approximately $0.8$ and $2$ $M_\odot$, and by luminosities centered around $\log (L / L_{\odot}) \approx 1.75$."
" Hence, the red giants observed by CoRoT are localized in a narrow interval range of mass and luminosity, which explains why the distributions in linewidth and amplitude are well centered, because most of the stars have similar physical properties."," Hence, the red giants observed by CoRoT are localized in a narrow interval range of mass and luminosity, which explains why the distributions in linewidth and amplitude are well centered, because most of the stars have similar physical properties."
" Concerning the linewidths, the dichotomy between resolved and unresolved modes is difficult to interpret because it can be related to the presence of non-radial modes."," Concerning the linewidths, the dichotomy between resolved and unresolved modes is difficult to interpret because it can be related to the presence of non-radial modes."
 A recent theoretical investigation of the power spectrum of red giants has been presented by ?.., A recent theoretical investigation of the power spectrum of red giants has been presented by \cite{Dupret09}.
 They consider different evolutionary stages for red giants and computed excitation and damping rates., They consider different evolutionary stages for red giants and computed excitation and damping rates.
 The radial and non-radial modes trapped in the envelope can be detected with a 150-day long observation., The radial and non-radial modes trapped in the envelope can be detected with a 150-day long observation.
" In terms of linewidth, they are close to the resolution actually observed in reffig:histolargamp.."," In terms of linewidth, they are close to the resolution actually observed in \\ref{fig:histolargamp}."
" From a theoretical point of view, it appears that radial modes are more likely to be resolved because they have a shorter lifetime (see?,fordetails) than the non-radial modes."," From a theoretical point of view, it appears that radial modes are more likely to be resolved because they have a shorter lifetime \citep[see][for details]{Dupret09} than the non-radial modes."
" But it would be dangerous to identify resolved modes as radial and unresolved as non-radial, because the precise values of the damping rate critically depend on the convection-oscillation interaction, which is still poorly known."," But it would be dangerous to identify resolved modes as radial and unresolved as non-radial, because the precise values of the damping rate critically depend on the convection-oscillation interaction, which is still poorly known."
 The maximum amplitude plotted in reffig:histolargamp can also be qualitatively explained., The maximum amplitude plotted in \\ref{fig:histolargamp} can also be qualitatively explained.
" Following ?,, the red-clump CoRoT stars have radii ranging from approximately 10 to 20Ro."," Following \cite{Miglio09}, the red-clump CoRoT stars have radii ranging from approximately $10$ to $20 \, R_\odot$."
" In terms of effective temperature, they range roughly between logTe=3.7 and logTeg=3.65."," In terms of effective temperature, they range roughly between $\log T_{\rm eff} = 3.7$ and $\log T_{\rm eff}=3.65$."
" Mode amplitudes scale as (see?,foradetaileddiscussionofthisrelation) In addition, vmax has been shown toscale as the cut-off frequency v. (seeforexample?):: where H, is the pressure scale height, and c; the sound speed."," Mode amplitudes scale as \citep[see][for a detailed discussion of this relation]{Samadi07}
 In addition, $\nu_{\rm max}$ has been shown toscale as the cut-off frequency $\nu_c$ \citep[see for example][]{Kjeldsen95}: where $H_p$ is the pressure scale height, and $c_s$ the sound speed."
" Then, from refeq:nu,,ax, , thehorizontalscatterseeninF reffig: amp,umaxcanbeexpected f romthedispersioninradius."," Then, from \\ref{eq:nu_max}, the horizontal scatter seen in \\ref{fig:amp_numax} can be expected from the dispersion in radius."
F romEq. refeq: ampand3theanti—correlationbetweentheamplitudeA max and Vmax is explained by the dispersion in effective temperature of stars belonging to the red clump., From \\ref{eq:amp} and \ref{eq:nu_max} the anti-correlation between the amplitude $A_{\rm max}$ and $\nu_{\rm max}$ is explained by the dispersion in effective temperature of stars belonging to the red clump.
" More precisely, refeq:amp shows that the higher Τομ, the higher the mode amplitude, and refeq:nu,,axshowsthatthehigherTe, the lower the vga."," More precisely, \\ref{eq:amp} shows that the higher $T_{\rm eff}$, the higher the mode amplitude, and \\ref{eq:nu_max} shows that the higher $T_{\rm eff}$, the lower the $\nu_{\rm max}$."
 In reffig:larg the variation of mode widths is shown versus the effective temperature of the stars., In \\ref{fig:larg} the variation of mode widths is shown versus the effective temperature of the stars.
 Apparently there is no link between temperature and mode width for the red giants., Apparently there is no link between temperature and mode width for the red giants.
" However, one must keep in mind the relatively large uncertainties on Τε that can flatten the observed distribution."," However, one must keep in mind the relatively large uncertainties on $T_{\rm eff}$ that can flatten the observed distribution."
" However, when the amplitudes are shown versus the ratio L/M, there is a clear correlation."," However, when the amplitudes are shown versus the ratio $L/M$ , there is a clear correlation."
 Given that L/M is proportional to, Given that $L/M$ is proportional to
,.
 Small spectrum-to-spectrum waveleneth shifts were corrected. using sky lines in the science spectra., Small spectrum-to-spectrum wavelength shifts were corrected using sky lines in the science spectra.
 In most of the spectra. the two or three brightest sky. emission lines were not completely. removed. in the sky. subtraction.," In most of the spectra, the two or three brightest sky emission lines were not completely removed in the sky subtraction."
 This did not alfect spectral classification or redshift measurement. but for presentation in Figs.," This did not affect spectral classification or redshift measurement, but for presentation in Figs."
 1. 2 we manually cleaned some of the strongest. residuals.," 1, 2 we manually cleaned some of the strongest residuals."
 Spectra of tio more candidates (FIRST 1343|4305 and FIRST 1405|5155) were obtained with similar instrumental set-up on the nights of 2005 July 12 ancl 13., Spectra of two more candidates (FIRST 1343+4305 and FIRST 1405+5155) were obtained with similar instrumental set-up on the nights of 2005 July 12 and 13.
 Pwo spectra per object were taken. shifting the object along the slit to minimize the ellect of detector artefacts and remove the OLL sky lines.," Two spectra per object were taken, shifting the object along the slit to minimize the effect of detector artefacts and remove the OH sky lines."
 For cach object. one 2D spectrum was subtracted from the other. to remove the background. then wavelength calibrated. aligned. in the spatial direction ancl coaclelect.," For each object, one 2D spectrum was subtracted from the other, to remove the background, then wavelength calibrated, aligned in the spatial direction and coadded."
 Exposure times were 2«1800 s for 1343|4305 and 2...1200 s for 1405|5155.," Exposure times were $2
\times 1800$ s for 1343+4305 and $2 \times 1200$ s for 1405+5155."
 The 13 objects include eight. QSOs. one 2=0.2705 emission line galaxy. (1911). and four LIate-tvpe stars.," The 13 objects include eight QSOs, one $z=0.2705$ emission line galaxy (ELG), and four late-type stars."
" The redshift, of each QSO was estimated. as the average of he values measured from individual emission-line centroids (excluding Lya. which is often. allected by Lya forest absorption)."," The redshift of each QSO was estimated as the average of the values measured from individual emission-line centroids (excluding $\alpha$, which is often affected by $\alpha$ forest absorption)."
 Six of the QSOs have3.1<z« 3.9. the other wo have z=0.897 and z=0.943.," Six of the QSOs have$3.1 < z <
3.9$ , the other two have $z=0.897$ and $z=0.943$."
 The PNG spectra of the eight. QSOs and the ELG are shown in Figs., The TNG spectra of the eight QSOs and the ELG are shown in Figs.
 1 ancl 2., 1 and 2.
 Fig., Fig.
" P also shows the SDSS DIU spectrum of FURST 1039|4931. classified ""unknown in SDSS. but which we identify as à QSO at z= 1.09."," 1 also shows the SDSS DR3 spectrum of FIRST 1039+4931, classified `unknown' in SDSS, but which we identify as a QSO at $z=1.09$ ."
 Fourof, Fourof
Dased on a number of methods of observation. the sun is known (ο lie in a cavitv of unusually low interstellar density.,"Based on a number of methods of observation, the sun is known to lie in a cavity of unusually low interstellar density."
 The cavity is believed to contain gas of temperature around 10* IX with a filling [actor greater than80%., The cavity is believed to contain gas of temperature around $^6$ K with a filling factor greater than.
. Denser material at the cavity walls has been mapped in Na by Sleiretal.(1999)., Denser material at the cavity walls has been mapped in Na by \citet{Sfeir99}.
. These measurements show the local cavity to extend in the plane of the Galaxy about 100 pe. but much farther perpendicular to the plane. possibly connecting to the lower halo (Crawfordetal.2002).," These measurements show the local cavity to extend in the plane of the Galaxy about 100 pc, but much farther perpendicular to the plane, possibly connecting to the lower halo \citep{Crayfish02}."
. Analvsis of the spatial and spectral distribution of the diffuse X-ray background and II shadowing reveal a relatively unabsorbed. “local” component with temperature about 1057 IX. emission measure ranging from about 0.0018 to 0.0058 ° pe. and a physical extent somewhat smaller than that of the houndary of the local cavity (Snowdenetal.1998:IxuntzSnowden2000:\leCammon&Sanders 1990).," Analysis of the spatial and spectral distribution of the diffuse X-ray background and HI shadowing reveal a relatively unabsorbed, ""local"" component with temperature about $^{6.1}$ K, emission measure ranging from about 0.0018 to 0.0058 $^{-6}$ pc, and a physical extent somewhat smaller than that of the boundary of the local cavity \citep{Sno98,KS00,MS90}."
". The collisional ionization equilibrium (CIE) plasma emission codes emploved in such modeling predict a cluster of emission lines of highly ionized iron (Fe - Fe XII) near 72 eV. with a combined strength of about 150 to 300 photons em7s ! ! (hereafter ""line units"" or LU)."," The collisional ionization equilibrium (CIE) plasma emission codes employed in such modeling predict a cluster of emission lines of highly ionized iron (Fe - Fe ) near 72 eV, with a combined strength of about 150 to 300 photons $^{-2}$ $^{-1}$ $^{-1}$ (hereafter ""line units"" or LU)."
 For a solar-abundance plasma in CIE near LO? Ix. the flux in the iron lines comprises about of the total radiated power.," For a solar-abundance plasma in CIE near $^{6}$ K, the flux in the iron lines comprises about of the total radiated power."
 Thus determining the strength of these lines observationally has implications for plasma lifetimes., Thus determining the strength of these lines observationally has implications for plasma lifetimes.
 Within the cavity exist warm. partially ionized parcels of gas commonly called “clouds.” in which the ionization fraction of helium is at or above Chat of hydrogen despite helium5 much higher ionization potential (Iximbleetal.1993).," Within the cavity exist warm, partially ionized parcels of gas commonly called ""clouds,"" in which the ionization fraction of helium is at or above that of hydrogen despite helium's much higher ionization potential \citep{Kimble93}."
. Fossil nonequilibrium ionization can in principle provide an explanation for this puzzle. but the simplest scenario. in which the clouds are recombining lrom a past impulsive event. is difficult to reconcile with the abundance of," Fossil nonequilibrium ionization can in principle provide an explanation for this puzzle, but the simplest scenario, in which the clouds are recombining from a past impulsive event, is difficult to reconcile with the abundance of"
2005: Llutawarakorn Cohen 2005. and references therein).,"2005; Hutawarakorn Cohen 2005, and references therein)."
 Alore data are needed to confirm these findings., More data are needed to confirm these findings.
 A search of a 23 23 arcsce region around 65 Ori C was made. but no OLI masers with peak flux densities 0.1 Jv were found. even near the most prominent. proplvds (LV. 16).," A search of a 23 $\times$ 23 arcsec region around $\theta^{1}$ Ori C was made, but no OH masers with peak flux densities $\geq$ 0.1 Jy were found, even near the most prominent proplyds (LV 1--6)."
" The densities in these regions have been estimated to be 10 10"" em? (Section 4.43). which are typical of OLL maser sources. while the temperatures are estimated to be 200350 Ix (Havwarcd. Houck Miles 1995). which are somewhat higher than usually encountered in OLL maser sources (c.g. Crageg. Sobolev Godfrey 2002)."," The densities in these regions have been estimated to be $^{5}$ $^{6}$ $^{-3}$ (Section \ref{proplyds2}) ), which are typical of OH maser sources, while the temperatures are estimated to be 200--350 K (Hayward, Houck Miles 1995), which are somewhat higher than usually encountered in OH maser sources (e.g. Cragg, Sobolev Godfrey 2002)."
 The non-detection of OLI masers might be explained by a low OLL column censity. which could arise through chemical evolution (e.g. Itodgers Charnely. 2001).," The non-detection of OH masers might be explained by a low OH column density, which could arise through chemical evolution (e.g. Rodgers Charnely 2001)."
 For our kinematic modelling we used only the 1665-MlIz nmasers., For our kinematic modelling we used only the 1665-MHz masers.
 “Phe celestial coordinates and racial velocities of the OLL masers give incomplete information on the, The celestial coordinates and radial velocities of the OH masers give incomplete information on the
active ancl inactive galaxies have the same bar fraction (Iloetal.1997:Mulchaey&Regan 2002).,"active and inactive galaxies have the same bar fraction \citep{ho97c, mulchaey97a, laine02}."
. Iloetal. speculate Chat (his is because racdially-(ransportecdl gas is prevented [rom reaching the nucleus.," \citeauthor{ho97c}
 speculate that this is because radially-transported gas is prevented from reaching the nucleus."
 If bars are indeed fueling galaxies. cireiumnuclear regions. then this should be reflected in the morphology of the cold circumnuclear interstellar medium (15M).," If bars are indeed fueling galaxies' circumnuclear regions, then this should be reflected in the morphology of the cold circumnuclear interstellar medium (ISM)."
 Martini establish a nuclear dust morphology. classification svstem with [our spiral classes (grand design. tightly wound. loosely wound. ancl chaotic spiral) aud (wo non-spiral classes (eliaotic and no structure) to quantify differences between various galaxy (vpes.," \citet{martini03a} establish a nuclear dust morphology classification system with four spiral classes (grand design, tightly wound, loosely wound, and chaotic spiral) and two non-spiral classes (chaotic and no structure) to quantify differences between various galaxy types."
 fined no differences in the nuclear cust structure of active and inactive galaxies., \citet{martini03b} find no differences in the nuclear dust structure of active and inactive galaxies.
 This study does find evidence (hat nuclear grand design spirals are primarily found in barred galaxies and that these grand. design spirals connect (o large scale dust lanes in barred. galaxies., This study does find evidence that nuclear grand design spirals are primarily found in barred galaxies and that these grand design spirals connect to large scale dust lanes in barred galaxies.
 Likewise. Martinietal. primarily [find tightly wound nuclear spirals in unbarred galaxies.," Likewise, \citeauthor{martini03b}
 primarily find tightly wound nuclear spirals in unbarred galaxies."
" All of these studies of the role of bars in Ineling central star formation or black holes simply compare ""barred versus “unbarred” galaxies.", All of these studies of the role of bars in fueling central star formation or black holes simply compare “barred” versus “unbarred” galaxies.
 This discretization glosses over. and over simplifies. the long-known continuum of barstveneths (deVaucouleurs1959).," This discretization glosses over, and over simplifies, the long-known continuum of barstrengths \citep{devaucouleurs59}."
. One early wav of quantilving the strength of a bar is the deprojected bar ellipticity e; 1995)., One early way of quantifying the strength of a bar is the deprojected bar ellipticity $\epsilon_b$ \citep{martin95}.
. The disadvantage of using the bar ellipticitv is (hat defining the barEe. ils exact dimensionsis a somewhat subjective process (Buta&B," The disadvantage of using the bar ellipticity is that defining the bar—i.e., its exact dimensions—is a somewhat subjective process \citep{buta01}."
lock2001).. (2000) introduce the parameter fi... which is a function of the bar axis ratio. aud therefore susceptible to Che same systemalics as ej. Bula&Dlock..," \citet{abraham00} introduce the parameter $f_{\mbox{\scriptsize bar}}$, which is a function of the bar axis ratio, and therefore susceptible to the same systematics as $\epsilon_b$. \citeauthor{buta01},"
 bv expanding on the method of Combes&Sanders(1981)... circumvent (his problem by using a force ratio. which thev call Qu.," by expanding on the method of \citet{combes81}, circumvent this problem by using a force ratio, which they call $Q_b$."
 Assuming that the light traces the underlying mass distribution. thev use near-infrared images {ο calculate a map of a galaxys potential.," Assuming that the light traces the underlying mass distribution, they use near-infrared images to calculate a map of a galaxy's potential."
 From these potential maps. auc with some assumptions about the characteristic scale-height. {μον then calculate the tangential force Fy and mean (axisvmimetric) radial force (F5).," From these potential maps, and with some assumptions about the characteristic scale-height, they then calculate the tangential force $F_T$ and mean (axisymmetric) radial force $\langle
F_R\rangle$."
 They define the ratio map Q as This ralio map has the property that in each of four quadrants Q; reaches a local extreniun., They define the ratio map $Q_T$ as This ratio map has the property that in each of four quadrants $Q_T$ reaches a local extremum.
" Letting Qax.f be the absolute value of such an extremum in the Ath quadrant. the barstrength Qy, is defined as The cited uncertainties on Q, are a nieasure of how much QP varies by quadrant."," Letting $Q_{T}^{\mbox{\scriptsize max},\,k}$ be the absolute value of such an extremum in the $k$ th quadrant, the barstrength $Q_b$ is defined as The cited uncertainties on $Q_b$ are a measure of how much $Q_{T}^{\mbox{\scriptsize max}}$ varies by quadrant."
 From a comparison with the three barstrength classes defined by deVancoulenrs (unbarred SA.," From a comparison with the three barstrength classes defined by \citeauthor{devaucouleurs59}
 (unbarred SA,"
Forty years after the discovery of rotating neutron stars much is unknown about their emission processes. and m particular the radio emission mechanism ts still largely not understood (??)..,"Forty years after the discovery of rotating neutron stars much is unknown about their emission processes, and in particular the radio emission mechanism is still largely not understood \citep{DLMK04,YL08}."
 Of the nearly two thousand known pulsars. six have been detected in GeV gamma-rays with high confidence. using the EGRET detector on the (CGRO) (?)..," Of the nearly two thousand known pulsars, six have been detected in GeV gamma-rays with high confidence, using the EGRET detector on the (CGRO) \citep{DJT99}."
 The Large Area Telescope (LAT) on the Gamma-ray Space Telescope (formerly theTelescope. or GLAST) went into orbit on 2008 June 11(2)..," The Large Area Telescope (LAT) on the Gamma-ray Space Telescope (formerly the, or GLAST) went into orbit on 2008 June \citep{WA08}."
 The sensitivity and time resolution of this instrument will allow it to discover tens or more of new gamma-ray pulsars (?).., The sensitivity and time resolution of this instrument will allow it to discover tens or more of new gamma-ray pulsars \citep{DAS08}.
 Notably. it will be able to determine the sources among the 169 unidentified EGRET sources that are pulsars.," Notably, it will be able to determine the sources among the 169 unidentified EGRET sources that are pulsars."
 However. even with a sensitivity more than 30 times greater than that of EGRET. the LAT's rate of gamma-ray photon detection will be small.," However, even with a sensitivity more than 30 times greater than that of EGRET, the LAT's rate of gamma-ray photon detection will be small."
 For example. the pulsar is the third brightest known gamma-ray pulsar. but will trigger the LAT only once every 500 revolutions of the neutron star (15 seconds). on average.," For example, the pulsar is the third brightest known gamma-ray pulsar, but will trigger the LAT only once every 500 revolutions of the neutron star (15 seconds), on average."
 While the pulsar should be detected by the LAT with high confidence in less than a day. it will take years to detect pulsars near the sensitivity threshold. with days separating individual photon arrival times.," While the pulsar should be detected by the LAT with high confidence in less than a day, it will take years to detect pulsars near the sensitivity threshold, with days separating individual photon arrival times."
 A search for pulsations using gamma-ray data alone is quite difficult in these conditions (?2)..," A search for pulsations using gamma-ray data alone is quite difficult in these conditions \citep{WA06,SR07}."
 Accurate knowledge of the rotation parameters increases LAT pulsed sensitivity., Accurate knowledge of the rotation parameters increases LAT pulsed sensitivity.
" However. many neutron stars slow down irregularly. à phenomenon known as ""timing noise"". making it difficult to extrapolate a pulsar's rotation frequency v from one epoch to another."," However, many neutron stars slow down irregularly, a phenomenon known as “timing noise”, making it difficult to extrapolate a pulsar's rotation frequency $\nu$ from one epoch to another."
 Consequently. in order to obtain the accurate ephemerides necessary for gamma-ray detection of pulsations. known pulsars must be observed regularly.," Consequently, in order to obtain the accurate ephemerides necessary for gamma-ray detection of pulsations, known pulsars must be observed regularly."
 In anticipation of the launch. and mindful of the requirement for accurate. contemporaneous timing parameters in order to observe pulsars at gamma-ray energies. we began an extensive. campaign of pulsar timing observations with the Parkes 64-meter radio telescope in Australia (?).. the Lovell 76-meter telescope at the Jodrell Bank observatory near Manchester. England (?).. and the 94-meter (equivalent) Nangaay radio telescope near Orleans. France.," In anticipation of the launch, and mindful of the requirement for accurate, contemporaneous timing parameters in order to observe pulsars at gamma-ray energies, we began an extensive campaign of pulsar timing observations with the Parkes 64-meter radio telescope in Australia \citep{RM01}, the Lovell 76-meter telescope at the Jodrell Bank observatory near Manchester, England \citep{DM02}, and the 94-meter (equivalent) Nançaay radio telescope near Orleans, France."
 The Parkes telescope is the only telescope in the campaign that observes sources south of —397., The Parkes telescope is the only telescope in the campaign that observes sources south of $-39$.
. ?. describes the 2002 FORT upgrade to the Nangaay receiver. with the new BON pulsar backend described in ? and ?..," \citet{GT05} describes the 2002 FORT upgrade to the Nançaay receiver, with the new BON pulsar backend described in \citet{ICGT06} and \citet{FC07}."
 These observatories carry out observing programs in support of the mission and. betwee! them. observe more than 200 pulsars with a large spin-dowr luminosity. £. as described below. on a regular basis.," These observatories carry out observing programs in support of the mission and, between them, observe more than 200 pulsars with a large spin-down luminosity, $\dot E$, as described below, on a regular basis."
 [i addition. about 10 pulsars with weak radio emission that are particularly strong candidates for gamma-ray emissitor are being observed periodically with the Green Bank radio," In addition, about 10 pulsars with weak radio emission that are particularly strong candidates for gamma-ray emission are being observed periodically with the Green Bank radio"
and mass loss by stellar winds.,and mass loss by stellar winds.
" This implies that stellar populations that form later will have more powerful winds, since they form out of an ISM that has already been enriched in metals by earlier populations."," This implies that stellar populations that form later will have more powerful winds, since they form out of an ISM that has already been enriched in metals by earlier populations."
" Figure 1 shows a sudden increase in wind power around 1 - 2x10®yr, just prior to the arrival of the first SNe, which is caused by the evolved stages of OB stars, i.e. the Wolf-Rayet stars."," Figure \ref{lum_SN} shows a sudden increase in wind power around 1 - $2\times10^6{\rm yr}$, just prior to the arrival of the first SNe, which is caused by the evolved stages of OB stars, i.e. the Wolf-Rayet stars."
 The increase in mass loss after 10°yr is caused by the low-mass stars on the AGB., The increase in mass loss after $10^8{\rm yr}$ is caused by the low-mass stars on the AGB.
" Except in situations where the metallicity of the stars is larger or equal to solar, the enrichment of the ISM is dominated by SNe (see Fig."," Except in situations where the metallicity of the stars is larger or equal to solar, the enrichment of the ISM is dominated by SNe (see Fig."
 8 of Leithereretal. 1992))., 8 of \citealt{lrd92}) ).
" Thus, it is important to know the composition of the material ejected by SNe as a function of the initial mass and metallicity of the stellar progenitors."," Thus, it is important to know the composition of the material ejected by SNe as a function of the initial mass and metallicity of the stellar progenitors."
 Several groups have used models of stellar evolution and nucleosynthesis to produce tables of chemical abundances for SN ejecta., Several groups have used models of stellar evolution and nucleosynthesis to produce tables of chemical abundances for SN ejecta.
 These studies are summarized in Table 1.., These studies are summarized in Table \ref{table_SNe}.
" The first column gives the authors of the papers; the second and third columns list the metallicities and initial masses considered, respectively; the fourth column indicates whether or not mass loss prior to the SN explosion was included in the model."," The first column gives the authors of the papers; the second and third columns list the metallicities and initial masses considered, respectively; the fourth column indicates whether or not mass loss prior to the SN explosion was included in the model."
" Although very useful, these studies are not fully satisfactory for our work."," Although very useful, these studies are not fully satisfactory for our work."
" The first three studies (Woosley&Weaver1995;Chieffi&Limongi2004;Nomotoetal. 2006,, hereafter N06) consider a wide range of metallicities, from no metallicity (Z= 0) to solar metallicity (Zo= 0.02), but are limited to initial masses M;<40Mo."," The first three studies \citealt{ww95,cl04,nomotoetal06}, hereafter N06) consider a wide range of metallicities, from no metallicity $Z=0$ ) to solar metallicity $Z_\odot=0.02$ ), but are limited to initial masses $M_i\leq40\,\msun$."
" The next three studies (Woosley&Heger2007,, hereafter WHO07; Limongi&Chieffi 2007;; Heger&Woosley 2010,, hereafter HW10) consider initial masses up to 100 - 120Mo, but only one value of the metallicity."," The next three studies \citealt{wh07}, hereafter WH07; \citealt{lc07}; \citealt{hw10}, hereafter HW10) consider initial masses up to 100 - $120\,\msun$, but only one value of the metallicity."
" Also, three of these studies do not include mass loss prior to the explosion, which is critical in our models since we include stellar wind effects."," Also, three of these studies do not include mass loss prior to the explosion, which is critical in our models since we include stellar wind effects."
 The study that comes the closest to our needs is the one of N06., The study that comes the closest to our needs is the one of N06.
 This is the only study that covers metallicities in the range Z=0 - Zo and includes mass loss., This is the only study that covers metallicities in the range $Z=0$ - $Z_\odot$ and includes mass loss.
" However, its mass range only goes from 13 to 40Mo."," However, its mass range only goes from 13 to $40\,\msun$."
 These tables need to be extrapolated both at the low-mass and high-mass end to cover the full range of SNe progenitor masses., These tables need to be extrapolated both at the low-mass and high-mass end to cover the full range of SNe progenitor masses.
" In this paper, we assume an IMF with lower and upper masslimits of 1 and 120Mo, respectively, and SNe progenitor masses in the range M;—8 - 120Mo."," In this paper, we assume an IMF with lower and upper masslimits of $1$ and $120\,\msun$, respectively, and SNe progenitor masses in the range $M_i=8$ - $120\,\msun$."
" The lower limit of 8Mo is the most commonly used, but that value is actually quite uncertain, and could have an important effect on the results (see Fig."," The lower limit of $8\msun$ is the most commonly used, but that value is actually quite uncertain, and could have an important effect on the results (see Fig."
 5 below)., \ref{masseject_pop} below).
" 'The top panel of Figure 2 shows the mass ejected by SNe versus initial mass and metallicity, calculated with the tables of N06 (solid curves)."," The top panel of Figure \ref{masseject} shows the mass ejected by SNe versus initial mass and metallicity, calculated with the tables of N06 (solid curves)."
 An interesting feature is the linear relation between M.j and M; at Z=0., An interesting feature is the linear relation between $M_{\rm ej}$ and $M_i$ at $Z=0$.
" Also, all the curves converge together at M;—13Mo, suggesting that for initial masses M;«13 Mo, the ejected mass is independent of metallicity."," Also, all the curves converge together at $M_i=13\,\msun$, suggesting that for initial masses $M_i<13\,\msun$ , the ejected mass is independent of metallicity."
" To extrapolate down to M;=8Mo, we used the composition for M;=13Mo, modulated using the linear regression at Z—0 calculated with the software Slope 1990)."," To extrapolate down to $M_i=8\,\msun$, we used the composition for $M_i=13\,\msun$, modulated using the linear regression at $Z=0$ calculated with the software Slope \citep{isobeetal90}."
. The result is also shown in Figure 2.., The result is also shown in Figure \ref{masseject}.
" Extrapolation up to 120Me can be tricky, especially if mass loss is considered."," Extrapolation up to $120\,\msun$ can be tricky, especially if mass loss is considered."
" Several approaches have been suggested in the literature, especiallyat the high-mass end."," Several approaches have been suggested in the literature, especiallyat the high-mass end."
 Martinez-Serranoetal.(2008) extrapolate the mass ejected M.; and chemical composition of the ejecta linearly up to Μι=100Mo. Oppe," \citet{martinezserranoetal08}
 extrapolate the mass ejected $M_{\rm ej}$ and chemical composition of the ejecta linearly up to $M_i=100\,\msun$."
nheimer&Davé(2008) assume similar ejecta for stars in the range Μι=35 - 100Mo and also for stars in the range M;=10 - 13Mo.," \citet{od08} assume similar ejecta for stars in the range $M_i=35$ - $100\,\msun$ and also for stars in the range $M_i=10$ - $13\,\msun$."
" Tornatoreetal.(2007) and Scannapiecoetal.(2005) assume that stars with initial masses larger than 40Mo end up directly in a black hole, with no ejecta."," \citet{tornatoreetal07} and \citet{scannapiecoetal05}
 assume that stars with initial masses larger than $40\,\msun$ end up directly in a black hole, with no ejecta."
 Using linear interpolation up to M;=120Meo would be risky.," Using linear interpolation up to $M_i=120\,\msun$ would be risky."
" The relation between M.; and M; becomes metallicity-dependent for M;>25 30Mo, implying that only two or three points would be available to extrapolate over a mass interval three times wider than the one of N06."," The relation between $M_{\rm ej}$ and $M_i$ becomes metallicity-dependent for $M_i>25$ - $30\,\msun$, implying that only two or three points would be available to extrapolate over a mass interval three times wider than the one of N06."
" Furthermore at Z=Zo, My eventually decreases with increasing initial mass and a linear extrapolation would eventually lead negative values before reaching M;—120Mo."," Furthermore at $Z=Z_\odot$, $M_{\rm ej}$ eventually decreases with increasing initial mass and a linear extrapolation would eventually lead negative values before reaching $M_i=120\,\msun$."
 Setting the ejected mass to zero for Mi>40Mo is not a good solution either.," Setting the ejected mass to zero for $M_i>40\,\msun$ is not a good solution either."
" Even if the SN results in the formation of a black hole, that black hole is never as massive as the progenitor (Woosleyetal.2002;; WHO7; Limongi&Chieffi2008;Zhanetal.Belczyn- 2010))."," Even if the SN results in the formation of a black hole, that black hole is never as massive as the progenitor \citealt{whw02}; WH07; \citealt{lc08,zwh08,belczynskietal10}) )."
" Using a copy of the M=40Mo at larger masses is not realistic either since the tendency clearly shows that there is more material ejected for larger initial masses, except at Zo."," Using a copy of the $M=40\,\msun$ at larger masses is not realistic either since the tendency clearly shows that there is more material ejected for larger initial masses, except at $Z_\odot$."
" Since none of the three extrapolation methods considered so far is satisfactory for extrapolating up to 120Mo, we developed an alternative method."," Since none of the three extrapolation methods considered so far is satisfactory for extrapolating up to $120\,\msun$, we developed an alternative method."
" We started by extrapolating the table of N06 at Z=0 and also Zo, by combining them with the tables of HW10 and WHOT, respectively."," We started by extrapolating the table of N06 at $Z=0$ and also $Z_\odot$ , by combining them with the tables of HW10 and WH07, respectively."
 The top panel of Figure 2 shows the Zo relation of WH07 and the Z=0 relation of HW10 (dotted curves).," The top panel of Figure \ref{masseject}
 shows the $Z_\odot$ relation of WH07 and the $Z=0$ relation of HW10 (dotted curves)."
 The Z=Ze relations of NO6 and WHO7 differ significantly in the range M;=20 - 40 Mo.," The $Z=Z_\odot$ relations of N06 and WH07 differ significantly in the range $M_i=20$ - $40\,\msun$ ."
 This is likely the consequence of using adifferent prescription for the mass, This is likely the consequence of using adifferent prescription for the mass
slrucliires enierging cospatially with granules.,structures emerging cospatially with granules.
 Thev appear first inside the granule. then move to the intergranular lanes where thev disappear (Centeno2010)..," They appear first inside the granule, then move to the intergranular lanes where they disappear \citep{Centeno:etal:2007,Gomory:etal:2010}. ."
 Around 23% of such loop-like features rise and thus may contribute to the heating of higher atmospheric lavers (MartinezGonzález&BellotRubio2009)., Around $23\%$ of such loop-like features rise and thus may contribute to the heating of higher atmospheric layers \citep{Marian:Luis:2009}.
. On the other hand. some TIF are associated with downlflows (προetal.2010).," On the other hand, some HIF are associated with downflows \citep{Kubo:etal:2010}."
. MIID simulations show (hat horizontal magnetic field may. appear during flux cancellations (Stein&Nordlund2006) or {lux emergence over single or multiple granules (Steineretal.2008:Cheungοἱ2007).," MHD simulations show that horizontal magnetic field may appear during flux cancellations \citep{Stein:Nordlund:2006} or flux emergence over single or multiple granules \citep{Steiner:etal:2008,Cheung:etal:2007}."
.. Additionally. a significant amount of small-scale horizontal field is possibly produced through local dynamo action 2008).," Additionally, a significant amount of small-scale horizontal field is possibly produced through local dynamo action \citep{Schuessler:Voegler:2008}."
". To estimate what fraction of HIF has its origin in each of these processes could. however. be challenging since their observable signature may. be similar,"," To estimate what fraction of HIF has its origin in each of these processes could, however, be challenging since their observable signature may be similar."
 Previous studies of HIE. were based on slit observations of selected features. that appear as single events. mostly associated with upílows.," Previous studies of HIF were based on slit observations of selected features that appear as single events, mostly associated with upflows."
 Ilere we use the first imaging observations obtained with the Bnaging Magnuetograph eXperiment (IMaX.MartinezPilletelal.2004:MartínezPilletet2010) onboardSUNRISE. a balloon-borne solar observatον (Bartholetal.2010:SolankiBerkeleldοἱGandorler2010).. to obtain statistical properties of HIF.," Here we use the first imaging observations obtained with the Imaging Magnetograph eXperiment \citep[IMaX,][]{Valentin:etal:2004,Valentin:etal:2010} onboard, a balloon-borne solar observatory \citep{Barthol:etal:2010,Solanki:etal:2010,Berkefeld:etal:2010,Gandorfer:etal:2010}, to obtain statistical properties of HIF."
 Mounted on a l-m aperture telescope. IMaX provides two-dimensional maps of the vector magnetic fiekl with exceptional spatial ancl temporal resolution.," Mounted on a 1-m aperture telescope, IMaX provides two-dimensional maps of the vector magnetic field with exceptional spatial and temporal resolution."
 Using these data. we study all structures that show significant linear polarization signal in the selected «quiet Sun time series.," Using these data, we study all structures that show significant linear polarization signal in the selected quiet Sun time series."
 We examine (heir properties. in particular (heir connection with the velocity field.," We examine their properties, in particular their connection with the velocity field."
 We use two data setsobtained on June 9 2009. 00:36:02-00:58:46 UT (data set 1) and," We use two data setsobtained on June 9 2009, 00:36:02-00:58:46 UT (data set 1) and"
likely real period with significance indicated by the contours.,likely real period with significance indicated by the contours.
" Even if the contours form a closed loop, we are naturally only interested if the highest peak in the power spectrum isabove the contours shown."," Even if the contours form a closed loop, we are naturally only interested if the highest peak in the power spectrum is the contours shown."
" The highest peak below the contours would mark a case, where there is only white noise in the data, as the lowest horizontal sections of the contours represent the case, where only white noise is present."," The highest peak below the contours would mark a case, where there is only white noise in the data, as the lowest horizontal sections of the contours represent the case, where only white noise is present."
 'The results are quite striking when compared to the power spectra alone., The results are quite striking when compared to the power spectra alone.
 Only in one dataset out of 12 we find a peak well above the contour., Only in one dataset out of 12 we find a peak well above the contour.
" That is the dataset showing a 50 min period (dataset 7, 3rd row, 1st column in Fig 2)."," That is the dataset showing a 50 min period (dataset 7, 3rd row, 1st column in Fig 2)."
 The bottom row datasets in Fig 1 seem to show clear periodic variability at periods around 15 min (1.1 mHz) in visual inspection., The bottom row datasets in Fig 1 seem to show clear periodic variability at periods around 15 min (1.1 mHz) in visual inspection.
" Indeed, the period analysis shows peaks around that period."," Indeed, the period analysis shows peaks around that period."
" However, the red noise analysis reveals that the peaks around 15 min (1.1 mHz) are at best significant (Fig 2, bottom row)."," However, the red noise analysis reveals that the peaks around 15 min (1.1 mHz) are at best significant (Fig 2, bottom row)."
 This is also the case for all the other peaks in Fig 2 (apart from the 50 min period)., This is also the case for all the other peaks in Fig 2 (apart from the 50 min period).
" This underlines the fact that, in the presence of significant amount of red noise, neither the peak in the power spectrum or even the peak together with rather obvious visual signal always guarantee a real periodicity!"," This underlines the fact that, in the presence of significant amount of red noise, neither the peak in the power spectrum or even the peak together with rather obvious visual signal always guarantee a real periodicity!"
projections of the rotation axes of both stars are. to within their uncertainties. perpendicular to a vector that lies in the plane of the orbit and is perpendicular to the line of sight.,"projections of the rotation axes of both stars are, to within their uncertainties, perpendicular to a vector that lies in the plane of the orbit and is perpendicular to the line of sight."
 What does that mean for the orientation axes of the stars?, What does that mean for the orientation axes of the stars?
 It is highly unlikely that the geometry is such that we see the projection of the rotation axes perpendicular to the orbital plane and the stellar rotation axes have a high inclination towards the observer., It is highly unlikely that the geometry is such that we see the projection of the rotation axes perpendicular to the orbital plane and the stellar rotation axes have a high inclination towards the observer.
 We therefore conclude that the stellar rotation axes are normal to the orbital plane. and aligned with each other and the rotation axis of the system.," We therefore conclude that the stellar rotation axes are normal to the orbital plane, and aligned with each other and the rotation axis of the system."
 This leaves the theoretical prediction of the apsidal motion unaltered for V1I43CCyg., This leaves the theoretical prediction of the apsidal motion unaltered for Cyg.
 Hence. the difference between expected (0.00089240.00015°/cycle) and measured apsidal motion (0.000705:0.00004 1/eycle). which just lies outside the 1-« error bars. is also unchanged.," Hence, the difference between expected $\pm$ $^{\circ}$ /cycle) and measured apsidal motion $\pm$ $^{\circ}$ /cycle), which just lies outside the $\sigma$ error bars, is also unchanged."
 The effect of a misalignment between the stellar rotation axes and the orbital spin axis on the apsidal motion has been studied by (1978).. Shakura (1985).. Companyetal. (1988).. and Petrova&Orlov (2003).," The effect of a misalignment between the stellar rotation axes and the orbital spin axis on the apsidal motion has been studied by \cite{kopal1978}, \cite{shakura1985}, \cite{company1988}, and \cite{petrova2003}."
. The contribution of the stellar rotation to the advance of the longitude of the periastron is reduced if the stellar rotation axis is tilted against the orbit spin axis until finally. when the axis of stellar rotation lays in the orbital plane. its contribution is half as large and with the opposite sign as when the stellar and orbital axes would be parallel.," The contribution of the stellar rotation to the advance of the longitude of the periastron is reduced if the stellar rotation axis is tilted against the orbit spin axis until finally, when the axis of stellar rotation lays in the orbital plane, its contribution is half as large and with the opposite sign as when the stellar and orbital axes would be parallel."
 In this situation. it contributes to a retrograde rotation of the periastron.," In this situation, it contributes to a retrograde rotation of the periastron."
 The contribution of the stellar rotation to the apsidal motion depends not only on the orientation of the axis. but also on the square of the angular stellar rotation rate.," The contribution of the stellar rotation to the apsidal motion depends not only on the orientation of the axis, but also on the square of the angular stellar rotation rate."
 As one measures only vsiné. a greater inclination towards the observer would mean a higher angular stellar rotation rate. and therefore a greater contribution. of the rotation. term to the overall apsidal motion.," As one measures only $v \sin i$, a greater inclination towards the observer would mean a higher angular stellar rotation rate, and therefore a greater contribution of the rotation term to the overall apsidal motion."
 We calculate that if the rotation axes of both stars would lie in the orbital plane. but have no inclination towards the observer. then the complete apsidal motion would be 0.00073°/eyele.," We calculate that if the rotation axes of both stars would lie in the orbital plane, but have no inclination towards the observer, then the complete apsidal motion would be $^{\circ}$ /cycle."
 If the rotation axes would have an inclination towards the observer of ; =70° in either of the two stars. or of 7 =60° in both stars. only then would the expected and measured apsidal motion be in agreement.," If the rotation axes would have an inclination towards the observer of $i$ $\approx 70^{\circ}$ in either of the two stars, or of $i$ $\approx 60^{\circ}$ in both stars, only then would the expected and measured apsidal motion be in agreement."
 The secondary. due to its higher vsin. has a larger influence on the rotational term of the apsidal motion than the primary component.," The secondary, due to its higher $v \sin i$, has a larger influence on the rotational term of the apsidal motion than the primary component."
 As already pointed out. it is very unlikely that the stellar and orbital spin axes span a large angle. while their projections on the sky are. 1n their uncertainties. parallel.," As already pointed out, it is very unlikely that the stellar and orbital spin axes span a large angle, while their projections on the sky are, in their uncertainties, parallel."
 Our findings do not support the hypothesis advocated by Petrova&Orlov(2003).. that a misalignment of the stellar rotation axes with the orbital spin could bring the theoretical and measured apsidal motion for a number of binary systems. including CCyg. into better agreement.," Our findings do not support the hypothesis advocated by \cite{petrova2003}, that a misalignment of the stellar rotation axes with the orbital spin could bring the theoretical and measured apsidal motion for a number of binary systems, including Cyg, into better agreement."
 Our work has excluded the option of a misalignment between the stellar rotation axes as a possible explanation for the difference between the expected and measured apsidal motion in I43CCyg., Our work has excluded the option of a misalignment between the stellar rotation axes as a possible explanation for the difference between the expected and measured apsidal motion in Cyg.
 It is therefore interesting to look at other possibilities that might explain this difference., It is therefore interesting to look at other possibilities that might explain this difference.
 As the apsidal motion constant (42) is an important source of uncertainty in the calculation of the expected apsidal motion. a new calculation of the apsidal motion constant for CCyg using modern codes for stellar evolution might be of value.," As the apsidal motion constant $k_{2}$ ) is an important source of uncertainty in the calculation of the expected apsidal motion, a new calculation of the apsidal motion constant for Cyg using modern codes for stellar evolution might be of value."
 In our analysis of the orbital data we found no indication of a third body in the CCye system. whose influence might also alter the apsidal motion.," In our analysis of the orbital data we found no indication of a third body in the Cyg system, whose influence might also alter the apsidal motion."
 However. because of the," However, because of the"
As in the HPMM model. the standard simulation set (set ]) has a constant initial mass ratio distribution. gai=1.5. and αοι-αμ0.75.,"As in the HPMM model, the standard simulation set (set 1) has a constant initial mass ratio distribution, $q_{\rm crit}=1.5$, and $\alpha_{\rm CE}=\alpha_{\rm th}=0.75$."
 The simulations give EHB stars at various stellar population ages., The simulations give EHB stars at various stellar population ages.
 In order to see the importance of individual evolution channels leading to the formation of EHB stars. I plotted in Fig.," In order to see the importance of individual evolution channels leading to the formation of EHB stars, I plotted in Fig."
 | the fractions of EHB stars from different channels (the Ist stable RLOF channel for wide EHB+MS binaries: the Ist CE ejection channel for close EHB+MS binartes: the 2nd stable RLOF channel for wide EHB+WD binaries: the 2nd CE ejection channel for close EHB+WD binaries: and the merger channel for single EHB stars) at stellar population age ¢ for the standard simulation set (set 1)., \ref{channel} the fractions of EHB stars from different channels (the 1st stable RLOF channel for wide EHB+MS binaries; the 1st CE ejection channel for close EHB+MS binaries; the 2nd stable RLOF channel for wide EHB+WD binaries; the 2nd CE ejection channel for close EHB+WD binaries; and the merger channel for single EHB stars) at stellar population age $t$ for the standard simulation set (set 1).
 Figure 2. shows the evolution of the distribution of orbital periods of EHB binaries with stellar population age ¢ for the standard simulation set (set 1)., Figure \ref{period} shows the evolution of the distribution of orbital periods of EHB binaries with stellar population age $t$ for the standard simulation set (set 1).
 The EHB binaries with orbital periods P<5d can be detected observationallyin à GC (Mont in. Catelan Altmann 2008)). and L therefore. showed. in Fig. 3..," The EHB binaries with orbital periods $P<5\,{\rm d}$ can be detected observationallyin a GC (Moni Bidin, Catelan Altmann \cite{mon08}) ), and I, therefore, showed, in Fig. \ref{close},"
 the fractions of the binaries among all the EHB stars. including both binaries and singles. at stellar population age t.," the fractions of the binaries among all the EHB stars, including both binaries and singles, at stellar population age $t$."
 In order to see how the fractions can be affected by model parameters. Fig.," In order to see how the fractions can be affected by model parameters, Fig."
 3 also displays other simulation sets with various model parameters., \ref{close} also displays other simulation sets with various model parameters.
 In the figure. I have applied the GK selection effect. which is the selection against EHB stars with companions of spectral type G and K (usually MS stars). and is the most important selection effect in observations of EHB ..," In the figure, I have applied the GK selection effect, which is the selection against EHB stars with companions of spectral type G and K (usually MS stars), and is the most important selection effect in observations of EHB ."
Globular Clusters have long been considered. às examples of aggregates of stars with the same chemical composition that are born all at the same time.,Globular Clusters have long been considered as examples of aggregates of stars with the same chemical composition that are born all at the same time.
 However. the last decade overwhelming observational evidence. spectroscopic and photometric. has been published that shows that the foregoing picture is not correct (e.g.. Gratton et al.," However, the last decade overwhelming observational evidence, spectroscopic and photometric, has been published that shows that the foregoing picture is not correct (e.g., Gratton et al."
 2004: Charbonnel 2005: Carretta et al., 2004; Charbonnel 2005; Carretta et al.
 2009: Piotto et al., 2009; Piotto et al.
 2005. 2007: Cohen and Melénndez 2005: Cohen et al.," 2005, 2007; Cohen and Melénndez 2005; Cohen et al."
 2005)., 2005).
 Summarizing. the abundances of the Fe-group elements. the a-elements and the s- and process elements are fairly constant from star to star but abundance variations of the light elements (C. Ν.Ο. Na. Mg and Al) have been observed in some stars of all Globular Clusters with a common pattern:C-N. Na and Mg-Al are anticorrelated.," Summarizing, the abundances of the Fe-group elements, the $\alpha$ -elements and the s- and r-process elements are fairly constant from star to star but abundance variations of the light elements (C, N, O, Na, Mg and Al) have been observed in some stars of all Globular Clusters with a common pattern:C-N, O-Na and Mg-Al are anticorrelated."
 In at least two Globular Clusters (co Cen and NGC 2808) one clearly distinguishes more than one sequence among the population of hydrogen burning stars., In at least two Globular Clusters $\omega$ Cen and NGC 2808) one clearly distinguishes more than one sequence among the population of hydrogen burning stars.
 In Globular Clusters with more than one main sequence. the bluest ones are helium enriched: in particular observations of NGC 2808 indicate that the population of hydrogen burning stars is made up of three different sequences: a normal one with Big Bang helium mass fraction ~0.25). an intermediate sequence with «0.3 and the bluest one with ~0.35-0.4.," In Globular Clusters with more than one main sequence, the bluest ones are helium enriched; in particular observations of NGC 2808 indicate that the population of hydrogen burning stars is made up of three different sequences: a normal one with Big Bang helium mass fraction $\sim$ 0.25), an intermediate sequence with $\sim$ 0.3 and the bluest one with $\sim$ 0.35-0.4."
 These observations support the self-pollution scenario where a younger generation of stars was formed out of gas that contains the matter lost by one or more older generations. and where part of it was nuclearly processed through the CNO. NeNa and the MgAI cycles.," These observations support the self-pollution scenario where a younger generation of stars was formed out of gas that contains the matter lost by one or more older generations, and where part of it was nuclearly processed through the CNO, NeNa and the MgAl cycles."
 Two self-pollution scenarios have been worked out in detail., Two self-pollution scenarios have been worked out in detail.
 Both scenarios discussed above are single star scenarios., Both scenarios discussed above are single star scenarios.
 However. there is increasing evidence that many stars are born as close binary components and that the observed binary," However, there is increasing evidence that many stars are born as close binary components and that the binary"
The N-rav gas mass fraction. fa... is defined as the ratio of the N-ray emitting gas mass to the total mass of a cluster.,"The X-ray gas mass fraction, $f_{\rm gas}$, is defined as the ratio of the X-ray emitting gas mass to the total mass of a cluster."
 Fhis quantity can be determined from the observed X-ray surface brightness and. the deprojected.. spectrallv-determined. gas temperature profile. under the assumptions of spherical svmunetry and hyelrostatic equilibrium.," This quantity can be determined from the observed X-ray surface brightness and the deprojected, spectrally-determined gas temperature profile, under the assumptions of spherical symmetry and hydrostatic equilibrium."
 To ensure that these assumptions are as accurate as possible. it is essential to limit the ως analysis to the hottest. most X-rav luminous. dynamically relaxed clusters available Section 3.1: for a detailed. discussion of the method. and current measurements sce? and references therein.]," To ensure that these assumptions are as accurate as possible, it is essential to limit the $f_{\rm gas}$ analysis to the hottest, most X-ray luminous, dynamically relaxed clusters available [Section \ref{fgasdata}; for a detailed discussion of the method and current measurements see and references therein.]"
 In order to study dark energy. use f measurements for a sample of 42 hot (K5zooZ7 5keV). X-ray luminous. dynamically relaxed: clusters.," In order to study dark energy, use $f_{\rm gas}$ measurements for a sample of 42 hot $kT_{2500}> 5$ keV), X-ray luminous, dynamically relaxed clusters."
" The fi; measurements are mace within""M an angle 652557ACDM forp each cluster. corresponding: {ο reson For a reference Dat AC'DAL cosmology (with £34,=0.3 and 44,2Tükms 13)."," The $f_{\rm gas}$ measurements are made within an angle $\theta^{\rm \Lambda CDM}_{2500}$ for each cluster, corresponding to $r_{2500}$ for a reference flat $\Lambda$ CDM cosmology (with $\Omega_{\rm m}=0.3$ and $H_{\rm 0}=70$ )."
 The JF measurements in the reference; cosmology £25ACDP?! are related to the true values finsABI as Non-radiative hvdrodynamical simulations suggest that f17TES is likely to be approximately constant in redshift.," The $f_{\rm gas}$ measurements in the reference cosmology $f^{\rm
 \Lambda CDM}_{\rm gas}$ are related to the true values $f^{\rm
 true}_{\rm gas}$ as Non-radiative hydrodynamical simulations suggest that $f^{\rm true}_{\rm gas}$ is likely to be approximately constant in redshift."
 Thus(?).. where sy=0.1675 is the observed. ratio of the mass in stars (both in. galaxies and intracluster light) to the X-ray. emitting eas mass. and by=0.82 is the depletion factor for the barvon fraction in clusters with respect to the cosmic mean value.," Thus, where $s_{\rm 0}=0.16h^{\rm 0.5}_{\rm 70}$ is the observed ratio of the mass in stars (both in galaxies and intracluster light) to the X-ray emitting gas mass, and $b_{\rm 0}=0.82$ is the depletion factor for the baryon fraction in clusters with respect to the cosmic mean value."
 As discussed bv?.. an angular correction factor is also required to account for the fact that new29S) needs not be exactly equal to Fuey ," As discussed by, an angular correction factor is also required to account for the fact that $f^{\rm true}_{\rm
 gas}(z;\theta^{true}_{2500})$ needs not be exactly equal to $f^{\rm
 true}_{\rm gas}(z;\theta^{\rm \Lambda CDM}_{2500})$."
Observations of large. relaxed elusters show that for the radial range of interest. OToxrfrosoo<12. the f.alr) profiles can be fit by a shallow power-law model with slope y=0.214+0.022..," Observations of large, relaxed clusters show that for the radial range of interest, $0.7<r/r_{\rm 2500}<1.2$, the $f_{\rm gas}(r)$ profiles can be fit by a shallow power-law model with slope $\eta=0.214\pm0.022$."
. ‘Thus. we have where Gesu=resonαν. and This correction factor is small ancl can be neglected for most analyses of current data. although its inclusion leads to slightly tighter constraints on dark energy (2).," Thus, we have where $\theta_{\rm 2500}=r_{\rm 2500}/d_{\rm A}$, and This correction factor is small and can be neglected for most analyses of current data, although its inclusion leads to slightly tighter constraints on dark energy ."
. However. [or future experiments of the precision being considered here. the inclusion of the angular correction term. becomes important.," However, for future experiments of the precision being considered here, the inclusion of the angular correction term becomes important."
 Following?.. we mocdifv equation (17)) to account. for systematic uncertainties in the fi; analysis: lere > allows [or departures from. the assumption of hvdrostatie equilibrium. cue to. non-thermal pressure support: A ids a normalization uncertainty relating to instrumental calibration and certain modelling issues: b(2)=do(l|ancdyc7) accounts for uncertainties in the cluster depletion factor. both in the normalization. by. anc possible linear. ay. and quadratic. εν. evolution withredshiftστο S(2)=soll|acs accounts for uncertainties in the stellar mass Using hvdrodynamic N-body simulations show that or measurements at. reso in.clusters. non-hermal pressure support is unlikely to exceed S per cent.," Following, we modify equation \ref{eq:uncorr}) ) to account for systematic uncertainties in the $f_{\rm gas}$ analysis: Here $\gamma$ allows for departures from the assumption of hydrostatic equilibrium, due to non-thermal pressure support; $K$ is a normalization uncertainty relating to instrumental calibration and certain modelling issues; $b(z)=b_{\rm 0}(1+\alpha_{\rm b}z+\beta_{\rm
 b}z^{\rm 2})$ accounts for uncertainties in the cluster depletion factor, both in the normalization, $b_0$, and possible linear, $\alpha_{\rm b}$, and quadratic, $\beta_{\rm b}$, evolution with; $s(z)=s_{\rm 0}(1+\alpha_{\rm s}z+\beta_{\rm s}z^{\rm 2})$ accounts for uncertainties in the stellar mass Using hydrodynamic N-body simulations show that for measurements at $r_{\rm 2500}$ in, non-thermal pressure support is unlikely to exceed $8$ per cent."
 Furthermore. if as suggested. by some current X-ray data(777). the gas viscosity is higher than that included. in current simulations. then non-thermal pressure support could be even lower.," Furthermore, if, as suggested by some current X-ray data, the gas viscosity is higher than that included in current simulations, then non-thermal pressure support could be even lower."
 Based on these findings. we adopt w default a uniform prior such that non-thermal pressure support lies in the range OS per cent (although a more »essimüstic range of O16 per cent is also. considered).," Based on these findings, we adopt by default a uniform prior such that non-thermal pressure support lies in the range $0-8$ per cent (although a more pessimistic range of $0-16$ per cent is also considered)."
" Since the use of an asymmetric prior would. bias the analysis. levering Qu, above the fiducial value. we employ an equivalent. rescaled svmuimetrie prior such that 1.(0/2)2]llí(a/2). where a=l1LOS/1.04."," Since the use of an asymmetric prior would bias the analysis, levering $\Omega_{\rm m}$ above the fiducial value, we employ an equivalent, rescaled symmetric prior such that $1-(a/2)<\gamma<1+(a/2)$ , where $a=|1-1.08|/1.04$."
 The depletion parameter. bu. relects the thermodynamic history of the X-ray emitting. cluster eas.," The depletion parameter, $b_{\rm 0}$ , reflects the thermodynamic history of the X-ray emitting cluster gas."
" Using non-raciative simulations of hot. massive clusters of comparable size to. the real clusters to. be used in the fax. experiment. obtained by=0.8240.03 at the radius of the measurements soo ( O.25ra) and found. no evidence for redshift evolution: a,=0.00+0.03 for measurements made at kÀO.5rein. spanning the redshift range O<zI."," Using non-radiative simulations of hot, massive clusters of comparable size to the real clusters to be used in the $f_{\rm gas}$ experiment, obtained $b_{\rm
 0}=0.82 \pm 0.03$ at the radius of the measurements $r_{\rm 2500}$ $\sim 0.25r_{\rm vir}$ ) and found no evidence for redshift evolution: $\alpha_{\rm b}=0.00\pm0.03$ for measurements made at $r \sim
0.5r_{vir}$ , spanning the redshift range $0<z<1$."
 As discussed. by7.. however. systematic uncertainties are associated with current predictions for b(z). dueto limitations in the accuracy of the physical approximations employed. in the simulations.," As discussed by, however, systematic uncertainties are associated with current predictions for $b(z)$, dueto limitations in the accuracy of the physical approximations employed in the simulations."
 Estimating the residual uncertainties in the prediction of b(z) that will be appropriate at the time of à future f data set (~2015 2020) is dillicult.," Estimating the residual uncertainties in the prediction of $b(z)$ that will be appropriate at the time of a future $f_{\rm gas}$ data set $\sim
2015-2020$ ) is difficult."
 We have chosen to use a range of values that extend from optimistic to pessimistic scenarios (see Table 3))., We have chosen to use a range of values that extend from optimistic to pessimistic scenarios (see Table \ref{table:sys}) ).
 Current opticalandnear infrared. data for. low-to-redshift clusters give sy=0.όρο(?77).., Current opticalandnear infrared data for low-to-intermediateredshift clusters give $s_{\rm 0}=0.16h_{\rm 70}^{\rm -0.5}$.
 Although. at. present. the constraints on s(2) for clusters at," Although, at present, the constraints on $s(z)$ for clusters at"
This is motivated by spot temperatures found for other highly active G and K stars (e.g. Strassmeier&Rice 1998.. al. 20049).,"This is motivated by spot temperatures found for other highly active G and K stars (e.g. \citealt{Strassmeier98}, , \citealt{ONeal04}) )."
 As a “bright spot” we adopt a value of of the photospheric flux., As a “bright spot” we adopt a value of of the photospheric flux.
 This roughly represents the average contrast of large spot groups on the Sun at visible wavelengths (Waltonetal. 2003.. Albregtsenetal. 1984)).," This roughly represents the average contrast of large spot groups on the Sun at visible wavelengths \citealt{Walton03}, \citealt{Albregtsen84}) )."
 Our two spot contrast scenarios are comparable to those adopted for CoRoT-2a by Lanzaetal.(2009)., Our two spot contrast scenarios are comparable to those adopted for CoRoT-2a by \citet{Lanza09}.
 Defining the spot contrast and shape in this way. three free parameters describe a given spot. namely the spot radius + as well as its central longitude and colatitude &.," Defining the spot contrast and shape in this way, three free parameters describe a given spot, namely the spot radius $r$ as well as its central longitude $\varphi$ and colatitude $\theta$."
 However. as illustrated by Fig. 3..," However, as illustrated by Fig. \ref{fig:X2longs},"
 the longitude 1s closely confined by the transit lightcurve. irrespective of the spot contrast and colatitude.," the longitude is closely confined by the transit lightcurve, irrespective of the spot contrast and colatitude."
 This is due to the well defined maximum of the transit bump., This is due to the well defined maximum of the transit bump.
 Thus only two undetermined parameters remain to optimize the fit of transit 56s lighteurve: r and ϱ., Thus only two undetermined parameters remain to optimize the fit of transit 56's lightcurve: $r$ and $\theta$.
 We calculated model lightcurves for grids 1n these two parameters. the resulting goodness-of-fit y is shown in Fig. 4..," We calculated model lightcurves for grids in these two parameters, the resulting goodness-of-fit $\chi^2$ is shown in Fig. \ref{fig:X2contours}."
" To ealeulae y"" we rebinned the lightcurve into 224 sec bins. and estimated the resulting errors c; assuming Gaussian. eror propagation:02."," To calculate $\chi^2$ we rebinned the lightcurve into 224 sec bins, and estimated the resulting errors $\sigma_{j}$ assuming Gaussian error propagation:."
 Here. M=3 is the number of free model parameters. namely the spot longitude. colatitude and radius.," Here, $M=3$ is the number of free model parameters, namely the spot longitude, colatitude and radius."
 N=8 gives the number of time bins used to constrain the modelled spot. see the interval limits indicated in Fig. 2.. 4..," $N=8$ gives the number of time bins used to constrain the modelled spot, see the interval limits indicated in Fig. \ref{fig:TransitLC}. \ref{fig:X2contours}."
 2 4. 5. 1.4. 5.. 1..," \ref{fig:TransitLC} \ref{fig:X2contours} \ref{fig:TransitMap} \ref{tab:SpotSolutions}.\ref{fig:X2contours}
 \ref{fig:TransitMap}, \ref{tab:SpotSolutions}."
An improved MIDPS 70n map. constructed using the most updated pipeline from MIPSGAL team. detects the presence of a second shell very similar to that seen at 24jn. Nebular lines and dust continuum are the main possible contributors to the 240n emission from objects embedded in a dusty nebula with a hot central component.,"An improved MIPS $70\,\mu$ m map, constructed using the most updated pipeline from MIPSGAL team, detects the presence of a second shell very similar to that seen at $24\,\mu$ m. Nebular lines and dust continuum are the main possible contributors to the $24\,\mu$ m emission from objects embedded in a dusty nebula with a hot central component."
 The possibility οἱ such a combination. with one kind of emission being predominant. has been suggested by Mizunoetal.(2010). to explain the 24jmi emission detected in the MIPSGAL Bubbles.," The possibility of such a combination, with one kind of emission being predominant, has been suggested by \citet{Mizuno10} to explain the $24\,\mu$ m emission detected in the MIPSGAL Bubbles."
 In the case of G79.29+0.46. the presence of similar shells at 24jmi and at 70jm. together with the lack of any. prominent emission line Falling within the response curve of the MIPS 24 yan band. as evident from the low-resolution IRS spectrum of the shell 2010).. leaves very little doubt that the shell emission is entirely clue to thermal dust CUSSION.," In the case of G79.29+0.46, the presence of similar shells at $24\,\mu$ m and at $70\,\mu$ m, together with the lack of any prominent emission line falling within the response curve of the MIPS $24\,\mu$ m band, as evident from the low-resolution IRS spectrum of the shell \citep{Jimenez_2010}, leaves very little doubt that the shell emission is entirely due to thermal dust emission."
 The fact that there are at least (wo nested shells provides strong constraints on the the origin of the nebula. as it is difficult to explain (he presence of multiple shells in the hypothesis of a nebula consisting of swept-up ISM material. as suggested by (1994).," The fact that there are at least two nested shells provides strong constraints on the the origin of the nebula, as it is difficult to explain the presence of multiple shells in the hypothesis of a nebula consisting of swept-up ISM material, as suggested by \cite{Higgs_94}."
. It is evident that the clusty shells consist of material ejected by the central object in different mass-loss episodes., It is evident that the dusty shells consist of material ejected by the central object in different mass-loss episodes.
" From the 24an emission profile. we have determined that the inner shell peaks at 100"" and the second one at 200"" [rom the central object."," From the $24\,\mu$ m emission profile, we have determined that the inner shell peaks at $100^{\prime \prime}$ and the second one at $200^{\prime \prime}$ from the central object."
 Such dust emission peaks can be related to the epoch when enhanced mass-loss took place., Such dust emission peaks can be related to the epoch when enhanced mass-loss took place.
" Assuming a distance of 1.7 kpe (Jimenez-Estebanetal.2010).. this corresponds to a linear distance of 0.32 pe and 1.64 pe. respectively,"," Assuming a distance of 1.7 kpc \citep{Jimenez_2010}, this corresponds to a linear distance of $0.82$ pc and $1.64$ pc, respectively."
 This implies. assuming a shell expansion velocity of ~30kmsec.+ al. 1996).. that the (vo mass-loss episodes occurred 2.7κLO! and 5.4x10! vears ago. or 1.6x10 and 3.1x10! vears ago. if a distance of 1 kpc. as suggested by Vinketal.(2008).. is used.," This implies, assuming a shell expansion velocity of $\sim 30\,\rm{km\,sec}^{-1}$ \citep{Waters_96}, that the two mass-loss episodes occurred $2.7 \times 10^{4}$ and $5.4 \times 10^{4}$ years ago, or $1.6 \times 10^{4}$ and $3.1 \times 10^{4}$ years ago, if a distance of 1 kpc, as suggested by \cite{Vink_08}, is used."
 Our results point out that mass-loss can occur in different episodes. lor which we derived characteristics timescales. ancl pose «quite strong constraints (hat stellar evolution," Our results point out that mass-loss can occur in different episodes, for which we derived characteristics timescales, and pose quite strong constraints that stellar evolution"
parametric model expects it to be there.,parametric model expects it to be there.
 Alternative methodologies. such as the nonparametric methodology (2?) used in this work. may allow posing inferential questions that are difficult to address using conventional methods.," Alternative methodologies, such as the nonparametric methodology \citep{GMN+2004,BSM+2007} used in this work, may allow posing inferential questions that are difficult to address using conventional methods."
 For exatuple. this particular wouparaimetric methodology allows validating mocdel-based. parametric fits agalust the confidence set for the nonparametric fit to the same data. possibly to rule them out as candidates for the true but unkuown regression function.," For example, this particular nonparametric methodology allows validating model-based, parametric fits against the confidence set for the nonparametric fit to the same data, possibly to rule them out as candidates for the true but unknown regression function."
 This methodology. also has tle formal advantage of being able to provide realistic uncertainties on number of features of the angular power spectrum that are simultaneously valid at the same level of confidence., This methodology also has the formal advantage of being able to provide realistic uncertainties on number of features of the angular power spectrum that are simultaneously valid at the same level of confidence.
 Such desirable leatures are arguably lacking iu most mainstream methodologies. includiug Bayesian. that are commonly used in cosinology. (," Such desirable features are arguably lacking in most mainstream methodologies, including Bayesian, that are commonly used in cosmology. ("
An incisive. iusighitful. aud discerning discussion about the relative merits of this methodology over statistical methods conventionally employed in cosmology can be found iu the two references cited above. aud is best read in tle original.),"An incisive, insightful, and discerning discussion about the relative merits of this methodology over statistical methods conventionally employed in cosmology can be found in the two references cited above, and is best read in the original.)"
 The four CMB augular power spectrum data sets (2???) released by the Wilkinson Microwave Anisotropy Probe (WMAP) (2). mission. representing cumulative observations at the end of 1. 3. 5. and 7 years of operation. present a unique opportuuity for statistical aualysis.," The four CMB angular power spectrum data sets \citep{HSV+2003,HNB+2007,NDH+2009,LDH+2011}
 released by the Wilkinson Microwave Anisotropy Probe (WMAP) \citep{BBH+2003} mission, representing cumulative observations at the end of 1, 3, 5, and 7 years of operation, present a unique opportunity for statistical analysis."
 For example. till date these are claimed to represent the most precise aud exteusive full-sky CMB measurements ever nade (ouly to be superseded by the Planck mission (2))).," For example, till date these are claimed to represent the most precise and extensive full-sky CMB measurements ever made (only to be superseded by the Planck mission \citep{TMP+2010}) )."
 The four data sets represent the evolution of data over a period of about a decade. thereby makiug it possible to assess progressive auc possibly systematic resolution of features of the spectrum.," The four data sets represent the evolution of data over a period of about a decade, thereby making it possible to assess progressive and possibly systematic resolution of features of the spectrum."
 From a statistical perspective. each of these moderately. large data sets (1ninimum of 899 data points for the WALAP I-vear release) is uot only hieteroskedastic. but also has substantial correlations that arise in typical data pipelines (????1)..," From a statistical perspective, each of these moderately large data sets (minimum of 899 data points for the WMAP 1-year release) is not only heteroskedastic, but also has substantial correlations that arise in typical data pipelines \citep{Tegmark1997,HBB+2003,HWH+2009,JBG+2007,JBD+2011}."
 lu this paper. we present a comparative nonparanmetric analysis of the WALAP 1-. 3-. 5-. aud T-year data sets for the angular power spectrum.," In this paper, we present a comparative nonparametric analysis of the WMAP 1-, 3-, 5-, and 7-year data sets for the angular power spectrum."
 Specifically. for each data realization. we address the following three key questions: (a) How well is the augular power spectrum determined by the ata alone? (," Specifically, for each data realization, we address the following three key questions: (a) How well is the angular power spectrum determined by the data alone? ("
b) How well is the ACDM. 1uodel supported by a mocdel-iudepeudent. nouparametric. ata-driven analysis? (,"b) How well is the $\Lambda$ CDM model supported by a model-independent, nonparametric, data-driven analysis? ("
c) What are the realistic uncertainties on peak/dip locations aud heights?,c) What are the realistic uncertainties on peak/dip locations and heights?
 Our analysis is based ou a uouparametric fuuction estimation methocology (22)... which is discussed lu ‘efinethod together with our extensions: Le.. a numerical formulation for minimization of a risk function subject to monotonicity coustraints. a prescription for obtaining uouparametric its that are closer to cosmological expectatious on smootless. aucl a method for sampling cosmologically jeaulngful power spectrum. varlatious from the confidence set of a uouparaimetric fit.," Our analysis is based on a nonparametric function estimation methodology \citep{GMN+2004,BSM+2007}, which is discussed in \\ref{method} together with our extensions; i.e., a numerical formulation for minimization of a inverse-noise-weighted risk function subject to monotonicity constraints, a prescription for obtaining nonparametric fits that are closer to cosmological expectations on smoothness, and a method for sampling cosmologically meaningful power spectrum variations from the confidence set of a nonparametric fit."
 Results are yesented in ‘elresults.. aud couclusion in 'efconclusion..," Results are presented in \\ref{results}, , and conclusion in \\ref{conclusion}. ."
The solid and dash lines represent the model results adopting Gaussian and exponential infall rate.,The solid and dash lines represent the model results adopting Gaussian and exponential infall rate.
" According to the assumption that there is 1Gyr delay for the halo formation, all of the gas infall throughout this paper begin at t=1Gyr."," According to the assumption that there is 1Gyr delay for the halo formation, all of the gas infall throughout this paper begin at $t=1\rm{Gyr}$."
" It shows that, comparing with the star formation rate predicted by Gaussian-infall model, the exponential-infall model predicts higher SFR at early stage and lower SFR later."," It shows that, comparing with the star formation rate predicted by Gaussian-infall model, the exponential-infall model predicts higher SFR at early stage and lower SFR later."
 This point directly results in the differences of the mass-SFR relations at intermediate redshifts predicted by these two models (see following discussions)., This point directly results in the differences of the mass-SFR relations at intermediate redshifts predicted by these two models (see following discussions).
" In order to compare with the observations, we plot the predictions of the exponential-infall model as dash lines in Fig."," In order to compare with the observations, we plot the predictions of the exponential-infall model as dash lines in Fig."
 4 and 5., 4 and 5.
" It can be seen that, although both the solid and dash lines can be roughly consistent with the local observations, the exponential-infall model does predict lower SFR/M, than observations at intermediate redshifts."," It can be seen that, although both the solid and dash lines can be roughly consistent with the local observations, the exponential-infall model does predict lower $SFR/M_*$ than observations at intermediate redshifts."
" Since the stellar population of local galaxy is resulted along its whole star formation history, local observations do not have the ability to distinguish whether the model is viable at different time steps."," Since the stellar population of local galaxy is resulted along its whole star formation history, local observations do not have the ability to distinguish whether the model is viable at different time steps."
" Fortunately, the observed data at intermediate redshifts are now available and can provide tighter constraints on the model of galactic evolution."," Fortunately, the observed data at intermediate redshifts are now available and can provide tighter constraints on the model of galactic evolution."
" In other words, our results suggest that the Gaussian infall rate may be more reasonable to describe the gas cooling process than the exponential infall rate."," In other words, our results suggest that the Gaussian infall rate may be more reasonable to describe the gas cooling process than the exponential infall rate."
" In fact, by fitting synthetic energy distribution to the multi-band photometry of a sample of actively star-forming galaxies at z~2, Maraston et al. ("," In fact, by fitting synthetic energy distribution to the multi-band photometry of a sample of actively star-forming galaxies at $z\sim2$, Maraston et al. ("
2010) concluded that adopting an exponentially increasing SFRs and a high starting redshift appear to provide more reasonable results than that of an exponentially declining SFR. in the case of star forming galaxies at redshift beyond ~1.,2010) concluded that adopting an exponentially increasing SFRs and a high starting redshift appear to provide more reasonable results than that of an exponentially declining SFR in the case of star forming galaxies at redshift beyond $\sim1$.
" Unfortunately, both their model and ours are phenomenological models."," Unfortunately, both their model and ours are phenomenological models."
 It is still beyond the scope of this paper to answer why the efficiency of gas cooling process or/and star formation process may be depressed at early stage and why the peak time of low-mass galaxy is later than high-mass systems., It is still beyond the scope of this paper to answer why the efficiency of gas cooling process or/and star formation process may be depressed at early stage and why the infall-peak time of low-mass galaxy is later than high-mass systems.
" Indeed, the semi-analytical models and studies using hydrodynamical simulations may provide more physical and reasonable explanation on how gas accreted onto the galaxies than phenomenological models."," Indeed, the semi-analytical models and studies using hydrodynamical simulations may provide more physical and reasonable explanation on how gas accreted onto the galaxies than phenomenological models."
" However, there is still a long way to go to fully understand the gas cooling processes."," However, there is still a long way to go to fully understand the gas cooling processes."
" For example, the semi-analytical models assumes that gas within galaxy halos initially reaches the temperature of the virial halo, while some studies using high-resolution cosmological hydrodynamical simulations found that the majority of baryons may never reach the virial temperature as they accreted onto galaxies (Keres et al."," For example, the semi-analytical models assumes that gas within galaxy halos initially reaches the temperature of the virial halo, while some studies using high-resolution cosmological hydrodynamical simulations found that the majority of baryons may never reach the virial temperature as they accreted onto galaxies (Keres et al."
 2005; Dekel & Birboim 2006)., 2005; Dekel $\&$ Birboim 2006).
 Brooks et al. (, Brooks et al. (
"2009) found that low-mass galaxies are instead dominated by accretion of gas that stays well below the viral temperature and even for galaxies at higher masses, cold flows dominate the growth of the disk at early times.","2009) found that low-mass galaxies are instead dominated by accretion of gas that stays well below the viral temperature and even for galaxies at higher masses, cold flows dominate the growth of the disk at early times."
" All these findings called the general virial temperature assumption into question, but may give more information to improve the semi-analytical models and help us to understand more clearly on how the gas gets into the galaxies."," All these findings called the general virial temperature assumption into question, but may give more information to improve the semi-analytical models and help us to understand more clearly on how the gas gets into the galaxies."
" Finally, comparing our model to that of BP00, the main difference is that BPO00 adopted the exponential infall rate while we adopt the Gaussian"," Finally, comparing our model to that of BP00, the main difference is that BP00 adopted the exponential infall rate while we adopt the Gaussian"
The corrected 0 TIT] 5007 line fux is (1.5540.12)101* ere cua2 D +. and its observed equivalent width is Wy=304L2Α..Lc. 15.71.22 in the resta.,"The corrected [O III] 5007 line flux is $(1.55 \pm 0.12) \times 10^{-17}$ erg $^{-2}$ $^{-1}$ $^{-1}$, and its observed equivalent width is $W_\lambda = 30 \pm 2$, $17.7 \pm 1.2$ in the restframe."
 For the I>lue. we derive au upper limit of «3.110τνcere ἂν εν100) and for its observed equivalent width ΕνTΑ..," For the $\beta$line, we derive an upper limit of $< 3.4 \times 10^{-18}$erg $^{-2}$ $^{-1}$ $^{-1}$ $\sim 1~\sigma$ ), and for its observed equivalent width $W_\lambda < 7$."
 We note however that this measurement iav be severely affected by the poor nieht sky subtraction., We note however that this measurement may be severely affected by the poor night sky subtraction.
" The contimmun flux at Ajj,=L716À.. corresponding to Άγ=2800A. is Εν=0.29pe Jv. with our measurement uncertain by ~104."," The continuum flux at $\lambda_{obs} = 4746\,$, corresponding to $\lambda_{rest} = 2800\,$, is $F_\nu = 0.29 ~\mu$ Jy, with our measurement uncertain by $\sim 10$."
. The coutinmun flux atf Aj41525 Á.. correspondiug to the restframe B baud. is Fy=O77 pJy. with our measurement unecrtain bw ~ ," The continuum flux at $\lambda_{obs} \sim 7525\,$ , corresponding to the restframe $B$ band, is $F_\nu = 0.77 ~\mu$ Jy, with our measurement uncertain by $\sim 7$."
Above. we report only the statistical uucertaimties of all fluxes: an additional svstematic mucertaimty of ~30% is inherited from the overall ux zero-poiut uncertainty.," Above, we report only the statistical uncertainties of all fluxes; an additional systematic uncertainty of $\sim 30$ is inherited from the overall flux zero-point uncertainty."
"For the following discussion. we will assume a Πατ cosinology as suggested. by recent results(6.9. deBernardise£al. 2000)) with μμ=65 lan E l Q4,=0.3. aud Ay=0.7.","For the following discussion, we will assume a flat cosmology as suggested by recent results, \cite{dab+00}) ) with $H_0 =
65$ km $^{-1}$ $^{-1}$, $\Omega_M = 0.3$, and $\Lambda_0 = 0.7$."
 For :=0.695. the Iuninosityv distance is 1.10«1075 cu. and L aresec corresponds to 7.65 proper kpe or 13.0 comoving kpc in projection.," For $z = 0.695$, the luminosity distance is $1.40 \times 10^{28}$ cm, and 1 arcsec corresponds to 7.65 proper kpc or 13.0 comoving kpc in projection."
 The gamma-ray fluence (iuteerated flux over tuno) is converted from count rates uncer the assuuption of a CRB spectrum. the spectral evolution. and the true duration of the GRD.," The gamma-ray fluence (integrated flux over time) is converted from count rates under the assumption of a GRB spectrum, the spectral evolution, and the true duration of the GRB."
 These quantities are estimated frou the GRB data itself but can lead to laree uncertaiutics (a factor of few) in the fluence determination., These quantities are estimated from the GRB data itself but can lead to large uncertainties (a factor of few) in the fluence determination.
 Iu table 1 we sunanarize the fluence of GRB 970228 as observed by all high cnerev experimeuts that detected the GRB., In table \ref{tab:energetics} we summarize the fluence of GRB 970228 as observed by all high energy experiments that detected the GRB.
 We determine the implied euergv release (col., We determine the implied energy release (col.
 5. table 1)) assuniue isotropic cussion.," 5, table \ref{tab:energetics}) ) assuming isotropic emission."
 Further we “standardize” the enerectics to the restframe 302000 keV in the following manner., Further we “standardize” the energetics to the restframe 30–2000 keV in the following manner.
 We first normalize the observed flueuces in a even bandpass (col., We first normalize the observed fluences in a given bandpass (col.
 2 and 3) to a bandpass defined. by 30/00]2) to 2000/(1|2) keV by a ratio of the integrated spectral shape over these two baucdpasses., 2 and 3) to a bandpass defined by $30 / (1 + z)$ to $2000 / (1 + z)$ keV by a ratio of the integrated spectral shape over these two bandpasses.
 The muplied energv release is then found assumnuius isotropic enission and using the Iuninosity distance measure for the assumed cosmology., The implied energy release is then found assuming isotropic emission and using the luminosity distance measure for the assumed cosmology.
 If no spectral fit is reported we find the median energv miplied. by assuniug the spectral shape is each of the average 51 spectra from Dand ((1993))., If no spectral fit is reported we find the median energy implied by assuming the spectral shape is each of the average 54 spectra from Band \nocite{bmf+93}) ).
 The reported errors reflect the nucertaimty in the redshift measure. fluence. aud spectral shape.," The reported errors reflect the uncertainty in the redshift measure, fluence, and spectral shape."
 Given the significantly higher eamuua-rav spectral and tinmg resolution of the TORS iustrumnent relative to the others. we favor the isotropic cucrey implied by the TORS analysis: [30.2000 keV vestframe}.," Given the significantly higher gamma-ray spectral and timing resolution of the TGRS instrument relative to the others, we favor the isotropic energy implied by the TGRS analysis: [30–2000 keV restframe]."
 That the nuplied euergy is a factor of ~2 3 higher using iieasurements frou BeppoSAX aud Ulysses reflects the muportauce of high signal-to-noise spectroscopy in ascertaiinue the fluence and hence the energv release., That the implied energy is a factor of $\sim 2$ —3 higher using measurements from BeppoSAX and Ulysses reflects the importance of high signal-to-noise spectroscopy in ascertaining the fluence and hence the energy release.
 The slow decline auc absence of a strong break iu the optical light curve(ey. Galama 11997)) sugsests that the CGRD cinission was ucarly isotropic (see also Siri.Piran&Παρα 1999)) aud so the knowledge of E is primarily luted by the accuracy of the fluence measurement.," The slow decline and absence of a strong break in the optical light curve, Galama \nocite{ggv+97}) ) suggests that the GRB emission was nearly isotropic (see also \cite{sph99}) ) and so the knowledge of $E$ is primarily limited by the accuracy of the fluence measurement."
 For the purpose deteriuuiug the position of the CRB within its host. we examined the IIST/STIS observatious taken on L7 Sept 1997 UT (Fruchterefal.1999)).," For the purpose determining the position of the GRB within its host, we examined the HST/STIS observations taken on 4.7 Sept 1997 UT \cite{fpt+99}) )."
 The observation consisted of eight 575s STIS clear (CCD50) exposures paired in to four 1150s to facilitate removal of cosmic raves.," The observation consisted of eight $\,$ s STIS clear (CCD50) exposures paired in to four 1150s to facilitate removal of cosmic rays."
 We processed these images using the drizzle techuique of Fruchter Took to create a final image with a plate scale of 0.0251 aresec |., We processed these images using the drizzle technique of Fruchter Hook \nocite{fh97} to create a final image with a plate scale of 0.0254 arcsec $^{-1}$.
 To enhance the low-surface brightuess host galaxy we snoothed this niage with a Gaussian with e=0.013 aresec., To enhance the low-surface brightness host galaxy we smoothed this image with a Gaussian with $\sigma = 0.043$ arcsec.
 The optical transient is well-detected in figure 2 (point source towards the South) aud clearly offset from the bulk of the detectable euission of the host., The optical transient is well-detected in figure \ref{fig:host} (point source towards the South) and clearly offset from the bulk of the detectable emission of the host.
 Two morphological features of the lost stand out: a bright knot manifested as an sharp 6-0 poak near the centroid of the host to north of the trausient and au exteusion from this kuot towards the trausieut., Two morphological features of the host stand out: a bright knot manifested as an sharp $\sigma$ peak near the centroid of the host to north of the transient and an extension from this knot towards the transient.
 Although. as we demonstrate below. this host is a subluuinous ealaxv(G.e.. not a classic late-type £. spiral galaxy] we attribute these features to a nucleus and a spiral-ari. respectively.," Although, as we demonstrate below, this host is a subluminous galaxy, not a classic late-type $L_*$ spiral galaxy) we attribute these features to a nucleus and a spiral-arm, respectively."
" It is not unusual for cavart galaxies to exhibit these canonical Hubble-«diagraun structures (ο, Odewalin. private connumuication)."," It is not unusual for dwarf galaxies to exhibit these canonical Hubble-diagram structures (S. Odewahn, private communication)."
 These feature have not previously been noted iu the literature., These feature have not previously been noted in the literature.
 Centroiding the trausieut and the nucleus compoucuts within a 3 pixel aperture radius about their respective peak. we fud an augular offset of 136+L1 mülliarcsec between the nucleus aud the optical trausieut.," Centroiding the transient and the nucleus components within a 3 pixel aperture radius about their respective peak, we find an angular offset of $436 \pm 14$ milliarcsec between the nucleus and the optical transient."
" With our assunied cosmology, this amounts to a projected. plivsical distance of 3:314011Πρ kpe."," With our assumed cosmology, this amounts to a projected physical distance of $3.34\, \pm\, 0.11\, h_{65}^{-1}$ kpc."
 We found haltlieht radius of the host galaxy using our final drizzled IST/STIS image: we mask a3 «4 3 pixel region around the position of the optical trausicut and iuspect the curveoferowth centered on the central bright knot. the supposed nucleus aud estimate the haltlheht radius to be 0.31 aresec or (physical) at a redshift of 2=0.695.," We found half-light radius of the host galaxy using our final drizzled HST/STIS image: we mask a 3 $\times$ 3 pixel region around the position of the optical transient and inspect the curve–of–growth centered on the central bright knot, the supposed nucleus and estimate the half-light radius to be 0.31 arcsec or (physical) at a redshift of $z=0.695$."
 The halt-light radius visually estimated from curveofgrowth in the ΝΕΡΟ Faliw and FGOGOW filters (see Castander&Lam 19993) is comparable., The half-light radius visually estimated from curve–of–growth in the WFPC F814W and F606W filters (see \cite{cl99c}) ) is comparable.
 Although there is some debate (at the 0.3 mae level iu Ay) as to the proper level of Galactic extinction toward CGRD 970228 (Castander&Lah1999.Couzalez.Fruchter&Disch1999.Fruchterc£αἱ. 1999)) we have chosen to adopt the value £(BVW)=0231 found from the dust maps of Schlegel.Fiukbeiner&Davis1998. anda Galactic reddening curve Ry=Ay/E(BVW)3.2.," Although there is some debate (at the 0.3 mag level in $A_V$ ) as to the proper level of Galactic extinction toward GRB 970228 \cite{cl99c,gfd99,fpt+99}) ) we have chosen to adopt the value $E(B-V)
= 0.234$ found from the dust maps of \cite{sfd98} and a Galactic reddening curve $R_V = A_V/E(B-V) = 3.2$."
 Using exteusive reanalysis of theLAST imagine data bv Calama the extinction corrected broadband colors of the host galaxy as V2 25.040.2. R=2L640.2. f.=22+ 0.2.," Using extensive reanalysis of the imaging data by Galama \nocite{gtv+00} the extinction corrected broadband colors of the host galaxy as $V = 25.0
\pm 0.2$ , $R_c = 24.6 \pm 0.2$, $I_c = 24.2 \pm 0.2$ ."
 These measures. consistent with those of Castander Lamb aud Fruchter ((1999).. are derived from the WEPC? colors aud broadband STIS flux.," These measures, consistent with those of Castander Lamb \nocite{cl99c} and Fruchter \nocite{fpt+99}, , are derived from the WFPC2 colors and broadband STIS flux."
 The errors reflect both the statistical error and the unecrtainty idu the spectral cherey distribution of the host galaxwv., The errors reflect both the statistical error and the uncertainty in the spectral energy distribution of the host galaxy.
 We lave not ineluded a contribution from the mneertainty im the Galactic extinction., We have not included a contribution from the uncertainty in the Galactic extinction.
 Usine the NICAIOS measurement, Using the NICMOS measurement
The present study suggests Chat if NCs in low-mass galaxies have seed. \IBIIs. then (heir inner densities should progressively decline as galaxies grow through merging.,"The present study suggests that if NCs in low-mass galaxies have seed MBHs, then their inner densities should progressively decline as galaxies grow through merging."
 This is al odds with the simple superposition of the NC density field for merging NC's without MDIIs 33. lower panel).," This is at odds with the simple superposition of the NC density field for merging NCs without MBHs 3, lower panel)."
 Although many previous theoretical studies investigated how NCs are formed. either by merging of SCs (e.g.. Tremaine et al.," Although many previous theoretical studies investigated how NCs are formed, either by merging of SCs (e.g., Tremaine et al."
 1975: Capuzzo-Dolcetta /Miocchi 2008) or bv dissipative gas dvnamics in galaxies (e.g.. Dekki et al.," 1975; Capuzzo-Dolcetta Miocchi 2008) or by dissipative gas dynamics in galaxies (e.g., Bekki et al."
 2006: Dekki 20075). thev did not predict (1) how DlIs can be formed in NC's and Gi) what a reasonable value is lor Pj.," 2006; Bekki 2007b), they did not predict (i) how BHs can be formed in NCs and (ii) what a reasonable value is for $F_{\rm BH}$."
 The formation of seed MDBIIs may be different from that of intermeciate-mass BIls inisolated globular clusters through merging of stellar-mass black holes (e.g.. OLeary et al.," The formation of seed MBHs may be different from that of intermediate-mass BHs in globular clusters through merging of stellar-mass black holes (e.g., O'Leary et al."
 2006). because the deeper gravitational potential wells of the NC host galaxies would play a role in retaining interstellar gas more efficiently.," 2006), because the deeper gravitational potential wells of the NC host galaxies would play a role in retaining interstellar gas more efficiently."
 It dis thus our future study to investigate how seed MBDBlIs can be formed in NC's at the epoch of NC formation in low-mass galaxies based on more sophisticated numerical simulations., It is thus our future study to investigate how seed MBHs can be formed in NCs at the epoch of NC formation in low-mass galaxies based on more sophisticated numerical simulations.
 We are grateful to (he anonvamous releree for valuable comments which improved the presentation of this paper., We are grateful to the anonymous referee for valuable comments which improved the presentation of this paper.
 Ix.D. acknowledges the financial support of the Australian Research Council throughout the course of this work., K.B. acknowledges the financial support of the Australian Research Council throughout the course of this work.
 Numerical computations reported here were carried out both on the GRAPE svstem at the University of New South Wales and on those kindly made available bv the Center lor computational astrophvsies (CICA) of the National Astronomical Observatory of Japan., Numerical computations reported here were carried out both on the GRAPE system at the University of New South Wales and on those kindly made available by the Center for computational astrophysics (CfCA) of the National Astronomical Observatory of Japan.
 This work was financially supported by CICA., This work was financially supported by CfCA.
Ilexing of the dise structure as its orientation with respect to the Roche potential changes due to the orbital motion of the donor star.,flexing of the disc structure as its orientation with respect to the Roche potential changes due to the orbital motion of the donor star.
" We tuned the luminosity to a value of L,-—2.510ergs to achieve the observed. precession rate of approximately 34.9 days.", We tuned the luminosity to a value of $L_* = 2.15 \times 10^{37} {\rm erg\thinspace s^{-1}}$ to achieve the observed precession rate of approximately $34.9$ days.
 This value of L. is approximately 10'4 higher than the value quoted in Table 2., This value of $L_*$ is approximately $10\%$ higher than the value quoted in Table 2.
 This discrepancy is. of course. well within the uncertainty arising from the distance adopted by MeCrayetal.(1982).," This discrepancy is, of course, well within the uncertainty arising from the distance adopted by \citet{McCrayEt:1982}."
.. Alore importantly. the factor implicitly introduced by our assumption of zero albedo is probably approximately 2. Lc. far larger than approximately 10%.," More importantly, the factor implicitly introduced by our assumption of zero albedo is probably approximately $2$ , i.e. far larger than approximately $10\%$."
 Lhe warp shape was very stable over many orbital periods: we ran this simulation for more than 60 orbital periods and the warp shape remained constant throughout., The warp shape was very stable over many orbital periods; we ran this simulation for more than 60 orbital periods and the warp shape remained constant throughout.
 The rate of precession of the dise was determined: as described in paper L1. Figure 4. shows the precession angle versus orbital phase for the model., The rate of precession of the disc was determined as described in paper I. Figure \ref{HerX1:Figure:herx1_prec_plot} shows the precession angle versus orbital phase for the model.
 The disc precession rate was determined by fitting a straight line to the data using a Numerical Recipes least squares method (Pressetal.LOSG).., The disc precession rate was determined by fitting a straight line to the data using a Numerical Recipes least squares method \citep{PressEt:1986}.
 The warped disc is inclined relative tothe orbital plane, The warped disc is inclined relative tothe orbital plane
The lifetime of protoplanetary discs around young low-mass stars has been the subject of numerous recent observational and theoretical studies (e.g. Luhman et al 2010: Ercolano. Clarke Hall 2011: Currie Kenyon 2009: Ercolano. Clarke Robitaille 2009: Sicilia-Aguilar et al 2008).,"The lifetime of protoplanetary discs around young low-mass stars has been the subject of numerous recent observational and theoretical studies (e.g. Luhman et al 2010; Ercolano, Clarke Hall 2011; Currie Kenyon 2009; Ercolano, Clarke Robitaille 2009; Sicilia-Aguilar et al 2008)."
 The interest is justitied by the key role played by this circumstellar material in the formation and evolution of planetary systems. by providing the gas and dust reservoirs from which planets form and through which they migrate.," The interest is justified by the key role played by this circumstellar material in the formation and evolution of planetary systems, by providing the gas and dust reservoirs from which planets form and through which they migrate."
 Dises around solar type stars are rarely seen for systems of age 10 Myr or older (e.g. Mamejek. 2009). implying that (giant) planet formation around such stars must occur within this timescale.," Discs around solar type stars are rarely seen for systems of age 10 Myr or older (e.g. Mamejek, 2009), implying that (giant) planet formation around such stars must occur within this timescale."
 There has been considerable interest recently with regards to planetary systems around lower mass stars (e.g. Pascuect et al 2011)., There has been considerable interest recently with regards to planetary systems around lower mass stars (e.g. Pascucci et al 2011).
 The attraction of M-dwarfs resides. first of all. in their larger population. assuming a Salpeter/Kroupa initial mass function (Salpeter 1955: Kroupa 2002) there are 50/10 0.2 M. stars for every | M. star.," The attraction of M-dwarfs resides, first of all, in their larger population, assuming a Salpeter/Kroupa initial mass function (Salpeter 1955; Kroupa 2002) there are 50/10 0.2 $_{\odot}$ stars for every 1 $_{\odot}$ star."
 Furthermore. their habitable zones (HZ) extend close to the parent star allowing for a stronger (detectable) radial velocity signal from xotentially neptune-size planets or smaller.," Furthermore, their habitable zones (HZ) extend close to the parent star allowing for a stronger (detectable) radial velocity signal from potentially neptune-size planets or smaller."
 There are. however. a number of possible drawbacks to he search of planetary systems around M-dwarfs. namely their stronger magnetic activity and the possibility of tidal locking for jxanets with small orbital separation from the star.," There are, however, a number of possible drawbacks to the search of planetary systems around M-dwarfs, namely their stronger magnetic activity and the possibility of tidal locking for planets with small orbital separation from the star."
 There is at resent no consensus with regards to whether either of these factors could prevent the development of life on these planets (for a recent review see Pascucci et al 2011)., There is at present no consensus with regards to whether either of these factors could prevent the development of life on these planets (for a recent review see Pascucci et al 2011).
 With regards to the actual ormation of the planets themselves there are further considerations o be made., With regards to the actual formation of the planets themselves there are further considerations to be made.
 The lower column densities of dises around late type stars may imply longer timescales for planet formation under the core accretion scenario. but this may be offset by the fact that the dises may be longer lived.," The lower column densities of discs around late type stars may imply longer timescales for planet formation under the core accretion scenario, but this may be offset by the fact that the discs may be longer lived."
 While absolute ages of star forming regions (or. worse. individual objects within a region) are known to be uncertain (e.g. Mayne Naylor 2008: Baratte. Chabrier. Gallardo 2009). the high fraction of dise bearing M-stars in 7 Chamaleontis. aged 8 Myr. has been interpreted as evidence for longer dise lifetimes around late type stars (Sicilia-Aguilar et al 2009).," While absolute ages of star forming regions (or, worse, individual objects within a region) are known to be uncertain (e.g. Mayne Naylor 2008; Baraffe, Chabrier, Gallardo 2009), the high fraction of disc bearing M-stars in $\eta$ Chamaleontis, aged 8 Myr, has been interpreted as evidence for longer disc lifetimes around late type stars (Sicilia-Aguilar et al 2009)."
 Furthermore. there is tentative evidence that the frequency," Furthermore, there is tentative evidence that the frequency"
temperature. (multiplied by 107).,temperature (multiplied by $10^3$ ).
" ""Phe lower panel of the Figure shows two estimates of mass of the first fragments in the disk.", The lower panel of the Figure shows two estimates of mass of the first fragments in the disk.
 Different authors estimate the volumes of the first unstable fragments sliehthy clilferently. but the reasonable range scems to be from Lf? to 241(2xHY.," Different authors estimate the volumes of the first unstable fragments slightly differently, but the reasonable range seems to be from $H^3$ to $2H \times (2\pi H)^2$."
" The two curves in the lower panel of Figure 1. should then encompass the reasonable outcomes. [roni My,=pll? to Ala.=ps "," The two curves in the lower panel of Figure \ref{fig:fig1} should then encompass the reasonable outcomes, from $M_{\rm frag} = \rho H^3$ to $M_{\rm frag} = \rho 8
\pi^2 H^3$."
From the Figure. the fragment mass is. in theobscrvationally interesting range of radii. Lo. /?70.1 Lope. MgALM.. and hence i£ disk were to rapidly and. completely collapse into clumps of mass of this order. one would expect Iow-niass stars or even giant planets to dominate the mass spectrum of collapsed objects.," From the Figure, the fragment mass is, in theobservationally interesting range of radii, i.e. $R\sim 0.1-1$ pc, $M_{\rm frag}\simlt \msun$, and hence if disk were to rapidly and completely collapse into clumps of mass of this order, one would expect low-mass stars or even giant planets to dominate the mass spectrum of collapsed objects."
" Numerical simulations with a constant cooling time show (e.g..Gammie.2001) that if the disk cooling time is at the threshold. for the fragmentation to take place. ren the first gas clumps will grow. very rapidly by. inelastic collisions with other clumps. possibly. until they reach the isolation.. mass Mis,(πετDDuMi (Levin.2003).."," Numerical simulations with a constant cooling time show \citep[e.g.,][]{Gammie01} that if the disk cooling time is at the threshold for the fragmentation to take place, then the first gas clumps will grow very rapidly by inelastic collisions with other clumps, possibly until they reach the isolation mass $M_{\rm iso} \sim (\pi R^2 \Sigma)^{3/2}/\mbh^{1/2}$ \citep{Levin03b}."
 If js is the case. then the main point of our paper — that gaars born in an accretion disk near a SMDLIID are massive on average is proven.because the isolation mass can be hundreds to as much as LO? Solar masses (Goodman&“Pan. 2004).," If this is the case, then the main point of our paper – that stars born in an accretion disk near a SMBH are massive on average – is proven,because the isolation mass can be hundreds to as much as $10^4$ Solar masses \citep{GoodmanTan04}."
. Llowever we suspect that Canimie(2001) simulations vielded no further gravitational collapse of the eas clumps precisely because the cooling time were kept constant.," However we suspect that \cite{Gammie01}
 simulations yielded no further gravitational collapse of the gas clumps precisely because the cooling time were kept constant."
 As the clump density increases. the clump frec-fall time decreases as xp.L7. and hence the clumps could not collapse as they could not. cool rapidly enough.," As the clump density increases, the clump free-fall time decreases as $\propto \rho^{-1/2}$, and hence the clumps could not collapse as they could not cool rapidly enough."
 Lt is quite likely that had the cooling time were allowed to decrease as the clumps get hotter. the clumps would collapse before they agelomerate into Larger ones.," It is quite likely that had the cooling time were allowed to decrease as the clumps get hotter, the clumps would collapse before they agglomerate into larger ones."
 We shall now assume that gravitational instabilities in the Qx1 cise resulted in the formation of first. proto-stars., We shall now assume that gravitational instabilities in the $Q\approx 1$ disc resulted in the formation of first proto-stars.
 According to the cliscussion in §??.. we conservatively assume that these. proto-stars are low mass objects. and show that in certain conditions even a small aclmixture of these to the accretion disk may significantly allect its evolution.," According to the discussion in \ref{sec:mfirst}, we conservatively assume that these proto-stars are low mass objects, and show that in certain conditions even a small admixture of these to the accretion disk may significantly affect its evolution."
 As the stars are born out ofthe gas in a turbulent disc. we assume that the initial stellar velocities are the sum of the bulk circular. Weplerian velocity. ey in the azimuthal direction and a random component with three dimensional dispersion magnitude a2ὃς.," As the stars are born out ofthe gas in a turbulent disc, we assume that the initial stellar velocities are the sum of the bulk circular Keplerian velocity $v_K$ in the azimuthal direction and a random component with three dimensional dispersion magnitude $\sigma_0 \approx c_s$."
 This also implies that at least initially stellar disk height-scale. //.. is roughly the same as that of the σας disk. ff.," This also implies that at least initially stellar disk height-scale, $H_*$, is roughly the same as that of the gas disk, $H$."
 Proto-stars would interact by direct collisions ancl N-body scatterings between themselves anc also via dynamical friction with the gas., Proto-stars would interact by direct collisions and N-body scatterings between themselves and also via dynamical friction with the gas.
 The rate for proto-stellar collisions. L/feou. is the sum of two terms. the ecometric cross-section of the colliding stars and the gravitational focusing term (ο.seeBin-ney&Tremaine. 1987).," The rate for proto-stellar collisions, $1/t_{\rm coll}$, is the sum of two terms, the geometric cross-section of the colliding stars and the gravitational focusing term \citep[e.g., see][]{Binney87}."
. One can show that L/foyQ=maxag/ ΗΝ is obvious that collisions are. unimportant as long as the collision radius. Aug~2Arete Che proto-star radius) is much smaller than the clisk height scale.," One can show that $1/t_{\rm coll} \Omega \simeq \hbox{max}[\Sigma_* R_{\rm coll}^2/M_*,
(\Sigma_*/\Sigma) R_{\rm coll}/H]$ , from which it is obvious that collisions are unimportant as long as the collision radius, $R_{\rm coll} \sim 2 R_{\rm
proto}$ (the proto-star radius), is much smaller than the disk height scale."
 In all of the cases considered. below this will be satisfied by few orders. of maenituce. therefore we shall neglect direct. collisions.," In all of the cases considered below this will be satisfied by few orders of magnitude, therefore we shall neglect direct collisions."
" The N-body evolution of the svstem of stars immoersed into a σας clisk is described by (Navakshin&Cuacdra.2005) where In.X&~ few is the Coulomb logarithm for stellar collisions. Cu7 few is the drag cocllicient for star-eas interactions CArtvmowicz.1994)... o is one-dimensional velocity dispersion. and. p,=X245. is the stellar surface density."," The N-body evolution of the system of stars immersed into a gas disk is described by \citep{NC05}
 where $\ln \Lambda*\sim$ few is the Coulomb logarithm for stellar collisions, $C_{\rm d}\sim$ few is the drag coefficient for star-gas interactions \citep{Artymowicz94}, $\sigma$ is one-dimensional velocity dispersion, and $\rho_* = \Sigma_*/2 H_*$ is the stellar surface density."
 Therefore. as long as the gas density pxpe. stellar velocity. dispersion. cannot grow as it is. damped by interactions with the gas too ellicientlv.," Therefore, as long as the gas density $\rho \simgt \rho_*$, stellar velocity dispersion cannot grow as it is damped by interactions with the gas too efficiently."
" Recalling that fpscNSA2 we fine that in this situation Thus. initially, when X.«MX. stars are. embedded in the gaseous disk and form a disk gcometricallv thinner than that of the eas."," Recalling that $\rho_* = \Sigma_*/2H_*$, we find that in this situation Thus, initially, when $\Sigma_*\ll \Sigma$, stars are embedded in the gaseous disk and form a disk geometrically thinner than that of the gas."
 However. if stellar surface. density grows and approaches that of the gaseous component. then the stellar. velocity dispersion. will run away.," However, if stellar surface density grows and approaches that of the gaseous component, then the stellar velocity dispersion will run away."
 The stars then form a ecometrically thicker disk (numerical simulations. to be reported in a future paper. confirm these predictions).," The stars then form a geometrically thicker disk (numerical simulations, to be reported in a future paper, confirm these predictions)."
 Galaxy disks apparently operate in this regime. with molecular gas having a much smaller scale height than stars.," Galaxy disks apparently operate in this regime, with molecular gas having a much smaller scale height than stars."
 Since the stars remain embedded. in the disk. they will continue to eain mass via gas accretion.," Since the stars remain embedded in the disk, they will continue to gain mass via gas accretion."
 Such aceretion has been previously considered by many authors (c.g..Lissauer.1987:Dateetal.2003:Goodman&Tan. 2004).," Such accretion has been previously considered by many authors \citep[e.g.,][]{Lissauer87,Bate03,GoodmanTan04}."
. We assume that the accretion rate is where the accretion rates in the brackets are the Bondi. the LGM ancl the Eeeington limit. respectively (e.g.Navak-shin. 2005).," We assume that the accretion rate is where the accretion rates in the brackets are the Bondi, the Hill and the Eddington limit, respectively \citep[e.g.][]{Nayakshin05}."
". The latter is calculated based on the Thomson opacity of [ree electrons instead of dust opacity because we assume that the cooler regions of acerction Dow onto the star are shielded from the stellar radiation bv the inner. hotter accretion How (Ixrumholzetal.. 2005): Apad—]10rM. [owhere r,=RE R.."," The latter is calculated based on the Thomson opacity of free electrons instead of dust opacity because we assume that the cooler regions of accretion flow onto the star are shielded from the stellar radiation by the inner, hotter accretion flow \citep{Krumholz05}: : $\dot M_{\rm Edd} = 10^{-3} r_* \msun$ $^{-1}$ where $r_* = R_*/\rsun$ ."
 Presence of the stars will lead to additional disc heating via radiation and outllows. and. N-bods scattering.," Presence of the stars will lead to additional disc heating via radiation and outflows, and N-body scattering."
 The energy liberation rate per surface area due to N-body interactions is given by where (derfd); stands for the first term only in equation, The energy liberation rate per surface area due to N-body interactions is given by where $(d\sigma/dt)_*$ stands for the first term only in equation
he maser to lic anywhere along the z-axis. with a distance corresponding to 30 aresee of LRe2).,"the maser to lie anywhere along the $z$ -axis, with a distance corresponding to 30 arcsec of IRc2)."
 The five-dimensional »wameter space was searched. within a reasonable domain. using a random number generator to sample the parameters.," The five-dimensional parameter space was searched, within a reasonable domain, using a random number generator to sample the parameters."
 The position in [ive-parameter space where the sum of he (absolute) velocity residuals is minimized was thereby ocated., The position in five-parameter space where the sum of the (absolute) velocity residuals is minimized was thereby located.
 The best fitting model has the parameter. values given in Table 2.., The best fitting model has the parameter values given in Table \ref{parameters}.
 The angles correspond to a rotation axis inclined. at 58to the linc-of-sight with a position angle on he skv of357., The angles correspond to a rotation axis inclined at to the line-of-sight with a position angle on the sky of.
 A disc at this orientation is plotted. in lig. 2..," A disc at this orientation is plotted in Fig. \ref{ra-deccore},"
 where it [its neatly inside the ‘hole’ in the OLI maser distribution that is centred on source I. Using the kinematic model we constructed. views of the three-climensional clistribution of OLL 1665-MlIZ masers. which are shown in Fig. 9..," where it fits neatly inside the `hole' in the OH maser distribution that is centred on source I. Using the kinematic model we constructed views of the three-dimensional distribution of OH 1665-MHz masers, which are shown in Fig. \ref{3dview}."
 Phe masers lie in an irregularly filleck torus. at. radial distances ranging [rom 430 au to 13200 au. with a mean radius of 6200 au.," The masers lie in an irregularly filled torus, at radial distances ranging from 430 au to 13200 au, with a mean radius of 6200 au."
 There is a well defined. inner cavity. of racius 71300 au.," There is a well defined inner cavity, of radius $\sim$ 1300 au."
 This cavity corresponds spatially with the SiO [ared disc region mapped by Wright et al. (, This cavity corresponds spatially with the SiO flared disc region mapped by Wright et al. (
1995. 1996). which has a radial velocity range of. 10 t0 |20 kms 1 that is roughly consistent with the range of 12 to [30J km  given by our kinematic model.,"1995, 1996), which has a radial velocity range of $-10$ to +20 km $^{-1}$ that is roughly consistent with the range of $-12$ to +30 km $^{-1}$ given by our kinematic model."
" ..The distribution⋠⋠⋠ in. radial. distance. ""Hoyrom the rotation axis is plotted in Fig. 10..", The distribution in radial distance from the rotation axis is plotted in Fig. \ref{radial}.
" The distribution in the z""-direction. parallel to the rotation axis. has a Lull width to hall maximum of 6000 au. and a total extent of 12000 au."," The distribution in the $z''$ -direction, parallel to the rotation axis, has a full width to half maximum of 6000 au, and a total extent of 12000 au."
" The best-fitting expansion. velocity is similar to that of the ""Low-velocitv. outflow! seen in LO masers. (Genzel et al.."," The best-fitting expansion velocity is similar to that of the `low-velocity outflow' seen in $_{2}$ O masers (Genzel et al.,"
. 1981)., 1981).
 Solid. body rotation becomes the dominant motion bevond a distance of 3240 au from the centre (a distance corresponding to 7.2 aresec)., Solid body rotation becomes the dominant motion beyond a distance of 3240 au from the centre (a distance corresponding to 7.2 arcsec).
 Rotation is therefore the dominant motion lor most of the svstem of OLL masers. with however a significant. component of expansion.," Rotation is therefore the dominant motion for most of the system of OH masers, with however a significant component of expansion."
 The rotational period in our mocel is 760 vr. while the expansion timescale varies from 7300 vr for the inner edgee ofthe maser cavity to 73000 vr for the masers most distant [rom the expansion centre.," The rotational period in our model is 760 yr, while the expansion timescale varies from $\sim$ 300 yr for the inner edge of the maser cavity to $\sim$ 3000 yr for the masers most distant from the expansion centre."
 Alost of the Orion nebula LUEobjects are found at the tips of the LI» ‘fingers’ in the bipolar outflow shown in Fig., Most of the Orion nebula HH–objects are found at the tips of the $_{2}$ `fingers' in the bipolar outflow shown in Fig.
 and appear to have their origin in a newly ereated massive star that gives rise to the infrared. source Htc 2 in the 107 L. Orion-BN/KL nebula in the OAIC1 cloud core., \ref{subaru} and appear to have their origin in a newly created massive star that gives rise to the infrared source IRc 2 in the $^{5}$ $_{\odot}$ Orion-BN/KL nebula in the OMC–1 cloud core.
 I. has also been suggested that a minority of the prominent LILobjects have their origin in the neighbouring star forming region OMC.IS (Smith et al., It has also been suggested that a minority of the prominent HH--objects have their origin in the neighbouring star forming region OMC–1S (Smith et al.
 2004)., 2004).
 However. excluding these few. Doi. O'Dell Llartigan (2002) have used. LIST proper-amotion measurements of the elobal expansion. of he svstem of Orion HIIobjects to demonstrate that the polar outflow is of Llubble type. i.c. the Low velocity is »oportional to distance from the expansion centre.," However, excluding these few, Doi, O'Dell Hartigan (2002) have used HST proper-motion measurements of the global expansion of the system of Orion HH–objects to demonstrate that the bipolar outflow is of Hubble type, i.e. the flow velocity is proportional to distance from the expansion centre."
" The jipolar How therefore consists of ""bullets! all ejected around a 1000 vr ago in a single explosive event.", The bipolar flow therefore consists of `bullets' all ejected around a 1000 yr ago in a single explosive event.
 Thus the expansion imescales determined. for the OLL masers bracket this L imescale., Thus the expansion timescales determined for the OH masers bracket this $_{2}$ timescale.
" These results suggest. that the Oll maser disc acquired its expansional motions in the same event. that oduced the LH» bullets and the LLLobjects found at the ips of the LH» ""fingers! in the bipolar outflow shown in Fig.", These results suggest that the OH maser disc acquired its expansional motions in the same event that produced the $_{2}$ bullets and the HH–objects found at the tips of the $_{2}$ `fingers' in the bipolar outflow shown in Fig.
 , 7.
The orientation of the rotation axis. determined. here agrees with that of the molecular outllow traced. in CO and Hl» (e.g. Chernin Wright. 1996: Ixzifu et al., The orientation of the rotation axis determined here agrees with that of the molecular outflow traced in CO and $_{2}$ (e.g. Chernin Wright 1996; Kaifu et al.
 2000)., 2000).
 Lt also coincides with the direction of the proper motions of source E and BN. and is close to the large-scale magnetic Ποιά direction inferred from. far-infrarecl ancl submillimetre polarization (Schleuning 1998 and references therein).," It also coincides with the direction of the proper motions of source I and BN, and is close to the large-scale magnetic field direction inferred from far-infrared and submillimetre polarization (Schleuning 1998 and references therein)."
 We note that the velocities of order 20 km  implied bv our kinematic model correspond. το proper. motions — mas nC. which. could be measured by MERLIN+. withinEN len vears.," We note that the velocities of order 20 km $^{-1}$ implied by our kinematic model correspond to proper motions $\sim$ 9 mas $^{-1}$, which could be measured by MERLIN within ten years."
 The major streams or arcs found in Orion-DN/IXL. have angular sizes greater than Ὁ aresec. corresponding to projected. sizes of at. least 2250 au. which are almost unprecedented for interstellar OLL masers.," The major streams or arcs found in Orion-BN/KL have angular sizes greater than 5 arcsec, corresponding to projected sizes of at least 2250 au, which are almost unprecedented for interstellar OH masers."
 Stream A has no obvious counterpart in the infrared., Stream A has no obvious counterpart in the infrared.
 However it points in the direction of the dominant. infrared. source BN. in the direction of the radio proper motions of BN and source I. Stream A has the appearance of a vapour trail that has," However it points in the direction of the dominant infrared source BN, in the direction of the radio proper motions of BN and source I. Stream A has the appearance of a vapour trail that has"
might be so.,might be so.
 We speculate that a better. understanding of accretion disc energy. release may require. consideration of more complicated. physical processes than are currently implemented in numerical codes., We speculate that a better understanding of accretion disc energy release may require consideration of more complicated physical processes than are currently implemented in numerical codes.
 We thank Mark Llurn for valuable help in finding references., We thank Mark Hurn for valuable help in finding references.
 We thank Alan Boss for useful comments and for sending us a copy of his review., We thank Alan Boss for useful comments and for sending us a copy of his review.
 We thank Andrew: Bagealey and Jim Stone for stimulating correspondence., We thank Andrew Baggaley and Jim Stone for stimulating correspondence.
" We acknowledge support from the Isaac Newton Institute. programme ""Dynamics of Dises and. Planets’.", We acknowledge support from the Isaac Newton Institute programme `Dynamics of Discs and Planets'.
the intrinsic profiles.,the intrinsic profiles.
 The effective radii derived from the residual-corrected profiles are very close to the intrinsic effective radii: in three of the cases the difference is less than 596., The effective radii derived from the residual-corrected profiles are very close to the intrinsic effective radii: in three of the cases the difference is less than $5\%$.
" For the n=1 extended component with a total flux equal to half of the compact component's flux the inferred radius is smaller than the intrinsic radius, comparable to the systematic error due to modeling uncertainties Section ??))."," For the $n=1$ extended component with a total flux equal to half of the compact component's flux the inferred radius is smaller than the intrinsic radius, comparable to the systematic error due to modeling uncertainties (see Section \ref{sec:psf}) )."
 We also tested n—4 and n—1 models(see with effective radii of several kpc for the n—1 extended component: these models are so well approximated by Sérrsic models with higher values of n (> 4) that normal Sérrsic profile fitting immediately retrieves the correct effective radii., We also tested $n=4$ and $n=1$ models with effective radii of several kpc for the $n=1$ extended component: these models are so well approximated by Sérrsic models with higher values of $n$ $>4$ ) that normal Sérrsic profile fitting immediately retrieves the correct effective radii.
" In conclusion, our method used on these deep data is sensitive to a faint extended component down to a surface brightness of H+28 mag arcsec?, and using our method we retrieve effective radii that are within lo of the true value."," In conclusion, our method used on these deep data is sensitive to a faint extended component down to a surface brightness of $H\approx 28$ mag $^{-2}$, and using our method we retrieve effective radii that are within $1\sigma$ of the true value."
" We note that the effective radii obtained using the conventional method are, in most cases, very close to the intrinsic effective radii."," We note that the effective radii obtained using the conventional method are, in most cases, very close to the intrinsic effective radii."
" However, the surface brightness profiles obtained in this way clearly deviate from the intrinsic profiles."," However, the surface brightness profiles obtained in this way clearly deviate from the intrinsic profiles."
 We have found that the galaxy under consideration is indeed remarkably small., We have found that the galaxy under consideration is indeed remarkably small.
" We have fitted a Sérrsic model to the observed flux distribution, and corrected"," We have fitted a Sérrsic model to the observed flux distribution, and corrected"
"that derived by Castanheira Kepler (2008, 2009) are in very good agreement.","that derived by Castanheira Kepler (2008, 2009) are in very good agreement."
 One of the most important structural parameters we want to constrain through asteroseismology of ZZ Ceti stars is the thickness of the H envelope in DA white dwarfs., One of the most important structural parameters we want to constrain through asteroseismology of ZZ Ceti stars is the thickness of the H envelope in DA white dwarfs.
" We have found a H layer mass of My=(1.250.7)x109M. for G117—B15A, about two order of magnitude thinner than the value predicted by canonical evolutionary computations, of My~107M.."," We have found a H layer mass of $M_{\rm
 H}= (1.25\pm 0.7) \times 10^{-6} M_*$ for $-$ B15A, about two order of magnitude thinner than the value predicted by canonical evolutionary computations, of $M_{\rm H} \sim 10^{-4} M_*$."
" Here, the analysis of a large number of ZZ Ceti stars allows us to explore the distribution of H envelope thicknesses from their pulsations."," Here, the analysis of a large number of ZZ Ceti stars allows us to explore the distribution of H envelope thicknesses from their pulsations."
 In Fig., In Fig.
 11 we present histograms of the distribution of H envelope thicknesses., \ref{histo-mh} we present histograms of the distribution of H envelope thicknesses.
 In the upper panel we show the results for the complete sample of 44 stars., In the upper panel we show the results for the complete sample of 44 stars.
" Note that there is a pronounced maximum of the distribution for log(Mu/M.) in the range —5 to —4, although there exists another, much less notorious maximum for log(Mu/M.) between —10 and —9."," Note that there is a pronounced maximum of the distribution for $\log (M_{\rm H}/M_*)$ in the range $-5$ to $-4$, although there exists another, much less notorious maximum for $\log
(M_{\rm H}/M_*)$ between $-10$ and $-9$."
" So, it is apparent from the figure that there exists arange of thicknesses of the H envelope in the studied DAV stars, with a strong peak at thick envelopes and another much lower peak at very thin envelopes, and an apparent paucity for intermediate thicknesses."," So, it is apparent from the figure that there exists a of thicknesses of the H envelope in the studied DAV stars, with a strong peak at thick envelopes and another much lower peak at very thin envelopes, and an apparent paucity for intermediate thicknesses."
 In the middle panel of Fig., In the middle panel of Fig.
" 11 we show the histogram corresponding to the asteroseismological models characterized by canonical (thick) H envelope thicknesses, that amount to 11 stars."," \ref{histo-mh} we show the histogram corresponding to the asteroseismological models characterized by canonical (thick) H envelope thicknesses, that amount to 11 stars."
" Finally, in the lower panel we display the histogram for the non-canonical thicknesses, that is, envelopes thinner than those predicted by standard evolutionary computations depending on the value of the stellar mass."," Finally, in the lower panel we display the histogram for the non-canonical thicknesses, that is, envelopes thinner than those predicted by standard evolutionary computations depending on the value of the stellar mass."
" As in previous sections, we refer this kind of envelopes as “thin” envelopes."," As in previous sections, we refer this kind of envelopes as “thin” envelopes."
 We recall that these “thin” envelopes have been generated in this work in order to extend the exploration of the parameter space of the models for asteroseismology., We recall that these “thin” envelopes have been generated in this work in order to extend the exploration of the parameter space of the models for asteroseismology.
" Note that in most of the analysed stars (34 stars from a total of 44) our asteroseismological models have ""thin"" H envelopes, as illustrated in Fig. 12.."," Note that in most of the analysed stars (34 stars from a total of 44) our asteroseismological models have “thin” H envelopes, as illustrated in Fig. \ref{mh-m-all}."
" It is important to note, however, that most of our derived envelope masses, even being thinner than the canonical values, cluster close to the envelope masses predicted by standard evolutionary computations, at variance with those of Castanheria Kepler (2009), who found a nearly homogeneous distribution of envelope masses in their fits (see their Fig."," It is important to note, however, that most of our derived envelope masses, even being thinner than the canonical values, cluster close to the envelope masses predicted by standard evolutionary computations, at variance with those of Castanheria Kepler (2009), who found a nearly homogeneous distribution of envelope masses in their fits (see their Fig."
 8)., 8).
 The mean value of the H layer mass is (My/M.)=2.71x10? according to our results.," The mean value of the H layer mass is $\langle M_{\rm H}/M_* \rangle=
2.71 \times 10^{-5}$ according to our results."
" This value is about 50 times larger than the value obtained by Castanheira Kepler (2009) with different samples, (Mu/M.)=5.01 1077."," This value is about 50 times larger than the value obtained by Castanheira Kepler (2009) with different samples, $\langle M_{\rm H}/M_* \rangle= 5.01 \times
10^{-7}$ ."
" In spite of this difference, both studies concur to the conclusion that an important fraction of DA white dwarfs might have been formed with a H mass smaller than the value predicted by standard evolutionary computations, a conclusion we have already suggested at end of Section 4.2 on the basis of our results on G117—B15A. In this paper, we have carried out the first asteroseismological application of the evolutionary DA white-dwarf models presented in Althaus et al. (2010b)?.."," In spite of this difference, both studies concur to the conclusion that an important fraction of DA white dwarfs might have been formed with a H mass smaller than the value predicted by standard evolutionary computations, a conclusion we have already suggested at end of Section \ref{g117b15a} on the basis of our results on $-$ B15A. In this paper, we have carried out the first asteroseismological application of the evolutionary DA white-dwarf models presented in Althaus et al. ."
of the screening potential are matched αἱr=ry so that the screening potential ancl its derivative be a continuous function with respect to the distance r.,of the screening potential are matched at$r=r_{0}$ so that the screening potential and its derivative be a continuous function with respect to the distance $r$.
 This procedure produces solutions for ry and 5 for the range of P-values 4—Dx90., This procedure produces solutions for $r_{0}$ and $b$ for the range of $\Gamma$ -values $4 \leq \Gamma \leq 90$.
 Outside this range we use the value of 6 which makes (3.1) and (3.2) continuous at r—1.171875a., Outside this range we use the value of $b$ which makes (3.1) and (3.2) continuous at $r$ $a$.
 In this case the first derivatives of (3.1) ancl (3.2) ave sliehtIy discontinuous at this point., In this case the first derivatives of (3.1) and (3.2) are slightly discontinuous at this point.
 The linearly decreasing part of the screening potential is identical to that employed by Itoh. Totsuji. Ichimaru (1977) and also bv Πο et al. (," The linearly decreasing part of the screening potential is identical to that employed by Itoh, Totsuji, Ichimaru (1977) and also by Itoh et al. ("
1979).,1979).
 The screening potential (3.1) ancl (3.2) fits the results of the numerical experiments excellentiv. (, The screening potential (3.1) and (3.2) fits the results of the numerical experiments excellently. (
See Figure 1 of Hoh οἱ al. (,See Figure 1 of Itoh et al. (
1979) for the accuracy of (his screening potential in reproducing the results of (he Monte Carlo computations.),1979) for the accuracy of this screening potential in reproducing the results of the Monte Carlo computations.)
 Note that this screening potential exactly cancels the Coulomb potential Z?e?/r at r=1.600., Note that this screening potential exactly cancels the Coulomb potential $Z^{2}e^{2}/r$ at $r=1.60a$.
 We further assume that the potential of mean force vanishes for r>1.600., We further assume that the potential of mean force vanishes for $r \geq 1.60a$.
 Given the explicit form of the screening potential. we are now in a position (ο calculate (he enhancement of the resonant (thermonuclear reaction rates.," Given the explicit form of the screening potential, we are now in a position to calculate the enhancement of the resonant thermonuclear reaction rates."
" A single resonance in the cross section of a nuclear reaction 0+1—32+3 can be represented most simply as a function of energy in terms of the classical Brei(-Wigner formula (Fowler. Caughlan. Zimmerman 1967) where ϱ 15 the reduced mass. E is the center-of-mass energy. £7, is the resonance energy. wy is the statistical weight factor. Dy is the partial widthfor the decay of the resonant state by reemission of O+1. D» is the partial width for emission of 24-32. D;—ΤιEso: is the sum over all partial widths."," A single resonance in the cross section of a nuclear reaction $0 + 1 \longrightarrow 2 + 3$ can be represented most simply as a function of energy in terms of the classical Breit-Wigner formula (Fowler, Caughlan, Zimmerman 1967) where $\mu$ is the reduced mass, $E$ is the center-of-mass energy, $E_{r}$ is the resonance energy, $\omega_{r}$ is the statistical weight factor, $\Gamma_{1}$ is the partial widthfor the decay of the resonant state by reemission of $0 + 1$, $\Gamma_{2}$ is the partial width for emission of $2 + 3$, $\Gamma_{tot}=\Gamma_{1}+\Gamma_{2}+\cdot
\cdot \cdot$ is the sum over all partial widths."
 The partial width D4 is proportional to the barrier penetration factor P(IE) lor the screened Coulomb potential., The partial width $\Gamma_{1}$ is proportional to the barrier penetration factor $P(E)$ for the screened Coulomb potential.
" where rj, is the classical turning point radius which satisfies the condition We consider the case (hat the resonance is sharp: that is. the full width at resonance. D, is considerably smaller than Che effective spread in energy of the interacting particles."," where $r_{tp}$ is the classical turning point radius which satisfies the condition We consider the case that the resonance is sharp; that is, the full width at resonance, $\Gamma_{r}$ , is considerably smaller than the effective spread in energy of the interacting particles."
 We further consider the ease Ty« D». Εν8 D».Cussons. Langanke. Liolios (2002) have," We further consider the case $\Gamma_{1} \ll \Gamma_{2}$ , $\Gamma_{tot} \approx \Gamma_{2}$ .Cussons, Langanke, Liolios (2002) have"
ccan operate only in a very restricted range in ΔΑ. AL. and pss,"can operate only in a very restricted range in $\mdot$ , $M$ , and $\rnu$."
 At this point we evaluate the importance of matter suppression on our results., At this point we evaluate the importance of matter suppression on our results.
 In Figure ὁ we plot the ratio A/Asta. which estimates the relative importance of the MSW matter potential to the collective potential (Eqs. [24]]-[25]]}).," In Figure \ref{fig:multiangle} we plot the ratio $\lambda/\lambda_{\rm MA}$, which estimates the relative importance of the MSW matter potential to the collective potential (Eqs. \ref{eq:lambda}] \ref{eq:lambda_MA}] ])."
 This ratio is evaluated for solutions at Leore Just inside of the shock. where it attains the smallest value.," This ratio is evaluated for solutions at $\lcrit$ just inside of the shock, where it attains the smallest value."
 If αλλνεν31. the collective oscillations are suppressed.," If $\lambda/\lambda_{\rm MA} \gg 1$, the collective oscillations are suppressed."
 We see that for large radii and small masses (3=1.2M. and ro= 60KkKn). the aare suppressed by the matter effects.," We see that for large radii and small masses $M = 1.2 \, \msun$ and $\rnu=60$ km), the are suppressed by the matter effects."
 However. this is also the parameter space where ooccur for AZ attainable by low-mass progenitors together with a stiff high-density EOS (Figure 2)).," However, this is also the parameter space where occur for $\mdot$ attainable by low-mass progenitors together with a stiff high-density EOS (Figure \ref{fig:fred}) )."
 Figure 3. shows that matter suppression effects are moderate for the other parameter combinations. but these combinations do not yield any decrease in ποσο ffor any realistic mass accretion rates.," Figure \ref{fig:multiangle} shows that matter suppression effects are moderate for the other parameter combinations, but these combinations do not yield any decrease in $\lcrit$ due to for any realistic mass accretion rates."
 Thus. for the region of parameter space where aare maximal. the matter suppression effects are largest. whereas where the matter suppresion is small. the effect of iis negligible.," Thus, for the region of parameter space where are maximal, the matter suppression effects are largest, whereas where the matter suppresion is small, the effect of is negligible."
 We investigate the effect of collective neutrino oscillations on the neutrino mechanism of core-collapse supernovae as parameterized by the critical neutrino luminosity LeapeWe assume. that neutrino energies and luminosities vary smoothly between an initial state at synchronization radius r4; and a final state end radius Fea. as summarized byDasguptaetal. (2012)..," We investigate the effect of collective neutrino oscillations on the neutrino mechanism of core-collapse supernovae as parameterized by the critical neutrino luminosity $\lcrit$.We assume that neutrino energies and luminosities vary smoothly between an initial state at synchronization radius $\rsync$ and a final state end radius $\rend$, as summarized by\citet{dasgupta12}. ."
 Thefinal states are dictated by the neutrino number conservation., Thefinal states are dictated by the neutrino number conservation.
" Without matter-suppression. we found that collective oscillations affect LO""... if Poue<r where à is the shock radius at LS,ope. dnd the full magnitude of the effect occurs if ra«mHr"," Without matter-suppression, we found that collective oscillations affect $\lcrit$ if $\rsync < \rscrit$, where $\rs^{\rm crit}$ is the shock radius at $\lcrit$, and the full magnitude of the effect occurs if $\rend < \rscrit$."
" The reduction of 1,77, depends on the assumed energy difference between vo. vw. and f£. and on the individual luminosities."," The reduction of $\lcrit$ depends on the assumed energy difference between $\nue$, $\nuebar$ and $\nux$, and on the individual luminosities."
 We find that neutrino energies of Thompsonetal.(2003) and equalluminosities in each flavor are favorable forCvO.. giving reduction of LUore Dy a factor of ~1.5 0.65. Fig. 23).," We find that neutrino energies of \citet{thompson03} and equalluminosities in each flavor are favorable for, giving reduction of $\lcrit$ by a factor of $\sim\! 1.5$ $\fred = 0.65$ , Fig. \ref{fig:fred}) )."
 The more recent calculations of Marek&Janka(2009) and Fischeretal.(2010.2012) predict slightly lower energies and approximately half the ες luminosity compared to £. and v..," The more recent calculations of \citet{marek09} and \citet{fischer10,fischer12} predict slightly lower energies and approximately half the $\nux$ luminosity compared to $\nue$ and $\nuebar$."
" For these parameter values we find that the 777, reduction reaches only about 104. but the parameter space in terms of AL. M. and rs is essentially the same."," For these parameter values we find that the $\lcrit$ reduction reaches only about $10\%$, but the parameter space in terms of $\mdot$, $M$, and $\rnu$ is essentially the same."
 We do not tind any increase of Leore for the range of parameters considered., We do not find any increase of $\lcrit$ for the range of parameters considered.
" Conversely. if the energy =), was increased to 25 MMeV or 35 MMeV while keeping ον= 13MMeV. 5,=15.5 MMeV. and luminosities of all flavors equal. L7, at low ΑΙ would be reduced by a factor of 2 and 3.5 Cfi20.5 and 0.3). respectively."," Conversely, if the energy $\epsnux^{\rm i}$ was increased to $25$ MeV or $35$ MeV while keeping $\epsnue^{\rm i}=13$ MeV, $\epsnuebar^{\rm i}=15.5$ MeV, and luminosities of all flavors equal, $\lcrit$ at low $\mdot$ would be reduced by a factor of $2$ and $3.5$ $\fred \simeq 0.5$ and $0.3$ ), respectively."
" We tind that ccan be important only for low AZ. small AZ. and large r, (see Fig. |."," We find that can be important only for low $\mdot$, small $M$ , and large $\rnu$ (see Fig. \ref{fig:osc},"
 left panel. red lines).," left panel, red lines)."
 This is best achieved in the lowest mass progenitors. in which AL decreases very rapidly due to their steep density structure.," This is best achieved in the lowest mass progenitors, in which $\mdot$ decreases very rapidly due to their steep density structure."
 However. for times 0.65ss after the collapse is initiated. AL is likely still too high to cause a explosion in an 11.2M. progenitor (seealsoChakraborty201La.b:Dasguptaetal. 2012).," However, for times $\lesssim 0.65$ s after the collapse is initiated, $\mdot$ is likely still too high to cause a -driven explosion in an $11.2\,\msun$ progenitor \citep[see also][]{chakraborty11a,chakraborty11b,dasgupta12}."
".. At late times. AL decreases rapidly. but the effect of oon Leee is likely offset by the simultaneous drop of r, as the PNS cools and the concomitant increase in AZ."," At late times, $\mdot$ decreases rapidly, but the effect of on $\lcrit$ is likely offset by the simultaneous drop of $\rnu$ as the PNS cools and the concomitant increase in $M$."
" Figure 2? shows that for smaller i, and larger A7. ddoes not have any effect."," Figure \ref{fig:fred} shows that for smaller $\rnu$ and larger $M$, does not have any effect."
" Thus. only if the decrease in ry 1s slow enough. perhaps due to a stiff equation of state. M might drop enough so that the decrease in L177""... due to ccan potentially influence the system before black hole formation or explosion via the ordinary neutrino mechanism."," Thus, only if the decrease in $\rnu$ is slow enough, perhaps due to a stiff equation of state, $\mdot$ might drop enough so that the decrease in $\lcrit$ due to can potentially influence the system before black hole formation or explosion via the ordinary neutrino mechanism."
 However. as is indicated in Figure 3.. these parameter combination are the ones most affected by matter suppression and aare unlikely.," However, as is indicated in Figure \ref{fig:multiangle}, , these parameter combination are the ones most affected by matter suppression and are unlikely."
 Finally. we note that even in our implementation of the parameter space where ccould operate is small and reduced even more due to matter suppression effects.," Finally, we note that even in our implementation of the parameter space where could operate is small and reduced even more due to matter suppression effects."
 Realistically. the potential of flavor conversion may be reduced even more.," Realistically, the potential of flavor conversion may be reduced even more."
 In particular. refinements in the treatment of the typically make the effect of sstill smaller. because the physical scale of conversion is moved to arger radii due to various multi-angle effects (Esteban-Preteletal.etal.2011).," In particular, refinements in the treatment of the typically make the effect of still smaller, because the physical scale of conversion is moved to larger radii due to various multi-angle effects \citep{esteban08,chakraborty11a,chakraborty11b,dasgupta12,sarikas11}."
" We find that the multi-angle effects are important especially for small A and large +, (Figure 33. where hhave the greatest potential of influencing the supernova explosion."," We find that the multi-angle effects are important especially for small $M$ and large $\rnu$ (Figure \ref{fig:multiangle}) ), where have the greatest potential of influencing the supernova explosion."
 If the physical scale of conversion is pushed toaradius larger than HU for a given M. M. rs the wwill not have any effect on LY!Me .," If the physical scale of conversion is pushed toaradius larger than $\rscrit$ for a given $\mdot$ , $M$ , $\rnu$, the will not have any effect on $\lcrit$ ."
 We thus conclude that aare unlikely to play a role in neutrino-driven explosions by evaluating these effects at the critical luminosity., We thus conclude that are unlikely to play a role in neutrino-driven explosions by evaluating these effects at the critical luminosity.
 This work is supported in part byan Alfred P. Sloan Foundation Fellowship and by NSF grant AST-0908816., This work is supported in part byan Alfred P. Sloan Foundation Fellowship and by NSF grant AST-0908816.
 We thank John Beacom. Evan OConnor. Christian Ott. Hans-Thomas Janka. and Alessandro Mirizzi.," We thank John Beacom, Evan O'Connor, Christian Ott, Hans-Thomas Janka, and Alessandro Mirizzi."
 We also thank the anonymous referee for comments and suggestions that helped to improve thepaper., We also thank the anonymous referee for comments and suggestions that helped to improve thepaper.
"in their statistical study that solar flares with such high (2:22 MK) temperatures have an X-ray class of about M3.0, i.e. emission from bothstrong (A4.4) andweak (A0.02), “up” coronal beams, if observed, would stand apart on a (temperature) vs. (GOES X-ray class) plot (neglecting any local heating by the beams; see Section 3.4 for a discussion).","in their statistical study that solar flares with such high $\approx$ 22 MK) temperatures have an X-ray class of about M3.0, 	i.e. emission from both (A4.4) and (A0.02), “up” coronal beams, if observed, would stand apart on a (temperature) vs. (GOES X-ray class) plot 	(neglecting any local heating by the beams; see Section \ref{sect:beamheating} for a discussion)."
 The new Hinode/XRT instrument has a whole suite of different filters., 	The new Hinode/XRT instrument has a whole suite of different filters.
 Figure 4 shows the spatial profile from coronal electron beams observed with some of them., 	Figure \ref{fig:XRT_prof} shows the spatial profile from coronal electron beams observed with some of them.
" As can be seen in Figure 5,, aweak “up” electron beam is observable with XRT, provided that a careful choice of image color scale is made."," 	As can be seen in Figure \ref{fig:BethinSimEbeam}, a “up” electron beam is observable with XRT, 	provided that a careful choice of image color scale is made."
" Optimal conditions are: This short section tries to estimate the effect of heating of the local corona by the *up"" beam: can the resulting X-ray thermal emission be greater than the X-ray non-thermal emission?", 	Optimal conditions are: 	This short section tries to estimate the effect of heating of the local corona by the non-thermal “up” beam: 	can the resulting X-ray thermal emission be greater than the X-ray non-thermal emission?
 The non-thermal power lost in collisions can in principle heat the local medium: the amount of non-thermal power dumped along each path element can be calculated., 	 	The non-thermal power lost in collisions can in principle heat the local medium: 	the amount of non-thermal power dumped along each path element can be calculated.
" Given a beam duration At, beam area, and in the absence of thermal losses (from either heat conductivity or thermal radiation), an upper limit to the temperature increase for the ambiant corona along the path of the beam can be determined (mathematical details in Appendix C))."," 	Given a beam duration $\Delta t$, beam area, and in the absence of thermal losses (from either heat conductivity or thermal radiation), an upper limit to the temperature increase for the ambiant corona along the path of the beam can be determined 	(mathematical details in Appendix \ref{appendix:openloopheating}) )."
" Asa consistency check on the assumption of no thermal losses, the timescale for heat conductivity losses can be very roughly estimated (see details in Appendix D)), the density scale height of the heated medium."," 	 	As a consistency check on the assumption of no thermal losses, the timescale for heat conductivity losses can be very roughly estimated (see details in Appendix \ref{appendix:closedloopheating}) ), 	using the density scale height of the heated medium."
" If this timescale is shorter than the beam duration, then heat losses should be included."," 	If this timescale is shorter than the beam duration, then heat losses should be included."
" The treatment presented in Appendix D is best applied to a closed loop system, but was used as proxy for our case with an open field line, taking the loop length L to be the density scale height."," 	The treatment presented in Appendix \ref{appendix:closedloopheating} is best applied to a closed loop system, but was used as proxy for our case with an open field line, 	taking the loop length $L$ to be the density scale height."
" In this treatment, the"," 	In this treatment, the"
or UV-T excess emission. and the absence ofB substantial. photometric. variability.aye outside. ofB eclipse.,or UV excess emission and the absence of substantial photometric variability outside of eclipse.
 Based on its membership in NGC 2264 (Sungetal.1997).. the estimated mass of the INT star is 0.5-1 M. and its age is 2-4 Myr.," Based on its membership in NGC 2264 \citep{Sung97}, the estimated mass of the K7 star is 0.5-1 $_\odot$ and its age is 2-4 Myr."
 In an attempt to learn more about (his unique svstenm we obtained high resolution spectra during the eclipse of December 2001., In an attempt to learn more about this unique system we obtained high resolution spectra during the eclipse of December 2001.
 We hoped to determine whether KIT 15D is a radial velocity variable. whether there was evidence for additional light in the svstem bevond that of (he INT star. and whether the occultation had any effect on the spectrum.," We hoped to determine whether KH 15D is a radial velocity variable, whether there was evidence for additional light in the system beyond that of the K7 star, and whether the occultation had any effect on the spectrum."
 In fact. we found dramatic changes in (he line profiles of Πα ancl 111. as well as weak forbidden emission lines (hat become much more visible during eclipse.," In fact, we found dramatic changes in the line profiles of $\alpha$ and $\beta$, as well as weak forbidden emission lines that become much more visible during eclipse."
" Evidently. the KID 15D system behaves like a ""natural coronagraph. allowing us to see details of its close circumstellar environment during eclipse."," Evidently, the KH 15D system behaves like a “natural coronagraph"", allowing us to see details of its close circumstellar environment during eclipse."
 Our evidence suggests that this WITS is actively accreting gas and driving a bipolar outflow. although probably not at the rate of a (vpical CIT.," Our evidence suggests that this WTTS is actively accreting gas and driving a bipolar outflow, although probably not at the rate of a typical CTTS."
 This calls into question the common practice of associating WTTS characteristics with the absence of an accretion disk., This calls into question the common practice of associating WTTS characteristics with the absence of an accretion disk.
 llish resolution echelle spectra of KIT 15D were obtained on the nights of UT. 2001 Nov. 29. when it was in its bright state just prior to eclipse. on UT 2001 Dec. 14. just past mid-eclipse. aud again on UT 2001 Dec. 20 during egress (see Figure 1).," High resolution echelle spectra of KH 15D were obtained on the nights of UT 2001 Nov. 29, when it was in its bright state just prior to eclipse, on UT 2001 Dec. 14, just past mid-eclipse, and again on UT 2001 Dec. 20 during egress (see Figure 1)."
 These data were collected with the Ultraviolet-Visual Echelle Spectrograph (UVES) on the European southern Observatorys Very Large Telescope (VLT). al Mount Paranal. Chile.," These data were collected with the Ultraviolet-Visual Echelle Spectrograph (UVES) on the European Southern Observatory's Very Large Telescope (VLT), at Mount Paranal, Chile."
 The wavelength range is ου 780 (ο 6810A., The wavelength range is $\sim$ 4780 to 6810.
.. A 50 eap centered on 5800 is present due to use of the red arm which emplovs a mosaic of two 4096 x 2048 CCDs (D'Odoricoetal.2000)., A 50 gap centered on 5800 is present due to use of the red arm which employs a mosaic of two 4096 x 2048 CCDs \citep{D00}.
. With a sslit. the spectral resolution is 744.000.," With a slit, the spectral resolution is $\sim$ 44,000."
 The spectra presented. here were reduced via the UVES pipeline., The spectra presented here were reduced via the UVES pipeline.
 Information regarding the reduction process can be found at http://www.eso.org/instrumen As a σος] on (his. the spectra were also reduced in the manner described by Valenti(1994).," Information regarding the reduction process can be found at http://www.eso.org/instruments/uves/. As a check on this, the spectra were also reduced in the manner described by \citet{Valenti94}."
. Both procedures make use of a sky subtraction algoritlim., Both procedures make use of a sky subtraction algorithm.
 No significant differences were found between the data reduced by these techniques and the UVES pipeline reduction is adopted here., No significant differences were found between the data reduced by these techniques and the UVES pipeline reduction is adopted here.
 The UVES spectra confirm that. out of eclipse. the primary light source in the KIT 15D svslem is a Ix WTTS.," The UVES spectra confirm that, out of eclipse, the primary light source in the KH 15D system is a K7 WTTS."
 The 29 Nov. spectrum was visually compared in detail to 61 Cve D. a tvpical INT V. to look for any evidence of a second source of light in the svstem.," The 29 Nov. spectrum was visually compared in detail to 61 Cyg B, a typical K7 V, to look for any evidence of a second source of light in the system."
 No additional features were found., No additional features were found.
 This spectrum was also compared (o a rotationally broadened. synthetic," This spectrum was also compared to a rotationally broadened, synthetic"
of cool-core clusters.,of cool-core clusters.
 The recent observation that magnetic fluctuations in the solar wind are bounded by the firehose and mirror stability thresholds strongly supports the expectation that equation (9)) will be satisfied in a turbulent plasma (e.g.Kasper.Lazarus&Gary2002:Hellingeretal.2006:Bale 2009).," The recent observation that magnetic fluctuations in the solar wind are bounded by the firehose and mirror stability thresholds strongly supports the expectation that equation \ref{eqn:marginality}) ) will be satisfied in a turbulent plasma \citep[e.g.][]{klg02,htkl06,bkhqss09}."
. There are two fundamental physical ways in which marginal stability to microscale instabilities can be maintained in a weakly collisional plasma., There are two fundamental physical ways in which marginal stability to microscale instabilities can be maintained in a weakly collisional plasma.
 microstabilities give rise to some effective particle scattering mechanism that isotropises the pressure (Schekochihin&Cowley2006:Sharmaetal.2006.2007)or hey modify on the average the structure and time evolution of he magnetic field tor. equivalently. of the rate of strain) so as to cancel the pressure anisotropy caused by the changing fields.," microstabilities give rise to some effective particle scattering mechanism that isotropises the pressure \citep{sc06,shqs06,sqhs07} they modify on the average the structure and time evolution of the magnetic field (or, equivalently, of the rate of strain) so as to cancel the pressure anisotropy caused by the changing fields."
 While here is no complete microphysical theory. existing calculations of yarticular cases (Schekochihinetal.2008:CalifanoSchekochihin&Cowley2010.inpreparation) all suggest the latter scenario.," While there is no complete microphysical theory, existing calculations of particular cases \citep{sckrh08,chkpst08,ipb09,rsrc10,rsc10} all suggest the latter scenario."
 In this work we willassume that this is what happens., In this work we will that this is what happens.
 Importantly. this means that the collision rate is moditied by he instabilities.," Importantly, this means that the collision rate is modified by the instabilities."
 Let us now use this assumption to calculate the heating rate (per unit volume) due to parallel viscous dissipation of motions., Let us now use this assumption to calculate the heating rate (per unit volume) due to parallel viscous dissipation of motions.
 From equations (6)) and (8). this rate is given by We seek to write this equation solely in terms of the ion pressure anisotropy. and therefore we require an additional equation relating the rate of strain (the term in parentheses) to the ion pressure anisotropy.," From equations \ref{eqn:sigma}) ) and \ref{eqn:energy}) ), this rate is given by We seek to write this equation solely in terms of the ion pressure anisotropy, and therefore we require an additional equation relating the rate of strain (the term in parentheses) to the ion pressure anisotropy."
 This is provided by Braginskii(1965): This equation states that the rate of strain due to turbulent motions generates a pressure anisotropy that is relaxed on the ion-ion collision timescale., This is provided by \citet{braginskii65}: This equation states that the rate of strain due to turbulent motions generates a pressure anisotropy that is relaxed on the ion-ion collision timescale.
 We interpret the right-hand side of equation (12)) as including contributions to the (average) turbulent rate of strain from both the microscopic and macroscopic motions (see Rosinetal.2010. for a detailed kinetic calculation of one example where this is justified)., We interpret the right-hand side of equation \ref{eqn:braginskii}) ) as including contributions to the (average) turbulent rate of strain from both the microscopic and macroscopic motions (see \citealt{rsrc10} for a detailed kinetic calculation of one example where this is justified).
 Under the assumption that the collision frequency is not moditied by the instabilities. equation. (123). together with equation (9)). states that microscale fluctuations adjust themselves in response to large-scale fluid motions in order to maintain and preserve marginality.," Under the assumption that the collision frequency is not modified by the instabilities, equation \ref{eqn:braginskii}) ), together with equation \ref{eqn:marginality}) ), states that microscale fluctuations adjust themselves in response to large-scale fluid motions in order to maintain and preserve marginality."
 Using equation C123) in equation (113). we find that In other words. the ion pressure anisotropy is a source of free energy that is eventually converted into heat by collisions.," Using equation \ref{eqn:braginskii}) ) in equation \ref{eqn:heating1}) ), we find that In other words, the ion pressure anisotropy is a source of free energy that is eventually converted into heat by collisions."
 With marginality to microscale instabilities imposed according to equation (9)). equation (13)) becomes Normalised to conditions representative of the centres of cool- clusters. this (per unit volume) is Note the lack of an explicit dependence on density and also. remarkably. on either the amplitude or the rate of strain of the turbulence.," With marginality to microscale instabilities imposed according to equation \ref{eqn:marginality}) ), equation \ref{eqn:heating2}) ) becomes Normalised to conditions representative of the centres of cool-core clusters, this (per unit volume) is Note the lack of an explicit dependence on density and also, remarkably, on either the amplitude or the rate of strain of the turbulence."
 However. the strong dependence on /5 does encode information about all of these.," However, the strong dependence on $B$ does encode information about all of these."
 As the turbulent velocity increases. so too will the strength of the (dynamo-generated) magnetic field (see Section ??)). and the dissipation rate (eq. 159) ," As the turbulent velocity increases, so too will the strength of the (dynamo-generated) magnetic field (see Section \ref{sec:velocities}) ), and the dissipation rate (eq. \ref{eqn:heating4}) )"
will increase accordingly., will increase accordingly.
 In other words. the dissipation rate can be self-regulating.," In other words, the dissipation rate can be self-regulating."
 This local self-regulation is completely independent of whatever global self-regulation may be offered by the external source that is providing the turbulent energy (e.g. the AGNs). as long as there is enough turbulence to maintain the pressure anisotropy at its stability threshold (eq. 9).," This local self-regulation is completely independent of whatever global self-regulation may be offered by the external source that is providing the turbulent energy (e.g. the AGNs), as long as there is enough turbulence to maintain the pressure anisotropy at its stability threshold (eq. \ref{eqn:marginality}) )."
 It should be stressed that the physical picture encapsulated by equation (159) is somewhat different from the conventional approach to turbulence theory., It should be stressed that the physical picture encapsulated by equation \ref{eqn:heating4}) ) is somewhat different from the conventional approach to turbulence theory.
 Namely. in standard. turbulence theory. one assumes that the energy input from external driving is fixed (i.e. given) and that all of that power is converted into turbulence and ultimately microphysically dissipated.," Namely, in standard turbulence theory, one assumes that the energy input from external driving is fixed (i.e. given) and that all of that power is converted into turbulence and ultimately microphysically dissipated."
 In other words. the dissipation rate will adjust according to the rate at which external energy is input.," In other words, the dissipation rate will adjust according to the rate at which external energy is input."
 In the ICM. there is a microscale constraint on the total turbulent rate of strain. namely. equation (91).," In the ICM, there is a microscale constraint on the total turbulent rate of strain, namely, equation \ref{eqn:marginality}) )."
 Although the dissipation can self-regulate via the strength of the magnetic field as described above. not all of the power provided by the external driving in fact need be locally thermalised via turbulence.," Although the dissipation can self-regulate via the strength of the magnetic field as described above, not all of the power provided by the external driving in fact need be locally thermalised via turbulence."
 Indeed. the turbulence may have an effective impedance! and only accept the amount of power that can be locally viscously dissipated without triggering the microinstabilities.," Indeed, the turbulence may have an effective `impedance' and only accept the amount of power that can be locally viscously dissipated without triggering the microinstabilities."
 A further discussion of these points is given at the end of Section ??.., A further discussion of these points is given at the end of Section \ref{sec:discussion}.
 The similarity between the coefficients in equations (39) and (15)) is striking and strongly suggests thatcores., The similarity between the coefficients in equations \ref{eqn:cooling2}) ) and \ref{eqn:heating4}) ) is striking and strongly suggests that.
 However. it is not enough simply to find a heating source capable of balancing cooling.," However, it is not enough simply to find a heating source capable of balancing cooling."
 One must also ensure that the resulting equilibrium is thermally stable., One must also ensure that the resulting equilibrium is thermally stable.
 This can be shown for our proposed heating mechanism as follows., This can be shown for our proposed heating mechanism as follows.
 In Fig. |.," In Fig. \ref{fig:stability},"
 we show the rates of parallel viscous heating (solid line) and radiative cooling (dashed line) at fixed magnetic and thermal pressures as a function of temperature., we show the rates of parallel viscous heating (solid line) and radiative cooling (dashed line) at fixed magnetic and thermal pressures as a function of temperature.
 The thermal equilibrium point where heating balances cooling is denoted by a black dot., The thermal equilibrium point where heating balances cooling is denoted by a black dot.
" The cooling rate (dashed line) scales as Z""7 in the Bremsstrahlung regime. while the parallel viscous heating rate (solid line) scales us 7""7."," The cooling rate (dashed line) scales as $T^{-3/2}$ in the Bremsstrahlung regime, while the parallel viscous heating rate (solid line) scales as $T^{-5/2}$."
 Hence. if the temperature is perturbed downwards. the heating rate increases faster than the rate of radiative cooling. and net heating restores the temperature to its equilibrium value.," Hence, if the temperature is perturbed downwards, the heating rate increases faster than the rate of radiative cooling, and net heating restores the temperature to its equilibrium value."
 On the other hand. if the temperature is perturbed upwards. the heating rate decreases faster than the rate of radiative cooling. and net cooling restores the temperature to its equilibrium value.," On the other hand, if the temperature is perturbed upwards, the heating rate decreases faster than the rate of radiative cooling, and net cooling restores the temperature to its equilibrium value."
 In other words.stable.," In other words,."
 This is in stark contrast to a thermal balance between radiative cooling and thermal conduction (dotted line). whose heating rate scales as 27/7 at fixed thermal pressure.," This is in stark contrast to a thermal balance between radiative cooling and thermal conduction (dotted line), whose heating rate scales as $T^{7/2}$ at fixed thermal pressure."
 The resulting equilibrium is unstable. with an isobaric perturbation resulting in either an isothermal temperature profile (e.g. see tig.," The resulting equilibrium is unstable, with an isobaric perturbation resulting in either an isothermal temperature profile (e.g. see fig."
 7 of Parrish.Quataert& 20093) or a cooling catastrophe., 7 of \citealt{pqs09}) ) or a cooling catastrophe.
 Thus. Spitzer conduction by itself cannot balance radiative cooling in a stable way (e.g. 2003b)..," Thus, Spitzer conduction by itself cannot balance radiative cooling in a stable way \citep[e.g.][]{bd88,soker03,kn03b}. ."
CDDF in the form δι) with 3z1.5 i| the cohunn density range NapΊου. Αι 20.,CDDF in the form $f(N_{\rm HI})\propto N_{\rm HI}^{-\beta}$ with $\beta\approx 1.5$ in the column density range log $N$ $)=18-20$ .
 Theslopeiscerysiinilartothooncdericcd forthe M illegMay ηνοκ ayortdbieio dang οτο gooda green FtQSOI iabsorption linesystems(scecSeet. 55.1)., The slope is very similar to the one derived for the Milky Way HVCs (Lockman et 2002; previous subsection) and is in good agreement with values derived for low-redshift QSO absorption-line systems (see 5.1).
 To combine the observatioual iuformation on the UVC population of the Milky Wav and ABL we have developed the custoun-written mmucrical codehalopath. which is based on a simple geometrical model assuming spherical syauinetry.," To combine the observational information on the HVC population of the Milky Way and M31 we have developed the custom-written numerical code, which is based on a simple geometrical model assuming spherical symmetry."
" The code allows us to model the radial distribution of eas iu the halos of galaxies, its nass distribution and its absorption-cross section frou any given vautage point inside aud outside the sphere."," The code allows us to model the radial distribution of gas in the halos of galaxies, its mass distribution and its absorption-cross section from any given vantage point inside and outside the sphere."
 Because of the wiknown size distribution of IIVCs we rere do no attempt to model individualclouds as UVC analogs. but instead cousider the volume-fllius neutral actorgas as main input parameter. from which all relevantof physical quantities (c.¢.. projected covering raction. column density. mass) can be easily obtained aud compared to observations.," Because of the unknown size distribution of HVCs we here do no attempt to model individual as HVC analogs, but instead consider the volume-filling factor of neutral gas as main input parameter, from which all relevant physical quantities (e.g., projected covering fraction, column density, mass) can be easily obtained and compared to observations."
 To support the model with the uecessary observational data. we assunie that the IVC populations of the Mille Wavy and MBL are identical in a statistical sense (same radial distribution aud same voluue filling factor of gas with log N(IEE 17.5).," To support the model with the necessary observational data, we assume that the HVC populations of the Milky Way and M31 are identical in a statistical sense (same radial distribution and same volume filling factor of gas with log $N$ $)\geq 17.5$ )."
 In view of the similarity of both ealaxies in terms of morphology. mass. bhuuinositw. etc.," In view of the similarity of both galaxies in terms of morphology, mass, luminosity, etc."
 his asstuuption is justified., this assumption is justified.
" As mentioned above. the sev parameter that describes the spatial cistribution of IIVCSs in our spherical model is the radius-depeudeut volunue-füllüug factor of optically thick IWC gas with os N(I 17.5. favet). whore Ris the physical radius (compared to the projected radius 7),"," As mentioned above, the key parameter that describes the spatial distribution of HVCs in our spherical model is the radius-dependent volume-filling factor of optically thick HVC gas with log $N$ $)\geq 17.5$, $f_{\rm v,HVC}(R)$, where $R$ is the physical radius (compared to the projected radius $r$ )."
 Because the mojected (area) covering fraction of IIVCs in the M21 wo can be described by an expoucutial (see above). we assunie that feave(R) follows au expoueutial. too. so hat we write: Tn this equation. fy is the volunc-fBliiug factor iu the ceuter of the sphere aud Pp: is the scale height df dis TSC ca," Because the projected (area) covering fraction of HVCs in the M31 halo can be described by an exponential (see above), we assume that $f_{\rm v,HVC}(R)$ follows an exponential, too, so that we write: In this equation, $f_{\rm v,0}$ is the volume-filling factor in the center of the sphere and $h_{\rm HVC}$ is the scale height of the HVC population."
ste cr in our model is the mean volume density Gry) iu the VC eas. as Gay) together with [νοο) deteruuiucs the neutral gas mass m VCS per radialt) bin (= radial volume element). Mintr)=Gui)jm. with mp as hywdrogeu mass aud jasfeaivet a factor that corrects for the presence of helium aud heavy eleiieuts in the eas.," Another important parameter in our model is the mean volume density $\langle n_{\rm HI}\rangle$ in the HVC gas, as $\langle n_{\rm HI}\rangle$ together with $f_{\rm v,HVC}(R)$ determines the neutral gas mass in HVCs per radial bin (= radial volume element), $M_{\rm HI}(r)=f_{\rm v,HVC}(R)\,\langle n_{\rm HI}\rangle\,\mu m_{\rm H}$, with $m_{\rm H}$ as hydrogen mass and $\mu$ as a factor that corrects for the presence of helium and heavy elements in the gas."
 Iu addition. Gay) deteziiues the mean column density. CN(ID). measured along any given line of sight through the halo. since. CVT) =tog?d. where dis the absorption-path length through the halo.," In addition, $\langle n_{\rm HI}\rangle$ determines the mean column density, $\langle 
N$ $\rangle$, measured along any given line of sight through the halo, since $\langle N$ $)\rangle=\langle 
n_{\rm HI}\rangle\,d$, where $d$ is the absorption-path length through the halo."
 The parameters CV(IEIJ)? aud Gia) ave coustrained by 210 observations aud ionization models of Galactic IVCs aud IIVCs., The parameters $\langle N$ $\rangle$ and $\langle n_{\rm HI}\rangle$ are constrained by 21cm observations and ionization models of Galactic IVCs and HVCs.
 Note that in this study we donof model the gas physics in the halo clouds. but consider ouly the spatial distribution of neutral halo gas. its column deusity distribution. its total mass. aud its infall rate.," Note that in this study we do model the gas physics in the halo clouds, but consider only the spatial distribution of neutral halo gas, its column density distribution, its total mass, and its infall rate."
" To model the sky covering faction of neutral gas from a vantage point the sphere (ie. to model the xojected neutral gas distribution iu the Milkv Way halo roni the position of the sun) we introduce additional coustraiuts based on results froii 210i observations of IVCs and ΗΧΟ,"," To model the sky covering fraction of neutral gas from a vantage point the sphere (i.e., to model the projected neutral gas distribution in the Milky Way halo from the position of the sun) we introduce additional constraints based on results from 21cm observations of IVCs and HVCs."
 First. we only consider gas as neutral iio gas if it is located at vertical distances +2GOO pe roni the midplane of the disk (whose oricutation can be chosen 3i the model).," First, we only consider gas as neutral halo gas if it is located at vertical distances $z>600$ pc from the midplane of the disk (whose orientation can be chosen in the model)."
 Second. we separate neutral halo eas close to the disk (sinall z-licights) from more distaut udo clouds via the parameter tive.," Second, we separate neutral halo gas close to the disk (small $z$ -heights) from more distant halo clouds via the parameter $z_{\rm IVC}$."
 This parameter enables us to distinguish between IVCs (2x inc) and TIVCs (20 tive)., This parameter enables us to distinguish between IVCs $z\leq z_{\rm IVC}$ ) and HVCs $z> z_{\rm IVC}$ ).
" Finally, the parameter cua defines the iufall velocity of the neutral halo gas: eig can be a function of Jf i. or be chosen fo be constaut for IN aud ITVC.or respectively"," Finally, the parameter $v_{\rm infall}$ defines the infall velocity of the neutral halo gas; $v_{\rm infall}$ can be a function of $R$ or $z$, or can be chosen to be constant for IVCs and HVCs, respectively."
",CRM neutral gas Gass) accretionCs rate per radial bin then is Thegiven by AM)dt—Mite)με/1."," The neutral gas (mass) accretion rate per radial bin then is given by $dM_{\rm HI}(r)/dt=M_{\rm HI}(r)\,v_{\rm infall}/r$."
 Using our geometrical model we are able reproduce the observed properties of the IVC population of the, Using our geometrical model we are able reproduce the observed properties of the HVC population of the
emitted lines are broader (han the absorption lines.,emitted lines are broader than the absorption lines.
 This leads to an absorption feature in the middle of an emission line which can sometimes cause apparent splitting of the line (e.g. the line at 1095.13 + in Figure 9))., This leads to an absorption feature in the middle of an emission line which can sometimes cause apparent splitting of the line (e.g. the line at 1095.13 $^{-1}$ in Figure \ref{fig9}) ).
 To solve this problem. we have processed each line list and inserted. HITRAN lines with intensities greater than 1xLO77 em/molecule al that temperature. denoted by “LID in the line lists.," To solve this problem, we have processed each line list and inserted HITRAN lines with intensities greater than $1\times10^{-22}$ cm/molecule at that temperature, denoted by `1H' in the line lists."
 We also simultaneously. removed (he emission lines showing this splitting effect. and also any. lines which are within -Ε0 005 L of each ILETRAN line with an intensity greater than 1x107? em/molecule.," We also simultaneously removed the emission lines showing this splitting effect, and also any lines which are within $\pm$ 0.005 $^{-1}$ of each HITRAN line with an intensity greater than $1\times10^{-22}$ cm/molecule."
 Our line lists therefore provide a complete representation of NIL; between 740 2100 ! at temperatures between 300 9 1370°C. A useful cheek for the quality of the calibratecl intensities determined between 740 2100 ! can be verified by an intensity sum comparison with the temperature scaled IIIETRAN intensities (Nassar&Ber, Our line lists therefore provide a complete representation of $_{3}$ between 740 – 2100 $^{-1}$ at temperatures between 300 – $^{\circ}$ C. A useful check for the quality of the calibrated intensities determined between 740 – 2100 $^{-1}$ can be verified by an intensity sum comparison with the temperature scaled HITRAN intensities \citep{nassar03}.
nath2003).. AC 300°C. the sum of the intensities in our linelist is only greater than the sum of the intensity scaled HITRAN lines but as the temperature increases we continue to exceed the HITRAN total intensity with a maximum ol greater al L200°C (Table 8)).," At $^{\circ}$ C, the sum of the intensities in our linelist is only greater than the sum of the intensity scaled HITRAN lines but as the temperature increases we continue to exceed the HITRAN total intensity with a maximum of greater at $^{\circ}$ C (Table \ref{tab8}) )."
 We attribute our larger values to an increase in the number of hot band lines present in the spectrum., We attribute our larger values to an increase in the number of hot band lines present in the spectrum.
 These hot Hines only have a small contribution at ‘low’ temperatures (800°C) but are more significant lor higher temperatures (> 1000*C*) as hot transitions become more favorable., These hot lines only have a small contribution at `low' temperatures $^{\circ}$ C) but are more significant for higher temperatures $>1000^{\circ}$ C) as hot transitions become more favorable.
 Indeed. (his comes as no surprise because the HEPRAN database consists mainly of fundamental transitions and highlights how our line lists are more suitable for astroplvsical applications.," Indeed, this comes as no surprise because the HITRAN database consists mainly of fundamental transitions and highlights how our line lists are more suitable for astrophysical applications."
It is well known that galaxies reside in environments that span a wide range of galaxy densities (number of galaxies per Mpe*).,It is well known that galaxies reside in environments that span a wide range of galaxy densities (number of galaxies per $^3$ ).
 Many authors have shown that galaxy density plays an important role in determining many galaxy properties. such as star formation rate. rest-frame colours. gas content and morphology (see. e.g.. Dressler1980:Kauffmannetal.2004:Baldry2006:Elli-sonetal. 2009).," Many authors have shown that galaxy density plays an important role in determining many galaxy properties, such as star formation rate, rest-frame colours, gas content and morphology (see, e.g., \citealt{dressler80, kauffmann04,baldry06,ellison09}) )."
 Hence. if we wish to understand the physical processes that drive galaxy evolution. we have to test for systematic differences between galaxies in various environments.," Hence, if we wish to understand the physical processes that drive galaxy evolution, we have to test for systematic differences between galaxies in various environments."
 In addition. it is equally well known hat galaxies are characterized by a wide range of total stellar masses.," In addition, it is equally well known that galaxies are characterized by a wide range of total stellar masses."
 Several works have shown that mass is a crucial parameter in driving galaxy evolution and have claimed that in some cases mass plays a more important role than the environment in influencing galaxy properties (see e.g. Pengetal.2010:Grützbauch201 La»).," Several works have shown that mass is a crucial parameter in driving galaxy evolution and have claimed that in some cases mass plays a more important role than the environment in influencing galaxy properties (see e.g. \citealt{peng10,ruth11a}) )."
 We note that to fully characterize the importance of the mass. it would be very interesting and important to have the total galaxy mass (dark+luminous). but that is observationally challenging to achieve.," We note that to fully characterize the importance of the mass, it would be very interesting and important to have the total galaxy mass (dark+luminous), but that is observationally challenging to achieve."
 Hence. all of the cited studies in this paper invetigate only the galaxy stellar mass. as tracer of the luminous galaxy matter.," Hence, all of the cited studies in this paper invetigate only the galaxy stellar mass, as tracer of the luminous galaxy matter."
 Among others. Kauffmannetal.(2004) have shown that at low-z. at fixed stellar mass. there is nearly no dependence of structural properties like Sersic index or concentration parameter on local galaxy density.," Among others, \cite{kauffmann04} have shown that at low-z, at fixed stellar mass, there is nearly no dependence of structural properties like Sersic index or concentration parameter on local galaxy density."
 Baldryetal.(2006) have found that the colour-mass and colour-concentration index relations do not depend strongly on environment. while the fraction of galaxies on the red sequence depends strongly on both stellar mass and environment.," \cite{baldry06} have found that the colour-mass and colour-concentration index relations do not depend strongly on environment, while the fraction of galaxies on the red sequence depends strongly on both stellar mass and environment."
 Mouhcineetal.(2007) have found no dependence of the relationship between galaxy stellar mass and. gas-phase oxygen abundance on local galaxy density., \cite{mouhcine07} have found no dependence of the relationship between galaxy stellar mass and gas-phase oxygen abundance on local galaxy density.
 At higher redshifts in ZCOSMOS. Scodeggioetal.(2009). observed a significant mass and optical colour segregation. in the sense that the median value of the mass distribution is larger and the rest-frame optical colour is redder in regions of high galaxy density.," At higher redshifts in zCOSMOS, \cite{scodeggio09} observed a significant mass and optical colour segregation, in the sense that the median value of the mass distribution is larger and the rest-frame optical colour is redder in regions of high galaxy density."
 However. considering only galaxies in a narrow range of stellar mass. they no longer observed any significant colour segregation with density.," However, considering only galaxies in a narrow range of stellar mass, they no longer observed any significant colour segregation with density."
"evolve, the convective envelope expands and the acoustic oscillation modes (p modes) decrease in frequency.","evolve, the convective envelope expands and the acoustic oscillation modes $p$ modes) decrease in frequency."
" At the same time, g-mode oscillations that exist in the core of the star increase in frequency as the core becomes more centrally condensed."," At the same time, $g$ -mode oscillations that exist in the core of the star increase in frequency as the core becomes more centrally condensed."
" Eventually, p- and g-mode frequencies overlap, resulting in oscillation modes that have a mixed character, behaving like g modes in the core and p modes in the envelope."," Eventually, $p$ - and $g$ -mode frequencies overlap, resulting in oscillation modes that have a mixed character, behaving like $g$ modes in the core and $p$ modes in the envelope."
" The frequencies of these modes are shifted as they undergo avoided crossings 1975;Aizenmanetal.1977),, which leads to (Osakisignificant deviations from the asymptotic relation, equation (1))."," The frequencies of these modes are shifted as they undergo avoided crossings \citep{Osaki75, Aizenman77}, which leads to significant deviations from the asymptotic relation, equation \ref{asymp}) )."
" This so-called mode bumping only affects non-radial modes, particularly J=1 but also [—2, and so it complicates the measurement of the small separations."," This so-called mode bumping only affects non-radial modes, particularly $l$ =1 but also $l$ =2, and so it complicates the measurement of the small separations."
" Nevertheless, as we show, it is still possible to measure average separations that can be plotted in the C-D diagram."," Nevertheless, as we show, it is still possible to measure average separations that can be plotted in the C-D diagram."
 In this paper we also discuss an asteroseismic diagram that uses the quantity ε (Section ??))., In this paper we also discuss an asteroseismic diagram that uses the quantity $\epsilon$ (Section \ref{Epsilon}) ).
" Despite being investigated by Christensen-Dalsgaard(1984),, this dimensionless phase offset has since been largely overlooked for its diagnostic potential."," Despite being investigated by \citet{C-D84}, this dimensionless phase offset has since been largely overlooked for its diagnostic potential."
" Recently, Bedding&Kjeldsen(2010) suggested that it could be useful in distinguishing odd and even modes when their identifications are ambiguous due to short mode lifetimes (see,e.g.,Appourchauxetal.2008;Benomar 2010b).."," Recently, \citet{Bedding10b} suggested that it could be useful in distinguishing odd and even modes when their identifications are ambiguous due to short mode lifetimes \citep[see, e.g.,][]{Appourchaux08,Benomar09,Bedding10}. ."
" UsingKepler data, Huberetal.(2010) have found that e and Av are related in red giants, implying that, like Av, e is a function of fundamental parameters."," Using data, \citet{Huber10} have found that $\epsilon$ and $\Delta\nu$ are related in red giants, implying that, like $\Delta\nu$ , $\epsilon$ is a function of fundamental parameters."
 A similar analysis was done forCoRoT data by Mosseretal.(2011b)., A similar analysis was done for data by \citet{Mosser11}.
. We discuss the use of ε for mode identification in Section ??.., We discuss the use of $\epsilon$ for mode identification in Section \ref{modeID}.
" Finally, we discuss an asteroseismic diagram for red-giant stars."," Finally, we discuss an asteroseismic diagram for red-giant stars."
 A recent breakthrough has been made with the discovery of sequences of mixed modes inKepler red giants (Becketal.2011)., A recent breakthrough has been made with the discovery of sequences of mixed modes in red giants \citep{Beck11}.
". Because these mixed modes exhibit g-mode behavior in the core of the star, they are particularly sensitive to the core structure."," Because these mixed modes exhibit $g$ -mode behavior in the core of the star, they are particularly sensitive to the core structure."
" Subsequently, Beddingetal.(2011) used the observed period spacings of these mixed modes, APy, to distinguish between red giants that are burning helium in their core and those that are still only burning hydrogen in a shell."," Subsequently, \citet{Bedding11} used the observed period spacings of these mixed modes, $\Delta P_\mathrm{obs}$, to distinguish between red giants that are burning helium in their core and those that are still only burning hydrogen in a shell."
 Mosseretal.(20118) have found similar results inCoRoT red giants., \citet{Mosser11b} have found similar results in red giants.
" In Section ?? we present the expected evolution of AP,y, with Av in an asteroseismic diagram for red giant stars.", In Section \ref{Gperiod} we present the expected evolution of $\Delta P_\mathrm{obs}$ with $\Delta\nu$ in an asteroseismic diagram for red giant stars.
 A grid of 51000 stellar models was calculated from the ZAMS to almost the tip of the red-giant branch using (Christensen-Dalsgaard2008a) with the EFF equation of state (Eggletonetal.1973)., A grid of 51000 stellar models was calculated from the ZAMS to almost the tip of the red-giant branch using \citep{C-D08a} with the EFF equation of state \citep{Eggleton73}.
". We used the opacity tables of Rogers&Iglesias(1995) and Kurucz for T« 10*KK, with the solar mixture of Grevesse& (1993)."," We used the opacity tables of \citet{RogersIglesias95}
 and \citet{Kurucz91} for $T<10^4$ K, with the solar mixture of \citet{GrevesseNoels93}."
". Rotation, overshooting and diffusion were not included."," Rotation, overshooting and diffusion were not included."
 The grid was created with fixed values of the mixing-length parameter (a= 1.8) and the initial hydrogen abundance (.X;— 0.7)., The grid was created with fixed values of the mixing-length parameter $\alpha=1.8$ ) and the initial hydrogen abundance $X_{\mathrm{i}}=0.7$ ).
 The grid covered masses in the range 0.7 to 2.4Mo with a resolution of 0.01Mo and metallicities in the range 0.011<Z0.028 with a resolution in log(Z/X) of 0.2 dex.," The grid covered masses in the range 0.7 to $2.4\,\mathrm{M}_\odot$ with a resolution of $0.01\,\mathrm{M}_\odot$ and metallicities in the range $0.011\leq Z\leq 0.028$ with a resolution in $\log (Z/X)$ of 0.2 dex."
 Figure 1 shows the H-R diagram for models of near-solar metallicity (Zo= for masses from 0.7 to 2.0M5.," Figure \ref{fig1} shows the H-R diagram for models of near-solar metallicity $Z_0=0.017$ ) for masses from 0.7 to $2.0\,\mathrm{M}_\odot$."
 Models that are 0.017)hotter than the approximate cool edge of the classical instability strip (Saio&Gautschy1998) are colored gray; they are not expected to show solar-like oscillations because they do not have a significant convective envelope.," Models that are hotter than the approximate cool edge of the classical instability strip \citep{Saio98}
 are colored gray; they are not expected to show solar-like oscillations because they do not have a significant convective envelope."
" Many of these stars will show classical pulsations as 6 Scuti, y Dor or roAp stars."," Many of these stars will show classical pulsations as $\delta$ Scuti, $\gamma$ Dor or roAp stars."
" However, we do note that Antocietal.(2011) announced evidence for solar-like oscillations in a 6 Scuti star."," However, we do note that \citet{Antoci11} announced evidence for solar-like oscillations in a $\delta$ Scuti star."
" The model parameters chosen, and the physics included in the models, do have an impact on the model frequencies obtained."," The model parameters chosen, and the physics included in the models, do have an impact on the model frequencies obtained."
" Several studies have already investigated the impact of the choice of these parameters, including composition, mixing, overshooting and diffusion (e.g.Monteiroetal.2002;Mazumdar2005;Gaietal. 2009),, so we have not investigated the breadth of this parameter space with our model grid."," Several studies have already investigated the impact of the choice of these parameters, including composition, mixing, overshooting and diffusion \citep[e.g.][]{Monteiro02,Mazumdar05,Gai09}, so we have not investigated the breadth of this parameter space with our model grid."
" Our aim is to investigate the bulk behavior of asteroseismic observables across a wide range of evolutionary states, from the ZAMS to the tip of the RGB."," Our aim is to investigate the bulk behavior of asteroseismic observables across a wide range of evolutionary states, from the ZAMS to the tip of the RGB."
" The adiabatic frequencies of every model were calculated using (Christensen-Dalsgaard 2008b),, adjusted to enable proper sampling of the extremely high order eigenmodes that occur in red giants."," The adiabatic frequencies of every model were calculated using \citep{C-D08b}, adjusted to enable proper sampling of the extremely high order eigenmodes that occur in red giants."
 Oscillation frequencies determined from stellar models include more modesthancan be observed., Oscillation frequencies determined from stellar models include more modesthancan be observed.
 It is therefore necessary to determine asteroseismic parameters from them with care so that they are directly comparable to the parameters measured from data., It is therefore necessary to determine asteroseismic parameters from them with care so that they are directly comparable to the parameters measured from data.
 Here we outline our approach., Here we outline our approach.
" It is important that we treat the frequencies from models and data the same, as much as possible, so"," It is important that we treat the frequencies from models and data the same, as much as possible, so"
Lt is now widely accepted that the centre of everymediumtolarge galaxy contains a supermassive black hole (SML.,It is now widely accepted that the centre of everymedium--to--large galaxy contains a supermassive black hole (SMBH).
 The mass AZ of this SML is observed to correlate strongly with properties of the host galaxy in two wavs., The mass $M$ of this SMBH is observed to correlate strongly with properties of the host galaxy in two ways.
 First ds the correlation with the stellar velocity dispersion σ of the galaxy bulge. (cL.Forrarese&Alerritt2000:Gebhardtetal.2000).. where toy=7/200kms+.," First is the correlation with the stellar velocity dispersion $\sigma$ of the galaxy bulge, \citep[cf.][]{2000ApJ...539L...9F,2000ApJ...539L..13G}, where $\sigma_{200} = \sigma/200~{\rm km\,s^{-1}}$."
" Second is the correlation with bulge stellar mass Ad, (cL.Lavine&Rix2004)..", Second is the correlation with bulge stellar mass $M_b$ \citep[cf. ][]{2004ApJ...604L..89H}.
 The first of these relations (1)) is considerably tighter than the second (2)). but both are uehly significant statistically.," The first of these relations \ref{msigobs}) ) is considerably tighter than the second \ref{mm}) ), but both are highly significant statistically."
 The existence of these relations strongly suggests a connection between the growth of the SAIBIL anc of its lost galaxy. despite the huge disparity in their masses.," The existence of these relations strongly suggests a connection between the growth of the SMBH and of its host galaxy, despite the huge disparity in their masses."
" The uncderlving reason is evidentlv that the aceretion energy Ey—GuMO released in building the SMIBIL Gvhere cree~ lids the energy cllicieney of accretion) greatly. exceeds the xnding energy of the bulge ££,~Mo by a factor Thus absorption of even a small fraction of the accretion energv released by the SAIBIL must. significantly: allect the bulge (sing2003).."," The underlying reason is evidently that the accretion energy $E_h = \epsilon_{\rm acc} Mc^2$ released in building the SMBH (where $\epsilon_{\rm acc} \sim 0.1$ is the energy efficiency of accretion) greatly exceeds the binding energy of the bulge $E_b \sim 
M_b\sigma^2$ by a factor Thus absorption of even a small fraction of the accretion energy released by the SMBH must significantly affect the bulge \citep{2003ApJ...596L..27K}."
 This suggests that the process connecting SAIBL growth and galaxy growth is some kind of feedback from the SAIBLL., This suggests that the process connecting SMBH growth and galaxy growth is some kind of feedback from the SMBH.
 Because galaxies are gencrally optically thin this feedback must. be mechanical. ancl so presumably involves matter expelled during the accretion process.," Because galaxies are generally optically thin this feedback must be mechanical, and so presumably involves matter expelled during the accretion process."
 This in turn strongly suggests that [eecdback is a consequence of superExddington accretion., This in turn strongly suggests that feedback is a consequence of super–Eddington accretion.
 This is plausible because the Soltan(1982). relation linking the growth of SAIBIs to luminous accretion. and the low observed fraction of active galaxies among all galaxies (e.g.Lleckmanctal. 2004).. together require that most SMDBIL growth occurs in such phases.," This is plausible because the \citet{1982MNRAS.200..115S} relation linking the growth of SMBHs to luminous accretion, and the low observed fraction of active galaxies among all galaxies \citep[e.g.][]{2004ApJ...613..109H}, , together require that most SMBH growth occurs in such phases."
 The remaining obstacle to explaining the Mygσ relation (1)) is the very inellicient. mechanical coupling of accretion enerev implied. by (3))., The remaining obstacle to explaining the $M_{\rm BH} - \sigma$ relation \ref{msigobs}) ) is the very inefficient mechanical coupling of accretion energy implied by \ref{bind}) ).
" Phis explains why the proposal by Silk&Rees(1998).. that a significant fraction ofa SMDBLIUSs Edclington energy rate (where # is the Thomson opacity) is deposited as feedback into the surrounding galaxy. implies SALBLLE masses of order only ~105LOA. rather than ~LO""AL. for a typical ealaxy (el.Wine—9010)."," This explains why the proposal by \citet{1998A&A...331L...1S}, that a significant fraction of a SMBH's Eddington energy rate (where $\kappa$ is the Thomson opacity) is deposited as feedback into the surrounding galaxy, implies SMBH masses of order only $\sim 10^4 - 10^5\msun$ rather than $\sim 10^8\msun$ for a typical galaxy \citep[cf.][]{2010MNRAS.402.1516K}."
" Instead. two further features. of the problem imply a theoretical relation. very close to the observed one (1)). where f,20.16is the barvon fraction relative to dark matter (cf.Wine2003. 2005).."," Instead, two further features of the problem imply a theoretical relation very close to the observed one \ref{msigobs}) ), where $f_g \simeq 0.16$is the baryon fraction relative to dark matter \citep[cf.][]{2003ApJ...596L..27K,2005ApJ...635L.121K}. ."
 These new features are (a), These new features are (a)
"binary stars undetected by UKIDSS, and sources affected by diffraction spikes, lie in the upper-right quadrant of the plot, indicating that UKIDSS indeed detected them as single, extended objects.","binary stars undetected by UKIDSS, and sources affected by diffraction spikes, lie in the upper-right quadrant of the plot, indicating that UKIDSS indeed detected them as single, extended objects."
 The five sources far off the diagonal have contradictory data in the different bands., The five sources far off the diagonal have contradictory data in the different bands.
" Whether due to noise or inherent source properties, such data will confuse any classifier."," Whether due to noise or inherent source properties, such data will confuse any classifier."
" Comparing our classifier and the UKIDSS pipeline to the Stripe 82 data, shows the mismatch rates of both classifiers, taking the SDSS r-band classifications as a reference."," Comparing our classifier and the UKIDSS pipeline to the Stripe 82 data, shows the mismatch rates of both classifiers, taking the SDSS $r$ -band classifications as a reference."
" To do this we have converted the posterior probabilities into class labels; an object is labelled as a star if P,>0.5, otherwise as a galaxy."," To do this we have converted the posterior probabilities into class labels; an object is labelled as a star if $\ps\geq0.5$, otherwise as a galaxy."
 We have limited the sources to those with 16«r20.5 so as to avoid saturated sources (r< 16) and sources for which the uncertainty of the SDSS labels is non-negligible (r= 20.5)., We have limited the sources to those with $16<r<20.5$ so as to avoid saturated sources $r\la16$ ) and sources for which the uncertainty of the SDSS labels is non-negligible $r\ga20.5$ ).
 It is clear that the Bayesian classifier is more accurate than the UKIDSS pipeline classifier; even though the difference in performance decreases for fainter magnitudes., It is clear that the Bayesian classifier is more accurate than the UKIDSS pipeline classifier; even though the difference in performance decreases for fainter magnitudes.
" For sources with 16.6<Y17.4, our classifier achieves amismatch rate of 0.0154, compared to 0.0314 for the UKIDSS pipeline."," For sources with $16.6\leq Y < 17.4$, our classifier achieves amismatch rate of $0.0154$, compared to $0.0314$ for the UKIDSS pipeline."
" At the faint end (Y> 20), the mismatch rates are 0.0679 (our classifier) and 0.0751 (UKIDSS pipeline)."," At the faint end $Y>20$ ), the mismatch rates are $0.0679$ (our classifier) and $0.0751$ (UKIDSS pipeline)."
" For all sources with 16«r20.5, the mismatch rate for the UKIDSS pipeline (0.0440) is more than double that of our classifier (0.0218)."," For all sources with $16<r<20.5$, the mismatch rate for the UKIDSS pipeline $0.0440$ ) is more than double that of our classifier $0.0218$ )."
" The good performance of both the UKIDSS pipeline classifier and our method over the entire sample is unsurprising, as most sources are detected with a sufficient signal-to-noise ratio that they can be classified without effort."," The good performance of both the UKIDSS pipeline classifier and our method over the entire sample is unsurprising, as most sources are detected with a sufficient signal–to–noise ratio that they can be classified without effort."
 However it is often the case that that the most important sources scientifically are those close to any new survey's detection limit — these objects would not have been detected by shallower surveys in the same band(s) and inevitably dominate the new discoveries from a given data-set., However it is often the case that that the most important sources scientifically are those close to any new survey's detection limit – these objects would not have been detected by shallower surveys in the same band(s) and inevitably dominate the new discoveries from a given data-set.
 Hence the inclusion of prior information in the Bayesian classifier is most important for just these sources where it results in significant numbers of more accurate classifications., Hence the inclusion of prior information in the Bayesian classifier is most important for just these sources where it results in significant numbers of more accurate classifications.
" Our method provides realistic estimates of the classification uncertainties and allows users, by setting constraints on the posterior classification probabilities Pi, to specify the completeness (the fraction of target class sources that have actually been selected) and contamination (the fraction of the selected sources which are not from the target class) of a given selection before starting observations."," Our method provides realistic estimates of the classification uncertainties and allows users, by setting constraints on the posterior classification probabilities $\ps$, to specify the completeness (the fraction of target class sources that have actually been selected) and contamination (the fraction of the selected sources which are not from the target class) of a given selection before starting observations."
 Thus users can design the selection to suit the survey's aims., Thus users can design the selection to suit the survey's aims.
 A practical application of our method would be to look at the amount of telescope time that would be required to follow-up a morphologically-selected sample of targets., A practical application of our method would be to look at the amount of telescope time that would be required to follow-up a morphologically-selected sample of targets.
" If one imagines a spectroscopic survey of faint stars, and one was to trust sseparators such as the ones used by UKIDSS or SDSS versus selecting sources with P;>0.9 from our method, then a certain proportion of telescope time would be spent observing compact / faint galaxies that were misclassified."," If one imagines a spectroscopic survey of faint stars, and one was to trust separators such as the ones used by UKIDSS or SDSS versus selecting sources with $\ps>0.9$ from our method, then a certain proportion of telescope time would be spent observing compact / faint galaxies that were misclassified."
" While there will certainly also be misclassified sources when selecting objects by basing the selection on P, their proportion can be greatly reduced."," While there will certainly also be misclassified sources when selecting objects by basing the selection on $\ps$, their proportion can be greatly reduced."
 Obviously there is a trade-off between completeness and efficiency when performing source selection., Obviously there is a trade-off between completeness and efficiency when performing source selection.
" lists, for different fluxes, both completeness and efficiency (the fraction of the selected sources which are actually of the target class) for different methods of selecting faint stars, namely selecting sources with P,>0.9 or P,>0.5, using the UKIDSS pipeline single-band or merged class labels, or selecting sources for whichthe UKIDSS pipeline posterior star probability exceeds 0.9."," lists, for different fluxes, both completeness and efficiency (the fraction of the selected sources which are actually of the target class) for different methods of selecting faint stars, namely selecting sources with $\ps>0.9$ or $\ps>0.5$, using the UKIDSS pipeline single-band or merged class labels, or selecting sources for whichthe UKIDSS pipeline posterior star probability exceeds $0.9$ ."
" While the efficiencies of the different methods are comparable for Y~17 and Y~ 18,"," While the efficiencies of the different methods are comparable for $Y\simeq17$ and $Y\simeq18$ ,"
theAepler blue stvagelers will provide empirical insight into the contribution of ordinary binary evolution to the creation of blue stragglers.,the blue stragglers will provide empirical insight into the contribution of ordinary binary evolution to the creation of blue stragglers.
 This will allow the contribution of stellar interactions in clusters to be better understood. since both primordial binaries ancl binaries formed or altered through interactions can produce blue stragelers.," This will allow the contribution of stellar interactions in clusters to be better understood, since both primordial binaries and binaries formed or altered through interactions can produce blue stragglers."
 Finally. (he white-clwarl/main-sequence binaries studied byAepler will experience a second phase of interaction when (he main-sequence star of today evolves anc begins to transfer matter to the white dwarf.," Finally, the white-dwarf/main-sequence binaries studied by will experience a second phase of interaction when the main-sequence star of today evolves and begins to transfer matter to the white dwarf."
 These svstems will be novae. some may become that eventually merge. and some may even experience Type la supernovae. or acerelion-induced collapse. through either the single-clegenerate or double-degenerate channel.," These systems will be novae, some may become double-degenerates that eventually merge, and some may even experience Type Ia supernovae, or accretion-induced collapse, through either the single-degenerate or double-degenerate channel."
Aepler will iclentily a set of these svstems (hat can be studied in a unique way., will identify a set of these systems that can be studied in a unique way.
 The primary goal of (heKepler mission is to search for terrestrial planets orbiting stus. especially in the zone of habitabilitv.," The primary goal of the mission is to search for terrestrial planets orbiting sun-like stars, especially in the zone of habitability."
 We do not vel know how common such planets are., We do not yet know how common such planets are.
 The results described in 83 establish. however. that orbiting white dwarls are well represented in theKepler data.," The results described in 3 establish, however, that orbiting white dwarfs are well represented in the data."
 White dwarls have radii similar to planetary radii and. as Figure 3 shows. many are likely to orbit in their host stars zone of habitability.," White dwarfs have radii similar to planetary radii and, as Figure 3 shows, many are likely to orbit in their host star's zone of habitability."
 It is therefore important to be able to distinguish between planets and white dwarts., It is therefore important to be able to distinguish between planets and white dwarfs.
 The discoveries of IKO-T4b and IXOI-31b illustrate that it is possible to identily transiting objects that are candidate white cwarls., The discoveries of KO-74b and KOI-81b illustrate that it is possible to identify transiting objects that are candidate white dwarfs.
 Yet. even though both svstems are likely to be products of mass Gansfer. (he natures of the hot compact objects aud. their evolutionary histories are not vet definitely established.," Yet, even though both systems are likely to be products of mass transfer, the natures of the hot compact objects and their evolutionary histories are not yet definitely established."
 Furthermore. not all white dwarls will be hot and Iuninous enough to produce distinctive eclipses.," Furthermore, not all white dwarfs will be hot and luminous enough to produce distinctive eclipses."
" While dwarls cool with age. ancl ""ultracool white dwarls with temperatures below 5000Hr IX have been discovered (Vidih et 2007: Ilarris et 2008)."," While dwarfs cool with age, and “ultracool” white dwarfs with temperatures below $5000$ K have been discovered (Vidrih et 2007; Harris et 2008)."
 The kev property that is different. for planets and white dwarls. irrespective of age. is (he mass.," The key property that is different for planets and white dwarfs, irrespective of age, is the mass."
 Mass measurements are (herelore of central importance. ideally through radial velocity measurements.," Mass measurements are therefore of central importance, ideally through radial velocity measurements."
 Interestingly enough. this may be difficult to do for some white-dwart blue straggler svstems. because high rates of stellar rotation ean result [rom mass (ransler and complicate the measurements.," Interestingly enough, this may be difficult to do for some white-dwarf blue straggler systems, because high rates of stellar rotation can result from mass transfer and complicate the measurements."
 On the other hand. high rotational velocities may be a signature (hat supports the mass (transfer scenario.," On the other hand, high rotational velocities may be a signature that supports the mass transfer scenario."
 As mentioned in 82. there are preliminary indications that the rotation rates of IXNOI-74a ancl INOI-S1a are high (Latham 2010).," As mentioned in 2, there are preliminary indications that the rotation rates of KOI-74a and KOI-81a are high (Latham 2010)."
 Even if high rates of rotation are rare. the large numbers of interesting svstems discovered bvAepler may make it challenging to obtain radial velocity. measurements for all of them.," Even if high rates of rotation are rare, the large numbers of interesting systems discovered by may make it challenging to obtain radial velocity measurements for all of them."
saluple.,sample.
 Observations covering the 12°. aarea in the TRS were carried out ou the 1.21 UNKST of the Anglo-Australian Observatory (AAO) πι 32005 October/November., Observations covering the $\times$ area in the HRS were carried out on the 1.2m UKST of the Anglo-Australian Observatory (AAO) in 2002 October/November.
 All observations were carried out as part of the 6dE Galaxy Survey (6dFCS) program beiug undertaken bv the AAO (Woulgunatsuetal.2003)., All observations were carried out as part of the 6dF Galaxy Survey (6dFGS) program being undertaken by the AAO \citep{wak03}.
. Specifically. the σαΕς aud our URS program observations were folded together to allow for joiut execution of both programs.," Specifically, the 6dFGS and our HRS program observations were folded together to allow for joint execution of both programs."
 When allocating fibers. the 1500 galaxies in the study were given highest priority within the σαΕς for the selected fields of observation.," When allocating fibers, the 1500 galaxies in the study were given highest priority within the 6dFGS for the selected fields of observation."
 However. whenever a GdF fiber yvecadue unassigned due to a conflict with the fiber selection from another target ealaxy. the fiber was then reassigned to a target from the σα ists.," However, whenever a 6dF fiber became unassigned due to a conflict with the fiber selection from another target galaxy, the fiber was then reassigned to a target from the 6dFGS lists."
 The blue magnitude limit for the 6dFCS is 16.75 Gwe. by< 16.75). hence there is considerable overlap between our target lists and the 6dECS.," The blue magnitude limit for the 6dFGS is 16.75 (i.e., $_J 
<$ 16.75), hence there is considerable overlap between our target lists and the 6dFGS."
 Over all the observed fies. approximately of all targets were taken from our original dist of 1500 ealaxics.," Over all the observed fields, approximately of all targets were taken from our original list of 1500 galaxies."
 Noticeable frou Figure 2.. our observed ealaxy inagnitude distribution closely ollows the maguitude distribution of the post-extraction IRS area of 2818 galaxies.," Noticeable from Figure \ref{f2}, our observed galaxy magnitude distribution closely follows the magnitude distribution of the post-extraction HRS area of 2848 galaxies."
 Duc to the xiehter laniting magnitude of 6dECGS. we have slightly less proportional coverage at our faint iuit.," Due to the brighter limiting magnitude of 6dFGS, we have slightly less proportional coverage at our faint limit."
 In addition. a few very faint objects were included. as part of the GdFCS. which again can vc seen In Figure 2..," In addition, a few very faint objects were included as part of the 6dFGS, which again can be seen in Figure \ref{f2}."
 Finally. a simall uuuber of GdFCGS objects lie within our cexcision radii around clusters. which is evident iu Figure 1..," Finally, a small number of 6dFGS objects lie within our excision radii around clusters, which is evident in Figure \ref{f1}."
 Observations and reductious were carried out along standard 6GdFCS procedures. which are bricily sunnuiuizeda in the next section.," Observations and reductions were carried out along standard 6dFGS procedures, which are briefly summarized in the next section."
 Eieht mehts were allocated to this project by the GdECS toan. but three were adversely affected by weatler (Table 1)).," Eight nights were allocated to this project by the 6dFGS team, but three were adversely affected by weather (Table \ref{tb1}) )."
 We used a combination of the 580V. aud 125BR. voluuc-phase holoeraphiec transiission eratines to optimize spectral coverage., We used a combination of the 580V and 425R volume-phase holographic transmission gratings to optimize spectral coverage.
 This procedure vielded au iustruimeutal resolution of LOA ((580V) and 6.6 (C125BR). while covering the wavelength range 3900 τουςAL. ie. from [OTJA3727 through Πα over the IRS redshift range.," This procedure yielded an instrumental resolution of 4.9 (580V) and 6.6 (425R), while covering the wavelength range 3900 $-$ 7600, i.e., from $\lambda$ 3727 through $\alpha$ over the HRS redshift range."
 Exposure times for cach erating are listed in Table 1.., Exposure times for each grating are listed in Table \ref{tb1}.
 HeCdNe arc aud quartz flat exposures were carried out before and after primary fields., HgCdNe arc and quartz flat exposures were carried out before and after primary fields.
 5[7 usable galaxy spectra were obtained from he cight nights allocated (Table 2))., 547 usable galaxy spectra were obtained from the eight nights allocated (Table \ref{shorttb2}) ).
 In Figure . individual feld ceuters are labeled and shown in reference to the survey area.," In Figure \ref{f1}, individual field centers are labeled and shown in reference to the survey area."
 Altogether. 100 fibers were operational during our sequence of observations.," Altogether, 100 fibers were operational during our sequence of observations."
 With 9 fibers donated to skw. this caves a total of 91 possible galaxy. redshifts per nuaeed field.," With 9 fibers donated to sky, this leaves a total of 91 possible galaxy redshifts per imaged field."
 Night 7 with the 58O0V. erating was rot reduced due to a telescope focus error. so redshifts were obtained for ouly of the 0511 Ποια (Table 1)).," Night 7 with the 580V grating was not reduced due to a telescope focus error, so redshifts were obtained for only of the 0811 field (Table \ref{tb1}) )."
 Although the signal-to-noise ratio was relatively low im many of our spectra (< 10). over vielded reliable redshifts (exchiding 0811).," Although the signal-to-noise ratio was relatively low in many of our spectra $<$ 10), over yielded reliable redshifts (excluding 0811)."
 Due to GdECS priorities aud ealaxy overcrowding. redshifts were obtained for some galaxies nof originally included in ow source lists.," Due to 6dFGS priorities and galaxy overcrowding, redshifts were obtained for some galaxies not originally included in our source lists."
 There remained 3 Galactic stars and 27 objects with nuusable spectra in the sample., There remained 3 Galactic stars and 27 objects with unusable spectra in the sample.
 The automatic GdF data reduction (6DFDR) package completes the following steps directly after observation: debiasing. fiber extraction. οδόταν removal. Hat ficldine. sky subtraction. and waveleugth calibration (Jonesetal.2001).," The automatic 6dF data reduction ) package completes the following steps directly after observation: debiasing, fiber extraction, cosmic-ray removal, flat fielding, sky subtraction, and wavelength calibration \citep{jon04}."
. As a final step. the files from cach exposure were co-added iuto single spectra.," As a final step, the files from each exposure were co-added into single spectra."
 Methods for the deteziinuation of galaxy redshitts fit into three basic categories depending ou their spectral characteristics: absorption. cussion. and those spectra containing both absorption and endssion features.," Methods for the determination of galaxy redshifts fit into three basic categories depending on their spectral characteristics: absorption, emission, and those spectra containing both absorption and emission features."
 For spectra exhibitiug absorption features. the TRAF based cross-correlation package.rvsao. was utilized to determine radial velocities against four template spectra: two stellar spectra obtained from the Coudé Feed spectral library (Jones1999) aud two spectra obtained from the sample (a Calactic star and a nearby galaxy whose redshift was also determined," For spectra exhibiting absorption features, the IRAF based cross-correlation package, was utilized to determine radial velocities against four template spectra: two stellar spectra obtained from the Coudé Feed spectral library \citep{jon99} and two spectra obtained from the sample (a Galactic star and a nearby galaxy whose redshift was also determined"
llere oy is one component of the stress.,Here $\sigma_{12}$ is one component of the stress.
 In the case of linear isotropic elasticity. it is known thal where gy is the (1— 2)-component of the stress given in (1.4)).," In the case of linear isotropic elasticity, it is known that where $\sigma_0$ is the $(1-2)$ -component of the stress given in \ref{eq::s}) )."
 Here eu(c0) appears to be the shear stress created at the point c bv a single dislocation positionned at the origin. with Burgers vector οι.," Here $\sigma_0(x)$ appears to be the shear stress created at the point $x$ by a single dislocation positionned at the origin, with Burgers vector $e_1$."
 With the convention that the sell-siress created by adislocation on itself is zero. i.e. lormally o5(0)=0. we see that we can rewrite the full dvnamies of particles satis[ving X4X for +4j. as follows Let us now introduce the “density” of clislocations where @ ancl 6 correspond respectively to the dislocations with positive ancl negative Burgers vector.," With the convention that the self-stress created by adislocation on itself is zero, i.e. formally $\sigma_0(0)=0$, we see that we can rewrite the full dynamics of particles satisfying $X^i\not= X^j$ for $i\not= j$, as follows Let us now introduce the “density” of dislocations where $\theta^+$ and $\theta^-$ correspond respectively to the dislocations with positive and negative Burgers vector."
 Again with the convention σµ(0)= 0. we can rewrite the dvnanies as," Again with the convention $\sigma_0(0)=0$ , we can rewrite the dynamics as"
there is an indication of small pressure and entropy distortions and the statistical analysis reveals that the fluctuations are quite large.,there is an indication of small pressure and entropy distortions and the statistical analysis reveals that the fluctuations are quite large.
 The pressure shape follows essentially the temperature shape., The pressure shape follows essentially the temperature shape.
 Some small-scale fluctuations in the temperature map are still seen., Some small-scale fluctuations in the temperature map are still seen.
 The image is extended to the north-west., The image is extended to the north-west.
 The results of the spectral analysis are reported in Table 6 and shown in Fig.6..," The results of the spectral analysis are reported in Table \ref{t:cl02:t}
 and shown in \ref{f:cl02}."
 The most significant feature is the presence of a region with extremely low entropy. seen as dotted cross in the entropy profile in Fig.6 at the 0.7so9 distance to the center to the south.," The most significant feature is the presence of a region with extremely low entropy, seen as dotted cross in the entropy profile in \ref{f:cl02} at the $0.7r_{500}$ distance to the center to the south."
 This gas is in pressure equilibrium with the cluster. leading to a suggestion that we observe the debris of accreted group.," This gas is in pressure equilibrium with the cluster, leading to a suggestion that we observe the debris of accreted group."
 A comparison with simulations would be useful here to shed more light on the stage of this suggested disruption., A comparison with simulations would be useful here to shed more light on the stage of this suggested disruption.
 Given the statistical uncertainty it is difficult to conclude on the origin of the extent towards the north-west in the lowest levels of the X-ray surface brightness (region 5)., Given the statistical uncertainty it is difficult to conclude on the origin of the extent towards the north-west in the lowest levels of the X-ray surface brightness (region 5).
 Presumably. this extension. located outside of rso9. 1s due to an. accretion of a filament.," Presumably, this extension, located outside of $r_{500}$, is due to an accretion of a filament."
 The hardness ratio map reveals a soft compact source in the center., The hardness ratio map reveals a soft compact source in the center.
 In the image we see some elongation to the north., In the image we see some elongation to the north.
 In the inner region the surface brightness distribution shows an. indication of a triangular shape with one tip of the triangle pointing towards the north and the other to the west., In the inner region the surface brightness distribution shows an indication of a triangular shape with one tip of the triangle pointing towards the north and the other to the west.
 Asaresult what we see is that there is colder material in the east compared to the west., As a result what we see is that there is colder material in the east compared to the west.
 The pressure map looks rather symmetric. but we have an asymmetric. entropy structure.," The pressure map looks rather symmetric, but we have an asymmetric entropy structure."
 While a possible scenario could be a slow infall of the material from the north- the west part of the cluster appears to be systematically hotter as compared to the eastern side. which could be an indication of a strong shock.," While a possible scenario could be a slow infall of the material from the north-east, the west part of the cluster appears to be systematically hotter as compared to the eastern side, which could be an indication of a strong shock."
 The spectroscopic analysis is reported in Table 7.— and Fig.7.., The spectroscopic analysis is reported in Table \ref{t:cl03:t} and \ref{f:cl03}.
 The point-like source appears to be the low-entropy core of the cluster. with one of the lowest entropies (77+4 keV cm?) in our sample.," The point-like source appears to be the low-entropy core of the cluster, with one of the lowest entropies $77\pm4$ keV $^2$ ) in our sample."
 The hot region on the west is characterized by both an enhancement in the pressure and entropy. yet of high statistical uncertainty.," The hot region on the west is characterized by both an enhancement in the pressure and entropy, yet of high statistical uncertainty."
 We attribute the appearance of this region to a forward shock of the Mach number of 3+I., We attribute the appearance of this region to a forward shock of the Mach number of $3\pm1$.
 The low entropy gas in the north east (region 9) is confirmed in the spectral analysis., The low entropy gas in the north east (region 9) is confirmed in the spectral analysis.
The behavior of the entropy in the outskirts of this cluster led us to a conclusion. supported by other clusters in this sample: the clusters in the advanced stage of interaction have systematically higher entropy at προ compared to the average trend.," The behavior of the entropy in the outskirts of this cluster led us to a conclusion, supported by other clusters in this sample: the clusters in the advanced stage of interaction have systematically higher entropy at $r_{500}$ compared to the average trend."
 We ascribe this result to the heating by the forward shock. induced during the merger.," We ascribe this result to the heating by the forward shock, induced during the merger."
 The. cluster seems to be quite relaxed judging from. the symmetric. appearance of the image and the pressure map., The cluster seems to be quite relaxed judging from the symmetric appearance of the image and the pressure map.
 The temperature map shows small amplitude fluctuations., The temperature map shows small amplitude fluctuations.
 According to the spectroscopic analysis. reported in Table 8 ," According to the spectroscopic analysis, reported in Table \ref{t:cl05:t} "
A possible interpretation for the peculiar observational properties of ΝΕΩΝ is that these systems are accreting close to their Eddington limit. suggesting that. compared to their Γον]. counterparts. they should. host smaller. black hole miasses(Mgg < 107 M.) as measured in the majority of the sources (Wandel et al.,"A possible interpretation for the peculiar observational properties of NLSy1 is that these systems are accreting close to their Eddington limit, suggesting that, compared to their BLSy1 counterparts, they should host smaller black hole masses $_{BH}$ $<$ $^{8}$ $_{\odot}$ ), as measured in the majority of the sources (Wandel et al."
 1999. Cirupe Mathur 2004. Whalen et al.," 1999, Grupe Mathur 2004, Whalen et al."
 2006)., 2006).
 Under the assumption that the IL; emitting region is gravitationally bounded to the central black hole. small black hole masses help in explaining the narrow emission lines observed in these objects.," Under the assumption that the $_{\beta}$ emitting region is gravitationally bounded to the central black hole, small black hole masses help in explaining the narrow emission lines observed in these objects."
 Lt has been shown that NLSy1 galaxies seem not to follow the Mzgg-e relation (Ixomossa Xu 2007. CGrupe Mathur 2004). suggesting that they may be AGNs in their early stage of development. where small black hole masses grow through accretion in already formed bulges with strong. implications for the black hole versus galaxy evolution (Cirupe Alathur 2004. Mathur et al.," It has been shown that NLSy1 galaxies seem not to follow the $_{BH}$ $\sigma$ relation (Komossa Xu 2007, Grupe Mathur 2004), suggesting that they may be AGNs in their early stage of development, where small black hole masses grow through accretion in already formed bulges with strong implications for the black hole versus galaxy evolution (Grupe Mathur 2004, Mathur et al."
 2001)., 2001).
 However. lately. Marconi et al. (," However, lately, Marconi et al. ("
2008) suggested that radiation. pressure due to ionizing photons could. significantly allect virial black hole mass estimates in highly accreting objects such as NLSv1. resulting in an unclerestimate of their masses.,"2008) suggested that radiation pressure due to ionizing photons could significantly affect virial black hole mass estimates in highly accreting objects such as NLSy1, resulting in an underestimate of their masses."
 The interest on NLSv1 has further increased. due to the detection of gamma-ray emission from four NLSw1 with (Abdo et al., The interest on NLSy1 has further increased due to the detection of gamma-ray emission from four NLSy1 with (Abdo et al.
 2009) suggesting that NLSv1 may also form a powerful radio jet and at the same time be powered bv black holes of moderate masses (Yuan et al., 2009) suggesting that NLSy1 may also form a powerful radio jet and at the same time be powered by black holes of moderate masses (Yuan et al.
 2008)., 2008).
 The hard. X-ravs is an cnerey range where NLSyv1 have been poorly investigated: so far. only studies on sparse objects are available.," The hard X-rays is an energy range where NLSy1 have been poorly investigated so far, only studies on sparse objects are available."
BeppoS observations of a small sample of NLSv1 detected hard. X-ray. emission. in only 2 out of 7? sources (Comastri 2000)., observations of a small sample of NLSy1 detected hard X-ray emission in only 2 out of 7 sources (Comastri 2000).
πολ is now providing detailed. broad-band: studies of targeted ον] (c.g.. Ponti et al.," is now providing detailed broad-band studies of targeted NLSy1 (e.g., Ponti et al."
 2010. Miniutti et al.," 2010, Miniutti et al."
 2009. ‘Terashima et al.," 2009, Terashima et al."
 2009)., 2009).
 Recent hard X-ray surveys performed by. the IBIS instrument (Uboertini et al., Recent hard X-ray surveys performed by the IBIS instrument (Ubertini et al.
 2003) on board (Winkler et al., 2003) on board (Winkler et al.
 2003) and the Burst Alert Telescope (BAT. Jarthelmy οἱ al.," 2003) and the Burst Alert Telescope (BAT, Barthelmy et al."
 2005) on board. CGohberels et al., 2005) on board (Geherels et al.
 2004) are imaging the hard X-ray sky providing a number of sources detected for the first time at these energies with half of them being newly discovered. (Malizia ct al., 2004) are imaging the hard X-ray sky providing a number of sources detected for the first time at these energies with half of them being newly discovered (Malizia et al.
 2010. Landi et al.," 2010, Landi et al."
 2010. Tueller et al.," 2010, Tueller et al."
 2010. TPueller et al.," 2010, Tueller et al."
 2009. Ajello et al.," 2009, Ajello et al."
 2008. Winter et al.," 2008, Winter et al."
 2008. Bassani et al.," 2008, Bassani et al."
 2006)., 2006).
 Indeed. the fourth LBIS survey (Bird et al.," Indeed, the fourth IBIS survey (Bird et al."
 2010) has allowed the detection of more than TOO hard X.ray sources over the whole sky above 20 keV. down to an average Hux level of about 1. αιτα and with positional accuracies ranging between 0.2 and ~5 arcmin. depending on the source strength.," 2010) has allowed the detection of more than 700 hard X–ray sources over the whole sky above 20 keV, down to an average flux level of about 1 mCrab and with positional accuracies ranging between 0.2 and $\sim$ 5 arcmin, depending on the source strength."
 Among the detected ACN by LBIS. a small sample of NLSvi is identified.," Among the detected AGN by IBIS, a small sample of NLSy1 is identified."
 A first analysis of the hard N-rav properties of a sample of five ΝΕΩΝ listed in the third LBIS catalogue (Bird ct al., A first analysis of the hard X-ray properties of a sample of five NLSy1 listed in the third IBIS catalogue (Bird et al.
 2007) has been presented in Malizia et al. (, 2007) has been presented in Malizia et al. (
2008). combining NICE (X-ray Telescope. Burrows et al.,"2008), combining /XRT (X-ray Telescope, Burrows et al."
 2005) and INTEGRAL/IBIS spectra., 2005) and /IBIS spectra.
 In this work. we present the broad-band X-ray properties of a sample of 1H NLSv detected by ancl present in the fourth LBIS catalogue1 (Bird et al.," In this work, we present the broad-band X-ray properties of a sample of 14 NLSy1 detected by and present in the fourth IBIS catalogue (Bird et al."
 2010)., 2010).
 New datasets for 5 NLSy1 of the sample have been combined with datato obtain a wide energy spectrum up to  100 keV. In 5 other objects. NICE data are available below 10 keV. and. for LO 16426|6536. only an XI detection is available.," New datasets for 5 NLSy1 of the sample have been combined with datato obtain a wide energy spectrum up to $\sim$ 100 keV. In 5 other objects, XRT data are available below 10 keV, and, for IGR J16426+6536, only an XRT detection is available."
 Published: best-fit spectral parameters for NGC 4051. Mk 766 and NGC 5506 were taken from the most recent X-ray dedicated: works (Terashima ct al.," Published best-fit spectral parameters for NGC 4051, Mrk 766 and NGC 5506 were taken from the most recent X-ray dedicated works (Terashima et al."
 2009. ‘Purner ct al.," 2009, Turner et al."
 2007 ancl Cuainazzi et al., 2007 and Guainazzi et al.
 2010. respectively).," 2010, respectively)."
 The paper is organized in the following manner: Section 2 deseribes the sample: in Section 3 the observation. and data reduction procedure of the I," The paper is organized in the following manner: Section 2 describes the sample; in Section 3 the observation and data reduction procedure of the ,"
 The paper is organized in the following manner: Section 2 deseribes the sample: in Section 3 the observation. and data reduction procedure of the IN," The paper is organized in the following manner: Section 2 describes the sample; in Section 3 the observation and data reduction procedure of the ,"
 The paper is organized in the following manner: Section 2 deseribes the sample: in Section 3 the observation. and data reduction procedure of the INT," The paper is organized in the following manner: Section 2 describes the sample; in Section 3 the observation and data reduction procedure of the ,"
 The paper is organized in the following manner: Section 2 deseribes the sample: in Section 3 the observation. and data reduction procedure of the INTE," The paper is organized in the following manner: Section 2 describes the sample; in Section 3 the observation and data reduction procedure of the ,"
 The paper is organized in the following manner: Section 2 deseribes the sample: in Section 3 the observation. and data reduction procedure of the INTEG," The paper is organized in the following manner: Section 2 describes the sample; in Section 3 the observation and data reduction procedure of the ,"
 The paper is organized in the following manner: Section 2 deseribes the sample: in Section 3 the observation. and data reduction procedure of the INTEGR," The paper is organized in the following manner: Section 2 describes the sample; in Section 3 the observation and data reduction procedure of the ,"
 The paper is organized in the following manner: Section 2 deseribes the sample: in Section 3 the observation. and data reduction procedure of the INTEGRA," The paper is organized in the following manner: Section 2 describes the sample; in Section 3 the observation and data reduction procedure of the ,"
 The paper is organized in the following manner: Section 2 deseribes the sample: in Section 3 the observation. and data reduction procedure of the INTEGRAL," The paper is organized in the following manner: Section 2 describes the sample; in Section 3 the observation and data reduction procedure of the ,"
 The paper is organized in the following manner: Section 2 deseribes the sample: in Section 3 the observation. and data reduction procedure of the INTEGRAL.," The paper is organized in the following manner: Section 2 describes the sample; in Section 3 the observation and data reduction procedure of the ,"
required at z>1.5 and that minor mergers become the dominant growth mechanism for massive galaxies only at lower redshift (Bernardi 2009; Bernardi et al.,required at $z\gsim 1.5$ and that minor mergers become the dominant growth mechanism for massive galaxies only at lower redshift (Bernardi 2009; Bernardi et al.
 2010b)., 2010b).
 Our Figure 5 supports such a picture: major mergers would move the z=2.3 objects approximately parallel to the solid lines in the two panels., Our Figure \ref{fig:comp1} supports such a picture: major mergers would move the $z=2.3$ objects approximately parallel to the solid lines in the two panels.
" A factor of 5 change in mass and size would bring them into much better agreement with the dotted and dashed z=0 relations in the panel on the left, but they would still lie slightly above the corresponding line in the panel on the right."," A factor of 5 change in mass and size would bring them into much better agreement with the dotted and dashed $z=0$ relations in the panel on the left, but they would still lie slightly above the corresponding line in the panel on the right."
" Subsequent minor mergers would increase the sizes and decrease the velocity dispersions, bringing both the sizesand densities into even better agreement. ("," Subsequent minor mergers would increase the sizes and decrease the velocity dispersions, bringing both the sizes densities into even better agreement. ("
Note that a small fractional increase in mass results in a larger fractional increase in size and an even larger fractional decrease in density.,Note that a small fractional increase in mass results in a larger fractional increase in size and an even larger fractional decrease in density.
" Indeed, because density is proportional to (o/r-)*, minor mergers are a great way to decrease the density for a modest change in mass.)"," Indeed, because density is proportional to $(\sigma/r_e)^2$, minor mergers are a great way to decrease the density for a modest change in mass.)"
" If the high redshift objects indeed have σ400 km s! (as our Figure 5 may suggest), the decrease in o associated with minor mergers will (in fact, may be required to) bring the number density of large o objects into better agreement with that seen locally (Sheth et al."," If the high redshift objects indeed have $\sigma\sim 400$ km $^{-1}$ (as our Figure \ref{fig:comp1} may suggest), the decrease in $\sigma$ associated with minor mergers will (in fact, may be required to) bring the number density of large $\sigma$ objects into better agreement with that seen locally (Sheth et al."
 2003)., 2003).
" On the other hand, selection effects (e.g. due to the small volume observed) could limit the detection of these very massive galaxies."," On the other hand, selection effects (e.g. due to the small volume observed) could limit the detection of these very massive galaxies."
" For example, the sample of ultramassive early-type galaxies of Mancini et al. ("," For example, the sample of ultramassive early-type galaxies of Mancini et al. ("
2010) is selected from a 2 deg? field.,2010) is selected from a 2 $^2$ field.
" In such a volume, if galaxies of M,~10!? Mo are yet present at z>1.5, as predicted by model like Fan et al. ("," In such a volume, if galaxies of $_{\star}\sim 10^{12}$ $_{\odot}$ are yet present at $z>1.5$, as predicted by model like Fan et al. ("
"2010), the number of detections should be around unity and therefore not necessary detected.","2010), the number of detections should be around unity and therefore not necessary detected."
 The detection of these massive objects (already difficult in the local universe) is thus a challenge for the high redshift universe., The detection of these massive objects (already difficult in the local universe) is thus a challenge for the high redshift universe.
" We thank L. Danese, C. Mancini R. Sheth and P. van Dokkum for helpful discussions and the anonymous referee for comments that have improved the presentation of our results."," We thank L. Danese, C. Mancini R. Sheth and P. van Dokkum for helpful discussions and the anonymous referee for comments that have improved the presentation of our results."
" M.B. is grateful for support provided by NASA grant ADP/NNX09AD02G. CM and JP acknowledge support from the Marie Curie Excellence Team Grant ’Unimass’, ref."," M.B. is grateful for support provided by NASA grant ADP/NNX09AD02G. CM and JP acknowledge support from the Marie Curie Excellence Team Grant 'Unimass', ref."
" MEXT-CT-2006-042754, of the European Community."," MEXT-CT-2006-042754, of the European Community."
" Funding for the Sloan Digital Sky Survey (SDSS) and SDSS-II Archive 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, and the Max Planck Society, and the Higher Education Funding Council for England."," Funding for the Sloan Digital Sky Survey (SDSS) and SDSS-II Archive 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, and the Max Planck Society, and the Higher Education Funding Council for England."
 The SDSS Web site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions., The SDSS Web site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions.
" The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, The University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The 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 Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, The University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The 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."
can already be seen in the double peakecl structure of the signature of the satellite S2 in the map presented in Fig...,can already be seen in the double peaked structure of the signature of the satellite S2 in the map presented in \ref{fig:polemap_s2}.
 Finally. the mCOC3 method is not. perfect ancl will certainly pick up stars from the field. population that appear to belong to a satellite because they are measured o have a compatible orbital angular momentum vector.," Finally, the mGC3 method is not perfect and will certainly pick up stars from the field population that appear to belong to a satellite because they are measured to have a compatible orbital angular momentum vector."
 These should. be weeded out. by making use of the [act hat the different star formation histories for the cilferent satellites will lead to different abundance patterns in heir stellar populations., These should be weeded out by making use of the fact that the different star formation histories for the different satellites will lead to different abundance patterns in their stellar populations.
 Gross distinctions (such as large overall metallicity cillerences) can be mace photometrically., Gross distinctions (such as large overall metallicity differences) can be made photometrically.
 Llowever. eventually the stars identified as part of a »otential satellite remnant should be targeted Lor detailed spectroscopic follow up in order to definitively ‘tag’ the stars o their progenitor galaxy and obtain accurate information on the progenitor's time of accretion.," However, eventually the stars identified as part of a potential satellite remnant should be targeted for detailed spectroscopic follow up in order to definitively `tag' the stars to their progenitor galaxy and obtain accurate information on the progenitor's time of accretion."
 We look forward the time ahead of us when. thanks to he Gaia mission. complementary spectroscopic data. and ellicient methods. of characterizing substructure in. phase space. we will enter the era of precision Galactic archaeology.," We look forward the time ahead of us when, thanks to the Gaia mission, complementary spectroscopic data, and efficient methods of characterizing substructure in phase space, we will enter the era of precision Galactic archaeology."
 We acknowledge support. from CONAACST.Méxxico erant 60354., We acknowledge support from CONACyT–Méxxico grant 60354.
 ο Alateu acknowledges support. [rom the predoctoral grant. of the Academia Nacional cde Ciencias Fissicas. Matemátticas v Naturales of Venezuela.," C. Mateu acknowledges support from the predoctoral grant of the Academia Nacional de Ciencias sicas, Matemátticas y Naturales of Venezuela."
the emission t¢» àrise in a jet. and comparing luminosity ancl variability of this component with that [rom (νο XN-3 and Gli 191511)5. we infer that the outllow from (νο N-1 is considerably tsteadier and has a significantly lower mass How rate.,"the emission to arise in a jet, and comparing luminosity and variability of this component with that from Cyg X-3 and GRS 1915+105, we infer that the outflow from Cyg X-1 is considerably steadier and has a significantly lower mass flow rate."
 Tx| gadiomm. spectra of these X-ray. binaries are much llater than those of the ‘flat-spectruny AGN which generally. peak somewhere in t1e mam regime and fall olf rapidly in the infrared., The radio–mm spectra of these X-ray binaries are much flatter than those of the `flat-spectrum' AGN which generally peak somewhere in the mm regime and fall off rapidly in the infrared.
 Lt is not at all clear whether niocdels of parially scll-absorbed syachrotron emission from conical jets wüch have been developed for these AGN can be extended o apply to the much higher-fIrequencey. Lat-spectrum emission we observe [rom Cve X-1. (νο X-3 and GRS 1915|1075.," It is not at all clear whether models of partially self-absorbed synchrotron emission from conical jets which have been developed for these AGN can be extended to apply to the much higher-frequency flat-spectrum emission we observe from Cyg X-1, Cyg X-3 and GRS 1915+105."
 Detailed spectral measurements in the mim regime. preferably combine with simultaneous. X-rav and: racio observations. should help us to improve the currently inadequate ünderstanding of the emission. mechanisms in this unusual olect.," Detailed spectral measurements in the mm regime, preferably combined with simultaneous X-ray and radio observations, should help us to improve the currently inadequate understanding of the emission mechanisms in this unusual object."
 Measurement of the shortest variability timescale (expected to be x1I sec for nonthermal emission with a brightness temperature of 10 71x. >10. min for an optically thick dust. cloud. at 150 k. or =l hr for optically thin free-[ree emission) will be important in uncerstancing the emissive mechanism.," Measurement of the shortest variability timescale (expected to be $\leq 1$ sec for nonthermal emission with a brightness temperature of $10^{12}$ K, $\geq 10$ min for an optically thick dust cloud at 150 K, or $\geq 1$ hr for optically thin free-free emission) will be important in understanding the emissive mechanism."
 Equally important will be measurement of. or stringent upper limits to. the level of linear polarisation of the Lat spectral component.," Equally important will be measurement of, or stringent upper limits to, the level of linear polarisation of the flat spectral component."
 Finally. we predict th:uU a Dat spectrum (subjmm component will also be detected. from the persistent. black hole candidate GX 339-4 in the Iow/hard state.," Finally, we predict that a flat spectrum (sub)mm component will also be detected from the persistent black hole candidate GX 339-4 in the low/hard state."
 We would ike to thank the referee for useful suggestions: adclitionally RPL would like to thank Ixinwah Wu and Robert) Voors for useful conversations., We would like to thank the referee for useful suggestions; additionally RPF would like to thank Kinwah Wu and Robert Voors for useful conversations.
 PLD would. like lo thank Bertrarid Lelloch for assistance with the LANAI observations., PD would like to thank Bertrand Lefloch for assistance with the IRAM observations.
 IRANI is funded by the Contre National de la Reererche Scientifique in France. the Alax-Plank-Gesellschaft. iu1 Germany and the Instituto. Geogra;ohico acional in Spain.," IRAM is funded by the Centre National de la Recherche Scientifique in France, the Max-Plank-Gesellschaft in Germany and the Instituto Geographico Nacional in Spain."
 The James Clerk Maxwell. Telescope is operate by the Joint Asronomy Centre on behalf. of he Partico Physies ancl Asronomv Research Council of he Unite Ixingdom. the Netherlands Organisation [or Scientific tesearch and. the ational Research Council of Canada.," The James Clerk Maxwell Telescope is operated by the Joint Astronomy Centre on behalf of the Particle Physics and Astronomy Research Council of the United Kingdom, the Netherlands Organisation for Scientific Research and the National Research Council of Canada."
 We acknowledge wit1 thanks the use of the quick-ook X-raw data provided: by theRANTLE team. anc he Green Bank Interferomeer data.," We acknowledge with thanks the use of the quick-look X-ray data provided by the team, and the Green Bank Interferometer data."
 We thank the stall al MRAO for maintenance anc operation of the ltvle Telescope. which is supported. by the PPARC.," We thank the staff at MRAO for maintenance and operation of the Ryle Telescope, which is supported by the PPARC."
 RPE is supported: by EC Marie. Curie Fellowship ERBEALBLOT 0172436., RPF is supported by EC Marie Curie Fellowship ERBFMBICT 972436.
"πι = 0 because the aem coefficients are defined so that aem=ai,πι.","$m$ = 0 because the $\alm$ coefficients are defined so that $\alm=a_{l,-m}$."
" Other than this, the distribution of ®¢,, is random."," Other than this, the distribution of $\plm$ is random."
" Also, note that for all [πα]>£, δι = 0."," Also, note that for all $|m| > \l$, $\plm$ = 0."
" We extracted the 9,,, from each of the Bianchi maps using (Górskietal.2005) and plotted them in the same way as we have described; the results are shown in Figure 4..", We extracted the $\plm$ from each of the Bianchi maps using \citep{heal} and plotted them in the same way as we have described; the results are shown in Figure \ref{figPhase}.
" The plots show that the ®¢,, are not random but have patterns, i.e. the harmonic modes manifest some form of phase correlation."," The plots show that the $\plm$ are not random but have patterns, i.e. the harmonic modes manifest some form of phase correlation."
" For all the Bianchi types, ®¢m = 0 for all odd m."," For all the Bianchi types, $\plm$ = 0 for all odd $m$."
" For the VIIo and V types, all the 9,,, are orthogonal i.e. they are either 0, 7/2, 7, or 37/2."," For the $_0$ and V types, all the $\plm$ are orthogonal i.e. they are either 0, $\pi/2$, $\pi$, or $3\pi/2$."
" Both the VIIo and VIL, types show sequences of increasing/decreasing phases, which are particularly prominent for m—2."," Both the $_0$ and $_h$ types show sequences of increasing/decreasing phases, which are particularly prominent for $m=2$."
" While some patterns are apparent in these plots, an even better way to visualize the phase correlations is to look at the phase differences which are defined here as: The phase differences are shown in Figure 5 and the correlations are much more apparent compared to the plots of 6,,,,."," While some patterns are apparent in these plots, an even better way to visualize the phase correlations is to look at the phase differences which are defined here as: The phase differences are shown in Figure \ref{figPhaseDif} and the correlations are much more apparent compared to the plots of $\plm$."
" All the A®,;,,, for the V type are lined up, i.e. either 0 or 7."," All the $\Delta\plm$ for the V type are lined up, i.e. either 0 or $\pi$."
" The A9;,, for the VIIo type are again orthogonal, but whereas in the phases the distribution of 0, 7/2, 7, and 37/2 seemed some what random, in the phase differences we see similar values ‘clump’ together."," The $\Delta\plm$ for the $_0$ type are again orthogonal, but whereas in the phases the distribution of 0, $\pi/2$, $\pi$, and $3\pi/2$ seemed some what random, in the phase differences we see similar values `clump' together."
" Similarly, the sequences of colours in the type VII; (see m=2 for example) are now even more prominent."," Similarly, the sequences of colours in the type $_h$ (see $m=2$ for example) are now even more prominent."
" So, strong correlations are observed in the phases and phases differences of the simulated Bianchi CMB maps."," So, strong correlations are observed in the phases and phases differences of the simulated Bianchi CMB maps."
 But we have only looked at large angular scales where there are only a small number of independent data points., But we have only looked at large angular scales where there are only a small number of independent data points.
" Even without noise, it is important to ask the question whether these correlations are likely to be statistically significant."," Even without noise, it is important to ask the question whether these correlations are likely to be statistically significant."
 One way to quantify this is to use atest.. This is a non-parametric statistical test which measures the maximum distance of a given distribution from a reference probability distribution., One way to quantify this is to use a. This is a non-parametric statistical test which measures the maximum distance of a given distribution from a reference probability distribution.
" In this case we want to show deviation from a random set of A, i.e. a uniform distribution, which is predicted by the concordance model."," In this case we want to show deviation from a random set of $\Delta \plm$, i.e. a uniform distribution, which is predicted by the concordance model."
" To calculate the Kolmogorov-Smirnov test statistic a set of phase differences A,,, are separated into bins of equal size between 0 and 2z.", To calculate the Kolmogorov-Smirnov test statistic a set of phase differences $\Delta \plm$ are separated into bins of equal size between 0 and $2\pi$ .
" The number of Ao;,, which fall into each bin are counted and a cumulative distribution derived.", The number of $\Delta \plm$ which fall into each bin are counted and a cumulative distribution derived.
" If the distribution is uniform, as in the case of the reference probability distribution, then the number of A6,,, in each of the bins should increase roughly linearly across the bins."," If the distribution is uniform, as in the case of the reference probability distribution, then the number of $\Delta \plm$ in each of the bins should increase roughly linearly across the bins."
 The difference between both the sample and uniform cumulative distributions is found for each bin and the biggest difference is the Kolmogorov-Smirnov statisticD., The difference between both the sample and uniform cumulative distributions is found for each bin and the biggest difference is the Kolmogorov-Smirnov statistic.
". 'To deduce the significance ofD,, a set of ten thousand tests have been run to generate sets of random angles of equal size to the sample sets."," To deduce the significance of, a set of ten thousand tests have been run to generate sets of random angles of equal size to the sample sets."
 was found for each of these sets and this data was used to find the significance of for the sample distributions from the Bianchi maps., was found for each of these sets and this data was used to find the significance of for the sample distributions from the Bianchi maps.
" The Kolmogorov-Smirnov statisticD,, and the derived probability of that statistic P(.D)), for all the Bianchi maps are detailed in Table 1.."," The Kolmogorov-Smirnov statistic, and the derived probability of that statistic ), for all the Bianchi maps are detailed in Table \ref{tableKS}."
 This table shows that there is indeed a significant deviation from a uniform distribution for the phase differences for all Bianchi types., This table shows that there is indeed a significant deviation from a uniform distribution for the phase differences for all Bianchi types.
" Of the 10000 random sets of data, none showed a value for as high as seen for the Bianchi cases."," Of the 10000 random sets of data, none showed a value for as high as seen for the Bianchi cases."
" The Bianchi VII, type was also considered at different redshifts to see how the correlations changed with time.", The Bianchi $_h$ type was also considered at different redshifts to see how the correlations changed with time.
 Table shows that in general value of gets more significant over time i.e. the correlations in the phase differences ofthe Bianchi maps become stronger over time.," Table \ref{tableKS}
 shows that in general value of gets more significant over time i.e. the correlations in the phase differences ofthe Bianchi maps become stronger over time."
If we want to improve our study of the kinematic cilferences between the GB and the LGD. we must work with residual velocities.,"If we want to improve our study of the kinematic differences between the GB and the LGD, we must work with residual velocities."
 This wav. the svstematic effects of the Galactic kinematies will not interfere with our comparison.," This way, the systematic effects of the Galactic kinematics will not interfere with our comparison."
 Thus. we now correct the space velocities of the stars in our sample from solar motion (using the classical estimation of Delhave(1965).. (U.. V... MW.) = (0.12. T) kms 1) and from Galactic differential rotation -using the values eiven bv Ixerr&Lynden-Dell(1986).," Thus, we now correct the space velocities of the stars in our sample from solar motion (using the classical estimation of \citet{Del65}, , $U_{\odot}$ , $V_{\odot}$, $W_{\odot}$ ) = (9, 12, 7) km $^{-1}$ ) and from Galactic differential rotation -using the values given by \citet{Ker86}."
. In order (o refine the analvsis of the velocity distributions. we must also eliminate outliers of kinematic nature that max be present in the sample.," In order to refine the analysis of the velocity distributions, we must also eliminate outliers of kinematic nature that may be present in the sample."
 That is. we eliminate the stars located in the regions of a very low density in (the velocity space lor our sample under study.," That is, we eliminate the stars located in the regions of a very low density in the velocity space for our sample under study."
 We achieve this bv running the OUTIXER algorithm (Cabrera-Cano&Alfaro1985).. which reduces the sample to a final number of 752 stars.," We achieve this by running the OUTKER algorithm \citep{Cab85}, which reduces the sample to a final number of 752 stars."
 We then separate again the sample into GB and LGD members., We then separate again the sample into GB and LGD members.
Now we want to compare both distributions in a N-dimensional space. where N-6 (phase space) or N=3 (velocity space).,"Now we want to compare both distributions in a N-dimensional space, where N=6 (phase space) or N=3 (velocity space)."
 In order (o achieve (his. we employ a niultidimensional. non-parametric (wo-samples test: (he Cramer test 2004).," In order to achieve this, we employ a multidimensional, non-parametric two-samples test: the Cramer test \citep{Bah04}."
. The test statistic is the difference of the sum of all (he Euclidean interpoint distances between the random variables from the two different samples: where X; and Y; are the point vectors of each sample member. and m.n are the respective size of the samples.," The test statistic is the difference of the sum of all the Euclidean interpoint distances between the random variables from the two different samples: where $\textbf{\emph{X}}_i$ and $\textbf{\emph{Y}}_i$ are the point vectors of each sample member, and m,n are the respective size of the samples."
 ὦ is a kernel function: for (Bis particular case we have used the Cramer kernel implemented by Franz(2004) in the R statistical environment opmentCoreTeam 2005)., $\phi$ is a kernel function; for this particular case we have used the Cramer kernel implemented by \citet{Fra04} in the R statistical environment \citep{R05}.
. Thus. an analvsis of the three-dimensional velocity space. (C.V.WW). vields that the GB and the LGD distributions are different with a of confidence.," Thus, an analysis of the three-dimensional velocity space, $(U, V,
W)$, yields that the GB and the LGD distributions are different with a of confidence."
 Similarly. (he Cramer test for the six dimensions of the phase space. (X.Y.Z.U.V.WW). rejects the possibility that the GB and the LGD distributions are the same with a confidence of a99%... Thus we confirm that the GB and the LGD are two dillerent stellar svstems in the sense that they show a clear statistical separation between their distributions in the phase space.," Similarly, the Cramer test for the six dimensions of the phase space, $(X, Y, Z, U, V, W)$, rejects the possibility that the GB and the LGD distributions are the same with a confidence of a. Thus we confirm that the GB and the LGD are two different stellar systems in the sense that they show a clear statistical separation between their distributions in the phase space."
 lt is unavoidable to take into consideration the contribution of the GB when the voung Disk is under study. because. as we have demonstrated. the velocitiesof theOD stars in the solar neighborhood are not statistically independent of their spatial positions.," It is unavoidable to take into consideration the contribution of the GB when the young Disk is under study, because, as we have demonstrated, the velocitiesof theOB stars in the solar neighborhood are not statistically independent of their spatial positions."
ouly significant at the 2e level. we fiud a slope in metallicity-DEF space that approaches a 50 confidence level.,"only significant at the $\sim 2 \sigma$ level, we find a slope in metallicity-DEF space that approaches a $5 \sigma$ confidence level."
 While we see that H I deficiency allects the overall nebular metallicity of cluster spirals. it is uportant to disentaugle this process from tle secular effects of galaxy mass.," While we see that H I deficiency affects the overall nebular metallicity of cluster spirals, it is important to disentangle this process from the secular effects of galaxy mass."
 Iu order to examine —he metallicity-DEF correlation iudepeudeutly of the mass-metallicity relatiouship. we cousider the illerential (O/H) offset between a galaxy and expectation values based on its Ve: and Ap.," In order to examine the metallicity-DEF correlation independently of the mass-metallicity relationship, we consider the differential (O/H) offset between a galaxy and expectation values based on its $V_C$ and $M_B$."
 We adopt Ve: as our primary tracer of a galaxys nass since. as mentioned iu[).. it is istauce-independent. unbiased by recent star formation. aud more tightly correlated with galactic —jetallicity.," We adopt $V_C$ as our primary tracer of a galaxy's mass since, as mentioned in, it is distance-independent, unbiased by recent star formation, and more tightly correlated with galactic metallicity."
 However. we include our analysis in terius of Alp for the sake of completeness.," However, we include our analysis in terms of $M_B$ for the sake of completeness."
 Fitting a linear treud to the abundance versus circular velocity plot for the field sample shown in Figure 5(a).. we derive a galaxys expected oxygeu abuudauce as 12+ log(O/H)=8.57+0.356xVc:/(200kis).," Fitting a linear trend to the abundance versus circular velocity plot for the field sample shown in Figure \ref{avgvvc_field}, we derive a galaxy's expected oxygen abundance as $12 + \log$ $ = 8.57+0.356 \times V_C/(200~\mathrm{km/s})$."
 Similarly. from Figure 5(b).. we derive 12+ log(O/H)=8.95—0.0591»(Mg+20) Figure 6 shows the offsets in log(O/H) (neasured - expected) versus DEF for the galaxies presented iu Figure L.," Similarly, from Figure \ref{avgvmag_field}, we derive $12 + \log$ $ = 8.95 - 0.0594 \times (M_B + 20)$ Figure \ref{avgvdef_corr} shows the offsets in log(O/H) (measured - expected) versus DEF for the galaxies presented in Figure \ref{avgvdef}."
 The comparisou to expectation values effectively removes tle scatter iutrodiuced by the MZR. aud the resulting correlation is obvious.," The comparison to expectation values effectively removes the scatter introduced by the MZR, and the resulting correlation is obvious."
 For the combined set of Pegasus and. Virgo spirals (excluding NGC 7515. which has a Ve: o£ 36 kin/s. far lower than any of the other galaxies examined here). the Pearson correlation coefficient. reaches 0.86 alter removal of the (O/H)-Ve: trend.," For the combined set of Pegasus and Virgo spirals (excluding NGC 7518, which has a $V_C$ of 36 km/s, far lower than any of the other galaxies examined here), the Pearson correlation coefficient reaches 0.86 after removal of the $V_C$ trend."
 Uo we instead remove the (O/H)-A/j trend. the correlation coefficient for the two saniples is 0.90.," If we instead remove the $M_B$ trend, the correlation coefficient for the two samples is 0.90."
 From this analysis. we couclude that. as expected. at least some of the scatter arouud the DEF-(O/H) correlation in Figure 1(a) is due to the MZR.," From this analysis, we conclude that, as expected, at least some of the scatter around the DEF-(O/H) correlation in Figure \ref{avgvdef_comp} is due to the MZR."
 ]t is important to note that while we see effects of the MZR in our sample. the observed metallicity offsets are not primarily driveu by galaxy mass.," It is important to note that while we see effects of the MZR in our sample, the observed metallicity offsets are not primarily driven by galaxy mass."
 This would be particularly likely if the H I deficient galaxies were systematically more massive than the H E normal sample., This would be particularly likely if the H I deficient galaxies were systematically more massive than the H I normal sample.
 IL this were the case. we would expect to see a correlation between DEF aud Ve.," If this were the case, we would expect to see a correlation between DEF and $V_C$."
 To test this possibility. we plot DEF versus Vc: in Figure 7..," To test this possibility, we plot DEF versus $V_C$ in Figure \ref{defvvc}."
 We observe uo correlation [or Pegasus or Virgo spirals. thus ruling out a mass offset between hydrogen normal/poor spirals.," We observe no correlation for Pegasus or Virgo spirals, thus ruling out a mass offset between hydrogen normal/poor spirals."
 We cau therefore conclude that H I deficiency is driviug metallicity augmentation indepeudenutly of galaxy mass., We can therefore conclude that H I deficiency is driving metallicity augmentation independently of galaxy mass.
 The observed correlation between heavy element content aud DEF observed lor Pegasus aud Virgo galaxies might suggest that these objects’ metallicity offsets are caused. entirely by H 1 deliciency. aud are independent of cluster membership.," The observed correlation between heavy element content and DEF observed for Pegasus and Virgo galaxies might suggest that these objects' metallicity offsets are caused entirely by H I deficiency, and are independent of cluster membership."
 However. a comparison to field spirals ref=es that notion.," However, a comparison to field spirals refutes that notion."
 In Figures I(c). and 6.. we have plotted the mean 12 + log(O/H) against DEF Lor field ealaxies from£).," In Figures \ref{avgvdef_field} and \ref{avgvdef_corr}, we have plotted the mean 12 + log(O/H) against DEF for field galaxies from."
. Our values of DEF for the field galaxies-which: we include in Table 6-—are adopted from(2009)., Our values of DEF for the field galaxies–which we include in Table \ref{virgofieldtab}- –are adopted from.
. We see that. uulike lor the cluster spirals. the abuudauces for field) galaxies are completely uncorrelated with DEF.," We see that, unlike for the cluster spirals, the abundances for field galaxies are completely uncorrelated with DEF."
 The Pearson correlation test confirms what visual inspection suggests: the (O/H)J-DEF correlation coefficient for the field sample is -0.16., The Pearson correlation test confirms what visual inspection suggests; the (O/H)-DEF correlation coefficient for the field sample is -0.16.
 While the measured metallicities for the field sample have a lower precision than our sample or the Virgo sample. it appears very tentatively that heavy element content. is ouly depeudent ou H I deficieucy if a galaxy has lost its H I through cluster-driveu mechatisius. as opposed to field objects that have always been gas-poor.," While the measured metallicities for the field sample have a lower precision than our sample or the Virgo sample, it appears very tentatively that heavy element content is only dependent on H I deficiency if a galaxy has lost its H I through cluster-driven mechanisms, as opposed to field objects that have always been gas-poor."
 However. further study of both field aud," However, further study of both field and"
The interaction of Hows with clouds may be a Κον mechanism for producing the broad. emission wings to Hla line profiles seen in regions containing concentrations of massive stars including super star clusters and many giant. regions. such as 30 Doradus (Chu&Wwennieutt1994:Alelnick.‘Tenor,"The interaction of flows with clouds may be a key mechanism for producing the broad emission wings to $\alpha$ line profiles seen in regions containing concentrations of massive stars including super star clusters and many giant regions, such as 30 Doradus \citep*{Chu:1994,Melnick:1999}."
io-Tagle&‘Lerlevich 1999)... Westmoquetteetal.(2007a.b) concluded. that the broad. component. arises in a turbulent boundary. laver at the interface. between hot eas IHlowing past cold gas stripped. from. clouds.," \citet{Westmoquette:2007a,Westmoquette:2007b}
 concluded that the broad component arises in a turbulent boundary layer at the interface between hot gas flowing past cold gas stripped from clouds."
 However. subsequent modelling has indicated that unrealistically high How speeds are needed. (Binettectal.2009).," However, subsequent modelling has indicated that unrealistically high flow speeds are needed \citep{Binette:2009}."
. Instead. we believe that the broad emission wings rellect the acceleration of— material along the tail ancl not just. turbulent. motions within the mixing laver.," Instead, we believe that the broad emission wings reflect the acceleration of material along the tail and not just turbulent motions within the mixing layer."
 Aoautiful filaunentarv structures are also seen in starburst superwinds (ee.Ceciletal.2001:Ohvamact 2002).," Beautiful filamentary structures are also seen in starburst superwinds \citep[e.g.,][]{Cecil:2001,Ohyama:2002}."
. While these may be material stripped. from. denser clouds. as seen in simulations (e.g..Cooperetal.2008).. the results in this paper indicate that some of the filaments may in [act have been formed directly out of an overrunning shell.," While these may be material stripped from denser clouds, as seen in simulations \citep[e.g.,][]{Cooper:2008}, the results in this paper indicate that some of the filaments may in fact have been formed directly out of an overrunning shell."
 We have demonstrated a new mechanism for the formation of tails behind dense clouds. which involves the removal and trailing. of material [rom an overrunning isothermal shell., We have demonstrated a new mechanism for the formation of tails behind dense clouds which involves the removal and trailing of material from an overrunning isothermal shell.
 The mechanism appears robust to a range of shell thicknesses and Mach. numbers. and the cloud. density contrast. though these parameters. influence the. tails properties.," The mechanism appears robust to a range of shell thicknesses and Mach numbers, and the cloud density contrast, though these parameters influence the tail's properties."
discrepancy. appears lo erow larger for lines al longer wavelengths.,discrepancy appears to grow larger for lines at longer wavelengths.
 We proposed a partial explanation by assuming that the interstellar medium along the Capella line sight is partially ionized. and therefore has a larger effective absorption column density than if (he medium is neutral.," We proposed a partial explanation by assuming that the interstellar medium along the Capella line sight is partially ionized, and therefore has a larger effective absorption column density than if the medium is neutral."
 However. constraints on the ionization Traction of II II dictate that it can only account for about half of the discrepancy.," However, constraints on the ionization fraction of H II dictate that it can only account for about half of the discrepancy."
 IC is plausible that the remaining discrepancy. is due to either the LEEEGS calibration uncertainties or svstematic errors in (theoretical line ratios., It is plausible that the remaining discrepancy is due to either the LETGS calibration uncertainties or systematic errors in theoretical line ratios.
 The atthors acknowledge the support by the NASA erants NAGS5-5419 and NNGGOAGLTGG., The authors acknowledge the support by the NASA grants NAG5-5419 and NNGG04GL76G.
quite uncertain. so that we clioose two cases απ η10Ὁ aud 107 for iustanee (see also Fig.5 iu section 5).,"quite uncertain, so that we choose two cases as $x_{\rm HI}=10^{-6}$ and $10^{-7}$ for instance (see also Fig.5 in section 5)."
 We will present away to coustrain cji frou the observations later., We will present a way to constrain $x_{\rm HI}$ from the observations later.
 Tn Figue 2. we show the expected spectra of the GRB afterglows.," In Figure 2, we show the expected spectra of the GRB afterglows."
 The solid. short-dashed. loug-dashed. dot-dashed. aud dotted curves are the expected afterglow spectra of the CRB at zs=22. 20. Ls. 15. and 13. respectively.," The solid, short-dashed, long-dashed, dot-dashed, and dotted curves are the expected afterglow spectra of the GRB at $z_{\rm S}=22$, 20, 18, 15, and 13, respectively."
 The observing time is assiuned to be 1 hour after the prompt euissiou in the observers frame., The observing time is assumed to be 1 hour after the prompt emission in the observer's frame.
 We find the clear Lya breaks in tle spectra., We find the clear $\alpha$ breaks in the spectra.
 Since yp=10.9 (or 10 *) at 15<«20 ds assunied in the panel (a) (or (hj). the IGM opacity is an order of unitv (or 0.1) iu the redshift range (see oq.{7).," Since $x_{\rm HI}=10^{-6}$ (or $10^{-7}$ ) at $15\leq z < 20$ is assumed in the panel (a) (or (b)), the IGM opacity is an order of unity (or 0.1) in the redshift range (see eq.[7])."
" Thus. the continuum bluer thaw ιο Lvo break of the CRBs withzs>15 still remains of 1ο order of 10 yJy (or 100 a Jv) in ~2 2.5jnu.. 1ο,111 fy-baud (see the thin solid curve indicated as Jv: we adopt ιο filter svstem of Bessell&Brett 1988))."," Thus, the continuum bluer than the $\alpha$ break of the GRBs with$z_S > 15$ still remains of the order of $10$ $\mu$ Jy (or 100 $\mu$ Jy) in $\sim 2$ –2.5, i.e.,in $K$ -band (see the thin solid curve indicated as $K$; we adopt the filter system of \citealt{bes88}) )."
 The spectral weak at 1.91(20.1216]1115]) lis due to the neutral hydrogen below 2=15., The spectral break at 1.94(=0.1216[1+15]) is due to the neutral hydrogen below $z=15$.
 Thus. the contimmui less than the break waveleusth iu the observers rane from the zy=15 source is completely extinguished.," Thus, the continuum less than the break wavelength in the observer's frame from the $z_{\rm S}\geq 15$ source is completely extinguished."
 The spectra of the source with τω<15 are the same as hose shown in Figure 1., The spectra of the source with $z_{\rm S} < 15$ are the same as those shown in Figure 1.
 For zy=22 case. the spectra shows the second break at 2.36(=0.1026]1|22])jnu.," For $z_{\rm S}=22$ case, the spectrum shows the second break at 2.36(=0.1026[1+22])."
. This is the Lv) break due to the neutral bydrogen ucar the CRB., This is the $\beta$ break due to the neutral hydrogen near the GRB.
 Were we have assumed ayyc1 for:>20., Here we have assumed $x_{\rm HI}\sim 1$ for$z\geq 20$.
 The structure corresponding to the reiouization history appears in the spectra of the CRB afterelows as shown in Figure 2 (see also Waitman&Loeb 19993)., The structure corresponding to the reionization history appears in the spectra of the GRB afterglows as shown in Figure 2 (see also \citealt{hai99}) ).
 If we could detect the continuum rising at 2.55(=0.1216]1|20]) Hu the spectrum of the CRB with :4=22. we would find the starting epoch of the first reionization as +=20.," If we could detect the continuum rising at 2.55(=0.1216[1+20]) in the spectrum of the GRB with $z_{\rm S}=22$, we would find the starting epoch of the first reionization as $z=20$."
 Ou the other hand. the end of the first reionization. iu other words. the transition epoch from the Pop III to II is realized from the spectral breaks at 1.91(020.1216]|1|15])pe.," On the other hand, the end of the first reionization, in other words, the transition epoch from the Pop III to II is realized from the spectral break at 1.94(=0.1216[1+15])."
 The suitable baud to determine the ionization history depends on the redshift of the reionizatiou epoch., The suitable band to determine the ionization history depends on the redshift of the reionization epoch.
 From Fieure 1 (sec also Table 2). we find that the 7. J. IT. aud a 1and spectroscopies are suitable for the reionization epoch at ον25 7T. 811. 11Lh and 1520. respectively.," From Figure 1 (see also Table 2), we find that the $I$, $J$, $H$, and $K$ -band spectroscopies are suitable for the reionization epoch at $z\simeq 5$ –7, 8–11, 11–14, and 15–20, respectively."
 Iu any case. observations to detect the spectral signatures in the NIR afterelow spectra of the GRBs are stronely eucourased.," In any case, observations to detect the spectral signatures in the NIR afterglow spectra of the GRBs are strongly encouraged."
 Tf μι is παλ. than 109. we can clearly see the difference from Fie.," If $x_{\rm HI}$ is smaller than $10^{-6}$, we can clearly see the difference from Fig."
 1 aud confirm the double relonization., 1 and confirm the double reionization.
 Iu the above discussion. we assunied eg109G aud 10*.," In the above discussion, we assumed $x_{\rm HI}=10^{-6}$ and $10^{-7}$."
 Let us argue what will happenfor different values of μα., Let us argue what will happenfor different values of $x_{\rm HI}$.
 Th ayy2Τοο. the remaining flux decreases exponentially because the ICAL opacity becomes much larger than unitv: for example. the flux is about 1 nJv for ey6<10©. aud about 1 pJv for μι=10.7.," If $x_{\rm HI}\ga 10^{-6}$, the remaining flux decreases exponentially because the IGM opacity becomes much larger than unity; for example, the flux is about 1 nJy for $x_{\rm HI}=6\times10^{-6}$, and about 1 pJy for $x_{\rm HI}=10^{-5}$."
 It is quite difficult to detect such a low-level fiux., It is quite difficult to detect such a low-level flux.
 The photometric observations are available easier tha the spectroscopy., The photometric observations are available easier than the spectroscopy.
 We examine the expected apparent. NIR colors of the CRB afterglows., We examine the expected apparent NIR colors of the GRB afterglows.
 Although we can discuss the apparent magnitude of the afterglows iu oue photometric filter. their dispersion is very large because the Μποςτν of the afterelows depends on many uncertain parameters such as the jet opeuing angle. the aubicut matter deusitv. the magnetic cherey fraction aud the relativistic electron eucrev fraction.," Although we can discuss the apparent magnitude of the afterglows in one photometric filter, their dispersion is very large because the luminosity of the afterglows depends on many uncertain parameters such as the jet opening angle, the ambient matter density, the magnetic energy fraction and the relativistic electron energy fraction."
 Ou the other laud. the dispersion of the apparent colors can be quite simall because the color zaoes not depend ou the absolute huninosity but ouly the PAectral shape which does not change significantly in the observed. NIR bauds.," On the other hand, the dispersion of the apparent colors can be quite small because the color does not depend on the absolute luminosity but only the spectral shape which does not change significantly in the observed NIR bands."
 The apparent iu a filter band denoted as i is defined by where £;ods the zero point flux density of the filter aud Fy is the mean flux density through the filter which is where 7; 1s the trausuussion cfiiciency of the filter aud foc7 is the flux density cuterine the filter.," The apparent in a filter band denoted as $i$ is defined by where $F_{i,0}$ is the zero point flux density of the filter and $F_i$ is the mean flux density through the filter which is where $T_{i,\nu}$ is the transmission efficiency of the filter and $f_\nu e^{-\tau_\nu}$ is the flux density entering the filter."
 If there is no intervene absorber between the source aud the telescope. T=O.," If there is no intervening absorber between the source and the telescope, $\tau_\nu=0$."
" The observed color between two filter bands. / aud { (the filter / is blucr than the filter /). is giveu by where (Gn;an;jur is the intriusic color of the source. aud Aun; aud Aon; are the absorption znouuts iu the filters / and oj. respectively,"," The observed color between two filter bands, $i$ and $j$ (the filter $i$ is bluer than the filter $j$ ), is given by where $(m_i - m_j)^{\rm int}$ is the intrinsic color of the source, and $\Delta m_i$ and $\Delta m_j$ are the absorption amounts in the filters $i$ and $j$, respectively."
 When we consider the NIR filter bauds aud high-: GRBs (for example +=15). the trinsic afterglow spectrum is predicted to be proportional to poH? from ~L minute to several hours after the burst occurrence and proportional to r’/? for later time in the standard afterglowmodel (Sari.Piran.&NaravauL998;Ciardi&Loeb 2000)..," When we consider the NIR filter bands and $z$ GRBs (for example $z=15$ ), the intrinsic afterglow spectrum is predicted to be proportional to $\nu^{-1/2}$ from $\sim 1$ minute to several hours after the burst occurrence and proportional to $\nu^{-p/2}$ for later time in the standard afterglowmodel \citep{sar98,ciardi00}. ."
 Other paraicters adopted are described in the beginning of the section 3., Other parameters adopted are described in the beginning of the section 3.
 Iu Table 3. we tabulate the intrinsic colors of the sources for the two cases of the spectral shape.," In Table 3, we tabulate the intrinsic colors of the sources for the two cases of the spectral shape."
" The absorption amount in the filter / is where a""iut=mjtroO) is the intrinsic (uo absorption) apparent magnitude.", The absorption amount in the filter $i$ is where $m_i^{\rm int} = m_i(\tau_\nu=0)$ is the intrinsic (no absorption) apparent magnitude.
 In a certain baud width A». the difference in the optical depth Az is estimated as [Az/7|=3/2012)TAL|ιτ)TAv/v| frou equation (7).," In a certain band width $\Delta \nu$, the difference in the optical depth $\Delta \tau$ is estimated as $| \Delta \tau/\tau | = 3/2 (1+z)^{-1} | \Delta (1+z) | \sim (1+z)^{-1}
| \Delta \nu/\nu |$ from equation (7)."
 Since Av of the filter transmission is naller than the effective frequency of the filter. ie. Aw»<1l. and also DES.Ar/ro«ld that is. the term ο6 in the integral of the ummerator in equation (13) can be regarded as alinost constant.," Since $\Delta \nu$ of the filter transmission is smaller than the effective frequency of the filter, i.e. $\Delta \nu/\nu < 1$, and also $z\ga 5$, $\Delta \tau/\tau \ll 1$, that is, the term $e^{-\tau_\nu}$ in the integral of the numerator in equation (13) can be regarded as almost constant."
 Teuce. we obtain approximately Aon;zm l.086z.g. where map is the effective ICAL opacity in the filter 7.," Hence, we obtain approximately $\Delta m_i \approx 1.086 \tau_{\rm eff}$ , where $\tau_{\rm eff}$ is the effective IGM opacity in the filter $i$."
 Now we can estimate the observed color by equation (12) i£ Ar; is known., Now we can estimate the observed color by equation (12) if $\Delta m_i$ is known.
 To know Ai; is equivalent to know he ICM effective opacity rag.This opacity is one between he redshift at which the Lya break comes iuto the filter xud width -- see Table 2) aud the source redshift τα) because the neutral hydrogen in:<af~Lye+}dn caauuuot absorb the photous passing through the filter /.," To know $\Delta m_i$ is equivalent to know the IGM effective opacity $\tau_{\rm eff}$ .This opacity is one between the redshift at which the $\alpha$ break comes into the filter band width $z_{\rm Ly\alpha,in}^i$ , see Table 2) and the source redshift $z_{\rm S}$ ) because the neutral hydrogen in $z<z_{\rm Ly\alpha,in}^i$ cannot absorb the photons passing through the filter $i$ ."
 We note hat the neutral bydrogen Iwing bevoud the redshift at which the Lyra break goes out of the filter band width (theone 000. Table 2) absorb the photons through the filter / because of the higher-order Lsiuan series lines ike LvJJ. Lv. ete," We note that the neutral hydrogen lying beyond the redshift at which the $\alpha$ break goes out of the filter band width $z_{\rm Ly\alpha,out}^i$ , see Table 2) absorb the photons through the filter $i$ because of the higher-order Lyman series lines like $\beta$, $\gamma$ , etc."
;and the pliotoionization process.,",and the photoionization process."
 As, As
spectral indices fixed to their values derived from the time-intcerated fit.,spectral indices fixed to their values derived from the time-integrated fit.
" We find Ey,(f.£j).1219015 for ty fixed at 25.08 (A?/d.o.f.= 7.52/8).", We find $E_{b} \sim (t-t_{0})^{-1.21 \pm 0.15}$ for $t_{0}$ fixed at $-25.0$ s $\chi^2/d.o.f.=7.52/8$ ).
 Additional fits with other larger values of fy gave slightly shallower indices. as expected if one compares the behavior to that of 9 aud ty.," Additional fits with other larger values of $t_{0}$ gave slightly shallower indices, as expected if one compares the behavior to that of $\beta$ and $t_{0}$."
 For an adiabatic fast-cooliug spherical blast-wave we expect the break cnerey to decay as 1.5. within two-siena of our measured value.," For an adiabatic fast-cooling spherical blast-wave we expect the break energy to decay as $-1.5$, within two-sigma of our measured value."
 As seen from the CCD in Figure 5. the spectral evolution of this burst is very close to that of the svuchrotron spectruu. although the rise of the burst tends to be somewhat harder in the soft color index than expected from evolution of the svuchrotron spectruu alone.," As seen from the CCD in Figure 5, the spectral evolution of this burst is very close to that of the synchrotron spectrum, although the rise of the burst tends to be somewhat harder in the soft color index than expected from evolution of the synchrotron spectrum alone."
 GRB9G0530 is of particular interest because of its striking temporal behavior., GRB960530 is of particular interest because of its striking temporal behavior.
 The burst has two distinct episodes of emission. each having a FRED-like time profile.," The burst has two distinct episodes of emission, each having a FRED-like time profile."
 The second episode. πιο weaker with a peak intensity ess than half of the first. occurs ~200 seconds after the first.," The second episode, much weaker with a peak intensity less than half of the first, occurs $\sim 200$ seconds after the first."
" As seen in Table 2. the low-enerev slope of the second episode is consistent with the fast-cooliug slope below 74,. rowever the value of p=3.76c0.37 is laree mainly )ecause the hieli-energy slope is not well-coustrained."," As seen in Table 2, the low-energy slope of the second episode is consistent with the fast-cooling slope below $\nu_{\rm m}$, however the value of $p = 3.76 \pm 0.37$ is large mainly because the high-energy slope is not well-constrained."
 The value of p derived for the first episode is not unreasonable. rowever the low-cnerey slope is roughly three-signia away roni the expected value of 0.5.," The value of $p$ derived for the first episode is not unreasonable, however the low-energy slope is roughly three-sigma away from the expected value of $-0.5$."
 The decay index for the second episode is Jjx:2.03. uot incousisteut with the expected values ο=LATALST and ο=3.75+1.57 or radiative and acliabatic fast-cooling. respectively.," The decay index for the second episode is $\beta \le -2.13$, not inconsistent with the expected values $\beta = -4.57 \pm 1.57$ and $\beta = -3.75 \pm 1.57$ for radiative and adiabatic fast-cooling, respectively."
 The CCD of the second eimissiou episode of this burst (Figure 6) indicates that during the decay the ciission evolves iuto the svuchrotrou spectrum., The CCD of the second emission episode of this burst (Figure 6) indicates that during the decay the emission evolves into the synchrotron spectrum.
 From Table 2. the low-cnerey iudex of this burst is nearly four-ieia from the value 0.5 expected im the fast-cooling regine.," From Table 2, the low-energy index of this burst is nearly four-sigma from the value $-0.5$ expected in the fast-cooling regime."
" Ποπονα, it docs lave p=2.2+ 0.05. consistent with typical afterglow values and particle acceleration models of relativistic shocks (c.¢.. Gallantetal. 2000))."," However, it does have $p = 2.2 \pm 0.08$ , consistent with typical afterglow values and particle acceleration models of relativistic shocks (e.g., \cite{gallant00}) )."
 Additionally. the change in slope. A is less than three-sigmia from the expected value of 0.9 for the cooling break im the slow-cooling regiae.," Additionally, the change in slope, $\Delta$ is less than three-sigma from the expected value of $-0.5$ for the cooling break in the slow-cooling regime."
 For slow-cooline. we expect the temporal slope to be f=0.53d:0.01 for Bopo and s=LIS40.08 for p>νο ," For slow-cooling, we expect the temporal slope to be $\beta = -0.53 \pm 0.04$ for $\nu < \nu_{\rm c}$ and $\beta = -1.15 \pm 0.08$ for $\nu > \nu_{\rm c}$."
For v>my in fast-cooliug we expect 9=1.60+0.08 (radiative) and 3=LASd0.408. (adiabatic)., For $\nu > \nu_{\rm m}$ in fast-cooling we expect $\beta = -1.60 \pm 0.08$ (radiative) and $\beta = -1.15 \pm 0.08$ (adiabatic).
 Our measured value of the decay. ο)=2.06 is muargnmallwv consisteut Qvithin fwo-sógenia] with the 5.radiative fast-cooling slope.," Our measured value of the decay, $\beta = -2.06_{+0.20}^{-0.21}$, is marginally consistent (within two-sigma) with the radiative fast-cooling slope."
 More notably. it is cousisteut. (vitlin one-sigma) with the value of p.," More notably, it is consistent (within one-sigma) with the value of $p$ ."
" A series of spectral fits during the tail of the burst holding the low and ligh-cnerey spectral iudices coustant show that £, decays with time described by a power-lay of the form Ey~(tty)ο for ty=16 s(\?/dof.=L02/3). mareinally consistent with the adiabatic evolution (spherical or jet) of my."," A series of spectral fits during the tail of the burst holding the low and high-energy spectral indices constant show that $E_{b}$ decays with time described by a power-law of the form $E_{b} \sim (t-t_{0})^{-0.96\pm0.26}$ for $t_{0} = 16$ s $\chi^2/d.o.f.=4.02/3)$, marginally consistent with the adiabatic evolution (spherical or jet) of $\nu_{\rm m}$."
 GRBOFL208 is the longest burst ever detected with DATSE., GRB971208 is the longest burst ever detected with BATSE.
 The temporal structure of the burst is a simple x00th FRED lasting several thousand seconds., The temporal structure of the burst is a simple smooth FRED lasting several thousand seconds.
 The Cluission is soft. with no cussion m chauucl b (E2300 τον).," The emission is soft, with no emission in channel 4 $E > 300$ keV)."
 The spectral paraicters tend to favor fast-cooling. t not strouelv. as the value of p=LOG40.0 Lis unusually veh.," The spectral parameters tend to favor fast-cooling, but not strongly, as the value of $p=4.06 \pm 0.04$ is unusually high."
 The value of A=L.18+0.01 is svell-deteriuiued. and very far from the value expected for slow-cooling (A=0.5).," The value of $\Delta = 1.48 \pm 0.04$ is well-determined, and very far from the value expected for slow-cooling $\Delta = 0.5$ )."
 Although iu apparent contradiction to this. he CCD pattern for this eveut (Figure 7) shows a strong resciublance to that of the tail of GRBOS90923 in Figure 5.," Although in apparent contradiction to this, the CCD pattern for this event (Figure 7) shows a strong resemblance to that of the tail of GRB9890923 in Figure 5."
 CGRD9802301 shows a low-energv slope consistent with fast-cooling but also a value of p=2.180.13. remarkably consistent with values of observed. afterglows.," GRB980301 shows a low-energy slope consistent with fast-cooling but also a value of $p = 2.48 \pm 0.13$, remarkably consistent with values of observed afterglows."
 The chauge in slope across the break energy is slicbitlv higher than that expected for slow cooling (but within two-sigima)., The change in slope across the break energy is slightly higher than that expected for slow cooling (but within two-sigma).
 If the spectrum is fast-cooliug. then we expect A=07120.13. based ou the measured hieh-enerev slope.," If the spectrum is fast-cooling, then we expect $\Delta = 0.74 \pm 0.13$, based on the measured high-energy slope."
 This value is within one-giia of the value A=0.69£0.13 that we derive from the measured slopes., This value is within one-sigma of the value $\Delta = 0.69 \pm 0.13$ that we derive from the measured slopes.
 For radiative evolution we expect 9)j=L&l+0.13. while for adiabatic evolution we expect )j=1.5620.15.," For radiative evolution we expect $\beta = -1.84 \pm 0.13$, while for adiabatic evolution we expect $\beta = -1.36 \pm 0.13$."
 Towever. we measure a iiuch steeper valueJ of 3=2.50)m sugecsting an evolution inconsisteut with the lvdrodvuamics of a spherical blast wave. but consistent with that of a jet.," However, we measure a much steeper value of $\beta = -2.50_{+0.05}^{-1.58}$, suggesting an evolution inconsistent with the hydrodynamics of a spherical blast wave, but consistent with that of a jet."
 The CCD patter for GRDB950301 is shown in Figure 6., The CCD pattern for GRB980301 is shown in Figure 6.
 Although very similar to the model pattern. the observed pattern appears to be displaced.," Although very similar to the model pattern, the observed pattern appears to be displaced."
 The measured low and high-cucrey spectral imdices for this event are notably different than those of other bursts listed in Table 2., The measured low and high-energy spectral indices for this event are notably different than those of other bursts listed in Table 2.
 The low-cnerey spectral iudex is consistent with the spectral slope below μι iu the slow-cooling mode and below m iu thefast-cooling regime., The low-energy spectral index is consistent with the spectral slope below $\nu_{\rm m}$ in the slow-cooling mode and below $\nu_{\rm c}$ in the regime.
 Tuterestingly. for the regine the ligh-cnereyv iudex is mareinally consistent with the spectral slope for MeoOyκμμ ," Interestingly, for the regime the high-energy index is marginally consistent with the spectral slope for $\nu_{\rm c} < \nu < \nu_{\rm m}$."
"The civect implication here is that m4, is above the BATSE window ud Las vet to evolve through.", The direct implication here is that $\nu_{\rm m}$ is above the BATSE window and has yet to evolve through.
 IIeuce the value of p is undetermined., Hence the value of $p$ is undetermined.
 The fix in the tail was too weak to follow the evolution of the spectrum with any reasonable accuracy., The flux in the tail was too weak to follow the evolution of the spectrum with any reasonable accuracy.
 From equation 3 aud Ll. clearly the temporal decay should be very shallow. unlike our measured value of 9—1.61," From equation 3 and 4, clearly the temporal decay should be very shallow, unlike our measured value of $\beta = -1.61_{+0.002}^{-0.013}$."
 This evolution is not consistent with the evolution of a UDspherical blast wave iuto a constant density medi., This evolution is not consistent with the evolution of a spherical blast wave into a constant density medium.
 The diverse temporal aud spectral properties of GRBs leave their origin open to different interpretations., The diverse temporal and spectral properties of GRBs leave their origin open to different interpretations.
" Frou our analysis. we have identified a subset of θα]Ταν bursts that exhibit smooth hiegh-cucrey( 25-300 keV) decay enission whose spectral properties are very simular to that of fast-cooliug svuchrotron cussion that results frou, a power-law distribution of relativistic electrons"," From our analysis, we have identified a subset of gamma-ray bursts that exhibit smooth high-energy$\sim$ 25-300 keV) decay emission whose spectral properties are very similar to that of fast-cooling synchrotron emission that results from a power-law distribution of relativistic electrons"
and. calibrated to a set of N-body simulations.,and calibrated to a set of $N$ -body simulations.
 These prove o be far more accurate (~14) than previousformulam., These prove to be far more accurate $\sim 1\%$ ) than previous.
.. Llowever these fits are only as accurate as the underlying simulations used in the fitting. which in this case were xovided by the VIRGOConsortium.," However these fits are only as accurate as the underlying simulations used in the fitting, which in this case were provided by the VIRGO."
".. In this paper we shall use the latter. more accurate fits based on the Halo Moclel ""unctional form."," In this paper we shall use the latter, more accurate fits based on the Halo Model functional form."
 While Smith et al. (, While Smith et al. (
2002) have compared heir fit to the non-linear matter power spectrum. here we compare for the first time the predicted convergence power with the results of our simulations in Section 5.1.,"2002) have compared their fit to the non-linear matter power spectrum, here we compare for the first time the predicted convergence power with the results of our simulations in Section 5.1."
 In addition to two-point statistics. higher-order statistical properties of the lensing fields are also of interest. as linear. evolution of the densitv field will introduce. non-Caussianity (oe. Jain et ab.," In addition to two-point statistics, higher-order statistical properties of the lensing fields are also of interest as non-linear evolution of the density field will introduce non-Gaussianity (e.g., Jain et al.,"
 2000)., 2000).
 Dernardeau et al. (, Bernardeau et al. (
1997) have investigated analytically the dependence. of higher-order moments in the convergence on the cosmological parameters. and in particular have discussed the ratio The significance of the S; statistic is that it is expected to be independent of the normalisation of the power spectrum. and can also be shown to be rather insensitive to the angular scale.,"1997) have investigated analytically the dependence of higher-order moments in the convergence on the cosmological parameters, and in particular have discussed the ratio The significance of the $S_3$ statistic is that it is expected to be independent of the normalisation of the power spectrum, and can also be shown to be rather insensitive to the angular scale."
 In the case of Oy=0. Dernardeau ct al. (," In the case of $\Omega_V=0$, Bernardeau et al. ("
1997) have shown that [or οςz1.,1997) have shown that for $z_s \simeq 1$.
" The ©,,, dependence is slighth weaker for sources at high redshift. and at low redshift 9S4 becomes approximately inversely proportional to O,,."," The $\Omega_m$ dependence is slightly weaker for sources at high redshift, and at low redshift $S_3$ becomes approximately inversely proportional to $\Omega_m$."
" Phe redshift dependence of 55 in an Einstein-de Sitter cosmology is approximately ος 4°"". ", The redshift dependence of $S_3$ in an Einstein-de Sitter cosmology is approximately $z_s^{-1.35}$ .
Jain et al. (, Jain et al. (
2000) have investigated the values for S5 in cillerent cosmologics for sources at ος=1. including an LODAL cosmology using N-body simulations based on reconstructing the convergence values from the shear. and including the ellects of noisy data.,"2000) have investigated the values for $S_3$ in different cosmologies for sources at $z_s = 1$, including an LCDM cosmology using $N$ -body simulations based on reconstructing the convergence values from the shear, and including the effects of noisy data."
" Using various statistics based on the reconstructed convergence. they show that there are clear dillerenees in the 54 values between the LODAL cosmologv ancl an open cosmology. ancl also claim that £2,, can be constrained to within an uncertainty of 0.1 0.2 in a deep survey of several square degrees."," Using various statistics based on the reconstructed convergence, they show that there are clear differences in the $S_3$ values between the LCDM cosmology and an open cosmology, and also claim that $\Omega_m$ can be constrained to within an uncertainty of 0.1 – 0.2 in a deep survey of several square degrees."
 We shall study the Ss statistic in more detail in Section 5.3., We shall study the $S_3$ statistic in more detail in Section 5.3.
 To evaluate the weak lensing statistics. we have applied the algorithm for computing the shear in three dimensions. as described by Couchman et al. (," To evaluate the weak lensing statistics, we have applied the algorithm for computing the shear in three dimensions, as described by Couchman et al. ("
"1999) to the cosmologica N-body simulations of the Livcra produced using the ""Hydra! i7V-bods hyelrodyvnaniics code (Couchman. Thomas Pearce. 1995).","1999) to the cosmological $N$ -body simulations of the Hydra produced using the `Hydra' $N$ -body hydrodynamics code (Couchman, Thomas Pearce, 1995)."
" Simulations of the LCDM. Dark Matter only cosmology were used. with QO,=038. Op=07. power spectrum shape parameter LP=0.25 and normalisation. vs. on scales of 8b.1 Mpe of 1.22."," Simulations of the LCDM Dark Matter only cosmology were used with $\Omega_m = 0.3,$ $\Omega_V =
0.7,$ power spectrum shape parameter $\Gamma = 0.25$ and normalisation, $\sigma_8$, on scales of $8h^{-1}$ Mpc of 1.22."
" The number of particles. each of mass 129.10415.! solar masses. was S6"" and the minimum value of the (variable) particle softening was chosen to be 0.000761.|>) in box units."," The number of particles, each of mass $1.29 \times 10^{11}h^{-1}$ solar masses, was $86^3$ and the minimum value of the (variable) particle softening was chosen to be $0.0007(1+z)$ in box units."
 The simulation volumes hack comoving side dimensions of 1005. Mpe., The simulation volumes had comoving side dimensions of $h^{-1}$ Mpc.
 To avoid obvious structure correlations between adjacent boxes. cach was arbitrarily translated. rotated (by multiples of 90°) and rellected about each coordinate axis. and in addition. cach complete run was performed. 10 times.," To avoid obvious structure correlations between adjacent boxes, each was arbitrarily translated, rotated (by multiples of $90^{\circ}$ ) and reflected about each coordinate axis, and in addition, each complete run was performed 10 times."
 The general procedure for establishing the locations within the simulations for the computations of the shear and for computing the values of the elements of the shear niatrices. is as described by Barber (2002). with the multiple lens plane theory being applied along the lines of sight.," The general procedure for establishing the locations within the simulations for the computations of the shear and for computing the values of the elements of the shear matrices, is as described by Barber (2002), with the multiple lens plane theory being applied along the lines of sight."
 In this work. a total of 455.« lines of sight were used and 300 evaluation locations for the three-climensional shear along each line of sight in cach simulation volume. thereby allowing regular sampling of the 2.67«2.6% field of view.," In this work, a total of $455 \times 455$ lines of sight were used and 300 evaluation locations for the three-dimensional shear along each line of sight in each simulation volume, thereby allowing regular sampling of the $2.6^{\circ} \times 2.6^{\circ}$ field of view."
 With this number of lines of sight. the angular resolution equates to the minimum value of the particle softening at the optimum. redshift. z=0.36. for lensing of sources at à redshift of 1.," With this number of lines of sight, the angular resolution equates to the minimum value of the particle softening at the optimum redshift, $z = 0.36$, for lensing of sources at a redshift of 1."
 To allow for the larger angular size of the minimum softening at low redshifts and also for the range of particle softening scales above the minimum: value. a resolution limit of 1 arcminute has been adopb for the data analyses.," To allow for the larger angular size of the minimum softening at low redshifts and also for the range of particle softening scales above the minimum value, a resolution limit of 1 arcminute has been adopted for the data analyses."
 A total of 14 source redshift slices were selected to give good statistical coverage of the redshifts of interest., A total of 14 source redshift slices were selected to give good statistical coverage of the redshifts of interest.
 These were redshifts of ος=0.10. 0.21. 0.29. 0.41. 0.49. 0.58. 0.72. 0.82. 0.88. 0.99. 1.53. 1.97. 3.07 and 3.57. corresponding to the redshifts of the simulation boxes.," These were redshifts of $z_s = 0.10,$ 0.21, 0.29, 0.41, 0.49, 0.58, 0.72, 0.82, 0.88, 0.99, 1.53, 1.97, 3.07 and 3.57, corresponding to the redshifts of the simulation boxes."
 Llerealter. we shall only quote these redshifts to one decimal place for brevity.," Hereafter, we shall only quote these redshifts to one decimal place for brevity."
 From the statistics. computed. in. cach of the 10 simulation runs. we computed the variances. the skewnesses. the statistic 5. and the power spectra for each of the source redshifts.," From the statistics computed in each of the 10 simulation runs, we computed the variances, the skewnesses, the statistic $S_3$, and the power spectra for each of the source redshifts."
" Phe two-point ancl higher-order moments were computed on angular scales. of /ο, 27.0. 4.0. /87.0. 16.0 and 32/.0 using a op-hat filter. ancl the power spectra values were computed for a set of 15 wavenumber bins. μαyvaced logarithmically."," The two-point and higher-order moments were computed on angular scales of $1'.0$, $2'.0$, $4'.0$, $8'.0$, $16'.0$ and $32'.0$ using a top-hat filter, and the power spectra values were computed for a set of 15 wavenumber bins, spaced logarithmically."
 Here. we report on the results [or these statisties as computed for the cllective convergence and the magnification Iluctuation. (i.c. the departure of 10 magnification value from unity).," Here we report on the results for these statistics as computed for the effective convergence and the magnification fluctuation (i.e., the departure of the magnification value from unity)."
 We computed. these statistics [rom the convergence values directly. ratherthan on convergence values reconstructed from the shear.," We computed these statistics from the convergence values directly, ratherthan on convergence values reconstructed from the shear."
 For the power spectra. the square of the absolute values of the Fourier transform of the convergence or magnification fluctuation were nornialised by multiplication by," For the power spectra, the square of the absolute values of the Fourier transform of the convergence or magnification fluctuation were normalised by multiplication by $\frac{L^2}{(2\pi)^2}.2\pi
\ell^2$ ,"
(at phase zero).,(at phase zero).
" The system is in a slightly overcontact configuration with fave,=6%. and the temperature difference between the components is small (AT=Τι,-T.180 K)."," The system is in a slightly overcontact configuration with $f_{\rm over}\approx 6\%$, and the temperature difference between the components is small $\Delta {\rm T=T_h-T_c}\approx 180$ K)."
 The optimal model of the system includes a bright spot in the neck region of the less massive. hotter component. enabling successful fitting of the slightly asymmetric light curves.," The optimal model of the system includes a bright spot in the neck region of the less massive, hotter component, enabling successful fitting of the slightly asymmetric light curves."
 This assumption is in accordance with mass exchange from the more massive primary to the secondary component that would cause the observed decrease in orbital period., This assumption is in accordance with mass exchange from the more massive primary to the secondary component that would cause the observed decrease in orbital period.
 At the same time. the hot region in the neck zone of the common envelope. located on the less massive secondary. can be interpreted as one consequence of an intensive energy transfer from the primary to the secondary.," At the same time, the hot region in the neck zone of the common envelope, located on the less massive secondary, can be interpreted as one consequence of an intensive energy transfer from the primary to the secondary."
 The distance of the system. estimated from the absolute magnitude obtained with our model. is within the uncertainty limits of the distance based on the new Hipparcos parallax of 85+ I8pe. given by vanLeeuwen|(2007).," The distance of the system, estimated from the absolute magnitude obtained with our model, is within the uncertainty limits of the distance based on the new Hipparcos parallax of $85 \pm 18 \rm pc$ , given by \citet{vanlee07}."
. We found it unnecessary to include a third light in the solution. and that supports the findings of Pribullaetal.(2009a).. who found no spectroscopic evidence of a third body in the system.," We found it unnecessary to include a third light in the solution, and that supports the findings of \citet{priba09}, who found no spectroscopic evidence of a third body in the system."
"= Comparison of our results with the parameters reported by Miloneetal.(1987).. which were based on the underestimatedvalue of the mass ratio from Miloneetal.(1985).. show that our solution. gives higher masses of the components CNlilone=0.56M.. . Ma,Milone=0.20M. anc Nl.thisstudy=0.80 Mos. Alastudy=0.38 Me). a smaller overcontact factor (Fui,=1796 and fugiguy= 6096) and larger radii (Μονο=0.67Ra. Ry.ion=OALRe and Retisstudy0.77 Re. 'Ryhisstudy=0.54 As). with approximately the same inclination and considerably lower temperatures. which is a consequence of the cooler spectral type assigned to this system by Pribullaetal.(2009a)."," Comparison of our results with the parameters reported by \citet{mila87}, which were based on the underestimatedvalue of the mass ratio from \citet{mila85}, show that our solution gives higher masses of the components ${\cal M}_{\rm c,\ Milone}=0.56\ M_\odot$ , ${\cal M}_{\rm h,\ Milone}=0.20\ M_\odot$ and ${\cal M}_{\rm c,\ this\ study}=0.80\ M_\odot$ , ${\cal M}_{\rm h,\ this\ study}=0.38\ M_\odot$ ), a smaller overcontact factor $f_{Milone}=17\%$ and $f_{this\ study}=6\%$ ) and larger radii ${\cal R}_{\rm c,\ Milone}=0.67\ R_\odot$, ${\cal R}_{\rm h,\ Milone}=0.41\ R_\odot$ and ${\cal R}_{\rm c,\ this\ study}=0.77\ R_\odot$ , ${\cal R}_{\rm h,\ this\ study}=0.54\ R_\odot$ ), with approximately the same inclination and considerably lower temperatures, which is a consequence of the cooler spectral type assigned to this system by \citet{priba09}."
. However. the absolute bolometric magnitudes and the estimated distances are 1 relatively good agreement.," However, the absolute bolometric magnitudes and the estimated distances are in relatively good agreement."
 MR Del (GSC 00518-1755. HD 195434. ADS 13940) is the brighter component of a visual binary system.," MR Del (GSC 00518-1755, HD 195434, ADS 13940) is the brighter component of a visual binary system."
 It is an eclipsing binary (Cutispotoetal.1997).. separated from its visual companion by [.8 at 71? (Masonetal...2001).," It is an eclipsing binary \citep{cuti97}, separated from its visual companion by $^{""}$ .8 at $^{\circ}$ \citep{mason01}."
 The whole system was classified as a halo population object or an old disk star by Cutispotoetal. (1997).. based on its proper motion and low metallicity (Carneyetal.1994:Sandage&Kowal1986).," The whole system was classified as a halo population object or an old disk star by \cite{cuti97}, , based on its proper motion and low metallicity \citep{carney94,sandkow86}."
 This makes it an interesting object. because it displays soft X-ray emission (Pyeetal.1995) and photospherie spot activity (Cutispotoetal.1997) despite its age.," This makes it an interesting object, because it displays soft X-ray emission \citep{pye95} and photospheric spot activity \citep{cuti97} despite its age."
 An out-of-eclipse variation with an amplitude of 0.04 mag. observed in the V band light curve of the system. was interpreted as coming from a large spot covering of the primary star's surface (Cutispotoetal.1997).," An out-of-eclipse variation with an amplitude of 0.04 mag, observed in the V band light curve of the system, was interpreted as coming from a large spot covering of the primary star's surface \citep{cuti97}."
. Although the system also displayed variations in. X-ray emission. which were thought to be coming from the eclipsing component of the visual binary. it was not correlated with the light curve (Cutispotoetal. 1997)..," Although the system also displayed variations in X-ray emission, which were thought to be coming from the eclipsing component of the visual binary, it was not correlated with the light curve \citep{cuti97}. ."
 The eclipsing component of the visual binary was later named MR Del by Kazarovetsetal.(1999)., The eclipsing component of the visual binary was later named MR Del by \citet{kaz99}.
". The dispute over the magnitudes of each of the components of the visual binary was ended by Masonetal.(2001).. who gave 9"".49 for the V band magnitude of MR Del. Clausenetal.(2001) obtained ubvy light curves of the system. and observed a flare event lasting for 25 minutes."," The dispute over the magnitudes of each of the components of the visual binary was ended by \citet{mason01}, who gave $^{m}$ .49 for the V band magnitude of MR Del. \citet{clau01} obtained ubvy light curves of the system, and observed a flare event lasting for 25 minutes."
 They also point out the night-to-night differences in the light curves. increasing in strength from y to u band. which they attribute to surface activity.," They also point out the night-to-night differences in the light curves, increasing in strength from y to u band, which they attribute to surface activity."
 Pribullaetαἱ.(2009b) observed the system spectroscopically., \citet{pribb09} observed the system spectroscopically.
They computedthe light contribution of the visual companionas L3/(L;+L2)= 0.1.,They computedthe light contribution of the visual companionas $\rm L_3/(L_1+L_2)=0.51$ .
 The broadening functions they employed to obtainradial velocities did notshow any evidence of photospheric spots., The broadening functions they employed to obtainradial velocities did notshow any evidence of photospheric spots.
 They found, They found
to the predictions of the hierarchical galaxy formation simulations (e.g. Benson et al.,to the predictions of the hierarchical galaxy formation simulations (e.g. Benson et al.
 2002). 1 will provide an important test for these simulations.," 2002), it will provide an important test for these simulations."
" Through out this paper. we adopt the A-cosmologyv with £€2,,=0.3 and O4=0.7. h=IHo/(100kmsec!INMpe1"," Through out this paper, we adopt the $\Lambda$ -cosmology with $\Omega_m=0.3$ and $\Omega_\Lambda = 0.7$, $h = {\rm H}_0/(100\; {\rm km~sec}^{-1} {\rm Mpc}^{-1})$."
 The parent sample is selected from the matehed 2MASS-2dFGRBRS catalog of Cole et al. (, The parent sample is selected from the matched 2MASS-2dFGRS catalog of Cole et al. (
2001). which has 45289 galaxies with measured J (1.25500). ος) and Iv; (2.1640) nagnitudes from the Extend Source Catalog (XSC) of 241ASS.,"2001), which has 45289 galaxies with measured J $\mu m$ ), $\mu m$ ) and ${\rm K_s}$ $\mu m$ ) magnitudes from the Extend Source Catalog (XSC) of 2MASS."
" The default. νου magnitude is used for the IX, band fluxes (Jarrett et al.", The default ${\rm K_{20}}$ magnitude is used for the ${\rm K_s}$ band fluxes (Jarrett et al.
 2000)., 2000).
 Among 45289 galaxies. 17173 have neasured redshifts from the 2dFGRS survey.," Among 45289 galaxies, 17173 have measured redshifts from the 2dFGRS survey."
 It is known that the coverage of the 2dEGIUS survey is not uniform. and there are holes between individual 2dF fields (Colless et al 2001).," It is known that the coverage of the 2dFGRS survey is not uniform, and there are holes between individual 2dF fields (Colless et al 2001)."
 In order (o minimize (he uncertainties in our pair statistics due to the uneven reclshilt coverage. we restrict (he parent sample to galaxies which have the redshilt completeness index e.>0.5. where ο. is defined as the ratio between the number of galaxies with measured redshifts and the total inunber of galaxies within 1 deg radius from the center of the galaxy in question.," In order to minimize the uncertainties in our pair statistics due to the uneven redshift coverage, we restrict the parent sample to galaxies which have the redshift completeness index $c_{z} \geq 0.5$, where $c_z$ is defined as the ratio between the number of galaxies with measured redshifts and the total number of galaxies within 1 deg radius from the center of the galaxy in question."
 Our final parent sample has 19053 galaxies. of which 14083 have measured redshifts redshift completeness).," Our final parent sample has 19053 galaxies, of which 14083 have measured redshifts redshift completeness)."
 The number counts of all galaxies and of ealaxies with measured redshifts in the parent sample are plotted in Fig.l., The number counts of all galaxies and of galaxies with measured redshifts in the parent sample are plotted in Fig.1.
" Apparently the saniple is complete down to WK, = 13.5. which is the completeness limit of the NSC (Jarret et al."," Apparently the sample is complete down to ${\rm K_s}$ = 13.5, which is the completeness limit of the XSC (Jarrett et al."
 2000)., 2000).
" There is no sienilicant dependence of the redshift completeness on the Ix, magnitude.", There is no significant dependence of the redshift completeness on the ${\rm K_s}$ magnitude.
 In the pair selection procedure. we search for neighbors around every galaxy. with a measured redshift in (he parent sample.," In the pair selection procedure, we search for neighbors around every galaxy with a measured redshift in the parent sample."
 Neighbors are not required to have measured redshifts., Neighbors are not required to have measured redshifts.
" Among the matches. we select pairs according to the following criteria: (1) The Ix, magnitude of the primary is not fainter than 12.5."," Among the matches, we select pairs according to the following criteria: (1) The ${\rm K_s}$ magnitude of the primary is not fainter than 12.5."
 A primary is defined as the brighter, A primary is defined as the brighter
Nelemanusetal.(2001). obtained VLT optical PAvectra of aan identified features of relatively low ionisation states of carbon aud oxveeu.,\citet{Nelemans04} obtained VLT optical spectra of and identified features of relatively low ionisation states of carbon and oxygen.
 This clearly identifies aas an UCXD and sugeests that the donor iu je system dn a carbon-oxvecu white dwarf., This clearly identifies as an UCXB and suggests that the donor in the system in a carbon-oxygen white dwarf.
 For aand 11626-67 there are clear indications wat the dises are dominated by Co and O. Werneretal.(2006) have also obtained VLT spectra aud compared them with detailed NLTE nodels for spectra of UCNBs.," For and 1626-67 there are clear indications that the discs are dominated by C and O. \citet{Werner06}
 have also obtained VLT spectra and compared them with detailed NLTE models for spectra of UCXBs."
 Uutortunately. 1 NTLE models do not sufficiently agree with 16 observed spectra for quantitative abundance analvsis.," Unfortunately, the NTLE models do not sufficiently agree with the observed spectra for quantitative abundance analysis."
 Although simple LTE models secur to fit the data better. they also caunot be used for quantitative measurements because NLTE effects nainly due to N-ray inmradiation. need to be taken into account.," Although simple LTE models seem to fit the data better, they also cannot be used for quantitative measurements because NLTE effects mainly due to X-ray irradiation, need to be taken into account."
 We have found several sinusoidal modulation in the optical lizhteurve of091., We have found several sinusoidal modulation in the optical lightcurve of.
. These modulations most likely arise frou either N-ray radiation of the iuner face of the secondary star and/or a superhunp modulation from the accretion disc. or quasi-periodic oscillations iu the accretion disc.," These modulations most likely arise from either X-ray irradiation of the inner face of the secondary star and/or a superhump modulation from the accretion disc, or quasi-periodic oscillations in the accretion disc."
 This is not surprising as UCNBs are known to show orbital modulations as well as QPOs., This is not surprising as UCXBs are known to show orbital modulations as well as QPOs.
 e.g. stroug 15 imiuute optical/UV. quasi-periodic oscillations were previously detected iu the aunmin CONB 1162667 (Chakrabartyctal. 2001).. showing that photometric variability iu an UCXD nee uot onlv occur near the orbital period.," e.g. strong 15 minute optical/UV quasi-periodic oscillations were previously detected in the min UCXB 1626–67 \citep{Chak01}, showing that photometric variability in an UCXB need not only occur near the orbital period."
 O'Brien(2005)., \citet{OBrien05} \\citep{Nelemans06}.
of primary eclipse.,of primary eclipse.
 In Fig., In Fig.
 G6 we sketch what we suggest would be the reflection elfect without any secondary eclipse: the asymmetry. namely the carly fall in brightness before the start of primary eclipse is probably caused by partial obscuration of the bright face of the companion star by the gas stream passing from it to the outer edge of the disc.," \ref{warnerfig6} we sketch what we suggest would be the reflection effect without any secondary eclipse; the asymmetry, namely the early fall in brightness before the start of primary eclipse is probably caused by partial obscuration of the bright face of the companion star by the gas stream passing from it to the outer edge of the disc."
 The rellection elfect ancl secondary eclipse are similar. but of ereater amplitude. to what we saw in the nova remnant DD Cir (Woudt Warner 2003). where we ascribed a shallow secondary eclipse to an optically thick almost edge-on disc passing across the heated hemisphere of the companion star.," The reflection effect and secondary eclipse are similar, but of greater amplitude, to what we saw in the nova remnant DD Cir (Woudt Warner 2003), where we ascribed a shallow secondary eclipse to an optically thick almost edge-on disc passing across the heated hemisphere of the companion star."
 In V597 Pup the total widths of the primary and secondary eclipses are both ~ -x0.15 of £u., In V597 Pup the total widths of the primary and secondary eclipses are both $\sim$ $\pm$ 0.15 of $P_{orb}$.
 There is great variability in the profile and. depth of the secondary. eclipse. as could be expected. from a disc of rapidly changing structure.," There is great variability in the profile and depth of the secondary eclipse, as could be expected from a disc of rapidly changing structure."
 Figs., Figs.
 5 and 6. show that the 0.2 mag decrease in brightness from February to March. 2009 has resulted in a deeper primary eclipse as the fading ejecta reduce the amount of in-Lill.," \ref{warnerfig5}
 and \ref{warnerfig6} show that the 0.2 mag decrease in brightness from February to March 2009 has resulted in a deeper primary eclipse as the fading ejecta reduce the amount of in-fill."
 Inspection of the individual light curves in Fig., Inspection of the individual light curves in Fig.
 4 shows that during primary ancl secondary eclipses there is Hickering similar to that ποσα out of eclipse. so at least one Lickering source is still visible curing eclipse.," \ref{warnerfig4} shows that during primary and secondary eclipses there is flickering similar to that seen out of eclipse, so at least one flickering source is still visible during eclipse."
 Apart from that. certainly the secondary anc possibly the primary eclipse. appear Lat bottomed. as in a total eclipse or a transit.," Apart from that, certainly the secondary and possibly the primary eclipse, appear flat bottomed, as in a total eclipse or a transit."
 The FP of the combined 2008 light. curves is shown in Fig. 7.., The FT of the combined 2008 light curves is shown in Fig. \ref{warnerfig7}.
 Phere ts red noise at low frequencies. associated with lckering and with harmonies of the orbital modulation. but an isolated cluster of peaks in the vicinity. of 3800 plz is evident.," There is red noise at low frequencies, associated with flickering and with harmonics of the orbital modulation, but an isolated cluster of peaks in the vicinity of 3800 $\mu$ Hz is evident."
 On detailed. examination five components are found. with the [frequencies and. amplitudes. listed. in Jab. 2..," On detailed examination five components are found, with the frequencies and amplitudes listed in Tab. \ref{warnertab2},"
 found from a 5 sinusoid simultaneous Least. squares fit., found from a 5 sinusoid simultaneous least squares fit.
 Uncertainties of the frequencies are all ~ £0.5 112 and of the amplitudes are 0.7 mmag., Uncertainties of the frequencies are all $\sim$ $\pm$ 0.5 $\mu$ Hz and of the amplitudes are $\pm$ 0.7 mmag.
 The phases (with arbitrary zero point) are quoted as fractions of evcles., The phases (with arbitrary zero point) are quoted as fractions of cycles.
 “Phe largest amplitude signal is at 261.9 s. As further evidence for the significance of these signals we produce in Fig., The largest amplitude signal is at 261.9 s. As further evidence for the significance of these signals we produce in Fig.
 S an O — € phase diagram relative to the central frequency. and comparison with the same diagram produced by a simulation using the five sinusoidal signals listed in Tab. 2..," \ref{warnerfig7b}
 an O – C phase diagram relative to the central frequency and comparison with the same diagram produced by a simulation using the five sinusoidal signals listed in Tab. \ref{warnertab2}."
 The mean splitting between the components in 2008 is 104.15 plz. which. within errors. is the same as the orbital [requeney.," The mean splitting between the components in 2008 is 104.15 $\mu$ Hz, which, within errors, is the same as the orbital frequency."
 Lt is therefore clear that in 2008 a quintuplet. of frequencies was present with internal splitting equal to the, It is therefore clear that in 2008 a quintuplet of frequencies was present with internal splitting equal to the
also introduce significant errors on the attenuation of galaxies.,also introduce significant errors on the attenuation of galaxies.
 In à previous paper (Bacs Dejonghe 2001. paper L) we described. four different methods to solve the R'E in a plane-parallel gcometry.," In a previous paper (Baes Dejonghe 2001, paper I) we described four different methods to solve the RTE in a plane-parallel geometry."
 “Phese methods. accomocate an arbitrary vertical distribution of stars and dust., These methods accomodate an arbitrary vertical distribution of stars and dust.
 We will now use these methods will allow us to ackelress both issues of the WE mentioned above., We will now use these methods will allow us to address both issues of the RTE mentioned above.
 On the one hand. we can adopt them for a disc galaxy model with a realistic vertical structure. and compare the results with those obtained by using the various approximate solutions.," On the one hand, we can adopt them for a disc galaxy model with a realistic vertical structure, and compare the results with those obtained by using the various approximate solutions."
 This will allow us to quantify the errors introduced by the cdillerent approximations. aud the importance of properly including scattering. effects.," This will allow us to quantify the errors introduced by the different approximations, and the importance of properly including scattering effects."
 On the other hand. we can apply these methods. to afamily of realistic galaxy models that can accomodate a wide range in distribution of stars anc dust.," On the other hand, we can apply these methods to a of realistic galaxy models that can accomodate a wide range in distribution of stars and dust."
 This. will allow us to investigate the influence of the geometry. of the stellar and dust components on the attenuation curve. without any simplifving assumptions on the RPE such as the neglect. of scattering.," This will allow us to investigate the influence of the geometry of the stellar and dust components on the attenuation curve, without any simplifying assumptions on the RTE such as the neglect of scattering."
 Last but not least. we can solve our RPE problems with four completely. different methods: consistency is then a guarantee for accuracy.," Last but not least, we can solve our RTE problems with four completely different methods: consistency is then a guarantee for accuracy."
 In Section. 2 we cdescribe the radiative transfer mechanism and the wavs to obtain the solution. and in Section 3. we present our set of disc galaxy models.," In Section 2 we describe the radiative transfer mechanism and the ways to obtain the solution, and in Section 3, we present our set of disc galaxy models."
 In Section 4 and 5 we discuss respectively the influence of scattering anc geometry on the attenuation curve as described above., In Section 4 and 5 we discuss respectively the influence of scattering and geometry on the attenuation curve as described above.
 In Section 6 we cliscuss the results., In Section 6 we discuss the results.
 In plane-parallel ecomoetryv. the RPE can be written as ∠∐↓⋅⋖⋅≼⇍⇂⊲↓∪⊔∖∖⊽↓↕⊀⊔⇍↓↥⊔↓⋜↧↳⋖⋅⊳∖⋜⋯⋜⋯⋏∙≟↓∢⋅⋜⊔⋅≼∼⊓⇤∕∣∖∖⋰∐↓↕↿⇂⊔⊾⇂⋅⋯∼∢⊾−∪⊔ ∠∐↓⋅⋖⋅≼⇍⇂⊲↓∪⊔∕∣∶↓⊳↾∐∐⋅↳⊔⋯∖⊽⊔⊏↥⇂⋯⊔⇂⊲↓↿⊲⊓⋅⊳," In plane-parallel geometry, the RTE can be written as where $I(z,\mu)$ is the specific intensity of the radiation at a height $z$ above the plane of the galaxy, and in a direction which makes an angle $\arccos\mu$ with the face-on direction $\mu=1$."
∖∐↕↿↓∏⊳∖∢⊾⊏↥⊔⋜⊔⊲↓∪⊔⋜⊔⋅⋖⊾ ↿↓↕⋖⋅∠⇂⊔⊳∖↿∪↓≻⋯⋰↓↿∙∖⇁∣⋅⋅↿∖∶⊐⊳↿↓↕⋖⋅⊳∖↿⋖⊾∐⋜⊔⋅⋖⋅⊔↓⊀↓⊳∖⊳∖⊲↓∖⋰↓↿∙∖⇁↗∣↴↿∖∶∃⊳↿↓∐⋅∠⇂⊔⊳∖↿ albedo c and the angular redistribution function (hereafter ARE) Weg).," The known quantities in this equation are the dust opacity $\kappa(z)$, the stellar emissivity $\eta_*(z)$, the dust albedo $\omega$ and the angular redistribution function (hereafter ARF) $\Psi(\mu,\mu')$."
" The RPE can be brought in another form by introducing the optical depth 7 instead of z. which vields with S,(r)=is(r)/n(r) is the stellar source function."," The RTE can be brought in another form by introducing the optical depth $\tau$ instead of $z$, which yields with $S_*(\tau) = \eta_*(\tau)/\kappa(\tau)$ is the stellar source function."
 This equation is to be solved for 0xτς75. the total optical (face-on) depth of the galaxy. Although the RTE can be solved for any point in the galaxy. we will focus on the attenuation ly). tthe fraction of the intensity that is attenuated by the dust detected by an observer at 7=0. into a certain clirection pi," This equation is to be solved for $0\leq\tau\leq\tau_0$, the total optical (face-on) depth of the galaxy, Although the RTE can be solved for any point in the galaxy, we will focus on the attenuation $A(\mu)$, the fraction of the intensity that is attenuated by the dust detected by an observer at $\tau=0$, into a certain direction $\mu$."
 Decause the IPIS is a linear equation. this fraction will be independent of the total amount of stellar emission.," Because the RTE is a linear equation, this fraction will be independent of the total amount of stellar emission."
 We can thus choose the normalization of the stellar emissivity (or the source function)., We can thus choose the normalization of the stellar emissivity (or the source function).
 We take which means that the intensity that leaves the galaxy in the absence of dust in the face-on direction equals 1., We take which means that the intensity that leaves the galaxy in the absence of dust in the face-on direction equals 1.
 In another direction fr. the clust-free intensity is then simply l/j and the attenuation (in magnitudes) is Beeause of the complexity. of the RPE. a lot. of authors have tried their ingenuity to find sophisticated. methods to solve it.," In another direction $\mu$, the dust-free intensity is then simply $1/\mu$ and the attenuation (in magnitudes) is Because of the complexity of the RTE, a lot of authors have tried their ingenuity to find sophisticated methods to solve it."
 In. paper Lowe presented four dillerent. methocls to solve the REIS in plane-parallel &cometry.. which can handle absorption and multiple scattering. arbitrary vertical distributions ofstars and dust and arbitrary phase functions.," In paper I we presented four different methods to solve the RTE in plane-parallel geometry, which can handle absorption and multiple scattering, arbitrary vertical distributions of stars and dust and arbitrary phase functions."
 For more details about these methods anc references to the literature we refer to paper L In this paper we will study the radiative transfer through a plane-parallel, For more details about these methods and references to the literature we refer to paper I. In this paper we will study the radiative transfer through a plane-parallel
Av and óvo» are affected by the errors in the treatment of the near-surface layers.,$\Delta \nu$ and $\delta \nu_{02}$ are affected by the errors in the treatment of the near-surface layers.
" Modeling indicates that, e.g., the ratio of ὄνρο to Av is less sensitive to surface layer effects (Roxburgh&Vorontsov2003;OtíFloranesetal. 2005)."," Modeling indicates that, e.g., the ratio of $\delta\nu_{02}$ to $\Delta\nu$ is less sensitive to surface layer effects \citep{Roxburgh03,OtiFloranes05,Mazumdar05}."
". Figure 8 shows a modified C-D diagram, which uses this frequency-separation ratio, although the surface dependency remains in Av."," Figure \ref{fig8} shows a modified C-D diagram, which uses this frequency-separation ratio, although the surface dependency remains in $\Delta\nu$."
" The isochrones are close to horizontal in this figure, showing that this ratio is an effective indicator of age."," The isochrones are close to horizontal in this figure, showing that this ratio is an effective indicator of age."
" We note that Av is typically measured from the |=1 modes when calculating this ratio, but since the |=1 modesdepart significantly from the asymptotic relation for more evolved stars, we have determined Av using only |=0 modes."," We note that $\Delta\nu$ is typically measured from the $l=1$ modes when calculating this ratio, but since the $l=1$ modesdepart significantly from the asymptotic relation for more evolved stars, we have determined $\Delta\nu$ using only $l=0$ modes."
" In the absence of avoided crossings, the difference between Av as measured from |=0 and |—1 modes is small, so we expect this change in the definition of the ratio óvo3/ Av to have little impact."," In the absence of avoided crossings, the difference between $\Delta\nu$ as measured from $l=0$ and $l=1$ modes is small, so we expect this change in the definition of the ratio $\delta\nu_{02}$ $\Delta\nu$ to have little impact."
 Variations on the C-D diagram may be constructed by using different small separations in place of ὄνρο., Variations on the C-D diagram may be constructed by using different small separations in place of $\delta\nu_{02}$.
" Mazumdar(2005) and Montalbánetal.(2010) have investigated the C-D diagram using óvoj for main-sequence and RGB stars, respectively."," \citet{Mazumdar05} and \citet{Montalban10} have investigated the C-D diagram using $\delta\nu_{01}$ for main-sequence and RGB stars, respectively."
" For subgiants, ὄνρι becomes poorly defined due to avoided crossings causing a major departure from the asymptotic relation andMetcalfeetal.2010;Campante2011;Mathuretal.2011,for examples)."," For subgiants, $\delta\nu_{01}$ becomes poorly defined due to avoided crossings causing a major departure from the asymptotic relation and][for ."
 We have therefore not considered the óvo1-Av C-D diagram here., We have therefore not considered the $\delta\nu_{01}$ $\Delta\nu$ C-D diagram here.
" The C-D diagram is clearly most useful for main-sequence stars, particularly for masses «1.5Mo, for which the evolutionary tracks are well separated."," The C-D diagram is clearly most useful for main-sequence stars, particularly for masses $<\!\!1.5\,\rm{M}_\odot$, for which the evolutionary tracks are well separated."
" As stars evolve off the main sequence, their tracks converge for the subgiant and red-giant evolutionary stages."," As stars evolve off the main sequence, their tracks converge for the subgiant and red-giant evolutionary stages."
 This convergence of the tracks means that the C-D diagram is not a good discriminant of age and mass for these stars., This convergence of the tracks means that the C-D diagram is not a good discriminant of age and mass for these stars.
" This behavior of the model tracks is consistent with early results of red giants observed byKepler (Beddingetal.2010a;Huberetal.2010) and the modeling results of Montalbánetal.(2010),, for which it was found that ὄνρο is an almost fixed fraction of Av."," This behavior of the model tracks is consistent with early results of red giants observed by \citep{Bedding10c,Huber10} and the modeling results of \citet{Montalban10}, for which it was found that $\delta\nu_{02}$ is an almost fixed fraction of $\Delta\nu$."
" This also explains theobservation by Metcalfeetal.(2010),, when modeling theKepler subgiant 111026764, that including ὄνρο in the fit to the models did not provide an additional constraint beyond that provided by Av."," This also explains theobservation by \citet{Metcalfe10}, when modeling the subgiant 11026764, that including $\delta\nu_{02}$ in the fit to the models did not provide an additional constraint beyond that provided by $\Delta\nu$."
" To compare the models with observations we have measured Av, dvog and e from the published frequency lists of 20 stars using the methods outlined in Section ??.."," To compare the models with observations we have measured $\Delta\nu$ , $\delta\nu_{02}$ and $\epsilon$ from the published frequency lists of 20 stars using the methods outlined in Section \ref{Measure}. ."
" The method described above was used for calculating dVo2 except that, apart from the Sun, the data did not"," The method described above was used for calculating $\delta\nu_{02}$ except that, apart from the Sun, the data did not"
back into a [ree-stveaminge regime.e with a substantially shorterA than is required to meet the power balance condition.,"back into a free-streaming regime, with a substantially shorter$\lambda$ than is required to meet the power balance condition."
 The turbulence then drains rapidly., The turbulence then drains rapidly.
 From the above two paragraphs. we conclude that the cascade would be truncated at a scale no smaller Chan the mininium of δρ and Ay.," From the above two paragraphs, we conclude that the cascade would be truncated at a scale no smaller than the minimum of $\lambda_p$ and $\lambda_f$."
 To assess the mininnun scale of dissipation for the Revnolds laver. we assume that the pitch angle scattering is dominated bv electron- Coulomb scattering.," To assess the minimum scale of dissipation for the Reynolds layer, we assume that the pitch angle scattering is dominated by electron-electron Coulomb scattering."
" Spitzer.(1967) [finds the Coulomb sell-collision lime. /,.. (o be where 7; is the electron temperature. ancl InX25 is determined by the effective long range cnlolf of the Coulomb force in a plasma."," \citet{Spitzer} finds the Coulomb self-collision time, $t_c$, to be where $T_e$ is the electron temperature, and $\ln\Lambda \backsim 25$ is determined by the effective long range cutoff of the Coulomb force in a plasma."
" The electron speed is given by c=/25T/m,. and thus where T,= /10!.For the range of observed temperatures in Revnoldsetal. (1999). 0.6«T,1.2. the electron mean free path falls in the range 8xο Ap<3xX10 em."," The electron speed is given by $v_e = \sqrt{2kT/m_e}$, and thus where $T_4 = T_e/10^4$ .For the range of observed temperatures in \citet{Reynolds}, , $0.6 < T_4 < 1.2$, the electron mean free path falls in the range $8 \times 10^{12}$ cm $\lambda_p < 3 \times 10^{13}$ cm."
 Taking the lower limit of this range fixes the lower bound of the cascade truncation scale., Taking the lower limit of this range fixes the lower bound of the cascade truncation scale.
" In the free streaming limit we can find Ay by setting ey=17,(SE)y. For the observed temperature range of 0.6<T;L2.IS I0PemAp>5x LOMem."," In the free streaming limit we can find $\lambda_{f}$ by setting $\epsilon_T = n_e (\frac{dE}{dt})_{f}$, For the observed temperature range of $0.6 < T_4 < 1.2$, $10^{15}$ $ > \lambda_{f} > 5 \times 10^{14}$ cm."
 This sels an upper bound on (he cascade (uncalion scale., This sets an upper bound on the cascade truncation scale.
 It should be noted that the fee streaming approximation is invalid in the Revnolcs laver as λεΑρτLOO at Τι=6., It should be noted that the free streaming approximation is invalid in the Reynolds layer as $\lambda_{f}/\lambda_p = 100$ at $T_4 = 6$.
 There are. on average 100 pitch angle scattering events per electron per encounter with a compression.," There are, on average 100 pitch angle scattering events per electron per encounter with a compression."
 Given (the low Iraction of encounters which result in a reflection. F. electrons cannot stream [reelv [rom one reflection site to thenext.," Given the low fraction of encounters which result in a reflection, $F$ , electrons cannot stream freely from one reflection site to thenext."
 The quantity £F is determined by (the pitch angle condition for reflection, The quantity $F$ is determined by the pitch angle condition for reflection
Ultraluminous infrared galaxies (ULIRGs) are defined as galaxies with Ly;=Lyiij>PL. (Il; =75 km ! +. αμ =0).,"Ultraluminous infrared galaxies (ULIRGs) are defined as galaxies with $\rm{L_{IR}=L_{8-1000 \mu m} > 10^{12}~L_\odot}$ $\rm{_0 =}$ 75 km $^{-1}$ $^{-1}$, $\rm{_0 = }$ 0)."
 Ground-based observations have shown that almost all of these galaxies are undergoing mergers (e.g. Sanders οἱ al., Ground-based observations have shown that almost all of these galaxies are undergoing mergers (e.g. Sanders et al.
 1933): these galactic mergers are thought to be the progenitors of some elliplical galaxies (e.g. Genzel et al., 1988); these galactic mergers are thought to be the progenitors of some elliptical galaxies (e.g. Genzel et al.
 2001: Veilleux et al., 2001; Veilleux et al.
 2002) and max be a phase through which galaxies pass before a quasar is formed., 2002) and may be a phase through which galaxies pass before a quasar is formed.
 ULIRGs in (he local universe may be compared wilh submillimeter sources al z= 1d observed with ihe SCUBA instrument (e.g. Smail et al., ULIRGs in the local universe may be compared with submillimeter sources at z = 1–4 observed with the SCUBA instrument (e.g. Smail et al.
 1997: Hughes et al., 1997; Hughes et al.
 1993)., 1998).
 The mean properties (Lay. M(IHs). and near-infrared colors) of the two classes are remarkably similar.," The mean properties $\rm{_{IR}}$, $_2$ ), and near-infrared colors) of the two classes are remarkably similar."
 Integration ol the light from the ULIRG/SCUDA population shows that it may account for most or all of (he submillimeter/Eu-inlrared background. as a result of the strong cosmological evolution of these sources.," Integration of the light from the ULIRG/SCUBA population shows that it may account for most or all of the submillimeter/far-infrared background, as a result of the strong cosmological evolution of these sources."
 It is thus important to study the nature of ULIRGs at modest redshifts in order to understand their evolution and star formation at high redshifts., It is thus important to study the nature of ULIRGs at modest redshifts in order to understand their evolution and star formation at high redshifts.
 One fandamental question that needs to be acldressed is whether the high huninositv of these galaxies results [rom starbursts or accretion onto supermassive black holes (8MDBIIS)., One fundamental question that needs to be addressed is whether the high luminosity of these galaxies results from starbursts or accretion onto supermassive black holes (SMBHs).
 Optical and infrared spectra suggest the energy source of ULIRGs is mostly from starbursts (e.g. Veilleux et al., Optical and infrared emission-line spectra suggest the energy source of ULIRGs is mostly from starbursts (e.g. Veilleux et al.
 1997: Genzel et al., 1997; Genzel et al.
 1993) while (he “warm” inlrared colors of some objects. especially the more luminous galaxies. suggest black hole driven activity (e.g. 9urace Sanders 1999).," 1998) while the “warm” infrared colors of some objects, especially the more luminous galaxies, suggest black hole driven activity (e.g. Surace Sanders 1999)."
 There nav exist an evolutionary sequence of merger-induced starburst galaxies (7cool ULIBRGs). then “warm ULIBRGs. and then eventually Quasi-Stellar Objects (QSOs).," There may exist an evolutionary sequence of merger-induced starburst galaxies (“cool” ULIRGs), then “warm” ULIRGs, and then eventually Quasi-Stellar Objects (QSOs)."
 II this sequence is valid. one would expect dominance by active galactic nuclei (AGNs) in “warm” ULIRGs and. indeed. they tend to have Sevfert-like optical ancl near-intrarecl spectra (see e.g. Veilleux οἱ al.," If this sequence is valid, one would expect dominance by active galactic nuclei (AGNs) in “warm” ULIRGs and, indeed, they tend to have Seyfert-like optical and near-infrared spectra (see e.g. Veilleux et al."
 1995. 1999a.b).," 1995, 1999a,b)."
 Such an evolutionary sequence can also be tested wilh X-ray observations., Such an evolutionary sequence can also be tested with X-ray observations.
eroups and clusters which do not have a companion within ry<1005.+ kpe and AV.<350km/s.,groups and clusters which do not have a companion within $r_{\rm p} <100 h^{-1}$ kpc and $\Delta V < 350 {\rm km/s}$.
 We stress the fact that this comparison sample of galaxies in groups shares the same environment ancl has the same redshift distributions than the sumple of galaxy pairs in groups., We stress the fact that this comparison sample of galaxies in groups shares the same environment and has the same redshift distributions than the sample of galaxy pairs in groups.
 The selection of galaxy pairs by using projected: velocity differences (AV) ancl projected: separation (19) has the drawback that spurious pairs can be included., The selection of galaxy pairs by using projected velocity differences $\Delta V$ ) and projected separation $r_{\rm p}$ ) has the drawback that spurious pairs can be included.
 Phe use of cut-olfs for both variables helps to diminsh the problem. although they do not solve it complete.," The use of cut-offs for both variables helps to diminsh the problem, although they do not solve it complete."
 In. particular. the ellects of spurious pairs are expected to be stronger in high density regions (Mamon 1986: LOST).," In particular, the effects of spurious pairs are expected to be stronger in high density regions (Mamon 1986; 1987)."
" In order to assess the effects of spurious pairs in our observational analvsis. we have used the 2dbCGIs mock catalog constructed by Merchánn. ancl Zancdivarez (2002) from a gravitacional numerical simulation of the concordance A cold dark matter universe (Q,,,=0.9... 0.7. LL = 7Okms7pe and ox= 0.9)."," In order to assess the effects of spurious pairs in our observational analysis, we have used the 2dFGRS mock catalog constructed by Merchánn and Zandivarez (2002) from a gravitacional numerical simulation of the concordance $\Lambda$ cold dark matter universe $\Omega_m=0.3, \Omega_{\gamma}=0.7$ , H = $70 {\rm
km s^{-1} Mpc^{-3}}$ and $\sigma_8=0.9$ )."
 The authors performed this simulations by using the HEY N-bocdy code developed by Couchman. Phomas Pearce DICA.(1995) with 1287 particles in à cubic comoving volume of 180 5.1 Alpe yer side. startinge at z=50.," The authors performed this simulations by using the HYDRA N-body code developed by Couchman, Thomas Pearce (1995) with $128^3$ particles in a cubic comoving volume of 180 $h^{-1}$ Mpc per side, starting at $z=50$."
" ποια the 2dPCGIBS mock catalog à mock galaxy. pair catalog was constructed by applying the same observational cut-olls defined in Paperl: ry,«1005.+ kpe and AV«350kms +.", >From the 2dFGRS mock catalog a mock galaxy pair catalog was constructed by applying the same observational cut-offs defined in PaperI: $r_{\rm p} < 100 \ h^{-1}$ kpc and $\Delta V < 350 {\rm km s^{-1}}$ .
" Sinilary. a close mock pair catalog was obtained by requiring: n,25h| kpe and AY«100kms."," Similary, a close mock pair catalog was obtained by requiring: $r_{\rm p} < 25 \ h^{-1}$ kpc and $\Delta V < 100 {\rm km s^{-1}}$."
 The orbital parameters such as major semi-axis. eccentricities. bounded: energy. ete;," The orbital parameters such as major semi-axis, eccentricities, bounded energy, etc.,"
 were estimated. for both. mock pair catalogs by assuming a two-bods problemi scenario., were estimated for both mock pair catalogs by assuming a two-body problem scenario.
 We adopted e<1 and negative bounded energy. to distinguish between real and spurious pairs., We adopted $e <1$ and negative bounded energy to distinguish between real and spurious pairs.
 We found that for the complete mock pair catalog. 71A were real pairs while for the close catalog. the percentage was larger: 7054.," We found that for the complete mock pair catalog, $71\%$ were real pairs while for the close catalog, the percentage was larger: $79\%$."
" We also impossed the condition of an extra neighbour within n,400h kpe and AV<500kms in order to segregate pairs according to environment.", We also impossed the condition of an extra neighbour within $r_{\rm p} < 400 \ h^{-1}$ kpc and $\Delta V < 500 \ {\rm km s^{-1}}$ in order to segregate pairs according to environmemt.
 bor ealaxy pairs in dense regions. we found that 734 and το were real pairs in all and close pair mock catalogs.5 respectively.," For galaxy pairs in dense regions, we found that $73\%$ and $79\%$ were real pairs in all and close pair mock catalogs, respectively."
 {From these estimations. we conclude that although spurious pairs are present. real binary svstenis Cleary dominate the statistics.," >From these estimations, we conclude that although spurious pairs are present, real binary systems cleary dominate the statistics."
 In agreement with previous work. we found that the contamination is larger in denser regions. however. the dillerences with that of low density environment are not significant. at least. when our cut-olf criteria. are. adopted.," In agreement with previous work, we found that the contamination is larger in denser regions, however, the differences with that of low density environment are not significant, at least, when our cut-off criteria are adopted."
 Nevertheless. we have. included estimations of the effects of spurious pairs along the paper that can help to further assess their impact on the results.," Nevertheless, we have included estimations of the effects of spurious pairs along the paper that can help to further assess their impact on the results."
 We firstly investigate whether galaxy pairs have a particular racial location in groups with respect to the control sample., We firstly investigate whether galaxy pairs have a particular radial location in groups with respect to the control sample.
 For this purpose. we have analysed the distribution. of projected: radial distance. fp. and relative velocity. V. of pairs with respect to the host group centre normalised to the UYgroup virial radius (yi) ancl ogroup mean velocity dispersion (0). respectively (2=Rpo/Ryiy and e=Vf).," For this purpose, we have analysed the distribution of projected radial distance, $R_D$, and relative velocity, $V$, of pairs with respect to the host group centre normalised to the group virial radius $R_{\rm Vir}$ ) and group mean velocity dispersion $\sigma$ ), respectively $D=R_D/R_{\rm Vir}$ and $v=V/\sigma$ )."
 We restrict. the analysis to groups with more than 1) members for the purpose of avoiding large uncertainties in the determination of eroup centre. mean velocity aad velocity dispersion owing to small number statistics.," We restrict the analysis to groups with more than 10 members for the purpose of avoiding large uncertainties in the determination of group centre, mean velocity and velocity dispersion owing to small number statistics."
" Since close pairs are the most likely to have tidally enhanced star formation activity we further restrict this analysis to close pairs ry,«25h.+ kpe.", Since close pairs are the most likely to have tidally enhanced star formation activity we further restrict this analysis to close pairs $r_p < 25 \ h^{-1}$ kpc.
 The resulting distributions of close pairs and of other member galaxies are shown in Fig.l and mο. 2..," The resulting distributions of close pairs and of other member galaxies are shown in \ref{fig1} and Fig. \ref{fig2},"
 [rom where it can be appreciated that close. pairs and the other group members are similarly concentrated ancl have a comparable relative velocity distribution with respect to the host group centre., from where it can be appreciated that close pairs and the other group members are similarly concentrated and have a comparable relative velocity distribution with respect to the host group centre.
 We have also computed the mean star formation birthrate parameter b=SERS<SER for cilferent bins of normalized groupcentric distance 2 for the group galaxy pairs. the close pairs and the control sample.," We have also computed the mean star formation birthrate parameter $b=SFR/<SFR>$ for different bins of normalized groupcentric distance $D$ for the group galaxy pairs, the close pairs and the control sample."
 The results from bFie.3 show clearly that the star formation in galaxy pairs and in the control sample strongly increases for larger groupcentric distance. approaching the mean value for field galaxies in the outskirts.," The results from \ref{brcentroran} show clearly that the star formation in galaxy pairs and in the control sample strongly increases for larger groupcentric distance, approaching the mean value for field galaxies in the outskirts."
 The similarity of these trends in both samples shows. on average. that the environment has the sume elfects in all group members.," The similarity of these trends in both samples shows, on average, that the environment has the same effects in all group members."
 A similar behaviour is found for the close pairs althought they have larger star formation activity. as expected.," A similar behaviour is found for the close pairs althought they have larger star formation activity, as expected."
 1n order to improve our understanding5 of the star formation properties of galaxy in pairs. we have caleulated the fraction of strong star forming galaxies (f=N(b beoud). where b is the mean birth rate parameter of the," In order to improve our understanding of the star formation properties of galaxy in pairs, we have calculated the fraction of strong star forming galaxies $f^\star = N(b > \bar{b}_{\rm con})$ ), where $\bar{b}_{\rm con}$ is the mean birth rate parameter of the"
eravitational pull of the dark matter.,gravitational pull of the dark matter.
 The peculiar velocity Ποια is a useful tool for probing the matter distribution as galaxy are likely to be unbiased traces of the matter velocity field. which in turn is simply related to the density field. in linear theory.," The peculiar velocity field is a useful tool for probing the matter distribution as galaxy are likely to be unbiased traces of the matter velocity field, which in turn is simply related to the density field in linear theory."
 Since peculiar velocities are a non-local function. of the dark. matter distribution then analvsing the peculiar velocity field. provides information on scales larger than the sampled region (Llolfmanetal.2001) as the velocity at à point is determined by the integral over he matter clistribution in a large volume., Since peculiar velocities are a non-local function of the dark matter distribution then analysing the peculiar velocity field provides information on scales larger than the sampled region \citep{hoff} as the velocity at a point is determined by the integral over the matter distribution in a large volume.
 In practice peculiar velocities are complicated by several actors., In practice peculiar velocities are complicated by several factors.
 The major one is that on small scales the density ield is hiehly nonlinear: these ellects Leal: into the velocity ieldl ancl cannot be described: analytically., The major one is that on small scales the density field is highly nonlinear; these effects leak into the velocity field and cannot be described analytically.
 A method. of adequately separating the contribution from. small scales compared to that of large scales must be sought. and this is he problemi we focus on in this paper.," A method of adequately separating the contribution from small scales compared to that of large scales must be sought, and this is the problem we focus on in this paper."
 Another major factor is the accuracy of the peculiar velocity measurements., Another major factor is the accuracy of the peculiar velocity measurements.
 This relies on knowing the distance o the galaxy through the cdistance-redshift relation which at low redshift is ez=fod|epee. where the redshift is the measured. spectroscopic redshift. d is the distance to he galaxy anc epee is its radial peculiar velocity.," This relies on knowing the distance to the galaxy through the distance-redshift relation which at low redshift is $cz=H_0d+v_{pec}$, where the redshift $z$ is the measured spectroscopic redshift, $d$ is the distance to the galaxy and $v_{pec}$ is its radial peculiar velocity."
 Pherclore o measure the peculiar velocity the distance to the galaxy must first be measured. and. this is itself a complicated ask.," Therefore to measure the peculiar velocity the distance to the galaxy must first be measured, and this is itself a complicated task."
 Relvine on the correct calibration of distance indicator relations. the calculated. distance is a relative distance measure which is strongly subject to a number of biases and also has very large uncertainties of around 20 percent. all of which translates to the peculiar velocity. (secStrauss&Willick1995.forareview )..," Relying on the correct calibration of distance indicator relations, the calculated distance is a relative distance measure which is strongly subject to a number of biases and also has very large uncertainties of around 20 percent, all of which translates to the peculiar velocity \cite[see][for a review]{S&W}."
 The simulations used in this paper contain the large statistical error but the cllect of acelitional biases is bevond the scope of this paper., The simulations used in this paper contain the large statistical error but the effect of additional biases is beyond the scope of this paper.
 Velocities are most sensitive {ο the cosmological parameter ex. roughly the amplitude of the power spectrum. at a scale of S5. Alpe. which is à measure of how clustered matter in the universe istoday.," Velocities are most sensitive to the cosmological parameter $\sigma_8$, roughly the amplitude of the power spectrum at a scale of $h^{-1}$ Mpc, which is a measure of how clustered matter in the universe is."
 Ht is still. not. well constrained by any cosmological probe., It is still not well constrained by any cosmological probe.
 The Wilkinson Microwave Anisotropy Probe (WALAP) Cosmic Microwave Background (CAIB) measurements (Spergelet.al.2007) rely on evolving the anisotropies forward to the present to infer the value of as. because it is defined at the present epoch.," The Wilkinson Microwave Anisotropy Probe (WMAP) Cosmic Microwave Background (CMB) measurements \citep{wmap} rely on evolving the anisotropies forward to the present to infer the value of $\sigma_8$, because it is defined at the present epoch."
 This will depend on many parameters that allect the erowth of structure. such as the mass of the neutrino and the amount or type of dark energy.," This will depend on many parameters that affect the growth of structure, such as the mass of the neutrino and the amount or type of dark energy."
 Allowing the mass of the neutrino to vary significantly alters the WALAD constraints on as (see Table 1))., Allowing the mass of the neutrino to vary significantly alters the WMAP constraints on $\sigma_8$ (see Table \ref{table:sig8}) ).
 Peculiar velocities provide the only way to measure ax essentially at recdshift zero., Peculiar velocities provide the only way to measure $\sigma_8$ essentially at redshift zero.
 Weak lensing. Lyman-a forest and cluster measurements are obtained only at higher redshifts. where dark energy was just starting to dominate.," Weak lensing, $\alpha$ forest and cluster measurements are obtained only at higher redshifts, where dark energy was just starting to dominate."
 See Table 1. for some current constraints on ox., See Table \ref{table:sig8} for some current constraints on $\sigma_8$.
 The range of values could possibly lie anywhere between 0.5 and 1., The range of values could possibly lie anywhere between 0.5 and 1.
 The dillerences in the values of ex will of course be in part due ic the fact that thes are from dilferent. experiments. and different parameters have been marginalised over.," The differences in the values of $\sigma_8$ will of course be in part due to the fact that they are from different experiments, and different parameters have been marginalised over."
 Pinning down an accurate value of ax today could help discriminate between dilferent. models that alleet clustering ancl the erowth of large scale structure such as dark energy mociels ancl mioclificd gravity., Pinning down an accurate value of $\sigma_8$ today could help discriminate between different models that affect clustering and the growth of large scale structure such as dark energy models and modified gravity.
 The motivation for this paper is the upcoming release of the peculiar velocity data from the Six Degree Field Galaxy Survey (dEGS.Jonesetal.2004).," The motivation for this paper is the upcoming release of the peculiar velocity data from the Six Degree Field Galaxy Survey \citep[6dFGS,][]{6df}."
.. GAGS has measurec the redshifts of around 150 000 galaxies over almost the entire southern sky. with a subsample of around 12 000 galaxies having peculiar velocity measurements. an order of magnitude larger than any peculiar velocity survey to date.," 6dFGS has measured the redshifts of around 150 000 galaxies over almost the entire southern sky, with a subsample of around 12 000 galaxies having peculiar velocity measurements, an order of magnitude larger than any peculiar velocity survey to date."
" ALL previous peculiar velocity surveys (egENEAR.vanellietal.1998:daCosta1996:Willick1997) have traced the velocity field only out to distances of arounc 17000 "" and sullered⋅ because of⋅ uneven sky coverage ane the small number of galaxies."," All previous peculiar velocity surveys \citep[eg ENEAR, Spiral Field I-Band (SFI) \& Mark III:][]{enear,sfi:gio,sfi:dacosta,markiii} have traced the velocity field only out to distances of around 7000 $^{-1}$ and suffered because of uneven sky coverage and the small number of galaxies."
 In addition to the new 6dbE€GS data an extended SEL sample (SELI|.Mastersetal.2006:Springobetal.2006) has recently been released. consisting of around 5000 spiral galaxies.," In addition to the new 6dFGS data an extended SFI sample \cite[SFI++,][]{sfi++1,sfi++} has recently been released consisting of around 5000 spiral galaxies."
 Furthermore the ever growing Type la supernova samples (cgJha.Riess.&Kirshner2007) mean that there is a wealth of data becoming available for peculiar velocity analysis., Furthermore the ever growing Type 1a supernova samples \citep[eg][]{jrk} mean that there is a wealth of data becoming available for peculiar velocity analysis.
" Results from previous surveys which apply likelihood analysis (seeZaroubietal.1997.2001:Ereudling1999.forMark.ΤΗ.ΙΟΝΙΟΛΙand.SELrespectively) seemed. to overestimate the combination o«(;"" significantly| compared to other probes at the time and to the current concordance cosmology."," Results from previous surveys which apply likelihood analysis \cite[see][for Mark III, ENEAR and SFI respectively]{zab97,zab,freud} seemed to overestimate the combination $\sigma_8\Omega_m^{0.6}$ significantly compared to other probes at the time and to the current concordance cosmology."
" Values of ex from those analyses were in the region of 1.7 to 2.4 after assuming (3,,=0.27.", Values of $\sigma_8$ from those analyses were in the region of 1.7 to 2.4 after assuming $\Omega_m=0.27$.
 Studies by llolfman&Zaroubi(2000). and Silbermanctal.(2001) show that this over-estimation mav be due to inaccurate modelling of the nonlinear part of the power spectrum. the small scales.," Studies by \cite{hoffzar} and \cite{silb} show that this over-estimation may be due to inaccurate modelling of the nonlinear part of the power spectrum, the small scales."
 This paper focuses on testing our ability to remove the bias from the nonlinear signal., This paper focuses on testing our ability to remove the bias from the nonlinear signal.
 In this paper we develop à practical approach in which we bin the velocities on a grid and thus erase small scale information., In this paper we develop a practical approach in which we bin the velocities on a grid and thus erase small scale information.
 Since this reduces the number of data points then it also makes a covariance matrix approach computationally feasible using the large amount of data from. upcoming surveys., Since this reduces the number of data points then it also makes a covariance matrix approach computationally feasible using the large amount of data from upcoming surveys.
 The paper is organised as follows., The paper is organised as follows.
 In Section 2 we introduce the radial peculiar velocity. correlation function, In Section \ref{section:pre} we introduce the radial peculiar velocity correlation function
To confirm the reality and (the nature of the [our spectroscopic components constituting the LAINB+3A\UNL model. we next study their radial brightness distributions.,"To confirm the reality and the nature of the four spectroscopic components constituting the LMXB+3MKL model, we next study their radial brightness distributions."
 Accorclingly. we again produced the XALM- Newton spectra (together with the blank-skv backgrounds and response matrices) of the extended emission in (he same wav as in § 2.1. but using 6 annular regions of 1 width each. from the nucleus to a radius of 6.," Accordingly, we again produced the ${\it XMM}$ ${\it Newton}$ spectra (together with the blank-sky backgrounds and response matrices) of the extended emission in the same way as in $\S$ 2.1, but using 6 annular regions of $\arcmin$ width each, from the nucleus to a radius of $\arcmin$."
 These spectra have actually been well (A2 == 1.09.1.16) reproduced by the same LMXD--3MKL model under the same conditions as used in 58 3.4 and 4. except that the metal abundances other (han nitrogen are fixed at 0.3 solar units.," These spectra have actually been well $\chi^{2}$ = 1.09–1.16) reproduced by the same LMXB+3MKL model under the same conditions as used in $\S$ 3.4 and 4, except that the metal abundances other than nitrogen are fixed at 0.3 solar units."
" Similarly. the Chandra /ACIS-8S3 spectra derived [rom the same annular regions were fitted successfully (A2/d.0.[. == 0.99.1.26) by the same LMXD-3MKL model,"," Similarly, the ${\it Chandra}$ /ACIS-S3 spectra derived from the same annular regions were fitted successfully $\chi^{2}$ = 0.99–1.26) by the same LMXB+3MKL model."
 In these fits to the EPIC and ACIS spectra using the different annuli. the three MIXL temperatures have always been found at ~ 0.6. ~ 0.3 and ~ 0.1 keV as shown in Figure 7.. alihough we sometimes had to fix some MIXL temperatures at their canonical values because of poor statistics.," In these fits to the EPIC and ACIS spectra using the different annuli, the three MKL temperatures have always been found at $\sim$ 0.6, $\sim$ 0.3 and $\sim$ 0.1 keV as shown in Figure \ref{fig:temperature}, although we sometimes had to fix some MKL temperatures at their canonical values because of poor statistics."
 The surface brightness of the four components from these fits is plotted in Figure 5 as a function of the radius., The surface brightness of the four components from these fits is plotted in Figure \ref{fig:luminosity} as a function of the radius.
" The results on the three diffuse X-ray components thus agree approximately within errors between the (wo satellites. even though the contribution from point sources is different: the ""diffuse"" spectra obtained with INAA- Neieton. and Chandra are contributed bv ~1556 and ~6% [rom luminous (=3xLOY ergs +) sources. respectively."," The results on the three diffuse X-ray components thus agree approximately within errors between the two satellites, even though the contribution from point sources is different; the “diffuse” spectra obtained with ${\it XMM}$ ${\it Newton}$ and ${\it Chandra}$ are contributed by $\sim 15\%$ and $\sim 6\%$ from luminous $\gtrsim 3 \times 10^{35}$ erg $^{-1}$ ) sources, respectively."
 The slight disagreement between them. seen in the innermost annulus. may be attributed to a much heavier point-source elimination Irom (he ΑΛ Newton image.," The slight disagreement between them, seen in the innermost annulus, may be attributed to a much heavier point-source elimination from the ${\it XMM}$ ${\it Newton}$ image."
 In Figure 8.. all (he MIXL. components exhibit gradually. decreasing; radial brightness profiles.," In Figure \ref{fig:luminosity}, all the MKL components exhibit gradually decreasing radial brightness profiles."
" Lf we fit them with an exponential function as xerid""4. where r is the projected radial distance from the nucleus ancl // is the scale height. we obtain //=1.00401.15. 2/.0dE0.41 and 1.6d0.3. for the 0.6. 0.3 and 0.1 keV components. respectively."," If we fit them with an exponential function as $\propto e^{-r/H}$, where $r$ is the projected radial distance from the nucleus and $H$ is the scale height, we obtain $H = 1\arcmin.00 \pm 0\arcmin.15$, $2\arcmin.0 \pm 0\arcmin.4$ and $1\arcmin.6 \pm 0\arcmin.3$, for the 0.6, 0.3 and 0.1 keV components, respectively."
 Thus. the 0.6 keV component is considerably more centrally peaked (han the other (vo. of which the profiles are not signilicantlv different.," Thus, the 0.6 keV component is considerably more centrally peaked than the other two, of which the profiles are not significantly different."
 The integrated. VALA-New/on Iuminosities of the three MIXL. components within 6' become ~L2xLO erg to ~L6xLO erg ! and ~4xLO erg !1 in the order of decreasing temperature.," The integrated ${\it XMM}$ ${\it Newton}$ luminosities of the three MKL components within $6\arcmin$ become $\sim 1.2 \times 10^{38}$ erg $^{-1}$, $\sim 1.6 \times 10^{38}$ erg $^{-1}$ and $\sim 4 \times 10^{37}$ erg $^{-1}$ in the order of decreasing temperature."
 The former two values are consistent with the ASCA results (Paper 1) within errors. where we identify the 0.9 keV RS component detected by ASC with the 0.6 keV MINL plasma here.," The former two values are consistent with the ${\it ASCA}$ results (Paper 1) within errors, where we identify the 0.9 keV RS component detected by ${\it ASCA}$ with the 0.6 keV MKL plasma here."
"First we adopt tvpical parameters interred trom the broadband afterelow fitting (e.g..Panaiteseu&Winer2002:Zhang.IXobavashi.Mészáros 2003): the isotropic equivalent energv E=10 erg. the opening hall-angle 9.=0.1. the ISM density n=0.1 em7. the spectral index p=2.2. (he initial Lorentz [actor 54=200. the duration in the source frame T/(lo:)-105s. and the plasma parameters e,=0.1. ej=0.01. Ry=I.","First we adopt typical parameters inferred from the broadband afterglow fitting \citep[e.g.,][]{panaitescu02,zhang03b}: the isotropic equivalent energy $E=10^{53}$ erg, the opening half-angle $\theta=0.1$ , the ISM density $n=0.1$ $^{-3}$, the spectral index $p=2.2$, the initial Lorentz factor $\gamma_{0}=200$, the duration in the source frame $T/(1+z)=10$ s, and the plasma parameters $\epsilon_{e}=0.1$, $\epsilon_{B}=0.01$, ${\cal R}_{B}=1$."
 Figure | shows the total fluxes of the forward ancl reverseshock emission at the observed frequency v=5 Gllz and the observed times. /=1 hr. 1 dax. LO days and 100 days. as a function of redshift z.," Figure \ref{fig:standard:z} shows the total fluxes of the forward and reverseshock emission at the observed frequency $\nu=5$ GHz and the observed times, $t=1$ hr, $1$ day, $10$ days and $100$ days, as a function of redshift $z$."
 The 5e sensitivities of the VLA and SIXA are also shown., The $5 \sigma$ sensitivities of the VLA and SKA are also shown.
 We can see that the radio afterglows can be detected up to z~30 even by the current VLA., We can see that the radio afterglows can be detected up to $z \sim 30$ even by the current VLA.
" Here we use (lie sensitivity. 8px ) Tu)... assuming (he signal-to-noise ratio (SNR) 5. the integration time {μη=1 dav. the band width Av=50 MIIz. Aug/Ti,~2x105 ? ! for the VEA. and Aur/Tu,~2x10? 7 F for the SKA."," Here we use the sensitivity, 23 ) ), assuming the signal-to-noise ratio (SNR) $5$, the integration time $t_{\rm int}=1$ day, the band width $\Delta \nu=50$ MHz, $A_{\rm eff}/T_{\rm sys} \sim 2 \times 10^{6}$ $^{-2}$ $^{-1}$ for the VLA, and $A_{\rm eff}/T_{\rm sys} \sim 2 \times 10^{8}$ $^{-2}$ $^{-1}$ for the SKA."
 Note that LOFAR will has the frequency range [rom ~10 to ~250 MIIZ. and not at ~5 GllIz.," Note that LOFAR will has the frequency range from $\sim 10$ to $\sim 250$ MHz, and not at $\sim 5$ GHz."
 In Figure 1.. the forward shock emission usually dominates the reverse shock one.," In Figure \ref{fig:standard:z}, , the forward shock emission usually dominates the reverse shock one."
 We can also see (hat the redshift dependence is rather weak., We can also see that the redshift dependence is rather weak.
 Figure 2. shows the light curves of the standard GRB afterglows at z=6 and v~200 AMIIZz and at 2=13 and ν~100 MIIz. which correspond (o the redshifted 21 cm band.," Figure \ref{fig:standard} shows the light curves of the standard GRB afterglows at $z=6$ and $\nu \sim 200$ MHz and at $z=13$ and $\nu \sim 100$ MHz, which correspond to the redshifted 21 cm band."
 The 5o sensitivities of the VLA. LOFAR and SINÀ are also shown.," The $5 \sigma$ sensitivities of the VLA, LOFAR and SKA are also shown."
 We see that LOFAR and SNA can detect the standard afterglows at low frequencies ~100 MIIZz and high redshift z 10. but it maa be difficult to detect them with the VLA.," We see that LOFAR and SKA can detect the standard afterglows at low frequencies $\sim 100$ MHz and high redshift $z \sim 10$ , but it may be difficult to detect them with the VLA."
 Here we assumed anintegration time of one-third of the observed time /. à band width Av=50 Mz. ΗΝ~3x10? ? for the VLA. Τον~4x10 em? Ktf for the LOFAR. andων~5x10* 7 ! for the SNA.," Here we assumed anintegration time of one-third of the observed time $t$ , a band width $\Delta \nu=50$ MHz, $A_{\rm eff}/T_{\rm sys} \sim 3 \times 10^{5}$ $^{-2}$$^{-1}$ for the VLA, $A_{\rm eff}/T_{\rm sys} \sim 4 \times 10^{6}$ $^{-2}$ $^{-1}$ for the LOFAR, and$A_{\rm eff}/T_{\rm sys} \sim 5 \times 10^{7}$ $^{-2}$ $^{-1}$ for the SKA."
" Note that εωςΤον, al ~100 MIIZ is lower than that at ~5GIIZ because of the galactic background.", Note that $A_{\rm eff}/T_{\rm sys}$ at $\sim 100$ MHz is lower than that at $\sim 5$GHz because of the galactic background.
"with Am,Απιο, where Am, is the mass of gas cooled in the time step.","with $\Delta m_*\sim \Delta 
m_c$, where $\Delta m_c$ is the mass of gas cooled in the time step."
 The upper mass limit for such a regime to be effective can thus be estimated from v2<eo]Egn©100 km/s (see Sect.," The upper mass limit for such a regime to be effective can thus be estimated from $v_c^2\lesssim \epsilon_0\,\eta\,E_{SN}\approx 100$ km/s (see Sect."
" 1; for a more detailed derivation see Dekel Birnboim 2005), which, at high zzz4—5 corresponds to DMmasses as low as mo710?Mc."," 1; for a more detailed derivation see Dekel Birnboim 2005), which, at high $z\approx 4-5$ corresponds to DMmasses as low as $m_{0}\approx 
10^9\,M_{\odot}$."
" Thus in progenitor haloes with m«mo the star formation at high z is self -regulated and is forced to remain below the limit set by the equilibrium between the feedback and the star formation (White Frenk 1991); on the other hand, in progenitors with m>mo the cold gas reservoir may grow (up to the maximal value (25/62) at high z, and the star formation rate is limited only by the efficiency of cold gas conversion into stars (determined by the timescale 74)."," Thus in progenitor haloes with $m<m_0$ the star formation at high $z$ is self -regulated and is forced to remain below the limit set by the equilibrium between the feedback and the star formation (White Frenk 1991); on the other hand, in progenitors with $m>m_0$ the cold gas reservoir may grow (up to the maximal value $\Omega_b/\Omega$ ) at high $z$, and the star formation rate is limited only by the efficiency of cold gas conversion into stars (determined by the timescale $\tau_d$ )."
" Thus, hierarchical clustering naturally predicts: 1) the star formation in progenitor clumps later included into massive galaxies to peaked at higher redshift compared to that taking place in progenitors of small-mass galaxies; and 2) the existence of a mass threshold mo below which the cold gas content of the DM clumps at high z is effectively reheated an the star formation is self-regulated."," Thus, hierarchical clustering naturally predicts: 1) the star formation in progenitor clumps later included into massive galaxies to peaked at higher redshift compared to that taking place in progenitors of small-mass galaxies; and 2) the existence of a mass threshold $m_0$ below which the cold gas content of the DM clumps at high $z$ is effectively reheated an the star formation is self-regulated."
" Such generic features are in qualitative agreement with the observation that bright galaxies are typically redder (de Vaucouleurs 1961; Bower, 1992)."," Such generic features are in qualitative agreement with the observation that bright galaxies are typically redder (de Vaucouleurs 1961; Bower, 1992)."
" In our model, the above two points combine with 3) a star formation efficiency that enforces the partition between gas rich and gas poor systems, above and below the threshold mo."," In our model, the above two points combine with 3) a star formation efficiency that enforces the partition between gas rich and gas poor systems, above and below the threshold $m_0$."
" Spcifically, we adopt ταοςm/m. derived from the disk model developed by Mo, Mao White (1998) (as described in Sect."," Spcifically, we adopt $\tau_d\propto m/m_c$ derived from the disk model developed by Mo, Mao White (1998) (as described in Sect."
 2)., 2).
" In fact, at high-z, the cold gas reservoir of progenitors clumps with πι«m is continuously depleted by effective feedback, as discussed above; this increases the timescale Tqοςm/m., thus suppressing star formation and avoiding the sudden conversion of cold gas into stars."," In fact, at $z$, the cold gas reservoir of progenitors clumps with $m<m_0$ is continuously depleted by effective feedback, as discussed above; this increases the timescale $\tau_d\propto m/m_c$, thus suppressing star formation and avoiding the sudden conversion of cold gas into stars."
" At later cosmic times, as the progenitor masses grow above the threshold mo, cold gas begins to accumulate in the progenitor clumps and is made available for star formation, which continues down to low redshifts."," At later cosmic times, as the progenitor masses grow above the threshold $m_0$, cold gas begins to accumulate in the progenitor clumps and is made available for star formation, which continues down to low redshifts."
 Such smooth star formation histories (the upper panel of fig., Such smooth star formation histories (the upper panel of fig.
 5) lead to the local faint blue population., 5) lead to the local faint blue population.
" On the other hand, in progenitor clumps with m>mo at high-z the cold gas is not effectively reheated; thus, the rapid cooling taking place at high-z leads to large m,./m ratios, which shorten the star formation timescale."," On the other hand, in progenitor clumps with $m>m_0$ at $z$ the cold gas is not effectively reheated; thus, the rapid cooling taking place at $z$ leads to large $m_c/m$ ratios, which shorten the star formation timescale."
" The cold gas is rapidly converted into stars, and begins to exhaust at zx;2 (see fig."," The cold gas is rapidly converted into stars, and begins to exhaust at $z\lesssim 2$ (see fig."
 5); at later times the star formation is further suppressed since now such galaxies have low m./m ratios., 5); at later times the star formation is further suppressed since now such galaxies have low $m_c/m$ ratios.
" Thereafter, such galaxies undergo an almost quiescent phase characterized by a fast drop of Πιν; such histories are typical of massive galaxies and of galaxies forming in biased regions of the primordial density field (which later become the galaxy environment), and originate the red population at ze0."," Thereafter, such galaxies undergo an almost quiescent phase characterized by a fast drop of $\dot m_*$; such histories are typical of massive galaxies and of galaxies forming in biased regions of the primordial density field (which later become the galaxy environment), and originate the red population at $z\approx 0$."
" 'The more effective is the star formation in high-z, gas rich haloes, the sharper is the transition between the regime and the supply-limited regime."," The more effective is the star formation in $z$, gas rich haloes, the sharper is the transition between the feedback-regulated regime and the supply-limited regime."
" In fact, when we adopt a star formation timescale not explicitly depending on m./m (like in most current SAMs), we obtain a smooth (non-bimodal) color distribution; this is shown in fig."," In fact, when we adopt a star formation timescale not explicitly depending on $m_c/m$ (like in most current SAMs), we obtain a smooth (non-bimodal) color distribution; this is shown in fig."
" 6, where the color distribution from our model is compared with that obtained on adopting fixed value for the ratio m./m=0.05 (the average value in Mo, Mao White 1998) in the expression for the function ag(v) defined in Sect."," 6, where the color distribution from our model is compared with that obtained on adopting a fixed value for the ratio $m_c/m=0.05$ (the average value in Mo, Mao White 1998) in the expression for the function $g(v)$ defined in Sect."
 2., 2.
" Note that this model still predictes a correlation between the color and the luminosity of present-day galaxies: as we discussed above, this is indeed a generic feature of hierarchical scenarios."," Note that this model still predictes a correlation between the color and the luminosity of present-day galaxies: as we discussed above, this is indeed a generic feature of hierarchical scenarios."
" In our fiducial model, we achieve redder color in an appreciable fraction of galaxies compared to the model with fixed m./m."," In our fiducial model, we achieve redder color in an appreciable fraction of galaxies compared to the model with fixed $m_c/m$."
" Summarizing, in our model the star formation in massive haloes at low redshift is suppressed by three concurring processes: i) at high -z, the rapid conversion of gas into stars, enhanced by our star formation timescale Tyοςm/m;., leads to a fast exhaustion of the cold gas reservoir; ii) at zx; 2, the cold gas reservoir of massive galaxies is depleted by major merging events (see Sect.2); iii) as a consequence of i) and ii), the ratio m./m in such galaxies is particularly low, leading"," Summarizing, in our model the star formation in massive haloes at low redshift is suppressed by three concurring processes: i) at high $z$, the rapid conversion of gas into stars, enhanced by our star formation timescale $\tau_d\propto m/m_c$, leads to a fast exhaustion of the cold gas reservoir; ii) at $z\lesssim 2$ , the cold gas reservoir of massive galaxies is depleted by major merging events (see Sect.2); iii) as a consequence of i) and ii), the ratio $m_c/m$ in such galaxies is particularly low, leading"
and Arp 299. respectively.,"and Arp 299, respectively."
 I£ sve include all regions in the fit. the values of the slopes area =1.68+0.08 and a=1664£0.05 respectively.," If we include all regions in the fit, the values of the slopes are $\alpha = -1.68\pm 0.08$ and $\alpha = -1.66\pm 0.05$ respectively."
" These slopes are within the values fitted for regious in the disks aud cireumnunclear regions of normal galaxies (οιοι, NWemuicutt et al."," These slopes are within the values fitted for regions in the disks and circumnuclear regions of normal galaxies (e.g., Kennicutt et al."
" 1989). and those fouud from fitting the huninosity functions of star clusters ίσιο, Zepf et al."," 1989), and those found from fitting the luminosity functions of star clusters (e.g., Zepf et al."
 1999: Whitmore 2000)., 1999; Whitmore 2000).
 A μπιν of studies have analyzed the statistical properties of regions (luminosities. sizes. density numbers) iu the disks of normal spiral galaxies in terms of the morphological tvpe of the galaxy aud the avm-iuterariu regions (see for instance the classical study of Nenuicutt ct al.," A number of studies have analyzed the statistical properties of regions (luminosities, sizes, density numbers) in the disks of normal spiral galaxies in terms of the morphological type of the galaxy and the arm-interarm regions (see for instance the classical study of Kennicutt et al."
 1989)., 1989).
 Because of the effect of the spatial resolution ou the properties of regions. we chose to compare the statistical properties of the regious in LIRCs with those of the circumutcelear regions of normal galaxies (asderived from LST/NICAIOS Pao observatious) studied bv Alouso-IHeorrero I&napen (2001).," Because of the effect of the spatial resolution on the properties of regions, we chose to compare the statistical properties of the regions in LIRGs with those of the circumnuclear regions of normal galaxies (as derived from /NICMOS $\alpha$ observations) studied by Alonso-Herrero Knapen (2001)."
 From this work. we have selected galaxics at the distance of the Virgo Cluster (Dist~17 Mpc). for which the NICS observations provide a resolution of ppe +. similar to that of NGC 3256. NGC 3690 and IC 691.," From this work, we have selected galaxies at the distance of the Virgo Cluster ${\rm Dist} \simeq 
17\,$ Mpc), for which the NIC3 observations provide a resolution of pc $^{-1}$, similar to that of NGC 3256, NGC 3690 and IC 694."
 Iu the secoud part of Table 3 we sununuuize the statistical properties of regions of the normal galaxies with the highest degree of central star foriing activity (as measured from the ceutral kpe We Iunuinositv): NGC L192. NGC 1389. IC 750. and NGC 1102.," In the second part of Table 3 we summarize the statistical properties of regions of the normal galaxies with the highest degree of central star forming activity (as measured from the central kpc $\alpha$ luminosity): NGC 4192, NGC 4389, IC 750, and NGC 4102."
 Fiewe [. shows histogrinis comparing the Πα huuinositics of regions in LIRCs aud uormal galaxies., Figure 4 shows histograms comparing the $\alpha$ luminosities of regions in LIRGs and normal galaxies.
 We have divided the normal galaxies iuto two groups. isolated galaxies (NGC 1192. NGC [389 and. NCC L102) and the interacting ealaxy IC 750.," We have divided the normal galaxies into two groups, isolated galaxies (NGC 4192, NGC 4389 and NGC 4102) and the interacting galaxy IC 750."
 In this fieure we also indicate the Πα luninosity of 20 Doradus. the xototvpical giant region.," In this figure we also indicate the $\alpha$ luminosity of 30 Doradus, the prototypical giant region."
 These listoerams not only show that elant regions are more common in LIRCs han in normal galaxies — even when comparing with the interacting svstem IC 750 mt also that the median regions iu LIRCis are at least an order of maguitude xiehter than im normal galaxies., These histograms not only show that giant regions are more common in LIRGs than in normal galaxies – even when comparing with the interacting system IC 750 – but also that the median regions in LIRGs are at least an order of magnitude brighter than in normal galaxies.
 The large population of giaut regions in LIRGs witha significant fraction being more tuuinous than 30 Doradus — is uuprecedeuted in normal ealaxies., The large population of giant regions in LIRGs – with a significant fraction being more luminous than 30 Doradus – is unprecedented in normal galaxies.
 There are a nuiuber of possible explanations., There are a number of possible explanations.
 We nay just be seeing the exteuded tail of the region LF which translates iuto a larger wuuber of the more massive lonizing star clusters. a extremely voune population of star fornune regions in LIRCs. or perhaps the bright reeious in LIRGs may represcut agerceations of ποσα regions.," We may just be seeing the extended tail of the region LF which translates into a larger number of the more massive ionizing star clusters, a extremely young population of star forming regions in LIRGs, or perhaps the bright regions in LIRGs may represent aggregations of normal regions."
 The typical Guedian) diameters for regions in normal galaxies aud LIRCs observed at the same spatial resolution are comparable (see Table 3)., The typical (median) diameters for regions in normal galaxies and LIRGs observed at the same spatial resolution are comparable (see Table 3).
 This seems o argue against the last possibility., This seems to argue against the last possibility.
 Even though the first ranked regions in LIRGs are typically a factor of two larger han in normal sealaxies. the lhuuinosities of the first-ranked (as well as median) regions in LIRCis would require agerceations of ten “normal” regious.," Even though the first ranked regions in LIRGs are typically a factor of two larger than in normal galaxies, the luminosities of the first-ranked (as well as median) regions in LIRGs would require aggregations of ten “normal” regions."
 Other yossibilities are then evolutionary effects aud the upper init to the mass of the ionizing clusters., Other possibilities are then evolutionary effects and the upper limit to the mass of the ionizing clusters.
 As can be seen from the simulations of reeion LFs by Oey Clark (1998) the age of the stellar population is one of the factors determining the high huninosity eud of the region LE., As can be seen from the simulations of region LFs by Oey Clark (1998) the age of the stellar population is one of the factors determining the high luminosity end of the region LF.
 For a population of regions formed in a suele burst. the high luuinosity end of the LF as well as the slope vary as the population ages.," For a population of regions formed in a single burst, the high luminosity end of the LF as well as the slope vary as the population ages."
 Iu the case of continuous creation of resious the high huninositv end of the LF remains approximately constant., In the case of continuous creation of regions the high luminosity end of the LF remains approximately constant.
 The vouth of a population of coeval regions could be a possibility to explain the excess of bright regions in LIRGs., The youth of a population of coeval regions could be a possibility to explain the excess of bright regions in LIRGs.
 As we shall see in the next section however. the regious in LIRGs show a range of ages. which means that the extreme Iuninosities of the regions in LIRGs are not due to the fact that they are all very young.," As we shall see in the next section however, the regions in LIRGs show a range of ages, which means that the extreme luminosities of the regions in LIRGs are not due to the fact that they are all very young."
 Since the fitted slopes of the region LFs of two LIRGs are consistent with the values found in normal ealaxies. the extraordinary huüuinosities of regious in LIRGs are simply reflecting a larger number of massive star clusters in LIRGs. rather than an anomalous stellar lass distribution.," Since the fitted slopes of the region LFs of two LIRGs are consistent with the values found in normal galaxies, the extraordinary luminosities of regions in LIRGs are simply reflecting a larger number of massive star clusters in LIRGs, rather than an anomalous stellar mass distribution."
" As discussed in Bekhki Couch (2001). the physical concitious (high eas pressure aud density of the interstellar medium) necessary for the formation of super star clusters can only be achieved in svstenis ""udergoius a rapid trausfer of eas to the central regions. that is. interacting galaxies."," As discussed in Bekki Couch (2001), the physical conditions (high gas pressure and density of the interstellar medium) necessary for the formation of super star clusters can only be achieved in systems undergoing a rapid transfer of gas to the central regions, that is, interacting galaxies."
 It is unlikely that these conditions are met in isolated disk oealaxies., It is unlikely that these conditions are met in isolated disk galaxies.
 Figure 2 shows that the enuüssion peaks of the regions are generally not spatially coincident with the location of the nearufrared star clusters., Figure 2 shows that the emission peaks of the regions are generally not spatially coincident with the location of the near-infrared star clusters.
 To quautifv this. we have cross-correlated the positions of the regious and the near-infrared clusters.," To quantify this, we have cross-correlated the positions of the regions and the near-infrared clusters."
" We counted a coincidence when the spatial separation between au region aud a cluster was equal or less than ((for the NIC? nuages) aud (for the NICS images). that is. a separation of 2 aud 1.5 pixels respectively,"," We counted a coincidence when the spatial separation between an region and a cluster was equal or less than (for the NIC2 images) and (for the NIC3 images), that is, a separation of 2 and 1.5 pixels respectively."
 The results from the cross-correlation are presented in the first part of Table 1 where we list the nuuber of detected regions. aud star clusters. together with 16 umber of coincidences.," The results from the cross-correlation are presented in the first part of Table 4 where we list the number of detected regions, and star clusters, together with the number of coincidences."
 As was clear frou Figure 2. re tuber of coimcidences is relatively small.," As was clear from Figure 2, the number of coincidences is relatively small."
 The oewcreasing nunber of colucideuces Gutermediate age reeious/clusters} for NCC 5653. NCC 68508 and VV 111 nav be the result of the poorer spatial resolutious of re NICS nuages. which implies that a coincidence is counted when the spatial separations are 6SLl? pc (90. 156pe for the 2 pixel separation).," The increasing number of coincidences (intermediate age regions/clusters) for NGC 5653, NGC 6808 and VV 114 may be the result of the poorer spatial resolutions of the NIC3 images, which implies that a coincidence is counted when the spatial separations are $68-117\,$ pc $90-156\,$ pc for the 2 pixel separation)."
 For comparison. 16 spatial separations for the galaxies observed with the NIC2 οποία are 21. 38pe (or 28—50 pe if we use the 2 jxxel separation).," For comparison, the spatial separations for the galaxies observed with the NIC2 camera are $21-38\,$ pc (or $28-50\,$ pc if we use the 2 pixel separation)."
 This lack of spatial coincidence between regious aud clusters has also been fouud iu birred and ringed galaxies with strong star formation activity (Alouso-Herrero et al., This lack of spatial coincidence between regions and clusters has also been found in barred and ringed galaxies with strong star formation activity (Alonso-Herrero et al.
 20015: Maoz et al., 2001b; Maoz et al.
 2001)., 2001).
 Theoretical arguneuts may offer iii explanation for the apparent offsets between the location of the SSCs and the regions iu LIRGs., Theoretical arguments may offer an explanation for the apparent offsets between the location of the SSCs and the regions in LIRGs.
 For instance. Tan MclIxee (2000) have proposed a model in which voung clusters within clouds with masses 5«105.5&«107ML. cau survive for up," For instance, Tan McKee (2000) have proposed a model in which young clusters within clouds with masses $5 \times 10^4 - 5 \times 10^5\,
{\rm M}_\odot$ can survive for up"
Fiewes 1 and 2 show the ΠΕ (black curve} aud the residuals for cach night.,Figures \ref{fig:bigplots} and \ref{fig:closeup} show the $\chi^2$ solution (black curve) and the residuals for each night.
 Figure 1 shows the time-biuned composite z aud +’ light curves. with 2 minute sampling.," Figure \ref{fig:comp} shows the time-binned composite $z'$ and $r'$ light curves, with 2 minute sampling."
 The data were combined after correcting the depths for spot variability [such that Foo>1(1Fy , The data were combined after correcting the depths for spot variability [such that $F \mapsto 1-(1-F)(1-\epsilon_j)$ ].
Table l| gives the results for cach parameter. based ou ej).the 15.856. 50%. aud 81.2% values of the cumulative posterior distribution for cach parameter. after mareinalizing over the other parameters.," Table \ref{tab:result} gives the results for each parameter, based on the $15.8\%$, $50\%$, and $84.2\%$ values of the cumulative posterior distribution for each parameter, after marginalizing over the other parameters."
 This table also gives some other parameters based on subsequeut steps in the analysis. described in the sections to follow.," This table also gives some other parameters based on subsequent steps in the analysis, described in the sections to follow."
 Iu order to assess any possible transit duration variations. we also performed a second analysis. iu which the orbital inclination / was allowed to be a free paralucter specific to cach night.," In order to assess any possible transit duration variations, we also performed a second analysis, in which the orbital inclination $i$ was allowed to be a free parameter specific to each night."
" Table 2. eives the transit depth 1,REIN €]. tine of coujuuction. and total transit duration for cach epoch."," Table \ref{tab:epoch} gives the transit depth $ \left(R_p/R_\star\right)^2/(1-\epsilon_j)$ ], time of conjunction, and total transit duration for each epoch."
 The depths are plotted asa function of epoch in Figure 5.., The depths are plotted as a function of epoch in Figure \ref{fig:depthvar}.
 Figure 6 shows the durations. and the residuals frou a linear ephemeris. as a function of epoch.," Figure \ref{fig:omc} shows the durations, and the residuals from a linear ephemeris, as a function of epoch."
 Despite our concerus about the effects of starspots on the light curves. we did not find auy significant variation of the transit depth or and duration with time. aud we did not πα any siguificaut departure frou a linear ephemeris.," Despite our concerns about the effects of starspots on the light curves, we did not find any significant variation of the transit depth or and duration with time, and we did not find any significant departure from a linear ephemeris."
 In addition. the out-of-trausit flux of GJ 1211 measured cirectly from the images was constant to within a few percent over the course of our observations (seo Figure 7)).," In addition, the out-of-transit flux of GJ 1214 measured directly from the images was constant to within a few percent over the course of our observations (see Figure \ref{fig:compstars}) )."
 There was apparently a decline by between 2009 and 2010. followed by a gradual rise throughout our 2010 observations.," There was apparently a decline by between 2009 and 2010, followed by a gradual rise throughout our 2010 observations."
 This should have been accompanied by variations m the measured transit depth. which is beneath our typical mcasirement precision of54.. auc hence it is not surprising that no such trend was observed.," This should have been accompanied by variations in the measured transit depth, which is beneath our typical measurement precision of, and hence it is not surprising that no such trend was observed."
 Based wpou this finding. oue wav to estimate the planet-to-star radius ratio is to assume that spots lave not significantly affected the transit depth.," Based upon this finding, one way to estimate the planet-to-star radius ratio is to assume that spots have not significantly affected the transit depth."
" We may then calculate the radius ratio based on the variance-weigehted average of the 16 transit deptlis 9;=UR,/R.elεἰ)E where the average is taken over all epochs j.", We may then calculate the radius ratio based on the variance-weighted average of the 16 transit depths $\delta_j \equiv (R_p/R_\star)_j^2 (1-\epsilon_j)^{-1}$: where the average is taken over all epochs $j$.
 This result or the radius ratio is slightly smaller than that reported in the discovery paper (0.11620+0.00067: Clhiarbonueau et al., This result for the radius ratio is slightly smaller than that reported in the discovery paper $0.11620 \pm 0.00067$; Charbonneau et al.
 2009). but the two results are consistent to within he uncertainties.," 2009), but the two results are consistent to within the uncertainties."
 Due to time variability of starspots at the level. his estimate is subject to a bias of a few percent. in the seuse that the planet-to-star radius ratio may actually be a few percentsinaller than 0.11610.," Due to time variability of starspots at the level, this estimate is subject to a bias of a few percent, in the sense that the planet-to-star radius ratio may actually be a few percent than $0.11610$."
 An even nore conservative stance would recognize that we cannot exclude even larger effects due to the time-independent colponcut of the starspot coverage (f. for example. the voles of the star were persistently darker than the rest of the photosphere).," An even more conservative stance would recognize that we cannot exclude even larger effects due to the time-independent component of the starspot coverage (if, for example, the poles of the star were persistently darker than the rest of the photosphere)."
" In that seuse we can only place au upper bound on the radius ratio: F2,/R,<0.1161 at confidence It should also be noted that the ας transit depth (1.883%+ 0.035%) was found to be slightly larecr than he z'-band trausit depth (1.310%+ 0.017%). although he difference is onlv at the 26 level."," In that sense we can only place an upper bound on the radius ratio: $R_p/R_\star \le 0.1161$ at confidence It should also be noted that the $r'$ -band transit depth $1.383\% \pm 0.035\%$ ) was found to be slightly larger than the $z'$ -band transit depth $1.340\% \pm 0.017\%$ ), although the difference is only at the $\sigma$ level."
 A deeper -wand transit is expected if cool starspots are affecting he results., A deeper $r'$ -band transit is expected if cool starspots are affecting the results.
 Iu contrast. models of the atinosphere of GJ 1211b generally predict that the transit depth should ave theopposite waveleugth dependence. with a deeper band transit2010).," In contrast, models of the atmosphere of GJ 1214b generally predict that the transit depth should have the wavelength dependence, with a deeper $z'$ -band transit."
 Those who would attempt to attribute ασ slight wavelenetl-depeudence of the transit depth to the auetarv atinosphere should beware of the confouudius effects of starspots., Those who would attempt to attribute any slight wavelength-dependence of the transit depth to the planetary atmosphere should beware of the confounding effects of starspots.
 Tn order to uuderstaud the structure aud atmosphere of GJ 1211b. we want to kuow its radius. rather than just theplauct-to-star radius ratio.," In order to understand the structure and atmosphere of GJ 1214b, we want to know its radius, rather than just theplanet-to-star radius ratio."
 This requires soe externally derived estimate of the stellar racius. or mass.," This requires some externally derived estimate of the stellar radius, or mass,"
The svmbiotic binary V407 Cvg was discovered in outburst at 7th magnitude by? on 2010 March 10. in stark contrast to occasional brightenings observed over the vears by a few magnitudes compared to historical low states in the range lr...,"The symbiotic binary V407 Cyg was discovered in outburst at 7th magnitude by\citet{2010IAUC.9130....1N} on 2010 March 10, in stark contrast to occasional brightenings observed over the years by a few magnitudes compared to historical low states in the range $17 m\rs{pg}$."
 The binary comprises a white dwarf (WD) and Mira-tvpe M6-7 red giant pulsating with a period of 763d. with an orbital period of 43 vr (?2)..," The binary comprises a white dwarf (WD) and Mira-type M6-7 red giant pulsating with a period of 763d, with an orbital period of 43 yr \citep{1990MNRAS.242..653M,2003ARep...47..777K}."
 Spectroscopy obtained by ? and €. two days after outburst showed very broad Jalmer lines: ? reported a full-width at halfl-maximunm (ENIIM) of 2760 km s on dav 2.3.2 and. described the outburst as a He/N nova expanding within the wind of the Mira companion. similar to the 2006 explosion of RS Oph (sce2.andreferencestherein) ," Spectroscopy obtained by \citet{2011MNRAS.410L..52M} and C. two days after outburst showed very broad Balmer lines; \citet{2011MNRAS.410L..52M}
 reported a full-width at half-maximum (FWHM) of 2760 km $^{-1}$ on day 2.3, and described the outburst as a He/N nova expanding within the wind of the Mira companion, similar to the 2006 explosion of RS Oph \citep[see][and references therein]{2008ASPC..401.....E}. ."
SiO maser enission. was, SiO maser emission was
hat the study of Mazzali et al. (,that the study of Mazzali et al. (
1996) has overestimated he wmuber of Be stars within the cluster.,1996) has overestimated the number of Be stars within the cluster.
 Of their sample of 13 Be stars we lave observed Ll of which we find 6 are in fact Be stars. the remainder are ordinary B stars.," Of their sample of 13 Be stars we have observed 11 of which we find 6 are in fact Be stars, the remainder are ordinary B stars."
 The uost Likely cause of this iuisideutification appears to lie with the subtraction of the strong aud spatially variable ΠΠ enusson within aud around the cluster., The most likely cause of this misidentification appears to lie with the subtraction of the strong and spatially variable HII emission within and around the cluster.
 We do not Πα evidence for the presence of a large population of Be stars with Io emission equivalent width beneath the detection threshold of photometric surveys such as Caehel et al. (1992)), We do not find evidence for the presence of a large population of Be stars with $\alpha$ emission equivalent width beneath the detection threshold of photometric surveys such as Grebel et al. \cite{greb}) )
 aud Weller ct al. (1998))., and Keller et al. \cite{kwb}) ).
 The equivalent width of cuuission and esa/ frou absorption presented by the De stars of our sample are uncorrolated.," The equivalent width of emission and $v\,sin\:i$ from absorption presented by the Be stars of our sample are uncorrelated."
 This indicates that the stars in the Be population possess esfP and disk size of random distribution. iu coutrast to the assertion of Mazzali ct al. (," This indicates that the stars in the Be population possess $v\;sin\:i$ and disk size of random distribution, in contrast to the assertion of Mazzali et al. ("
1996) that there is a general alizumoent of Be star rotation axes Within the cluster.,1996) that there is a general alignment of Be star rotation axes within the cluster.
"found that the magnetic field strength, the scattering optical depth, and the average particle velocity did not vary significantly between different observations.","found that the magnetic field strength, the scattering optical depth, and the average particle velocity did not vary significantly between different observations."
" We measured a hydrogen column density of (2.36+0.05)x107? cm-?, assuming solar abundances (Anders Grevesse 1989)."," We measured a hydrogen column density of $(2.36 \pm 0.05) \times
10^{22}$ $^{-2}$, assuming solar abundances (Anders Grevesse 1989)."
" We, therefore, performed all further STEMS fits fixing the hydrogen column density at the above value and forcing the parameters DB, 7, and B to be constant between different observations."," We, therefore, performed all further STEMS fits fixing the hydrogen column density at the above value and forcing the parameters , $\tau$, and $\beta$ to be constant between different observations."
 We still allowed the temperature and the model normalization to vary individually for all spectra., We still allowed the temperature and the model normalization to vary individually for all spectra.
" We obtained good fits to all 13 spectra, with a x?/dof = 2370/2438."," We obtained good fits to all 13 spectra, with a $\chi^2/$ dof = 2370/2438."
" In this combined fit, we found a magnetic field strength of B=(5.03-0.3)x1014 G, a scattering optical depth of T=8.7€0.9 and particle velocity of 6=0.37+0.01."," In this combined fit, we found a magnetic field strength of $B = (5.0 \pm 0.3)
\times 10^{14}$ G, a scattering optical depth of $\tau = 8.7 \pm 0.9$ and a particle velocity of $\beta = 0.37 \pm 0.01$."
" Below, we discuss athe time evolution of the temperature T and the source flux based on these combined fits."," Below, we discuss the time evolution of the temperature $T$ and the source flux based on these combined fits."
 Note that errors reported throughout the paper are σ., Note that errors reported throughout the paper are 1 $\sigma$.
 We also investigated the potential effects of 1the cross calibration between the Chandra/ACIS in CC mode and the XMM-Newton/EPIC-pn on the determination of spectral parameters., We also investigated the potential effects of the cross calibration between the /ACIS in CC mode and the /EPIC-pn on the determination of spectral parameters.
" To this end, we used two data sets, observation ID 7593 with aand 0410580101 with which were selected because they occurred at comparable source fluxes."," To this end, we used two data sets, observation ID 7593 with and 0410580101 with which were selected because they occurred at comparable source fluxes."
" We fit both spectra using STEMS as well as the empirical blackbody plus power law model, accounting for interstellar absorption in both cases."," We fit both spectra using STEMS as well as the empirical blackbody plus power law model, accounting for interstellar absorption in both cases."
" In this analysis, we again forced the absorption parameter to remain constant for both spectra as it is not observed to vary over time."," In this analysis, we again forced the absorption parameter to remain constant for both spectra as it is not observed to vary over time."
" In Figure 1,, we present the two spectra along with the best fitting STEMS models."," In Figure \ref{fig:twospec}, we present the two spectra along with the best fitting STEMS models."
 We found all parameters of both continuum models to be consistent between theChandra and XMM spectra to within 1 c errors., We found all parameters of both continuum models to be consistent between the and XMM spectra to within 1 $\sigma$ errors.
 These results ensure that the use of two different instruments does not introduce any systematic biases in the joint spectral analysis., These results ensure that the use of two different instruments does not introduce any systematic biases in the joint spectral analysis.
 We present in Figure 2 the history of the unabsorbed X-ray flux of iin the 0.8—6.5 keV band., We present in Figure \ref{fig:flxhist} the history of the unabsorbed X-ray flux of in the $-$ 6.5 keV band.
 The first observation took place four days after the intermediate event (Feroci et 22002)., The first observation took place four days after the intermediate event (Feroci et 2002).
" The source flux declined rapidly in the period soon after this event, dropping from (1.34+0.02)x107! erg cm""? s! to (1.16+0.02)x1071! erg cm? s! in only about six days."," The source flux declined rapidly in the period soon after this event, dropping from $1.34 \pm 0.02) \times
10^{-11}$ erg $^{-2}$ $^{-1}$ to $1.16 \pm 0.02) \times
10^{-11}$ erg $^{-2}$ $^{-1}$ in only about six days."
 An even faster decline was seen in the contemporaneousBeppoSA observations: the source flux in the 2—10 keV band wasX (3.1+0.3)x1071! erg cm? s! on 2001 April 18 and declined to (1.06+x10:11 ergcm? s! in 11 days (Esposito et al.," An even faster decline was seen in the contemporaneous observations: the source flux in the $-$ 10 keV band was $3.1 \pm 0.3) \times
10^{-11}$ erg $^{-2}$ $^{-1}$ on 2001 April 18 and declined to $1.06 \pm 0.04) \times 10^{-11}$ erg$^{-2}$ $^{-1}$ in 11 days (Esposito et al."
 2007)., 2007).
0.04) We observed a similar trend following the 2006 reactivation of the source as its flux drops from (8.6+0.1)x1077? erg cm? s! to (7.90.1)x107? erg cm? s-! in three days.," We observed a similar trend following the 2006 reactivation of the source as its flux drops from $8.6 \pm 0.1)
\times 10^{-12}$ erg $^{-2}$ $^{-1}$ to $7.9 \pm 0.1) \times
10^{-12}$ erg $^{-2}$ $^{-1}$ in three days."
 We further studied these long term persistent flux variations of aas follows: we determined the relative times of the first eight observations (which took place before 2006) with respect to the onset of the April 2001 outburst and those of the remaining five observations with respect to the onset of the March 2006 activation., We further studied these long term persistent flux variations of as follows: we determined the relative times of the first eight observations (which took place before 2006) with respect to the onset of the April 2001 outburst and those of the remaining five observations with respect to the onset of the March 2006 activation.
 We present in Figure 3 the unabsorbed flux as a function of relative time since each respective outburst onset., We present in Figure \ref{fig:flxhistlog} the unabsorbed flux as a function of relative time since each respective outburst onset.
 We found that in both outbursts the source flux declined rather gradually until about 600 days after the onset and exhibited a sharper decline trend beyond ~600 days., We found that in both outbursts the source flux declined rather gradually until about 600 days after the onset and exhibited a sharper decline trend beyond $\sim 600$ days.
 We also found that wwas at its lowest X-ray flux level of 6.8x10-1? erg cm~? s-! before the March 2006 reactivation.," We also found that was at its lowest X-ray flux level of $6.8 \times
10^{-12}$ erg $^{-2}$ $^{-1}$ before the March 2006 reactivation."
" Following the source re-brightening afterthe 2006 outburst, the flux reached that level again in the last pointed observation."," Following the source re-brightening afterthe 2006 outburst, the flux reached that level again in the last pointed observation."
" To better understand the nature of these flux variations in 1900+14,, we investigated a possible correlation between the flux and the only varying STEMS"," To better understand the nature of these flux variations in , we investigated a possible correlation between the flux and the only varying STEMS"
"the form where 1l€;.j.k rsand Aj. By; ane Cj, are the coefficients.","the form where $1 \le i,~j,~k \le r s$ and $A_i$ , $B_{ij}$ and $C_{ijk}$ are the coefficients."
 Here the q; are the ciscretised values of the clepenclet| variables (or the aniplitucles of the relevant spectral modes): typically these represeut a vector of the values of the [Lui properties., Here the $q_i$ are the discretised values of the dependent variables (or the amplitudes of the relevant spectral modes); typically these represent a vector of the values of the fluid properties.
 We also note here that there is an implicit sum over repeated iudices., We also note here that there is an implicit sum over repeated indices.
 Hereinalter. to fix ideas. we shall think of the q; as representing the amplitudes of the spectral nodes of a vector of «epeudent variables — and shall give a concrete example in tle next. section.," Hereinafter, to fix ideas, we shall think of the $q_i$ as representing the amplitudes of the spectral modes of a vector of dependent variables — and shall give a concrete example in the next section."
 The forcing f;(/) can then be interpreted as the statistical forcing of the relevant spectral mode., The forcing $f_i(t)$ can then be interpreted as the statistical forcing of the relevant spectral mode.
 One way to formulate the cumulant expausion is by carrying out a Reynolds decomposition of the dynamical variable d; into the sum of a mean value aud a fuctuatiou (or eddy): where we defer. for now. choosing the type of averaging denoted by the angular brackets ( ," One way to formulate the cumulant expansion is by carrying out a Reynolds decomposition of the dynamical variable $q_i$ into the sum of a mean value and a fluctuation (or eddy): where we defer, for now, choosing the type of averaging denoted by the angular brackets $\langle \rangle$."
Typical choices are temporal or zonal Or averages over an ensemble of initial conditiousor an eusenmble of realisatious., Typical choices are temporal or zonal or averages over an ensemble of initial conditionsor an ensemble of realisations.
The large range of ionization states present in the absorber implies (hat the absorption arises [rom gas that is distributed over a wide range of ionization parameter £.,The large range of ionization states present in the absorber implies that the absorption arises from gas that is distributed over a wide range of ionization parameter $\xi$.
 Throughout this work. we use the following convention for the ionization parameter £=L/(ngr) in units of lon. where L is the ionizing luminosity. pj; is the IE number density. and ris the distance from the ionizing source.," Throughout this work, we use the following convention for the ionization parameter $\xi = L / (n_Hr^2)$ in units of , where $L$ is the ionizing luminosity, $n_H$ is the H number density, and $r$ is the distance from the ionizing source."
" We apply the Absorption Measure. Distribution GLU D) analvsis in order to obtain the total hvdrogen column density Ny, along the line of sight.", We apply the Absorption Measure Distribution $AMD$ ) analysis in order to obtain the total hydrogen column density $N_H$ along the line of sight.
" The A/D can be expressed as: and The relation between the ionic column densities ;/V;4, and the -ALUD is then expressed as: where ον is (ae measured ion column density. 1. is the element abundance with respect to hvdrogen assumed to be constant throughout the absorber. and. f;i;,(log£) is the fractional ion abundance with respect to the total abundance of its element."," The $AMD$ can be expressed as: and The relation between the ionic column densities $N_{ion}$ and the $AMD$ is then expressed as: where $N_{ion}$ is the measured ion column density, $A_z$ is the element abundance with respect to hydrogen assumed to be constant throughout the absorber, and $f_{ion}(\log\xi)$ is the fractional ion abundance with respect to the total abundance of its element."
 We aim at recovering (he LMD [or the different kinematic components of3516., We aim at recovering the $AMD$ for the different kinematic components of.
". For the AALD. we seek a distribution ON,/O(log£) that after integration (eq. 5))"," For the $AMD$, we seek a distribution $\partial N_H /
\partial(\mathrm{\log}\xi)$ that after integration (eq. \ref{eqAMD}) )"
 will produce all of the measured ionic column densities., will produce all of the measured ionic column densities.
" In. this procedure. one must take into account the full dependence of /;4, on £."," In this procedure, one must take into account the full dependence of $f_{ion}$ on $\xi$."
" We employ the ecode (Ixallman&Bautista2001) version 2.1kn3 to caleulate f4,Clog£) using the continuum derived in 3.1.. and extrapolated to the range of 1. 1000 Rvdbere."," We employ the code \citep{kal01} version 2.1kn3 to calculate $f_{ion}(\log\xi)$ using the continuum derived in \ref{sec:continuum}, and extrapolated to the range of 1 – 1000 Rydberg."
 During the fit. the AALD bin values are the only parameters left [ree to vary.," During the fit, the $AMD$ bin values are the only parameters left free to vary."
 The AND errors are calculated by. varving each bin from its best-fit value while the whole distribution is refitted., The $AMD$ errors are calculated by varying each bin from its best-fit value while the whole distribution is refitted.
 This procedure is repeated until 4?=1.," This procedure is repeated until $\Delta
\chi ^2= 1$."
 The fact that changes in theLUD in one bin can be compensated by varving the AAJ) inother bins dominates the 4437D uncertainties., The fact that changes in the$AMD$ in one bin can be compensated by varying the $AMD$ inother bins dominates the $AMD$ uncertainties.
 This is what limits ihe munber of bins and the AAD resolution in £ or 7., This is what limits the number of bins and the $AMD$ resolution in $\xi$ or $T$ .
 Indeed. we choose the narrowest," Indeed, we choose the narrowest"
stream inipact point across the face of a tilted accretion disk that precesses iu the retrograde direction (see2009:Foulkesetal. 2006).,"stream impact point across the face of a tilted accretion disk that precesses in the retrograde direction \citep[see][]{wms00,wb07,wts09,foulkes06}."
.. As in the stream source for positive zuperhlunps. the modulation results because the accretion stream mipact point has a periocically-varving depth in the potential well of the primary star.," As in the stream source for positive superhumps, the modulation results because the accretion stream impact point has a periodically-varying depth in the potential well of the primary star."
" Finding the term ""negative period excess” nunecessarile tureid. ino this work we refer— to the e/— defined as Τρήσαν. it is found that for svstenis showing both positive and negative superhumps that ejje -—2 (Patterson1999:Retteretal. 2002).."," Finding the term “negative period excess” unnecessarily turgid, in this work we refer to the $\epsilon_-$ defined as Empirically, it is found that for systems showing both positive and negative superhumps that $\epsilon_+/\epsilon_-\sim2$ \citep{patterson99,retterea02}. ."
 We show in Figure 5. a snapshot from ag =0.10 siuulatiou that demonstrates the plhivsical origiu of jeeative superhunps., We show in Figure \ref{fig: sph-} a snapshot from a $q=0.40$ simulation that demonstrates the physical origin of negative superhumps.
 At orbit 100. the disk particles were tilted 5° about the 4-axis and the simulation restarted.," At orbit 400, the disk particles were tilted $5^\circ$ about the $x$ -axis and the simulation restarted."
 The ereeu line in the Figure runing diagoually hough the primary indicates the location of the line of trodes: the disk uidplane includes this line. but is below he orbital plane to the right of the line. and above the orbital plane to the left of the line.," The green line in the Figure running diagonally though the primary indicates the location of the line of nodes; the disk midplane includes this line, but is below the orbital plane to the right of the line, and above the orbital plane to the left of the line."
 The disk particles are again color-coded by Iuninositv. aud the brightest articles are shown with lavecr svinbols.," The disk particles are again color-coded by luminosity, and the brightest particles are shown with larger symbols."
 The ballistic accretion stream cau be followed frou the L1 point to the inpact point near the line of nodes., The ballistic accretion stream can be followed from the L1 point to the impact point near the line of nodes.
 The simulation light curve is derived from the “surface” particles as described in Wood&Burke(2007)., The simulation light curve is derived from the “surface” particles as described in \citet{wb07}.
. The times of maxiuumuu of he negative superluup light curve occur when accretion stream maüpact point is deepest in the potential of the wimary and on the side of the disk facing the observer., The times of maximum of the negative superhump light curve occur when accretion stream impact point is deepest in the potential of the primary and on the side of the disk facing the observer.
 A second observer viewing the disk from the opposite side would still see negative «ΡΟπάς. but autiphased ο those of the first.," A second observer viewing the disk from the opposite side would still see negative superhumps, but antiphased to those of the first."
 ILwius introduced ai viable model for positive superliups aud their evolution. let ux now compare the uodel to the V3LL Lyr photometry.," Having introduced a viable model for positive superhumps and their evolution, let us now compare the model to the V344 Lyr photometry."
 The primary science mission of the NASA Discovery wission is to discover aud characterize terrestrial auets in the habitable zoue of Sun-like stars using the ransit method (Doruckietal.2010:Haasct2010).," The primary science mission of the NASA Discovery mission is to discover and characterize terrestrial planets in the habitable zone of Sun-like stars using the transit method \citep{borucki10,haas10}."
. The spacecraft is in an Earth-trailiug orbit. allowing it ο view its roughly 150.000 target stars continuously or the 3.5-vr mission lifetime.," The spacecraft is in an Earth-trailing orbit, allowing it to view its roughly 150,000 target stars continuously for the 3.5-yr mission lifetime."
 The photometer has no shutter and stares contiuuouslv at the target field., The photometer has no shutter and stares continuously at the target field.
 Each inteeration lasts 6.51 s. Due to memory and bandwidth coustraiuts. only data from the pre-selected tarect apertures are kept.," Each integration lasts 6.54 s. Due to memory and bandwidth constraints, only data from the pre-selected target apertures are kept."
 can observe up to 170.000 targets using the loue-cadence (LC mode. swine 270 inteerations over 29.[ uum. aud up to 512 targets in the short-cadence (SC) mode. sunning 9 integrations for au effective exposure tine of 58.8 s. There are gaps iu the data streams resulting frou. for example. mouthlv data downloads using the ligh-eain autenua and quarterly 907 spacecraft rolls. as well as unplanned safeauodoe aud loss of fine point events.," can observe up to 170,000 targets using the long-cadence (LC) mode, summing 270 integrations over 29.4 min, and up to 512 targets in the short-cadence (SC) mode, summing 9 integrations for an effective exposure time of 58.8 s. There are gaps in the data streams resulting from, for example, monthly data downloads using the high-gain antenna and quarterly $^\circ$ spacecraft rolls, as well as unplanned safe-mode and loss of fine point events."
 For further details of the spacecraft commussioniue. target tables. data collection and processing. and performance nmetries. see Πααςetal.(2010).. al. (2010)... and Caldwellctal.C2010).," For further details of the spacecraft commissioning, target tables, data collection and processing, and performance metrics, see \citet{haas10}, \citet{koch10}, and \citet{caldwell10}."
. data are provided as quarterly FITS files bx the Science Operations Center after being processed through the standard data reduction pipeline (Jenkiusetal.2010)., data are provided as quarterly FITS files by the Science Operations Center after being processed through the standard data reduction pipeline \citep{jenkins10}.
. The raw data are first corrected for Dias. sunear induced by the shutterless readout. and sky background.," The raw data are first corrected for bias, smear induced by the shutterless readout, and sky background."
" Tie series are extracted using simple aperture photometry (SAP) using an optimal aperture for cach star. aud these ""SAP light curves” are what we use in this study."," Time series are extracted using simple aperture photometry (SAP) using an optimal aperture for each star, and these “SAP light curves” are what we use in this study."
 The dates aud times for the beeiuniug and eud of Q2. Q3 and QL are listed in Table 1..," The dates and times for the beginning and end of Q2, Q3 and Q4 are listed in Table \ref{tbl: quarters}. ."
 The full SAP lieht curve for quarters Q2. Q3. and Qt is shown in fux units iu Figure 6..," The full SAP light curve for quarters Q2, Q3, and Q4 is shown in flux units in Figure \ref{fig: lcrawflux3}."
 In Figure 2 of Paper II we show the full SAP light curve in Kp magnitude units., In Figure 2 of Paper II we show the full SAP light curve in Kp magnitude units.
 As noted in Paper Π and evideut πι Figure 6.. the superoutbursts begin as normal DN outbursts.," As noted in Paper II and evident in Figure \ref{fig: lcrawflux3}, the superoutbursts begin as normal DN outbursts."
 The Q2 data begin at BID 2155002.5008., The Q2 data begin at BJD 2455002.5098.
 For simplicity we will below refer to events as occurriug on. or exaniple. dav 70. which should be interpreted to mean BJD 2155070 — that is we take BJD 2155000 to be our &ducial tine refercuce.," For simplicity we will below refer to events as occurring on, for example, day 70, which should be interpreted to mean BJD 2455070 – that is we take BJD 2455000 to be our fiducial time reference."
 Iu this paper. we focus ou the superhunp aud orbital sjeunals present in the data.," In this paper, we focus on the superhump and orbital signals present in the data."
 The outburst behavior of hese data in the coutext of coustrainiug the thermal-viscous limit evele is published separately (Paper IT)., The outburst behavior of these data in the context of constraining the thermal-viscous limit cycle is published separately (Paper II).
 To remove the large-uuplitude outburst behavior from he raw light curvo — ie. to high-pass filter the data we subtracted a boxcar-simoothed copy of the light curve from the SAP light curve.," To remove the large-amplitude outburst behavior from the raw light curve – i.e., to high-pass filter the data – we subtracted a boxcar-smoothed copy of the light curve from the SAP light curve."
 The window width was aken to be the superluimp evcle leugth (2.2 hr or 135 yoluts)., The window width was taken to be the superhump cycle length (2.2 hr or 135 points).
 To minimize the effects of data gaps. we split he data into a separate file anytime we had a data eap of more than 1 evcle.," To minimize the effects of data gaps, we split the data into a separate file anytime we had a data gap of more than 1 cycle."
 This resulted in LO data ος»., This resulted in 10 data chunks.
 Ouce the data residual light curve was calculated. we again recombined the data into a single file.," Once the data residual light curve was calculated, we again recombined the data into a single file."
" The results or Q2. Q3. aud QL ave shown in Figures 7.. ὃν, auc 9.. respectively."," The results for Q2, Q3, and Q4 are shown in Figures \ref{fig: reslc1}, \ref{fig: reslc2}, and \ref{fig: reslc3}, respectively."
 We also calculated the fractional amplitude light curve w dividing the raw light curve by the smoothed licht curve. and subtracting 1.0.," We also calculated the fractional amplitude light curve by dividing the raw light curve by the smoothed light curve, and subtracting 1.0."
 However. as expected. the amplitudes of the photometric signals in the residual ight curve are more nearly coustaut than those iu the ractional amplitude light curve.," However, as expected, the amplitudes of the photometric signals in the residual light curve are more nearly constant than those in the fractional amplitude light curve."
 This is because the superhunip signals — both positive and negative — have auplitudes determined by physical processes within the disk that are not strong functions of the overall disk Iumiuositv., This is because the superhump signals – both positive and negative – have amplitudes determined by physical processes within the disk that are not strong functions of the overall disk luminosity.
 Tn Figure 10 we show the discrete Fourier transform auplitude spectra for the current data set., In Figure \ref{fig: 2dDFT} we show the discrete Fourier transform amplitude spectra for the current data set.
 We took the rausforms over 2000 frequency poiuts spanuing 0 to 70 evcles per day., We took the transforms over 2000 frequency points spanning 0 to 70 cycles per day.
 Each transform is of a 5 day window of he data. aud the window was moved roughly 1/2 dav yetwoeen subsequent trausformes.," Each transform is of a 5 day window of the data, and the window was moved roughly 1/2 day between subsequent transforms."
 The color scale indicates he logarithm ofthe residual count light curve amplitude in units of counts per cadence., The color scale indicates the logarithm of the residual count light curve amplitude in units of counts per cadence.
 Iu Figure 11. we show a naenified view including ouly frequencies 9.5 to 12.5 c/d o better bring out the 3 fundamental frequencies in the Ssvsteni., In Figure \ref{fig: 2dDFTzoom} we show a magnified view including only frequencies 9.5 to 12.5 c/d to better bring out the 3 fundamental frequencies in the system.
 Figures 10. and 1l are rich with information., Figures \ref{fig: 2dDFT} and \ref{fig: 2dDFTzoom} are rich with information.
" The )ositive superliuups (P,=2.20lr) dominatethe power Or davs 58NO and ~162190.", The positive superhumps $P_+ = 2.20$hr) dominatethe power for days $\sim$ 58–80 and $\sim$ 162–190.
 In Figure 11. we see he that time evolution of the fiudamental oscillation," In Figure \ref{fig:
2dDFTzoom} we see the that time evolution of the fundamental oscillation"
(e.g. Fig. 5)).,(e.g. Fig. \ref{fvmap}) ).
" As already mentioned, BELO4 and BELOS favored the rotating toroid scenario."," As already mentioned, BEL04 and BEL05 favored the rotating toroid scenario."
" In contrast, other authors (Gibb et al. 2004;;"," In contrast, other authors (Gibb et al. \cite{gibb};"
 Araya et al. 2008)), Araya et al. \cite{araya}) )
" preferred the outflow interpretation, thus posing a problem that we wish to address with our new SMA data."," preferred the outflow interpretation, thus posing a problem that we wish to address with our new SMA data."
" Besides the (possible) existence of rotation and/or outflow, the situation in G31.41 is complicated by the existence of infall, detected by Girart et al. (2009))"," Besides the (possible) existence of rotation and/or outflow, the situation in G31.41 is complicated by the existence of infall, detected by Girart et al. \cite{gira}) )"
 as an inverse P-Cygni profile of the C34S((7-6) line observed with the SMA., as an inverse P-Cygni profile of the (7–6) line observed with the SMA.
" Therefore, before making a comparative discussion of the different models for the velocity gradient, we need to verify to what extent our mmeasurements may be affected by infall."," Therefore, before making a comparative discussion of the different models for the velocity gradient, we need to verify to what extent our measurements may be affected by infall."
" As already discussed in Sect. 3.2,,"," As already discussed in Sect. \ref{soutf},"
 Fig., Fig.
 9 clearly reveals that the aand, \ref{fcospts} clearly reveals that the and
Studies of ineteoritic material have revealed the presence of short-lived racioactivities in the early solar system (Wasserbure1985:Cameron1993:PodosekanclNichols1997:Vanhala2000:Mclxeeganetal. 2000).,"Studies of meteoritic material have revealed the presence of short-lived radioactivities in the early solar system \citep{was85,cam93,pod97,gos00,mck00}."
".. The origin of these dozen or so confirmed (! Ca.26 AL, 6pe ""Be, Lu Ato. ""n pq, PHal 3 PPLDC and >2Hpg) or suspected OTe.mele MCLAor. POSPpp, ang 092?? b) short-livec 'aclionuclides |as been a subject of inteuse investigation over the last few vears."," The origin of these dozen or so confirmed $^{41}$ Ca,$^{26}$ Al, $^{60}$ Fe, $^{10}$ Be, $^{53}$ Mn, $^{107}$ Pd, $^{182}$ Hf, $^{129}$ I, and $^{244}$ Pu) or suspected $^{99}$ Tc, $^{36}$ Cl, $^{205}$ Pb, and $^{92}$ Nb) short-lived radionuclides has been a subject of intense investigation over the last few years."
 The‘e are two basic ways to explal1 the procuction of the radioactivities: via stellar nucleosyuthesis ο‘through loca ILOCluction iu the early solar system., There are two basic ways to explain the production of the radioactivities: via stellar nucleosynthesis or through local production in the early solar system.
 A stellar nucleosyntletic source (a supernova or an ACB star) has been the leacliig explanation Or most o ‘the nuclei (Caueron1993.2001a:Wasserburgetal.1991.1995.1993).," A stellar nucleosynthetic source (a supernova or an AGB star) has been the leading explanation for most of the nuclei \citep{cam93,cam01a,was94,was95,was98}."
. This source works well for the longer-lived radioactivities. because tiere 1s plenty of time to have heu produced in stellar interiors aud ther inixec into the interstellar inecdiuum. including the moeclar cloud core ron1 which the solar system was formed.," This source works well for the longer-lived radioactivities, because there is plenty of time to have them produced in stellar interiors and then mixed into the interstellar medium, including the molecular cloud core from which the solar system was formed."
" Howeve ""the case is more complicate| fo‘the racdionuclides - ineau life less than a few iiljon years - sluce their presence sesa time limit “one milion years or less for the time available beween tlieir production and tjelr incorporalol the solar system material."," However, the case is more complicated for the shortest-lived radionuclides - mean life less than a few million years - since their presence sets a time limit of one million years or less for the time available between their production and their incorporation in the solar system material."
 This ias led to the 1nulation of the idea of the riegered origirol je solar sysem (CameronaudTruran1977:Boss1995:Cameronetal.1997:xdVauliala. 2000)... which suggests that the formaion of the solar system was initiated whet al iterstellar stock wave propagating from a uearby explosive stellar event impacted ou a molecilar “LOUd core.," This has led to the formulation of the idea of the triggered origin of the solar system \citep{cam77,bos95,cam97,vab98,bos00}, which suggests that the formation of the solar system was initiated when an interstellar shock wave propagating from a nearby explosive stellar event impacted on a molecular cloud core."
 In addition to trigeMDeriug the collapse o ‘the core earlier than i would have occurrec herwise. {1e shock wave also euriched it with [reshly synthesized reiclioactivities produced at the ellar site aud carried by the shock wave.," In addition to triggering the collapse of the core earlier than it would have occurred otherwise, the shock wave also enriched it with freshly synthesized radioactivities produced at the stellar site and carried by the shock wave."
 Another possibility for the origin of the ‘aclionuclices is to have theu produced locally iu ile solar nebula., Another possibility for the origin of the radionuclides is to have them produced locally in the solar nebula.
 According to this scenario. he racioniclides were prod(cec diwiug spallation reactious involving energetic particles emanatiue [rom p'otosolar flares (8ieal.1997).," According to this scenario, the radionuclides were produced during spallation reactions involving energetic particles emanating from protosolar flares \citep{shu97}."
. Sitce ije racioacti‘ilies are produced locally. there a‘e Πο time coustraints for the fortation of the soar Sysleln. all ierelore uo need to connect the origin o Γιie solar system with a nearby explosive Sellar evel. as long as all the detected shortes-lived radioactivitles can be procuced through tiis luecjalisin.," Since the radioactivities are produced locally, there are no time constraints for the formation of the solar system, and therefore no need to connect the origin of the solar system with a nearby explosive stellar event, as long as all the detected shortest-lived radioactivities can be produced through this mechanism."
 The curent meteorite data sugeMODests that the best explanation lor he origin o ude racioactivill rectires both scenarios., The current meteorite data suggests that the best explanation for the origin of the radioactivities requires both scenarios.
 Local irraciiation moclels appea ‘to have clillicity in matchiie the observ abuidauce ratios of the nuclides. especially that of 77Al to HCa (Srinivasanal. 1993).," Local irradiation models appear to have difficulty in matching the observed abundance ratios of the nuclides, especially that of $^{26}$ Al to $^{41}$ Ca \citep{sri96,sah98,lee98}."
". Even if it may be possile to ὀνοισοιje. this probleu by assumiLeD> shieding of the refractory inclusions by a less refractory mantle (CGounelleetal.2001)... loca procuction scenarios cannot account [or ""Ee. and it herefore reeires a stellar iucleosynthletic SOULce (Goswami.Marhasaudαρα]2001)."," Even if it may be possible to overcome this problem by assuming shielding of the refractory inclusions by a less refractory mantle \citep{gou01}, local production scenarios cannot account for $^{60}$ Fe, and it therefore requires a stellar nucleosynthetic source \citep{gos01}."
. The detection of the short-lived isotope ! Be in ai Alleide inclusion (Mcelxeeganetal. 2000).. has stirred urther debate. since the nuclide is thought to be produced only by nuclear spallation reactious.," The detection of the short-lived isotope $^{10}$ Be in an Allende inclusion \citep{mck00}, has stirred further debate, since the nuclide is thought to be produced only by nuclear spallation reactions."
 Therefore. its existence has been used to argue," Therefore, its existence has been used to argue"
"but over our observing window the exoplanet’s orbit led to velocity shifts over 60 km/s. Because the data must be shifted in velocity space to account for the shift of the planet's spectrum, sections of the spectrum with high transmittance may be shifted to line up with spectral regions of low transmittance; this benefits us by moderating extinction of lines with strong telluric counterparts.","but over our observing window the exoplanet's orbit led to velocity shifts over 60 km/s. Because the data must be shifted in velocity space to account for the shift of the planet's spectrum, sections of the spectrum with high transmittance may be shifted to line up with spectral regions of low transmittance; this benefits us by moderating extinction of lines with strong telluric counterparts."
" However, to avoid degrading our detectable signal by combining low-transmittance data with high-transmittance data, we weighted the value for each shifted spectral channel by the stochastic-noise SNR (based on detected photons and transmittance at the pre-shifted Finally, we"," However, to avoid degrading our detectable signal by combining low-transmittance data with high-transmittance data, we weighted the value for each shifted spectral channel by the stochastic-noise SNR (based on detected photons and transmittance at the pre-shifted wavelength)."
" wavelength).applied a high-pass filter to the residuals for each set to remove variations in the continuum due to movement of the star on the detector over the course of the night by creating a smoothed version of the spectrum using a boxcar average with a window sufficiently large that any narrow features would be significantly reduced 20 resolving and then subtracted the filtered(~ spectrum to elements),achieve a final rms scatter of 70.001."," Finally, we applied a high-pass filter to the residuals for each set to remove variations in the continuum due to movement of the star on the detector over the course of the night by creating a smoothed version of the spectrum using a boxcar average with a window sufficiently large that any narrow features would be significantly reduced $\sim20$ resolving elements), and then subtracted the filtered spectrum to achieve a final rms scatter of $\sim$ 0.001."
 We evaluated the loss of narrow features due to the filtering by injecting synthetic emission lines and determined that the high pass filter preserved of their amplitudes., We evaluated the loss of narrow features due to the filtering by injecting synthetic emission lines and determined that the high pass filter preserved of their amplitudes.
 Flux calibration was performed by normalizing the observed continuum flux to the predicted flux based on the K-band stellar magnitude (?) and effective temperature (?).., Flux calibration was performed by normalizing the observed continuum flux to the predicted flux based on the K-band stellar magnitude \citep{cutri2003p?} and effective temperature \citep{vanbelle2009p1085}.
" In order to understand the origin of the excess emission signal detected by S10 between 3.0 and μπι, we must first understand the potential contributing emitting species and their spectral characteristics."," In order to understand the origin of the excess emission signal detected by S10 between 3.0 and $\mu$ m, we must first understand the potential contributing emitting species and their spectral characteristics."
" S10 suggest that methane emission at 3.3m provides the best fit to their data, but there are clearly other species with transitions in this spectral region that may also be sufficiently abundant to produce detectable emission in the planet’s atmosphere."," S10 suggest that methane emission at $\mu$ m provides the best fit to their data, but there are clearly other species with transitions in this spectral region that may also be sufficiently abundant to produce detectable emission in the planet's atmosphere."
" In order to constrain the potential molecular species that could be producing emission, we generated models of line emission for a range"," In order to constrain the potential molecular species that could be producing emission, we generated models of line emission for a range"
on the value of 0.1 used for the Εν.,on the value of 0.1 used for the LSB's.
 As was expected. we obtain smaller values of A than for the LSs.," As was expected, we obtain smaller values of $\lambda$ than for the LSB's."
 For the rest of the mass sequence we obtain identical values of A. which is what the analytic results of section (2) led us to expect.," For the rest of the mass sequence we obtain identical values of $\lambda$, which is what the analytic results of section (2) led us to expect."
 Here again having taken self. similar halos. and obtaining constant A for the normal late tvpe sequence. we obtain self similar final rotation curves. which ave all scaled versions of each other.," Here again having taken self similar halos, and obtaining constant $\lambda$ for the normal late type sequence, we obtain self similar final rotation curves, which are all scaled versions of each other."
 Figures (14) and (15) are analogous to (12) and (13). but for a total mass of {ουAl) 10.5.," Figures (14) and (15) are analogous to (12) and (13), but for a total mass of $log(M)=10.5$ ."
 The description of the previous model applies here., The description of the previous model applies here.
 The values of z for this mass sequence are the same as were found for the LSB galaxies and are also shown in Figure (8). Le. we do not find a significant. dillerences in the formation epochs of these two galaxy types.," The values of $z$ for this mass sequence are the same as were found for the LSB galaxies and are also shown in Figure (8), i.e. we do not find a significant differences in the formation epochs of these two galaxy types."
 The blue colors and large gas fractions of LSB galaxies are better explained in terms of slow evolution timescales. in this case naturally arising from the low surface density (Firmani ‘Tutukov 1994. Firmani et al 1996). and not as rellecting recent formation epochs.," The blue colors and large gas fractions of LSB galaxies are better explained in terms of slow evolution timescales, in this case naturally arising from the low surface density (Firmani Tutukov 1994, Firmani et al 1996), and not as reflecting recent formation epochs."
 Figure. (16) shows 2y;es.AZ for the normal spirals and for the LSB sequence., Figure (16) shows $R_M vs. M$ for the normal spirals and for the LSB sequence.
 The modeled galaxies lie on a line of slope 0.46., The modeled galaxies lie on a line of slope 0.46.
 Phe arguments of section (2) would suggest Rap=RyfA =RapκALM? Lea slope of 0.43.," The arguments of section (2) would suggest $R_{M}=R_{d}/\lambda$ $\Rightarrow R_{M} \propto M^{1/\beta}$ i.e., a slope of 0.43."
 Again. the agreement of the two independent approaches 1s encouraging.," Again, the agreement of the two independent approaches is encouraging."
 It can be seen that the decrease in the rotation curve appears at the same relative radial distances for both types of galaxies., It can be seen that the decrease in the rotation curve appears at the same relative radial distances for both types of galaxies.
 Thus a relation of this nature is à robust prediction of this approach. awaiting more cases like DDO 154. which lies at the cross in Figure (16) (an error in the acloptecl distance of a factor of 1.4 would make it coincide with the moclels).," Thus a relation of this nature is a robust prediction of this approach, awaiting more cases like DDO 154, which lies at the cross in Figure (16) (an error in the adopted distance of a factor of 1.4 would make it coincide with the models)."
 Figure (17) is analogous to Figure (12). but shows the rotation curves in a log-log plot. where the characteristic shapes can be better appreciated.," Figure (17) is analogous to Figure (12), but shows the rotation curves in a log-log plot, where the characteristic shapes can be better appreciated."
 Lt is clear that. the barvonic component dominates interior to around. IOkpc. and the dark component outwards of this.," It is clear that the baryonic component dominates interior to around 10kpc, and the dark component outwards of this."
 It can be seen that both the barvonie component and the dark halo reaction, It can be seen that both the baryonic component and the dark halo reaction
Using ο). the equation of spherical hydrostatic equilibrium is The solution begins at the upper boundary by assuming an initial value of Αμ).,"Using $g(r)$, the equation of spherical hydrostatic equilibrium is The solution begins at the upper boundary by assuming an initial value of $k_{\mathrm{R}}(1)$."
 Then. following ?.. we assume all properties. except pressure and density. are constant above r(1). and that these variables decrease with a constant scale height.," Then, following \citet{1974ApJS...28..343M}, we assume all properties, except pressure and density, are constant above $r(1)$, and that these variables decrease with a constant scale height."
" This leads to The gas pressure. P..(1). is derived from the total pressure by subtracting values for radiation. pressure. P,(1). and turbulent pressure. P((1). rf these are known."," This leads to The gas pressure, $P_{\mathrm{g}}(1)$, is derived from the total pressure by subtracting values for radiation pressure, $P_{\mathrm{r}}(1)$, and turbulent pressure, $P_{\mathrm{t}}(1)$, if these are known."
 The gas pressure and the temperature are then used to interpolate an updated value for kg(1) from the input model., The gas pressure and the temperature are then used to interpolate an updated value for $k_{\mathrm{R}}(1)$ from the input model.
 This procedure is iterated until the upper boundary pressure converges to «Ify., This procedure is iterated until the upper boundary pressure converges to $< 10^{-6}$.
 With the upper boundary condition established. Eq.," With the upper boundary condition established, Eq."
 ο is integrated for Pi. again using the Bulirsch-Stoer method.," \ref{eq:sph_hydro}
 is integrated for $P_{\mathrm{tot}}$, again using the Bulirsch-Stoer method."
 At each step the gas pressure is found as described above. and the gas pressure and temperature are used to interpolate the corresponding value for the Rosseland mean opacity.," At each step the gas pressure is found as described above, and the gas pressure and temperature are used to interpolate the corresponding value for the Rosseland mean opacity."
 This method of solving the hydrostatic equilibrium is also applicable to the plane-parallel atmosphere with e(r)=g and without solving for the radius., This method of solving the hydrostatic equilibrium is also applicable to the plane-parallel atmosphere with $g(r) = g$ and without solving for the radius.
 To test our implementation. we have incorporated the modified version of subroutinettaup.. with both the Bulirsh-Stoer and the fifth-order Runga- routines. into andAtLas_OS.," To test our implementation, we have incorporated the modified version of subroutine, with both the Bulirsh-Stoer and the fifth-order Runga-Kutta routines, into and."
. The maximum difference between the Bulirsch-Stoer (or the fifth-order Runga-Kutta) method and the original Hamming method was less than our output numerical resolution of 1 part in 10+ at all but two of the 72 depth points., The maximum difference between the Bulirsch-Stoer (or the fifth-order Runga-Kutta) method and the original Hamming method was less than our output numerical resolution of 1 part in $10^4$ at all but two of the 72 depth points.
 Therefore. the percentage difference between the nethods is zero except at these two depths. where the differences are only 0.021% and 0.014%.," Therefore, the percentage difference between the methods is zero except at these two depths, where the differences are only $0.021\%$ and $0.014\%$."
 It is clear that the pressure solution ts being done correctly., It is clear that the pressure solution is being done correctly.
 and solve the radiative transfer using the integral equation. method., and solve the radiative transfer using the integral equation method.
 The complication. introduced. by a geometrically extended. spherically symmetric atmosphere is that the angle between a ray of light and the radial direction varies with depth.," The complication introduced by a geometrically extended, spherically symmetric atmosphere is that the angle between a ray of light and the radial direction varies with depth."
 Numerous methods are available for solving this problem. of which we have chosen to use the reorganization of the ?. method.," Numerous methods are available for solving this problem, of which we have chosen to use the \citet{1971JQSRT..11..589R} reorganization of the \citet{1964CR...258..3189F} method."
 Following the approach described by ?.. we solve the radiative transfer along a set of rays parallel to the central ray directed toward the distant observer. as shown in Fig. 4..," Following the approach described by \citet{1978stat.book.....M}, we solve the radiative transfer along a set of rays parallel to the central ray directed toward the distant observer, as shown in Fig. \ref{fig:sph_geo}."
" A subset of these rays intersect the ""core"" of the star. defined as the deepest radial optical depth. which we usually set to be τε= 100."," A subset of these rays intersect the “core” of the star, defined as the deepest radial optical depth, which we usually set to be $\tau_{\mathrm{R}} = 100$ ."
 We sample the surface of the core using 10 rays., We sample the surface of the core using 10 rays.
 We tried both equal steps of jj—cos@ covering the interval 1.0€p0.1 in steps of Au=0.1. which is shown in Fig. 4..," We tried both equal steps of $\mu = \cos \theta$ covering the interval $1.0 \leq \mu \leq 0.1$ in steps of $\Delta \mu = 0.1$, which is shown in Fig. \ref{fig:sph_geo},"
 and a finer spacing toward the edge of the core by distributing the rays as p=1.0.0.85.0.7.0.55.0.4.0.25.0.2.0.15.0.1.0.05.," and a finer spacing toward the edge of the core by distributing the rays as $\mu = 1.0, 0.85, 0.7, 0.55, 0.4, 0.25, 0.2, 0.15, 0.1, 0.05$."
 We found the results to be almost identical. so we chose to use the equal µ spacing.," We found the results to be almost identical, so we chose to use the equal $\mu$ spacing."
 For the core rays. the lower boundary condition. of the radiative transfer is the diffusion approximation.," For the core rays, the lower boundary condition of the radiative transfer is the diffusion approximation."
 From the core to the surface we follow the convention used by Kurucz in his plane-parallel models by having 72 depth points., From the core to the surface we follow the convention used by Kurucz in his plane-parallel models by having 72 depth points.
 For the central ray these depth points are distributed eight per decade with equal steps of the Alogzr;=0.125 from logry=2 to -6.875., For the central ray these depth points are distributed eight per decade with equal steps of the $\Delta \log \tau_{\mathrm{R}} = 0.125$ from $\log \tau_{\mathrm{R}} = 2$ to -6.875.
 For the off-center core rays the steps will be different. depending on the projection.," For the off-center core rays the steps will be different, depending on the projection."
 The tangent rays are those that terminate at the radius perpendicular to the central ray. and which are tangent to a particular atmospheric shell at that point. as shown in Fig. 4..," The tangent rays are those that terminate at the radius perpendicular to the central ray, and which are tangent to a particular atmospheric shell at that point, as shown in Fig. \ref{fig:sph_geo}."
 The spacing between the shells is set by the central ray. and these spacings define the impact parameters of all the tangent rays.," The spacing between the shells is set by the central ray, and these spacings define the impact parameters of all the tangent rays."
 With this geometry. we calculated values of peat the intersection of each ray toward the distant observer with each atmospheric depth. and from these we compute the integration weights at each point over the surface of each atmospheric shell at every depth.," With this geometry, we calculated values of $\mu$ at the intersection of each ray toward the distant observer with each atmospheric depth, and from these we compute the integration weights at each point over the surface of each atmospheric shell at every depth."
 The lower boundary condition for the radiative transfer of the tangent rays Is the assumption of symmetry at the perpendicular radius., The lower boundary condition for the radiative transfer of the tangent rays is the assumption of symmetry at the perpendicular radius.
 At the surface of the atmosphere the rays toward the distant observer have ji values that depend on the steps described above., At the surface of the atmosphere the rays toward the distant observer have $\mu$ values that depend on the steps described above.
 When we want to use these surface intensities. such as to predict the observable center-to-limb variation. we map the computed 7(u) onto a specified set of p-values using a cubie spline interpolation.," When we want to use these surface intensities, such as to predict the observable center-to-limb variation, we map the computed $I(\mu)$ onto a specified set of $\mu$ -values using a cubic spline interpolation."
 This solution with the ?— organization uses the same equations as the original ? method., This solution with the \citet{1971JQSRT..11..589R} organization uses the same equations as the original \citet{1964CR...258..3189F} method.
 Therefore. in theplane-parallel case. in. which both can be used. the results must be exactly the same.," Therefore, in theplane-parallel case, in which both can be used, the results must be exactly the same."
 To test this. we created two," To test this, we created two"
operating at GGlIz. with GGL channels. and thirteen. 143mm antennas (?.Tavloretal.inprep.)..,"operating at GHz, with $\times$ GHz channels, and thirteen m antennas \citep[][Taylor et al. in prep.]{Padin:2002}."
 CII2 has à aarcmin field of view and 6aarcmin resolution so that at moderate recdshifts (2~0.3) it can observe out to the largest radii of galaxy clusters., CBI2 has a arcmin field of view and arcmin resolution so that at moderate redshifts $z \sim 0.3$ ) it can observe out to the largest radii of galaxy clusters.
 La future work we will present the application of the procedure outlined here to observations of a number of massive galaxy clusters with CBP., In future work we will present the application of the procedure outlined here to observations of a number of massive galaxy clusters with CBI2.
 We adopt a ACDAL cosmology with O3;=0.3. Oy=0.7 and My=TOkkmss + throughout this paper unless otherwise stated.," We adopt a $\Lambda$ CDM cosmology with $\Omega_\rmn{M} = 0.3$, $\Omega_\lambda = 0.7$ and $H_0 = 70$ $^{-1}$ $^{-1}$ throughout this paper unless otherwise stated."
 In the past most of the joint analvsis of SZ and X-ray data from observations of galaxy. clusters made use of the isothermal 3 model prescription. for modelling the ICM (??)..," In the past most of the joint analysis of SZ and X-ray data from observations of galaxy clusters made use of the isothermal $\beta$ model prescription for modelling the ICM \citep{Cavaliere:1976,Cavaliere:1978}."
 This model is typically used to fit regions of the cluster within res. the radius at which the mean enclosed density is 2500 times the universal critical density at the recishift of the cluster.," This model is typically used to fit regions of the cluster within $r_{2500}$, the radius at which the mean enclosed density is 2500 times the universal critical density at the redshift of the cluster."
 At relatively small radii the isothermal οὐ nmiocdel is found to be accurate in reproducing the average observable and physical properties of many clusters (seee.g. ??7).. Llo," At relatively small radii the isothermal $\beta$ model is found to be accurate in reproducing the average observable and physical properties of many clusters \citep[see
e.g.][]{Grego:2000, Reese:2002, LaRoque:2006}."
wever. deep X-ray spectral observations of nearby cluster samples using (scoe.g.7) and (seec.g.2). show that at larger radii the ICM temperature declines with radius.," However, deep X-ray spectral observations of nearby cluster samples using \cite[see e.g.][]{Vikhlinin:2006} and \cite[see
e.g.][]{Pratt:2007} show that at larger radii the ICM temperature declines with radius."
 llence for low-resolution pointed SZ observations that are sensitive to the outskirts of the cluster gas. there is a clear requirement for à more physically motivated non-isothermal mocel that is simple enough to be constrained by the data.," Hence for low-resolution pointed SZ observations that are sensitive to the outskirts of the cluster gas, there is a clear requirement for a more physically motivated non-isothermal model that is simple enough to be constrained by the data."
 There have been a number of recent approaches amongst. SZ ancl X-ray observers to relax the assumption ol isothermality in clusters and model the ICM in a physica wav., There have been a number of recent approaches amongst SZ and X-ray observers to relax the assumption of isothermality in clusters and model the ICM in a physical way.
 For observations of nearby relaxed. clusters. 7 developed a mocified :3 model of the electron density to fit the observed cores and steeper outer profiles of relaxe clusters.," For observations of nearby relaxed clusters, \cite{Vikhlinin:2006} developed a modified $\beta$ model of the electron density to fit the observed cores and steeper outer profiles of relaxed clusters."
 In that work the temperature is. paramoeterizec bv a broken power law at large radii and declines in the central cooling region as given by 2.., In that work the temperature is parameterized by a broken power law at large radii and declines in the central cooling region as given by \cite{Allen:2001}.
 The aco software pipeline developed by 2? uses separate. parametrization of the eas. dark matter and stellar components. assuming hyerostatic equilibrium. to jointhy fit to high significance X-rav spectra [rom andNeiwlon.. weak lensing shear from. Canada-France-Hawaii telescope. optical data on the brightest cluster galaxy from. the Hubble. space telescope and the SZ elfect. from the Cosmic Background Imager.," The JACO software pipeline developed by \cite{Mahdavi:2007} uses separate parametrization of the gas, dark matter and stellar components, assuming hydrostatic equilibrium, to jointly fit to high significance X-ray spectra from and, weak lensing shear from Canada-France-Hawaii telescope, optical data on the brightest cluster galaxy from the Hubble space telescope and the SZ effect from the Cosmic Background Imager."
 For sulliciently resolved SZ maps. the temperature and mass profiles can be reconstructed. by. de-projection techniques. for example see. ?? for a comparison of the method to simulations anc ? for direct application to SZ and X-ray. data.," For sufficiently resolved SZ maps, the temperature and mass profiles can be reconstructed by de-projection techniques, for example see \cite{Ameglio:2007,Ameglio:2009} for a comparison of the method to simulations and \cite{Nord:2009} for direct application to SZ and X-ray data."
 However with many SZ experiments the data are generally not very well resolved. and so combined analvsis with X-ray. surface. brightness data requires the application of a parameterized model that reproduces the observed temperatures anc masses fron X-ray observations and simulations.," However with many SZ experiments the data are generally not very well resolved, and so combined analysis with X-ray surface brightness data requires the application of a parameterized model that reproduces the observed temperatures and masses from X-ray observations and simulations."
 7. successfully use an NEW parameterized pressure profile developed by 2? to fit to data [rom the Sunvaev-Zeldovich Array (SZÀX). and then combine with X-ray surface brightness to reproduce temperature profiles out to large radii.," \cite{Mroczkowski:2009} successfully use an NFW parameterized pressure profile developed by \cite{Nagai:2007} to fit to data from the Sunyaev-Zel'dovich Array (SZA), and then combine with X-ray surface brightness to reproduce temperature profiles out to large radii."
 Vhis model has also been adopted by 2 in order derive a universal pressure profile from observations of the Ποο cluster sample., This model has also been adopted by \cite{Arnaud:2010} in order derive a universal pressure profile from observations of the REXCESS cluster sample.
 Recently 7? have developed. an analvtical cluster model based: on assuming a polvtropic relationship between the eas density and temperature. and parameterise the total mass using a generalised NEW model.," Recently \cite{Bulbul:2010} have developed an analytical cluster model based on assuming a polytropic relationship between the gas density and temperature, and parameterise the total mass using a generalised NFW model."
 In order to account for cool-core behaviour the resulting radial expressions are modified. by the same core taper used by. 2.., In order to account for cool-core behaviour the resulting radial expressions are modified by the same core taper used by \cite{Vikhlinin:2006}.
 The CBI2 array has relatively low spatial resolution. ancl a laree field-of-view. and hence a simple parameterized model is required. that is accurate over the bulk of the volume of the cluster.," The CBI2 array has relatively low spatial resolution, and a large field-of-view, and hence a simple parameterized model is required that is accurate over the bulk of the volume of the cluster."
 We could choose any function of eas density ancl temperature as the basis for our gas model. e.g. pressure (xZn.) or entropy CxZn.2).," We could choose any function of gas density and temperature as the basis for our gas model, e.g. pressure $\propto Tn_\rmn{e}$ ) or entropy $\propto Tn_\rmn{e}^{-2/3}$ )."
 For example 7. choose to use a four-parameter model for the cluster pressure profile., For example \cite{Nagai:2007} choose to use a four-parameter model for the cluster pressure profile.
" We choose to parameterize the IC'M based. on the entropy. because there is evidence from both observations and simulations that it can be modelled: as a simple power-law over most of the cluster volume (sec relsection:cntropy,,odelbefow).", We choose to parameterize the ICM based on the entropy because there is evidence from both observations and simulations that it can be modelled as a simple power-law over most of the cluster volume (see \\ref{section:entropy_model} below).
 Mecombinethisiil, We combine this with an NFW parametrization of the dark matter halo component.
haniN FMparametric ragsur facebrightnessandiow resolulionS Zdala," By modelling the gas in this way, the underlying physics of cluster gas in hydrostatic equilibrium is encoded into the model from the outset, and is simple enough to be constrained by X-ray surface brightness and low-resolution SZ data."
 IEhisalsoavoidsad hocparemclrizalionoflheclecl rondensityandtemperalurcandtherefore , This also avoids ad-hoc parametrization of the electron density and temperature and therefore removes the possibility of introducing unphysical solutions for the total mass.
, The following section describes in detail the physical basis and parametrization of this model.
We construct a parametric model. that is. physically consistent anc is therefore a reasonable description of the ICAL on the angular scales to which CBI2 is sensitive., We construct a parametric model that is physically consistent and is therefore a reasonable description of the ICM on the angular scales to which CBI2 is sensitive.
" A suitable parametrization of the dark matter content is the hierarchical clustering NEW. profile (?7).. where the dark matter (DM) density as a function of radius is given hy where pou ds the universal critical density for closure (at the redshift of the cluster). ry is the scale radius ancl 6, is the characteristic density contrast."," A suitable parametrization of the dark matter content is the hierarchical clustering NFW profile \citep{Navarro:1995}, , where the dark matter (DM) density as a function of radius is given by where $\rho_{\rmn{crit}}$ is the universal critical density for closure (at the redshift of the cluster), $r_{\rmn{s}}$ is the scale radius and $\delta_{\rmn{c}}$ is the characteristic density contrast."
 Phe DM virial ractius Γον is defined in this model as the radius of à sphere at which the mean interior DM density is equal to. 200944., The DM virial radius $r_\rmn{DM}$ is defined in this model as the radius of a sphere at which the mean interior DM density is equal to $200\rho_{\rmn{crit}}$.
 Note that the true virial radius of the cluster is slightly larger (10percent ) since one must also take into account the contribution [fromthe gas when calculating the total mass.," Note that the true virial radius of the cluster is slightly larger $\sim 10\,\rmn{per cent}$ ) since one must also take into account the contribution fromthe gas when calculating the total mass."
 Ht is related to the scale radius by where ουν ds known as the DAL concentration parameter., It is related to the scale radius by where $c_\rmn{DM}$ is known as the DM concentration parameter.
 This is related to the DM density contrast (?) by, This is related to the DM density contrast \citep{Navarro:1996} by
"Also the first term on the right side of Eq.(X1)) can be written as the product of a dimensional factor and a dimensionless one: with m;=m;/M,. Finally. once defined a dimensionless time being l4.=(79/6M)? the bulge crossing time. Eq.Al may be written as: This implies that. once assigned the initial conditions r;(0). v;(0). the existence of a unique solution for the Eq. (A7))","Also the first term on the right side of \ref{xdot}) ) can be written as the product of a dimensional factor and a dimensionless one: with $m'_i=m_i/M_b$ Finally, once defined a dimensionless time being $t_{cross}=(r_b^3/GM_b)^{1/2}$ the bulge crossing time, \ref{xdot} may be written as: This implies that, once assigned the initial conditions ${\bf r}_i'(0)$, ${\bf v}_i'(0)$, the existence of a unique solution for the Eq. \ref{new}) )"
" ensures that all the results obtained can be scaled in terms ol the ratios rry. m/My and (/1,,.."," ensures that all the results obtained can be scaled in terms of the ratios $r/r_b$, $m/M_b$ and $t/t_{cross}$."
 As described in ling(1966).. in a single-mass isotropic King model the phasespace stellar distribution function is given by: E- is (he energy of a star. ο} is (he mean gravitational potential eenerated by (he cluster and a is a normalization constant.," As described in \citet{king66}, in a single-mass isotropic King model the phase–space stellar distribution function is given by: where is the energy of a star, $\psi(r)$ is the mean gravitational potential generated by the cluster and $\alpha$ is a normalization constant."
" The ‘global’ parameter C is related to the tidal radius r, by the implicit relation", The `global' parameter $C$ is related to the tidal radius $r_t$ by the implicit relation
Contrary to previous work. we do not allow lor compositional disconünuities in the abundances of heavy. elements in (he envelope.,"Contrary to previous work, we do not allow for compositional discontinuities in the abundances of heavy elements in the envelope."
 We also assume that the temperature prolile is adiabatic. as anv radiative laver. if present al all. should be confined to a small region(Guillotetal.2003).," We also assume that the temperature profile is adiabatic, as any radiative layer, if present at all, should be confined to a small region\citep{gshs03}."
. The hydrostatic structure is computed with the theory. of rotating figures developed to the ΕΙ order in the rotational perturbation., The hydrostatic structure is computed with the theory of rotating figures developed to the $^{\rm th}$ order in the rotational perturbation.
 We use the EOS [or hydrogen and helium as described in Section 2., We use the EOS for hydrogen and helium as described in Section 2.
 As an improvement over (hie previous models. we explicitly take the EOS of rocks and ices into account.," As an improvement over the previous models, we explicitly take the EOS of rocks and ices into account."
 We use ihe SESAME EOS 7154 of water (SESAMElibrary1992) às à proxy for all ices (1150 being bv [ar the most abundant) and the SESAME EOS 7100 of div sand (SESAME for the rock-Iorming heavy elements., We use the SESAME EOS 7154 of water \citep{sesame} as a proxy for all ices $_2$ O being by far the most abundant) and the SESAME EOS 7100 of dry sand \citep{sesame} for the rock-forming heavy elements.
 We account for (he condensation of rocks/silicates in an approximate fashion by setting their abundance to zero lor temperatures 2<2500Kk. Water condenses around 300IXIx. but this is not included as it has a negligible effect on the interior structure and gravitational moments.," We account for the condensation of rocks/silicates in an approximate fashion by setting their abundance to zero for temperatures $T<2500\,$ K. Water condenses around K, but this is not included as it has a negligible effect on the interior structure and gravitational moments."
 In the absence of a suitable theory. the EOS of mixtures of H. He. water. and dry said is obtained by applving the additive volume rule (see $4.1. however).," In the absence of a suitable theory, the EOS of mixtures of H, He, water, and dry sand is obtained by applying the additive volume rule (see 4.1, however)."
 The 3-Iaver model is simplistic and the interiors of Jupiter aud Saturn are undoubtedly nore complex., The 3-layer model is simplistic and the interiors of Jupiter and Saturn are undoubtedly more complex.
 Due to the scarcity of data and ils current level of precision. more elaborate nodels are not justified at this point. however.," Due to the scarcity of data and its current level of precision, more elaborate models are not justified at this point, however."
 We believe that (he most significant sources of uncertainty have been taken into account in (his study. which represents the most extensive sequence of interior niodels computed for Jupiter aud Saturn so far.," We believe that the most significant sources of uncertainty have been taken into account in this study, which represents the most extensive sequence of interior models computed for Jupiter and Saturn so far."
 For each EOS considered. à range of core masses (M) and masses of heavy elements in (he envelope (M) is obtained after varying the other parameters and rejecting models that do not reproduce (he gravitational moments.," For each EOS considered, a range of core masses $M_{\rm core}$ ) and masses of heavy elements in the envelope $M_{\sss Z}$ ) is obtained after varying the other parameters and rejecting models that do not reproduce the gravitational moments."
 Ivesults obtained [or Jupiter by only fitüng ζω and J ave shown in Fig. 7.., Results obtained for Jupiter by only fitting $R_{\rm eq}$ and $J_2$ are shown in Fig. \ref{fig:boites-jup-reqj2}.
 What is particularly striking is (hat there is very little overlap between (he solutions for (he clilferent EOS and (hat the result for the basic interior properties. M; and Mz. greatly depends on," What is particularly striking is that there is very little overlap between the solutions for the different EOS and that the result for the basic interior properties, $M_{\rm core}$ and $M_{\sss Z}$ , greatly depends on"
eas (Douteimps et al.,gas (Bontemps et al.
 1996)., 1996).
 Iu this paper. we present high resolution images of the Class 0 protostar III 21 MMS observed iu the 6.9 nua continui using the Very Large Array (VLA).," In this paper, we present high resolution images of the Class 0 protostar HH 24 MMS observed in the 6.9 mm continuum using the Very Large Array (VLA)."
 Iu 2 we describe our observatious., In 2 we describe our observations.
 In 3 we report the results of the 6.9 nuu magie., In 3 we report the results of the 6.9 mm imaging.
 In Lowe discuss the plivsical properties of the dust σος sources iu the ΠΠ 21 AIMS region., In 4 we discuss the physical properties of the dust continuum sources in the HH 24 MMS region.
 The ΠΠ 24 AIMS region was observedbservatory! using the VLA of theNational Radio Astronomy in the standard Q-hand continu mode T»(13.3 GIIz or A = 6.9 nun) in two observing tracks., The HH 24 MMS region was observed using the VLA of the National Radio Astronomy in the standard $Q$ -band continuum mode (43.3 GHz or $\lambda$ = 6.9 mm) in two observing tracks.
 phase and amplitude were determined b observing the nearby quasar 0532|075 (PAIN 40532|0732)., The phase and amplitude were determined by observing the nearby quasar 0532+075 (PMN J0532+0732).
" The phase tracking center was noggy = O5!L6M@O8.38° and ogg = ιο 13.36"".", The phase tracking center was $\alpha_{2000}$ = $^{\rm h}$ $^{\rm m}$ $^{\rm s}$ and $\delta_{2000}$ = $-$ $'$ $''$.
 The first track was carried out in the D-array configuration with tweuty-five autenuas on 2005 March 30., The first track was carried out in the D-array configuration with twenty-five antennas on 2003 March 30.
 The flux deusitv of 0532|075 was bootstrapped from the quasar 0512|198 (3€ 117) assumnuiue that its flux density is 0.72 Jv. which is the fiux density measured within a day of our observations (VLA Calibrator Flux Density )).," The flux density of 0532+075 was bootstrapped from the quasar 0542+498 (3C 147) assuming that its flux density is 0.72 Jy, which is the flux density measured within a day of our observations (VLA Calibrator Flux Density )."
 The bootstrapped flux density of 0532|O75 is 1.05 Js., The bootstrapped flux density of 0532+075 is 1.05 Jy.
 The second track was in the C-urav configuration with tweuty-three autenuas ou 20014 March 2., The second track was in the C-array configuration with twenty-three antennas on 2004 March 2.
 The fux calibration was cone bv observing the quasar 0713]138 (QSO DOT10|139)., The flux calibration was done by observing the quasar 0713+438 (QSO B0710+439).
 The flux. density of 0713]138 was set to 0.20 Jv. which is the flux aeasured within 2 davs of our observations according to the VLA Calibrator Flux Deusity Database. and the bootstrapped flux density of 0532|075 is 0.70 Jy.," The flux density of 0713+438 was set to 0.20 Jy, which is the flux measured within 2 days of our observations according to the VLA Calibrator Flux Density Database, and the bootstrapped flux density of 0532+075 is 0.70 Jy."
 Maps were mace using a CLEAN aleorithin., Maps were made using a CLEAN algorithm.
 Figure le shows the map of the 6.9 wan coutim» toward the ΠΠ 21. AIMS region from the C- and the D-airvay data combined., Figure $a$ shows the map of the 6.9 mm continuum toward the HH 24 MMS region from the C- and the D-array data combined.
 The peak intensity is 5.66 την beam+., The peak intensity is 5.66 mJy $^{-1}$.
 ΠΙ 2. MAIS was clearly detected and shows an extended structure., HH 24 MMS was clearly detected and shows an extended structure.
 Detailed structures of compact objects were revealed by miagiug with the C-array data ouly (Fie., Detailed structures of compact objects were revealed by imaging with the C-array data only (Fig.
 15)., $b$ ).
 ΠΠ 21 AIMS was resolved iuto two objects. and another source was detected ~3” east of ΠΠ 21 MMS.," HH 24 MMS was resolved into two objects, and another source was detected $\sim$ $''$ east of HH 24 MMS."
 Their coordinates and peak intensities are listed in Table 1., Their coordinates and peak intensities are listed in Table 1.
 Source 1. the brightest oue. is near the 3.6 (2002)cmi contimmiun source detected by Reipurth ct al. ," Source 1, the brightest one, is near the 3.6 cm continuum source detected by Reipurth et al. ("
and is clongated in the southeast-nortlavest direction.,2002) and is elongated in the southeast-northwest direction.
 Tn contrast. source 2 is elongated in the northeast-southwest direction.," In contrast, source 2 is elongated in the northeast-southwest direction."
" The separation between sources l aud 2 is —0.9"" or 360 AU at a distance of LOO pe CAuthouv-Twirog 1982).", The separation between sources 1 and 2 is $\sim$ $''$ or 360 AU at a distance of 400 pc (Anthony-Twarog 1982).
 Source 3 was detected over the detection lait of 0.1 uy lQ4S/N = 6) in the C-mrray map (Fig., Source 3 was detected over the detection limit of 0.4 mJy $^{-1}$ (S/N = 6) in the C-array map (Fig.
 15). and it can also be seen in the € and D-array map (Fie.," $b$ ), and it can also be seen in the C and D-array map (Fig."
 la) as a weak peak., $a$ ) as a weak peak.
 Source 3 is unresolved., Source 3 is unresolved.
 Since it was uot detected iu other wavelengths. the nature of source )ds unclear.," Since it was not detected in other wavelengths, the nature of source 3 is unclear."
 Iu low-anass star forming regious. continuum cussion in the ceutimeter-millimeter band is usually cither frec-free radiatiou from hot ionized gas or thermal radiation from cold dust. or a combination of both.," In low-mass star forming regions, continuum emission in the centimeter-millimeter band is usually either free-free radiation from hot ionized gas or thermal radiation from cold dust, or a combination of both."
 The frec-free enissijon usually has ai simall ) spectral index. while the dust emission las a large C22) spectral index (Revnolds 1986: Anelada et al.," The free-free emission usually has a small $\lesssim$ 1) spectral index, while the dust emission has a large $\gtrsim$ 2) spectral index (Reynolds 1986; Anglada et al."
 1998)., 1998).
 The SED was exanuned to investigate the enuissiou ruechiauisui of TIT 2EAINIS., The SED was examined to investigate the emission mechanism of HH 24 MMS.
 Since sources 1 and 2 are resolved iu the 6.9 nua uid only. SED of the whole WIT 214 MIMS system was constructed.," Since sources 1 and 2 are resolved in the 6.9 mm band only, SED of the whole HH 24 MMS system was constructed."
" The total iux of the TMT 21 MMS system. neasured ina 1"" « I"" box. is 12.0 2 0.5 11Jv (from the nap shown in Fie."," The total flux of the HH 24 MMS system, measured in a $''$ $\times$ $''$ box, is 12.0 $\pm$ 0.5 mJy (from the map shown in Fig."
 le). aud the SED in the waveleneth range offirst 3.6 cin to 3. nua is shown in Fieure 2.," $a$ ), and the SED in the wavelength range of 3.6 cm to 3.4 mm is shown in Figure 2."
 We tried to fit the SED of IIII 21 MMS as a sun of two power-law components. one from the frec-ree enüssion and the other from the dust enission. over he wavelength rauge of 3. laua to 3.63 emi (8.3ss ιν).," We first tried to fit the SED of HH 24 MMS as a sum of two power-law components, one from the free-free emission and the other from the dust emission, over the wavelength range of 3.4 mm to 3.6 cm (8.3–88 GHz)."
 The best ft has spectral indices of 2.1 + 0.3 aud 3.7 + 0.2 (Fie., The best fit has spectral indices of 2.1 $\pm$ 0.3 and 3.7 $\pm$ 0.2 (Fig.
 2 panel)., 2 ).
" It was found that acceptable fits cau only have large (22) spectral iudices for both conmonuents, which clearly means that the cmission is uostlv from dust aud that the free-free cuission is ieelieible in the wavelength rauge considered."," It was found that acceptable fits can only have large $>$ 2) spectral indices for both components, which clearly means that the emission is mostly from dust and that the free-free emission is negligible in the wavelength range considered."
 Then. as the dust oenuission sccis to be dominating even iu the ceutimeter wavelengths. the SED was fitted again with a sinegle-compouent power-law distribution.," Then, as the dust emission seems to be dominating even in the centimeter wavelengths, the SED was fitted again with a single-component power-law distribution."
 The fts were made using three data points. excluding the 3.6 cua data. to avoid any contribution from free-free cluission.," The fits were made using three data points, excluding the 3.6 cm data, to avoid any contribution from free-free emission."
 The best Gt has a spectral iudex of a = 2.8 + 0.2 in the millimeter range (Fig., The best fit has a spectral index of $\alpha$ = 2.8 $\pm$ 0.2 in the millimeter range (Fig.
 2 pancl)., 2 ).
 Extrapolating the best-&t SED to longer waveleugtlis. a substantial fraction (9053) ofTherefore. the 3.6 ei flux seenis to conie from the dust cussion.," Extrapolating the best-fit SED to longer wavelengths, a substantial fraction $\sim$ ) of the 3.6 cm flux seems to come from the dust emission."
 the frec-free cnussion. if au. must be verv weak.," Therefore, the free-free emission, if any, must be very weak."
 If of the 3.6 clu flux comes from optically thin frec-free emission. its contribution to the 6.9 uuu flux would be ouly ~0.2% (or 0.02 1nJv).," If of the 3.6 cm flux comes from optically thin free-free emission, its contribution to the 6.9 mm flux would be only $\sim$ (or 0.02 mJy)."
 That is. the 6.9 mun fux of IIT 21 MIMS is almost entirely from dust.," That is, the 6.9 mm flux of HH 24 MMS is almost entirely from dust."
 As the imillimeter continua flux is mostly frou dust. the mass of the cussion structure cau be estimated frou the SED.," As the millimeter continuum flux is mostly from dust, the mass of the emission structure can be estimated from the SED."
 To derive the mass from the dust continui flux. the nass opacity given by Beckwith Sarecut (1991) is assumed. where v is the frequency. mg = 1200 GIIz aud ) is the opacity iudex.," To derive the mass from the dust continuum flux, the mass opacity given by Beckwith Sargent (1991) is assumed, where $\nu$ is the frequency, $\nu_0$ = 1200 GHz, and $\beta$ is the opacity index."
 This opacity is for total mass of gas and dust., This opacity is for total mass of gas and dust.
 The opacity iudex of IIT 21 MMS js J5n2=Oa., The opacity index of HH 24 MMS is $\beta \approx \alpha - 2 = 0.8$.
 This small value of .} nuplies the presence of large dust erains probably caused by the erain growth iu the high density enviroment (6.8.. Alivake Nakagawa 1993). which was pointed out bv several authors previously(Chandler et al.," This small value of $\beta$ implies the presence of large dust grains probably caused by the grain growth in the high density environment (e.g., Miyake Nakagawa 1993), which was pointed out by several authors previously (Chandler et al."
" 1995: ""Thompson ct al.", 1995; Ward-Thompson et al.
 1995)., 1995).
" The dust temperature. Z,. used ia previous works ranges from 12 IK to 100 IK (Phillips et al."," The dust temperature, $T_d$, used in previous works ranges from 12 K to 100 K (Phillips et al."
 2001: Chandler et al., 2001; Chandler et al.
 1995)., 1995).
 ITere we adopt 7; = 20 £5 Is from Ward- et al. (, Here we adopt $T_d$ = 20 $\pm$ 5 K from Ward-Thompson et al. (
1995).,1995).
" In the 6.9 nuu maps. the peak brightness temperature is about 8 EK. and the mean brightness teniperature ina 17 & 1"" box is less than 1 Ik. Since the brightuess temperature is ich lower thu the dust temperature. the optical depth of the 6.9 nu"," In the 6.9 mm maps, the peak brightness temperature is about 8 K, and the mean brightness temperature in a $''$ $\times$ $''$ box is less than 1 K. Since the brightness temperature is much lower than the dust temperature, the optical depth of the 6.9 mm"
" In the 6.9 nuu maps. the peak brightness temperature is about 8 EK. and the mean brightness teniperature ina 17 & 1"" box is less than 1 Ik. Since the brightuess temperature is ich lower thu the dust temperature. the optical depth of the 6.9 nuu"," In the 6.9 mm maps, the peak brightness temperature is about 8 K, and the mean brightness temperature in a $''$ $\times$ $''$ box is less than 1 K. Since the brightness temperature is much lower than the dust temperature, the optical depth of the 6.9 mm"
The observational trends of extremely metal-poor (EAP) stars reflect SN nucleosvntliesis of Population (Pop) HII. or almost metal-DIree stars.,"The observational trends of extremely metal-poor (EMP) stars reflect SN nucleosynthesis of Population (Pop) III, or almost metal-free stars."
 Their observed abundances show «quite, Their observed abundances show quite
if thermal equilibrium were to hold.,if thermal equilibrium were to hold.
 In our case we have neglected (lor excellent. wellknown reasons) the exchange of energv of (he particles with the background. [Iuid. so we cannot expect (rue thermal equilibrium to hold. but since we have included. all major scattering processes. we expect equilibrium(£€.. detailed balance except for energy. equipartition) to hold at least in so far as the angular part is concerned.," In our case we have neglected (for excellent, well–known reasons) the exchange of energy of the particles with the background fluid, so we cannot expect true thermal equilibrium to hold, but since we have included all major scattering processes, we expect equilibrium, detailed balance except for energy equipartition) to hold at least in so far as the angular part is concerned."
 It is probably worthwhile to remark (hat a similar assumption on iw is made by Chancrasekhar (1949. Ch.," It is probably worthwhile to remark that a similar assumption on $w$ is made by Chandrasekhar (1949, Ch."
 IV. Section 31. Eq.," IV, Section 31, Eq."
" 29-1),", 29-1).
 We now rewrite Eq., We now rewrite Eq.
 2. by means of a new scattering probability. Vμια). to be defined as lollows: Π 15 simply the probability (hat a particle is deflected from its initial direction along i. to a new direction µ’+a.," \ref{main} by means of a new scattering probability, $W(\mu';\alpha)$, to be defined as follows: $W$ is simply the probability that a particle is deflected from its initial direction along $\mu'$ , to a new direction $\mu'+\alpha$."
 By means of this new quantity Eq., By means of this new quantity Eq.
 2. can be recast as: while the detailed balance equationbecomes: The scattering equation in the form 24. is exactly identical to (hat given by Landau and Lifshtiz (1984. Section 21. Eq.," \ref{main} can be recast as: while the detailed balance equationbecomes: The scattering equation in the form \ref{main2} is exactly identical to that given by Landau and Lifshtiz (1984, Section 21, Eq."
 21.1). so that their derivation of the FokkerPlanck immediatelv applies.," 21.1), so that their derivation of the Fokker–Planck immediately applies."
 Please note however (hat our sign convention differs from (heirs: what we call a is for them —q., Please note however that our sign convention differs from theirs: what we call $\alpha$ is for them $-q$.
 Following step by step (heir derivation we find (hat the definitions In the two integrals above. we have taken the integration range (to extend from —x: to +x. because we have assumed the validity of the SPAS regime. in which case HW(jio)has one verv strong. narrow peak around a= 0:," Following step by step their derivation we find that with the definitions In the two integrals above, we have taken the integration range to extend from $-\infty$ to $+\infty$, because we have assumed the validity of the SPAS regime, in which case $W(\mu;\alpha)$has one very strong, narrow peak around $\alpha = 0$ :"
Rowan-Robinson (2002. in preparation).,"Rowan-Robinson (2002, in preparation)."
 Part of our near-Lht survey is in the NI ELAIS region. which was not observed at 6.7 Lun. The σαν. observations were carried out using the STELIRCam instrument at the 122m telescope of the WWhipple Observatory on Mount. Hopkins.," Part of our near-IR survey is in the N1 ELAIS region, which was not observed at 6.7 $\umu$ m. The near-IR observations were carried out using the STELIRCam instrument at the 1.2-m telescope of the Whipple Observatory on Mount Hopkins."
 A description of these J- and A-band data (taken during 21 nights between April 1997 and. Alay 1999). reduction. as well as photometry is found in Vàiisiunen et ((2000).," A description of these $J$ - and $K$ -band data (taken during 21 nights between April 1997 and May 1999), reduction, as well as photometry is found in Väiisännen et (2000)."
" Ehe survey area ds approximately 1 square degree. two thires of it is in the ELAIS N2 region (centered. at RA=16b36m00s. DEC=41deg 06700"") and the rest in NI G2A=16h09m00s. deg DECZ5440/007)."," The survey area is approximately 1 square degree, two thirds of it is in the ELAIS N2 region (centered at RA=16h36m00s, $41\deg 06\arcmin 00\arcsec$ ) and the rest in N1 (RA=16h09m00s, $54\deg 40\arcmin 00\arcsec$ )."
 Phere is a small offset. between the simultaneously. observed. FOVSs in the 7; and A bands. resulting in slightly dillerent source catalogues. in the respective bands.," There is a small offset between the simultaneously observed FOVs in the $J$ and $K$ bands, resulting in slightly different source catalogues in the respective bands."
 The 2MLASS 2nd incremental. data release (Cutri 2000) partially covers the NI and N2 regions., The 2MASS 2nd incremental data release (Cutri 2000) partially covers the N1 and N2 regions.
 ‘This allows us to directly. cross-check our bright. (A.< 14.5) shotometry with 2ALASS., This allows us to directly cross-check our bright $K < 14.5$ ) photometry with 2MASS.
 This is important also because we will later use 2ALASS data in connection with a comparion sample of nearby. galaxies from the literature., This is important also because we will later use 2MASS data in connection with a comparion sample of nearby galaxies from the literature.
 Ehe ‘default’ yhotometry of 24LASS was found to agree very well with our photometry for both stars and galaxies., The 'default' photometry of 2MASS was found to agree very well with our photometry for both stars and galaxies.
 Our data rom Alt.tlopkins (while deeper due to longer integration ime) are. in fact. taken with a very similar telescope and instrument than the 2ALASS data.," Our data from Mt.Hopkins (while deeper due to longer integration time) are, in fact, taken with a very similar telescope and instrument than the 2MASS data."
 The ELAIS ISOCAM catalogue has 1322 and 2203 sources in total for aff ELAS regions in the 6.7 and 15 [un bands. respectively.," The ELAIS ISOCAM catalogue has 1322 and 2203 sources in total for ELAIS regions in the 6.7 and 15 $\umu$ m bands, respectively."
 These were matched with our near-IR. catalogue. which comes from a much smaller area.," These were matched with our near-IR catalogue, which comes from a much smaller area."
 The ELAIS v.3 catalogue includes many double. or even multiple. detections from the edges of neighbouring individual rasters and repeated observations — thus we had to purge the catalogue.," The ELAIS v.1.3 catalogue includes many double, or even multiple, detections from the edges of neighbouring individual rasters and repeated observations – thus we had to purge the catalogue."
 We searched. for ISOCAAL objects separated initially by17.. then37. and finally ab each step neighbours were merged if they had the same near-It counterpart.," We searched for ISOCAM objects separated initially by, then, and finally – at each step neighbours were merged if they had the same near-IR counterpart."
 Ultimately. the matched and. purged catalogue consists of 217 and 158 ΝΕ sources matched with the LW2 and L3 ELAIS catalogue. respectively.," Ultimately, the matched and purged catalogue consists of 217 and 158 NIR sources matched with the LW2 and LW3 ELAIS catalogue, respectively."
 Of these. 53 are common to both ISOCAM filters. and due to LW? coverage they are all in the N2 region.," Of these, 53 are common to both ISOCAM filters, and due to LW2 coverage they are all in the N2 region."
 Table 1 gives the total number of ISO sources. the NIE. indentifications and their classification per field. filter. and reliability class.," Table 1 gives the total number of ISO sources, the NIR indentifications and their classification per field, filter, and reliability class."
 Notably.adf those ISOCAAM sources detected in both filters were identified. as well as all L2 sources with REL=2.," Notably, those ISOCAM sources detected in both filters were identified, as well as all LW2 sources with REL=2."
 The probability ofa chance appearance of aa ty=17 mag object. withinIN the ssearch raclius is 0.03.2 estimated from surface densities of near-H1t objects Vaiisánnen et al.," The probability of a chance appearance of a $K=17$ mag object within the search radius is 0.03, estimated from surface densities of near-IR objects Väiisännen et al."
 2000)., 2000).
 More than 90 per cent of the matches are brighter than ἐν=16.5 mag we thus conclude that the purely positional matching is highly accurate., More than 90 per cent of the matches are brighter than $K=16.5$ mag – we thus conclude that the purely positional matching is highly accurate.
 And since. we will be using only those micd-Li sources with a near-LR. counterpart. we consider the sourcelist to be verv reliable.," And since we will be using only those mid-IR sources with a near-IR counterpart, we consider the sourcelist to be very reliable."
 Vhe ELAIS fields were surveved. also with ISOPLIIOTT at 90 and. 175 qun. Since the mid- to fu-IIt. colours. of ELAILS sources are discussed in another work (Morel et 22002. in preparation). we do not discuss them further here. except to note that δ of our 29 galaxies with data from both ISOCAM bands ancl near-H. photometry. also have 90 tun κος available.," The ELAIS fields were surveyed also with ISOPHOT at 90 and 175 $\umu$ m. Since the mid- to far-IR colours of ELAIS sources are discussed in another work (Morel et 2002, in preparation), we do not discuss them further here, except to note that 8 of our 29 galaxies with data from both ISOCAM bands and near-IR photometry, also have 90 $\umu$ m fluxes available."
 In addition. 20 of the 29 are included in the ELAIS VLA catalogue (Ciliegi 1999).," In addition, 20 of the 29 are included in the ELAIS VLA catalogue (Ciliegi 1999)."
 Since in this work we need to compare Illuxes between nearby ancl distant. galaxies. total Huxes are required for both the near and mid-infrared.," Since in this work we need to compare fluxes between nearby and distant galaxies, total fluxes are required for both the near and mid-infrared."
 In Vàiisaànnen et al. (, In Väiisännen et al. (
"2000) we found the “BE"" magnitudes [rom SExtractor (Bertin Arnouts 1996) to be the most robust ancl accurate over a wide range of magnitudes ancl source profiles.",2000) we found the `BEST' magnitudes from SExtractor (Bertin Arnouts 1996) to be the most robust and accurate over a wide range of magnitudes and source profiles.
" The Ixron-tvpe ""BEST-magnitudes are presented in Table 2. but we caleulated also various aperture magnitudes and there is no dilference in any final results if large enough apertures are used."," The Kron-type `BEST'-magnitudes are presented in Table 2, but we calculated also various aperture magnitudes and there is no difference in any final results if large enough apertures are used."
 The £5O-fluxes are measured. from characteristic emporal signatures of individual pixels. as described. in Serjeant et. ((2000).," The -fluxes are measured from characteristic temporal signatures of individual pixels, as described in Serjeant et (2000)."
 Instead of conventional aperture whotometry the value of the peak pixel is corrected to total lux using PSE modeling., Instead of conventional aperture photometry the value of the peak pixel is corrected to total flux using PSF modeling.
 Phe adopted correction [actors were 1.54 at 6.7pun and 2.36 at. 15jun.. Phe correction for he LAW? filter is more uncertain due to much undersampled SE., The adopted correction factors were 1.54 at $6.7 \umu$ m and 2.36 at $15 \umu$ m. The correction for the LW2 filter is more uncertain due to much undersampled PSF.
 Strictly. iis correction is appropriate for point sources only. which results in a potentially serious underestimation of Hlluxes for extended: objets.," Strictly, this correction is appropriate for point sources only, which results in a potentially serious underestimation of fluxes for extended objets."
" However. the size of the ISOCAAL pixel is6"". and the large majority. of our sources are smaller than this and we trust that the point source aperture Correction gives an accurate value [or them."," However, the size of the ISOCAM pixel is, and the large majority of our sources are smaller than this and we trust that the point source aperture correction gives an accurate value for them."
 Nevertheless. we examined the largest ELAIS galaxies individually (using their. ΑΗ half-light. radii ancl testing with clillerent apertures) to ect an estimate of correction factors to the mid-Ilt lluxes.," Nevertheless, we examined the largest ELAIS galaxies individually (using their NIR half-light radii and testing with different apertures) to get an estimate of correction factors to the mid-IR fluxes."
. We conclude that only 4 of the galaxies. all of which are included in Fig. 1.," We conclude that only 4 of the galaxies, all of which are included in Fig. \ref{nir-early},"
 definitely need a significant aperture correction., definitely need a significant aperture correction.
 For the largest galaxy in our sample (ELAISCI5 163508|405933). referred to as | dn Table 2 and Fig. L..," For the largest galaxy in our sample (ELAISC15 J163508+405933), referred to as `B' in Table 2 and Fig. \ref{nir-early},"
 we adopt Duxes from Morel et al (2002. in preparation). mocified in accordance with our new calibration (Section 2.6)).," we adopt fluxes from Morel et al (2002, in preparation), modified in accordance with our new calibration (Section \ref{calib}) )."
 The correction is very. large. approximately a factor of4.," The correction is very large, approximately a factor of 4."
 Phe other three galaxies labeled Αν ον and CD. respectively. are significantly smaller. and [or these we adopt an approximate correction factor of 1.5.," The other three galaxies labeled `A', `C', and `D', respectively, are significantly smaller, and for these we adopt an approximate correction factor of 1.5."
 We plot the NIR/MIIU ELAIS data in Figs., We plot the NIR/MIR ELAIS data in Figs.
 2. and 3. as a Function of A-magnitude. using all the matched. near-LHi and. ISOCAAL detections.," \ref{relstar_matches1}
 and \ref{relstar_matches2} as a function of $K$ -magnitude, using all the matched near-IR and ISOCAM detections."
We also matched all the sources in our field with optical data from POSS plates. using,We also matched all the sources in our field with optical data from POSS plates using
lower mass limit of MM. and an upper limit of MAL. (Concon 1992).,lower mass limit of $_\odot$ and an upper limit of $_\odot$ (Condon 1992).
 In any galaxy. most of the stellar mass. is located in low mass stars. therefore to calculate the tota SER. including the mass contained in stars with masses lower than MAL. we need. to multiply the factor 24.4 in Equation | by 9.," In any galaxy most of the stellar mass is located in low mass stars, therefore to calculate the total SFR, including the mass contained in stars with masses lower than $_\odot$ we need to multiply the factor 24.4 in Equation \ref{SFR} by 9."
 Combining Equation 1 with the caleulatec supernova rate we obtain a SER. for NGC 3077 of 0.28 AL. vear*., Combining Equation \ref{SFR} with the calculated supernova rate we obtain a SFR for NGC 3077 of 0.28 $_\odot$ $^{-1}$.
 The estimated SER is in reality a upper limi because the presented observations are. sensitive to older SNRs which we did not detect., The estimated SFR is in reality a upper limit because the presented observations are sensitive to older SNRs which we did not detect.
 Assuming that the flux of a SNR decay with a rate of ~L& | (e.g. Ixronberg Sramek 1992. Muxlow et al.," Assuming that the flux of a SNR decay with a rate of $\sim$ $^{-1}$ (e.g. Kronberg Sramek 1992, Muxlow et al."
 1994). the three sigma detection limit o£ 180 pv/beam allows to detect older SNRs with ages of SSO vears. implying a lower supernova rate £w- 1.14 10 +.," 1994), the three sigma detection limit of 180 $\mu$ Jy/beam allows to detect older SNRs with ages of 880 years, implying a lower supernova rate $\nu_{\rm SN}$ = 1.14 $\times 10^{-3}$ $^{-1}$."
 This fact produce a change in the caleulated SER of about14%., This fact produce a change in the calculated SFR of about.
 The Dux density of the SNR was calculated by using the AIDS task which add the observed Ηχος within the area defined by the SNIt at three times the noise level., The flux density of the SNR was calculated by using the AIPS task which add the observed fluxes within the area defined by the SNR at three times the noise level.
 We obtain a [lux of 21004175 pdx., We obtain a flux of $\pm 175$ $\mu$ Jy.
 For this SNR. the relation between the size anc the flux density is consistent. with the relation found by. Muxlow et al. (," For this SNR, the relation between the size and the flux density is consistent with the relation found by Muxlow et al. ("
1994) for à sample of SNRs detected in M 82 and the LMC.,1994) for a sample of SNRs detected in M 82 and the LMC.
 This relation. where the flux density is inversely proportional to the diameter. is not consistent with simple aciabatic losses in a svnchrotron-emitting source and an extra source of relativistic particles must come from other reservoir of energv in the form of thermal or kinetic energy. present in the remnant. (Miley 1980).," This relation, where the flux density is inversely proportional to the diameter, is not consistent with simple adiabatic losses in a synchrotron-emitting source and an extra source of relativistic particles must come from other reservoir of energy in the form of thermal or kinetic energy present in the remnant (Miley 1980)."
" EELhe ratio. between radio. and X-rayB fluxes Ry 4 10""6 EFsogu/Fs ds highly variable and depends on the nature of the object. the surrounding media. prior to the supernova explosion and the time at which the supernova remimant is observed."," The ratio between radio and X-ray fluxes $_{\rm r-x}$ = $\times~10^9$ $_{\rm 5GHz}$ $_{\rm x}$ is highly variable and depends on the nature of the object, the surrounding media prior to the supernova explosion and the time at which the supernova remmant is observed."
 Table 2 shows the value of Ry4 for a small sample of SNRs which include the brightest SNRs in our galaxy. Cassiopcia A and Crab nebula.," Table \ref{Tab:RadioXray} shows the value of $_{\rm r-x}$ for a small sample of SNRs which include the brightest SNRs in our galaxy, Cassiopeia A and Crab nebula."
 For the galactic SNRs the radio data which includes morphological type. (ux and spectral index. was obtained from the Green catalogue (Green 2004).," For the galactic SNRs the radio data which includes morphological type, flux and spectral index, was obtained from the Green catalogue (Green 2004)."
 This catalogue is based. on observations at 1 Gllz., This catalogue is based on observations at 1 GHz.
 We used the given spectral index to estimate the lux at 5 Cllz in order to compare with our observations., We used the given spectral index to estimate the flux at 5 GHz in order to compare with our observations.
 For the case of SNIOSSZ we used the cata compiled. by Arctxaga et al. (, For the case of SN1988Z we used the data compiled by Aretxaga et al. (
1999) and for the case of NGC7793-826. he data from Pannuti ct al. (,"1999) and for the case of NGC7793-S26, the data from Pannuti et al. ("
2002).,2002).
 Phe X-ray. cata are rom the compilation by Seward ct al. (, The X-ray data are from the compilation by Seward et al. (
2005) except SI and οὐ from Ott et al. (,2005) except S1 and S3 from Ott et al. (
2003). SNIOOGAD from Dyer ct al. (,"2003), SN1006AD from Dyer et al. ("
2001). SNIOSSZ [rom Aretxaga et al. (,"2001), SN1988Z from Aretxaga et al. ("
1999) and NGC7T793-826 [rom Pannuti et al. (,1999) and NGC7793-S26 from Pannuti et al. (
2002).,2002).
 Phe value of Ryx goes [rom 1.02.103 for the case of SNIO0GAD to 0.2722 for Vela., The value of $_{\rm r-x}$ goes from $\times 10^{-4}$ for the case of SN1006AD to 0.2722 for Vela.
 The value of Ryx for S1 is within the observed range., The value of $_{\rm r-x}$ for S1 is within the observed range.
 The other candidates to ολ] 5 and οὐ were not detected by the present observations., The other candidates to SNRs – S5 and S6 – were not detected by the present observations.
 The Xray lluxes of 85 and S6 are 50 and 6 times respectively lower than the Xray ας of SL (see Table 12)., The Xray fluxes of S5 and S6 are 50 and 6 times respectively lower than the Xray flux of S1 (see Table \ref{tab:points}) ).
 Assuming that in both cases the ratio between the X-ray and radio Duxes is equal to the ratio observed in SI. Ry 4(SI)2 10.8.10.3 then the expected radio llux for 85 and 86 is below the 30 detection Limit.," Assuming that in both cases the ratio between the X-ray and radio fluxes is equal to the ratio observed in S1, $_{\rm r-x}$ (S1)= $\times 10^{-4}$ then the expected radio flux for S5 and S6 is below the $\sigma$ detection limit."
 1n the Chandra image of NGC 3077. the sources 82 and S3 are separated by1”.," In the Chandra image of NGC 3077, the sources S2 and S3 are separated by."
 Phis separation is roughly the ENIM of the point-spread-function., This separation is roughly the FWHM of the point-spread-function.
 S2 and83 cach have an X-ray spectrum that was fitted to a power law., S2 andS3 each have an X-ray spectrum that was fitted to a power law.
 Phese objects were proposed to be either. X-ray binaries or background active galactic nuclei (Ott et al., These objects were proposed to be either X-ray binaries or background active galactic nuclei (Ott et al.
 2003)., 2003).
 Figure 3. shows the map of the radio source coincident with the position of 53., Figure \ref{Radio_S3} shows the map of the radio source coincident with the position of S3.
 The measured intensity peak is 3904 60 py beam.1 which is equivalent to a brightness temperature of about SOOO Ix. typical of an LIL region.," The measured intensity peak is $\pm$ 60 $\mu$ Jy $^{-1}$ which is equivalent to a brightness temperature of about 8000 K, typical of an HII region."
 Notice that these observations did not rule out the possibility that. the observed. radio source is an old SNR and further observations at longer wavelength with similar angular resolution and sensitivity are necessary., Notice that these observations did not rule out the possibility that the observed radio source is an old SNR and further observations at longer wavelength with similar angular resolution and sensitivity are necessary.
 53 has a hy <= 10 which is within the range of values observed. in SNRs., S3 has a $_{\rm r-x}$ = $\times 10^{-4}$ which is within the range of values observed in SNRs.
" However the observed ratio li,x in well studied SNRs (Lable 2)) covers at. least 5 order of magnitudes therefore the Ryx value can not be usec to discriminate between SNRs and other kind of objects.", However the observed ratio $_{\rm r-x}$ in well studied SNRs (Table \ref{Tab:RadioXray}) ) covers at least 5 order of magnitudes therefore the $_{\rm r-x}$ value can not be used to discriminate between SNRs and other kind of objects.
 Due to the calculated. brightness temperature and the X-ray spectrum of 83 the probability that the observed racio emission is coming from an HILL region is the most plausible., Due to the calculated brightness temperature and the X-ray spectrum of S3 the probability that the observed radio emission is coming from an HII region is the most plausible.
 83 is probably embebed. by the LIE nebula but the ray lux from the binary and the radio Fux have not a common origin., S3 is probably embebed by the HII nebula but the Xray flux from the binary and the radio flux have not a common origin.
 The free.free emission associated to an LLL region can ος translated to the number of ionizing photons. Ney by (Condon 1992). The flux density estimated for the LIL region associated with S3 was T47+127 μον.," The free–free emission associated to an HII region can be translated to the number of ionizing photons, $\rm N_{\rm UV}$ by (Condon 1992), The flux density estimated for the HII region associated with S3 was $\pm$ 127 $\mu$ Jy."
 LE owe assume that the observed. [lux has a thermal origin. we can estimate the thermal luminosity. Ly.," If we assume that the observed flux has a thermal origin, we can estimate the thermal luminosity, $_{\rm T}$ ."
 We calculated that the number, We calculated that the number
(c 35%)) of giant. planets around early M. cdbwar stars (~0.5.4.) than that found by the Joppler surveys. again orbiting at larger distances (han those probed by the Doppler survevs.,"$\sim$ ) of giant planets around early M dwarf stars $\sim 0.5 M_\odot$ ) than that found by the Doppler surveys, again orbiting at larger distances than those probed by the Doppler surveys."
 Evidently even early M. dwarls might also have a significant. population of relatively wide eas giant. planets., Evidently even early M dwarfs might also have a significant population of relatively wide gas giant planets.
 Core aceretion is unable. however. to form massive planets bevond ~ 35 AU. even in the most favorable circumstances (e.g.. Levison Stewart 2001: Thommes. Duncan. Levison 2002: Chambers 2006). and gravitational scattering outward appears to be unable to lead to stable wide orbits (Doclson-Robinson οἱ al.," Core accretion is unable, however, to form massive planets beyond $\sim$ 35 AU, even in the most favorable circumstances (e.g., Levison Stewart 2001; Thommes, Duncan, Levison 2002; Chambers 2006), and gravitational scattering outward appears to be unable to lead to stable wide orbits (Dodson-Robinson et al."
 2009: Raymond. Armitage. Gorelick 2010).," 2009; Raymond, Armitage, Gorelick 2010)."
" Disk instability (Boss 1997) is then the remaining candidate mechanism for forming, wide eas giant planets (Dodson-Robinson et al.", Disk instability (Boss 1997) is then the remaining candidate mechanism for forming wide gas giant planets (Dodson-Robinson et al.
 2009; Boley 2009)., 2009; Boley 2009).
 Previous models found. that disk instability could readily produce giant planets at distances of 20 AU to 30 AU (Boss 2003). but not at distances of LOO AU to 200 AU (Boss 2006a).," Previous models found that disk instability could readily produce giant planets at distances of 20 AU to 30 AU (Boss 2003), but not at distances of 100 AU to 200 AU (Boss 2006a)."
 Here we present results for intermecdiate-size disks (20 AU to 60 AU) for a range of central protostar masses (0.1 to 2.0 AL. ). to learn if the disk instability mechanism for eiant planet formation is consistent wilh the results of the Doppler and direct imaging surveys to date.," Here we present results for intermediate-size disks (20 AU to 60 AU) for a range of central protostar masses (0.1 to 2.0 $M_\odot$ ), to learn if the disk instability mechanism for giant planet formation is consistent with the results of the Doppler and direct imaging surveys to date."
 The caleulations were performed with a numerical code (hat solves the tliree dimensional equations of hvdrodyvnanmies and radiative transfer in the diffusion approximation. as well as the Poisson equation for the gravitational potential.," The calculations were performed with a numerical code that solves the three dimensional equations of hydrodynamics and radiative transfer in the diffusion approximation, as well as the Poisson equation for the gravitational potential."
 This same basic code has been used in all of the author's previous studies of disk instability., This same basic code has been used in all of the author's previous studies of disk instability.
 The code is second-order-accurate in both space and time., The code is second-order-accurate in both space and time.
 A complete description of the entire code. including hydrodynamics and raciative transler. may be found in Boss Myhill (1992). with the following exceptions: The central protostar is assumed to move in such a wav as to preserve (he location of the center of mass of (he entire svstem (Boss 1993). which is accomplished by altering the location of (he point mass source of (he star's gravitational potential to balance the center of mass of the disk.," A complete description of the entire code, including hydrodynamics and radiative transfer, may be found in Boss Myhill (1992), with the following exceptions: The central protostar is assumed to move in such a way as to preserve the location of the center of mass of the entire system (Boss 1998), which is accomplished by altering the location of the point mass source of the star's gravitational potential to balance the center of mass of the disk."
 The Pollack et al. (, The Pollack et al. (
1994) Hosseland mean opacities are used for the dust grains that dominate the opacities in these models.,1994) Rosseland mean opacities are used for the dust grains that dominate the opacities in these models.
 The energy equation of state in use since 1959 is described by Boss (2007)., The energy equation of state in use since 1989 is described by Boss (2007).
 A this-limiter for the diffusion approximation radiative transfer was not emploved. as il appears (o have only a modest effect on midplane temperatures (Boss 2003).," A flux-limiter for the diffusion approximation radiative transfer was not employed, as it appears to have only a modest effect on midplane temperatures (Boss 2008)."
 Recent tests of the radiative transfer scheme are described in Boss (2009)., Recent tests of the radiative transfer scheme are described in Boss (2009).
" The equations are solved on a spherical coordinate erid with V,=101 (including the central erid cell. which contains (he central protostar). Ny=23 in »/2>00. and AQ=256. with Αν being increased (ο 512 once fragments begin forming."," The equations are solved on a spherical coordinate grid with $N_r = 101$ (including the central grid cell, which contains the central protostar), $N_\theta = 23$ in $\pi/2 \ge \theta \ge 0$, and $N_\phi = 256$, with $N_\phi$ being increased to 512 once fragments begin forming."
 The radial grid is uniformly spaced with Ar=0.4 AU between 20 and 60 AU., The radial grid is uniformly spaced with $\Delta r = 0.4$ AU between 20 and 60 AU.
 The @ grid is compressed, The $\theta$ grid is compressed
"Candidate objects for flexion analysis are selected using SExtractor in a two-pass strategy similar to those of and (2007)),, with some modifications.","Candidate objects for flexion analysis are selected using SExtractor in a two-pass strategy similar to those of and , with some modifications."
" The first pass is intended to select the large, bright, cluster member galaxies and foreground objects."," The first pass is intended to select the large, bright, cluster member galaxies and foreground objects."
 These objects are then removed from the image in a process we describe below., These objects are then removed from the image in a process we describe below.
" The resulting “cleaned” image is then used in the second pass to identify the smaller, fainter, lensed background galaxy images."," The resulting “cleaned” image is then used in the second pass to identify the smaller, fainter, lensed background galaxy images."
" In all cases, a co-added, four-filter image is used for object detection to increase the signal-to-noise ratio of faint object detections, and the individual filter images are used for photometry."," In all cases, a co-added, four-filter image is used for object detection to increase the signal-to-noise ratio of faint object detections, and the individual filter images are used for photometry."
" SExtractor uses the input data images and pixel weights to produce a background image, noise image, and object image for each of the four filters."," SExtractor uses the input data images and pixel weights to produce a background image, noise image, and object image for each of the four filters."
 The background and noise images contain position-variable estimates of the background surface brightness and the total surface brightness variance across the field., The background and noise images contain position-variable estimates of the background surface brightness and the total surface brightness variance across the field.
 The object image is the same as the input image except that any pixels not determined to be associated with a detected object are set to zero., The object image is the same as the input image except that any pixels not determined to be associated with a detected object are set to zero.
" In the first pass, we select objects of large area (area >50 pixel?) to a low threshold (SNR > 1)."," In the first pass, we select objects of large area (area $>50$ $^2$ ) to a low threshold (SNR $>1$ )."
" This identifies object-associated pixels down to the background level, including the faint Intra-Cluster Light (ICL) associated with the central cluster galaxies."," This identifies object-associated pixels down to the background level, including the faint Intra-Cluster Light (ICL) associated with the central cluster galaxies."
" The detected objects are matched with known foreground and cluster member objects from literatureP)mainBodyCitationEnd5259]duc--:02,coe4-:10b.", The detected objects are matched with known foreground and cluster member objects from literature.
 All known objects at a spectroscopic redshift 2«0.2 are selected to be cleaned from the image., All known objects at a spectroscopic redshift $z<0.2$ are selected to be cleaned from the image.
" All pixels associated with any known object location, as determined in the SExtractor object image using a friends-of-friends algorithm, are replaced with Gaussian-distributed noise."," All pixels associated with any known object location, as determined in the SExtractor object image using a friends-of-friends algorithm, are replaced with Gaussian-distributed noise."
 The object pixels are cleaned in the four-filter detection image and in each individual filter image as well., The object pixels are cleaned in the four-filter detection image and in each individual filter image as well.
" T'he standard deviation of the noise, as determined by SExtractor and"," The standard deviation of the noise, as determined by SExtractor and"
become degenerate there (Hurley.Pols&Tout2000).,become degenerate there \citep{hurl00}.
". For these stars. when they reach the ""ZAHB their mean densities decrease with increasing mass. just ZAMS."," For these stars, when they reach the `ZAHB', their mean densities decrease with increasing mass, just ZAMS."
. However. for stars with AM< 2.0 electrons in the hydrogen-exhausted core are highly degenerate before helium ignition occurs.," However, for stars with $M
<$ 2.0, electrons in the hydrogen-exhausted core are highly degenerate before helium ignition occurs."
 The radius of these stars on the ZAHB depends mainly on the mass of the exhausted core at the time of helium ignition and on the mass the overlying envelope., The radius of these stars on the ZAHB depends mainly on the mass of the hydrogen-exhausted core at the time of helium ignition and on the mass the overlying envelope.
 The mean density of these stars on the ZAHB does not on the total mass. but it is usually less than of stars with AJ~ 2.0 M.," The mean density of these stars on the ZAHB does not on the total mass, but it is usually less than of stars with $M \simeq$ 2.0 ."
.. Thus ZAHB star with A7~ 2.0 has the highest mean density., Thus ZAHB star with $M \simeq$ 2.0 has the highest mean density.
 Furthermore. for stars with Af« 2.0 the temperature and density distributions in the core are unique functions of the core mass 1974).," Furthermore, for stars with $M <$ 2.0 the temperature and density distributions in the core are unique functions of the core mass \citep{iben74}."
. For stars with AZ< 1.6AL... when they reach the ZAHB. decrease with the decrease in the total mass. but the core mass is approximately equal.," For stars with $M < $ 1.6, when they reach the ZAHB, decrease with the decrease in the total mass, but the core mass is approximately equal."
 Their mean densities are approximately equal too. which leads to a similar value of for these stars on the ZAHB.," Their mean densities are approximately equal too, which leads to a similar value of for these stars on the ZAHB."
 The mass of many ZAHB stars in cluster with Z = 0.02 and age = 1.2 Gyr is about 2.0Al... hence the frequency of the dominant RC peak of this cluster is larger than that of other clusters.," The mass of many ZAHB stars in cluster with Z = 0.02 and age $\simeq$ 1.2 Gyr is about 2.0, hence the frequency of the dominant RC peak of this cluster is larger than that of other clusters."
 The mass of RC stars clusters with Z = 0.02 and age > 2.4 Gyr is less than 1.6AL... so that the locations of the dominant RC of these clusters are almost same.," The mass of RC stars clusters with Z = 0.02 and age $>$ 2.4 Gyr is less than 1.6, so that the locations of the dominant RC of these clusters are almost same."
 The asteroseismical observation for red giant stars of clusters with age & 2.4 Gyr may provide a help to test the theory of the degeneracy of hydrogen-exhausted core., The asteroseismical observation for red giant stars of clusters with age $\lesssim$ 2.4 Gyr may provide a help to test the theory of the degeneracy of hydrogen-exhausted core.
 Differing from the MS peak that in young clusters. the RC peak all clusters.," Differing from the MS peak that in young clusters, the RC peak all clusters."
 This is because the RC stars near the ZAHB exist in clusters with different ages in our simulations., This is because the RC stars near the ZAHB exist in clusters with different ages in our simulations.
 The histograms of radius and mass of clusters with age — 0.5 and 5.0 Gyr are shown in Fig. 5.., The histograms of radius and mass of clusters with age = 0.5 and 5.0 Gyr are shown in Fig. \ref{figmr}.
 The mass only one peak. at about 0.8AL... which is caused by IMF.," The mass only one peak, at about 0.8, which is caused by IMF."
 However. the distributions of the radius are similar to those of andAv.," However, the distributions of the radius are similar to those of and."
 There are three peaks in of cluster with age = 0.5 Gyr., There are three peaks in of cluster with age = 0.5 Gyr.
" The ‘low-radius” peak to the HF peak ofAv... the ""middle-radius! peak the MS peak ofAv... and the *high-radius” peak the RC peak ofAv."," The `low-radius' peak to the HF peak of, the `middle-radius' peak the MS peak of, and the `high-radius' peak the RC peak of."
. However. when age = 5 Gyr. there is no middle-radius! peak in the distribution of radius and also no MS peak in the distribution ofAv.," However, when age = 5 Gyr, there is no `middle-radius' peak in the distribution of radius and also no MS peak in the distribution of."
.. This clearly shows that the MS peak is caused by many young MS starsradii.. and the distribution of is more sensitive to the distribution of radius than to that of mass.," This clearly shows that the MS peak is caused by many young MS stars, and the distribution of is more sensitive to the distribution of radius than to that of mass."
 Moreover. Fig.," Moreover, Fig."
" 5. shows that both the “low-mass” peak and ""ow-radius! peak are significant for the cluster with Z = 0.02 and age = 0.5 Gyr.", \ref{figmr} shows that both the `low-mass' peak and `low-radius' peak are significant for the cluster with Z = 0.02 and age = 0.5 Gyr.
 They to the HF peaks., They to the HF peaks.
 However. Fig.," However, Fig."
 | shows that the MS peaks of and more significant than the HF peaks., \ref{fig1} shows that the MS peaks of and more significant than the HF peaks.
 This is because the of ‘low-mass’ stars decreases more quickly with increasing mass than that of middle-mass! stars in the cluster., This is because the of `low-mass' stars decreases more quickly with increasing mass than that of `middle-mass' stars in the cluster.
 For example. when the mass of a star with Z = 0.02 increases from 0.8 to 0.9AL... its radius increases from 0.727 to 0.806 2. at 0.5 Gyr. which leads to a decrease of about 17.5 in of star.," For example, when the mass of a star with Z = 0.02 increases from 0.8 to 0.9, its radius increases from 0.727 to 0.806 $R_{\odot}$ at 0.5 Gyr, which leads to a decrease of about 17.5 in of star."
 However. when the mass of a star increases from 1.55 to 1.65AL... its radius increases from 1.566 to L644 2... which results in a decrease of about 3.5 in of star.," However, when the mass of a star increases from 1.55 to 1.65, its radius increases from 1.566 to 1.644 $R_{\odot}$, which results in a decrease of about 3.5 in of star."
 Thus. although the number of stars with mass between 0.8 and 0.9 is about twice as much as that of stars with mass between 1.55 and 1.65AL... the interval of of the former is 5 times as wide as that of the latter.," Thus, although the number of stars with mass between 0.8 and 0.9 is about twice as much as that of stars with mass between 1.55 and 1.65, the interval of of the former is 5 times as wide as that of the latter."
 Therefore the MS peaks are more significant than the HF peaku, Therefore the MS peaks are more significant than the HF peaks.
 Using Eggleton's stellar evolution code. we calculated the evolutions of stars with Z 2 0.02 and mass between 1.55 and 1.65AL.," Using Eggleton's stellar evolution code, we calculated the evolutions of stars with Z = 0.02 and mass between 1.55 and 1.65."
.. Our ealeulations show that these stars have an approximate radius between 1.465 and 1.492 ]t. at the age of about 40 Myr. which leads to almost same mean density. i.e. almost sameAv.," Our calculations show that these stars have an approximate radius between 1.465 and 1.492 $\mathrm{R}_{\odot}$ at the age of about 40 Myr, which leads to almost same mean density, i.e. almost same."
.. However. the mean density of a MS star decreases with age.," However, the mean density of a MS star decreases with age."
 Since a high mass star evolves faster than a lower mass star. the mean density of star with A/ = 1.65 decreases faster than that of star with A7 = 1.55AL.," Since a high mass star evolves faster than a lower mass star, the mean density of star with $M$ = 1.65 decreases faster than that of star with $M$ = 1.55."
.. Thus the of stars with mass between I.55 and 1.65 disperses gradually with increasing age., Thus the of stars with mass between 1.55 and 1.65 disperses gradually with increasing age.
 For example. the difference between these two models is about 3.5 at the age of 0.5 Gyr. but it is about 8 at the age of 1.0 Gyr.," For example, the difference between these two models is about 3.5 at the age of 0.5 Gyr, but it is about 8 at the age of 1.0 Gyr."
 Thus MS peak exists only in young clusters., Thus MS peak exists only in young clusters.
 It moves toward a low frequency and disperses gradually with increasing age., It moves toward a low frequency and disperses gradually with increasing age.
 Figs., Figs.
 | and 3. show that there is another peak on the left of the MS gap for cluster with age = 5.0 Gyr., \ref{fig1} and \ref{fig3} show that there is another peak on the left of the MS gap for cluster with age = 5.0 Gyr.
 For stars with Al< 1.3ML... when their central convection ceases. the central hydrogen is not exhausted.," For stars with $M <$ 1.3, when their central convection ceases, the central hydrogen is not exhausted."
 The lower the mass. the more the hydrogen.," The lower the mass, the more the hydrogen."
 Thus these stars can stay between MS hook and Hertzsprung gap for a long time. which leads to the presence of a peak or bump between the RC-MS gap and the MS gap.," Thus these stars can stay between MS hook and Hertzsprung gap for a long time, which leads to the presence of a peak or bump between the RC-MS gap and the MS gap."
 For he cluster with Z = 0.02 and age = 7.0 Gy. the peak can become a bump.," For the cluster with Z = 0.02 and age = 7.0 Gy, the peak can become a bump."
 For stars with Af> 1.3AL... when the central convection ceases. the central hydrogen is almost exhausted.," For stars with $M >$ 1.3, when the central convection ceases, the central hydrogen is almost exhausted."
 After the MS wok. they evolve rapidly into the Hertzsprung gap.," After the MS hook, they evolve rapidly into the Hertzsprung gap."
 In addition. the igher the mass. the shorter the thermal time-scale.," In addition, the higher the mass, the shorter the thermal time-scale."
" Therefore the number of stars in the MS gap of a young’ cluster is less than that in the MS gap of an ""old cluster. and there is no the peak between he MS gap and RC-MS gap in ‘young’ clusters."," Therefore the number of stars in the MS gap of a `young' cluster is less than that in the MS gap of an `old' cluster, and there is no the peak between the MS gap and RC-MS gap in `young' clusters."
 The MS hook akes place after the central hydrogen abundance of stars decreases o about 0.05., The MS hook takes place after the central hydrogen abundance of stars decreases to about 0.05.
 The central hydrogen abundance of stars in the MS gap is about 0.05-0.001. but that of stars in the peak on the left of he MS gap is less than 0.001.," The central hydrogen abundance of stars in the MS gap is about 0.05-0.001, but that of stars in the peak on the left of the MS gap is less than 0.001."
" For clusters with A, 01.3M... he central hydrogen abundance of most stars in the lower boundary of histogram of of MS stars should be about 0.05."," For clusters with $M_{hook}
>$ 1.3, the central hydrogen abundance of most stars in the lower boundary of histogram of of MS stars should be about 0.05."
 Thus he asteroseismical observation for turn-off stars of ‘middle-age’ clusters is very important for testing theories of stellar evolution and stellar population synthesis., Thus the asteroseismical observation for turn-off stars of `middle-age' clusters is very important for testing theories of stellar evolution and stellar population synthesis.
 Moreover. Figs.," Moreover, Figs."
 |. and 6. show that there is a sharp peak inthe distributions of and of MS stars of clusters with age = 5.0 and 8.5 Gyr., \ref{fig1} and \ref{pz3} show that there is a sharp peak inthe distributions of and of MS stars of clusters with age = 5.0 and 8.5 Gyr.
 When age increases from 5.0 to 8.5 Gyr for, When age increases from 5.0 to 8.5 Gyr for
"for core He burning, but the impact on stars at the lower end of the range will be reduced.","for core He burning, but the impact on stars at the lower end of the range will be reduced."
" For the purposes of this paper we adopt a conservative limiting case approach, independently inferring fucl consumption bounds from models with and without overshoot."," For the purposes of this paper we adopt a conservative limiting case approach, independently inferring fuel consumption bounds from models with and without overshoot."
" The progenitor lifetime is the difference between the cluster age (744,2) and the cooling age of the WD (7.44).", The progenitor lifetime is the difference between the cluster age ) and the cooling age of the WD ).
 Stellar evolutionary tracks spanning a range of stellar mass and metallicity are then interpolated to yield the best-fittine progenitor mass (Mj))., Stellar evolutionary tracks spanning a range of stellar mass and metallicity are then interpolated to yield the best-fitting progenitor mass ).
 WD spectra modeled by theoretical cooling curves constrain ((Section ??))., WD spectra modeled by theoretical cooling curves constrain (Section \ref{sec:mf}) ).
 Set by the distance to the cluster and metallicity. the cluster turn-off luminosity is à direct indicator ofτοµς.," Set by the distance to the cluster and metallicity, the cluster turn-off luminosity is a direct indicator of."
". The cluster color-magnitude diagram (CMD), [Fe/H|. and E(B—V) are the three main data inputs in main sequence fitting algorithms used to constrain the distance modulus to the cluster."," The cluster color-magnitude diagram (CMD), $[Fe/H]$ , and $E(B-V)$ are the three main data inputs in main sequence fitting algorithms used to constrain the distance modulus to the cluster."
" $09 first assume, using measurements from the literature, a metallicity and reddening for cach cluster (see their Table 2 and 3 for their sources and values, respectively)."," S09 first assume, using measurements from the literature, a metallicity and reddening for each cluster (see their Table 2 and 3 for their sources and values, respectively)."
" To obtain the cluster distance, they empirically fit the main sequence of V-(B— V)CMDs using a sample of of field dwarfs with known metallicities and Hipparcos parallaxes (Percivaletal.2003).."," To obtain the cluster distance, they empirically fit the main sequence of $V$ $(B-V)$ CMDs using a sample of of field dwarfs with known metallicities and Hipparcos parallaxes \citep{Percival03}."
" Once the distance is known, the turn-off luminosity is measured."," Once the distance is known, the turn-off luminosity is measured."
 S09 interpolate the isochrones (both with and without convective overshooting) of Pietrinfernietal.(2004) in both turn-off luminosity and metallicity to constrain the best fit cluster age., S09 interpolate the isochrones (both with and without convective overshooting) of \citet{Pietrinferni04} in both turn-off luminosity and metallicity to constrain the best fit cluster age.
" We adopt the cluster parameters, namely cluster age and composition, presented in S09 for three of the nine clusters in our analysis."," We adopt the cluster parameters, namely cluster age and composition, presented in S09 for three of the nine clusters in our analysis."
" The composition measurements included in S09 of the Hyades, NGC 6819, and NGC 1039 are either taken from the most recent, high resolution studies of these clusters or are in agreement with current measurements."," The composition measurements included in S09 of the Hyades, NGC 6819, and NGC 1039 are either taken from the most recent, high resolution studies of these clusters or are in agreement with current measurements."
" Additionally, the computed distances to these clusters align with previous distance investigations citealtPerryman98:;; Kaliraietal. 2001:: and Jones&Prosser1996. for the Hyades, NGC 6819, and NGC 1039 respectively)."," Additionally, the computed distances to these clusters align with previous distance investigations \\citealt{Perryman98}; \citealt{Kalirai01}; and \citealt{Jones96} for the Hyades, NGC 6819, and NGC 1039 respectively)."
 We scarched the literature for revised metallicity measurements of and/or distance determinations to all the clusters in our sample., We searched the literature for revised metallicity measurements of and/or distance determinations to all the clusters in our sample.
" For six of the clusters, we modify the cluster composition, distance, or both from the values found in S09."," For six of the clusters, we modify the cluster composition, distance, or both from the values found in S09."
" In two of these six clusters, S09 either had difficulty with their main sequence (MS) fitting technique due to poor data (in the case of NGC 3532) or chose a reddening value significantly different than that calculated in the recent literature (M37)."," In two of these six clusters, S09 either had difficulty with their main sequence (MS) fitting technique due to poor data (in the case of NGC 3532) or chose a reddening value significantly different than that calculated in the recent literature (M37)."
 In other clusters in our sample. severalhigh resolution spectroscopic studies over the last decade have," In other clusters in our sample, severalhigh resolution spectroscopic studies over the last decade have"
One of the hard problems in non-perturbative quantum gravity [1]. is to construct a full set of physically meaningful observable quantities [2]..,One of the hard problems in non-perturbative quantum gravity \cite{india} is to construct a full set of physically meaningful observable quantities \cite{observables}.
 In (his paper. we point out that there is a natural set of quantities that one can define in quantum general relativity. which are gauge invariant. have a natural physical interpretation. and could play the role plaved by (he »-point functions in «quantum field theory.," In this paper, we point out that there is a natural set of quantities that one can define in quantum general relativity, which are gauge invariant, have a natural physical interpretation, and could play the role played by the $n$ -point functions in quantum field theory."
 We denote these quantity as H functions. or n-net functions.," We denote these quantity as $W$ functions, or $n$ -net functions."
 As the n-point functions in a cuantum [field theory. (hese quantities are not natural quantities of the corresponding classical field theory. namely in general relativity.," As the $n$ -point functions in a quantum field theory, these quantities are not natural quantities of the corresponding classical field theory, namely in general relativity."
 Nevertheless. (hey capture the plivsical content of the quantum theory. and are related to the classical theory.," Nevertheless, they capture the physical content of the quantum theory and are related to the classical theory."
 The VW functions are strictly related. to the three-geometry (o. (hree-geometry transition amplitude studied by Hawking [3].., The $W$ functions are strictly related to the three-geometry to three-geometry transition amplitude studied by Hawking \cite{haw}.
 However. they are not transition amplitudes between states in which the classical (hree-eeometry has an arbitrary sharp value. but rather transition aanplitudes betweeneigenshales of the three-geometry.," However, they are not transition amplitudes between states in which the classical three-geometry has an arbitrary sharp value, but rather transition amplitudes between of the three-geometry."
 In loop quantum gravity |4].. these eigenstates are characterized by discretized. geometries and are labelled bv abstract spin networks |5.6].. or s-knots.," In loop quantum gravity \cite{loop}, these eigenstates are characterized by discretized geometries and are labelled by abstract spin networks \cite{spinnet,carlolee}, or $s$ -knots."
 Thus the VW functions are rather transition amplitudes between states with fixed amounts of “quanta of geometry., Thus the $W$ functions are rather transition amplitudes between states with fixed amounts of “quanta of geometry”.
 This is analogous to the n-point ΠοΙον in field theory. which are not transition amplitudes between field configurations. but rather transition szumplitucdes between states characterized by a fixed nunber of “quanta of field” — (hat is. particles.," This is analogous to the $n$ -point functions in field theory, which are not transition amplitudes between field configurations, but rather transition amplitudes between states characterized by a fixed number of “quanta of field” – that is, particles."
" Furthermore. the HW. [unctüons eeneralize the three-geometry to Lhree-egeometry amplitude (a 2-point ΠΟΠο) to arbitrary 2-point functions: more precisely, we define the HW. functions as a fanctional W(s) over an A of abstract (not necessarily connected) spin networks."," Furthermore, the $W$ functions generalize the three-geometry to three-geometry amplitude (a 2-point function) to arbitrary $n$ -point functions; more precisely, we define the $W$ functions as a functional $W(s)$ over an $\cal A$ of abstract (not necessarily connected) spin networks."
 In this respect. the VW. functions are analogous to the Wightman distributions [7]. (hence the choice of the letter VW).," In this respect, the $W$ functions are analogous to the Wightman distributions \cite{W}
 (hence the choice of the letter $W$ )."
 We start [rom a general definition of the WV. hunctions. based on canonical «quantum eravily.," We start from a general definition of the $W$ functions, based on canonical quantum gravity."
 We show that the W functions are well defined diffeomorphism invariant observable quantities and we clarify their physical interpretation., We show that the $W$ functions are well defined diffeomorphism invariant observable quantities and we clarify their physical interpretation.
 In (his paper we focus on the case in which the dynamics is “real”. in a sense delined below.," In this paper we focus on the case in which the dynamics is “real”, in a sense defined below."
 The physical meaning of this realitv and (he extension of the formalism to (he general case are discussed al the end of the paper., The physical meaning of this reality and the extension of the formalism to the general case are discussed at the end of the paper.
 A crucial property of (he Wightman functions is the possibility of reconstructing the quantum field theory from them — a subtle application of the beautihul Gelfancd-Naimark-Seeel (GNS) representation theorem in the theoryof C* , A crucial property of the Wightman functions is the possibility of reconstructing the quantum field theory from them – a subtle application of the beautiful Gelfand-Naimark-Segel (GNS) representation theorem in the theoryof $C^{*}$ 
" 2~2.5. z>1 2=5.80. ~LOEADL. naturale €=LyATyer Ay.4=Loa/Lgaa epnanu/om. στ ps=1.15 LOPAL.. ΠαAF,/LOAL..)=IS.« τνLOSE0.1)E 2=5.8 (εΟ.Τ)E galaxieszl. 2=5.80 Af, :. Mya. "," $z\sim 2.5$ $z>4$ $z=5.80$ $\sim 10^{4}~{\rm M_\odot}$ $e$ $\epsilon\equiv L_{\rm bol}/\dot M_{\rm bh}c^2$ $\dot M_{\rm bh}$$\eta\equiv L_{\rm
bol}/L_{\rm Edd}$ $L_E=4\pi GM_{\rm bh} c \mu_e m_p/\sigma_T$ $\sigma_T$ $\mu_e=1.15$ $10^9M_\odot$ $\ln
(10^9M_\odot/10M_\odot)=18.4$$e$ $\sim 7\times 10^8
(\epsilon/0.1)\eta^{-1}$ $z=5.8$ $(\epsilon/0.1)\eta^{-1}\la 1$ $z=5.80$ $M_{\rm bh}$ $z$ $M_{\rm
halo}$ "
"In the three dimensional rotating magnetic field structure. the thickness of the gap feo is a function of the distance to the star along the field line μη,","In the three dimensional rotating magnetic field structure, the thickness of the gap $h_2$ is a function of the distance to the star along the field line $x$."
 We define the gap fraction f measured on the stellar surface as (Wang et al..," We define the gap fraction $f$ measured on the stellar surface as (Wang et al.,"
" 2010). where fs is the stellar radius. and ri(ó,) is the polar cap radius and depends on polar angle in three-dimensional magnetic field geometry."," 2010), where $R_s$ is the stellar radius, and $r_p(\phi_p)$ is the polar cap radius and depends on polar angle in three-dimensional magnetic field geometry."
 Note that because the electric field Ly ds proportional to BAS. which is almost constant along the field line for the dipole field. it can be found that. £y f.," Note that because the electric field $E_{||}$ is proportional to $Bh^2_2$, which is almost constant along the field line for the dipole field, it can be found that $E_{||}\propto{}f^2$ ."
 Vhis indicates that the strength ofthe electric field and resultant emissivity of the curvature radiation increase with the fractional gap thickness., This indicates that the strength of the electric field and resultant emissivity of the curvature radiation increase with the fractional gap thickness.
 The height(z) measured [rom the last-open field. lines is a function of distance Gr) along the magnetic field. line., The $z$ ) measured from the last-open field lines is a function of distance $x$ ) along the magnetic field line.
 1n order to make it easy to distinguish the two lavers in any .r. we introduce the factor e to represent the magnetic Ποιά. lines at à given laver and take α=1 for the field lines.," In order to make it easy to distinguish the two layers in any $x$, we introduce the factor $a$ to represent the magnetic field lines at a given layer and take $a=1$ for the last-open field lines."
 relation between the z and the a is approximated. as where ανν Corresponds to the upper boundary of the gap., The relation between the $z$ and the $a$ is approximated as where $a_{min}$ corresponds to the upper boundary of the gap.
" In this paper. the dimensionless thickness (,,;,; is assumed to be the same for different polar angle ©, because each laver should. have a similar polar cap shape on the stellar surface. and. is chosen as the fitting parameter of the light curve."," In this paper, the dimensionless thickness $a_{min}$ is assumed to be the same for different polar angle $\phi_p$ because each layer should have a similar polar cap shape on the stellar surface, and is chosen as the fitting parameter of the light curve."
" The thickness e,,;, determines the width of the pulse peaks and the phase separation between two main peaks.", The thickness $a_{min}$ determines the width of the pulse peaks and the phase separation between two main peaks.
 Our caleulation method for the phase-average spectrum and phase-resolved spectra is based. on Tang et al. (, Our calculation method for the phase-average spectrum and phase-resolved spectra is based on Tang et al. (
2008).,2008).
 In a volume clement AV. there are AN=An particles accelerated. by the electric field. that is. described. by equation (10)).," In a volume element $\Delta{V}$, there are $\Delta{N}=\Delta{V}n$ particles accelerated by the electric field that is described by equation \ref{electric_3}) )."
 Phe accelerated particles release the power gained from the accelerating electric. field. efye. through the curvature radiation process.," The accelerated particles release the power gained from the accelerating electric field, $eE_{\parallel}c$, through the curvature radiation process."
 The total radiation power for cach particle is ρω=2eesi)387GF). where £F= 04).," The total radiation power for each particle is $l_{cur}(\vec{r})=2e^2c\gamma^4_e(\vec{r})/3s^2(\vec{r})$, where $\vec{r}=(x,~z,~\phi_p)$ ."
 Phe typical local Lorentz [actor >. of the primary particles can be obtained by requiring e£(c=fo. which elves The photon spectrum at cach position of radiation is where \=EEG). Duo)=(8NheFP)/s(P) is the characteristic energy of the radiated curvature photons. ο is curvature radius. and. £4)=Idys(λάδι where ντο is the modified Bessel functions of order 5/3.x," The typical local Lorentz factor $\gamma_e$ of the primary particles can be obtained by requiring $eE_{\parallel}c=l_{cur}$, which gives The photon spectrum at each position of radiation is where $\chi=E_{\gamma}/E_{cur}(\vec{r})$, $E_{cur}(\vec{r})
=(3/2)\hbar{}c\gamma_e^3(\vec{r})/s(\vec{r})$ is the characteristic energy of the radiated curvature photons, $s(\vec{r})$ is curvature radius, and $F(\chi)=\int^{\infty}_{\chi}K_{5/3}(\xi)d\xi$, where $K_{5/3}$ is the modified Bessel functions of order 5/3.,"
67. where where the first term represents the solid angle caused by the curvature of the magnetic field line and the second term is the minimum emission angle measured from the direction of the magnetic field linc., where where the first term represents the solid angle caused by the curvature of the magnetic field line and the second term is the minimum emission angle measured from the direction of the magnetic field line.
 Here Af is the gird size of the cell along field line., Here $\Delta{l}$ is the gird size of the cell along field line.
" With equation (8)). we express the number density. at each point as n(F)=BBC]gle.0,)]."," With equation \ref{cdensity}) ), we express the number density at each point as $n(\vec{r})=\frac{\Omega B}{2\pi c} [1-g(z,\phi_p)]$."
 The volume element at cach position can be calculated where 2z:rh3(R.:)By is the total magnetic Dux through in the gap. and. IN4 and Ne are the number of the grids in the direction of the trans-Licld direction (z-clirection) and the azimuthal direction. respectively.," The volume element at each position can be calculated where $2{\pi}r_{p}h_2(R_s)B_s$ is the total magnetic flux through in the gap, and $N_A$ and $N_B$ are the number of the grids in the direction of the trans-field direction (z-direction) and the azimuthal direction, respectively."
" The total photon fluxreceived at Earth is where PF; represents the position of the i!"" cell. from which the emission can be observed. and D is the distance to the pulsar from Earth."," The total photon fluxreceived at Earth is where $\vec{r}_i$ represents the position of the $^{th}$ cell, from which the emission can be observed, and $D$ is the distance to the pulsar from Earth."
 We note that because τη depends on the viewing angle and the inclination angle. the spectrum (17)) is a function of the viewing angle and. the inclination angle.," We note that because $r_i$ depends on the viewing angle and the inclination angle, the spectrum \ref{spectrum}) ) is a function of the viewing angle and the inclination angle."
 To calculate the phase-resolvecl spectra anc the light curves. the arrival times of the photons are binned by. pulse phase.," To calculate the phase-resolved spectra and the light curves, the arrival times of the photons are binned by pulse phase."
 For cxample. Figure 2. represents photon-mapping on the plane spanned by the viewing angle and the pulse phase using the rotating dipole fields (section 2.3)).," For example, Figure \ref{skymap} represents photon-mapping on the plane spanned by the viewing angle and the pulse phase using the rotating dipole fields (section \ref{geometry}) )."
" For each viewing angle. the number of the photons measured at pulse phases between c, and c» is calculated from Lt has been considered that the positions of the first and the second. peaks of the pulsar are determined by the geometry of the magnetic field."," For each viewing angle, the number of the photons measured at pulse phases between $\psi_1$ and $\psi_2$ is calculated from It has been considered that the positions of the first and the second peaks of the pulsar are determined by the geometry of the magnetic field."
 In this study. we adopt the rotating vacuum dipole field to calculate the light curves and spectra.," In this study, we adopt the rotating vacuum dipole field to calculate the light curves and spectra."
 For the rotating dipole. the magnetic field Bir) is given by (Cheng. Rucerman Zhang. 2000). where (1= is the magnetic moment vector. FÉ is the radial unit vector. and à isthe inclination angle.," For the rotating dipole, the magnetic field $\vec{B}(r)$ is given by (Cheng, Ruderman Zhang, 2000), where $\dot{\mu}=\mu(\hat{x}\sin{\alpha}\cos{{\Omega}t}
+\hat{y}\sin{\alpha}\sin{{\Omega}t}+\hat{z}\cos{\alpha})$ is the magnetic moment vector, $\hat{r}$ is the radial unit vector, and $\alpha$ isthe inclination angle."
" The lItunge-Ixutta. method. is emploved to trace out field lines and (o [find the polar cap rim No(Op).Yutóu). Zutós,)]."," The Runge-Kutta method is employed to trace out field lines and to find the polar cap rim $[X_0(\phi_p), Y_0(\phi_p), Z_0(\phi_p)]$ ."
" Once the upper boundary (04,,;, ts chosen. we trace the"," Once the upper boundary $a_{min}$ is chosen, we trace the"
"of a 20Me sstar with initial surface rotation of 300kms""! for cases 1, 2 and 3.","of a $20$ star with initial surface rotation of $300\,{\rm km\,s^{-1}}$ for cases 1, 2 and 3."
" Although the centrifugal force causes some change in a star's structure, its evolution is strongly affected by changes in the chemical composition."," Although the centrifugal force causes some change in a star's structure, its evolution is strongly affected by changes in the chemical composition."
 Fig 1 shows how the composition of the rotating 20 ccase-1 star differs from a non-rotating 20 sstar at the end of the main sequence., Fig \ref{abundances} shows how the composition of the rotating $20$ case-1 star differs from a non-rotating $20$ star at the end of the main sequence.
 The difference in the rotation-induced mixing produces the variation in results between the various cases., The difference in the rotation-induced mixing produces the variation in results between the various cases.
 Fig., Fig.
" 2 shows the angular velocity profile and the diffusion coefficient for vertical angular momentum transport in radiative zones predicted by each of cases 1, 2 and 3 at the zero-age main sequence (ZAMS)."," \ref{diff} shows the angular velocity profile and the diffusion coefficient for vertical angular momentum transport in radiative zones predicted by each of cases 1, 2 and 3 at the zero-age main sequence (ZAMS)."
" Note that, even though the stars have the same surface rotation, their core rotation and hence total angular momentum content can vary significantly between models Despite their similar treatments, cases 1 and 3 have quite different initial rotation profiles."," Note that, even though the stars have the same surface rotation, their core rotation and hence total angular momentum content can vary significantly between models Despite their similar treatments, cases 1 and 3 have quite different initial rotation profiles."
 This is largely due to our choice of calibration., This is largely due to our choice of calibration.
" Because in case 3 we ignore mean molecular weight gradients, the overall efficiency of mixing must be reduced to match our calibration criterion (section 2.7))."," Because in case 3 we ignore mean molecular weight gradients, the overall efficiency of mixing must be reduced to match our calibration criterion (section \ref{testmodels}) )."
 This means that shear diffusion is much weaker relative to advection and so a profile with more differential rotation results., This means that shear diffusion is much weaker relative to advection and so a profile with more differential rotation results.
 Had we chosen to calibrate the mixing by reducing Co instead of C we would have found the opposite effect., Had we chosen to calibrate the mixing by reducing $C_0$ instead of $C_1$ we would have found the opposite effect.
 This highlights one possible pitfall of including multiple free parameters within a given system., This highlights one possible pitfall of including multiple free parameters within a given system.
 Case 2 is dominated by diffusion because of the diffusive treatment of meridional circulation., Case 2 is dominated by diffusion because of the diffusive treatment of meridional circulation.
 Recall that meridional circulation is treated advectively in cases 1 and 3 so is not included in the diffusion coefficient., Recall that meridional circulation is treated advectively in cases 1 and 3 so is not included in the diffusion coefficient.
 In fact it is responsible for production of the shear at the ZAMS despite turbulence trying to restore solid body rotation., In fact it is responsible for production of the shear at the ZAMS despite turbulence trying to restore solid body rotation.
" Because there is no perturbation to the rotation at the start of the main sequence, the star in case 2 rotates as a solid body."," Because there is no perturbation to the rotation at the start of the main sequence, the star in case 2 rotates as a solid body."
 As the star evolves and mass is lost from its surface the solid body rotation is disturbed., As the star evolves and mass is lost from its surface the solid body rotation is disturbed.
" Even so, because of the strong diffusion, case 2 stars never deviate far from solid body rotation as can be seen in Fig. 3.."," Even so, because of the strong diffusion, case 2 stars never deviate far from solid body rotation as can be seen in Fig. \ref{diff2}."
 We note that case-1 stars reach the end of the main sequence with a higher mass than those in case 2 or case 3., We note that case-1 stars reach the end of the main sequence with a higher mass than those in case 2 or case 3.
 This is because case-2 and case-3 stars have a longer main-sequence life owing to more efficient mixing at the core-envelope boundary., This is because case-2 and case-3 stars have a longer main-sequence life owing to more efficient mixing at the core–envelope boundary.
 This allows hydrogen to be mixed into the core more rapidly than in case 1., This allows hydrogen to be mixed into the core more rapidly than in case 1.
 This also leads to larger core masses in cases 2 and 3 compared to case 1., This also leads to larger core masses in cases 2 and 3 compared to case 1.
 We see in Fig., We see in Fig.
 2 that the predicted diffusion coefficients for cases 1 and 2 are similar throughout most of the envelope., \ref{diff} that the predicted diffusion coefficients for cases 1 and 2 are similar throughout most of the envelope.
" By the TAMS, the diffusion predicted by case 2 is significantly lower than the other two cases."," By the TAMS, the diffusion predicted by case 2 is significantly lower than the other two cases."
 This is possibly because rising shear owing to rapid hydrostatic evolution at the TAMS causes the diffusion in cases 1 and 3 to increase while in case 2 diffusion is dominated instead by the circulation., This is possibly because rising shear owing to rapid hydrostatic evolution at the TAMS causes the diffusion in cases 1 and 3 to increase while in case 2 diffusion is dominated instead by the circulation.
" Unsurprisingly, the diffusion coefficient in case 3 is similar in form to case 1 but significantly smaller, a result of our choice of C1."," Unsurprisingly, the diffusion coefficient in case 3 is similar in form to case 1 but significantly smaller, a result of our choice of $C_1$."
 We note however that the diffusion coefficient predicted by the two cases is very similar by the end of the main sequence., We note however that the diffusion coefficient predicted by the two cases is very similar by the end of the main sequence.
" Also, the diffusion coefficient at"," Also, the diffusion coefficient at"
At lower black hole masses. logmpg8.5. our quasar mocel oediets an excess of fainter quasars vet to be seen in the ~2 data.,"At lower black hole masses, $\log m_{\rm BH}\sim 8.5$, our quasar model predicts an excess of fainter quasars yet to be seen in the $z\sim2$ data."
 At higher redshift. z=4. the model shows he continuing build-up of massive black holes but with Less activity at lower masses.," At higher redshift, $z=4$, the model shows the continuing build-up of massive black holes but with less activity at lower masses."
 By late times. 2=0.5. massive lack hole mass growth has largely stopped. while the Low mass holes continue to grow.," By late times, $z=0.5$, massive black hole mass growth has largely stopped while the low mass holes continue to grow."
 This last behaviour is a black hole manifestation. of he popular “downsizing” paradigm (??)..," This last behaviour is a black hole manifestation of the popular “downsizing” paradigm \citep{Heckman2004, Merloni2008}."
 Lt is interesting hat such shift in black hole mass growth with time arises naturally from. the model constraints alone., It is interesting that such shift in black hole mass growth with time arises naturally from the model constraints alone.
 LE we skip ahead to eure 10. (Section 4.2)) we can see the reason why., If we skip ahead to figure \ref{fig:evolution} (Section \ref{sec:application}) ) we can see the reason why.
 Here. dashed lines show the changing space density of halos/quasars with time. while horizontal dotted. lines show black hole mass.," Here, dashed lines show the changing space density of halos/quasars with time, while horizontal dotted lines show black hole mass."
" At high redshift. very low space density contours are mostly flat (or only slowly rising) and correspond. to a fixed black hole mass of ~LO""IAL.."," At high redshift, very low space density contours are mostly flat (or only slowly rising) and correspond to a fixed black hole mass of $\sim 10^{9-10} M_\odot$."
 At lower redshifts all density. contours turn over. sharply. and black bole mass decreases by up to a few ordoers-of-magnitude at fixed space density.," At lower redshifts all density contours turn over sharply, and black hole mass decreases by up to a few orders-of-magnitude at fixed space density."
 Hence. downsizing is predicted. for all objects at 2ὃν," Hence, downsizing is predicted for all objects at $z \simlt 2$."
 At 222 the moelel predicts that. low space density objects. (i.c. the most massive) should show no downsizing trends (relative to >= 2). while higher space density objects (Le. closer to L) should be ~upsizine”. especially above redshifts z~4.," At $z \simgt 2$ the model predicts that low space density objects (i.e. the most massive) should show no downsizing trends (relative to $z=2$ ), while higher space density objects (i.e. closer to $L^*$ ) should be “upsizing”, especially above redshifts $z \sim 4$."
 Section 2.1. and equation S. provide an analytic prediction for how black hole and dark matter halo mass are related., Section \ref{sec:mapping} and equation \ref{eqn:mass2bh} provide an analytic prediction for how black hole and dark matter halo mass are related.
 This relationship includes a redshift. dependence through Etz)25Owl|2)?Ox}?. implying that the mpgAlea ralio should evolve with time. with more massive black holes occupying dark matter halos of a fixed mass at higher redshifts relative to lower redshi," This relationship includes a redshift dependence through $E(z) = [\Omega_{\rm m} (1+z)^3 + \Omega_\Lambda]^{1/2}$, implying that the $m_{\rm BH}-M_{\rm vir}$ ratio should evolve with time, with more massive black holes occupying dark matter halos of a fixed mass at higher redshifts relative to lower redshift."
 In figure 7. we use equation S to plot the hole-to-halo mass relation at five dillerent e»ochs. from +=Oto 2= 5.," In figure \ref{fig:BHhalo} we use equation \ref{eqn:mass2bh} to plot the hole-to-halo mass relation at five different epochs, from $z=0$ to $z=5$ ."
 At any given redshift the ratiο increases with increasing halo mass. implving that black holes become proportionally largerὃν the more massive the haOo ls.," At any given redshift the ratio increases with increasing halo mass, implying that black holes become proportionally larger the more massive the halo is."
 The evolution in the amplitude of mpg/Mya with redshift can also be clearly seen. with the ratio changing by a factor of ~5 between >= Oand z=2. increasing to a factor of 20 by 2=5.," The evolution in the amplitude of $m_{\rm BH}$ $M_{\rm vir}$ with redshift can also be clearly seen, with the ratio changing by a factor of $\sim 5$ between $z=0$ and $z=2$, increasing to a factor of $20$ by $z=5$."
 Previous authors have attempted to quantify the change in black hole to host galaxyfhalo properties with time ??7).. ," Previous authors have attempted to quantify the change in black hole to host galaxy/halo properties with time \citep[e.g.][]{Robertson2006, McLure2006, Croton2006b}."
Evolution of this type is a clear prediction. of our model., Evolution of this type is a clear prediction of our model.
 Our results are similar to those found by 2? using different techniques (seealso?).., Our results are similar to those found by \cite{Wyithe2006} using different techniques \citep[see also][]{Wyithe2003}.
 We can cquivalently recast figure 7 as a changing mass-to-light ratio using Equation 7.., We can equivalently recast figure \ref{fig:BHhalo} as a changing mass-to-light ratio using Equation \ref{eqn:mass2mag}.
 The right axis in ligure 7. shows this result., The right axis in figure \ref{fig:BHhalo} shows this result.
 Llalos with masses greater than 10741. host quasars with mass-to-lieht ratios less than unity regardless of the redshift of interest., Halos with masses greater than $10^{14}M_\odot$ host quasars with mass-to-light ratios less than unity regardless of the redshift of interest.
 This is also true of all lower mass CMx10b. ) quasarfhalo svstems at recshifts z22., This is also true of all lower mass $M_{\rm vir} \simlt 10^{13} M_\odot$ ) quasar/halo systems at redshifts $z\simgt 2$.
 The clustering of a given population of quasars will depend both on the masses of quasar hosts ancl the luminosity range which defines the quasar sample., The clustering of a given population of quasars will depend both on the masses of quasar hosts and the luminosity range which defines the quasar sample.
 Both key observations used to constrain our quasar model. the mpg—0 relation and quasar luminosity function. are relevant to shape the model 2-point function.," Both key observations used to constrain our quasar model, the $m_{\rm BH}-\sigma$ relation and quasar luminosity function, are relevant to shape the model 2-point function."
 In figure S. we present the observed and model projected correlation functions at five discrete redshifts [rom z=1 to 2o4., In figure \ref{fig:CFs} we present the observed and model projected correlation functions at five discrete redshifts from $z=1$ to $z=4$.
 The left three panels are taken from ?. using the 20Z data. whereas the right two panels are those from ? with the SDSS data.," The left three panels are taken from \cite{Porciani2004} using the 2QZ data, whereas the right two panels are those from \cite{Shen2007} with the SDSS data."
 Phe marked redshift in cach panel indicates, The marked redshift in each panel indicates
simulations of clump configurations | and 2 respectively. while the other simulations are R-MHD calculations of the same clump configurations with varying field strengths and orientations.,"simulations of clump configurations 1 and 2 respectively, while the other simulations are R-MHD calculations of the same clump configurations with varying field strengths and orientations."
 The field strengths were approximately £2I8.53. and 160ο and are referred to as weak. medium. and strong respectively.," The field strengths were approximately $B\simeq18,\ 53,$ and $160\,\mu$ G and are referred to as weak, medium, and strong respectively."
 R2-R10 are R-MHD simulations of configuration 1: R2-R4 are weak field models. RS-R7 have a medium field. and RS-RIO a strong field.," R2–R10 are R-MHD simulations of configuration 1: R2–R4 are weak field models, R5–R7 have a medium field, and R8–R10 a strong field."
 RI2-RI5 are R-MHD simulations of configuration 2: RII-RIA have a weak field and RIS a medium field., R12–R15 are R-MHD simulations of configuration 2: R11–R14 have a weak field and R15 a medium field.
" For the field orientation. ""parallel denotes parallel to the radiation propagation vector along the centre of the simulation (B= Lyx). and ‘perpendicular’ denotes a field in the 7j— 2 plane."," For the field orientation, `parallel' denotes parallel to the radiation propagation vector along the centre of the simulation $\mathbf{B}=B_0\hat{\mathbf{x}}$ ), and `perpendicular' denotes a field in the $y$ $z$ plane."
" Field orientations were chosen to be either parallel or perpendicular, or oriented SO” from the .r-axis and 50° from the j-axis in the yes plane."," Field orientations were chosen to be either parallel or perpendicular, or oriented $80^{\circ}$ from the $x$ -axis and $50^{\circ}$ from the $y$ -axis in the $y$ $z$ plane."
 The simulations with the latter field configuration (R3. R4. R7. RIO) produced very similar results to the perpendicular models (R2. R5. and R8) for configuration | so they were not run for as long as the other models and were not run at all for configuration 2.," The simulations with the latter field configuration (R3, R4, R7, R10) produced very similar results to the perpendicular models (R2, R5, and R8) for configuration 1 so they were not run for as long as the other models and were not run at all for configuration 2."
" Whether a field is weak or strong is largely determined by its dynamical importance. set by the plasma parameter 3=Szp,/L7. the ratio of thermal to magnetic pressure."," Whether a field is weak or strong is largely determined by its dynamical importance, set by the plasma parameter $\beta\equiv 8\pi
p_g/B^2$, the ratio of thermal to magnetic pressure."
 Since ionised gas in H regions is largely isothermal. as is dense molecular gas. the therma pressure is approximately proportional to density.," Since ionised gas in H regions is largely isothermal, as is dense molecular gas, the thermal pressure is approximately proportional to density."
 Hence a field of 50 7G could be strong or weak depending on whether the gas is ionised or neutral. and on its density.," Hence a field of $50\,\mu$ G could be strong or weak depending on whether the gas is ionised or neutral, and on its density."
" The plasma parameter is shown in Table 3. for a range of gas pressures encounterec in the photoionisation simulations: (1) the initial conditions have a constant pressure of py=1.3810Hdynecm7 (or μου=em Ιώ: (09) gas at the background density of ny=200cm7 and the ionised gas temperature of 7/cNOUO K ns p,=442010jJ'dyenecnm>. and (3) the peak pressure ypically encountered in the simulations is py10xdvnecni2"," The plasma parameter is shown in Table \ref{tab:PlasmaBeta} for a range of gas pressures encountered in the photoionisation simulations: (1) the initial conditions have a constant pressure of $p_g=1.38\times10^{-11}\,\mathrm{dyne}\,\mathrm{cm}^{-2}$ (or $p_g/k_{\mathrm{B}}=10^5\,\mathrm{cm}^{-3}\,\mathrm{K}$ ); (2) gas at the background density of $n_{\mathrm{H}}=200\,\mathrm{cm}^{-3}$ and the ionised gas temperature of $T\simeq8\,000\,$ K has $p_g=4.42\times10^{-10}\,\mathrm{dyne}\,\mathrm{cm}^{-2}$, and (3) the peak pressure typically encountered in the simulations is $p_g\sim10^{-8}\,\mathrm{dyne}\,\mathrm{cm}^{-2}$."
 For weak field simulations the gas pressure clearly dominates and or the strong field the situation is reversed: for the medium field case the initial conditions are magnetically dominated but. once ionised. the gas pressure is larger.," For weak field simulations the gas pressure clearly dominates and for the strong field the situation is reversed; for the medium field case the initial conditions are magnetically dominated but, once ionised, the gas pressure is larger."
 Thus it is expected that the weak field results will largely follow the R-HD results. the strong field simulations should show very different behaviour. and the medium tield models will lie somewhere in between.," Thus it is expected that the weak field results will largely follow the R-HD results, the strong field simulations should show very different behaviour, and the medium field models will lie somewhere in between."
 The gas pressures in hese simulations are comparable to those estimated for the pillars and their environment in M16 (see the discussion in MLIOJ. but it should be borne in mind that other massivestar-forming regions can have significantly higher (or lower) gas pressures.," The gas pressures in these simulations are comparable to those estimated for the pillars and their environment in M16 (see the discussion in ML10), but it should be borne in mind that other massivestar-forming regions can have significantly higher (or lower) gas pressures."
 Three main observable consequences of the magnetic field are expected (??.ef): (1) For weak magnetic fields the field orientation will be be changed by the dynamics of the photoionisation process. (," Three main observable consequences of the magnetic field are expected \citep[cf.]{Wil07,HenArtDeCEA09}: (1) For weak magnetic fields the field orientation will be be changed by the dynamics of the photoionisation process. ("
2) When the field is sufficiently strong the density structure of the neutral gas will be significantly altered because gas can only move along field lines: RDI produces a sheet rather than an axisymmetric compression. (,2) When the field is sufficiently strong the density structure of the neutral gas will be significantly altered because gas can only move along field lines; RDI produces a sheet rather than an axisymmetric compression. (
3) Strong magnetic fields will contine the photoevaporation flow changing its observable properties.,3) Strong magnetic fields will confine the photoevaporation flow changing its observable properties.
 We first plot projections through the simulation domain showing column density of neutral gas and the projected magnetic field., We first plot projections through the simulation domain showing column density of neutral gas and the projected magnetic field.
 Following this we show emission maps in recombination radiation., Following this we show emission maps in recombination radiation.
 R2. R5. and R8 proved most useful for showing the effects of increasing field strength so we focus most of our analysis on these three simulations.," R2, R5, and R8 proved most useful for showing the effects of increasing field strength so we focus most of our analysis on these three simulations."
 The column density is calculated as in MLIO by integrating the neutral gas number density along the line of sight (LOS)., The column density is calculated as in ML10 by integrating the neutral gas number density along the line of sight (LOS).
 Note that because we do not consider molecules explicitly. the column densities should be divided by 2 to give NOH»).," Note that because we do not consider molecules explicitly, the column densities should be divided by 2 to give $_2$ )."
 The projected magnetic field is more difficult to calculate since it must be a weighted integral. for example to calculate the polarisation of background starlight induced by aligned dust grains (ef.observa-tionsofM16by ?)..," The projected magnetic field is more difficult to calculate since it must be a weighted integral, for example to calculate the polarisation of background starlight induced by aligned dust grains \citep[cf.\ observations of M16
by][]{SugWatTamEA07}."
 For our integration we assume a constant gas- ratio and weight the integral by gas density., For our integration we assume a constant gas-to-dust ratio and weight the integral by gas density.
 To allow for the possibility that grain alignment may be less effective at high densities (e.g.2). we limit the density weighting to a maximum density. Musas=2.5lOem this is rather ad-hoc but it has a very limited effect on the projected field orientation as long US Minas.zolOlem.," To allow for the possibility that grain alignment may be less effective at high densities \citep[e.g.][]{GooJonLadEA95} we limit the density weighting to a maximum density, $n_{\mathrm{max}}=2.5\times10^4\,\mathrm{cm}^{-3}$; this is rather ad-hoc but it has a very limited effect on the projected field orientation as long as $n_{\mathrm{max}}\gtrsim
10^4\,\mathrm{cm}^{-3}$."
 The projected field may be calculated by integrating the Stokes ( and ( parameters along the LOS and subsequently recovering the field orientation using trigonometric relations (see 2).., The projected field may be calculated by integrating the Stokes $Q$ and $U$ parameters along the LOS and subsequently recovering the field orientation using trigonometric relations \citep[see][]{ArtHenMelEA10}. .
 With the approximations described above the, With the approximations described above the
the diagonal elements of the covariance matrix. than the data themselves would suggest. the results are equivalent to a situation with larger nominal measurement uncertainties (and hence broader V7 minima) than implied by the original covariance matrix.,"the diagonal elements of the covariance matrix than the data themselves would suggest, the results are equivalent to a situation with larger nominal measurement uncertainties (and hence broader $\chi^2$ minima) than implied by the original covariance matrix."
 However. when iis determined. from a limited set of measurements. C tends to differ significantly from the true inverse.," However, when is determined from a limited set of measurements, $\mathrm{\Cb^{-1}}$ tends to differ significantly from the true inverse."
 Hence. using the standard covariance matrix in fitting should lead to measurements with nominally tighter errors than ridge regression techniques. but those measurements may in fact be significantly offset from the true value of the parameter we are attempting to determine.," Hence, using the standard covariance matrix in fitting should lead to measurements with nominally tighter errors than ridge regression techniques, but those measurements may in fact be significantly offset from the true value of the parameter we are attempting to determine."
 This can cause the parameter results to have larger spread about the true value than optimal., This can cause the parameter results to have larger spread about the true value than optimal.
 When we add some degree of ridge regression. the inverse of the covariance matrix is better behaved. and hence is less likely to yield a discrepant result.," When we add some degree of ridge regression, the inverse of the covariance matrix is better behaved, and hence is less likely to yield a discrepant result."
 By varying the strength of the ridge regression conditioning. we can choose different tradeoffs between the bias and variance of parameter estimates.," By varying the strength of the ridge regression conditioning, we can choose different tradeoffs between the bias and variance of parameter estimates."
 In general. we want both of these contributions to be small: in the next section we investigate what degree of conditioning minimizes their sum.," In general, we want both of these contributions to be small; in the next section we investigate what degree of conditioning minimizes their sum."
 In this section we will evaluate how the conditioning of the covariance matrix affects the determination of correlation function parameters and ultimately the reconstruction ofop(zk., In this section we will evaluate how the conditioning of the covariance matrix affects the determination of correlation function parameters and ultimately the reconstruction of.
 By domg so. we will be able to optimize the reconstruction of the true redshift distribution of the photometric sample.," By doing so, we will be able to optimize the reconstruction of the true redshift distribution of the photometric sample."
 We assess this by measuring the integrated mean squared error. i.e. the variance plus the bias squared.," We assess this by measuring the integrated mean squared error, i.e. the variance plus the bias squared."
 This is commonly referred to in statistics literature as the ‘risk’., This is commonly referred to in statistics literature as the 'risk'.
 By focusing on the risk in some quantity we are optimizing for the minimum combined effect of variance and bias: either large random errors or large bias would lead to a large risk., By focusing on the risk in some quantity we are optimizing for the minimum combined effect of variance and bias: either large random errors or large bias would lead to a large risk.
 We hence define the risk to be R(X)=4X-Xq)). where X—Xiye is the difference between the measured parameter value and its true value.," We hence define the risk to be $\mathcal{R}\mathrm{(X)=\left<(X-X_{true})^2\right>}$, where $\mathrm{X-X_{true}}$ is the difference between the measured parameter value and its true value."
 At times we will also refer to the fractional risk of a parameter. which we define as R(X)=OXXue)Χρ," At times we will also refer to the fractional risk of a parameter, which we define as $\mathcal{\tilde R}\mathrm{(X)=\langle(X-X_{true})^2\rangle/X^2_{true}}$."
 Since we utilize three different types of correlation measurements in the reconstruction of we look at how changing the level of conditioning of the o4)...covariance matrix affects each one individually.," Since we utilize three different types of correlation measurements in the reconstruction of, we look at how changing the level of conditioning of the covariance matrix affects each one individually."
" We optimized the conditioning of the covariance matrix for the autocorrelation of the photometric sample using a Monte Carlo simulation where we use the covariance matrix of ccaleulated from the 24 fields (e.. the 24 different w,,light cones) as our ""true"" covariance matrix. and then use it to generate realizations of correlated noise about à selected"," We optimized the conditioning of the covariance matrix for the autocorrelation of the photometric sample using a Monte Carlo simulation where we use the covariance matrix of calculated from the 24 fields (i.e., the 24 different light cones) as our “true” covariance matrix, and then use it to generate realizations of correlated noise about a selected"
colors and the color selection is very efficient in selecting galaxies of the appropriate magnitude and redshift.,colors and the color selection is very efficient in selecting galaxies of the appropriate magnitude and redshift.
 Even in the CNOC2 survey most of these weights are equal to 1 (Yeeal.1996) for most galaxies., Even in the CNOC2 survey most of these weights are equal to 1 \citep{yee96} for most galaxies.
" For these reasons, we do not adopt this weight in our study."," For these reasons, we do not adopt this weight in our study."
" Following Ρ00 the number of close companions per galaxy in a flux-limited sample can be expressed as: and the total companion luminosity: The sums run over the {=1,...,Ni; primary galaxies: N¢, and are the number and summed luminosity of galaxies from L.,the secondary sample that are dynamically close (as defined above) to the ;' primary galaxy and are expressed as: where the sums run over those j=1,...,V» galaxies in the secondary sample that fulfill the criteria for being dynamically close to the i galaxy in the primary sample."," Following P00 the number of close companions per galaxy in a flux-limited sample can be expressed as: and the total companion luminosity: The sums run over the $i=1,...,N_1$ primary galaxies: $N_{c_i}$ and $L_{c_i}$ are the number and summed luminosity of galaxies from the secondary sample that are dynamically close (as defined above) to the $i^{th}$ primary galaxy and are expressed as: where the sums run over those $j=1,...,N_2$ galaxies in the secondary sample that fulfill the criteria for being dynamically close to the $i^{th}$ galaxy in the primary sample."
 The weights to be applied to the secondary sample correct for spatial incompleteness (wj wÀ) and the flux-limit of the survey (S(z;)) for each j* companion., The weights to be applied to the secondary sample correct for spatial incompleteness $w^j_b$ $w^j_v$ ) and the flux-limit of the survey $S(z_j)$ ) for each $j^{th}$ companion.
 We do not apply the spectroscopic incompleteness weight wg because we use the alternate method described above to calculate the contribution from missed close pairs., We do not apply the spectroscopic incompleteness weight $w_{\theta}$ because we use the alternate method described above to calculate the contribution from missed close pairs.
 The weights are defined in the previous subsections., The weights are defined in the previous subsections.
" Similar weights also need to be applied to the primary sample, to correct for spatial incompleteness and the mean density: where Wy,=fi and wi,=1/2 (i.e., the reciprocals of the weights applied to the secondary sample)."," Similar weights also need to be applied to the primary sample, to correct for spatial incompleteness and the mean density: where $w^i_{b_1}=f_b^i$ and $w^i_{v_1}=1/2$ (i.e., the reciprocals of the weights applied to the secondary sample)."
 No spectroscopic completeness weight is needed for the primary sample., No spectroscopic completeness weight is needed for the primary sample.
 In order to convert a pair fraction into a merger rate the timescale for the merger event needs to be estimated., In order to convert a pair fraction into a merger rate the timescale for the merger event needs to be estimated.
 Merger timescales are difficult to determine and depend on the poorly known details of the merger process and how the potential of the individual galaxies reacts to the merger episode., Merger timescales are difficult to determine and depend on the poorly known details of the merger process and how the potential of the individual galaxies reacts to the merger episode.
 The more commonly used timescales in previous work and semi-analytic models are based on dynamical friction arguments., The more commonly used timescales in previous work and semi-analytic models are based on dynamical friction arguments.
" The dynamical friction timescale can be calculated as etal.2000):: where is initial physical pair separation in kpc, v. is the circular rvelocity in km s~!, M is the mass and A is the Coulomb logarithm."," The dynamical friction timescale can be calculated as \citep{patton00}: where r is initial physical pair separation in kpc, $v_c$ is the circular velocity in km $^{-1}$, $M$ is the mass and $\Lambda$ is the Coulomb logarithm."
" Assuming r=20/1 kpc, ve=260 km s! and InA=2 for equal mass mergers, we get a typical dynamical friction timescale between 0.1 and 0.3 Gyrs over the range of masses we sample."," Assuming $r=20\,h^-1$ kpc, $v_c=260$ km $^{-1}$ and $\ln \Lambda=2$ for equal mass mergers, we get a typical dynamical friction timescale between 0.1 and 0.3 Gyrs over the range of masses we sample."
" The calibration Kitzbichler&White(2009) for the merger timescale of bypairs in N-body simulations with Μ5x10? Mo and a velocity separation of 300 km s! yields 0.9 Gyr, while the estimated merger timescale from the N-body simulations of Boylan-Kolchinetal.(2008) is ~0.8 Gyr for the mass ratios we consider."," The calibration by \cite{kitzbichler08} for the merger timescale of pairs in N-body simulations with $M > 5 \times 10^9$ $_{\odot}$ and a velocity separation of 300 km $^{-1}$ yields 0.9 Gyr, while the estimated merger timescale from the N-body simulations of \cite{boylan08} is $\sim 0.8$ Gyr for the mass ratios we consider."
" A comparison between merger timescale by dynamical friction and in N-body simulations by Boylan-Kolchinetal.(2008) shows that the dynamical friction formula underestimates the merger timescale by a factor between 1.7 and 3.3 for mergers of mass ratio 1:3 to 1:10 respectively, and leads to a overestimate of the mass accretion rate (mainly via minor mergers)."," A comparison between merger timescale by dynamical friction and in N-body simulations by \cite{boylan08} shows that the dynamical friction formula underestimates the merger timescale by a factor between 1.7 and 3.3 for mergers of mass ratio 1:3 to 1:10 respectively, and leads to a overestimate of the mass accretion rate (mainly via minor mergers)."
 We can now apply the above procedure to the 2SLAQ sample., We can now apply the above procedure to the 2SLAQ sample.
" Out of 7889 galaxies we find a total of one dynamically close pair (we find a second pair, but it lies within the 3” exclusion circle)."," Out of 7889 galaxies we find a total of one dynamically close pair (we find a second pair, but it lies within the $3''$ exclusion circle)."
" This yields a pair fraction ΝΕΟ=0.047% and a luminosity accretion rate L,=2.5x107 Lo."," This yields a pair fraction $N_c=0.047\%$ and a luminosity accretion rate $L_c=2.5 
\times 10^7$ $L_{\odot}$."
 For galaxies within z«0.55 this is Ν.=0.041%., For galaxies within $z < 0.55$ this is $N_c=0.041\%$.
" Normally, errors on these quantities can be estimated by or jack-knifing, but this is not feasible with a bootstrapsample of resamplingonly two objects."," Normally, errors on these quantities can be estimated by bootstrap resampling or jack-knifing, but this is not feasible with a sample of only two objects."
 We then proceed to estimate an upper limit to the pair fraction and the merger rate., We then proceed to estimate an upper limit to the pair fraction and the merger rate.
been sugeested bv IIbeuyetal.(2003).. Burrowsctal.(2006.2007a} aud Fortneyetal.(2007)..,"been suggested by \citet{hubeny03}, , \citet{burr06,burr07} and \citet{fort07b}."
. Receutly. Burrowsetal.(2007a.b) suggested that model spectra could match the observatious of and if a stratospheric absorber of uukuowu colmposition (possibly tholins. polvacetylenes. TiO or VO) were present in the atmosphere of the planet.," Recently, \citet{burr07,burr07b} suggested that model spectra could match the observations of and if a stratospheric absorber of unknown composition (possibly tholins, polyacetylenes, TiO or VO) were present in the atmosphere of the planet."
" The presence of a stratospheric absorber would vield a thermal inversion in the plauetary atmosphere aud the presence of the water features iu clussion for a variety of heat redistribution parameters P,,.", The presence of a stratospheric absorber would yield a thermal inversion in the planetary atmosphere and the presence of the water features in emission for a variety of heat redistribution parameters $_{n}$.
 Our observations sugeest the presence of a thermal inversion laver and a possible stratospheric absorber in the atmosphere of the plauct., Our observations suggest the presence of a thermal inversion layer and a possible stratospheric absorber in the atmosphere of the planet.
 The solid liue aud open squares in Fie., The solid line and open squares in Fig.
" 3) depict an atmospheric model ofXO-1b.. following the methodology of Burrowsetal.(2006.2007a) with a thermal inversion aud a stratosploric absorber of opacity of #, — 0.1 cm? /g and redistribution parameter of P, = 0.3."," \ref{fig:atmo} depict an atmospheric model of, following the methodology of \citet{burr06,burr07} with a thermal inversion and a stratospheric absorber of opacity of $\kappa _{e}$ = 0.1 $^{2}$ /g and redistribution parameter of $_{n}$ = 0.3."
" The latter model fits the data better than the canonical cloudless model with P, = 0.5 (dot-dashed curve aud open circles for averaged band ratios).", The latter model fits the data better than the canonical cloudless model with $_{n}$ = 0.3 (dot-dashed curve and open circles for averaged band ratios).
 The baud-averaged fiux ratios for the amodel with a stratospheric absorber (open squares) are within the error bars for the 3.6. 1.5. and SJO micron chaunels. but are inconsisteut bv 2.76 with the baud-averaged flux ratios for the 5.5 micron channel.," The band-averaged flux ratios for the model with a stratospheric absorber (open squares) are within the error bars for the 3.6, 4.5, and 8.0 micron channels, but are inconsistent by $\sigma$ with the band-averaged flux ratios for the 5.8 micron channel."
 This is similar to the situation for the IRAC fit to the observations by ΠΟ 209158b by I&uutsonetal.(2008)., This is similar to the situation for the IRAC fit to the observations by HD 209458b by \citet{knutson07b}.
. The absorber-free canonical model (cdot-dashed line) is clearly inconsistent with our observatious (Fie. 34) , The absorber-free canonical model (dot-dashed line) is clearly inconsistent with our observations (Fig. \ref{fig:atmo}) )
of NO-1b iu all 1 channels by 1o. 7.1o. 6.30. 3.74]. respectively.," of XO-1b in all 4 channels by $\sigma$, $\sigma$, $\sigma$, $\sigma$ ], respectively."
 Binrowsetal.(2007b) and Fortueyetal.(2007) sugecsted that the presence of the stratospheric absorber might be correlated with the incident flux from the star at the sub-stellar point on the planct. the precise level of which is vet to be refined.," \citet{burr07b} and \citet{fort07b} suggested that the presence of the stratospheric absorber might be correlated with the incident flux from the star at the sub-stellar point on the planet, the precise level of which is yet to be refined."
 The presence of au iracdiation-iuduced stratospheric absorber las Όσοι sugeested by Burrowsctal.(2007a) for (see our Fie. £)), The presence of an irradiation-induced stratospheric absorber has been suggested by \citet{burr07} for (see our Fig. \ref{fig:comp}) )
 with a sub-stellay fux of —1.07 < 10? erg en 78 bata distance ¢ = 0.015 AU., with a sub-stellar flux of $\sim$ 1.07 $\times$ $^9$ erg cm $^{-2}$ s $^{-1}$ at a distance $a$ = 0.045 AU.
 Interestingly. has a lower sub-stella fux of ~ (0.19 « 10? erg cin? s LÀ and a senüanajor axis of & = (0.0188 AU. but still manifests evidence for a thermal inversion.," Interestingly, has a lower sub-stellar flux of $\sim$ 0.49 $\times$ $^9$ erg cm $^{-2}$ s $^{-1}$ and a semi-major axis of $a$ = 0.0488 AU, but still manifests evidence for a thermal inversion."
 A recent study of the broadband infrared spectiuii of (see our Fig. 1)), A recent study of the broadband infrared spectrum of (see our Fig. \ref{fig:comp}) )
 bv Charbonneauctal. finds no evidence for an atmospheric thermal inversion. despite a similar sub-stellar point flix of ~ οι « 10? ere cni 2 (Burrowsetal.20075) with a sinaller senaanajor axis & = 0.0313 AU.," by \citet{charb08} finds no evidence for an atmospheric thermal inversion, despite a similar sub-stellar point flux of $\sim$ 0.47 $\times$ $^9$ erg cm $^{-2}$ s $^{-1}$ \citep{burr07b} with a smaller semi-major axis $a$ = 0.0313 AU."
 Further study of planetary atimospheres should refine the concept of this sub-stellar flux boundary with respect to the presence/abseuce of a stratospheric absorber aud thermal inversion., Further study of planetary atmospheres should refine the concept of this sub-stellar flux boundary with respect to the presence/absence of a stratospheric absorber and thermal inversion.
 Atinospheric water detection las been claimed in the transit broadbaud spectra of by Tinettial.(2007) and inits secondary eclipse spectra by Fortuey&Marley (2007)., Atmospheric water detection has been claimed in the transit broadband spectra of by \citet{tin07} and in its secondary eclipse spectra by \citet{fort07}.
.. Burrowsetal.(2007a) also. found evidence for water vapor cinission iu the atimosphere of209155b., \citet{burr07} also found evidence for water vapor emission in the atmosphere of.
. Our data can be interpreted as evidence for rovibrational band of water emission lougward of ~ 1.0 ΠΠΤΟΝ. Which manifests itself as a flux cuhancement iu Fie.," Our data can be interpreted as evidence for rovibrational band of water emission longward of $\sim$ 4.0 microns, which manifests itself as a flux enhancement in Fig."
 3. compared to the cloudless model., \ref{fig:atmo} compared to the cloudless model.
" The depth of the flux ratio trough near the 3.6 micron channel in the atmospheric models withstratospheric absorber stronely depends on the redistribution paramcter P, (Burrowsot"," The depth of the flux ratio trough near the 3.6 micron channel in the atmospheric models withstratospheric absorber strongly depends on the redistribution parameter $_{n}$ \citet{burr07b},"
stellar mass.,stellar mass.
 The bivariate luminosity function is shown in Figure 4.., The bivariate luminosity function is shown in Figure \ref{fig:BLF}.
 The most. striking feature of the bivariate luminosity function is the strong mass dependence of the radio loud fraction (equal to the cumulative fraction in the lowest radio luminosity bin)., The most striking feature of the bivariate luminosity function is the strong mass dependence of the radio loud fraction (equal to the cumulative fraction in the lowest radio luminosity bin).
 This result was also found by Best (2005h).. with the radio loud fraction fr-xALY.," This result was also found by Best \shortcite{Paper2}, with the radio loud fraction $f_{RL} \propto \Mstar\/^{1.8}$."
 A vital question is whether this implies that in the more massive hosts the radio sources are on for longer. or whether they are simply triggered more frequently. (with the duration of a tvpical active phase being the same for all masses)," A vital question is whether this implies that in the more massive hosts the radio sources are on for longer, or whether they are simply triggered more frequently (with the duration of a typical active phase being the same for all masses)."
 We address this question in subsequent sections hy emploving detailed radio source mocdeling., We address this question in subsequent sections by employing detailed radio source modeling.
 We model radio loud AGNs as an evolutionary phase in the lifetime of every galaxy., We model radio loud AGNs as an evolutionary phase in the lifetime of every galaxy.
" Phe source is radio loud when the svichrotron jet is ""on: and once it switches oll or the source Luminosity [alls below the detection threshold. the source becomes radio quiet."," The source is radio loud when the synchrotron jet is “on”; and once it switches off or the source luminosity falls below the detection threshold, the source becomes radio quiet."
" We assume the black hole mass is already in place when the jet switches on. consistent with results of various semianalvtie models (e.g. Ixaullmann Lachnelt 2000: Bower 2006: Croton 2006) ancl observed black hole accretion rates in. quasars (llopkinsetal.2006:Yu&‘Tremaine2003). and hence jet injection is represented. by a top hat function. with the durations of on and olf phases denoted as £4, and f."," We assume the black hole mass is already in place when the jet switches on, consistent with results of various semianalytic models (e.g. Kauffmann Haehnelt 2000; Bower 2006; Croton 2006) and observed black hole accretion rates in quasars \cite{HopkinsEA06,YuTremaine03}, and hence jet injection is represented by a top hat function, with the durations of on and off phases denoted as $\tOn\/$ and $\tOff\/$."
 To account for the initial rise in the source radio power. we assume the source initially evolves in a [lat atmosphere (such as a galaxy core). followed by two power-law profiles of the form ptr)=pis{-}' corresponding to expansion within a galaxy. followed by a steeper cluster atmosphere (see Figure 5)).," To account for the initial rise in the source radio power, we assume the source initially evolves in a flat atmosphere (such as a galaxy core), followed by two power-law profiles of the form $\rho (r) = \rhoCore\/ \left( \frac{r}{\rCore\/} \right)^{-\beta}$ corresponding to expansion within a galaxy, followed by a steeper cluster atmosphere (see Figure \ref{fig:atmosphere}) )."
 We adopt the models of Xlexander (2000) for the initial evolution within the core. anc IWaiser Alexander (1997). and Ixalser (1997) for evolution in a power-law profile.," We adopt the models of Alexander \shortcite{Alexander00} for the initial evolution within the core, and Kaiser Alexander \shortcite{KA97} and Kaiser \shortcite{KDA97} for evolution in a power-law profile."
 As the racio source ages. it will sulfer aciabatic. svnchrotron and inverse Compton losses.," As the radio source ages, it will suffer adiabatic, synchrotron and inverse Compton losses."
 Once energy supply from the jet ceases. we assume the radio luminosity quickly drops to à value below our detection threshold.," Once energy supply from the jet ceases, we assume the radio luminosity quickly drops to a value below our detection threshold."
" In. practice. the cocoon will enter a ""coasting phase (kaiser&Cotter2002): however the radio Luminosity declines rapidly in this phase. rendering our approach sulficientIy accurate."," In practice, the cocoon will enter a “coasting” phase \cite{KaiserCotter02}; however the radio luminosity declines rapidly in this phase, rendering our approach sufficiently accurate."
 These models describe the evolution of powerful (ETIv- radio sources., These models describe the evolution of powerful (FR-II) radio sources.
 Although our sample consists of both these objects and the less powerful EIt-IEs. our approach is justified in the following sections bv the relative paucity of resolved sources with FR-L morphologies.," Although our sample consists of both these objects and the less powerful FR-Is, our approach is justified in the following sections by the relative paucity of resolved sources with FR-I morphologies."
 For an active jet. source size and radio luminosity are functions of core density p core radius r. transition radius Moa. between the galaxy ancl cluster power laws. density exponents Sou. and Oya. jet opening angle 6 (related to the axial ratio Ay of the source) ancl jet. power Qiao.," For an active jet, source size and radio luminosity are functions of core density $\rhoCore\/$ , core radius $\rCore\/$ , transition radius $\rTrans\/$ between the galaxy and cluster power laws, density exponents $\betaGalaxy\/$ and $\betaCluster\/$, jet opening angle $\theta$ (related to the axial ratio $\RT\/$ of the source) and jet power $\Qjet\/$."
 In adopting values for these parameters we are guided by observations of nearby. X-ray luminous elliptical galaxies ancl relaxed: clusters., In adopting values for these parameters we are guided by observations of nearby X-ray luminous elliptical galaxies and relaxed clusters.
 In. the inner regions (Allenοἱal. 2006).. power law exponents 3 O.8-1.2 and core radius Moe09l1 kpe provide a good fit tor10 kpe.," In the inner regions \cite{AllenEA06}, power law exponents $\beta \sim 0.8$ $1.2$ and core radius $\rCore\/ \sim 1$ kpc provide a good fit to $r \sim 10$ kpc."
 Density profiles of nearby. relaxed. galaxy clusters (Vikhlininctal.2006) are welblitted by a double power-law. with inner regions having hone.~ OS-Ld. and μον 018-26.," Density profiles of nearby relaxed galaxy clusters \cite{VikhlininEA06} are well-fitted by a double power-law, with inner regions having $\betaGalaxy\/ \sim 0.8$ $1.1$, and $\betaCluster\/ \sim 1.8$ $2.6$ ."
 ‘Transition between the two power laws occurs at ria.«50- 200 kpe., Transition between the two power laws occurs at $\rTrans\/ \sim 50$ $200$ kpc.
" As Figure ο illustrates. racio source tracks in the »»wer-size(P-D) plane are rather flat and henee not. very sensitive to the exact value of fig, For OS<uuu1.2 until the late phases (1 a few times LO” vears) of their ifetimes. when the sources begin to suller appreciably from inverse Compton losses (Ixaiseretal.1997). and/or enter the steeper partofthe atmosphere."," As Figure \ref{fig:exampleTracks} illustrates, radio source tracks in the power-size(P-D) plane are rather flat and hence not very sensitive to the exact value of $\betaGalaxy\/$ for $0.8 \leq \betaGalaxy\/ \leq 1.2$ until the late phases $1-$ a few times $10^8$ years) of their lifetimes, when the sources begin to suffer appreciably from inverse Compton losses \cite{KDA97} and/or enter the steeper partofthe atmosphere."
 At that point. the losses will vpically be the dominant factor indetermining the radio yower of the source.," At that point, the losses will typically be the dominant factor indetermining the radio power of the source."
 This allows us to Gx os.= 1.0. Joe=19 and uu.=50 in kpeour models.," This allows us to fix $\betaGalaxy\/=1.0$ , $\betaCluster\/=1.9$ and $\rTrans\/=50$ kpc in our models."
 Conservation, Conservation
Anv of the four solutions to the equivalent fourth-order polynomial must be a solution ol either equation CÀ4)) or (A5)). and the number or nature of the roots of each equation can change only at the eritical points outlined above.,"Any of the four solutions to the equivalent fourth-order polynomial must be a solution of either equation \ref{etam_eq}) ) or \ref{etap_eq}) ), and the number or nature of the roots of each equation can change only at the critical points outlined above."
" The roots correspondingto equation (A4)) are shown in Figure 4.. for an array of /1,4/ {ου equivalently |£—7) values. given 1C—d (a). and ji=LO (b). and AH,=7/3."," The roots correspondingto equation \ref{etam_eq}) ) are shown in Figure \ref{chandra_fig}, for an array of $H_d / H_g$ (or equivalently $|\xi-\eta|$ ) values, given $\mu=1$ (a), and $\mu=10$ (b), and $k_y H_d=\pi/3$."
" On the left the diagrams in Figure 4.. al small 77;/11, (or on the right of Figure LH... at large |£— j|). there is a pair of complex roots."," On the left the diagrams in Figure \ref{chandra_fig}, at small $H_d / H_g$ (or on the right of Figure \ref{chandra_plot_fig}, at large $|\xi - \eta|$ ), there is a pair of complex roots."
" In Figure tbh. these two complex roots become real as |£—i| becomes less than £,—ip since then a |£—7|=const. line crosses the P- and S-branches four times. implying all four roots are real."," In Figure \ref{chandra_fig}b b, these two complex roots become real as $|\xi-\eta|$ becomes less than $\xi_t - \eta_t$ since then a $|\xi-\eta|=const.$ line crosses the $P$ - and $S$ -branches four times, implying all four roots are real."
 Moving further risht in Figure tbh (or left in Figure 11)). one of those roots becomes complex when |£—|«€2+y. and the other real root disappears when |£—j|<9 my.," Moving further right in Figure \ref{chandra_fig}b b (or left in Figure \ref{chandra_plot_fig}) ), one of those roots becomes complex when $|\xi-\eta| < \beta+\eta_0$, and the other real root disappears when $|\xi-\eta| < \beta-\eta_0$ ."
 In Figure daa. at lower jc a complex root is present whenever a real root exists.," In Figure \ref{chandra_fig}a a, at lower $\mu$, a complex root is present whenever a real root exists."
 At the far right in Figures daa and 4bb (corresponding to the region of Figure Ll with |£—7|< i). there are no solutions.," At the far right in Figures \ref{chandra_fig}a a and \ref{chandra_fig}b b (corresponding to the region of Figure \ref{chandra_plot_fig} with $|\xi-\eta| < \eta_0$ ), there are no solutions."
 There is a range of values of |£—j| with all real solutions (implying stability for that set of parameters) if the P-branch has a section with |di/d£|<1., There is a range of values of $|\xi-\eta|$ with all real solutions (implying stability for that set of parameters) if the $P$ -branch has a section with $|\dif\eta/\dif\xi|<1$.
 When that happens (as for the po=10 case of Figure 4bb). the points of the P-branch with |di/d£|=1 lie very close to the (2.=) and (£5.0) points.," When that happens (as for the $\mu=10$ case of Figure \ref{chandra_fig}b b), the points of the $P$ -branch with $|\dif\eta/\dif\xi|=1$ lie very close to the $(\beta,-\eta_0)$ and $(\xi_0,0)$ points."
 So. a good approximation for the opening of such stability eap is £y>9+ayy.," So, a good approximation for the opening of such stability gap is $\xi_0 > \beta+\eta_0$."
 While it is straightforward to find a precise criterion for the existence of (his gap. il is of limited practical signilicance since the gap closes lor longer wavelengths (whieh vield more efficient vertical mixing).," While it is straightforward to find a precise criterion for the existence of this gap, it is of limited practical significance since the gap closes for longer wavelengths (which yield more efficient vertical mixing)."
 We consider more significant the fact that there are no solutions. real or complex. for |£—5|< my. since this vields a necessary (but. not sufficient)condition for instability.," We consider more significant the fact that there are no solutions, real or complex, for $|\xi-\eta|<\eta_0$ , since this yields a necessary (but not sufficient)condition for instability."
center of M31 (Davidee 2001). where (here are spectroscopic signatures of an intermediate age population (e.g. Davidee 1997: SillChenko. Durenkov. Vlasvuk 1998).,"center of M31 (Davidge 2001), where there are spectroscopic signatures of an intermediate age population (e.g. Davidge 1997; Sil'Chenko, Burenkov, Vlasyuk 1998)."
 Adopting a distance modulus for the Galactie Center of 14.5. then the two brightest AGB stars in the sample of Galactic Bulee stars studied by Frogel Whitlord (1987). which are numbers 239 and 181 in their target list. have My between 9 ancl 9.5.," Adopting a distance modulus for the Galactic Center of 14.5, then the two brightest AGB stars in the sample of Galactic Bulge stars studied by Frogel Whitford (1987), which are numbers 239 and 181 in their target list, have $_K$ between –9 and –9.5."
 Many of the brightest ACB stars in M32 are LPVs with amplitudes of 1.0 magnitude in A (Davidge Rigaut 2004). ancl so the non-variable AGD-tip in M32 corresponds to Mj22—8.5.," Many of the brightest AGB stars in M32 are LPVs with amplitudes of 1.0 magnitude in $K$ (Davidge Rigaut 2004), and so the non-variable AGB-tip in M32 corresponds to $_K \approx -8.5$."
 Isochrones with solar metallicity from the compilation discussed by Girardi et al. (, Isochrones with solar metallicity from the compilation discussed by Girardi et al. (
2002) indicate that this AGB-tip brightness is appropriate for a svsten with an age (hat is in excess of 1 Gyr. in agreement with studies of the integrated spectrum of M32 (O'Connell 1950: Davidge 1990: Dica. Alloin. Schmidt 1990: del Durgo et al.,"2002) indicate that this AGB-tip brightness is appropriate for a system with an age that is in excess of 1 Gyr, in agreement with studies of the integrated spectrum of M32 (O'Connell 1980; Davidge 1990; Bica, Alloin, Schmidt 1990; del Burgo et al."
 2001: Worthey. 2004: Rose et al., 2001; Worthey 2004; Rose et al.
 2005)., 2005).
 In the present study. three locations that are dominated bv lieht [rom one star are identified in the central arcsec of M32. while a fourth location that is dominated by light from two stars that have very different. velocities is also identified.," 	In the present study, three locations that are dominated by light from one star are identified in the central arcsec of M32, while a fourth location that is dominated by light from two stars that have very different velocities is also identified."
 These are the closest-in individual stars {ο be detected near the center of M32 al visible/near-intrarecl wavelengths., These are the closest-in individual stars to be detected near the center of M32 at visible/near-infrared wavelengths.
 While five stus constitute an obviously limited sample. the data are sufficient to demonstrate the application of the technique.," While five stars constitute an obviously limited sample, the data are sufficient to demonstrate the application of the technique."
 Even though the number of sources that are dominated by a single star and (hat can be identified at (he diffraction limit of an 3 metre telescope near the center of nearby galaxies like M32 is modest. a 20 30 metre telescope that delivers moderately high Strehl ratios should be able to detect roughly an order of magnitude more resolved sources.," Even though the number of sources that are dominated by a single star and that can be identified at the diffraction limit of an 8 metre telescope near the center of nearby galaxies like M32 is modest, a 20 – 30 metre telescope that delivers moderately high Strehl ratios should be able to detect roughly an order of magnitude more resolved sources."
 The data used in this paper were discussed previously by Davidge οἱ al. (, 	The data used in this paper were discussed previously by Davidge et al. (
2008) in their investigation of cE galaxies.,2008) in their investigation of cE galaxies.
 In briel. spectra of M32. were recorded with NIFS+ALTAIR on Gemini North (GN) on the night of October 23. 2005 during NIFS commissioning.," In brief, spectra of M32 were recorded with $+$ ALTAIR on Gemini North (GN) on the night of October 23, 2005 during NIFS commissioning."
 ALTAIR (Herriot et al., ALTAIR (Herriot et al.
 2000) is the facilitv AO svstem at GN. while NIFS (MeGregor οἱ al.," 2000) is the facility AO system at GN, while NIFS (McGregor et al."
 2003) is an integral field spectrograph for use in the 0.9— 2.5jmi wavelength interval., 2003) is an integral field spectrograph for use in the $0.9 - 2.5\mu$ m wavelength interval.
 NIFS samples a 3xJ arcsec? area on the skv with 29 0.1x3 arcsec? slitlets., NIFS samples a $3 \times 3$ $^2$ area on the sky with 29 $0.1 \times 3$ $^2$ slitlets.
 A spectrum with a dispersion 5300 is recorded on the 2048x ILAWAILI-2RG IIgC«lTe detector in one of three C/.H. or A) almospheric windows during a single exposure.," A spectrum with a dispersion 5300 is recorded on the $2048 \times 2048$ HAWAII-2RG HgCdTe detector in one of three $J, H$, or $K$ ) atmospheric windows during a single exposure."
 The bright semi-stellar nucleus of M32 served as the reference source for AO correction., 	The bright semi-stellar nucleus of M32 served as the reference source for AO correction.
 six GOO sec exposures were recorded in (he A —band. and each observation of M32. was Followed by that of a blank sky field.," Six 600 sec exposures were recorded in the $K-$ band, and each observation of M32 was followed by that of a blank sky field."
 Each M32 + sky. pair was differenced. and (he results were clivided by a flat-field frame.," Each M32 $+$ sky pair was differenced, and the results were divided by a flat-field frame."
 The flat-fielded data were wavelength calibrated using an, The flat-fielded data were wavelength calibrated using an
analysed using the CLAO version 2.1 and 2.2.,analysed using the CIAO version 2.1 and 2.2.
 The data were taken with the chip at a temperature of -120C and were gain-corrected using acisD2000-01-29gainNO003.[its [rom the July 2001 recalibration., The data were taken with the chip at a temperature of -120C and were gain-corrected using acisD2000-01-29gainN0003.fits from the July 2001 recalibration.
 The observation was relatively unalfected by background flares ancl only a small amount of exposure was removed. leaving an effective exposure (ime of 551565.," The observation was relatively unaffected by background flares and only a small amount of exposure was removed, leaving an effective exposure time of 55756s."
 Asiromelrv was corrected using a revised geometry file (telDI999-07-22ge0mNO004.(its) which is believed to provide positions across the full ACIS field accurate to about 1 arcsecond., Astrometry was corrected using a revised geometry file (telD1999-07-23geomN0004.fits) which is believed to provide positions across the full ACIS field accurate to about 1 arcsecond.
 The standard sereening (good. (ime intervals ancl grade filtering for grades 0.2.4.5.6) was applied to generate a cleaned event file.," The standard screening (good time intervals and grade filtering for grades 0,2,4,5,6) was applied to generate a cleaned event file."
 The X-ravs [rom Arp 220 extend over 20 kpe (Paper II). but emission above 2 keV is restricted to the central few kpe.," The X-rays from Arp 220 extend over 20 kpc (Paper II), but emission above 2 keV is restricted to the central few kpc."
 Figure 1 is a true X-ray color image of the Arp 220 nuclear region., Figure \ref{fig1} is a true X-ray color image of the Arp 220 nuclear region.
 Π was smoothed in separate bands of 0.2-1 (red). 1-2 (green) and 2-10 keV. (blue) using the CIAO adaptive smoothing routinecsmoofh.," It was smoothed in separate bands of 0.2-1 (red), 1-2 (green) and 2-10 keV (blue) using the CIAO adaptive smoothing routine."
 The image shows that the nuclear region of Arp 220 is clearly distinguished [rom the rest of the object by being the site of much harder emission., The image shows that the nuclear region of Arp 220 is clearly distinguished from the rest of the object by being the site of much harder emission.
 The centroid of the soft emission is displaced 1.5 arcseconds to the northwest of (he haud emission., The centroid of the soft emission is displaced 1.5 arcseconds to the northwest of the hard emission.
 The hard emission coincides with a cust lane in the galaxy (Jov et al., The hard emission coincides with a dust lane in the galaxy (Joy et al.
 1936). and indeed the soft emission is suppressed there.," 1986), and indeed the soft emission is suppressed there."
 ILowever. the absence of hard. emission away from the nucleus shows that the spectral change is due to a different (wpe of source. and nol merelv an absorption effect.," However, the absence of hard emission away from the nucleus shows that the spectral change is due to a different type of source, and not merely an absorption effect."
 Figure 2. shows an image of the hard. emission (>4 keV) coming from the nuclear regions of Arp 220. together with circles indicating the area within 1” of the well-studied dual radio and IH. nuclei (see eg.," Figure \ref{fig2} shows an image of the hard emission $>4$ keV) coming from the nuclear regions of Arp 220, together with circles indicating the area within 1” of the well-studied dual radio and IR nuclei (see eg."
 Scoville et al., Scoville et al.
 1993)., 1998).
 The positional matehi between. the racdio/IH. nuclei aud the hard emission is 1. within the expected. pointing accuracy of Chandra. (," The positional match between the radio/IR nuclei and the hard emission is $\sim$ 1”, within the expected pointing accuracy of Chandra. ("
The surprising lack of detections of USNO stars in the field limits our ability to improve the astrometric accuracy. but (hree galaxies are found within one arcsecond of (heir published positions.),"The surprising lack of detections of USNO stars in the field limits our ability to improve the astrometric accuracy, but three galaxies are found within one arcsecond of their published positions.)"
 Previous observations of Arp 220 have shown the presence of hard emission. using. for example. Beppo/SAX (Iwasawa et al.," Previous observations of Arp 220 have shown the presence of hard emission, using, for example, Beppo/SAX (Iwasawa et al."
 2001)., 2001).
 ILowever. it is only with the angular resolution ol Chandra that we have been able to localise some of this emission to the region of the," However, it is only with the angular resolution of Chandra that we have been able to localise some of this emission to the region of the"
The distance moduli obtained based on several independent theoretical ancl empirical calibrations are consistent.,The distance moduli obtained based on several independent theoretical and empirical calibrations are consistent.
 The maximum difference of 0.04 mag between the results [rom the calibrations of Sollima et al. (, The maximum difference of 0.04 mag between the results from the calibrations of Sollima et al. (
2008) and Bono et al. (,2008) and Bono et al. (
20035) is certainly not significant taking into account all uncertainties. which affect the whole process of constructing the mentioned calibrations.,"2003b) is certainly not significant taking into account all uncertainties, which affect the whole process of constructing the mentioned calibrations."
 ILowever. i( is interesting to note that a very. similar difference between the distance moduli derived using these two calibrations was recently obtained by Pietrzvisski οἱ al. (," However, it is interesting to note that a very similar difference between the distance moduli derived using these two calibrations was recently obtained by Pietrzyńsski et al. ("
2008) for the Sculptor galaxy (ΡΟΗ)=—1.83 dex).,2008) for the Sculptor galaxy $[Fe/H] = -1.83$ dex).
 Therefore. perhaps there is just a zero point offset in the sense that the distances from the calibration of Sollima et al. (," Therefore, perhaps there is just a zero point offset in the sense that the distances from the calibration of Sollima et al. ("
2008) are slightly shorter compared {ο those from the calibration of Bono et al. (,2008) are slightly shorter compared to those from the calibration of Bono et al. (
2003b).,2003b).
 Taking into account (he errors associated with the adopted calibrations. mean metallicity. photonmetric zero point and absorption correction. we estimate (he svstematic error of our distance determination to be of 0.11 mag.," Taking into account the errors associated with the adopted calibrations, mean metallicity, photometric zero point and absorption correction, we estimate the systematic error of our distance determination to be of 0.11 mag."
 Therelore our best distance modulus determination to the LMC is: 18.5840.03 (statistical) 0.11 (svstematic) mag., Therefore our best distance modulus determination to the LMC is: $18.58 \pm 0.03$ (statistical) $\pm 0.11$ (systematic) mag.
 It is worthwhile to mention that the observed fields are located not only close to the LMC center. but also opposite each other around il. so the corrections for the (ilt. of this ealaxv with respect to the line of sight are expected to be very small.," It is worthwhile to mention that the observed fields are located not only close to the LMC center, but also opposite each other around it, so the corrections for the tilt of this galaxy with respect to the line of sight are expected to be very small."
 Indeed applying the geometrical model of van der Marel et al. (, Indeed applying the geometrical model of van der Marel et al. (
2002) to correct our data lor this effect. we obtain a distance modulus shorter by 0.01 mag.,"2002) to correct our data for this effect, we obtain a distance modulus shorter by 0.01 mag."
 Comparing our distance result [rom the present field RIS Lyrae stars (to (he distance obtained by DallOra el al. (, Comparing our distance result from the present field RR Lyrae stars to the distance obtained by Dall'Ora el al. (
2004) for the Reticulum cluster. (here is evidence that the cluster could be very slightly nearer than the LAIC center. by about3%.. but this small difference is clearly within the combined uncertainties. even the statistical ones. of both determinations.,"2004) for the Reticulum cluster, there is evidence that the cluster could be very slightly nearer than the LMC center, by about, but this small difference is clearly within the combined uncertainties, even the statistical ones, of both determinations."
 Very recently Sollima et al. (, Very recently Sollima et al. (
2008). using (their calibration ancl the I. data of a sample of RRL stars presented by Borissova et al. (,"2008), using their calibration and the IR data of a sample of RRL stars presented by Borissova et al. ("
2004). obtained a distance modulus to the LMC of 18.5640.18 mag.,"2004), obtained a distance modulus to the LMC of $18.56 \pm 
0.13$ mag."
 Our distance moduli derived based on this same calibration are virtually ihe same. which reinforces both results.," Our distance moduli derived based on this same calibration are virtually the same, which reinforces both results."
 Our distance modulus agrees verv well with the most LMC distance moduli derived [rom other independent techniques (Freecinan et al., Our distance modulus agrees very well with the most LMC distance moduli derived from other independent techniques (Freedman et al.
 2001: Benedict et al., 2001; Benedict et al.
 2002: Walker 2003)., 2002; Walker 2003).
 In parücular this result is very similar to the measurements obtained based on the near infrared photometry of Cepheids (Persson et al., In particular this result is very similar to the measurements obtained based on the near infrared photometry of Cepheids (Persson et al.
 2004) and the red elump stars (Alves et al., 2004) and the red clump stars (Alves et al.
 2002: Grocholski Sarajedini 2002; Pieltrzvisski Gieren 20024)., 2002; Grocholski Sarajedini 2002; Pietrzyńsski Gieren 2002a).
condition where wo—κο Is the augular velocity of the zero angular momentum observer with respect to distant observers aud the subscript “A” means the quantities at the Alfvénn point.,condition where $\omega\equiv -g_{t\phi}/g_{\phi\phi}$ is the angular velocity of the zero angular momentum observer with respect to distant observers and the subscript “A” means the quantities at the Alfvénn point.
 Thus. the ratio of the otal angular nomoeutui to the total cuerey of the fow is detezuined by the location of the Alfvén point and Org.," Thus, the ratio of the total angular momentum to the total energy of the flow is determined by the location of the Alfvénn point and $\Omega_F$ ."
" When 0<Ogwy (classified as “type IT im Paper ID). where zi is the angular velocity of the lack hole. ene Alfvéun point A/"" or AC’? appears in the ru, plauc,"," When $0<\Omega_F<\omega_{\rm H}$ (classified as “type II” in Paper I), where $\omega_{\rm H}$ is the angular velocity of the black hole, Alfvénn point $^{in}$ or $^{out}$ appears in the $r$ $u_p$ plane."
" When «yp<OFΌμως (“type E] or Quin<Op<0 προ HE). Αντόν points AM” and AM""! appear. where O,, and O4 are the ini aud maximum augular frequency for the light surfaces to exist iu tlhe maguetosphere."," When $\omega_{\rm H}<\Omega_F<\Omega_{\rm max}$ (“type I”) or $\Omega_{\rm min}< \Omega_F< 0$ (“type III”), Alfvénn points $^{in}$ and $^{in/out}$ appear, where $\Omega_{\rm min}$ and $\Omega_{\rm max}$ are the minimum and maximum angular frequency for the light surfaces to exist in the magnetosphere."
 If two Alfvén volts appear in tle εν plauc. the pbysieal flow solution passes through one of them.," If two Alfvénn points appear in the $r$ $u_p$ plane, the physical flow solution passes through one of them."
" The Alfvóun point abeled by ""Z9 or ""out corresponds to inside or outside the separation poiut r=ry (SP) which is defined rv n!—0.", The Alfvénn point labeled by ” or ” corresponds to inside or outside the separation point $r=r_{\rm sp}$ ) which is defined by $\alpha'=0$.
" Atr=ry, the gravitational force aud the centrifugal force on plasma are balanced if the poloidal velocity of the plasma is zero. hence the teria separation point."," At $r=r_{\rm sp}$, the gravitational force and the centrifugal force on plasma are balanced if the poloidal velocity of the plasma is zero, hence the term separation point."
 Although the Alfvénn point is classified iuto three types. one can interpret that the MIID flow of type 1. IL or IIT accretes outo a slow-rotatiug. rapid-rotating or counterrotating black hole. respectively. when the value of Of is specified.," Although the Alfvénn point is classified into three types, one can interpret that the MHD flow of type I, II or III accretes onto a slow-rotating, rapid-rotating or counter-rotating black hole, respectively, when the value of $\Omega_F$ is specified."
 From equations (10)) and (16)). we can express the total cucrey £ aud the total augular momentum £L as functions of the Alfvénn radius aud the injection point as follows: where €=οOpL>0 cau he specified at the plana injection point aud the Alfvéun point.," From equations \ref{eq:pol-eq}) ) and \ref{eq:AP}) ), we can express the total energy $E$ and the total angular momentum $L$ as functions of the Alfvénn radius and the injection point as follows: where ${\cal E} \equiv E-\Omega_F L > 0 $ can be specified at the plasma injection point and the Alfvénn point."
" The condition of a negative energv ATID accretion flow. (ges|ge,£g)4<0. is unchanged from the cold limit case (see Paper D."," The condition of a negative energy MHD accretion flow, $ (g_{tt}+g_{t\phi}\Omega_F)_{\rm A}<0 $, is unchanged from the cold limit case (see Paper I)."
 Therimal effects on the hot plazua flow are only included in &. aud modify the amplitiuce of the iugoius energy aud aneular momentum.," Thermal effects on the hot plasma flow are only included in ${\cal E}$, and modify the amplitude of the ingoing energy and angular momentum."
 For a physical solution for accretion outo a black hole. we also require that the critical conditions at both fast aud slow maguetosonic poiuts must be satisfied.," For a physical solution for accretion onto a black hole, we also require that the critical conditions at both fast and slow magnetosonic points must be satisfied."
 In this section. we discuss restrictions on the remaimine field-aligned parameters: we see that the locations of the fast aud slow maguctosouic points give the total energv audthe particle numberflux along the magnetic field lines.," In this section, we discuss restrictions on the remaining field-aligned parameters; we see that the locations of the fast and slow magnetosonic points give the total energy andthe particle numberflux along the magnetic field lines."
 The differeutial form: of the poloidal equation (10)) is written by (see Paper D) where, The differential form of the poloidal equation \ref{eq:pol-eq}) ) is written by (see Paper I) where
"most of the MIR dark clumps are larger than 30"" (see Table 1,, Cols. (","most of the MIR dark clumps are larger than $30\arcsec$ (see Table \ref{table:clumps}, Cols. ("
6) and (7)).,6) and (7)).
" Because dust continuum emission is optically thin at (sub)mm wavelengths, the 870 um radiation intensity is given by where Βα70(Τᾳ) is the Planck function with dust temperature Ta."," Because dust continuum emission is optically thin at (sub)mm wavelengths, the 870 $\mu$ m radiation intensity is given by where $B_{870}(T_{\rm d})$ is the Planck function with dust temperature $T_{\rm d}$."
" According to the Ossenkopf Henning (1994, hereafter OH94) dust model used in the present paper (see Sect."," According to the Ossenkopf Henning (1994, hereafter OH94) dust model used in the present paper (see Sect."
" 5.1 for more details), the ratio of dust opacities per unit dust mass at and 870 um, xs/Ks7o, and thus the correponding ratio of the optical thicknesses, Tg/Tg70, is about 865."," 5.1 for more details), the ratio of dust opacities per unit dust mass at and 870 $\mu$ m, $\kappa_8/\kappa_{870}$, and thus the correponding ratio of the optical thicknesses, $\tau_8/\tau_{870}$, is about 865."
 The obtained ratio is consistent with the results of Johnstone et al. (, The obtained ratio is consistent with the results of Johnstone et al. (
2003) and Ormel et al. (,2003) and Ormel et al. (
"2005), who found that (assuming Ty=15 K) «s/Ksso640 and 870, respectively.","2005), who found that (assuming $T_{\rm d}=15$ K) $\kappa_{8}/\kappa_{850}\sim640$ and 870, respectively."
" By using this ratio, and the rs values derived above, estimates for the dust temperatures, Ty, towards the submm peaks can be derived from Eq.( 5))."," By using this ratio, and the $\tau_8$ values derived above, estimates for the dust temperatures, $T_{\rm d}$, towards the submm peaks can be derived from Eq.( \ref{eq:flux}) )."
 The resulting values are listed in Col. (, The resulting values are listed in Col. (
4) or Table 4..,4) or Table \ref{table:extinction}.
 The quoted errors are the minimum-maximum errors derived from the uncertainty in Tg., The quoted errors are the minimum-maximum errors derived from the uncertainty in $\tau_8$.
" The uncertainties of the Ty estimates are very large in the southern part (SMM 1, SMM 2; in the case of SMM 3 and"," The uncertainties of the $T_{\rm d}$ estimates are very large in the southern part (SMM 1, SMM 2; in the case of SMM 3 and"
Dodelson 5.. M. Ixaplinghat IE. Stewart. Phys.,"Dodelson S., M. Kaplinghat E. Stewart, Phys."
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ATE 1307—294. in which both the spin and (win kIIz QPO Irequencies have been measured.,"XTE $-$ 294, in which both the spin and twin kHz QPO frequencies have been measured."
 The spin frequencies. disposed in Table 1. are from van der Ixlis (2006). Ménndez Belloni (2007). Yin et al. (," The spin frequencies, disposed in Table 1, are from van der Klis (2006), Ménndez Belloni (2007), Yin et al. ("
2007). Altamirano et al. (,"2007), Altamirano et al. ("
2008). and their references.,"2008), and their references."
 For 4U 06144-09 we adopt the updated spin frequency of 415 Hz (Strohiayer. Markwardt Ixuulkers 2008).," For 4U 0614+09 we adopt the updated spin frequency of 415 Hz (Strohmayer, Markwardt Kuulkers 2008)."
 The dots with error bars represent the measured values. ancl (he solid lines stand for theoretical relations.," The dots with error bars represent the measured values, and the solid lines stand for theoretical relations."
 We distinguish the νους vs. v/s relations for SSCS and LSCS. and accordingly adopt relation. (27) to fit the data for 4U 06144-09. 4U 1608—52. 4U 1686-53. and 4U 1128—34. and relation (23) for the other (wo sources. 4U 1915—05 and NTE —294.," We distinguish the $\nu_2/\nu_s$ vs. $\nu_1/\nu_s$ relations for SSCS and LSCS, and accordingly adopt relation (27) to fit the data for 4U $+$ 09, 4U $-$ 52, 4U $-$ 53, and 4U $-$ 34, and relation (28) for the other two sources, 4U $-$ 05 and XTE $-$ 294."
 For each source. (he value of 5 or 9 for best fitting is also shown in the figure.," For each source, the value of $\varepsilon$ or $\delta$ for best fitting is also shown in the figure."
 It is noted that a Cluster of the values (~0.3— 0.9) of £ and 9 can well reproduce the observed relations., It is noted that a cluster of the values $\sim 0.3-0.9$ ) of $\varepsilon$ and $\delta$ can well reproduce the observed relations.
 In the left panel of Fig., In the left panel of Fig.
 3 we show the observed and predicted relations for all of the six sources., 3 we show the observed and predicted relations for all of the six sources.
 In the right panel we plot the relation between «Ανως and v/v. bv use of the parameter z or ὁ that we have got., In the right panel we plot the relation between $\Delta\nu/\nu_s$ and $\nu_1/\nu_s$ by use of the parameter $\varepsilon $ or $\delta$ that we have got.
" For SSCS the peak separation of the (win kIIz QPOs is less than the spin frequency. ie. Av—p,-—-(1-—Εν--230,+νι)«0. and decreases with νι or ve: lor LSCS the peak separation is more than the spin frequency. ie. Av=(V1+02—1r9p,>νι. and increases with the increasing 74 or 75."," For SSCS the peak separation of the twin kHz QPOs is less than the spin frequency, i.e., $\Delta \nu - \nu _s = -( 1-1/\sqrt {1 +
\varepsilon ^2})(\nu _1 + \nu _s )< 0$, and decreases with $\nu_1$ or $\nu_2$; for LSCS the peak separation is more than the spin frequency, i.e., $\Delta \nu = (\sqrt {1 + \delta ^2} - 1)\nu _1 +
\nu _s > \nu _s$, and increases with the increasing $\nu_1$ or $\nu_2$."
" In the former group. Av is around v, lor 4U 06144-09 and 4U 1728-34. ind 7/2 lor 4U 1608—52 and 4U 1636—523 (Miller et al."," In the former group, $\Delta\nu$ is around $\nu_s$ for 4U $+$ 09 and 4U $-$ 34, and $\nu_s/2$ for 4U $-$ 52 and 4U $-$ 53 (Miller et al."
 1998: van der Ixlis 1997: Stella. Vietri Morsink 1999: Lewin van der Ixlis 2006: Mendez Belloni 2007).," 1998; van der Klis 1997; Stella, Vietri Morsink 1999; Lewin van der Klis 2006; M'endez Belloni 2007)."
 Our final note is that when the Alfveen speed is equal to the acoustic speed of the plasma. ie. a=A. Eq. (," Our final note is that when the Alfv́een speed is equal to the acoustic speed of the plasma, i.e. $ \eta= \lambda$, Eq. ("
26) will recover to the expression in (he sonic-point beat-frequency model (Miller οἱ al.,26) will recover to the expression in the sonic-point beat-frequency model (Miller et al.
 1998)., 1998).
 In this case the peak separation is equal to the spin Irequency and almost invariant., In this case the peak separation is equal to the spin frequency and almost invariant.
 In this paper we propose a resonant. MIID moclel for the twin kilohertz QPOs in LMXDs., In this paper we propose a resonant MHD model for the twin kilohertz QPOs in LMXBs.
 The modes of the MIID waves vertical and parallel to (he accretion disc are derived. and the twin kHz QPOs lrequencdes are identified with the lvequencies of the two resonant modes.," The modes of the MHD waves vertical and parallel to the accretion disc are derived, and the twin kHz QPOs frequencies are identified with the frequencies of the two resonant modes."
 In (his model the twin kIIz QPO Irequencies are correlated with (he spin frequencies. and the separation frequencies also change with the QPO frequencies.," In this model the twin kHz QPO frequencies are correlated with the spin frequencies, and the separation frequencies also change with the QPO frequencies."
 We show (hat the measured, We show that the measured
candidate classes. mpea and unid. to the least likely class. mpec.,"candidate classes, mpca and unid, to the least likely class, mpcc."
 Note that the fraction of EMP stars in class mpea is somewhat lower than that in class unid. probably due to the fact that turnoff metal-poor stars are rather weak-lined. making the divisions between these classes rather difficult.," Note that the fraction of EMP stars in class mpca is somewhat lower than that in class unid, probably due to the fact that turnoff metal-poor stars are rather weak-lined, making the divisions between these classes rather difficult."
 The numbers of targets in mpee is rather small (16). hence it is perhaps not surprising that no EMP stars were found in this class.," The numbers of targets in mpcc is rather small (16), hence it is perhaps not surprising that no EMP stars were found in this class."
 As discussed above. the MDF derived from our follow-up observations contains a significant bias towards the more metal-deficient candidates. and must be taken into account to recover a reasonable representation of the “true” MDF.," As discussed above, the MDF derived from our follow-up observations contains a significant bias towards the more metal-deficient candidates, and must be taken into account to recover a reasonable representation of the “true” MDF."
 Therefore. we adopted the sealing factor procedure described n Paper V. For each metal-poor class. the MDF of the observed candidates is scaled by a factor calculated from the division of the total number in the class by the observed number (as listec 1 the last column in Table 1)).," Therefore, we adopted the scaling factor procedure described in Paper V. For each metal-poor class, the MDF of the observed candidates is scaled by a factor calculated from the division of the total number in the class by the observed number (as listed in the last column in Table \ref{tab:mpclass}) )."
 Then the scaled MDFs of the four classes are co-added to produce a general MDF for the entire HES candidate sample., Then the scaled MDFs of the four classes are co-added to produce a general MDF for the entire HES candidate sample.
" Similarly to Paper V. the main ""Sifference between the directly observed and the scaled MDF is the increasing ratio of the relatively metal-rich stars in the mpeb and mpce classes."," Similarly to Paper V, the main difference between the directly observed and the scaled MDF is the increasing ratio of the relatively metal-rich stars in the mpcb and mpcc classes."
 The normalized fraction of the scalec MDF ts listed in the first column of Table 3.., The normalized fraction of the scaled MDF is listed in the first column of Table \ref{tab:TO_volume_MDF}.
 As pointed out in. Paper IV. and V. the combination of the KP index with or for the purpose to select metal-poor candidates in the HES has proven rather efficient.," As pointed out in Paper IV and V, the combination of the KP index with or for the purpose to select metal-poor candidates in the HES has proven rather efficient."
 Following the metallicity distribution predicted by the Simple Model. we apply our quantitative selection criteria to à simulated sample of metal-poor stars.," Following the metallicity distribution predicted by the Simple Model, we apply our quantitative selection criteria to a simulated sample of metal-poor stars."
 The results of the theoretical selection fractions shown in Figure 4.., The results of the theoretical selection fractions shown in Figure \ref{fig:selfrac}.
 The selection fractions for both and are shown., The selection fractions for both and are shown.
 It is clear that the selection criteria are able to reject the majority of stars with greater than —2.0., It is clear that the selection criteria are able to reject the majority of stars with greater than $-2.0$.
 For both colors. a high completeness (up to almost 100%)) is reached for stars with—3.," For both colors, a high completeness (up to almost ) is reached for stars with."
0.. ForV)o.. the redder candidates exhibit a larger selection fraction (due to less contamination from hot stars among the bluer candidates).," For, the redder candidates exhibit a larger selection fraction (due to less contamination from hot stars among the bluer candidates)."
 The selection fraction. however. does not differ much among the different cutoffs.," The selection fraction, however, does not differ much among the different cutoffs."
 This is as expected since the blue cutoff in 1s already fairly red so that fewer hot candidates enter the sample., This is as expected since the blue cutoff in is already fairly red so that fewer hot candidates enter the sample.
" As pointed out in. Paper V. for a magnitude-limited survey the relative survey volume explored by the observed stars differs with the stars"" metallicities. which could also be readily inferred from Figure 5.."," As pointed out in Paper V, for a magnitude-limited survey the relative survey volume explored by the observed stars differs with the stars' metallicities, which could also be readily inferred from Figure \ref{fig:YYiso}."
 Besides. as described in Section and Table 1.. the HES follow-up procedure ts basically a metallicity-biased survey. which favors candidates with lower metallicities.," Besides, as described in Section \ref{sec:sample} and Table \ref{tab:mpclass}, the HES follow-up procedure is basically a metallicity-biased survey, which favors candidates with lower metallicities."
 Thus it is interesting to investigate to what extent this effect could impact our sample and the resulting derived MDF., Thus it is interesting to investigate to what extent this effect could impact our sample and the resulting derived MDF.
 Moreover. we aim at deriving a corrected MDF that i5 metallicity/volume- unbiased suitable for the comparison with other observational results and theoretical models.," Moreover, we aim at deriving a corrected MDF that is metallicity/volume- unbiased suitable for the comparison with other observational results and theoretical models."
 The basic idea of this correction is to derive the survey volume for stars with different metallicities. referenced to a specific metallicity.," The basic idea of this correction is to derive the survey volume for stars with different metallicities, referenced to a specific metallicity."
" Here we adopt—2.0.. because it is near the peak of our sample. and also close to the metallicity above which we expect the observed MDF to deviate from the ""true"" MDF due to metallicity selection bias."," Here we adopt, because it is near the peak of our sample, and also close to the metallicity above which we expect the observed MDF to deviate from the “true” MDF due to metallicity selection bias."
 It is thus convenient for later comparisons (the choice of a different reference will not strongly affect the relative fraction of each bin of the corrected MDF)., It is thus convenient for later comparisons (the choice of a different reference will not strongly affect the relative fraction of each bin of the corrected MDF).
 Based on the definition of the survey volume. the corrected volume referenced to in a specific bin can be directly estimated from V.=ο...," Based on the definition of the survey volume, the corrected volume referenced to in a specific bin can be directly estimated from $V=10^{0.6(M_\mathrm{V}(ref)-M_\mathrm{V})}$."
 As for the turnoff sample. stars within a and bin could be either à MSTO star or a subgiant. which obviously explore different survey volumes.," As for the turnoff sample, stars within a and bin could be either a MSTO star or a subgiant, which obviously explore different survey volumes."
 Therefore. another step in the correction Is used to estimate the ratio of the MSTO stars to subgiants in the sample.," Therefore, another step in the correction is used to estimate the ratio of the MSTO stars to subgiants in the sample."
" Using the luminosity functions from the Y isochrones and assuming an IMF slope of x=1.35 (Salpeter index). for any specific and ""νε can obtain the number of stars per cubic parsec per absolute magnitude interval for both the MSTO and subgiant branches."," Using the luminosity functions from the $Y^2$ isochrones and assuming an IMF slope of $x=1.35$ (Salpeter index), for any specific and we can obtain the number of stars per cubic parsec per absolute magnitude interval for both the MSTO and subgiant branches."
 Hence a relative density ratio of MSTO stars versus subgiants for the sample is obtained., Hence a relative density ratio of MSTO stars versus subgiants for the sample is obtained.
 Given the relative number of MSTO stars and subgiants in each and bin. we can then obtain the corrected number of stars within a specific and bin by combining the volume and the fraction corresponding to the MSTO and subgiant stars.," Given the relative number of MSTO stars and subgiants in each and bin, we can then obtain the corrected number of stars within a specific and bin by combining the volume and the fraction corresponding to the MSTO and subgiant stars."
 Based on this procedure. we derive the volume-corrected MDF of the sample and compare it with the observed one.," Based on this procedure, we derive the volume-corrected MDF of the sample and compare it with the observed one."
about 4 magnitudes over the period. 2005 November and 2009 September.,about 4 magnitudes over the period 2005 November and 2009 September.
 In order to ect insight into the origin of the observed. variations we plotted colourmagnitude diagrams., In order to get insight into the origin of the observed variations we plotted colour--magnitude diagrams.
 Figure 2. (left) shows that the fading in 20052006 was nearly grev in the fe and do bands., Figure \ref{Fig_cmd} (left) shows that the fading in 2005–2006 was nearly grey in the $_\mathrm{C}$ and $_\mathrm{C}$ bands.
 ]ts reason may be that in minimum. whatever is the origin of the decline. the star itself is too [aint to. be detected. only the light scattered [rom the disc atmosphere. thus bluer in colour. can be observed.," Its reason may be that in minimum, whatever is the origin of the decline, the star itself is too faint to be detected, only the light scattered from the disc atmosphere, thus bluer in colour, can be observed."
 The transient. peal shows different colour variation: the star became redder and brighter and then bluer and fainter., The transient peak shows different colour variation: the star became redder and brighter and then bluer and fainter.
 This colour behaviour is characteristic of UN Orionis (UXor) type variables close to the light curve minima (e.g.Bibo&Thé1991).. and is attributed. to the increasing proportion of scattered. light when the star is obscured by a circumstellar dust. clump.," This colour behaviour is characteristic of UX Orionis (UXor) type variables close to the light curve minima \citep[e.g.][]{Bibo}, and is attributed to the increasing proportion of scattered light when the star is obscured by a circumstellar dust clump."
 This diagram suggests that the optical source in the dim phases (segments LL and IV. of the light. curve) was the starlight scattered: [rom the disc atmosphere., This diagram suggests that the optical source in the dim phases (segments II and IV of the light curve) was the starlight scattered from the disc atmosphere.
 During the low-brightness phase (filled. circles). PW Cop. was redder when fainter: this behaviour can result [rom either enhanced extinction or vanishing hot spots on the stellar surface due to the decreasing accretion rate., During the low-brightness phase (filled circles) PV Cep was redder when fainter: this behaviour can result from either enhanced extinction or vanishing hot spots on the stellar surface due to the decreasing accretion rate.
 In the rising phase the star turned brighter and redder. indicating that instead. of the scattered. light direct. light. [rom the central star could. be detected.," In the rising phase the star turned brighter and redder, indicating that instead of the scattered light direct light from the central star could be detected."
 The data obtained in 2010 indicate that the star completed. a full loop in this diagram from 2008 April to H0 April., The data obtained in 2010 indicate that the star completed a full loop in this diagram from 2008 April to 2010 April.
 The near-infrared data in Fig., The near-infrared data in Fig.
 2. (right) show that the facing in 20052006 was accompanied by a slight decrease ofthe Lfdy. colour index. indicative of decreasing emission from the cust sublimation zone of the disc. whereas an extinction change of elyc7 mag can account [for the photometric variations around the transient. peak in 2008.," \ref{Fig_cmd} (right) show that the fading in 2005–2006 was accompanied by a slight decrease of the $H-K_\mathrm{s}$ colour index, indicative of decreasing emission from the dust sublimation zone of the disc, whereas an extinction change of $A_\mathrm{V} \approx 7$ mag can account for the photometric variations around the transient peak in 2008."
 Phe different colour behaviour suggests the dillerent nature of the two brightness drops., The different colour behaviour suggests the different nature of the two brightness drops.
 Phe strong decrease of the 14IN. colour index at the bottom ofthe diagram. measured in 2009 October. clearly suggests the fall of the inner disc emission during the low-brightness phase.," The strong decrease of the $H-K_\mathrm{s}$ colour index at the bottom of the diagram, measured in 2009 October, clearly suggests the fall of the inner disc emission during the low-brightness phase."
 The data obtained. in the bright. fading. and rising phases of the light curve. CIable 42). allow us to. inspect. the wavelength. dependence of variations in the mid- and. far-infrared regions.," The data obtained in the bright, fading, and rising phases of the light curve (Table \ref{Tab_Spitzer}) ) allow us to inspect the wavelength dependence of variations in the mid- and far-infrared regions."
 We plotted in Fig., We plotted in Fig.
 3 the Iux ratios between the different segments of the light curve as a function of wavelength., \ref{Fig_deltaft} the flux ratios between the different segments of the light curve as a function of wavelength.
" In addition to our own measurements. the bright state dataalso include and A, data from Connelleyetal. (2008)... and the fading phase data set contains JA. data measured. on 2007. May. 13. (Lorenzettietal. 2009).. as well as the (Ishibaraetal.2010). fluxes at 9 and im. and catalog data"," In addition to our own measurements, the bright state dataalso include and $K_\mathrm{s}$ data from \citet{Connelley}, and the fading phase data set contains $_\mathrm{s}$ data measured on 2007 May 13 \citep{Lorenzetti09}, , as well as the \citep{Ishihara} fluxes at 9 and $\mu$ m, and catalog data"
evele with 12 spectra.,cycle with 12 spectra.
 In total. we obtained 251 spectra covering binary phases 0.2-1.0.," In total, we obtained $\times$ 251 spectra covering binary phases 0.2-1.0."
 Phe spectra were reduced using optimal extraction (Horne 1986) after debiasing and lat-fielding the CCD images., The spectra were reduced using optimal extraction (Horne 1986) after debiasing and flat-fielding the CCD images.
 Sky subtraction emploved rolvnomials [fitted to sky regions on either. side. of the object., Sky subtraction employed polynomials fitted to sky regions on either side of the object.
 Arc spectra were extracted from the same rows as he object ones., Arc spectra were extracted from the same rows as the object ones.
 The are lines drifted by <I dduring he observations., The arc lines drifted by $<1$ during the observations.
 Phe wavelength calibration was performed using CuNe and Cur arc lines for the red and blue spectra. respectively. and is accurate to 0.04AL.," The wavelength calibration was performed using CuNe and CuAr arc lines for the red and blue spectra, respectively, and is accurate to 0.04."
 A comparison star racl been included. in the slit which was subsequently. used o correct the object spectra for atmospheric and slit losses., A comparison star had been included in the slit which was subsequently used to correct the object spectra for atmospheric and slit losses.
 The absolute flux scale was defined by observing the Lux standard GI91D2D (Oke 1990)., The absolute flux scale was defined by observing the flux standard G191B2B (Oke 1990).
 The average spectrum. displaved in Fig.," The average spectrum, displayed in Fig."
 1. shows a wealth of emission lines. mainly Balmer. and.LL lines.," 1, shows a wealth of emission lines, mainly Balmer, and lines."
 Note the red CCD has 3 bad. columns which are marked on the red spectrum in Fig., Note the red CCD has 3 bad columns which are marked on the red spectrum in Fig.
 1., 1.
 The [ continuum increases redward. ring from 37.15-50.01. mw (4130-4180A)) tto S.33-EU.01 mJy (4750-4800A)).— tto. 9490.01 mv. 3650.4).," The $_{\nu}$ continuum increases redward, rising from $\pm$ 0.01 mJy ) to $\pm$ 0.01 mJy ) to $\pm$ 0.01 mJy )."
 Table 1 gives the integrated Ηχος (41000 km +. equivalent widths. and. EWLAIs of the emission lines.," Table 1 gives the integrated fluxes $\pm1000$ km $^{-1}$, equivalent widths, and FWHMs of the emission lines."
 The Bowen fluorescence lines at 4647 and NILL 4640 together with the 4686 line indicate a high temperature region (Schachter et al., The Bowen fluorescence lines at 4647 and NIII 4640 together with the 4686 line indicate a high temperature region (Schachter et al.
 1991)., 1991).
 In addition to 4686. we note lines from the Pickering series (see Fig.," In addition to 4686, we note lines from the Pickering series (see Fig."
 1)., 1).
 Odd-numbered lines are seen between the Balmer lines whereas he even-numbered lines of the Pickering series contribute but less than 19 per cent to the Dalmer-line. Duxes., Odd-numbered lines are seen between the Balmer lines whereas the even-numbered lines of the Pickering series contribute – but less than 13 per cent – to the Balmer-line fluxes.
 The Pickering series of are seen in some AM Iler-vpe systems (Schachter et al., The Pickering series of are seen in some AM Her-type systems (Schachter et al.
 1991: see also the spectrum of he magnetic nova V1500 €vg in Horne Schneider 1989)., 1991; see also the spectrum of the magnetic nova V1500 Cyg in Horne Schneider 1989).
 The lux ratio of the Pickering line. 4542. to that of 4686 is 0.10.," The flux ratio of the Pickering line, 4542, to that of 4686 is 0.10."
 This is within the ratio range 0.10-0.19 found in the AM Ller svstem E2003|225 (Alukai et al., This is within the ratio range 0.10-0.19 found in the AM Her system E2003+225 (Mukai et al.
 1986) rut very. clillerent from case B recombination (0.035: Seaton 1978)., 1986) but very different from case B recombination (0.035; Seaton 1978).
 Apparently. the density of the emission region must av an important role in this discrepancy.," Apparently, the density of the emission region must play an important role in this discrepancy."
 Still et al. (, Still et al. (
1998) obtained blue spectra of RX 0558|53 in December 1994 and red. spectra in. February 1995.,1998) obtained blue spectra of RX J0558+53 in December 1994 and red spectra in February 1995.
 There is a remarkable difference between our spectra and those of Still et al., There is a remarkable difference between our spectra and those of Still et al.
 Phe emission-line intensities in March 1995 have increased over those in February L995 by a factor of 3.3 for the Balmer lines and w 1.9 for (see Fig., The emission-line intensities in March 1995 have increased over those in February 1995 by a factor of 3.3 for the Balmer lines and by 1.9 for (see Fig.
 1 in Still et al)., 1 in Still et al.).
 The continuum also shows an increase of 1.9 times in the blue but only changes by 15 per cent in the red., The continuum also shows an increase of 1.9 times in the blue but only changes by 15 per cent in the red.
 ‘The time variations are shown in Fig., The time variations are shown in Fig.
 2 for the continuum bands. 6600-6650 aand 4750-4800 and for the Ha. 11.HL. emission lines.," 2 for the continuum bands 6600-6650 and 4750-4800 and for the $\alpha$, $\beta$, emission lines."
 Gaps in these light curves show times when arc spectra were obtained., Gaps in these light curves show times when arc spectra were obtained.
 We adopt the following orbital ephemeris (Lhorstensen 1997. private communication) TGD)=2449474.6446(15)|0.172624€(1)££ where 7; is the apparent inferior conjunction of the emission-line source (bluc-to-red crossing).," We adopt the following orbital ephemeris (Thorstensen 1997, private communication) $ T_{o}(HJD) = 2 449474.6446(15) + 0.172624(1)~E$ where $T_{o}$ is the apparent inferior conjunction of the emission-line source (blue-to-red crossing)."
 A correction of 0.1 evcles anti-clockwise (see 7) to the apparent inferior conjunction of the emission-line source gives. the inferior conjunction of the secondary star., A correction of 0.1 cycles anti-clockwise (see 7) to the apparent inferior conjunction of the emission-line source gives the inferior conjunction of the secondary star.
 In general. emission anisotropies on the disc can move away the inferior conjunction of the emission-line. source. from. the inferior conjunction of the secondary star (see. for example. IS Aqr: Robinson et al.," In general, emission anisotropies on the disc can move away the inferior conjunction of the emission-line source from the inferior conjunction of the secondary star (see, for example, AE Aqr; Robinson et al."
 1991: Welsh et al., 1991; Welsh et al.
 1993)., 1993).
 There is no eclipse or any large variation in the, There is no eclipse or any large variation in the
L describe four semi-analvtie models which make predictions for the amplitude of halo correlations. one due to Mo (1996. hereafter. AIW). one due to Sheth. Mo (1999 — hereafter. SMT). one due to Sheth and (1999 hereafter ST). and one based on a mocel bv Lee — (1998 hereafter LS) ancl extended: in ST.,"I describe four semi-analytic models which make predictions for the amplitude of halo correlations, one due to Mo \markcite{MW}
 (1996 – hereafter MW), one due to Sheth, Mo \markcite{SMT}
 (1999 – hereafter SMT), one due to Sheth and \markcite{ST}
 (1999 – hereafter ST), and one based on a model by Lee \markcite{LS} (1998 – hereafter LS) and extended in ST."
" The input parameters for these models are the power Es»ectrum. of matter fluctuations 264) (extrapolated using incar gravitv to today) and the background: cosmology of 10 universe (specified. here in terms of Oy, anc O4. the contributions of matter ancl a cosmological constant to the critical clensity toclay)."," The input parameters for these models are the power spectrum of matter fluctuations $P(k)$ (extrapolated using linear gravity to today) and the background cosmology of the universe (specified here in terms of $\Omega_{\rm m}$ and $\Omega_\Lambda$, the contributions of matter and a cosmological constant to the critical density today)."
 Lowill compare the predictions of 1ese mocels with observations of the halo correlation length πο(ο). defined such that ο)=1 where £(r) is the halo correlation Function.," I will compare the predictions of these models with observations of the halo correlation length $r_0(d)$, defined such that $\xi(r_0)=1$ where $\xi(r)$ is the halo correlation function."
" Also. d is the mean halo separation for 1f halo sample in question. and the sample is chosen to contain only those halos with ""richness"" greater than some value."," Also, $d$ is the mean halo separation for the halo sample in question, and the sample is chosen to contain only those halos with “richness” greater than some value."
" In this context Louse ""richness"" CR) to denote any xvameter which correlates with halo mass (typical examples or clusters are galaxy number counts and X-ray luminosity).", In this context I use “richness” ${\cal R}$ ) to denote any parameter which correlates with halo mass (typical examples for clusters are galaxy number counts and X-ray luminosity).
" ] will assume that the parameter # can be monotonically ransformed. into an ""inferred. mass” Mo=fÜR) which is correlated with the true mass with known conditional obabilitv pCA[A).", I will assume that the parameter $R$ can be monotonically transformed into an “inferred mass” ${\cal M}=f({\cal R})$ which is correlated with the true mass with known conditional probability $p({\cal M}|M)$.
 For each model. the procedure. for computing the correlation length for a sample of halos with mean separation d is as follows.," For each model, the procedure for computing the correlation length for a sample of halos with mean separation $d$ is as follows."
Iu radio poluiuetry. two orthogonal secuses of polarization are received aud propagated through separate signal paths.,"In radio polarimetry, two orthogonal senses of polarization are received and propagated through separate signal paths."
 Each signal therefore experiences a different series of amplification. attenuation. mixing. and filtering before sampling or detection is performed.," Each signal therefore experiences a different series of amplification, attenuation, mixing, and filtering before sampling or detection is performed."
 Whereas efforts are mace to match the componeuts of the observatory equiplucut. cach will realistically have a unique frequency response to the input signal.," Whereas efforts are made to match the components of the observatory equipment, each will realistically have a unique frequency response to the input signal."
 Even a simple uusimatch iu sienal path length will result iu a relative phase ditfereuce vetween the two polarizations that varics linearly with TYequencev., Even a simple mismatch in signal path length will result in a relative phase difference between the two polarizations that varies linearly with frequency.
 Iu fact. any plivsicallv realizable svstei will transform he radiation in a frequeney-dependent manner.," In fact, any physically realizable system will transform the radiation in a frequency-dependent manner."
 Where variations across the smallest bandwidth available may © considered uceleible. post-detection calibration aud correction techniques may be used to invert the ranstormation and recover the original polarimetric state.," Where variations across the smallest bandwidth available may be considered negligible, post-detection calibration and correction techniques may be used to invert the transformation and recover the original polarimetric state."
 However. the transformation may vary significantly: across the band. causing the polarization vector to conibine destructively when integrated iu frequency.," However, the transformation may vary significantly across the band, causing the polarization vector to combine destructively when integrated in frequency."
 This phenomenon is known as “bandwidth depolarization” of the signal. aud results iu irreversible decimation of the degree of polarization.," This phenomenon is known as “bandwidth depolarization” of the signal, and results in irreversible decimation of the degree of polarization."
 It is therefore desirable to perform polarimetric corrections at sufficicutly high spectral resolution. which is available onlv at the cost of temporal resolution uuless phase coliereuce is maintained.," It is therefore desirable to perform polarimetric corrections at sufficiently high spectral resolution, which is available only at the cost of temporal resolution unless phase coherence is maintained."
 Conventional post-detection correction techniques therefore prove msufBcieut when high time resolution is also a necessity., Conventional post-detection correction techniques therefore prove insufficient when high time resolution is also a necessity.
 For example. certain pulsar experiments require high time resolution iu order to resolve key features iu the average pulse profile.," For example, certain pulsar experiments require high time resolution in order to resolve key features in the average pulse profile."
 As well. it has been shown that insufficient time resolution can also lead to depolarization (Gaugadharactal1999).," As well, it has been shown that insufficient time resolution can also lead to depolarization \citep{gxv+99}."
. These considerations iotivate the development of a method for phasc-cohercut polarimetric trausformation., These considerations motivate the development of a method for phase-coherent polarimetric transformation.
 Further iupetus is provided by the growing nuniber of baseband recording svstenis at observatories around the world. the enuhauced flexibility made available through use of off-line data reduction software. and the iucreasing conrputational power of affordable facilities.," Further impetus is provided by the growing number of baseband recording systems at observatories around the world, the enhanced flexibility made available through use of off-line data reduction software, and the increasing computational power of affordable facilities."
 A method has previously been presented for the pliase-coherent correction of interstellar dispersion smiearing., A method has previously been presented for the phase-coherent correction of interstellar dispersion smearing.
 Convolution is performed by multipling the spectrum of basehat data with the inverted frequency response of the imterstellu iuediuu (ISM). as modeled by the cold plasima dispersion relation (ITaukius&Rickett1975).," Convolution is performed by multiplying the spectrum of baseband data with the inverted frequency response of the interstellar medium (ISM), as modeled by the cold plasma dispersion relation \citep{hr75}."
. The curent development extends the concept of couvolution to multiplication of the vector ΠροςΈα by the iuverse of the frequency response matrix., The current development extends the concept of convolution to multiplication of the vector spectrum by the inverse of the frequency response matrix.
" The toi ""matrix convolution” is used to distinguish this operation from to-dinieusioual convolution. such as would be performed on an mage."," The term “matrix convolution” is used to distinguish this operation from two-dimensional convolution, such as would be performed on an image."
 Whereas the frequency response matrix may be composed of various factors. such as those arising from the ISM aud ionosphere. this paper will be restricted to considering only the instrumental response.," Whereas the frequency response matrix may be composed of various factors, such as those arising from the ISM and ionosphere, this paper will be restricted to considering only the instrumental response."
 Following a brief review of matrix couvolution aud its relationship to the transformation properties of radiation. a technique is proposed by which the instrmucutal frequency response matrix may be determined aud used to calibrate phase-colerceut baschand data.," Following a brief review of matrix convolution and its relationship to the transformation properties of radiation, a technique is proposed by which the instrumental frequency response matrix may be determined and used to calibrate phase-coherent baseband data."
 As a preliminary illustration. the method is applied to full-poluization observations of the millisecond pulsu.1715.. from two cifferent receiver svstenis.," As a preliminary illustration, the method is applied to full-polarization observations of the millisecond pulsar, from two different receiver systems."
 The results agree well with previously published polarimetry for this pulsar (Navarroetal.1991)., The results agree well with previously published polarimetry for this pulsar \citep{nms+97}.
. Consider a luear system with impulse response. j(f).," Consider a linear system with impulse response, $j(t)$."
 Presented with an input signal. e(f). the output of this svstem is given bv the couvolution. e/(f)=j(f)«e(t).," Presented with an input signal, $e(t)$, the output of this system is given by the convolution, $e^\prime(t)=j(t)*e(t)$."
 Iu the two-dimensional case. cach output signal is given by a linear combination of the iuput signals. Now let e4(f) aud co(f) be the comples-valued analytic sijenals associated with two real time series. providing the Instantaneous aniplitudes and phases of two orthogonal senses of polarization.," In the two-dimensional case, each output signal is given by a linear combination of the input signals, Now let $e_1(t)$ and $e_2(t)$ be the complex-valued analytic signals associated with two real time series, providing the instantaneous amplitudes and phases of two orthogonal senses of polarization."
 By defining the analytic vector.," By defining the analytic vector,"
is negligible.,is negligible.
 Again. while deriving Eq.CA193) the x derivatives of zeroth order quantities have been discarded.," Again, while deriving \ref{eq:tdw}) ) the $x$ derivatives of zeroth order quantities have been discarded."
" The equation of motion in the shock rest frame accounting for the displacement+ current are: Using. Eq.CA17)) and developping: the Eq.(A20)) to the first. order we finally: get after. some manipulations:: used the shorthand notation 6. =NEcz/cwith ONc, the speed D sound. and: ' defines the Alfvénn velocity squared (as measured s"," The equation of motion in the shock rest frame accounting for the displacement current are: Using \ref{Eq:CE2}) ) and developping the \ref{Eq:Mot}) ) to the first order we finally get after some manipulations: We used the shorthand notation $\beta_{\rm s}^2=c_{\rm s}^2/c^2$ with $c_{\rm s}$ the speed of sound, and: which defines the Alfvénn velocity squared (as measured upstream)."
" The quantity «. which carries: the. dimension of. aNNI ""a is defined as follows:  charge density py is. related Achterberg.to the cosmic- 18 p., through the Maxwell equation: indeedAmato, E., M. In the limit £4.«| and £,«I. the system governing the evolution of the perturbed quantities reads: To analyze the instabilities. it is convenient to make the following. reduction:. 2=KalyD.""TN ou;=Bali- b; and. 27"" unchanged."," The quantity $\kappa$, which carries the dimension of a wavenumber, is defined as follows: The plasma charge density $\rho_{\rm pl}$ is indeed related to the cosmic-ray charge density $\rho_{\rm cr}$ through the Maxwell equation: hence: In the limit $\beta_{\rm A}\ll1$ and $\beta_{\rm s}\ll1$, the system governing the evolution of the perturbed quantities reads: To analyze the instabilities, it is convenient to make the following reduction: $\hat D = k_x\beta_{\rm sh}\Gamma_{\rm sh} \tilde D$, $\delta u_j= \beta_{\rm sh}\Gamma_{\rm sh} \tilde u_j$; $b_j$ and ${\delta w \over w}$ unchanged."
" The ordering for doing simplifications is consistent with the expected physics: we assume A,KK,«Kurs mPauly and Du.=—Pyk./ky⋅ at the same order than previous terms."," The ordering for doing simplifications is consistent with the expected physics: we assume $k_y, k_z, k_* \ll
k_x$, $u_z \ll \beta_{\rm sh}\Gamma_{\rm sh}$ and $\tilde Du_z = -
\Gamma_{\rm sh}k_*/ k_x$ at the same order than previous terms."
" The system∖ reads: "" one gets the intermediate system:", The simplified system reads: Thus one gets the intermediate system:
" The system∖ reads: "" one gets the intermediate system: ", The simplified system reads: Thus one gets the intermediate system:
" The system∖ reads: "" one gets the intermediate system: 2", The simplified system reads: Thus one gets the intermediate system:
" The system∖ reads: "" one gets the intermediate system: 2B", The simplified system reads: Thus one gets the intermediate system:
show only one period of significant decline.,show only one period of significant decline.
" Orbits that are predominantly radial, on the other hand, typically undergo two or more pericentric passages, with each successive passage bringing the galaxy closer to the centre of the group."," Orbits that are predominantly radial, on the other hand, typically undergo two or more pericentric passages, with each successive passage bringing the galaxy closer to the centre of the group."
" In these cases we see two (or more) periods of significant decline in the bound mass of gas, as expected."," In these cases we see two (or more) periods of significant decline in the bound mass of gas, as expected."
" In spite of the widely varying orbits, the simple analytic model with a= 2, 0.5<8«0.7 (shown is 8=2/3), and tram=fsouna performs remarkably well in predicting the mass loss seen in the simulations."," In spite of the widely varying orbits, the simple analytic model with $\alpha = 2$ , $0.5 < \beta < 0.7$ (shown is $\beta =
2/3$ ), and $t_{\rm ram} = \beta t_{\rm sound}$ performs remarkably well in predicting the mass loss seen in the simulations."
 For all orbits and at all times the model predicts M(t) to within +10% accuracy., For all orbits and at all times the model predicts $M(t)$ to within $\approx 10\%$ accuracy.
" Finally, it is interesting to note that if the standard (but unphysical) instantaneous ram pressure stripping model were adopted, the implication would be that a should vary as a function of the orbit."," Finally, it is interesting to note that if the standard (but unphysical) instantaneous ram pressure stripping model were adopted, the implication would be that $\alpha$ should vary as a function of the orbit."
" In particular, from 88, one would infer relatively low values of a (~2— 5) for more circular orbits and relatively high values of a (~6— 10) for more radial orbits."," In particular, from 8, one would infer relatively low values of $\alpha$ $\sim 2-5$ ) for more circular orbits and relatively high values of $\alpha$ $\sim 6-10$ ) for more radial orbits."
" However, o is a geometric constant that is not expected to depend on the orbit."," However, $\alpha$ is a geometric constant that is not expected to depend on the orbit."
 This consideration provided one of the original motivations for us to explore models where the stripping is not instantaneous., This consideration provided one of the original motivations for us to explore models where the stripping is not instantaneous.
" As we have demonstrated, a fixed value of az2 works well for all orbits when one takes into account the finite time required for stripping."," As we have demonstrated, a fixed value of $\alpha \approx 2$ works well for all orbits when one takes into account the finite time required for stripping."
 We now investigate variations in total mass of the galaxy., We now investigate variations in total mass of the galaxy.
 This will mainly have the effect of changing the gravitational restoring force (per unit area) of the galaxy at all radii by a constant factor., This will mainly have the effect of changing the gravitational restoring force (per unit area) of the galaxy at all radii by a constant factor.
" As indicated by 99, the analytic model matches the higher mass ratio interactions (lower galaxy masses) well at all times but does less well for the low mass ratio 10:1 at late times."," As indicated by 9, the analytic model matches the higher mass ratio interactions (lower galaxy masses) well at all times but does less well for the low mass ratio 10:1 at late times."
" In particular, the analytic model predicts that there ought to be no further stripping following first pericentric passage while the simulations show evidence for further stripping."," In particular, the analytic model predicts that there ought to be no further stripping following first pericentric passage while the simulations show evidence for further stripping."
 What is the origin of this behaviour?, What is the origin of this behaviour?
 Inspection of the 10:1 simulation reveals that the gaseous halo of the galaxy undergoes significant expansion at late times while the analytic model uses the initial gas distribution (see 110)., Inspection of the 10:1 simulation reveals that the gaseous halo of the galaxy undergoes significant expansion at late times while the analytic model uses the initial gas distribution (see 10).
" The expansion, in turn, makes the gas more susceptible to ram pressure stripping, and this accounts for the decline in the bound gas mass at late times."," The expansion, in turn, makes the gas more susceptible to ram pressure stripping, and this accounts for the decline in the bound gas mass at late times."
 The physical reason for the expansion of the gaseous halo is as follows., The physical reason for the expansion of the gaseous halo is as follows.
" At early times, the ram pressure exceeds the restoring force per unit area of the outer gas, which leads to stripping."," At early times, the ram pressure exceeds the restoring force per unit area of the outer gas, which leads to stripping."
" This stripping proceeds until pericentric passage, when [και is largest."," This stripping proceeds until pericentric passage, when $P_{\rm ram}$ is largest."
" The remaining bound gaseous halo following pericentric passage is of higher mean density and pressure than the initial system, since all of the low density (less bound) material has been removed."," The remaining bound gaseous halo following pericentric passage is of higher mean density and pressure than the initial system, since all of the low density (less bound) material has been removed."
" Following pericentre, the galaxy moves out to large group-centric radii, where the pressure and density of the ICM are relatively low compared to pericentre."," Following pericentre, the galaxy moves out to large group-centric radii, where the pressure and density of the ICM are relatively low compared to pericentre."
" As a result, the gaseous halo of the galaxy becomes over-pressurised with respect to the local ICM and begins to expand."," As a result, the gaseous halo of the galaxy becomes over-pressurised with respect to the local ICM and begins to expand."
 This effect is larger in the case of more massive galaxies since they are more over-pressurised with respect to the ICM., This effect is larger in the case of more massive galaxies since they are more over-pressurised with respect to the ICM.
" The expansion proceeds until approximately apocentre is reached, at which point the galaxy begins to move back into denser and higher pressure regions of the group. ("," The expansion proceeds until approximately apocentre is reached, at which point the galaxy begins to move back into denser and higher pressure regions of the group. ("
This effect is also responsible for the mild decline in bound gas mass for the highly tangential orbital case plotted in the top right-hand panel of 88.),This effect is also responsible for the mild decline in bound gas mass for the highly tangential orbital case plotted in the top right-hand panel of 8.)
" It is important to note that this over-pressurisation effect is not a numerical artifact, it is a real effect that should be experienced by massive galaxies with orbits that have large energies and tangential components."," It is important to note that this over-pressurisation effect is not a numerical artifact, it is a real effect that should be experienced by massive galaxies with orbits that have large energies and tangential components."
 Modelling this effect may be possible with some effort., Modelling this effect may be possible with some effort.
" The expansion of the gaseous halo at late times is adiabatic, which greatly simplifies matters."," The expansion of the gaseous halo at late times is adiabatic, which greatly simplifies matters."
 One could therefore compute the radial properties of the gaseous halo as a function of time using the Lagrangian entropy distribution of the gas and assuming hydrostatic equilibrium with an outer boundary condition that the pressure must match that of the ambient ICM., One could therefore compute the radial properties of the gaseous halo as a function of time using the Lagrangian entropy distribution of the gas and assuming hydrostatic equilibrium with an outer boundary condition that the pressure must match that of the ambient ICM.
" However, this procedure is complicated by the fact that one must also know the distribution of the galaxy’s dark matter halo out to the radius of maximum expansion."," However, this procedure is complicated by the fact that one must also know the distribution of the galaxy's dark matter halo out to the radius of maximum expansion."
" While the dark matter profile at small and intermediate radii is sufficiently similar to the initial distribution, this is not the case at very large radii."," While the dark matter profile at small and intermediate radii is sufficiently similar to the initial distribution, this is not the case at very large radii."
 A proper treatment therefore requires that we factor in dark matter stripping and heating., A proper treatment therefore requires that we factor in dark matter stripping and heating.
" This could potentially be achieved by combining our analytic ram pressure model with existing analytic models of dark matter stripping and heating (e.g., Taylor Babul 2001; Benson et 2002)."," This could potentially be achieved by combining our analytic ram pressure model with existing analytic models of dark matter stripping and heating (e.g., Taylor Babul 2001; Benson et 2002)."
" However, this is beyond the scope of the present study and we leave it for future work."," However, this is beyond the scope of the present study and we leave it for future work."
" Finally, we stress that the expansion effect just described is relevant to cases where both of the following are true: (1) the mass of the galaxy is greater than about of the mass of the group; and (2) the orbithas an appreciable tangential component and a large enough energy such that"," Finally, we stress that the expansion effect just described is relevant to cases where both of the following are true: (1) the mass of the galaxy is greater than about of the mass of the group; and (2) the orbithas an appreciable tangential component and a large enough energy such that"
"Finally,: we compare our results with: two different⋅⋅ compilations of cosmic SFR based on the rest-frame UV huuinositv-densitv technique aud with a compilation of various other techuiques.","Finally, we compare our results with two different compilations of cosmic SFR based on the rest-frame UV luminosity-density technique and with a compilation of various other techniques."
 The a- empirical paralucterization was fitted to the data sects after converting to cosinoloey Cl., The $\alpha$ $\beta$ empirical parameterization was fitted to the data sets after converting to cosmology $\cal C$ 1.
 The various contours are shown in Figure 19 with full references quoted in the caption., The various contours are shown in Figure \ref{fig:contours-all} with full references quoted in the caption.
 For the first UV compilation. we took the 10 data points with error frou figure 9 ofSteidel(1999) barsformal confidence boundarieset Ial. versus ," For the first UV compilation, we took the 10 data points with error bars from figure 9 of\citet{steidel99} and calculated formal confidence boundaries in $\alpha$ versus $\beta$."
The anduo extinction calculatediud extinction corrected data were stars separately., The no extinction and extinction corrected data were considered separately.
 This compilation promotes a high value of 3~ Lwith a depending on extinction., This compilation promotes a high value of $\beta\sim4$ with $\alpha$ depending on extinction.
 For the second UV. compilation. we took 9 data points error bars from ⋅⋡⋅∖↽∙≻⊳⊲↽⋅∖⊲↜⋠∙⋠↽≱⋠⋅figure 13 of anCowie. Songaila.&Dargerwilfor the 28004. ]lunuinositv deusitv excluding those used iu the first compilation.," For the second UV compilation, we took 9 data points with error bars from figure 13 of \citet*{CSB99} for the luminosity density excluding those used in the first compilation."
⋅⋅ À minium⋅⋅ error of: 0.07 τςin the log was used to calculate the boundaries., A minimum error of 0.07 in the log was used to calculate the boundaries.
" This compilation promotes ""a eradual decline” iu the UV. luninosity density for :€1.5 ∙ witha=i~|150", This compilation promotes “a gradual decline” in the UV luminosity density for $z\la1.5$ with $\alpha=\beta\sim1.5$.
 For the other compilation.700 we recomputed the bootstrap error from the measurements of JJ given by Ποσο(2002) exchiding the UV measurements included above.," For the other compilation, we recomputed the bootstrap error from the measurements of $\beta$ given by \citet{Hogg02} excluding the UV measurements included above."
 This new value was ο=3.2c0.9., This new value was $\beta=3.2\pm0.9$.
 A precise interpretation of Figure 19 depends on the he accuracy of the errors used in the aualvsis., A precise interpretation of Figure \ref{fig:contours-all} depends on the the accuracy of the errors used in the analysis.
 Caven the analysis preseuted here. the two UV compilations (talking either extinction model from the first) are consistent at he 3e level with Ls<52.9 and LO<a 0.7. mit not quite consistent at the 26 level.," Given the analysis presented here, the two UV compilations (taking either extinction model from the first) are consistent at the $\sigma$ level with $1.8 < \beta < 2.9$ and $-1.0 < \alpha < 0.7$ , but not quite consistent at the $\sigma$ level."
 Our results are indepenudenutlv cousisteut with these ranges of values but, Our results are independently consistent with these ranges of values but
because of the transition from the FIISC to Class 0. which occurs from 2x104 vears until 5.5x10! vears.,"because of the transition from the FHSC to Class 0, which occurs from $\times 10^4$ years until $\times 10^4$ years."
 This transition timescale is the same as that used in Lee et al. (, This transition timescale is the same as that used in Lee et al. (
2004). but much longer than the 100 vears assumed by Young Evans (2005).,"2004), but much longer than the 100 years assumed by Young Evans (2005)."
 The evolution of the spectral energy distribution (SED) around 5x101 vears is presented in Fig., The evolution of the spectral energy distribution (SED) around $5\times 10^4$ years is presented in Fig.
 2., 2.
 An accretion. burst occurred at 5.1x10! vears. alter which a quiescent state continues until the next burst 107 vears later.," An accretion burst occurred at $5.1\times 10^4$ years, after which a quiescent state continues until the next burst $10^4$ years later."
 The accretion luminosity powered in the burst phase at 5.1xLO! vears is about 5L... whereas the accretion luminosities at 5.0 and 5.4 x10! vears are about 0.004 and 0.02L... respectively.," The accretion luminosity powered in the burst phase at $5.1\times 10^4$ years is about 5, whereas the accretion luminosities at 5.0 and 5.4 $\times 10^4$ years are about 0.004 and 0.02, respectively."
 The model SED at 5.4x10! vears fits well the observed SED of IRAM 04191., The model SED at $5.4\times 10^4$ years fits well the observed SED of IRAM 04191.
 The total huminositv in the model is about 0.09L... where the luminosity arising from heating bv the ISRF (~0.07 }) is larger than the infernal luminosity (~0.02 L..}).," The total luminosity in the model is about 0.09, where the luminosity arising from heating by the ISRF $\sim 0.07$ ) is larger than the internal luminosity $\sim 0.02$ )."
 This result is not verv consistent with that of Dunham οἱ al. (, This result is not very consistent with that of Dunham et al. (
2006). who found that the internal luminosity must be greater than 0.04L.,"2006), who found that the internal luminosity must be greater than 0.04."
... However. the density. profile and ISRF in their model are significantly different from ours. making it hard to directly compare the two results.," However, the density profile and ISRF in their model are significantly different from ours, making it hard to directly compare the two results."
 The densitv and dust temperature profiles are shown in Fie., The density and dust temperature profiles are shown in Fig.
 3 at the same lime steps shown for the SEDs in Fig., 3 at the same time steps shown for the SEDs in Fig.
 2., 2.
 The infall radius is 0.014 pe (2800 AU) when the accretion burst occurs at 5.1x104., The infall radius is 0.014 pc (2800 AU) when the accretion burst occurs at $5.1\times 10^4$.
 The density at the infall radius is about 2x10? *., The density at the infall radius is about $2\times 10^5$ $^{-3}$.
 The density profile has the power law index of ~1.5 and 2.0 inside and outside the infall radius. respectively.," The density profile has the power law index of $\sim 1.5$ and 2.0 inside and outside the infall radius, respectively."
 Except for the accretion burst. phase. the dust temperature is below the CO evaporation temperature (20 IX) at almost all radii.," Except for the accretion burst phase, the dust temperature is below the CO evaporation temperature $\sim 20$ K) at almost all radii."
 In prestellar cores. which are very evolved starless cores. carbon-bearing molecules such as CS and CO are readily frozen-out onto grain surfaces (Berein Langer 1997. Aikaava el al.," In prestellar cores, which are very evolved starless cores, carbon-bearing molecules such as CS and CO are readily frozen-out onto grain surfaces (Bergin Langer 1997, Aikawa et al."
 2001. Lee et al.," 2001, Lee et al."
 2003. Lee et al.," 2003, Lee et al."
 2004)., 2004).
" In contrast. nitrogen-bearing molecules such as Noll and NIL, are considered good tracers of (column) densitv in cold. dense cores since Ne. the parent molecule of Noll anc δι. has a long formation (ünmescale such that 1 becomes abundant later in the core evolution."," In contrast, nitrogen-bearing molecules such as $_2$ $^+$ and $_3$ are considered good tracers of (column) density in cold, dense cores since $_2$, the parent molecule of $_2$ $^+$ and $_3$ , has a long formation timescale such that it becomes abundant later in the core evolution."
 Therefore. the comparison between CO and Noll abundances is a good indicator of the physical properties of a dense core.," Therefore, the comparison between CO and $_2$ $^+$ abundances is a good indicator of the physical properties of a dense core."
 The low binding energy of No on grain surfaces has also been suggested as an explanation for the long-lived molecules in the cold regions (Lee et al., The low binding energy of $_2$ on grain surfaces has also been suggested as an explanation for the long-lived molecules in the cold regions (Lee et al.
 2004)., 2004).
 However. Obberg et al. (," However, Öbberg et al. ("
2005) showed that the binding energy of No on grain surfaces is not different from that of CO.,2005) showed that the binding energy of $_2$ on grain surfaces is not different from that of CO.
 The hieh abundance of Noll in the cold. dense regions may be due to the replenishment of No through the interactions between Nelland grains since Nell recombines with electrons on," The high abundance of $_2$ $^+$ in the cold, dense regions may be due to the replenishment of $_2$ through the interactions between $_2$ $^+$and grains since $_2$ $^+$ recombines with electrons on"
Classical Be stars (Porter&Rivinius2003) are rapiclly rotating earlv-tvpe stars that exhibit Balmer emission lines.,Classical Be stars \citep{2003PASP..115.1153P} are rapidly rotating early-type stars that exhibit Balmer emission lines.
 lt is widely agreed that these lines. which are generally double-peaked. originate in a relatively thin circumstellar disc that is in approximately Ixeplerian. rotation (Okazaki2007.andreferences therein)..," It is widely agreed that these lines, which are generally double-peaked, originate in a relatively thin circumstellar disc that is in approximately Keplerian rotation \citep[and references
therein]{2007ASPC..361..230O}."
 While the precise mechanism »v which the disc is formed remains controversial. it is likely o resemble a viscous decretion dise that is expelled by the action of a torque at its inner boundary. (Leeetal.1991:Porter&Rivinius 2003)..," While the precise mechanism by which the disc is formed remains controversial, it is likely to resemble a viscous decretion disc that is expelled by the action of a torque at its inner boundary \citep{1991MNRAS.250..432L,2003PASP..115.1153P}."
 Alany Be stars show cvelical variations in their clouble-vcaked emission lines over vears or decades. with the red and blue peaks alternately becoming more prominent (OkazakiLOOT.andreferencestherein)..," Many Be stars show cyclical variations in their double-peaked emission lines over years or decades, with the red and blue peaks alternately becoming more prominent \citep[and references
therein]{1997A&A...318..548O}."
 An explanation of this phenomenon was given by Okazaki (1901)... who »oposed that a low-frequency. one-armed oscillation mode (Ixato1983) occurs in the disc.," An explanation of this phenomenon was given by \citet{1991PASJ...43...75O}, , who proposed that a low-frequency, one-armed oscillation mode \citep{1983PASJ...35..249K}
 occurs in the disc."
 Phis is equivalently to saving hat the disc becomes eccentric and the slow precession of its elliptical shape gives rise to the evelical changes in the observed. emission lines., This is equivalently to saying that the disc becomes eccentric and the slow precession of its elliptical shape gives rise to the cyclical changes in the observed emission lines.
 I5ccentric dises. in which fluid elements. solid. particles or stars follow elliptical orbits of variable eccentricity around a central mass. have further applications in svstenis as diverse as planetary rings. protoplanetary systems. close binary stars and galactic nuclei.," Eccentric discs, in which fluid elements, solid particles or stars follow elliptical orbits of variable eccentricity around a central mass, have further applications in systems as diverse as planetary rings, protoplanetary systems, close binary stars and galactic nuclei."
 A detailed understanding of the origin of cecentricity and the rates of precession in the circumstellar clises of Be stars would therefore be of general interest., A detailed understanding of the origin of eccentricity and the rates of precession in the circumstellar discs of Be stars would therefore be of general interest.
 Okazaki(1901) originally considered a disc that orbits in a point-mass potential and obtainecl a sequence of retrograde modes in which the precession of the disc is in a direction opposite to its rotation., \citet{1991PASJ...43...75O} originally considered a disc that orbits in a point-mass potential and obtained a sequence of retrograde modes in which the precession of the disc is in a direction opposite to its rotation.
 Retrogracle precession is à natural consequence of the pressure forces in the disc. which cause a small departure from Ixeplerian rotation and allow the cecentricity to propagate in a wavelike manner.," Retrograde precession is a natural consequence of the pressure forces in the disc, which cause a small departure from Keplerian rotation and allow the eccentricity to propagate in a wavelike manner."
 The global modes found by Okazaki(1901). are weighted towards the outer part of the disc and their periods become extremely long as the outer radius of the disc is increased to realistic values., The global modes found by \citet{1991PASJ...43...75O} are weighted towards the outer part of the disc and their periods become extremely long as the outer radius of the disc is increased to realistic values.
 Papaloizouetal.(1992) and Savonije&Lecemskerk(1993) considered the clleet of the quacrupole gravitational potential associated with the rotational deformation of the star. which tends to cause a progracde precession of elliptical orbits.," \citet{1992A&A...265L..45P} and \citet{1993A&A...276..409S} considered the effect of the quadrupole gravitational potential associated with the rotational deformation of the star, which tends to cause a prograde precession of elliptical orbits."
 Vhey showed that. when the quadrupole οσοι is taken into account. prograde modes can be obtained that are naturally confined. in the inner part of the disc and are insensitive to the outer boundary. condition.," They showed that, when the quadrupole effect is taken into account, prograde modes can be obtained that are naturally confined in the inner part of the disc and are insensitive to the outer boundary condition."
 Subsequent observations confirmed. that the precession. is indeed. prograde (CIeltingetal.LO94).., Subsequent observations confirmed that the precession is indeed prograde \citep{1994A&A...288..558T}.
 However. Okazaki(1997). founcl that confined progracle modes can be obtained only when the disc is sullicientIv cool. so that the quadrupole elect. dominates over the tendency of pressure to produce retrograde precession and extended: modes.," However, \citet{1997A&A...318..548O} found that confined prograde modes can be obtained only when the disc is sufficiently cool, so that the quadrupole effect dominates over the tendency of pressure to produce retrograde precession and extended modes."
 He concluded that a different mechanism is required in the hotter. dises. of earlv-tvpe. De. stars such as the prototype 5. Cas. and. proposed that radiative line forces could explain the required prograceprecession.," He concluded that a different mechanism is required in the hotter discs of early-type Be stars such as the prototype $\gamma$ Cas, and proposed that radiative line forces could explain the required progradeprecession."
 Unfortunately the modelling of radiative forces is subject to considerable uncertainty., Unfortunately the modelling of radiative forces is subject to considerable uncertainty.
 Pitt&EEarmanec(2006). found," \citet{2006A&A...447..277F}
 found"
appearance similar to that of a distant. luminous elliptical ealaxv (consider just the filled. circles in the upper left panel of Fig.,appearance similar to that of a distant luminous elliptical galaxy (consider just the filled circles in the upper left panel of Fig.
 1)., 1).
 Like dwarf irregular galaxies. Alrk 1460 has voung stars and an emission-line spectrum (Pustilnik et al.," Like dwarf irregular galaxies, Mrk 1460 has young stars and an emission-line spectrum (Pustilnik et al."
 1999)., 1999).
 Blue compact cwarl (XD) galaxies with rtat ight profiles have been known to exist for some time (e.g. Kunth. Aaurogocarto Vigroux 1955).," Blue compact dwarf (BCD) galaxies with $r^{1/4}$ light profiles have been known to exist for some time (e.g. Kunth, Maurogodarto Vigroux 1988)."
 Doublier (1998) places a number of these objects on a magnitude vs. central surface-brightness. plot. and finds that they lie close to the highest surface-brightness red compact eiwarfs like M32. several mag ? brighter than Mrk. 1460.," Doublier (1998) places a number of these objects on a magnitude vs. central surface-brightness plot, and finds that they lie close to the highest surface-brightness red compact dwarfs like M32, several mag $^{-2}$ brighter than Mrk 1460."
 X. well-studied example is NGC 1510 (Disney Pottasch 1977. Ixinman 1978). which also shows strong emission lines.," A well-studied example is NGC 1510 (Disney Pottasch 1977, Kinman 1978), which also shows strong emission lines."
 Unlike Mrk 1460. however. this galaxy exhibits considerable clumpiness (IEZichendorf Nieto 1984).," Unlike Mrk 1460, however, this galaxy exhibits considerable clumpiness (Eichendorf Nieto 1984)."
 Alore generally. BCDs possess localized regions undergoing intense star formation burst where the surface brightnesses is extremely high.," More generally, BCDs possess localized regions undergoing intense star formation burst where the surface brightnesses is extremely high."
 In. Mrk. 1460. however. the voung stars exist on a galactic scale and are not just restricted to any particular star-forming region.," In Mrk 1460, however, the young stars exist on a galactic scale and are not just restricted to any particular star-forming region."
 Galaxies with the properties of Alrk 1460 have not turned up in field optical spectroscopic (e.g. Ellis et al., Galaxies with the properties of Mrk 1460 have not turned up in field optical spectroscopic (e.g. Ellis et al.
 1996. Lin ct al.," 1996, Lin et al."
 1996) or LIL (e.g. Zwaan 1998) surveys (however see Drinkwater et al., 1996) or HI (e.g. Zwaan 1998) surveys (however see Drinkwater et al.
 1988 for some possible counterparts in the Fornax Cluster)., 1988 for some possible counterparts in the Fornax Cluster).
 They are presumably very. rare., They are presumably very rare.
 ‘Vhis is not surprising. since the current star-formation rate of 0.1 AL. + exhausts the HE gas in 2)107 vr. which is small compared to a Hubble time.," This is not surprising, since the current star-formation rate of 0.1 $_{\odot}$ $^{-1}$ exhausts the HI gas in $2 \times 10^8$ yr, which is small compared to a Hubble time."
 Lt is likely that Alrk 1460 will evolve into an old high surface-brightness dwark albeit one at least two magnitudes fainter than UGC 6805 once fading is taken into account. (this would be the lowest. luminosity rt galaxy known).," It is likely that Mrk 1460 will evolve into an old high surface-brightness dwarf, albeit one at least two magnitudes fainter than UGC 6805 once fading is taken into account (this would be the lowest luminosity $r^{1/4}$ galaxy known)."
 Its final surface brightness will probably be close to what it is now: Mrk 1460 does not possess enough cold gas (unless it is in molecular form. but there is no ZAs detection at this position) to convert to stars via an extreme dissipative collapse. which is what would. be required: were Alrk 1460 to turn into a very. high. surface-brightness red compact chwarf like M32.," Its final surface brightness will probably be close to what it is now: Mrk 1460 does not possess enough cold gas (unless it is in molecular form, but there is no $IRAS$ detection at this position) to convert to stars via an extreme dissipative collapse, which is what would be required were Mrk 1460 to turn into a very high surface-brightness red compact dwarf like M32."
 So what happened to cause this galaxy to. have hese anomalous properties?, So what happened to cause this galaxy to have these anomalous properties?
 Making pi ealaxies by violent relaxation on timescales short compared. to stellar »opulation evolutionary timescales does not seenr to » a problem. (Lyneen-Bell 1967. van. AMbada 1982).," Making $r^{1\over{4}}$ galaxies by violent relaxation on timescales short compared to stellar population evolutionary timescales does not seem to be a problem (Lynden-Bell 1967, van Albada 1982)."
 Llowever. why this happened. in this particular case. and not in most low-luminosity star-formüng galaxies (which lave exponential profiles and lower surface. brightnesses) is unclear.," However, why this happened in this particular case, and not in most low-luminosity star-forming galaxies (which have exponential profiles and lower surface brightnesses) is unclear."
 Wo might be an environmental effect: “Lully Verheijen (19977) suggest that tidal interactions can raciallv scramble he barvonic mass. presumably through eas collisions.," It might be an environmental effect: Tully Verheijen (1997) suggest that tidal interactions can radially scramble the baryonic mass, presumably through gas collisions."
 “Phe barvonic matter transferred. inward during an encounter with another ealaxy can become sullicientlv. concentrated. that it becomes self-gravitating., The baryonic matter transferred inward during an encounter with another galaxy can become sufficiently concentrated that it becomes self-gravitating.
 AX self-eravitating disk will then further rearrange itself into a racially stable configuration (Alestel 1963)., A self-gravitating disk will then further rearrange itself into a radially stable configuration (Mestel 1963).
 The result is a high concentration of barvons towards the center of the galaxy. which in turn leads to the high surface brightness relative to what is seen in most. low-Iuminosity galaxies.," The result is a high concentration of baryons towards the center of the galaxy, which in turn leads to the high surface brightness relative to what is seen in most low-luminosity galaxies."
 A related: possibility is that Merk. 12460. formed out of a dense. sell-eravitating σας cloud assembled: via a hyvelrodvnamic shock process (Barnes Lernquist 1992). perhaps in proximity to another galaxy in the Ursa Major Cluster.," A related possibility is that Mrk 1460 formed out of a dense, self-gravitating gas cloud assembled via a hydrodynamic shock process (Barnes Hernquist 1992), perhaps in proximity to another galaxy in the Ursa Major Cluster."
 Alore generally. understanding the physical mechanisms at work would be helped significantly by obtaining a sample of objects like AIrk 1460.," More generally, understanding the physical mechanisms at work would be helped significantly by obtaining a sample of objects like Mrk 1460."
 Such galaxies are distinctive in spectroscopic surveys since their surface. brightnesses are high and their emission lines are strong., Such galaxies are distinctive in spectroscopic surveys since their surface brightnesses are high and their emission lines are strong.
 This will shortly be possible as large samples of galaxies with known recshilts ancl morphological information become available from the new generation of wide-field deep redshift. surveys like the Sloan Digital Sky Survey and the 2DE Survey., This will shortly be possible as large samples of galaxies with known redshifts and morphological information become available from the new generation of wide-field deep redshift surveys like the Sloan Digital Sky Survey and the 2DF Survey.
(?) pre-processed data from the CFHTLS-Deep (ugriz- and COSMOS survey (u-band).,\citep{2004PASP..116..449M} pre-processed data from the CFHTLS-Deep $ugriz$ -bands) and COSMOS survey $u$ -band).
 We retrieve from the CADC archive relevant images available at 21/07/2008., We retrieve from the CADC archive relevant images available at 21/07/2008.
 The data were observed with MEGACAM@CFHT and reduced with the THELI imaging reduction pipeline (2).., The data were observed with MEGACAMCFHT and reduced with the THELI imaging reduction pipeline \citep{2005AN....326..432E}.
 The properties of the reduced images are summarised in Table |. ( the limiting magnitudes reported in the table are [-σ limits in a circular aperture with a diameter of twice the seeing FWHM)., The properties of the reduced images are summarised in Table \ref{tab:images} ( the limiting magnitudes reported in the table are $\sigma$ limits in a circular aperture with a diameter of twice the seeing FWHM).
 The data reduction and catalogue creation are carried out identically to the one of the CFHTLS-Wide survey described in ?.., The data reduction and catalogue creation are carried out identically to the one of the CFHTLS-Wide survey described in \cite{2009A&A...493.1197E}.
 Here. we quickly summarise the most important reduction- and catalogue creation steps: In contrast to the method applied in ? we modify the estimation of photometric redshifts (photo-z) in the following points: By these measures a tilt in the photo-z vs. spec-z comparison. as reported in? can be avoided.," Here, we quickly summarise the most important reduction- and catalogue creation steps: In contrast to the method applied in \cite{2009A&A...493.1197E} we modify the estimation of photometric redshifts $z$ ) in the following points: By these measures a tilt in the $z$ vs. $z$ comparison, as reported in \cite{2009A&A...493.1197E} can be avoided."
 With thousands of publie spectroscopic redshifts from the VIMOS VLT Deep Survey (VVDS) on the DI field (?).. the ZCOSMOS survey on the D2 field (?).. and the DEEP2 survey on the D3 field (?).. we test the performance of our photo-Z's. For a safe sample (ODDS> >0.9: see also. in the magnitude range 17«i24 we find a scatter of c=0.033 of the quantity Az—(5i−/+ after rejecting of outliers (objects with —Az>(1 0.15)— and no significant bias.," With thousands of public spectroscopic redshifts from the VIMOS VLT Deep Survey (VVDS) on the D1 field \citep{2005A&A...439..845L}, the zCOSMOS survey on the D2 field \citep{2007ApJS..172...70L}, , and the DEEP2 survey on the D3 field \citep{2007ApJ...660L...1D}, we test the performance of our $z$ 's. For a safe sample \citep[$\mathrm{ODDS}> >0.9; see also in the magnitude range $17<i<24$ we find a scatter of $\sigma=0.033$ of the quantity $\Delta
z=\left(z_{\rm phot}-z_{\rm spec}\right)/\left(1+z_{\rm spec}\right)$ after rejecting of outliers (objects with $\Delta z > 0.15$ ) and no significant bias."
 Figure 1. shows a comparison of the spectroscopic redshifts with our photo-Z's on the three fields., Figure \ref{fig:zz} shows a comparison of the spectroscopic redshifts with our $z$ 's on the three fields.
 Note that these accurate low-redshift photo-z's for relatively bright objects do not imply directly à similar photo-z performance at higher redshifts and fainter magnitudes., Note that these accurate low-redshift $z$ 's for relatively bright objects do not imply directly a similar $z$ performance at higher redshifts and fainter magnitudes.
 This results shoulc be regarded more as a quality check for the data reductior and the multi-colour photometry., This results should be regarded more as a quality check for the data reduction and the multi-colour photometry.
 Furthermore. we also carried out a eross-correlation analysis of galaxies in photo-z bins.," Furthermore, we also carried out a cross-correlation analysis of galaxies in $z$ bins."
 The results can be found in the appendix AppendixA:., The results can be found in the appendix \ref{app:cross}.
. We simulate a colour catalogue of galaxiesbased on templates fromthe library of ?. - in the same way as presented in ?. for the ESO Deep Public Survey (DPS):, We simulate a colour catalogue of galaxiesbased on templates fromthe library of \cite{1993ApJ...405..538B} - in the same way as presented in \cite{2007A&A...462..865H} for the ESO Deep Public Survey (DPS):
variability. with PDS that are well described by power laws with 5 ~1.,", with PDS that are well described by power laws with $\gamma$ $\sim$ 1."
 We preseut the 2005. Noveniber PDS in Fie. l..," We present the 2005, November PDS in Fig. \ref{ngc300pds}."
 The axes are log scaled. and normalised to give raus? variability: the expected noise is ubtracted.," The axes are log scaled, and normalised to give $^{2}$ variability; the expected noise is subtracted."
 We note that no background flaring occurred iu this observation. so there is no question of the PDS being au artefact of flaring or background filtering.," We note that no background flaring occurred in this observation, so there is no question of the PDS being an artefact of flaring or background filtering."
 This variability is certainly significant. as fitting the PDS with zero power vields a u of TL for 21 degrees of freedom (dof).," This variability is certainly significant, as fitting the PDS with zero power yields a $\chi^2$ of 74 for 24 degrees of freedom (dof)."
 We present the rans., We present the r.m.s.
 variability aud best fit 5 for cach observation of NGC300 N-1 in Table 2.., variability and best fit $\gamma$ for each observation of NGC300 X-1 in Table \ref{300pds}.
 We note that the PDS from Obs., We note that the PDS from Obs.
 3 is different to the PDS from the other observations: this difference is likely due to the eclipse that occurs in Obs., 3 is different to the PDS from the other observations; this difference is likely due to the eclipse that occurs in Obs.
 3 (see7).., 3 \citep[see ][]{carp07a}.
 We preseut the 0.310 keV. combined pulMOS liehteurve of ICLO N-1 in the top paucl of Fig. 2:," We present the 0.3–10 keV, combined pn+MOS lightcurve of IC10 X-1 in the top panel of Fig. \ref{ic10lc};"
 the backeround has been subtracted. aud intervals of higho background have been removed.," the background has been subtracted, and intervals of high background have been removed."
 The lishteurve has 100 s resolution., The lightcurve has 100 s resolution.
 The system is lighly variable throughout the observation. with a large intensity dip near the beeimniug," The system is highly variable throughout the observation, with a large intensity dip near the beginning."
 This dip max be intrinsic to the N-ray source. or due to al increase in line-of-sight absorption. such as an eclipse.," This dip may be intrinsic to the X-ray source, or due to an increase in line-of-sight absorption, such as an eclipse."
 The bottoni panel shows the harducss ratio for cach time bin. defined as the ratio of 2.510 keV counts to 0.32.5 keV counts.," The bottom panel shows the hardness ratio for each time bin, defined as the ratio of 2.5–10 keV counts to 0.3–2.5 keV counts."
 The harduess ratio is variable at the 3a level. aud appears to be higher during the intensity dip at tho start of the observation. hiutiug at photo-clectric absorption: however. we cannot determine the plase of this iuteusitv dip with the current orbital ephemeris.," The hardness ratio is variable at the $\sigma$ level, and appears to be higher during the intensity dip at the start of the observation, hinting at photo-electric absorption; however, we cannot determine the phase of this intensity dip with the current orbital ephemeris."
 The variability is also consistent with stochastic variations in a source with a PDS described by + —1., The variability is also consistent with stochastic variations in a source with a PDS described by $\gamma$ $\sim$ 1.
 The PDS create roni this lightcurve is preseuted in Fig. 3::, The PDS created from this lightcurve is presented in Fig. \ref{ic10pds};
 as before. the v-axis is normalised to show the rans power. and the expecte noise is subtracted.," as before, the y-axis is normalised to show the $^{2}$ power, and the expected noise is subtracted."
 This PDS is also acceptably fitted by a power law with + = l1. with. \?/dof = 35/21.," This PDS is also acceptably fitted by a power law with $\gamma$ = 1, with $\chi^2$ /dof = 35/24."
 As with NGC300 X-1. the ταις.," As with NGC300 X-1, the r.m.s."
 variability is ereater than for Galactic LAINBs. at 18924.. exchiding the large intensity dip.," variability is greater than for Galactic LMXBs, at $\pm$, excluding the large intensity dip."
 The PDS observed from NCC300 N-1 aud 1010 X- me characteristic of disc-fe NBs at Hel accretion rates. albeit with fractional rau.s.," The PDS observed from NGC300 X-1 and IC10 X-1 are characteristic of disc-fed XBs at high accretion rates, albeit with fractional r.m.s."
 varlabilitics ~h 10 times higher than observed in Galactic NBs (seec.g.?).., variabilities $\sim$ 5–10 times higher than observed in Galactic XBs \citep[see e.g.][]{vdk95}.
 However. they are also similar to the variability observed in certain wiud-fed ΠΑΛΙΟΣ," However, they are also similar to the variability observed in certain wind-fed HMXBs."
", Hence. we iust examine the chussion spectra of NCC300 N-1 and 1010 N-1 if we are to determine their natures."," Hence, we must examine the emission spectra of NGC300 X-1 and IC10 X-1 if we are to determine their natures."
 7. modeled. the spectra from the four observations of NOGC300. N-! together., \citet{carp07a} modeled the spectra from the four observations of NGC300 X-1 together.
 They used an absorbed. colmponent model. cousistiug of a power law £. aud an cussion line.v," They used an absorbed, two-component model, consisting of a power law , and an emission line.;"
arv: the absorption and normalizatious for each compoucut were individually varied for each observation., the absorption and normalizations for each component were individually varied for each observation.
" For their best uodel. P — 1140.03 . the line energy was 120.01 το), with a width of (LO7+0.01 keV. They quote a reduced v of 1.15 for 1083 dof: rowever. thisB equates to X PAN/dof: = 15ο10.0. which is rejected at alevel aud is thereforeunacceptable."," For their best model, $\Gamma$ = $\pm$ 0.03 , the line energy was $\pm$ 0.01 keV, with a width of $\pm$ 0.01 keV. They quote a reduced $\chi^2$ of 1.15 for 1033 dof; however, this equates to $\chi^2$ /dof = 1188/1033, which is rejected at alevel and is thereforeunacceptable."
 We therefore cxaminec the spectra of δις000 N-1 more carefully., We therefore examined the spectra of NGC300 X-1 more carefully.
"In this subsection we analyze the dependence of pair classification on projected distances, r,, and relative velocities, AV, between members.","In this subsection we analyze the dependence of pair classification on projected distances, $r_p$, and relative velocities, $\Delta V$, between members."
" For this purpose, we show in Fig."," For this purpose, we show in Fig."
" 3 density contours in the r,-AV plane for galaxies of the different interaction classes, M, T and N."," \ref{rpVMTN} density contours in the $r_p$ $\Delta V$ plane for galaxies of the different interaction classes, $M$, $T$ and $N$."
" The gray scale correspond to different percentages of pairs enclosed in a given As expected, given that the classification is based on visual appearance in projection, there is a trend for lower r, values for M and T types."," The gray scale correspond to different percentages of pairs enclosed in a given As expected, given that the classification is based on visual appearance in projection, there is a trend for lower $r_p$ values for $M$ and $T$ types."
" Nevertheless, the classification cannot be reduced to a relative distance criterion and therefore a visual inspection of images is required to detect the interaction-driven morphological disturbances."," Nevertheless, the classification cannot be reduced to a relative distance criterion and therefore a visual inspection of images is required to detect the interaction-driven morphological disturbances."
 We find that the distribution of relative radial velocities is significantly lower in M types as compared to T and N types., We find that the distribution of relative radial velocities is significantly lower in $M$ types as compared to $T$ and $N$ types.
 We cross-correlate our sample of galaxy pairs with the galaxy zoo catalog (Lintott et al., We cross-correlate our sample of galaxy pairs with the galaxy zoo catalog (Lintott et al.
 2011) to compare the two classification schemes., 2011) to compare the two classification schemes.
" Galaxy Zoo comprises a morphological classification of nearly 900,000 galaxies drawn from the Sloan Digital Sky Survey, contributed by hundreds of thousands of volunteers in order to cover a wide coverage of the galaxy survey, however due to the large number of classifiers it becomes complex to maintain a unified criteria and a reliable classification."," Galaxy Zoo comprises a morphological classification of nearly 900,000 galaxies drawn from the Sloan Digital Sky Survey, contributed by hundreds of thousands of volunteers in order to cover a wide coverage of the galaxy survey, however due to the large number of classifiers it becomes complex to maintain a unified criteria and a reliable classification."
" They define six categories (elliptical, spiral, spiral clockwise, spiral anticlockwise, merger or uncertain) and give the fraction of votes in each of the six categories."," They define six categories (elliptical, spiral, spiral clockwise, spiral anticlockwise, merger or uncertain) and give the fraction of votes in each of the six categories."
 Objects classified as mergers are identified as galaxies with signs of collision., Objects classified as mergers are identified as galaxies with signs of collision.
" We find 1417 common pairs in the two catalogs, where 596 pairs are classified as disturbed (M or T), while only"," We find 1417 common pairs in the two catalogs, where 596 pairs are classified as disturbed $M$ or $T$ ), while only"
where fis the mean free path eiven by and the uunber density of particles. à» is Hence the mean free path cau be reduced to and the exposed shell mass depends only ou particle size. aud is specifically independent of the disk density (or total disk mass in this case) Because the PR lifetime of this shell is also proportional to particle size. the mass infall rate at the inner disk edee is essentially constant for the case of eeomoetric optics and around | for the parameters eiven above.,"where $l$ is the mean free path given by and the number density of particles, $n$ is Hence the mean free path can be reduced to and the exposed shell mass depends only on particle size, and is specifically independent of the disk density (or total disk mass in this case) Because the PR lifetime of this shell is also proportional to particle size, the mass infall rate at the inner disk edge is essentially constant for the case of geometric optics and around $^{-1}$ for the parameters given above."
 For silicate particles sialler than around pau. gcometric optics is not appropriate: radiative coupling becomes more effective until around jn. then less effective at sinaller radii (Artvinewicz1988).," For silicate particles smaller than around $\mu$ m, geometric optics is not appropriate; radiative coupling becomes more effective until around $\mu$ m, then less effective at smaller radii \citep{art88}."
. Phe maxinuun implied mass infall rate due to PR drag caleulated in this απο is l0ieess+ aud a few to several orders of iiaeuitude shorter than the inferred metal accretion rates for DAZ white dwarts.," The maximum implied mass infall rate due to PR drag calculated in this manner is $1.0\times
10^4$ $^{-1}$ and a few to several orders of magnitude shorter than the inferred metal accretion rates for DAZ white dwarfs."
 It should be noted that this model does not apply to disk particles excepting those at the iunermost edge which are exposed to the full starlight., It should be noted that this model does not apply to disk particles excepting those at the innermost edge which are exposed to the full starlight.
 IHTosvever. such particles should rapidly sublinate at some radius aud are then no longer subject to radiation drag. further corroborating that PR forces cannot account for the necessary dust/eas infall rates.," However, such particles should rapidly sublimate at some radius and are then no longer subject to radiation drag, further corroborating that PR forces cannot account for the necessary dust/gas infall rates."
state and opacity tables will be constructed im the phase space of (D.p.T. Z) covering the typical parameter values for cooling neutron stars.,"state and opacity tables will be constructed in the phase space of $B, \rho, T, Z$ ) covering the typical parameter values for cooling neutron stars."
paritv asvnunelry may be produced by (he svstematics associated. wilh kinematic dipole.,parity asymmetry may be produced by the systematics associated with kinematic dipole.
 This study also shows that the effect of the WAIAP kinematic dipole may extend to the hieher multipoles {ο22., This study also shows that the effect of the WMAP kinematic dipole may extend to the higher multipoles $l\sim 22$.
 The Planck survevor possesses wide lrequency. coverage and svslematics distinct [rom the WMADP., The Planck surveyor possesses wide frequency coverage and systematics distinct from the WMAP.
 In particular. it may take advantage of both CODE and WAIAP results [or the dipole calibration and meanwhile Planck satellite will have high signal-to-noise ratio in polarization data.," In particular, it may take advantage of both COBE and WMAP results for the dipole calibration and meanwhile Planck satellite will have high signal-to-noise ratio in polarization data."
 Therefore. we may apply the similar tests on the CAIB TE and EE data from the Planck survevor. ancl hope to resolve (he association between (he parity asviuelry and kinematic clipole.," Therefore, we may apply the similar tests on the CMB TE and EE data from the Planck surveyor, and hope to resolve the association between the parity asymmetry and kinematic dipole."
 We appreciate useful discussions with P. Coles., We appreciate useful discussions with P. Coles.
" We acknowledge the use of the Legacy Archive for Microwave ""ds Data Analvsis (LAMIBDA).", We acknowledge the use of the Legacy Archive for Microwave Background Data Analysis (LAMBDA).
 Our data analysis made the use of HEALPix (Gorskietal.2005). and GLESP (Doroshkevichοἱal.2005)., Our data analysis made the use of HEALPix \citep{healpix} and GLESP \citep{glesp}.
. This work is supportedin part bx Danmarks -- which allowed the establishment of the Danish Discovery Center.," This work is supported in part by Danmarks Grundforskningsfond, which allowed the establishment of the Danish Discovery Center."
 This work is supported by FNU grant. 272-06-0417. 272-07-0528 and 21-04-0355.," This work is supported by FNU grant 272-06-0417, 272-07-0528 and 21-04-0355."
much of the difference between our two luminosity estimates for the second brightest source in NGC 3379.,much of the difference between our two luminosity estimates for the second brightest source in NGC 3379.
 Excluding the central AGN. there are 39 detected sources in the central 5 kpe of the galaxy (see the luminosity function in Fig.," Excluding the central AGN, there are 39 detected sources in the central 5 kpc of the galaxy (see the luminosity function in Fig."
 3)., 3).
 We first fitted the luminosity function of all 39 sources using the maximum likelihood method in Crawford. Jauncey Murdoch (1970) to a power-law model (N(>L)—KL *) and obtained a best-fit index of α=0.60+0.15 (lo error).," We first fitted the luminosity function of all 39 sources using the maximum likelihood method in Crawford, Jauncey Murdoch (1970) to a power-law model $N(>L)=k L^{-\alpha}$ ) and obtained a best-fit index of $\alpha=0.60\pm 0.15$ $1 \sigma$ error)."
 This gives a reasonable fit at low fluxes. but significantly overestimates the number of brighter sources.," This gives a reasonable fit at low fluxes, but significantly overestimates the number of brighter sources."
 We then repeated the analysis only including sources detected at more than 46 and obtained an acceptable fit with α=0.80+0.2 (see Fig., We then repeated the analysis only including sources detected at more than $4 \sigma$ and obtained an acceptable fit with $\alpha=0.80\pm 0.2$ (see Fig.
 3)., 3).
 The luminosity function. does not have a break near the Eddington-limit of a neutron star (Li;=1.6«107P? ergs em7? s7!) as observed in some early-type galaxies (Sarazin et al., The luminosity function does not have a break near the Eddington-limit of a neutron star $L_{edd} = 1.6 \times 10^{-15}$ ergs $^{-2}$ $^{-1}$ ) as observed in some early-type galaxies (Sarazin et al.
 2001)., 2001).
 The flattening of the luminosity function at low fluxes may be due to the presence of extended emission in the center of the galaxy which raises the detection threshold in this region., The flattening of the luminosity function at low fluxes may be due to the presence of extended emission in the center of the galaxy which raises the detection threshold in this region.
 Kim Fabbiano (2004) recently derived the luminosity function for a sample of early-type galaxies. including NGC 3379. but they only included sources beyond the central 20” and within the Dos ellipse (5.4 by 4.89.," Kim Fabbiano (2004) recently derived the luminosity function for a sample of early-type galaxies, including NGC 3379, but they only included sources beyond the central $20^{\prime\prime}$ and within the $D_{25}$ ellipse $5.4^{\prime}$ by $4.8^{\prime}$ )."
 However. they obtained a best-fit index of 6=1.8 for the differential luminosity function. which corresponds to the same index we find for the cumulative luminosity function.," However, they obtained a best-fit index of $\beta=1.8$ for the differential luminosity function, which corresponds to the same index we find for the cumulative luminosity function."
 Colbert et al. (, Colbert et al. (
2004) calculated the pomt source luminosity function in 23 late-type galaxies and 9 early-type galaxies. including NGC 3379.,"2004) calculated the point source luminosity function in 23 late-type galaxies and 9 early-type galaxies, including NGC 3379."
 Fitting the luminosity function of the 12 sources with luminosities greater than 1079 eres s7! and within the Dos ellipse. they obtained a best-fit index for the cumulative luminosity function of 1.07. which is consistent with our results within the errors.," Fitting the luminosity function of the 12 sources with luminosities greater than $10^{38}$ ergs $^{-1}$ and within the $D_{25}$ ellipse, they obtained a best-fit index for the cumulative luminosity function of $1.07$, which is consistent with our results within the errors."
 In general. star forming galaxies have flatter luminosity functions than early-type galaxies.," In general, star forming galaxies have flatter luminosity functions than early-type galaxies."
 For example. Colbert et al.," For example, Colbert et al."
 find an average index for spiral and starburst galaxies of of @=0.60.8 compared to ellipticals with α~1.4., find an average index for spiral and starburst galaxies of of $\alpha=0.6-0.8$ compared to ellipticals with $\alpha \approx 1.4$.
" However. the average slope of the 14 ellipticals analyzed in the Kim Fabbiano (2004) sample is (t=0.9, which is consistent with our result for NGC 3379."," However, the average slope of the 14 ellipticals analyzed in the Kim Fabbiano (2004) sample is $\alpha=0.9$, which is consistent with our result for NGC 3379."
 While the ratio of the combined X-ray luminosity of the detected point sources in NGC 3379 to the optical luminosity of the galaxy is consistent with other early-type galaxies observed by Chandra (Colbert et al., While the ratio of the combined X-ray luminosity of the detected point sources in NGC 3379 to the optical luminosity of the galaxy is consistent with other early-type galaxies observed by Chandra (Colbert et al.
 2004). the point sources have a much more centrally peaked surface brightness profile than the optical light of the galaxy (see Fig.," 2004), the point sources have a much more centrally peaked surface brightness profile than the optical light of the galaxy (see Fig."
 4)., 4).
 The optical surface brightness profile in Fig., The optical surface brightness profile in Fig.
 4 is based on the de Vaucouleurs profile for NGC 3379 found by Capaccioli et al. (, 4 is based on the de Vaucouleurs profile for NGC 3379 found by Capaccioli et al. (
"1990) with r,=54.8"" and µε=22.24 mag arcsec7.",1990) with $r_e=54.8^{\prime\prime}$ and $\mu_e = 22.24$ mag $^{-2}$.
 For comparison. Finoguenov Jones (2002) found that there was a deficit of detected point sources in the core of M84 compared to the optical surface brightness profile of the galaxy.," For comparison, Finoguenov Jones (2002) found that there was a deficit of detected point sources in the core of M84 compared to the optical surface brightness profile of the galaxy."
 However. there is significantly more diffuse emission in M84 compared to NGC 3379. and the deficit of point sources in the core may be due to the lower sensitivity of detecting point sources in the presence of diffuse emission.," However, there is significantly more diffuse emission in M84 compared to NGC 3379, and the deficit of point sources in the core may be due to the lower sensitivity of detecting point sources in the presence of diffuse emission."
 Accounting for the lower sensitivity of detecting point sources in the core of NGC 3379. would only increase the excess of point sources within the central few kpe.," Accounting for the lower sensitivity of detecting point sources in the core of NGC 3379, would only increase the excess of point sources within the central few kpc."
 Of all the discrete sources in NGC 3379. only the ULX has sufficient counts for a detailed spectral analysis (see $3).," Of all the discrete sources in NGC 3379, only the ULX has sufficient counts for a detailed spectral analysis (see $\S 3$ )."
 To help in the identification of the detected point sources. we followed Prestwich et al. (," To help in the identification of the detected point sources, we followed Prestwich et al. ("
2003) and extracted counts in a soft band from 0.3-1.0 keV. a medium band from 1.0-2.0 keV and a hard band from 2.0-8.0 keV. We then computed a soft X-ray color from (M-S)/T and a hard X-ray color from MT. where T is the total number of counts in all 3 bands.,"2003) and extracted counts in a soft band from 0.3-1.0 keV, a medium band from 1.0-2.0 keV and a hard band from 2.0-8.0 keV. We then computed a soft X-ray color from (M-S)/T and a hard X-ray color from (H-M)/T, where T is the total number of counts in all 3 bands."
 The resulting color-color diagram for all non-nuclear sources detected at more than +o and within the central 5 kpe is shown in Fig., The resulting color-color diagram for all non-nuclear sources detected at more than $4 \sigma$ and within the central 5 kpc is shown in Fig.
 5., 5.
 The circle in Fig., The circle in Fig.
 5 delineates the color-color region associated with LMXBs determined by Prestwich et al., 5 delineates the color-color region associated with LMXBs determined by Prestwich et al.
 This, This
system alone remains vet uncertain. because the correct AIL ratio of stars as well as the amount of dark. matter in the progenitor galaxy is unavailable.,"system alone remains yet uncertain, because the correct $M/L$ ratio of stars as well as the amount of dark matter in the progenitor galaxy is unavailable."
 As a useful mocdel parameter to incorporate this ambieuity for the current kinematic analysis. we set a quantity fo as the fraction of the debris particles relative to halo stars near the Sun. so that the normalization of the halo density is fixed for the given number of the neighbor debris and. f.," As a useful model parameter to incorporate this ambiguity for the current kinematic analysis, we set a quantity $f$ as the fraction of the debris particles relative to halo stars near the Sun, so that the normalization of the halo density is fixed for the given number of the neighbor debris and $f$."
 A typical value of. f or the conversion of the simulated particles to the stars is estimated in the following manner., A typical value of $f$ for the conversion of the simulated particles to the stars is estimated in the following manner.
" Alodel 1 (model 2) viels 21 (74) particles at D<2 kpc. giving {)0 mass density of p,=0.41.3).10! M. H near the Sun. whereas the total mass density ancl metal-poor hao density have been derived as 8S«LO? M. ? (Crates. Gyuk. Turner 1995) and 6.2.107 M. 7 (CGoutel. Flynn. Baheall 1998). respectively."," Model 1 (model 2) yields 21 (74) particles at $D < 2$ kpc, giving the mass density of $\rho_g = 0.4 (1.3) \times 10^{-4}$ $_\odot$ $^{-3}$ near the Sun, whereas the total mass density and metal-poor halo density have been derived as $8 \times 10^{-3}$ $_\odot$ $^{-3}$ (Gates, Gyuk, Turner 1995) and $6.4 \times 10^{-5}$ $_\odot$ $^{-3}$ (Gould, Flynn, Bahcall 1998), respectively."
 Then. if the debris sars (wlΑΛ ων~LOT AL.) are distributed in the same manner as the simulated particles (with Mi;—5.74Lo” M. ) which would be a reasonable approximation in view of he clissipationless nature of stars. the mass density of the debris stars in the solar neighborhood can be estimated as ο=OO7) M. 7. which is about 1% of he halo density.," Then, if the debris stars (with $M_{stars} \sim 10^7$ $_\odot$ ) are distributed in the same manner as the simulated particles (with $M_{tot} =5.74 \times 10^8$ $_\odot$ ), which would be a reasonable approximation in view of the dissipationless nature of stars, the mass density of the debris stars in the solar neighborhood can be estimated as $(M_{stars}/M_{tot}) \rho_g = O(10^{-6})$ $_\odot$ $^{-3}$, which is about 1 of the halo density."
 Thus. f. defined here at D«2 kpe. is expected to be of order of a few percents.," Thus, $f$, defined here at $D<2$ kpc, is expected to be of order of a few percents."
 GWN recently. reported. their spectroscopic survey of ~2000 E/O stars down to V.=19.5 mag. in the direction against Galactic rotation (/.b)=(27707.45 )and (2707.|33° where radial velocities in combination of distances larecly reflect orbital angular momentum.," GWN recently reported their spectroscopic survey of $\sim 2000$ F/G stars down to $V = 19.5$ mag, in the direction against Galactic rotation $(l,b) = (270^\circ , -45^\circ)$ and $(270^\circ , +33^\circ)$, where radial velocities in combination of distances largely reflect orbital angular momentum."
 Their calibration of the stars at clistances of a few kpc from the Sun leads to the discovery of two stellar streams at ci;~100 kms + anc ~300 km s which are not explained by any existing Galactic components (see their Fig.2 and 3).," Their calibration of the stars at distances of a few kpc from the Sun leads to the discovery of two stellar streams at $v_{los}\sim 100$ km $^{-1}$ and $\sim 300$ km $^{-1}$ , which are not explained by any existing Galactic components (see their Fig.2 and 3)."
" While the stream at cei,LOO kim “was reproduced by their mode of a merging satellite in prograde rotation. the stream a Clow~BOO kin + remains vet unexplainect."," While the stream at $v_{los} \sim 100$ km $^{-1}$ was reproduced by their model of a merging satellite in prograde rotation, the stream at $v_{los}\sim 300$ km $^{-1}$ remains yet unexplained."
 Figure 3a shows the Όρος clistribution for the sinulatec debris of model 2 ancl halo stars of ο=0.7 (i.e. withou disks) at 1<Do«5 κρο 260°<|280°. and two Liccls for b.," Figure 3a shows the $v_{los}$ distribution for the simulated debris of model 2 and halo stars of $q=0.7$ (i.e. without disks) at $1<D<5$ kpc, $260^\circ<l<280^\circ$, and two fields for $b$ ."
 Figure 3b shows when disk stars are incorporated., Figure 3b shows when disk stars are incorporated.
" As is evident. the debris stars from c Cen's progenitor galaxy form a local peak at ej;300 Km ἐν whieh is provi bv many stars having (y,~100 km s! (Fig."," As is evident, the debris stars from $\omega$ Cen's progenitor galaxy form a local peak at $v_{los}\sim 300$ km $^{-1}$, which is provided by many stars having $v_\phi \sim -100$ km $s^{-1}$ (Fig."
 2)., 2).
 T is in good agreement with the ej;300 km 1 slres discovered by GWN., This is in good agreement with the $v_{los}\sim 300$ km $^{-1}$ stream discovered by GWN.
 X more Ilattened halo than the cz q=0.7. which is possible within a range of 0.55<qs (CB). vields a higher peak. since the density contrast of he debris relative to halo is made higher in this survey region.," A more flattened halo than the case $q=0.7$, which is possible within a range of $0.55 \le q \le 0.7$ (CB), yields a higher peak, since the density contrast of the debris relative to halo is made higher in this survey region."
 We also make a plot formodel 1 but do not present it here as it is essentially thesame as Figure 3 for model 2., We also make a plot formodel 1 but do not present it here as it is essentially thesame as Figure 3 for model 2.
 This, This
"with νιCQ)TSG40.2ς104ο2,",with $\mbox{N(}^{12}\mbox{CO)=7.86}\pm0.2\times10^{17}\mbox{ cm}^{-2}$.
 However. this would indicate a PCO PCO ratio of only 2.2. umch lower than the mean ratio fond in the local ISM (Wilson 1999).," However, this would indicate a $^{12}$ $^{13}$ CO ratio of only 2.2, much lower than the mean ratio found in the local ISM (Wilson 1999)."
 This indicates all of the observed £C0 lines are likely optically thick., This indicates all of the observed $^{12}$ CO lines are likely optically thick.
 To co‘ain the temperature of the absorbing gas. we modeled CO eas with à column deusity 2.12«1019cm7. estimated using the ΝΟ) ancl mean isotopic ratio of 6946 from Wilson (1999). and varied the turbulence and teniserature.," To constrain the temperature of the absorbing gas, we modeled $^{12}$ CO gas with a column density $2.42\times10^{19}\mbox{ cm}^{-2}$, estimated using the $^{13}$ CO) and mean isotopic ratio of $\pm$ 6 from Wilson (1999), and varied the turbulence and temperature."
 We could not inodel all tic PCO trasitions o a single temperature. with the low-J ‘ausitiolis always showing higher otical depths thai1 pernitted 1wv fits to the hieh-J transitions.," We could not model all the $^{12}$ CO transitions to a single temperature, with the low-J transitions always showing higher optical depths than permitted by fits to the high-J transitions."
" This is likev clue to unItidle velocity coniponents being viewed diu he ow-J transitions. whicj would account or the «ifference in veloc‘atv shift atc width from the jeh-J t‘ausitiojs,"," This is likely due to multiple velocity components being viewed in the low-J transitions, which would account for the difference in velocity shift and width from the high-J transitions."
 We lis fit only the hieh-J P(25-27. 30) transitions. and the eooducss-of-fit. shown in Fie.," We thus fit only the high-J P(25-27, 30) transitions, and the goodness-of-fit, shown in Fig."
 T. indicaος the gas is likely 370+20Ix with a Doppler »vaπο Verh214L2kans," 7, indicates the gas is likely $370\pm20\mbox{ K}$ with a Doppler b-value $\mbox{v}_{turb}=2.1\pm0.2\mbox{ km s}^{-1}$."
 If he CO is selfshiclding aid the 6 YBCO is raised to 100. similar to he ratios ound in 809. t10.0 Valles would no change mic jas the temperature would still be ~35r|k aud Veurh~Pions1," If the $^{12}$ CO is self-shielding and the $^{12}$ $^{13}$ CO is raised to 100, similar to the ratios found in S09, these values would not change much as the temperature would still be $\sim350\mbox{ K}$ and $\mbox{v}_{turb}\sim2\mbox{ km s}^{-1}$."
" We find he inodel for the COs eas has degenerate fits x changing the microtiurlence aud temperature. so we use the Do»pler b-value o 24luis5 found with the CO eas, and fixl T300 Iaid Χίο)=2.9«1019αι3."," We find the model for the $_{2}$ gas has degenerate fits by changing the microturbulence and temperature, so we use the Doppler b-value of $2.1\mbox{ km s}^{-1}$ found with the CO gas, and find $\mbox{T=300 K}$ and $\mbox{N(CO}_{2})=2.9\times10^{16}\mbox{ cm}^{-2}$."
" We further find upper limits for Coll, and ICN. two other organic molecules amdetected toward IRS 16 (Lalinis et al."," We further find upper limits for $_{2}$ $_{2}$ and HCN, two other organic molecules detected toward IRS 46 (Lahuis et al."
 2006). to compare molecular abnuudance ratios.," 2006), to compare molecular abundance ratios."
 To eet upper lits on column deusities. we note that temperatures of both the CO and CO. gases toward DG Tan D are similar to that found toward IRS 16 (1060 and 300Ik. respectively). so we start with the assiuuption that if Πο and IICN are present. they wonld have simular temperatures to IRS 16 (700 and 100. Ts. respectively).," To get upper limits on column densities, we note that temperatures of both the CO and $_{2}$ gases toward DG Tau B are similar to that found toward IRS 46 (400 and $\mbox{300 K}$, respectively), so we start with the assumption that if $_{2}$ $_{2}$ and HCN are present, they would have similar temperatures to IRS 46 (700 and 400 K, respectively)."
 To derive the upper linits. we individually modeled the absorption spectrin for the molecules at those temperatures.," To derive the upper limits, we individually modeled the absorption spectrum for the molecules at those temperatures."
 We then used the 1nodel-seneated profiles to measure feature strengths at varOs wavelengths in the DC Tau D spectra. eiving 1 DE! distribution of feature strengths we would expect to measure given only the spectral noise.," We then used the model-generated profiles to measure feature strengths at various wavelengths in the DG Tau B spectrum, giving us a distribution of feature strengths we would expect to measure given only the spectral noise."
 We then set the upper limit as the cohunun density that would provide a 26 inteerated intensity., We then set the upper limit as the column density that would provide a $\sigma$ integrated intensity.
" We find the upper limit on the Coll, CO» ratio ( 0.19) is not very different from the ratio measured for IRS 16 (0.3). sugeesting the nou-detection of Πο in our data may be the result of the lower absorbing cobuun in this source."," We find the upper limit on the $_{2}$ $_{2}$ $_{2}$ ratio (< 0.19) is not very different from the ratio measured for IRS 46 (0.3), suggesting the non-detection of $_{2}$ $_{2}$ in our data may be the result of the lower absorbing column in this source."
 The upper lanit on the COs ratio (0.22) is a factor of two sinaller than was measured for IRS 16 (0.5)., The upper limit on the $_{2}$ ratio (< 0.22) is a factor of two smaller than was measured for IRS 46 (0.5).
 Modeling the eas at ligher te1iperatures with similar cohuun densitics decreases the integrated intensity of the absorption features. so higher gas teniperatures would result in higher upper hlinits on the cobuun densities.," Modeling the gas at higher temperatures with similar column densities decreases the integrated intensity of the absorption features, so higher gas temperatures would result in higher upper limits on the column densities."
 A temperature increase of 50Ik woul raise the cobuun deusitv upper laut bv ~15% for both inolecules., A temperature increase of $\mbox{50 K}$ would raise the column density upper limit by $\sim$ for both molecules.
 If we model the molecules at 300Ix. like he CO» gas. the upper limits of the Ου Πο COs. aud CO. ratios wold be 0.06 and 0.18. respectively.," If we model the molecules at $\mbox{300 K}$, like the $_{2}$ gas, the upper limits of the $_{2}$ $_{2}$ $_{2}$ and $_{2}$ ratios would be 0.06 and 0.18, respectively."
 The eiission. as secu. toward DC Tan D. is a feature commonly found by Spitzer IRS toward TTSs (Lahnuis ot al.," The emission, as seen toward DG Tau B, is a feature commonly found by Spitzer IRS toward TTSs (Lahuis et al."
 2007)., 2007).
 Ciüddel et al. (, Güddel et al. (
2010) showed that among TTS the emission strength increases with the jet mass loss rate. the latter as inferred from the high velocity component of the emission.,"2010) showed that among TTS the emission strength increases with the jet mass loss rate, the latter as inferred from the high velocity component of the emission."
 Muudt Fried (1983) found that TTI 159.[OT] a jet associated with DG Tan D. has a 11ass loss rate of 10ὉMoyrl," Mundt Fried (1983) found that HH 159, a jet associated with DG Tau B, has a mass loss rate of $10^{-9}\mbox{ M}_{\bigodot}\mbox{ yr}^{-1}$."
 Tf we asstune DC Tan D is 115pe away. our measured huninosityB ofoe 7.5«41077DIMcress+ is+ sinilar+. to that of TTSB with comparable mass loss rates (cf.," If we assume DG Tau B is $\mbox{145 pc}$ away, our measured luminosity of $7.5\times10^{27}\mbox{ ergs s}^{-1}$ is similar to that of TTS with comparable mass loss rates (cf."
 Fig., Fig.
 5. Caiddel et al.," 5, Güddel et al."
 2010)., 2010).
 As we do not see CoII» aud IICN in the disk. a simple explanation is they have low abundances in the disk.," As we do not see $_{2}$ $_{2}$ and HCN in the disk, a simple explanation is they have low abundances in the disk."
 This could possibly be due to plotodissociation., This could possibly be due to photodissociation.
 The ciission may be an indication the gas is irradiated[NeH] by X-rays (Classeold et al., The emission may be an indication the gas is irradiated by X-rays (Glassgold et al.
 2007). andor UV irradiation (Hollenbach Corti 2009). which in turn could reduce the Cols aud ICN in the disk.," 2007), and/or UV irradiation (Hollenbach Gorti 2009), which in turn could reduce the $_{2}$ $_{2}$ and HCN in the disk."
 However. many T Tauri stars with cuiission similar to or stronger than that of DC Tau B show emission in Colls and IICN (Carr Najita 2011. in prep).," However, many T Tauri stars with emission similar to or stronger than that of DG Tau B show emission in $_{2}$ $_{2}$ and HCN (Carr Najita 2011, in prep)."
 Alternatively. as CoILo and IICN are couunoulv found in circuustellar disks (Pontoppidan ct al.," Alternatively, as $_{2}$ $_{2}$ and HCN are commonly found in circumstellar disks (Pontoppidan et al."
 2010). these species could be in the disk but sinuiply not in our line of sieht.," 2010), these species could be in the disk but simply not in our line of sight."
 This may be implied by the most striking difference etween DC Tan Band IRS 16: while the coluun deusity of CO toward DG Tan D is only 10 times that toward IRS 16. the eas ratios to CO 11DG Tan Ba e of hat found toward IRS 16 (see Table 6).," This may be implied by the most striking difference between DG Tau B and IRS 46: while the column density of CO toward DG Tau B is only 10 times that toward IRS 46, the gas ratios to CO in DG Tau B are of that found toward IRS 46 (see Table 6)."
 Also. the Inuits on the ratios N(CCSID)). NCCO) aud NOICNN(C‘O) are uuch smaller for DOG. Tan B than he measired ratios oward GV Tan N (Cibb et al.," Also, the limits on the ratios $_{2}$ $_{2}$ )/N(CO) and N(HCN)/N(CO) are much smaller for DG Tau B than the measured ratios toward GV Tau N (Gibb et al."
 2007)., 2007).
 While t10 arec CO column toward DG Tan B implies we are probing a aree amount of disk material. we are not detecting the arge columns of other easeous species.," While the large CO column toward DG Tau B implies we are probing a large amount of disk material, we are not detecting the large columns of other gaseous species."
 The disk chemistry model in Agüundez ct al. (, The disk chemistry model in Agúnndez et al. (
2008) lav provide further insight into hne disk coiditious olx«b by our observations.,2008) may provide further insight into the disk conditions probed by our observations.
 They focus their 1nodels on tlj6 photon dominated region o| fhe disk. and 1SC ;ohot«eemistrv to estimate the steaclv state abuLaces of siuple organic molecules.," They focus their models on the photon dominated region of the disk, and use photochemistry to estimate the steady state abundances of simple organic molecules."
 They show the CoII» aid IICN iwe low abundances for disk radii 1.5AU. ancl the COs is laree for radii 1AU.," They show the $_{2}$ $_{2}$ and HCN have low abundances for disk radii $\mbox{>1.5 AU}$ , and the $_{2}$ is large for radii $\mbox{<1 AU}$."
 Wule the cliperatures we ineasured for CO aud COs are cooer han expected for radii 1 AU. the vertical structure hese nolecules is not available.," While the temperatures we measured for CO and $_{2}$ are cooler than expected for radii <1 AU, the vertical structure of these molecules is not available."
 One possible scenari is the line of sight passes below the main teniperati inversio1 laver., One possible scenario is the line of sight passes below the main temperature inversion layer.
 Doppnoenn of al. (, Doppmann et al. (
2008) note GV. Tan N has a arger m.SiO πο...jui other Class I YSOs in Tiris (tvpical Nm1: Furlan et al.,2008) note GV Tau N has a larger $\tau_{SiO}/\tau_{CO_{2}ice}$ than other Class I YSOs in Taurus (typically $\le4$; Furlan et al.
 2008). ancl sugecs this could lappCll if à majoriv of the probed. silicate Is residing ia wa21 region o the disk atinosphere.," 2008), and suggest this could happen if a majority of the probed silicate is residing in a warm region of the disk atmosphere."
 We calculate his atio for DG Ται D and IRS 16 for comyarison., We calculate this ratio for DG Tau B and IRS 46 for comparison.
 To do this. we ned a polvuoiial fit acToss the features to determune the initial continua.," To do this, we used a polynomial fit across the features to determine the initial continua."
" For he silicate cature. we fi to the continni iu the 13-11. unu regkn. aud to the contimuun o'hween the water and ""mehanol"" ice a wavelenetls 7.5 ul. For t1C CO» eature. we asstune the CO» ice is located at larger disk racΠ than the silicate. as found by Watson et al. ("," For the silicate feature, we fit to the continuum in the 13-14.8 m region, and to the continuum between the water and ""methanol"" ice at wavelengths <7.8 m. For the $_{2}$ feature, we assume the $_{2}$ ice is located at larger disk radii than the silicate, as found by Watson et al. ("
2001). so t11ο 100 Is absor‘bing froma coutimmun already ichiding the silicate absorpon features.,"2004), so the ice is absorbing from a continuum already including the silicate absorption features."
 We thus use a continui or DG Tau D that is modifiedfrom that used in Watso ret al. (, We thus use a continuum for DG Tau B that is modifiedfrom that used in Watson et al. (
200). found by fitting the spectrum at wavelengths 13- yun and15.6 uuu. The continua fits are shown,"2004), found by fitting the spectrum at wavelengths 13-14.8 m and>15.6 m. The continuum fits are shown"
satisfy the above conditions.,satisfy the above conditions.
 We consider in this plot only objects that experienced at least one merger event., We consider in this plot only objects that experienced at least one merger event.
 The solid line shows the mean number of mergers for subhaloes that were accreted at ο«0.5. while the dotted line shows the resulting merger rate for objects accreted between 1.," The solid line shows the mean number of mergers for subhaloes that were accreted at $z<0.5$, while the dotted line shows the resulting merger rate for objects accreted between $0.5< z \leq 1$ ."
 The figure shows that in both cases. the slope of the lines become shallower close to the accretion time. ic. mergers between substructures are suppressed. because of the lareec velocity dispersion of the parent haloes.," The figure shows that in both cases, the slope of the lines become shallower close to the accretion time, i.e. mergers between substructures are suppressed because of the large velocity dispersion of the parent haloes."
 Laterestingly. haloes that were accreted earlier experience. on average. one more major merger than haloes accreted at later times.," Interestingly, haloes that were accreted earlier experience, on average, one more major merger than haloes accreted at later times."
 We repeat the same analysis looking at the merging rate as a function of environment., We repeat the same analysis looking at the merging rate as a function of environment.
 Fie., Fig.
 11. shows the cumulative number of mergers for subhaloes in our five samples., \ref{mergenv} shows the cumulative number of mergers for subhaloes in our five samples.
 The mean number of mergers Increases as a function of the parent halo mass. although subhaloes in the sample S4 experience on average fewer mergers than subhaloes in the sample 85.," The mean number of mergers increases as a function of the parent halo mass, although subhaloes in the sample S4 experience on average fewer mergers than subhaloes in the sample S5."
 ‘This is not surprisingD since subhaloes in the surroundings5 of, This is not surprising since subhaloes in the surroundings of
Lakes place including how flix evolves in the process are not vel well understood.,takes place including how flux evolves in the process are not yet well understood.
 IIere we have introduced a simple model for reconnection at an isolated non-ideal region threaded bv a magnetic separator in an effort to better understand the basics of the process., Here we have introduced a simple model for reconnection at an isolated non-ideal region threaded by a magnetic separator in an effort to better understand the basics of the process.
 Our first new finding is (hat reconnection events in the neiehbourhood of a separator can (and if sulliciently strong do) create new separators., Our first new finding is that reconnection events in the neighbourhood of a separator can (and if sufficiently strong do) create new separators.
 This occurs even though the null points theniselves remain in an ideal region., This occurs even though the null points themselves remain in an ideal region.
 Such a bifurcation of separators has to occur in pairs 3. 5. 7... separators) and the reverse process is. of course. also possible.," Such a bifurcation of separators has to occur in pairs 3, 5, 7, ... separators) and the reverse process is, of course, also possible."
 The fan planes of the two null points divide the space into distinct regions which can be distinguished due to (he connectivity of their field lines with respect to any. surface enclosing the configuration., The fan planes of the two null points divide the space into distinct regions which can be distinguished due to the connectivity of their field lines with respect to any surface enclosing the configuration.
 Each bihucation introduces a new pair of flix domains wilh a connectivity different from their neighbouring fhixes., Each bifurcation introduces a new pair of flux domains with a connectivity different from their neighbouring fluxes.
 The rate of change of flux between four neighbouring flux domains is usually found bv the integral of the parallel electric field along their dividing separator., The rate of change of flux between four neighbouring flux domains is usually found by the integral of the parallel electric field along their dividing separator.
 ILowever. in cases where multiple separators thread the non-ideal region the change in flux between domains is more complicated. as expressed here by Equation(12).. ancl it will typically be less (han the maximum of rates along the separators due to recursive reconnection between separators.," However, in cases where multiple separators thread the non-ideal region the change in flux between domains is more complicated, as expressed here by Equation, and it will typically be less than the maximum of rates along the separators due to recursive reconnection between separators."
 Furthermore. consideraGons of asymmetric cases show that the maximum of fEdl does not have (o occur along a separator and hence even [or a single separator and a single isolated reconnection region the maxiniun integrated parallel electric field may not correspond to (the rate of change of flux between domains.," Furthermore, considerations of asymmetric cases show that the maximum of $\int {\bf E}_\| dl$ does not have to occur along a separator and hence even for a single separator and a single isolated reconnection region the maximum integrated parallel electric field may not correspond to the rate of change of flux between domains."
 In three dimensions the topology of the magnetic field must be known before a meaningful reconnection rate can be determined., In three dimensions the topology of the magnetic field must be known before a meaningful reconnection rate can be determined.
 Finally. the nature of (he magnete flix evolution in a separator reconnection process shows several distinguishing characteristics including rotational flux velocities (hat are split along the separator.," Finally, the nature of the magnetic flux evolution in a separator reconnection process shows several distinguishing characteristics including rotational flux velocities that are split along the separator."
 These characteristics are present regardless of whether the separator, These characteristics are present regardless of whether the separator
for momentum. thermal energy and so on reduce to the exact fluid equations.,"for momentum, thermal energy and so on reduce to the exact fluid equations."
 The reader is referred to Monaghan(1992) for a review., The reader is referred to \citet{mon} for a review.
 The code used for this work is based on a vectorised version of the three-dimensional accretion dise code developed by Murray (1996)., The code used for this work is based on a vectorised version of the three-dimensional accretion disc code developed by \citet{mur96}.
 There are four key elements of physics that must be included in a code that attempts to describe the behaviour of a system like GRS | 105. accreting near the Eddington limit: an implementation of the viscous instability to drive the outburst. a description of the tidal forces of the secondary star on the disc. the effect of self-irradiation of the dise by the X-rays generated near the primary and mass loss when the Eddington limit is breached.," There are four key elements of physics that must be included in a code that attempts to describe the behaviour of a system like GRS $+$ 105, accreting near the Eddington limit: an implementation of the viscous instability to drive the outburst, a description of the tidal forces of the secondary star on the disc, the effect of self-irradiation of the disc by the X-rays generated near the primary and mass loss when the Eddington limit is breached."
 We will describe each of these in turn., We will describe each of these in turn.
 The dise instability. which is driven by the onset of ionization in the temperature range 6.000 to 7.000 K. is implemented by a viscous switch based on the local dise conditions.," The disc instability, which is driven by the onset of ionization in the temperature range 6,000 to 7,000 K, is implemented by a viscous switch based on the local disc conditions."
" The viscosity. 7. is given by the formula of Shakura&Sunyaev(1973): where c, is the local sound speed. // the scale height and a djs the viscosity parameter."," The viscosity, $\nu$, is given by the formula of \citet{sha}: where $c_{\rmn s}$ is the local sound speed, $H$ the scale height and $\alpha$ is the viscosity parameter."
 It is well known that the increase in temperature at the transition from quiescence to outburst is insufficient to provide the angular momentum transport required to drive the mass accretion rates observed during an outburst., It is well known that the increase in temperature at the transition from quiescence to outburst is insufficient to provide the angular momentum transport required to drive the mass accretion rates observed during an outburst.
 Hence. it is inferred that the heating is accompanied by an increase in the viscosity parameter a.," Hence, it is inferred that the heating is accompanied by an increase in the viscosity parameter $\alpha$ ."
 In previous SPH studies of outbursts in accretion dises. a was allowed to change instantaneously (Murray 1998).. or on some fixed time-scale (Trussetal.2000).. but ὃς was kept fixed.," In previous SPH studies of outbursts in accretion discs, $\alpha$ was allowed to change instantaneously \citep{mur98}, or on some fixed time-scale \citep{tru00}, but $c_{\rmn{s}}$ was kept fixed."
 Here. we allow the sound speed as well as the viscosity parameter to vary on a time-scale that is determined by the local conditions.," Here, we allow the sound speed as well as the viscosity parameter to vary on a time-scale that is determined by the local conditions."
 Recently. a similar method was applied to the outbursts of cataclysmic variables CTruss.Wynn&Wheatley2004).," Recently, a similar method was applied to the outbursts of cataclysmic variables \citep{tru04}."
.. The method is able to reproduce a full. realistic outburst amplitude with none of the scaling factors required by the previous schemes that used a constant sound speed everywhere.," The method is able to reproduce a full, realistic outburst amplitude with none of the scaling factors required by the previous schemes that used a constant sound speed everywhere."
" In this approach. we would not reproduce the expected temperature profile of a disc in steady state. where c,x2277. because we have lower and upper bounds to the sound speed (but allow a continuum of states between)."," In this approach, we would not reproduce the expected temperature profile of a disc in steady state, where $c_{\rmn{s}} \propto R^{-3/8}$, because we have lower and upper bounds to the sound speed (but allow a continuum of states between)."
 However. as we shall see. once the outburst is underway the dise as a whole spends little or none of its time in a single state and most of its behaviour is governed by local processes: changes in sound speed and mass loss occur in relatively small regions. rather than globally across the disc.," However, as we shall see, once the outburst is underway the disc as a whole spends little or none of its time in a single state and most of its behaviour is governed by local processes; changes in sound speed and mass loss occur in relatively small regions, rather than globally across the disc."
 It is not clear. then. that a fully self- calculation - computationally. this remains inviable in a two-dimensional hydrodynamic simulation of this magnitude - would produce vastly different results.," It is not clear, then, that a fully self-consistent calculation - computationally, this remains inviable in a two-dimensional hydrodynamic simulation of this magnitude - would produce vastly different results."
 Until this becomes possible. we believe that the method we describe here. which allows for realistic local changes in sound speed. offers a better prospect than the fully-isothermal schemes of the past.," Until this becomes possible, we believe that the method we describe here, which allows for realistic local changes in sound speed, offers a better prospect than the fully-isothermal schemes of the past."
 The sound speed and temperature are changed in response to the local surface density calculated at the position of each particle., The sound speed and temperature are changed in response to the local surface density calculated at the position of each particle.
" We define critical surface densities. V,,,4 and “avin to trigger an outburst and to return to quiescence respectively."," We define critical surface densities, $\Sigma_{\rmn{max}}$ and $\Sigma_{\rmn{min}}$ to trigger an outburst and to return to quiescence respectively."
 These critical values scale almost linearly with radius in the dise (Ludwig.Meyer-Hofmeister&Ritter 199:4)., These critical values scale almost linearly with radius in the disc \citep{lud}.
". When the surface density at a particle crosses one of these values. both the sound speed and the viscosity parameter are changed smoothly according to and The thermal time-scale for the change. /,,. is defined as the ratio ofthe heat content per unit (projected) area of the disc. Nez. to the total rate of energy loss per unit area. which taking into account both faces of the disc is 0/NCM,/42%."," When the surface density at a particle crosses one of these values, both the sound speed and the viscosity parameter are changed smoothly according to and The thermal time-scale for the change, $t_{\rmn{th}}$, is defined as the ratio of the heat content per unit (projected) area of the disc, $\Sigma 
c_{\rmn{s}}^{2}$, to the total rate of energy loss per unit area, which taking into account both faces of the disc is $9 \nu \Sigma GM_{1} / 4R^{3}$."
 Therefore. the thermal time-scale The calculations are performed in the full Roche potential of a binary ystem.," Therefore, the thermal time-scale The calculations are performed in the full Roche potential of a binary system."
 In this way the tidal influence of the secondary star is intrinsic to the scheme., In this way the tidal influence of the secondary star is intrinsic to the scheme.
 For the mass ratio gq=MS/0.07 inferred for GRS 1915] 105. we expect the tides to have a significant effect on the orbits near the outer edge of the accretion disc. and to launch a two-armed spiral wave.," For the mass ratio $q = M_2 / M_1 \sim 0.07$ inferred for GRS $+$ 105, we expect the tides to have a significant effect on the orbits near the outer edge of the accretion disc, and to launch a two-armed spiral wave."
 Mass transfer from the secondary star is implemented by the injection of particles at the inner Lagrangian point., Mass transfer from the secondary star is implemented by the injection of particles at the inner Lagrangian point.
 The rate of mass injection is independent of the physical conditions at the edge of the dise and is kept constant throughout the ealeulation. regardless of whether the disc is quiescent or in outburst.," The rate of mass injection is independent of the physical conditions at the edge of the disc and is kept constant throughout the calculation, regardless of whether the disc is quiescent or in outburst."
" We use a simple model due to King&Ritter(1998).. in which the X-rays emitted near the black hole keep the dise in the hot. high viscosity state out to a certain radius/*, which is determined by the central accretion rate."," We use a simple model due to \citet{kin98}, in which the X-rays emitted near the black hole keep the disc in the hot, high viscosity state out to a certain radius$R_{\rmn{h}}$ which is determined by the central accretion rate."
 Matching the irradiation temperature to the minimum temperature to keep hydrogen ionised. 7H. we have," Matching the irradiation temperature to the minimum temperature to keep hydrogen ionised, $T_{\rmn{H}}$ , we have"
We build the nieasured SED for he 210 coufirmed Ly u emitting galaxies. using up to 15 photometric baids.,"We build the measured SED for the 210 confirmed $\mu$ m emitting galaxies, using up to 15 photometric bands."
 These SEDs are compared ο. semui-enipirical tenipates from 7.. which are uticularlv well acapte to fitting infrared cuitting ealaxies.," These SEDs are compared to semi-empirical templates from \citet{pol07}, which are particularly well adapted to fitting infrared emitting galaxies."
 There are several templates for Elliptical. Spiral. Starburst ealaxics. and ACN.," There are several templates for Elliptical, Spiral, Starburst galaxies, and AGN."
 These are sed on results from he GRASIL (7?) code combined with photomeric data from IR ealaxics and AGN., These are based on results from the GRASIL \citep{silv98} code combined with photometric data from IR galaxies and AGN.
 The vest-fit is the template with he lowest chi-square., The best-fit is the template with the lowest chi-square.
 Figue 7 shows a few exanrples of confriuec chster members which rave photometry in the representative xuaciwidtlis (optical. Near-IR and Mia-IB) aud redshifts vetween 0.015-0.035.," Figure \ref{sedpops} shows a few examples of confirmed cluster members which have photometry in the representative bandwidths (optical, Near-IR and Mid-IR) and redshifts between 0.015-0.035."
 The total iifrarec Iuninositv is found by πορταιο the flux density between 1000502 ofthe best fit template., The total infrared luminosity is found by integrating the flux density between $\mu$ m of the best fit template.
" Ouly bof the 2] cluster mcuibers correspoucd to a best-fit templa which is completely dominaed bv an ACN,", Only 4 of the 210 cluster members correspond to a best-fit template which is completely dominated by an AGN.
 To determine the galaxy stellar mass. we use the y.cllay 110del templates o£ ?. witha Ixroupa initial mass function (?).. adopting a solar metallicity.," To determine the galaxy stellar mass, we use the stellar model templates of \citet{mar05} with a Kroupa initial mass function \citep{kro01}, adopting a solar metallicity."
 These models describe the stellay cussion from the UV to the Near-IR and we limit the fits to the optical and Near-IR portion of our observed SED. up to ouly TRAC 3.6 and L5yjan. We iodify the template SEDs in accordance with the ? extinction law. allowing E(D-V) to vary between 0 and 1.," These models describe the stellar emission from the UV to the Near-IR and we limit the fits to the optical and Near-IR portion of our observed SED, up to only IRAC 3.6 and $\mu$ m. We modify the template SEDs in accordance with the \citet{cal00} extinction law, allowing E(B-V) to vary between 0 and 1."
 We then fit our observed SEDs to the host of available ? cluplates. aud retrieve he stellar lass from he best-fit model.," We then fit our observed SEDs to the host of available \citet{mar05} templates, and retrieve the stellar mass from the best-fit model."
 Photomeric points from our Near-IR photometry. aud those from the TRAC banes help to tightly coustrain f1e SED fit around the stellar mass bunip.," Photometric points from our Near-IR photometry, and those from the IRAC bands help to tightly constrain the SED fit around the stellar mass bump."
 Table 2 eives the calculated stellar nass for the 210 MIPS neniIOLS, Table \ref{elines} gives the calculated stellar mass for the 210 MIPS members.
", We convert the total infrared huninositv to a star formation rate (listed in Table 2)) using the Ikeunicutt relationship (?)..", We convert the total infrared luminosity to a star formation rate (listed in Table \ref{elines}) ) using the Kennicutt relationship \citep{ken98}.
 The specific star formation rate is simply the SER divided by the stellar mass., The specific star formation rate is simply the SFR divided by the stellar mass.
 It is a useful paralucterization since Coma ds host to a variety of ealaxies., It is a useful parameterization since Coma is host to a variety of galaxies.
 For example. a dwart starburst galaxy may have auch smaller SER than a large passive elliptical. vet a higher value of sSFR.," For example, a dwarf starburst galaxy may have a much smaller SFR than a large passive elliptical, yet a higher value of sSFR."
 Iu most of our discussion. we preset the ratio fy. define as the «7. the timescale over which the galaxy is assumed to form stars at the currently observed rate.," In most of our discussion, we present the ratio $_{sb}$, defined as the $\times$$\tau$, the timescale over which the galaxy is assumed to form stars at the currently observed rate."
 We take 7= LOOAIvr following ?..," We take $\tau\,=\,$ $\,$ Myr following \citet{fad06}."
" Starinrst ealaxies here are those with fy,0.1.", Starburst galaxies here are those with $_{sb} >$ 0.1.
 Figure ὃ shows the specific star formation rates with the ealaxv flux at each of tle Mid-TR wavelengths., Figure \ref{nspec} shows the specific star formation rates with the galaxy flux at each of the Mid-IR wavelengths.
 A range of μα hDuninosities eive high specific star formation rates. sugeesting that fitting the total SED. which fiuds both the mass. as well as the star formation rate. may provide a break in the ceegcueracy that exists when deriving star formation rates purely from the [jin Iuninosity.," A range of $\mu$ m luminosities give high specific star formation rates, suggesting that fitting the total SED, which finds both the mass, as well as the star formation rate, may provide a break in the degeneracy that exists when deriving star formation rates purely from the $\mu$ m luminosity."
 We separate Figure 8 into four regions of SSER., We separate Figure \ref{nspec} into four regions of sSFR.
 The passive ealaxies have SER « 5410. ! |. low star formers have 5.10 κ sSFR « 5«10 1. normal star foriuins galaxies have «10 < sSFR « (0 |o and staybursts have sSFR > O11 Lo," The passive galaxies have sSFR $<$ $\times$ $^{-4}$ $^{-1}$, low star formers have $\times$ $^{-4}$ $<$ sSFR $<$ $\times$ $^{-3}$ $^{-1}$, normal star forming galaxies have $\times$ $^{-3}$ $<$ sSFR $<$ 0.1 $^{-1}$, and starbursts have sSFR $>$ 0.1 $^{-1}$."
 λίαν of the MIPS-detected galaxies are passive. and the IR cmiussion is likely a result of dust expelled by the large umuber of stars at later stages of their evolution (?7)..," Many of the MIPS-detected galaxies are passive, and the IR emission is likely a result of dust expelled by the large number of stars at later stages of their evolution \citep{tem08,cal10}."
 The best-fit SED ealaxy type. as given by the (upizical SED. is plotted as a histogram with specific star formation in Figure 8..," The best-fit SED galaxy type, as given by the empirical SED, is plotted as a histogram with specific star formation in Figure \ref{sfrtype}."
 The Elliptical. SU. aud Spiral galaxy types correspond well to the expected behavior of the desiguatious we set based ou the sSFR. with passive (< 5410 {Gyr i) corresponding to ellipticals.," The Elliptical, S0, and Spiral galaxy types correspond well to the expected behavior of the designations we set based on the sSFR, with passive $<$ $\times$ $^{-4}$ $^{-1}$ ) corresponding to ellipticals."
 The few ACN are also cisplaved., The few AGN are also displayed.
 We now turn to a ciscussiou of the star formation rates based on SED fitting., We now turn to a discussion of the star formation rates based on SED fitting.
 Iu examining the galaxy colors. we find that the most red ealaxies have the lowest sSFRs. and that a few ealaxies with normal specific SETS are also red.," In examining the galaxy colors, we find that the most red galaxies have the lowest sSFRs, and that a few galaxies with normal specific SFRs are also red."
 We compare the SSERs based on SED fitting. to values based purely on MIPS tau observations. confirnune earlier results aud extending to lower stellar mass.," We compare the sSFRs based on SED fitting, to values based purely on MIPS $\mu$ m observations, confirming earlier results and extending to lower stellar mass."
 Additionally. we find that fits includiug TOjnn data estimate slightly higher sSFRs than those frou: MIPS tran observatious alone.," Additionally, we find that fits including $\mu$ m data estimate slightly higher sSFRs than those from MIPS $\mu$ m observations alone."
 We compare the obscured sSFRs to extiuctiou- star formation rates derived from Πα Cluission lines., We compare the obscured sSFRs to extinction-corrected star formation rates derived from $\alpha$ emission lines.
 As we will sec. the extinction corrected mnobscured values are able to completely," As we will see, the extinction corrected unobscured values are able to completely"
The observational evidence of the present accelerated cosmic expansion represents one of the major challenges to our understanding of the Universe.,The observational evidence of the present accelerated cosmic expansion represents one of the major challenges to our understanding of the Universe.
 The standard ACDAL cosmological model identifies the origin of this acceleration with a cosmological constant term in the field. equations of General Relativity., The standard $\Lambda $ CDM cosmological model identifies the origin of this acceleration with a cosmological constant term in the field equations of General Relativity.
 However. this interpretation sullers of extremely severe. fine-tuning problems. and possible alternative explanations of the accelerated: expansion in erms of a Dark ποιον (DIE) dynamical field. have been xoposed (asc.g.by—??7)..," However, this interpretation suffers of extremely severe fine-tuning problems, and possible alternative explanations of the accelerated expansion in terms of a Dark Energy (DE) dynamical field have been proposed \citep[as \eg by ][]{Wetterich_1988,Ratra_Peebles_1988,
 ArmendarizPicon_etal_2000}."
 Among these. particular attention has been recently. devoted to coupled. DE models (CDE) (????7) where a direct. interaction between the DE ielel and Cold. Dark Matter. (CDM). particles determines reculiar features. in the background. expansion of the Universe (eg2).. in the evolution of linear. density »erturbations (e.g.2).. and even in the nonlinear dynamics of collapsed. structures at small scales (e.g.77) lt," Among these, particular attention has been recently devoted to coupled DE models (cDE) \citep{Wetterich_1995,Amendola_2000,Farrar_Peebles_2004,Baldi_2010}
 where a direct interaction between the DE field and Cold Dark Matter (CDM) particles determines peculiar features in the background expansion of the Universe \citep[\eg][]{Amendola_2000}, in the evolution of linear density perturbations \citep[\eg][]{DiPorto_Amendola_2008}, and even in the nonlinear dynamics of collapsed structures at small scales \citep[\eg][]{Baldi_etal_2010,Baldi_2010}."
 ds herefore of crucial importance in the present cosmological investigation to devise observational tests capable to distinguish. between the standard ACDAL cosmoloey and alternative DIE moclels as the eDE scenario (??)..," It is therefore of crucial importance in the present cosmological investigation to devise observational tests capable to distinguish between the standard $\Lambda $ CDM cosmology and alternative DE models as the cDE scenario \citep{Honorez_etal_2010,Baldi_Pettorino_2010}."
 In the present work. we explore the possibility to use the observed properties of the diffuse barvonie matter at high redshifts as a direct. probe to test ancl constrain CDE cosmologies.," In the present work, we explore the possibility to use the observed properties of the diffuse baryonic matter at high redshifts as a direct probe to test and constrain cDE cosmologies."
 Standard. cosmological models based on cold. dark matter plus a cosmological constant predict. that. most of the barvons at high. redshift are in a cdilluse form. the Interealactic Aleclium (GM). anc fill a significant portion of the Universe. giving rise to the so-called cosmic web: a network of median Uuctuated filaments interconnecting galaxies and tracing the underlying dark matter distribution.," Standard cosmological models based on cold dark matter plus a cosmological constant predict that most of the baryons at high redshift are in a diffuse form, the Intergalactic Medium (IGM), and fill a significant portion of the Universe, giving rise to the so-called cosmic web: a network of median fluctuated filaments interconnecting galaxies and tracing the underlying dark matter distribution."
 A great. progress in the study of the IGAL has been recently mace thanks to the large data sets available ancl in particular high resolution quasar (QSO) spectra or LILES) and the low resolutionSurvey (SDSS) QSO spectra: the present limitations appear to be of systematic nature rather than statistical., A great progress in the study of the IGM has been recently made thanks to the large data sets available and in particular high resolution quasar (QSO) spectra or HIRES) and the low resolution (SDSS) QSO spectra: the present limitations appear to be of systematic nature rather than statistical.
 High and low-resolution QSO spectra of. clistant sources are thus very useful in characterizing the properties of the underlying mass density Geld at 2=6 along the line- (e.g.222???) and are now routinely analvzed to reconstruct the matter distribution in threc-dimoensions.," High and low-resolution QSO spectra of distant sources are thus very useful in characterizing the properties of the underlying mass density field at $z=2-6$ along the line-of-sight \citep[\eg][]{bi,croft02,viel04,mcdonald05,meiksin09}
 and are now routinely analyzed to reconstruct the matter distribution in three-dimensions."
"More than a decade after the discovery of cosmic acceleration (Riessetal.1998:Perlmutteretal.1999)., its cause (dubbed ""dark energy"" for convenience) remains shrouded in mystery.","More than a decade after the discovery of cosmic acceleration \citep{Riess98,Perl99}, its cause (dubbed “dark energy” for convenience) remains shrouded in mystery."
 While current observational data are consistent with dark energy being a cosmological constant. the uncertainties are large. and do not rule out models with dynamical scalar fields (see. e.g.. 2009)). or models that modify general relativity (see e.g. Sahni&Habib1998:ParkerO'Callaghan.Gregory.&Pourtsidou 2009)).," While current observational data are consistent with dark energy being a cosmological constant, the uncertainties are large, and do not rule out models with dynamical scalar fields (see, e.g., ), or models that modify general relativity (see e.g., \citealt{SH98,Parker99,Boisseau00,DGP00,Freese02,Capozziello05,Pad08,Kahya09,OCallaghan09}) )."
 For recent reviews. see," For recent reviews, see"
.2in The anisotropy of stellar orbits in elliptical galaxies can be estimated frou the temperature of the lot interstellar gas through which they move.,.2in The anisotropy of stellar orbits in elliptical galaxies can be estimated from the temperature of the hot interstellar gas through which they move.
 These two quite different galactic attributes are intimately related by the Jeaus equation for the stars aud the condition for hydrostatic equilibrium in the eas., These two quite different galactic attributes are intimately related by the Jeans equation for the stars and the condition for hydrostatic equilibrium in the gas.
 This simple relationship is valuable since both the anisotropy aud eas teniperature are dificult to extract from optical aud N-rav observations. respectively.," This simple relationship is valuable since both the anisotropy and gas temperature are difficult to extract from optical and X-ray observations, respectively."
 Many inassive elliptical galaxies are nearlv spherical (Merritt. Trembly 1996) aud slowly rotating. but their stellar velocity ellipsoids are not iu general isotropic.," Many massive elliptical galaxies are nearly spherical (Merritt Trembly 1996) and slowly rotating, but their stellar velocity ellipsoids are not in general isotropic."
" The non-splherical nature of the stellar velocity dispersion is represeuted by the piaraueter where o, is the radial stellar velocity dispersion aud 0; is he dispersion iu a transverse direction. Le. σὲ=6502."," The non-spherical nature of the stellar velocity dispersion is represented by the parameter where $\sigma_r$ is the radial stellar velocity dispersion and $\sigma_t$ is the dispersion in a transverse direction, i.e. $\sigma_t^2 = \sigma_{\theta}^2 = \sigma_{\phi}^2$."
 If the orbits are predominantly radial. 0κ ine of sight velocity profile becomes more strongly peaked han a Gaussian profile with increasing projected radius R: if the orbits are mostly tangential x2<0. he profile is more flat-topped and becomes broader with increasing radius.," If the orbits are predominantly radial, $0 < \beta < 1$, the line of sight velocity profile becomes more strongly peaked than a Gaussian profile with increasing projected radius $R$; if the orbits are mostly tangential, $-\infty \le \beta < 0$, the profile is more flat-topped and becomes broader with increasing radius."
" Both ο) aud the ealactic poteutial P(r) can be determined from optical observations of the ine of sight. velocity dispersion a(R). the optical surface xiehtuess distribution and the deviation of the stellar ine profiles from, a Css as expressed by the Lue-svinmnetric cocticient /CR) ina Gauss-Termite expansion (o.c. van der Marel Fraux 1993)."," Both $\beta(r)$ and the galactic potential $\Phi(r)$ can be determined from optical observations of the line of sight velocity dispersion $\sigma(R)$, the optical surface brightness distribution and the deviation of the stellar line profiles from a Gaussian as expressed by the line-symmetric coefficient $h_4(R)$ in a Gauss-Hermite expansion (e,g, van der Marel Franx 1993)."
 Stellar line profiles observed iu most massive E galaxies indicate a. preference for radial orbits with οὐ~0.3 (Bender. Saglia Gerhard. 1991 Gerhard et al.," Stellar line profiles observed in most massive E galaxies indicate a preference for radial orbits with $\beta \sim 0.3$ (Bender, Saglia Gerhard 1994; Gerhard et al."
 1998: Saelia ct al., 1998; Saglia et al.
 2000)., 2000).
 Accurate (r0) profiles from optical data require high quality data aud cousiderable care im reduction and analysis., Accurate $\beta(r)$ profiles from optical data require high quality data and considerable care in reduction and analysis.
 The radially anisotropic nature of stellar orbits in huuinous elliptical galaxies provides iuportaut and otherwise unavailable iuformation about the inerger düstorv of these ealaxies (Naab. Burkert Ieruquit 1999). so an improved or inclepeudcut cleternunation of 3(7) would be desirable.," The radially anisotropic nature of stellar orbits in luminous elliptical galaxies provides important and otherwise unavailable information about the merger history of these galaxies (Naab, Burkert Hernquist 1999), so an improved or independent determination of $\beta(r)$ would be desirable."
" Similarly. the racial variation of the hot eas temperature Tir)~Tu,10* Kom elliptical galaxies depends ou the spatial and spectral resolutions of X-ray detectors and the accuracy of the threc-dineusioual decomposition that converts T as a function of projected radius Π to plivsical radius +."," Similarly, the radial variation of the hot gas temperature $T(r) \sim T_{vir} \sim 10^7$ K in elliptical galaxies depends on the spatial and spectral resolutions of X-ray detectors and the accuracy of the three-dimensional decomposition that converts $T$ as a function of projected radius $R$ to physical radius $r$."
 Du addition. it is often uuclear whether the hot eas at anv radius has a single temperature or a multitude of temperatures as nüght be expected if the eas were cooling.," In addition, it is often unclear whether the hot gas at any radius has a single temperature or a multitude of temperatures as might be expected if the gas were cooling."
 It is unclear if the gas cools at all., It is unclear if the gas cools at all.
 For example. lugh resolution X-ray spectra with NADINewton of the large E salaxv NGC 1636 fail to show cission lines expected from gas at intermediate temperatures. such as the 0.571 keV OVII line (Nu et al.," For example, high resolution X-ray spectra with XMM-Newton of the large E galaxy NGC 4636 fail to show emission lines expected from gas at intermediate temperatures, such as the 0.574 keV OVII line (Xu et al."
" 2002). sugecstine that the gas is not cooling below ~17,;.,/2 as im classical cooling flows."," 2002), suggesting that the gas is not cooling below $\sim T_{vir}/3$ as in classical cooling flows."
 However. Breeman. Miller biu (2001) detected the OVI doublet in NCC 1636 emitted from eas at To~3«107 K. implying that cooling near the expected rate may occur after all.," However, Bregman, Miller Irwin (2001) detected the OVI doublet in NGC 4636 emitted from gas at $T \sim 3 \times 10^5$ K, implying that cooling near the expected rate may occur after all."
 As an additional source of confusion. the observed N-rayv spectra can often be significantly improved by assuming two quite different discrete temperatures at each ealactic radius (e.g. Buote 2002 for NGC 1399: Duote oet al.," As an additional source of confusion, the observed X-ray spectra can often be significantly improved by assuming two quite different discrete temperatures at each galactic radius (e.g. Buote 2002 for NGC 1399; Buote et al."
 Ww02a and Tana et al., 2002a and Tamura et al.
 2003 for NGC 5011)., 2003 for NGC 5044).
 While the origin and plysical nature of eas with only two, While the origin and physical nature of gas with only two
Foundation.,Foundation.
Figure 5 presents the resulting profiles.,Figure \ref{f:afr1} presents the resulting profiles.
 The examination of these profiles reveals that the Afo parameter Is not constant with the radial distance but increases with it., The examination of these profiles reveals that the $Af\rho$ parameter is not constant with the radial distance but increases with it.
" The increase of Af with the radial distance could be interpreted — if observed only for March 23 -- by a decrease of the ""Sust production rate with time. the regions observed close to the center of the coma containing ""younger"" dust particles."," The increase of $Af\rho$ with the radial distance could be interpreted – if observed only for March 23 – by a decrease of the dust production rate with time, the regions observed close to the center of the coma containing “younger” dust particles."
 The similar profiles obtained one week later (see Fig. 4)), The similar profiles obtained one week later (see Fig. \ref{f:rmag}) )
" permit to ""Siscard this hypothesis and lead to the conclusion that this variation of the Af parameter with the cometocentric distance is due to a variation in the intensity that does not follow the 1/p ntensity variation assumed by à nucleus releasing dust particles.", permit to discard this hypothesis and lead to the conclusion that this variation of the $Af\rho$ parameter with the cometocentric distance is due to a variation in the intensity that does not follow the $1/\rho$ intensity variation assumed by a nucleus releasing dust particles.
 The more plausible explanation for such a behavior ts a steady state process (at least at the timescale of our observations) created by a source of dust., The more plausible explanation for such a behavior is a steady state process (at least at the timescale of our observations) created by a source of dust.
 Such an interpretation is coherent with the general view provided by the different images., Such an interpretation is coherent with the general view provided by the different images.
" In the case of a 1/p intensity variation for the intensity. profile /(p) the Afo parameter is more or less independent of p because Afp=kxFoom/p and FoamIMκοπο[rdr=22k'K""p (where Κ. ko and k” are some constants and F,.,,, is the coma flux)."," In the case of a $1/\rho$ intensity variation for the intensity profile $I(\rho)$ the $Af\rho$ parameter is more or less independent of $\rho$ because $Af\rho=k\times F_{com}/\rho$ and $F_{com}=\int_0^\rho k'2\pi rI(r)dr=\int_0^\rho k'2\pi rk''/r dr=2\pi k'k''\rho$ (where $k$, $k'$ and $k''$ are some constants and $F_{com}$ is the coma flux)."
 In the case of our observations Afp increases with p because /(o) varies as p with x«| leading to F4=ctexp? with y>I., In the case of our observations $Af\rho$ increases with $\rho$ because $I(\rho)$ varies as $\rho ^{-x}$ with $x<1$ leading to $F_{com}=cte\times\rho^y$ with $y>1$.
" It is possible to use the global Af parameter to derive an approximate dust production rate by using this equation with Afp=100a (see ? for more details): We used the following parameters: grain radius αι.=0.5x10 mm. volumetric mass kke.m? and geometric albedo p,=0.05."," It is possible to use the global $Af\rho$ parameter to derive an approximate dust production rate by using this equation with $Af\rho=100~m$ (see \citet{lorin:2007} for more details): We used the following parameters: grain radius $a_{gr}=0.5\times 10^{-6}$ m, volumetric mass $d=1000$ $^{-3}$ and geometric albedo $p_v=0.05$."
" For the dust ejection velocity τος we used the formula v,=465877? mm.s!. with & the heliocentric distance expressed in AU (?).."," For the dust ejection velocity $v_{gr}$ we used the formula $v_{gr}=465R^{-0.5}$ $^{-1}$, with $R$ the heliocentric distance expressed in AU \citep{delsemme:1982}."
 These parameters lead to a total dust production rate of Q=86 kg.s7!., These parameters lead to a total dust production rate of $\simeq$ 86 $^{-1}$.
 Such a production rate can be compared to the upper limit obtained with our April 2001 observations (2).. which was 28 em for Afp and 0.45 Ke.s! for the dust production rate Q (with similar parameters to the one mentioned above).," Such a production rate can be compared to the upper limit obtained with our April 2001 observations \citep{lorin:2007}, which was 28 cm for $\rho$ and 0.45 $^{-1}$ for the dust production rate Q (with similar parameters to the one mentioned above)."
 The dust production rate has increased by at least a factor of 2200 between 2001 and 2005 outburst., The dust production rate has increased by at least a factor of $\simeq$ 200 between 2001 and 2005 outburst.
 The fact that the dust is created by a diffuse source impacts the interpretation of the Afp parameter in terms of the dust production rate., The fact that the dust is created by a diffuse source impacts the interpretation of the $Af\rho$ parameter in terms of the dust production rate.
 The above formula is based on a 1/p distribution., The above formula is based on a $1/\rho$ distribution.
 With a flatten dust distribution the dust production would be slightly smaller for à same Afp value., With a flatten dust distribution the dust production would be slightly smaller for a same $Af\rho$ value.
 The Q value provided above should be regarded. consequently. as an upper limit.," The $Q$ value provided above should be regarded, consequently, as an upper limit."
 We have also tried to compute color ratios., We have also tried to compute color ratios.
 We have subtracted the sky background for and V-band data. divided by the exposure time and corrected for the zero point before computing the ratio.," We have subtracted the sky background for R-band and V-band data, divided by the exposure time and corrected for the zero point before computing the ratio."
 Figure 6. presents the ratio of the R-band to the V-band data (the one with the best signal-to-noise)., Figure \ref{f:color} presents the ratio of the R-band to the V-band data (the one with the best signal-to-noise).
 It can be seen that the redenning increases with cometocentric distance., It can be seen that the redenning increases with cometocentric distance.
 This color change is probably indicative of a grain fragmentation process., This color change is probably indicative of a grain fragmentation process.
 According to the Mie scattering theory. the light scattered by dust particles depends on the grain radius and," According to the Mie scattering theory, the light scattered by dust particles depends on the grain radius and"
redshift.,redshift.
 Αι <1.2. the Ips;yy passband samples he rest-frame optical (A>3700A)). which ήχος uorphological biases associated with observatious iade in the rest-frame ultraviolet where ealaxics typically exhibit more ireenlar morphologics.," At $z < 1.2$, the $I_{\rm F814W}$ passband samples the rest-frame optical $\lambda
> 3700$ ), which minizes morphological biases associated with observations made in the rest-frame ultraviolet where galaxies typically exhibit more irregular morphologies."
 The impact (or lack. hereof) of auv morphological A-correctiou is addressed uther in 83., The impact (or lack thereof) of any morphological $K$ -correction is addressed further in \ref{sec_results}.
 Throughout our analysis. all sizes (75) jiwe been converted to physical kpe. according to the DEEP2/DEEP? spectroscopic redshift aud assuimiug a IIubble paramcter of 5-—1.," Throughout our analysis, all sizes $r_{e}$ ) have been converted to physical kpc, according to the DEEP2/DEEP3 spectroscopic redshift and assuming a Hubble parameter of $h =
1$."
 Finally. note that the nultidvizzled Z£ST/ACS images. from which structural xopertieswere measured. have a pixel scale of 0.037 per κο]aud a potut-spread function (PSF) of 0.127 EWIIME your.=Ol to +=1.2. the spatial resolution therefore varies from ~0.5 1 kpe per PSF FWIIM to ~0.95 ft spe per PSF FWIHAL," Finally, note that the multidrizzled /ACS images, from which structural propertieswere measured, have a pixel scale of $0.03^{\prime\prime}$ per pixeland a point-spread function (PSF) of $0.12^{\prime\prime}$ FWHM; from $z=0.4$ to $z = 1.2$, the spatial resolution therefore varies from $\sim \! 0.5$ $h^{-1}$ kpc per PSF FWHM to $\sim \! 0.95$ $h^{-1}$ kpc per PSF FWHM."
" To investigate the relatiouship between ealaxy structive and euvironnient amongst the ligh-mass portion of the red sequence. we define a subsample of DEEP2/DEEP3 ealaxics at 0.1<LZ1.2 with stellar nass jiu the range 10ΑΕΠα?M.)<1. on the red sequence νο, rest-frame color of B1).4% and with robust environment and morphology measurements (i.e. away from a survey edee and with e,<0.75)? The median redshift for this swhbsauple of 623 ealaxics is 0.76 and the median stellar ias is logy)(AL/h2? 10.6 "," To investigate the relationship between galaxy structure and environment amongst the high-mass portion of the red sequence, we define a subsample of DEEP2/DEEP3 galaxies at $0.4 < z < 1.2$ with stellar mass in the range $10 < \log_{10}({\rm M}_{\star} / h^{-2}\
{\rm M}_{\sun}) < 11$, on the red sequence (i.e., rest-frame color of $U -B > 1$ and with robust environment and morphology measurements (i.e., away from a survey edge and with $\sigma_{n} < 0.75$ The median redshift for this subsample of $623$ galaxies is $0.76$ and the median stellar mass is $\log_{10}({\rm M}_{\star} / h^{-2}\ {\rm M}_{\sun}) \sim 10.6$ ."
Iu Figure 2.. we show the redshift distribution for all sources in the EGS with a secure redshift (Q1. 3. 1) in the joiut DEEP2/DEEPS3 sample alongside the color-maguitude distribution for all galaxies at koocc1.2. with Lunes of constant stellar iuass overlaid aud with lines illustratiug the survey magnitude Dit at several discrete redshift values;," In Figure \ref{fig_cmdz}, we show the redshift distribution for all sources in the EGS with a secure redshift $Q = -1$, $3$, $4$ ) in the joint DEEP2/DEEP3 sample alongside the color-magnitude distribution for all galaxies at $0.4 < z < 1.2$, with lines of constant stellar mass overlaid and with lines illustrating the survey magnitude limit at several discrete redshift values."
 Note that we restrict our primary subsample to a redshift ranec over which the DEEP? and DEED? selection function is relatively flat., Note that we restrict our primary subsample to a redshift range over which the DEEP2 and DEEP3 selection function is relatively flat.
 Tlowever. over this somewhat broad redshift range the sample is iucomplete at the adopted mass limit.," However, over this somewhat broad redshift range the sample is incomplete at the adopted mass limit."
" For example. at ;=0.9 the Rap=2L1 magnitude luit of DEEP? inchides all ealaxies with stellar mass >10195AL,/5.2.AL. independent of color. but prefercutially iisscs red galaxies at lower niasses (sce 2008.2010b:reffgand."," For example, at $z=0.9$ the $R_{\rm AB}=24.1$ magnitude limit of DEEP2 includes all galaxies with stellar mass $> \! 10^{10.8}\ {\rm
 M}_{\star}/h^{-2}\ {\rm M}_{\sun}$ independent of color, but preferentially misses red galaxies at lower masses (see \\ref{fig_cmdz}) )."
 Thisincompletenessinthi gala upopulationisaddcr Wel etal. OCCHI, This incompleteness in the galaxy population is addressed in more detail in \ref{sec_results}.
 Iu order to study the relationship between galaxy properties aud cuviromment at fixed stellar ass. as we aiu to do here. the galaxy sample under study is often restricted to a narrow range in stellar mass sucht that correlations between stellar mass and euviroumnenut are negligible.," In order to study the relationship between galaxy properties and environment at fixed stellar mass, as we aim to do here, the galaxy sample under study is often restricted to a narrow range in stellar mass such that correlations between stellar mass and environment are negligible."
 ITowever. at intermediate redshift. sample sizes are generallv limited iu umber such that using a particularly narrow stellar mass range (e.g... 20.1. 0.2 dex in width) significantly reduces the statistical power ofthe sample.," However, at intermediate redshift, sample sizes are generally limited in number such that using a particularly narrow stellar mass range (e.g., $\sim \! 0.1$ $0.2$ dex in width) significantly reduces the statistical power of the sample."
 For this reason. broader stellar mass bius (6.9. 70.5 dex) are couunonly eiuploved.," For this reason, broader stellar mass bins (e.g., $\sim \! 0.5$ dex) are commonly employed."
 However. if the shape of the stellaz mass function depends on euvironmneut (as sugeested by 2010)).et en je typical stellar mass within a broad nass biu may differ significantly from one deusitv regine to another.," However, if the shape of the stellar mass function depends on environment (as suggested by ), then the typical stellar mass within a broad mass bin may differ significantly from one density regime to another."
 Such an effect would clearly impact the ability to study 1e relationship between galaxy size aud euvironnmient at chxed stellar mass., Such an effect would clearly impact the ability to study the relationship between galaxy size and environment at fixed stellar mass.
" For this reason. we instead select those galaxies withiu re top 154 of the overdensity distribution for all red galaxies at 10<los44(M,/hb?M.)11 and Liloo:«L2 (a subsample of 953 salaxies). aud roni the corresponding bottom 50% of the overdeusity distribution we randonilv craw 1000 subsamples (each composed of 93 ealaxies) so as to matel the joint redshift. stellar iuüass and Sérrsic index cdlistributious of the galaxies in the high-density The average euvironnient for the ligh-deusity subset is logy(1|63)= L31. with an interquartile ()) ranee of 1.15 1.11. while the low-density subsample is biased to considerably less-deuse cuvirous with an average overdeusity of logyy(1|05)=0.12 and an interquartile range of (0.30 n"," For this reason, we instead select those galaxies within the top $15\%$ of the overdensity distribution for all red galaxies at $10 <
\log_{10}({\rm M}_{\star} / h^{-2}\ {\rm M}_{\sun}) < 11$ and $0.4 < z
< 1.2$ (a subsample of $93$ galaxies), and from the corresponding bottom $50\%$ of the overdensity distribution we randomly draw 1000 subsamples (each composed of $93$ galaxies) so as to match the joint redshift, stellar mass, and Sérrsic index distributions of the galaxies in the high-density The average environment for the high-density subset is $\log_{10}(1+\delta_3) = 1.31$ , with an interquartile ) range of $1.15$ $1.41$, while the low-density subsample is biased to considerably less-dense environs with an average overdensity of $\log_{10}(1+\delta_3) = -0.12$ and an interquartile range of $-0.30$ $0.12$."
 As shown by(2006).. the high-density subsample is comprised largely of group members. while the low-density population is dominated by “field” salaxies2007).," As shown by, the high-density subsample is comprised largely of group members, while the low-density population is dominated by “field” galaxies."
. By matching in redshift. we remove the projection of anv possible residual correlation between our chvirollment measurements aud redshift Gar concert witli the known redshift dependence of the survevs stellar-mass limit) onto the observed size-cuviroument relation.," By matching in redshift, we remove the projection of any possible residual correlation between our environment measurements and redshift (in concert with the known redshift dependence of the survey's stellar-mass limit) onto the observed size-environment relation."
 Tn addition. matching according to redshift alleviates any possible impact frou: morphological Av-correctionus associated with measuring all structural parameters m the ZST/ACS Pgiw passbaud.," In addition, matching according to redshift alleviates any possible impact from morphological $K$ -corrections associated with measuring all structural parameters in the /ACS $I_{\rm
 F814W}$ passband."
 Finally. recognizing the correlations between environnieut and parameters such as color. star-formation rate. aud morphology (1.6..al.carly- versus late-type} at 2~1l we ALTalso force the Sérrsic indices ‘of ποquinior aw to match those of the ligh- population. which coutrols for the coutribution of dusty disk galaxies to our red-sequeuce population.," Finally, recognizing the correlations between environment and parameters such as color, star-formation rate, and morphology (i.e., early- versus late-type) at $z \sim 1$, we also force the Sérrsic indices of the low-density subsample to match those of the high-density population, which controls for the contribution of dusty disk galaxies to our red-sequence population."
 Matching based ou rest-frame color. iu lieu of Sévrsic oeidex. would coufuse reddened disk sealaxies with red urb-tvpe svstenis.," Matching based on rest-frame color, in lieu of Sérrsic index, would confuse reddened disk galaxies with red early-type systems."
 Members of the low-densitv subsample are crawn aH‘andouly from within a three-dinieusional window with iueusious of |[A:| <O.0L randonily-[AloeAL/)7M.|< 02. ud |An| subsample.L.5ofa selected objectthis in the high- <," Members of the low-density subsample are drawn randomly from within a three-dimensional window with dimensions of $|\Delta z| < 0.04$ , $|\Delta \log_{10}({\rm M}_{\star} / h^{-2}\ {\rm M}_{\sun})| < 0.2$ , and $|\Delta n| < 1.5$ of a randomly-selected object in the high-density subsample."
 Varving the size of windowby factors of a few in each dimension has no siguificaut effect on our results., Varying the size of this window by factors of a few in each dimension has no significant effect on our results.
 Caven the raucdom nature of the matching. sole objects are repeated in the low-deusity subsamples.," Given the random nature of the matching, some objects are repeated in the low-density subsamples."
 However. for cach subsample of 93 ealaxies. 270% of the," However, for each subsample of $93$ galaxies, $> \! 70\%$ of the"
"second. because //>/4,;. the granularity of the svstem makes scales </y, inaccessible to the (hud description: the same argument makes supersonic turbulence most probably irrelevant lo ring svstenis.","second, because $H \gtrsim l_M$, the granularity of the system makes scales $\lesssim l_M$ inaccessible to the fluid description; the same argument makes supersonic turbulence most probably irrelevant to ring systems."
" Because Re, is ab least of the order of 107. the order of magnitude estimates of Eqs. (17))"," Because ${Re}_m$ is at least of the order of $10^3$, the order of magnitude estimates of Eqs. \ref{lm}) )"
 and (18)) are sensibly smaller than the mean flow lengthancl velocity scales to which /4; and ray ave usually assumed to be comparable., and \ref{vm}) ) are sensibly smaller than the mean flow lengthand velocity scales to which $l_M$ and $v_M$ are usually assumed to be comparable.
 Nevertheless. thev are in good order of magnitude agreement wilh the available evidence.," Nevertheless, they are in good order of magnitude agreement with the available evidence."
 Consider. for example. the simulation of Couette flow reported in Beche£al.(1995).. and further exploited in BechandAndersson(199Gb) to «quantilv the structure of the Reynolds stress in (he central region of Couette flows.," Consider, for example, the simulation of Couette flow reported in \citet{Bech95}, and further exploited in \citet{Bech96b} to quantify the structure of the Reynolds stress in the central region of Couette flows."
 For Couette flows Eq. (18)), For Couette flows Eq. \ref{vm}) )
" gives ta;~c,/40.", gives $v_M\sim\Delta v_x/40$.
 The simulation just mentioned has a Revnolds of 5200. ie. well above the threshold of transition to turbulence.," The simulation just mentioned has a Reynolds of $5200$, i.e. well above the threshold of transition to turbulence."
 The behavior of the Reynolds stress as afunction of the distance to the wall is represented on Fie., The behavior of the Reynolds stress as afunction of the distance to the wall is represented on Fig.
" la of Bech (1996b).. ancl. alter accounting for the particular normalization adopted in theireraph!?.. one finds οcAv,//30 for this simulation. which is nearly identical to the estimatededuced from Eq. (13))."," 1a of \citet{Bech96b}, and, after accounting for the particular normalization adopted in their, one finds $v_M\simeq \Delta
v_x/30$ for this simulation, which is nearly identical to the estimatededuced from Eq. \ref{vm}) )."
" Even if one takes into account the fact that the value of Av, which is relevant for the bulk of the flow is smaller than the one adopted in Eq. (13))", Even if one takes into account the fact that the value of $\Delta v_x$ which is relevant for the bulk of the flow is smaller than the one adopted in Eq. \ref{vm}) )
 bv a factor e4. the two estimates of ea; still agree within a factor of ~3.," by a factor $\sim 4$, the two estimates of $v_M$ still agree within a factor of $\sim 3$."
" Another estimate of the same quantity [or non-rotating [ree shear flows is obtained [rom the of (00,00,) in Fig."," Another estimate of the same quantity for non-rotating free shear flows is obtained from the of $\langle \delta v_x \delta
v_y\rangle$ in Fig."
" Lt Gat Q= 0) of DidokhtiandTritton (1992).. and gives ry,~Av./ 10. which differs from the order of magnitude estimate quoted above by a [actor of 4."," 14 (at $Q=0$ ) of \citet{Bid92}, , and gives $v_M\sim \Delta v_x/10$ , which differs from the order of magnitude estimate quoted above by a factor of $\sim 4$ ."
 Some, Some
photometry after converting magnitudes to [Iuxes using Colinaetal.(1996.UBWRI) anc Cohenοἱal.(2000.Ην)...,photometry after converting magnitudes to fluxes using \citet[][$UBVRI$]{1996AJ....112..307C} and \citet[][$JHK$]{2003AJ....126.1090C}.
 The photometry. Zig ancl log g values. and resulüng angular diameters for the calibrators are listed in Table 1..," The photometry, $T_{\rm eff}$ and log $g$ values, and resulting angular diameters for the calibrators are listed in Table \ref{calibrators}."
 There were no hints of excess emission associated wilh a low-mass stellar companion or circunmistellar disk in (he calibrators’ SED [its (see Figure 1))., There were no hints of excess emission associated with a low-mass stellar companion or circumstellar disk in the calibrators' SED fits (see Figure \ref{seds}) ).
 The observed quantity of an interferometer is defined as the visibility (V). which is fit wilh a model of a unilormly-illuminated disk (UD) that represents the observed Lace of the star.," The observed quantity of an interferometer is defined as the visibility $V$ ), which is fit with a model of a uniformly-illuminated disk (UD) that represents the observed face of the star."
" Diameter fits (o V. were based upon the UD approximation given by V.—2J4(70)/. where J; is the first-order. Bessel function and c=zD0,5A.|. where B is the projected baseline al the stars position. Fp is the apparent UD angular diameter of (he star. and A is the effective wavelength of the observation (Shao&Colavila 1992).. "," Diameter fits to $V$ were based upon the UD approximation given by $V = 2 J_1(x) / x$, where $J_1$ is the first-order Bessel function and $x = \pi B \theta_{\rm UD} \lambda^{-1}$, where $B$ is the projected baseline at the star's position, $\theta_{\rm UD}$ is the apparent UD angular diameter of the star, and $\lambda$ is the effective wavelength of the observation \citep{1992ARAandA..30..457S}. ."
Table 2. lists the Moclified Julian Date (MJD). projected baseline at the time of observation (2). projected baseline position angle (0). calibrated visibility (V). aud error in V. (06V) for + Dra.," Table \ref{calib_visy} lists the Modified Julian Date (MJD), projected baseline at the time of observation $B$ ), projected baseline position angle $\Theta$ ), calibrated visibility $V$ ), and error in $V$ $\sigma V$ ) for $\iota$ Dra."
 Figure + shows the UD fit to the observed. visibilities and it is clear that this is not a sufficient model., Figure \ref{vvsb_ud} shows the UD fit to the observed visibilities and it is clear that this is not a sufficient model.
 A more realistic model of a stars disk involves limb-cdarkening (LD). particularly in Chis case because most of (he observations are on the third lobe of the visibility curve where secondary effects such as limb darkening play à more important role (han in the curve between B=0 and the first null.," A more realistic model of a star's disk involves limb-darkening (LD), particularly in this case because most of the observations are on the third lobe of the visibility curve where secondary effects such as limb darkening play a more important role than in the curve between $B$ =0 and the first null."
 Lacouretal.(2008) analvzed multiple LD prescriptions for the IX1.5 HI star Arcturus and found the power law model to be a sullicient approximation., \citet{2008AandA...485..561L} analyzed multiple LD prescriptions for the K1.5 III star Arcturus and found the power law model to be a sufficient approximation.
 We chose to use this model because. Arcturus’ spectral (vpe is very close to that of + Dra., We chose to use this model because Arcturus' spectral type is very close to that of $\iota$ Dra.
 The model was based on Hestrotfer(1997): where /(j) is the brightness of a point source al wavelength A. (1) is the brightness al the center.B jp—=να(2)‘Pi2θε). rP isio the angularB distanceio fromPH the stars+M center.+and ip is the limb-darkenecd angular diameter.," The model was based on \citet{1997AandA...327..199H}: where $I(\mu)$ is the brightness of a point source at wavelength $\lambda$, $I$ (1) is the brightness at the center, $\mu = \sqrt{1-({\rm 2}r/\theta_{\rm LD})^2}$, $r$ is the angular distance from the star's center,and $\theta_{\rm LD}$ is the limb-darkened angular diameter."
" In terms of the stars visibilities. (he power law prescription becomes where r, djsthe radial spatial frequenev. D is the Euler function (F(&--1) = fl)."," In terms of the star's visibilities, the power law prescription becomes where $v_r$ isthe radial spatial frequency, $\Gamma$ is the Euler function $\Gamma (k$ +1) = $k$ !),"
 (Lacourοἱal. 20083).. ancl & is the number of terms used.," $\alpha = 0.258 \pm 0.003$ \citep{2008AandA...485..561L}, and $k$ is the number of terms used."
 We tried a range, We tried a range
one of the brightest. most intrinsically luminous. and violently variable AGNs of the LAT sample (Abdo et al.,"one of the brightest, most intrinsically luminous, and violently variable AGNs of the LAT sample (Abdo et al."
 20106: Abdo et al., 2010c; Abdo et al.
 20104)., 2010d).
 The field of PKS 1502+106 had been observed on 24-26 January 2006 by IBIS for a total integration time of 83 ks., The field of PKS 1502+106 had been observed on 24-26 January 2006 by IBIS for a total integration time of 83 ks.
 The observation. analysed by Ubertini et al. (," The observation, analysed by Ubertini et al. ("
2008) in the light of the report. resulted in the detection of a new source. IGR 1150391022. at a flux level of 1.6 mCrab (1... 2.45x107! erg em? s7! in the 18-60 keV )).,"2008) in the light of the report, resulted in the detection of a new source, IGR J15039+1022, at a flux level of 1.6 mCrab (i.e., $2.45 \times 10^{-11}$ erg $^{-2}$ $^{-1}$ in the 18-60 keV )."
 The IBIS source. located at RA = 15:03:53.76 and Dec = 310:22:08.4 (error radius of ~5 aremin). has been tentatively identified with the Seyfert | galaxy Mkn 841 (z=0.036). and has been included in the Fourth IBIS/ISGRI soft gamma-ray survey catalog (Bird et al.," The IBIS source, located at RA = 15:03:53.76 and Dec = +10:22:08.4 (error radius of $\sim$ 5 arcmin), has been tentatively identified with the Seyfert 1 galaxy Mkn 841 $z = 0.036$ ), and has been included in the Fourth IBIS/ISGRI soft gamma-ray survey catalog (Bird et al."
 2010) and in the second AGN catalog (Beckmann et al., 2010) and in the second AGN catalog (Beckmann et al.
 2009)., 2009).
 Ubertini et al. (, Ubertini et al. (
2008) note that PKS 1502106 is 11 arcmin away from IGR J15039+1022 and is not detected in the January 2006 IBIS observation.,2008) note that PKS 1502+106 is 11 arcmin away from IGR J15039+1022 and is not detected in the January 2006 IBIS observation.
 They derive a 2-sigma upper limit flux of 0.7 mCrab for the blazar in the range 18-60 keV. assuming a Crab-like spectrum.," They derive a 2-sigma upper limit flux of 0.7 mCrab for the blazar in the range 18-60 keV, assuming a Crab-like spectrum."
 Prompted by the detection of the gamma-ray outburst. we activated observations starting on 9 August 2008 (see preliminary images in Blazek Hudee 2009).," Prompted by the detection of the gamma-ray outburst, we activated observations starting on 9 August 2008 (see preliminary images in Blazek Hudec 2009)."
 Simultaneous observations withSwift XRT and with the Nordic Optical Telescope (NOT) were also organized., Simultaneous observations with XRT and with the Nordic Optical Telescope (NOT) were also organized.
 We report here the results and discuss them in the context of AGN models., We report here the results and discuss them in the context of AGN models.
 The source PKS 15024106 (whose catalogued optical J2000 coordinates are RA = 15:04:24.98. Dee = +10:29:39.2) was observed by the/NTEGRAL satellite (Winkler et al.," The source PKS 1502+106 (whose catalogued optical J2000 coordinates are RA = 15:04:24.98, Dec = +10:29:39.2) was observed by the satellite (Winkler et al."
 2003) for 203 ks in Revolution 711 between 2008 August 09. 01:53 UT and 2008 August 11. 15:12 UT.," 2003) for 203 ks in Revolution 711 between 2008 August 09, 01:53 UT and 2008 August 11, 15:12 UT."
 The on-source time for IBIS/ISGRI (Ubertini et al., The on-source time for IBIS/ISGRI (Ubertini et al.
 2003: Lebrun et al., 2003; Lebrun et al.
 2003) was 194.5 ks., 2003) was 194.5 ks.
 The target is in the JEM-X (Lund et al., The target is in the JEM-X (Lund et al.
 2003) field of view for 46 ks in Rev. 711., 2003) field of view for 46 ks in Rev. 711.
 The screening. reduction. and analysis of the IBIS/ISGRI and JEM-X data have been performed using the Offline Scientific Analysis (OSA) v. 7.0 and v. 8.0. respectively. publicly available through the Science Data (SDC. Courvoisier et al.," The screening, reduction, and analysis of the IBIS/ISGRI and JEM-X data have been performed using the Offline Scientific Analysis (OSA) v. 7.0 and v. 8.0, respectively, publicly available through the Science Data (ISDC, Courvoisier et al."
 2003)., 2003).
 The IBIS/ISGRI and JEM-X data have been accumulated into final images with algorithms implemented in. the software as described in Goldwurm et al. (, The IBIS/ISGRI and JEM-X data have been accumulated into final images with algorithms implemented in the software as described in Goldwurm et al. (
2003) and Westergaard et al. (,2003) and Westergaard et al. (
2003). respectively.,"2003), respectively."
 Following similar methods. we have also re-analyzed the archival IBIS and JEM-X observation obtained on 24-26 January 2006 (Ubertini et al.," Following similar methods, we have also re-analyzed the archival IBIS and JEM-X observation obtained on 24-26 January 2006 (Ubertini et al."
 2008)., 2008).
 The source has been also observed with the OMC (Mas-Hesse et al., The source has been also observed with the OMC (Mas-Hesse et al.
 2003) with a standard V-band Johnson filter., 2003) with a standard $V$ -band Johnson filter.
 The data have been extracted with default settings. using ao 4x3 pixels binning. which ts appropriate for point-like sources.," The data have been extracted with default settings, using a $3 \times 3$ pixels binning, which is appropriate for point-like sources."
 X-ray and optical/UV observations of the blazar field have been accomplished from 7 to 22 August 2008 withSwift XRT and UVOT (Gehrels et al., X-ray and optical/UV observations of the blazar field have been accomplished from 7 to 22 August 2008 with XRT and UVOT (Gehrels et al.
 2004; Burrows et al., 2004; Burrows et al.
 2005: Roming et al., 2005; Roming et al.
 2005). respectively.," 2005), respectively."
 The pointing included the location of the Seyfert 1 Mkn 841., The pointing included the location of the Seyfert 1 Mkn 841.
 The results of the analysis of the data of PKS 15024106 have been reported by Abdo et al. (, The results of the analysis of the data of PKS 1502+106 have been reported by Abdo et al. (
2010b).,2010b).
 Following similar procedures as those adopted by those authors. we have independently reduced the XRT and UVOT data of the blazar and of the Seyfert 1.," Following similar procedures as those adopted by those authors, we have independently reduced the XRT and UVOT data of the blazar and of the Seyfert 1."
 Like in Abdo et al. (, Like in Abdo et al. (
2010b). for the blazar. given its low count rate («0.5 counts s! ). only photon counting data were considered and XRT grades 0—12 were selected.,"2010b), for the blazar, given its low count rate $<0.5$ counts $^{-1}$ ), only photon counting data were considered and XRT grades 0–12 were selected."
 No pile-up correction was required., No pile-up correction was required.
 For the Seyfert. we also considered window timing mode data.," For the Seyfert, we also considered window timing mode data."
" The source events were extracted in circular regions centered on the sources with radii depending on the source intensity (10-20 pixels. | pixel ~2737). while background events were extracted in source-free annular regions around the sources,"," The source events were extracted in circular regions centered on the sources with radii depending on the source intensity (10–20 pixels, 1 pixel $\sim2\farcs
37$ ), while background events were extracted in source-free annular regions around the sources."
 XRT spectra were extracted for each of the two sources from the observation of 8 August 2008. that is the one with the longest exposure time (12.5 ks).," XRT spectra were extracted for each of the two sources from the observation of 8 August 2008, that is the one with the longest exposure time (12.5 ks)."
 Ancillary response files were generated with and account for different extraction regions. vignetting and Point-Spread Function (PSF) corrections.," Ancillary response files were generated with and account for different extraction regions, vignetting and Point-Spread Function (PSF) corrections."
 We used the vO10 spectral redistribution matrices in the Calibration Database maintained by HEASARC., We used the v010 spectral redistribution matrices in the Calibration Database maintained by HEASARC.
 ΑΙ spectra were rebinned with a minimum of 20 counts per energy bin to allow y fitting within (v11.3.2)., All spectra were rebinned with a minimum of 20 counts per energy bin to allow $\chi^2$ fitting within (v11.3.2).
 For the spectral fitting we fixed the hydrogen column density to the Galactic value of 2.22x10°? em? (Kalberla et al., For the spectral fitting we fixed the hydrogen column density to the Galactic value of $2.22 \times 10^{20}$ $^{-2}$ (Kalberla et al.
 2005)., 2005).
 We extracted XRT light curves from the same image regions as for the spectra for source and background in the band kkeV. For our analysis. we considered time bins ranging from 1000 to 12000 s. to ensure that each light curve point would have at least 30 source-plus-background counts.," We extracted XRT light curves from the same image regions as for the spectra for source and background in the band keV. For our analysis, we considered time bins ranging from 1000 to 12000 s, to ensure that each light curve point would have at least 30 source-plus-background counts."
 The exposure requirements were that the bins be at least In each case. the light curves were corrected for PSF losses. Le.. losses due to the extraction region geometry. and bad/hot pixels and columns falling within this region.," The exposure requirements were that the bins be at least In each case, the light curves were corrected for PSF losses, i.e., losses due to the extraction region geometry, and bad/hot pixels and columns falling within this region."
 Likewise. the UVOT data of both sources were reduced and analyzed following procedures similar to those used by Abdo et al. (," Likewise, the UVOT data of both sources were reduced and analyzed following procedures similar to those used by Abdo et al. ("
2010b).,2010b).
 The photometry of Mkn 841 may include partial contamination from the host galaxy bulge., The photometry of Mkn 841 may include partial contamination from the host galaxy bulge.
" We used an aperture of 6"" for the v.b.u filter images and 12” for the UV filters."," We used an aperture of $^{\prime\prime}$ for the v,b,u filter images and $^{\prime\prime}$ for the UV filters."
 We have also reduced and analyzed the Mkn 841 data of 3 February 2007. that have been included in the Seyfert UVOT study of Grupe et al. (," We have also reduced and analyzed the Mkn 841 data of 3 February 2007, that have been included in the Seyfert UVOT study of Grupe et al. ("
2010).,2010).
to a subsequent paper.,to a subsequent paper.
 The preseut observations. while based on a simall sample. appear to confirm that many of the optically faintChandra sources lie in luminous biel redshift Bilal which are relatively evolved.," The present observations, while based on a small sample, appear to confirm that many of the optically faint sources lie in luminous high redshift galaxies which are relatively evolved."
 All three N-rav. sources behind A2390 lio in red galaxies with vedshifts between :=Ll and 2=, All three X-ray sources behind A2390 lie in red galaxies with redshifts between $z=1.4$ and $z=3$.
 The observed absolute A maguitudes are 27.1.26.5. 26.7) for sources [1.2.3]. where Source 1 is placed at its spectroscopic redshift aud Sources 2 aud 3 at their photometric redshifts of ρω=15 aud phot=2.5.," The observed absolute $K'$ magnitudes are $-27.1,-26.5,-26.7$ ] for sources [1,2,3], where Source 1 is placed at its spectroscopic redshift and Sources 2 and 3 at their photometric redshifts of $z_{phot}=1.5$ and $z_{phot}=2.5$."
 When the chister magnification of [2.1.2.5.7.5] and the aperture to isophotal correction is accounted for. these become 27.2.25.8.91. 1 where all absolute magnitudes are calculated for [y=65 and au Q=&.1 A=2 Universe.," When the cluster magnification of [2.1,2.8,7.8] and the aperture to isophotal correction is accounted for, these become $-27.2,-25.8,-24.8$ ], where all absolute magnitudes are calculated for $H_0$ =65 and an $\Omega={1\over 3}$, $\Lambda={2\over 3}$ Universe."
 Thus. the ealaxies are comparable to or slightly more luminous than the local £..," Thus, the galaxies are comparable to or slightly more luminous than the local $L_\ast$."
 When corrected for maenification. the 2.7 kkeW X-ray Iuuinosities lie iu the 104! to 1015 tb range.," When corrected for magnification, the $2-7$ keV X-ray luminosities lie in the $10^{44}$ to $10^{45}$ $^{-1}$ range."
 All of the sources have sjeuificaut excess elt iu the mid-infrared. presumably as a result of reprocessing of the ACN light by hot dust (AWWihnan. Fabian (απο 2000).," All of the sources have significant excess light in the mid-infrared, presumably as a result of reprocessing of the AGN light by hot dust \markcite{wilman2000}W Wilman, Fabian Gandhi 2000)."
 The very large maeuification of the evolved high redshift Source 3 is the key to its identification., The very large magnification of the evolved high redshift Source 3 is the key to its identification.
 There may be uunerous objects of this type in field samples which are sinplv too faint to pick out uxiug NIR color selection., There may be numerous objects of this type in field samples which are simply too faint to pick out using NIR color selection.
 The combination of very deep hard X-ray aud optical data will allow us to select stich sources for intensive study., The combination of very deep hard X-ray and optical data will allow us to select such sources for intensive study.
 For the lughest redshift source. the demaenitied N-rav flux would bes 410 2 ssLaud the Z iaguitude would be 26.," For the highest redshift source, the demagnified X-ray flux would be $3\times 10^{-15}$ $^{-2}$ $^{-1}$ and the $I$ magnitude would be 26."
 It is at these levels that we may find further examples in the field. samples., It is at these levels that we may find further examples in the field samples.
 AJB acknowledecs support fou NASA through Hubble Fellowship eraut IF-01117.01-A awarded by the Space Telescope Science. Tustitute. which is operated bv the Association of Universities for Research in Astrouoiv. Iuc.. for NASA under coutract NAS 5-26555.," AJB acknowledges support from NASA through Hubble Fellowship grant HF-01117.01-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."
throne AJB. LLC. and EMIT acknowledge support from NSF erants AS'T-008ISL7. AST-008[S16 and AST-0071208. and CSC and ACF thank the Roval Society for support.," AJB, LLC, and EMH acknowledge support from NSF through grants AST-0084847, AST-0084816 and AST-0071208, and CSC and ACF thank the Royal Society for support."
 We would like to thank Rolf I&uditzki aud Toui Soneaila for critically reacing the first draft of this paper., We would like to thank Rolf Kudritzki and Toni Songaila for critically reading the first draft of this paper.
is plotted.,is plotted.
 In all of our three models. more than half of the mass is concentrated inside the evlinder with ze=0.242...," In all of our three models, more than half of the mass is concentrated inside the cylinder with $\varpi \approx 0.2 R_e$."
 Figure 5. shows the specific angular momentum j as a function of the evlindrical mass fraction m. normalized so that {>fama)d==1.," Figure \ref{fig:jm} shows the specific angular momentum $j$ as a function of the cylindrical mass fraction $m_{\varpi}$ , normalized so that $\int_0^1 
j(m_{\varpi})\, dm_{\varpi}=1$."
 The j(mcz-z)-curves for the three models are almost. indistinguishable except in the region where mzz 1., The $j(m_{\varpi})$ -curves for the three models are almost indistinguishable except in the region where $m_{\varpi}\approx 1$ .
 The spike of the curve near mz=1 can be understood from Figure 4.. where we see that maz1 when wih.zo0.6.," The spike of the curve near $m_{\varpi}=1$ can be understood from Figure \ref{fig:mpmWD}, where we see that $m_{\varpi}\approx 1$ when $\varpi/R_e \ga 0.6$."
 l1lowever. j=(MSOxxou.," However, $j=(M/J)\Omega 
\varpi^2\, \propto \varpi^2$."
 These two make the values of j in the interval 0.67<j£j(nz—1)<1 squeeze to the region ms1. and the spike results.," These two make the values of $j$ in the interval $0.6^2 \la j/j(m_{\varpi}=1) \le 1$ squeeze to the region $m\approx 1$, and the spike results."
 We shall point out in the next section that this spike causes a serious numerical problem in the construction of the equilibrium models of the collapsed objects., We shall point out in the next section that this spike causes a serious numerical problem in the construction of the equilibrium models of the collapsed objects.
 The problem can be solved bv truncating the upper part of the ης}. curve., The problem can be solved by truncating the upper part of the $j(m_{\varpi})$ curve.
 The physical justification is that the material in the outer region contributes only a very small fraction of the total mass and angular momentum of the star. as illustrated in Table 2. for Alodel 1. Phe situations for the other two models are very similar and so are not shown.," The physical justification is that the material in the outer region contributes only a very small fraction of the total mass and angular momentum of the star, as illustrated in Table \ref{outlayers} for Model I. The situations for the other two models are very similar and so are not shown."
" We see that material in the region where zcjfj,1.9 jionz)£j(1)>0.81] contributes less than 10.7 of the total mass and 10.ο the total angular momentum.", We see that material in the region where $\varpi/R_e > 0.9$ $j(m_{\varpi})/j(1)> 0.81$ ] contributes less than $10^{-5}$ of the total mass and $10^{-4}$ of the total angular momentum.
 So the upper 19 per cent of the j(m—)-curve has little influence to the inner structure of the collapsed star., So the upper 19 per cent of the $j(m_{\varpi})$ -curve has little influence to the inner structure of the collapsed star.
 While this region is important for the structure of the star's outer lavers. that part of the star is not of our primary interest since the mass there is too small to develop any instability. that can produce a substantial amount of eravitational raciation.," While this region is important for the structure of the star's outer layers, that part of the star is not of our primary interest since the mass there is too small to develop any instability that can produce a substantial amount of gravitational radiation."
 In this section. we present the equilibrium new-born neutron-star models that may result. from the collapse of the three white dwarfs computed in the previous section.," In this section, we present the equilibrium new-born neutron-star models that may result from the collapse of the three white dwarfs computed in the previous section."
 Instead of performing hyedrodynamic simulations. we adopt a simpler approach: First. we assume the collapsed stars are axisvmmetric and are in rotational equilibrium with no meridional circulation.," Instead of performing hydrodynamic simulations, we adopt a simpler approach: First, we assume the collapsed stars are axisymmetric and are in rotational equilibrium with no meridional circulation."
 Second. we assume the EOS is barotropic. P=Pp).," Second, we assume the EOS is barotropic, $P=P(\rho)$."
 Vhese two assumptions imply that (1) the angular velocity © is a function of ze only. οὃς=0. and (2) the Solberg condition is satislied. which states that dj/dx0 for stable barotropic stars in rotational equilibrium (see F'Fassoul. 1978).," These two assumptions imply that (1) the angular velocity $\Omega$ is a function of $\varpi$ only, $\partial \Omega/\partial z=0$, and (2) the Solberg condition is satisfied, which states that $dj/d\varpi>0$ for stable barotropic stars in rotational equilibrium (see Tassoul 1978)."
" Phe angular velocity profile (00/02.= 0) is observed in the simulations. of Mónnchmoever. Janka ancl Mülller (Mónnchmoever Mülller 1988: Janka Mónnchmever 1989ab).ανα, we areonly interested in the structure of the neutron stars within a few minutes after core bounce."," The angular velocity profile $\partial \Omega/\partial z=0$ ) is observed in the simulations of Mönnchmeyer, Janka and Mülller (Mönnchmeyer Mülller 1988; Janka Mönnchmeyer 1989ab).Third, we areonly interested in the structure of the neutron stars within a few minutes after core bounce."
 The timescale is much shorter, The timescale is much shorter
Most of the 0.5—2 keV soft X-ray Background CXRB) has been resolved by ROSAT (Hasinger et al 1999: Lehmann et al 2001) and recently most of the harder 2—7 keV XRB has been resolved by Chandra (Mushotzky et al 2000: Giacconi et al 2001: Barger et al 2001: Brandt et al 2001) and XMM (Hasinger et al 2001).,Most of the 0.5–2 keV soft X-ray Background (XRB) has been resolved by ROSAT (Hasinger et al 1999; Lehmann et al 2001) and recently most of the harder 2–7 keV XRB has been resolved by Chandra (Mushotzky et al 2000; Giacconi et al 2001; Barger et al 2001; Brandt et al 2001) and XMM (Hasinger et al 2001).
 The source identifications are incomplete at the present time bu indicate that about one third of the sources are associated. with normal quasars. another third with optically-bright galaxies and the last third with optically-faint galaxies (Mushotzky et al 2000: Barger et al 2000: Alexander et al 2001).," The source identifications are incomplete at the present time but indicate that about one third of the sources are associated with normal quasars, another third with optically-bright galaxies and the last third with optically-faint galaxies (Mushotzky et al 2000; Barger et al 2000; Alexander et al 2001)."
 X-ray hardness ratios indicate that the fainter sources are generally harder and consisten with absorbed sources., X-ray hardness ratios indicate that the fainter sources are generally harder and consistent with absorbed sources.
 This contirms obscuration models for the XRB (Setti Woltjer 1989: Madau. Ghisellini Fabian 1994: Comastri et al 1995: Gilli. Salvati Hasinger 2001).," This confirms obscuration models for the XRB (Setti Woltjer 1989; Madau, Ghisellini Fabian 1994; Comastri et al 1995; Gilli, Salvati Hasinger 2001)."
 Detailed studies. including X-ray spectroscopy of the brighter sources (e.g. Crawford et al 2001) have however shown that the column densities of absorbing material lie in the range of 1077 to a few times 107em.?.," Detailed studies, including X-ray spectroscopy of the brighter sources (e.g. Crawford et al 2001) have however shown that the column densities of absorbing material lie in the range of $10^{22}$ to a few times $10^{23}\psqcm$."
" Such columns are insufficient to produce the vf, peak in the XRB at about 30 keV (Marshall et al 1982).", Such columns are insufficient to produce the $\nu I_{\nu}$ peak in the XRB at about 30 keV (Marshall et al 1982).
 In order to match this peak. sources with columns exceeding 1.51075em.> are required. i.e. sources which are Compton thick.," In order to match this peak, sources with columns exceeding $1.5\times 10^{24}\psqcm$ are required, i.e. sources which are Compton thick."
 Here we address this issue and ask whether such sources should have been observed in Chandra and XMM images. and whether their apparent absence indicates a problem. for the obscuration model of the XRB.," Here we address this issue and ask whether such sources should have been observed in Chandra and XMM images, and whether their apparent absence indicates a problem for the obscuration model of the XRB."
 Compton-thick sources are certainlywt found in the local Universe. with two of the nearest active galactic nuclei (AGN). the Circinus galaxy and NGCA945 (Matt et al 2000. and references therein) being in this class.," Compton-thick sources are certainly found in the local Universe, with two of the nearest active galactic nuclei (AGN), the Circinus galaxy and NGC4945 (Matt et al 2000, and references therein) being in this class."
 Good examples of powerful Compton-thick AGN are NGC6240 (Vignati et al 1999) which is at low redshift and 00910444109 which is at redshift +=0.442 (Franceschini et al 2000: Iwasawa et al 2001)., Good examples of powerful Compton-thick AGN are NGC6240 (Vignati et al 1999) which is at low redshift and 09104+4109 which is at redshift $z=0.442$ (Franceschini et al 2000; Iwasawa et al 2001).
 The main issue is whether Compton-thick quasars are common., The main issue is whether Compton-thick quasars are common.
" Sources which are mildly Compton-thick (107!<NyO7""em. =) show direct emission peaking above 10 keV. When they are heavily Compton thick GVg2107em.7. this emission peak is down-scattered by Compton recoil and is therefore highly degraded."," Sources which are mildly Compton-thick $10^{24}<N_{\rm
H}<10^{25}\psqcm$ ) show direct emission peaking above 10 keV. When they are heavily Compton thick $N_{\rm H}>10^{25}\psqcm$, this emission peak is down-scattered by Compton recoil and is therefore highly degraded."
 How much is seen in the 2-8 keV band from low redshift Compton-thick objects depends almost completely on how much emission is scattered into our line of sight., How much is seen in the 2–8 keV band from low redshift Compton-thick objects depends almost completely on how much emission is scattered into our line of sight.
" For example. the ""irect line of sight to the well-known obscured AGN 11068 has a column density exceeding 107cni7 (Matt et al 1997). the X-ray emission seen is all scattered. flux."," For example, the direct line of sight to the well-known obscured AGN 1068 has a column density exceeding $10^{25}\psqcm$ (Matt et al 1997), the X-ray emission seen is all scattered flux."
 The +=0.92 hyperluminous IRAS galaxy F15307. known to host a quasar from," The $z=0.92$ hyperluminous IRAS galaxy F15307, known to host a quasar from"
We have argued that ΑΠΟ turbulence and the associated angular moet transport may die away in dwart novae in quiescence.,We have argued that MHD turbulence and the associated angular momentum transport may die away in dwarf novae in quiescence.
 I£ there are no other siguificaut sources of angular momentum transport in disks. then this is the plvsical origin of episodic accretion in dwarf novac.," If there are no other significant sources of angular momentum transport in disks, then this is the physical origin of episodic accretion in dwarf novae."
 We have proposed a scenario in which a global lydrodvuamiuc mstabilitv heats the outer disk. thereby raising the couductivitv aud initiating the outburst.," We have proposed a scenario in which a global hydrodynamic instability heats the outer disk, thereby raising the conductivity and initiating the outburst."
 This scenario is a modification of the staucdard disk stability model that provides a plysical explanation for episodic accretion vet retaius many of the standard models most attractive features., This scenario is a modification of the standard disk instability model that provides a physical explanation for episodic accretion yet retains many of the standard model's most attractive features.
 We are grateful to $. Balbus. J.-M. ILuueury. J. Ille. S. Ieuvon. J.-P. Lasota. R. Naravan. E. Quatacrt. J. Ravinoud. IL Vauhala. and E. Vishuiac for helpful conuneuts.," We are grateful to S. Balbus, J.-M. Hameury, J. Hawley, S. Kenyon, J.-P. Lasota, R. Narayan, E. Quataert, J. Raymond, H. Vanhala, and E. Vishniac for helpful comments."
 P. Woefich provided a code for calculating electron abunudauces., P. Hoeflich provided a code for calculating electron abundances.
 This work was supported ly NASA evant NACAV 55-2836., This work was supported by NASA grant NAGW 5-2836.
 KM. was supported bv an SAO Predoctoral Fellowship aud a French UWieher Education \Gnistry eraut., KM was supported by an SAO Predoctoral Fellowship and a French Higher Education Ministry grant.
strounding star-forming regions of the galaxy. allowing us to pinpoint the precise enviromneuts that produce GRB-SNe aud place these host sites in context with their elobal host galaxy properties.,"surrounding star-forming regions of the galaxy, allowing us to pinpoint the precise environments that produce GRB-SNe and place these host sites in context with their global host galaxy properties."
 Tere we present spatially-resolved spectroscopy of the πο 100316D/SN. 2010bh host) ealaxy., Here we present spatially-resolved spectroscopy of the GRB 100316D/SN 2010bh host galaxy.
 These observations allow us to place the propertics of the explosion site in the context of the broad host properties., These observations allow us to place the properties of the explosion site in the context of the broad host properties.
 We discuss the observations aud deseribe the analysis technique in 82., We discuss the observations and describe the analysis technique in 2.
 We derive spatially-resolved line fluxes. line ratios. iietallicities. aud star-formation rates (SFRs} across the host galaxy. with a particular focus on the GRB-SN explosion site iu §3.," We derive spatially-resolved line fluxes, line ratios, metallicities, and star-formation rates (SFRs) across the host galaxy, with a particular focus on the GRB-SN explosion site in 3."
 Finally. we cousider the iuplications that these results for our understaudius of LORB host galaxies aud the progenitor population iu 1.," Finally, we consider the implications that these results for our understanding of LGRB host galaxies and the progenitor population in 4."
 Throughout the paper we use the standard cosmological panuneters Ty=Tl hn | 1. ο=0.27. aud Q4—0.73.," Throughout the paper we use the standard cosmological parameters $H_0=71$ km $^{-1}$ $^{-1}$ , $\Omega_m=0.27$, and $\Omega_\Lambda=0.73$."
" On 2010 Mav ο UT we obtained a 2100 s spectrum of the 22010bh. explosion site (hereafter. “site”). using the Low Dispersion Survey Spectrograph (LDSS3) on the Magellan/Clav 6.5-n telescope at Las Campanas Observatory. using the l' center slit: seeing was 0.88"" (as measured frou acquisition images mn kc) aud the spectral resolutiou was8."," On 2010 May 8 UT we obtained a 2400 s spectrum of the 2010bh explosion site (hereafter, “site”), using the Low Dispersion Survey Spectrograph (LDSS3) on the Magellan/Clay 6.5-m telescope at Las Campanas Observatory, using the 1"" center slit; seeing was 0.88"" (as measured from acquisition images in $r$ ) and the spectral resolution was."
"5À.. A second spectrum was obtained on 2010 May 10 UT for a total exposure time of 15080 s. with the Lo blue slit aligned alone the extended bright region of the host galaxy couples. (hereafter. “host”): seciug was 0.627 (as measured frou, acquisition iuases in /) and the spectral resolution was9."," A second spectrum was obtained on 2010 May 10 UT for a total exposure time of 1800 s, with the 1"" blue slit aligned along the extended bright region of the host galaxy complex (hereafter, “host”); seeing was 0.62"" (as measured from acquisition images in $i$ ) and the spectral resolution was."
"0À.. The slit positio-S for the “site” aud ""host? observations are shown iu Figure 1 (top left aud top right. respectively)."," The slit positions for the “site"" and “host"" observations are shown in Figure 1 (top left and top right, respectively)."
 As the aininass was low (~1. 1.5) the impact ou the spectra from not observing at the parallactic angle is expected to be niüiunmuial., As the airmass was low $\sim 1.4-1.5$ ) the impact on the spectra from not observing at the parallactic angle is expected to be minimal.
 We also acquired observations of the spectrophotometric standard stars EG 131 and LTT 3861 (Bessell et 11999. Παιν et 11991) for flux calibration of the vsite” aud “host” spectra respectively.," We also acquired observations of the spectrophotometric standard stars EG 131 and LTT 3864 (Bessell et 1999, Hamuy et 1994) for flux calibration of the “site"" and “host"" spectra respectively."
 All spectra were taken using the using the VPILAI evisu. and cover the waveleneth rauge3800-72004.," All spectra were taken using the using the VPH-All grism, and cover the wavelength range."
.. To locate the explosion site of CRB 100316D/SN 2010bh along the slit iu the “site” spectrum we astrometrically aligned the r-baud acquisition lage with au r-baud nage of the CRD-SN from 2010 March 19.99 UT obtained with the same instrument., To locate the explosion site of GRB 100316D/SN 2010bh along the slit in the “site” spectrum we astrometrically aligned the $r$ -band acquisition image with an $r$ -band image of the GRB-SN from 2010 March 19.99 UT obtained with the same instrument.
 Using 65 objects im common to the two images. we find an astrometric accuracy of lo=16 mas in each coordinate.," Using 65 objects in common to the two images, we find an astrometric accuracy of $1\sigma=16$ mas in each coordinate."
" This is significantly: better than a siuele pixel (0.19), but we expect an overall svstcmatic wncertaiuty of about +1 pixel due to the overall slit positionine."," This is significantly better than a single pixel $0.19''$ ), but we expect an overall systematic uncertainty of about $\pm 1$ pixel due to the overall slit positioning."
 We veduced the data using standard routines inIRAF?.. iucludiug bias correction. flatficlding. aud cosmic rav removal.," We reduced the data using standard routines in, including bias correction, flatfielding, and cosmic ray removal."
 To isolate the host galaxy ciission lines. aud to remove contamination from a foreground star in the bright southwestern region of the host complex In our “site” observations (see Figure 1). we fit the continuum of both objects with a legeudre polynomial using the ΠΑΕ task aud used this fit o subtract the contimmuni from our fwo-dinensiona spectra.," To isolate the host galaxy emission lines, and to remove contamination from a foreground star in the bright southwestern region of the host complex in our “site"" observations (see Figure 1), we fit the continuum of both objects with a legendre polynomial using the IRAF task and used this fit to subtract the continuum from our two-dimensional spectra."
 The results ave shown in Figure 2., The results are shown in Figure 2.
 We extracted line profiles alone the spatial direction or four enüssiou nes in cach of our observe wo-dimensional spectra: ΠΠ. |OITIJA5007. Πα. an NTJAG58L.," We extracted line profiles along the spatial direction for four emission lines in each of our observed two-dimensional spectra: $\beta$, $\lambda 5007$, $\alpha$, and $\lambda 6584$."
 The bright Πα and |OTTA5007 features were raced using the IRAF task with an optima extraction aleorithin that ideutified aud rejected deviant jxels., The bright $\alpha$ and $\lambda 5007$ features were traced using the IRAF task with an optimal extraction algorithm that identified and rejected deviant pixels.
" For the weaker [NIT|AG58lL and UL? features. the ine profiles were extracted by applying the robust spatia xofile of the Πο aud |OIIT|A5007 features. respectively,"," For the weaker $\lambda 6584$ and $\beta$ features, the line profiles were extracted by applying the robust spatial profile of the $\alpha$ and $\lambda 5007$ features, respectively."
" Flux calibration was then applied using a seusitivitv ""nctiou of the standard stars EG 131 and ETT 3861 with he TIRAF taskssetairmass.standard. aud and determuning the response of the pixels corresponding o the onuisxion line waveleneths."," Flux calibration was then applied using a sensitivity function of the standard stars EG 131 and LTT 3864 with the IRAF tasks, and and determining the response of the pixels corresponding to the emission line wavelengths."
 Finally. the fiux-calibrated line profiles were corrected for a Galactic oreground extinction of £(5.V)=0.116 (Schlegel et 11998. Chornock et 22010).," Finally, the flux-calibrated line profiles were corrected for a Galactic foreground extinction of $E(B-V) = 0.116$ (Schlegel et 1998, Chornock et 2010)."
 Usine the ratio of the Πα aud IL features. we determined that host extinction was negligible across both of our host profiles and required uo additional correction of the line profiles: this is iu aereciment with the results of Choruock et ((2010). who also measured a negligible level of extinction iu the explosion site HIT region.," Using the ratio of the $\alpha$ and $\beta$ features, we determined that host extinction was negligible across both of our host profiles and required no additional correction of the line profiles; this is in agreement with the results of Chornock et (2010), who also measured a negligible level of extinction in the explosion site HII region."
 Our final line profiles are plotted in Figure 1., Our final line profiles are plotted in Figure 1.
" We used our extracted profiles of the ITJ. ΟΠΗ A507. Πα. and [NIT AG58 E cniission lines to construct emission lue diagnostic ratio profiles for both the ""site"" ar ""host"" observations."," We used our extracted profiles of the $\beta$, [OIII] $\lambda$ 5007, $\alpha$, and [NII] $\lambda$ 6584 emission lines to construct emission line diagnostic ratio profiles for both the “site"" and “host"" observations."
 Our two diagnostic ratios of interest are [NIT] AGS L/Ilo. and [OTT A5007/1L7.., Our two diagnostic ratios of interest are [NII] $\lambda$ $\alpha$ and [OIII] $\lambda$ $\beta$.
 The [NII λοῦσι Πα ratio is stronglv correlated with metallicity (Veilleux Osterbrock 1987. Iewlev et 22001). due to the dependence of the [NII| flax on primary ane secondary nitrogen production (e.g. Clhiappiui et 22005. Mallery: et 22007).," The [NII] $\lambda$ $\alpha$ ratio is strongly correlated with metallicity (Veilleux Osterbrock 1987, Kewley et 2001), due to the dependence of the [NII] flux on primary and secondary nitrogen production (e.g. Chiappini et 2005, Mallery et 2007)."
 However. Ikevley Dopita (2002) also note that. due to the low ionization potentia of [NIT] AG5sSI. this ratio is also somewhat sensitive o the ionization parameter of the hosteuviromueut?.," However, Kewley Dopita (2002) also note that, due to the low ionization potential of [NII] $\lambda$ 6584, this ratio is also somewhat sensitive to the ionization parameter of the host."
. Similarly. |OITI] A5007/TE3 is sensitive to the harduess of he ionizing radiation field. making it a useful tracer of he ionization parameter (Baldwin et 11981).," Similarly, [OIII] $\lambda$ $\beta$ is sensitive to the hardness of the ionizing radiation field, making it a useful tracer of the ionization parameter (Baldwin et 1981)."
 While his ratio can also be double-valued with metallicity. it is far more sensitive to the ionization parameter at lower netallicities (IXewlev et 22001).," While this ratio can also be double-valued with metallicity, it is far more sensitive to the ionization parameter at lower metallicities (Kewley et 2004)."
 Since the iouization xuaneter itself is inversely cdepeudeut on metallicity (Dopita ct 22006). these two ratios ultimately allow us to isolate ictallicitv as the fundamental plysical xuanmeter driving the evolution of our spatial profile.," Since the ionization parameter itself is inversely dependent on metallicity (Dopita et 2006), these two ratios ultimately allow us to isolate metallicity as the fundamental physical parameter driving the evolution of our spatial profile."
 Another advantage to both of these diagnostic ratios is heir inscusitivity to reddening corrections. due to the close proximity of the cmussiou lines beige compared m cach case (we found that effects from both the host aud heforeground Galactic extinction were negligible in our analyses).," Another advantage to both of these diagnostic ratios is their insensitivity to reddening corrections, due to the close proximity of the emission lines being compared in each case (we found that effects from both the host and theforeground Galactic extinction were negligible in our analyses)."
 With profiles for both the [NII| A655 L/TIo aud OM A5007 > diagnostic ratios. we used the Pettiui Pagel (2001: hereafter PPO calibration of the O3N2 netallicity diagnostic to constructL) metallicity profiles for," With profiles for both the [NII] $\lambda$ $\alpha$ and [OIII] $\lambda$ $\beta$ diagnostic ratios, we used the Pettini Pagel (2004; hereafter PP04) calibration of the $O3N2$ metallicity diagnostic to construct metallicity profiles for"
"mass, thereby leading to steeper profiles for larger masses.","mass, thereby leading to steeper profiles for larger masses."
" As we stated in the introduction, the computations of the mean. profiles (in fact, the typical profile) around halos has independently been made by Barkana(2004)."," As we stated in the introduction, the computations of the $\it mean$ profiles (in fact, the typical profile) around halos has independently been made by \citet[][]{Barkana}."
" He used the spherical model and, in principle, imposed on the initial profile the same constraint as we do."," He used the spherical model and, in principle, imposed on the initial profile the same constraint as we do."
 The computing procedure he followed was somewhat different involving some approximations., The computing procedure he followed was somewhat different involving some approximations.
" He do not give explicitly the equation defining the profile, so"," He do not give explicitly the equation defining the profile, so"
parameter) aud in those dominated by powerful magnetic coronae (at low/hiegh accretion rates for low/ligh viscosities. respectively).,"parameter) and in those dominated by powerful magnetic coronae (at low/high accretion rates for low/high viscosities, respectively)."
 The latter depends ou the angular momentum of the ceutral hole (aigh spin favors the generation of powerful jets) aud on the iuner boundary coudition for the accretion flow. and can be tackled ouly by a full eeneral relativistic treatment of the inner disc.," The latter depends on the angular momentum of the central hole (high spin favors the generation of powerful jets) and on the inner boundary condition for the accretion flow, and can be tackled only by a full general relativistic treatment of the inner disc."
" Different combinations of the two factors may cause the variety of radio properties of ACN th,", Different combinations of the two factors may cause the variety of radio properties of AGN \cite{mei01}.
 Some of the properties of the different solutious can be sununarized by the diagram that places thei in the surface density (X) accretion rate (2) plane (at fixed distance from the ceutral source). as shown in Fie. 1..," Some of the properties of the different solutions can be summarized by the diagram that places them in the surface density $\Sigma$ )–accretion rate $\dot m$ ) plane (at fixed distance from the central source), as shown in Fig. \ref{fig_branches}."
 For low values of the viscosity paraicter ay. the solutions split iuto two separate brauches: the optically thin aud the optically thick one.," For low values of the viscosity parameter $\alpha_0$, the solutions split into two separate branches: the optically thin and the optically thick one."
 Optically thin solutions exist only at low accretion rates: they are the ADAF (thermally stable) aud SLE (Shapiro-Liehtiman-Eardleyv. thermally unstable}.," Optically thin solutions exist only at low accretion rates: they are the ADAF (thermally stable) and SLE (Shapiro-Lightman-Eardley, thermally unstable)."
 Also at low i5. a geomotrically thin. eas pressure doniuated solon exists. with an optically thin corona whose relative power is f~\/2ey: this solution becomes unstable (and loses its corona) at the value of the a‘cretion rate for which radiation pressure becomes lareer than eas pressure at the eiven distauce from the black hole.," Also at low $\dot m$, a geometrically thin, gas pressure dominated solution exists, with an optically thin corona whose relative power is $f\sim \sqrt{2\alpha_0}$; this solution becomes unstable (and loses its corona) at the value of the accretion rate for which radiation pressure becomes larger than gas pressure at the given distance from the black hole."
 At even ligher accretion rates onlv a radiativelv iucffcieut. optically thick solution exists (slim disc’). which is thermally stable.," At even higher accretion rates only a radiatively inefficient, optically thick solution exists (`slim disc'), which is thermally stable."
 The topology of the diagram chanecs for high viscosity parameter: the advective. radiatively inefficieut solutions (ADAF. slim disc) becomes a single xanch. while radiatively οποιο solutions fori a secoud one.," The topology of the diagram changes for high viscosity parameter: the advective, radiatively inefficient solutions (ADAF, slim disc) becomes a single branch, while radiatively efficient solutions form a second one."
 Of those. ouly corona-doninated. for accretion rates ibove a critical value. are stable.," Of those, only corona-dominated, for accretion rates above a critical value, are stable."
 Fie., Fig.
 Lo also shows iu parenthesis the additional processes. beside those aken iuto account by the mocel. likely to be relevaut for each kind of accretion uode.," \ref{fig_branches} also shows in parenthesis the additional processes, beside those taken into account by the model, likely to be relevant for each kind of accretion mode."
 They are meant to be indicative of the open theoretical issues iu the field. and will likely indicate the direction of the research i the mauediate ture.," They are meant to be indicative of the open theoretical issues in the field, and will likely indicate the direction of the research in the immediate future."
individual broad peaks of the erav Dine result [rom various ice ancl dust) species such as Ε.Ο. forsterite. enstatite. diopside. and possibly — carbonates (see Ixeniper et 22002a. 22).,"individual broad peaks of the gray line result from various ice and dust species such as $_2$ O, forsterite, enstatite, diopside, and – possibly – carbonates (see Kemper et 2002a, 2)."
 Our aim has been (o examine whether the assignments of the jam and jam bands to dolomite and calcite is compatible wilh (he optical constants and powder spectra presented in 33. and. if so. for which temperatures and particle shapes (his is the case.," Our aim has been to examine whether the assignments of the $\mu$ m and $\mu$ m bands to dolomite and calcite is compatible with the optical constants and powder spectra presented in 3, and, if so, for which temperatures and particle shapes this is the case."
 For answering (his questions. the detectability of ας ab wavelengths between 35 and ym depending on the dust temperature also plavs a kev role.," For answering this questions, the detectability of bands at wavelengths between 35 and $\mu$ m depending on the dust temperature also plays a key role."
 A detailed view of the jm band is elven in re[tresid2.., A detailed view of the $\mu$ m band is given in \\ref{f:resid2}.
 It can be seen from this figure (when compared to 60Ixinthe75105jmrel CabsealceDE)thatonlyforemeanC DEparticleshapedistribulionofcaleiteqrains.," It can be seen from this figure (when compared to \\ref{f:Cabs_Cal_CDE}) ) that only for a mean CDE particle shape distribution of calcite grains, the bandwidth is as large as in the case of the NGC 6302 spectrum."
thebandwidlhisastarg ," For a weighted CDE, the bandwidth is smaller by (at the relevant cryogenic temperatures)."
function for a mean CDE multiplied by a Planck fanetion for a temperature. of KIN. A dust temperature of G0IXIN. is hardly compatible with the observations. both with respect to the jam band profile and with respect to the emergence of a ~42 yan feature (see dotted lines in 8 and 9)).," The best fit is achieved by the $_{abs}$ /V function for a mean CDE multiplied by a Planck function for a temperature of K. A dust temperature of K is hardly compatible with the observations, both with respect to the $\mu$ m band profile and with respect to the emergence of a $\sim$ $\mu$ m feature (see dotted lines in \ref{f:resid1} and \ref{f:resid2}) )."
 The ealeite data derived from {ransniission spectroscopy of powder (dash-dotted line in rel:resid2)) roughly reproduce (he observed band profile as well., The calcite data derived from transmission spectroscopy of powder (dash-dotted line in \\ref{f:resid2}) ) roughly reproduce the observed band profile as well.
 lt is noteworthy that the ji. band. profile of NGC 6302 obtained by temper οἱ ((2002a) is better fitted. by the PE spectrum of an caleile powder sample which is broader ancl peaks αἱ a larger wavelength., It is noteworthy that the $\mu$ m band profile of NGC 6302 obtained by Kemper et (2002a) is better fitted by the PE spectrum of an calcite powder sample which is broader and peaks at a larger wavelength.
 This may be due to the use oL different ISO LAWS spectra (a mean of seven aa single) or due to some uncertaintv in the continuum subtraction., This may be due to the use of different ISO LWS spectra (a mean of seven a single) or due to some uncertainty in the continuum subtraction.
While most work ou the composition of the Ixuiyer belt has focused ou the surface composition. all of the spectral and photonetric resuts discussed. probe an insignificantly small depth iuto the surface.,"While most work on the composition of the Kuiper belt has focused on the surface composition, all of the spectral and photometric results discussed probe an insignificantly small depth into the surface."
 To uuderstaud te true composition o. IXBOs requires an understaudiug of the bulk composition., To understand the true composition of KBOs requires an understanding of the bulk composition.
 Detailed measurenent of the ulls composition is of course impossible. but oue important proxy — tlie ice-to-rock fractio is availalle lor some ΝΕΟΣ.," Detailed measurement of the bulk composition is of course impossible, but one important proxy – the ice-to-rock fraction – is available for some KBOs."
 Measurement of the ice-to-rock ratio requi‘es Ineastllreljent of the «ity whicL dn turi. requires measurement of the mass aud radius ol the objects.," Measurement of the ice-to-rock ratio requires measurement of the density which, in turn, requires measurement of the mass and radius of the objects."
 Wile measuret of the size of an object is possible through multiple meaus (to date far infrared radiometry f'om the Spizer Space Telescope has been the domiuaut method). a ineasurement of tle Wass Is ouly »ossible if the object has a satellite whose orbit is known.," While measurement of the size of an object is possible through multiple means (to date far infrared radiometry from the Spitzer Space Telescope has been the dominant method), a measurement of the mass is only possible if the object has a satellite whose orbit is known."
 ΛΕΡΟΣ were expected to be a relatively homogeneous group., KBOs were expected to be a relatively homogeneous group.
 They all are thought to have grown eradually tlurouel accretlon. saupliug similar regious of the solar nebula. so thetr compositious should have been early identica.," They all are thought to have grown gradually through accretion, sampling similar regions of the solar nebula, so their compositions should have been nearly identical."
 lucdeed. when Plto was the only known large Ixuiper belt object. its deusity of ~2 ο cm was lasen o lndicate a 730-70 ice-rock tix ii the outer solar —nebula as a whole (Mcelxiinon&Mueller1OSS).," Indeed, when Pluto was the only known large Kuiper belt object, its density of $\sim$ 2 g $^{-3}$ was taken to indicate a $\sim$ 30-70 ice-rock mix in the outer solar nebula as a whole \citep{1988Natur.335..240M}."
 One o ‘th biggest outer soar system surprises of the past few νουIX ljerefore. has been the discovery tlat ie ice fraction meas'ed in IKBOs varies from essentially 0 to ] (Figure 10).," One of the biggest outer solar system surprises of the past few years, therefore, has been the discovery that the ice fraction measured in KBOs varies from essentially 0 to 1 (Figure 10)."
 Objects have been fou1 with densities sieuiicantly less than 1g em.7 (Μιellereta.2009: inclicating both a near-unity ice fraction and significant po‘osity. wlile other ojects have been [οιud witl densities of nearly sure rock (Fraser&Brown2010)..," Objects have been found with densities significantly less than 1 g $^{-3}$ \citep{2009DPS....41.6204M,2010Icar..207..978B}
 indicating both a near-unity ice fraction and significant porosity, while other objects have been found with densities of nearly pure rock \citep{2010ApJ...714.1547F}."
 Examninaion of the measured ¢ensities diameter reveals that he deusity measurements have extremely arge uncertainties., Examination of the measured densities diameter reveals that the density measurements have extremely large uncertainties.
 The laree error bars are a fuiction of he uncertainty intl e Ineaswed sizes alic Liie 3-times-hügher uucertainties in tlie associated volumes., The large error bars are a function of the uncertainty in the measured sizes and the 3-times-higher uncertainties in the associated volumes.
 Detailec| understaucdiug of the trends andxd causes of ice-rock fractiol sin the Ixuipe “belt clearly reqires significantly higher quality size nieasurernients., Detailed understanding of the trends and causes of ice-rock fractions in the Kuiper belt clearly requires significantly higher quality size measurements.
 Eveu wit1 tliese large uncertainies. however. wo trends are appareut.," Even with these large uncertainties, however, two trends are apparent."
 First. there is a general trend for an ---icrease in density as a function of size.," First, there is a general trend for an increase in density as a function of size."
 While au object with a fixe ice fraction will uucdergo a εἶθιsity increase witli increased size owlig to the small cleusity increase that occurs due to the chaigeo ol ice to higher dersity phase as pressure is increased. the general t'eid of inereasect density with size seen iu tlie Ixuiper belt is siguificauly larger than expected unless the rock fraction itself is ine'easiug in larger ob.jec« (Fig.," While an object with a fixed ice fraction will undergo a density increase with increased size owing to the small density increase that occurs due to the change of ice to higher density phase as pressure is increased, the general trend of increased density with size seen in the Kuiper belt is significantly larger than expected unless the rock fraction itself is increasing in larger objects (Fig."
 10)., 10).
 The second general trend is he difference iu «eusities between objects which exclusively have sla| satelites aud those which have larger satelites., The second general trend is the difference in densities between objects which exclusively have small satellites and those which have larger satellites.
 The objects which exclusively have small satellites — Hatunea. Quaoar. :ik Eris — have beet hypothesized to have uudergone [n]0giant. impacts wi‘h led to these satellite (Brownetal.2006)..," The objects which exclusively have small satellites – Haumea, Quaoar, and Eris – have been hypothesized to have undergone giant impacts which led to these satellite \citep{2006ApJ...639L..43B}."
 Iuerestinely. these objects have higher densities than every other measured ob.ject.," Interestingly, these objects have higher densities than every other measured object."
 Such a wide rauge of ice-rock ratios is astouncliug., Such a wide range of ice-rock ratios is astounding.
 No dynamical evideuce exists that the large, No dynamical evidence exists that the large
"surveys (?), and from the MOIRCS sample (?).","surveys \citep{Conselice2008}, and from the MOIRCS sample \citep{Keenan2010}
."
" In addition, we show K-band counts based on the UKIDSS- Deep Field data (UKIDSS-UDF;?).."," In addition, we show K-band counts based on the UKIDSS-Ultra Deep Field data \citep[UKIDSS-UDF;][]{Cirasuolo2010}."
 The two stellar population synthesis models give similar predictions for the J-band number counts which agree with the data., The two stellar population synthesis models give similar predictions for the $J$ -band number counts which agree with the data.
" Both predict too many faint objects in the K, and K bands.", Both predict too many faint objects in the $K_s$ and K bands.
" As shown by ?,, and as this paper will clarify, this is because the semi-analytic model overpredicts the abundance of low-mass galaxies at high redshift."," As shown by \citet{Guo2011}, and as this paper will clarify, this is because the semi-analytic model overpredicts the abundance of low-mass galaxies at high redshift."
" The two stellar population synthesis models predict similar counts at both bright (low redshift, near infrared emission) and faint (high redshift, red optical emission) apparent magnitudes, but they disagree at intermediate apparent magnitudes."," The two stellar population synthesis models predict similar counts at both bright (low redshift, near infrared emission) and faint (high redshift, red optical emission) apparent magnitudes, but they disagree at intermediate apparent magnitudes."
" As we will see in more detail below, the difference is a consequence of TB-AGB emission from stars with ages of one or two Gyr which is fully included in the ? but not in the ? stellar population model."," As we will see in more detail below, the difference is a consequence of TB-AGB emission from stars with ages of one or two Gyr which is fully included in the \citet{Maraston2005} but not in the \citet{Bruzual2003} stellar population model."
" Predicted number counts for the IRAC 3.6um, 4.5um and 5.8um bands are plotted against Spitzer (?),, FIREWORKS (?) and NEWFIRM (7) observations."," Predicted number counts for the IRAC $3.6\rm{\mu m}$, $4.5\rm{\mu m}$ and $5.8\rm{\mu m}$ bands are plotted against Spitzer \citep{Fazio2004}, FIREWORKS \citep{Wuyts2008} and NEWFIRM \citep{Whitaker2011} observations."
" Both the models and the observations show a pronounced change in slope at an apparent magnitude near 20, but the break is stronger in the observations than in the model and occurs at slightly brighter apparent magnitudes."," Both the models and the observations show a pronounced change in slope at an apparent magnitude near 20, but the break is stronger in the observations than in the model and occurs at slightly brighter apparent magnitudes."
" As a result, the models under-predict the number of bright objects (low redshift, emission longwards of the rest-frame K-band) and over-predict the number of faint objects (high redshift, emission in the rest-frame JHK region)."," As a result, the models under-predict the number of bright objects (low redshift, emission longwards of the rest-frame K-band) and over-predict the number of faint objects (high redshift, emission in the rest-frame $JHK$ region)."
 The latter underprediction is even more pronounced here than in the K-band and again is likely due to the overabundance of lower mass galaxies at z>1 in the model., The latter underprediction is even more pronounced here than in the K-band and again is likely due to the overabundance of lower mass galaxies at $z\geq 1$ in the model.
 The deficit of bright galaxies is visible also in the z—0 rest-frame K-band luminosity function (Fig. 5))., The deficit of bright galaxies is visible also in the $z=0$ rest-frame $K$ -band luminosity function (Fig. \ref{fig:LfK}) ).
" Since ? tuned their semi- model to match the observed low-redshift stellar mass function, this deficit implies overly large mass-to-near-infrared-light ratios which might be explained by overly small stellar metallicities."," Since \citet{Guo2011} tuned their semi-analytic model to match the observed low-redshift stellar mass function, this deficit implies overly large mass-to-near-infrared-light ratios which might be explained by overly small stellar metallicities."
" Indeed, ? showed that the most massive low-redshift galaxies in the ? version of the model have stellar metallicities which are too low by about a factor of two (the dashed red lines in their Figs 4 and 10)."," Indeed, \citet{Henriques2010} showed that the most massive low-redshift galaxies in the \citet{DeLucia2007}
 version of the model have stellar metallicities which are too low by about a factor of two (the dashed red lines in their Figs 4 and 10)."
pper pixel ancl a spectral resolution of LLA..,per pixel and a spectral resolution of $\sim11$.
 The ARGUS aperture was oriented with north to the top of the aperture [or all the observations in June 1993. and with north toward the top left-hand corner of the aperture for the observation of 3€215 in Jan 1995.," The ARGUS aperture was oriented with north to the top of the aperture for all the observations in June 1993, and with north toward the top left-hand corner of the aperture for the observation of 3C215 in Jan 1995."
 The cata were reduced. in ULAR using the steps described. in. detail for the quasar 3C254 in. Crawford Vaneerriest (1996)., The data were reduced in IRAF using the steps described in detail for the quasar 3C254 in Crawford Vanderriest (1996).
 In. summary. alter correction for bad CCD columns. the individual frames of cach quasar were median-combined to remove cosmic ray events and then bias-subtracted: (with a bias estimated from the zero response at the bluewavelength part of the chip).," In summary, after correction for bad CCD columns, the individual frames of each quasar were median-combined to remove cosmic ray events and then bias-subtracted (with a bias estimated from the zero response at the blue-wavelength part of the chip)."
 The data were corrected. for spatial distortion. Dat-fielded: using a normatisecl exposure of a tungsten lamp. anc wavelength-calibrated: using exposures of a Neon-eMNMelium Lamp.," The data were corrected for spatial distortion, flat-fielded using a normalised exposure of a tungsten lamp, and wavelength-calibrated using exposures of a Neon-Helium lamp."
 They were then Ilux-calibrated. corrected. for both atmospheric extinction. and for Galactic reddening along the line of sight (bx the chy listecl in Table. 1.. which was estimated. [rom Galactic hydrogen column densities in the direction of each quasar Stark 1992). and converted using the relation of Bohlin. Savage Drake (LOTS). assuming lt of 3.2 and the reddening aw of Cardelli. Clavton Mathis (1989)).," They were then flux-calibrated, corrected for both atmospheric extinction, and for Galactic reddening along the line of sight (by the $A_V$ listed in Table \ref{tab:obslog}, which was estimated from Galactic hydrogen column densities in the direction of each quasar ;Stark 1992), and converted using the relation of Bohlin, Savage Drake (1978), assuming R of 3.2 and the reddening law of Cardelli, Clayton Mathis (1989))."
 The cata were hen separated into spectra from individual libres., The data were then separated into spectra from individual fibres.
 Sky (and scattered-light) subtraction used the average spectrum from ibres that were neither too near the edge of the aperture. nor too close to the source itself: typically a total of 5 or 6 sky fibres per row.," Sky (and scattered-light) subtraction used the average spectrum from fibres that were neither too near the edge of the aperture, nor too close to the source itself; typically a total of 5 or 6 sky fibres per row."
 A separate sky spectrum was constructed o subtract [rom cach row of the hexagon. using the mean spectrum of all chosen sky fibres in that and the two adjacent LOWS.," A separate sky spectrum was constructed to subtract from each row of the hexagon, using the mean spectrum of all chosen sky fibres in that and the two adjacent rows."
 Like the data presented. in Crawford Vancelerricst (1996: 1997). the Hux calibration is imperfect in that some Hux has been lost from the calibration data at wavelengths greater thanTOOOA.," Like the data presented in Crawford Vanderriest (1996; 1997), the flux calibration is imperfect in that some flux has been lost from the calibration data at wavelengths greater than."
. In practice this has little consequence for the observations presented here. as we are modelling the dynamics. cistribution and ionization state of the extended emission-line region (IEEELIt) using the OLTA3727. and AOLHL]A5007 emission lines.," In practice this has little consequence for the observations presented here, as we are modelling the dynamics, distribution and ionization state of the extended emission-line region (EELR) using the $\lambda3727$, and $\lambda$ 5007 emission lines."
 Only two of our sample quasars (96351 and ος294) are at high enough redshift [or some of the lines to be observed at wavelengths appreciably bevondTOOOA., Only two of our sample quasars (3C281 and 3C334) are at high enough redshift for some of the lines to be observed at wavelengths appreciably beyond.
. For these two quasars the Εικ calibration error has been simply corrected by comparing the well-defined power-law slope of the quasar nuclear continuum to high-quality optical/UV spectra in the literature (ef, For these two quasars the flux calibration error has been simply corrected by comparing the well-defined power-law slope of the quasar nuclear continuum to high-quality optical/UV spectra in the literature (c.f.
 CV96)., CV96).
 Even if this correction is not sullicient. only widelv-paced line intensity ratios The spectral fitting of the emission lines was done using QDP Clennant 1991).," Even if this correction is not sufficient, only widely-spaced line intensity ratios The spectral fitting of the emission lines was done using QDP (Tennant 1991)."
 Small complexes of neighbouring ines were [it together (eg narrow and broad with OL[AA4959.5007). over a wavelength range of a few iundred. Angstroms in cach individual fibre spectrum.," Small complexes of neighbouring lines were fit together (eg narrow and broad with $\lambda\lambda$ 4959,5007) over a wavelength range of a few hundred ngstroms in each individual fibre spectrum."
 arrow lines within such a complex were constrained to have he same redshift and velocity width as each other. and were it by a Gaussian (a satisfactory fit even to the OL] doublet at this resolution).," Narrow lines within such a complex were constrained to have the same redshift and velocity width as each other, and were fit by a Gaussian (a satisfactory fit even to the [OII] doublet at this resolution)."
 Where an emission lino was unresolved (generally only. toward the edges of the ARGUS aperture) he FWHIAL used in the fitting was fixed at an average of the immediately neighbouring fibres: line fits.," Where an emission line was unresolved (generally only toward the edges of the ARGUS aperture), the FWHM used in the fitting was fixed at an average of the immediately neighbouring fibres' line fits."
 We present an introduction to ancl results for individual quasars in order of increasing recshilt., We present an introduction to and results for individual quasars in order of increasing redshift.
 3€C323.1 is one of the nearest. radio-loud quasars. ancl is located on the outskirts of the compact. cluster of galaxies Z1545.1|2104 (Oenmler. Gunn Oke 1972: Hintzen Scott 1978: Yee οσα 1984).," 3C323.1 is one of the nearest radio-loud quasars, and is located on the outskirts of the compact cluster of galaxies Z1545.1+2104 (Oemler, Gunn Oke 1972; Hintzen Scott 1978; Yee Green 1984)."
 Ht is associated: with a steep-spectrum triple radio source which is straight and symmetric over à 360 deizmeter (Dogers 1994)., It is associated with a steep-spectrum triple radio source which is straight and symmetric over a $\sim360$ diameter (Bogers 1994).
 The quasar Dies in a Iuminous elliptical host galaxy (Neugebauer. Matthews Armus 1995: Dahcall 1997). with several continuum companions.," The quasar lies in a luminous elliptical host galaxy (Neugebauer, Matthews Armus 1995; Bahcall 1997), with several continuum companions."
 Lhe dominant companion is a compact galaxy located 2.7i aresec approximately West at a similar redshift to the quasar (Neugebauer 1995: Canalizo Stockton 199 here are two other objects in the field. one at 19 aresee East and one further North (eg MeLbeod Rieke 1994: Les 1996).," The dominant companion is a compact galaxy located 2.7 arcsec approximately West at a similar redshift to the quasar (Neugebauer 1995; Canalizo Stockton 1997); there are two other objects in the field, one at 19 arcsec East and one further North (eg McLeod Rieke 1994; Hes 1996)."
 Hutchings. Johnson Pyke (1988) fined continuum concensations 1.3. arcsec NW and 3 aresec S. alter subtraction of the quasar light.," Hutchings, Johnson Pyke (1988) find continuum condensations 1.3 arcsec NW and 3 arcsec S, after subtraction of the quasar light."
 has long been known to show an asvnimetric emission-line region. extended. approximately from south-cast to west across the quasar core (SAIST: Hes 1996).," 3C323.1 has long been known to show an asymmetric emission-line region, extended approximately from south-east to west across the quasar core (SM87; Hes 1996)."
 The spectral smape of the broad emission line is slightly skew (ce Brotherton 1996) and thus not. perfectly fit by à svmmetri© gaussian centred about the narrow line component: οherwise fitting niocls to in QDDP is straightforward., The spectral shape of the broad emission line is slightly skew (eg Brotherton 1996) and thus not perfectly fit by a symmetric gaussian centred about the narrow line component; otherwise fitting models to in QDP is straightforward.
 Whilst. the ARGUS aperture encompasses the companion galaxy to the west of the quasar core. the continuum detection level of our observation is not sullicientIv. sensitive to detect it (the ellicieney of the ARGUS svstem is only around half that of a long- spectrum).," Whilst the ARGUS aperture encompasses the companion galaxy to the west of the quasar core, the continuum detection level of our observation is not sufficiently sensitive to detect it (the efficiency of the ARGUS system is only around half that of a long-slit spectrum)."
 We detect the continuum light from the, We detect the continuum light from the
As mentioned above. the most commonlv-invoked. physical model for the velocity residuals in 95433 is “phase jitter” in the jet. precession.,"	As mentioned above, the most commonly-invoked physical model for the velocity residuals in SS433 is “phase jitter” in the jet precession."
 Since the precession phase affects both jets similarly. it naturally explains the correlation between (he z4 ancl το residuals.," Since the precession phase affects both jets similarly, it naturally explains the correlation between the $z_1$ and $z_2$ residuals."
 If such jitter can occur over limescales of weeks or months. it can also explain the long-term residual correlations evident in Figures 2-3.," If such jitter can occur over timescales of weeks or months, it can also explain the long-term residual correlations evident in Figures 2-3."
 We analvzed this $9433 data set following the example of Margon&Anderson(1939).. determining phase errors from the velocity residuals above.," 	We analyzed this SS433 data set following the example of \citet{MargonAnderson}, determining phase errors from the velocity residuals above."
 We simply defined. the phase error to be the phase dillerence between the actual phase of the observation given ils epoch and the kinematic model parameters in Table 2 and the closest model point with the same observed velocity., We simply defined the phase error to be the phase difference between the actual phase of the observation given its epoch and the kinematic model parameters in Table 2 and the closest model point with the same observed velocity.
 As can be seen in Figure 4. some observed velocity amplitudes. exceed (he masinnun model velocity amplitude. ancl such points were dropped [rom (his analvsis.," As can be seen in Figure 4, some observed velocity amplitudes exceed the maximum model velocity amplitude, and such points were dropped from this analysis."
 We then divided the data set into 10-day intervals ancl calculated the average and standard deviation of the phase errors [rom all phase measurements doing that interval (including both z4 and το)., We then divided the data set into 10-day intervals and calculated the average and standard deviation of the phase errors from all phase measurements doing that interval (including both $z_1$ and $z_2$ ).
 For 10-dav intervals with only 1 phase measurement we have no estimate of the standard deviation. and thus dropped such intervals from the analvsis.," For 10-day intervals with only 1 phase measurement we have no estimate of the standard deviation, and thus dropped such intervals from the analysis."
 We plot the resulting phase noise measurements in Figure 6., We plot the resulting phase noise measurements in Figure 6.
 We repeated this same analvsis using a 30-clav interval for averaging. with the results shown in Figure 7.," We repeated this same analysis using a 30-day interval for averaging, with the results shown in Figure 7."
 We note (hat while (here are occasional trends in (he residuals on (imescales of several hundred days. no obvious trend is apparent over the full time span in either panel of Figure 7.," 	We note that while there are occasional trends in the residuals on timescales of several hundred days, no obvious trend is apparent over the full time span in either panel of Figure 7."
 The 1999 data are marginally inconsistent with zero phase residual (al the 2.80 level for one of the two data points in Figure 6b)., The 1999 data are marginally inconsistent with zero phase residual (at the $2.8 \sigma$ level for one of the two data points in Figure 6b).
 ILowever. it is clear (hat this phase residual is less (han many prior apprently secular deviations [rom the kinematic model in Figures 6-7.," However, it is clear that this phase residual is less than many prior apprently secular deviations from the kinematic model in Figures 6-7."
 HE we assume (that some period derivative is present in 95423 over (he span of our observations. {hese secular deviations could mask its elleets up to o~0.05 evceles.," If we assume that some period derivative is present in SS433 over the span of our observations, these secular deviations could mask its effects up to $\Delta \phi \sim 0.05$ cycles."
 Given the span of our observations. (his corresponds to an upper limit on the period derivative of P«5xI07.," Given the span of our observations, this corresponds to an upper limit on the period derivative of $\dot P < 5 \times 10^{-5}$."
 As mentioned above. an alternate physical explanation for the velocity residuals in Figures 2-4 is noise in (he intrinsic velocity of (he jets.," 	As mentioned above, an alternate physical explanation for the velocity residuals in Figures 2-4 is noise in the intrinsic velocity of the jets."
 To investigate (his possibility further. we calculated the intrinsic jet velocity necessary to match each observed Doppler shift. eiven 9.i.ly.andp [rom the best-fit parameter set in Table 1.," To investigate this possibility further, we calculated the intrinsic jet velocity necessary to match each observed Doppler shift, given $\theta, \ i , \ t_0 , \ {\rm and} \ p$ from the best-fit parameter set in Table 1."
 We plot the corresponding values lor Jj]=© versus time in Figure 5 and versus precessional phase in Figure 9.," We plot the corresponding values for $\beta
= {v \over{c}}$ versus time in Figure 8 and versus precessional phase in Figure 9."
 The average valueof 9 we find is 0.254 with a standard. deviation of 0.024., 	The average valueof $\beta$ we find is 0.254 with a standard deviation of $0.024$ .
 Given, Given
of a rastered spectrolicliograim is stretched out in the x-direction when the targeted region is located on the solar disk.,of a rastered spectroheliogram is stretched out in the x-direction when the targeted region is located on the solar disk.
 Iu this study. the CDS rastered image was observed froimà 17:00:28 to 19:01:00 UT. cousistiug of 60 pointing positious.," In this study, the CDS rastered image was observed from 17:00:28 to 19:01:00 UT, consisting of 60 pointing positions."
 The FOV is 260.«210°., The FOV is $^{''}\times240^{''}$.
 The pointing differcuce between CDS NIS 1: auc NIS 2 has been corrected when applyingαρ in SSW IDL library., The pointing difference between CDS NIS 1 and NIS 2 has been corrected when applying in SSW IDL library.
 We first built up EUNIS rastered slit-lobe tages in selected spectral lines for LW and SW chanucls using all exposure frames., We first built up EUNIS rastered slit-lobe images in selected spectral lines for LW and SW channels using all exposure frames.
 Fieure d. shows the LW 301 sslit-lobe image aud the SW composite image frou three coronal lines. 1715Α. 177.2 aud 180.1A.," Figure \ref{fgfov} shows the LW 304 slit-lobe image and the SW composite image from three coronal lines, 174.5, 177.2 and 180.4."
. We then determined the pointing. roll anele. aud actual spatial scale of EUNIS slit images by coaliguiug them with EIT images in 301 aand 195 ppasshands using the method as described in Wanectal. (2010).," We then determined the pointing, roll angle, and actual spatial scale of EUNIS slit images by coaligning them with EIT images in 304 and 195 passbands using the method as described in \citet{wan10}."
. For the EUNIS LW images we obtained the actual pixel size of 0.926 pixel| and the roll angle of 27.17 counterclockwise frou tle , For the EUNIS LW images we obtained the actual pixel size of $^{''}$ .926 $^{-1}$ and the roll angle of $^{\circ}$ .47 counterclockwise from the North.
For tho SW inages we obtained the actual pixel size of North. 0.920 pixelt and the roll augle of 37.61., For the SW images we obtained the actual pixel size of $^{''}$ .920 $^{-1}$ and the roll angle of $^{\circ}$ .64.
 The measurements show that the LW aud SW chanuels have nearly the same pixel size and roll angele. and they were well co-poiuted in the direction perpendicular to the slit with a small offset of 18.5 iu solar x-direction aud an offset of LOS”.5 in solar y-direction.," The measurements show that the LW and SW channels have nearly the same pixel size and roll angle, and they were well co-pointed in the direction perpendicular to the slit with a small offset of $^{''}$ .5 in solar x-direction and an offset of $^{''}$ .5 in solar y-direction."
 Figure 1 shows the coaligued EUNIS-07 SW and LW slit-lobe images. indicating that their FOVs are mostly overlaid iu the slit part.," Figure \ref{fgfov} shows the coaligned EUNIS-07 SW and LW slit-lobe images, indicating that their FOVs are mostly overlaid in the slit part."
 Figure 2. illustrates their cospatial rastered slit images in 317 Hine of LAW channel and 188 line of SW channel.," Figure \ref{fgefv}
 illustrates their cospatial rastered slit images in 347 line of LW channel and 188 line of SW channel."
 The pointing of EIS LAV baud was determined by coaligning the 256 rrastered πάσα obtained during 18:0215:51 UT with the average image of EIT 301 at 18:01 and 18:09 UT., The pointing of EIS LW band was determined by coaligning the 256 rastered image obtained during 18:02–18:54 UT with the average image of EIT 304 at 18:01 and 18:09 UT.
 The pointing of EIS SW band was determined by coaligning the 195 rraster image with the average image of EIT 195 at 17:55 and 18:22 UT. where the average was made after the two EIT images were rotated to a common time.," The pointing of EIS SW band was determined by coaligning the 195 raster image with the average image of EIT 195 at 17:55 and 18:22 UT, where the average was made after the two EIT images were rotated to a common time."
 The measured pointings for both bands are the same considering the existing offsets between them., The measured pointings for both bands are the same considering the existing offsets between them.
 Figure 3 illustrates the accurate coaliguimenuts between EUNIS-07 and EIS iu both lanes.," Figure \ref{fgcfv}
 illustrates the accurate coalignments between EUNIS-07 and EIS in both bands."
 The pointing of CDS NIS was deteriuimed by coaligning the 301 (secoud order) rastered nuage observed duriug 19:00 UT with the EIT 301 image at 15101 UT., The pointing of CDS NIS was determined by coaligning the 304 (second order) rastered image observed during $-$ 19:00 UT with the EIT 304 image at 18:01 UT.
" Fieure Lt illustrates a good coaligmment between EUNIS aud CDS NIS as seen iu 301A aand 368 rrastered images,", Figure \ref{fgcdsmap} illustrates a good coalignment between EUNIS and CDS NIS as seen in 304 and 368 rastered images.
 Comparisons between the FOVs of coaligned EUNIS.. EIS. aud CDS NIS are shown in Figure 1..," Comparisons between the FOVs of coaligned EUNIS, EIS, and CDS NIS are shown in Figure \ref{fgfov}. ."
 Radiometric calibration of the EUNIS-06 LAW channel was carricd out in August 2006 aud that of the EUNIS-07 LW channel was in May. 2008., Radiometric calibration of the EUNIS-06 LW channel was carried out in August 2006 and that of the EUNIS-07 LW channel was in May 2008.
 They were performed at the RAL in the same facility and using the same EUV light source as was used for preflight calibrations of CDS (Lanectal.2002)., They were performed at the RAL in the same facility and using the same EUV light source as was used for preflight calibrations of CDS \citep{lan02}.
.. Recalibration of the German PTB πο source against the primary EUV radiation standard of DESSY-II(English: Berlin Electrou Storage Ring Society for Svuchrotron. Radiation) iu March 2007 showed that it had remained stable within its uncertainty., Recalibration of the German PTB light source against the primary EUV radiation standard of BESSY-II Berlin Electron Storage Ring Society for Synchrotron Radiation) in March 2007 showed that it had remained stable within its uncertainty.
 The eud-to-eund calibration of EUNIS-07 was made using the 301 line at S8 individual locations. and using 11 cistinet Ne features between 300 and 370 aat 176 individual locationscovering the iustrunieuts," The end-to-end calibration of EUNIS-07 was made using the 304 line at 88 individual locations, and using 11 distinct Ne features between 300 and 370 at 176 individual locationscovering the instrument's"
the plasma frequencyzy.,the plasma frequency$\omega_p$.
" Given that the interior is an excellent example of fixed positive ions and mobile electrons. we can define the plasma frequency here in terms of the electrons only: where we have used the geometric mean number density in the numerical evaluation: 75, and co are the electron rest mass and electric constant. respectively."," Given that the interior is an excellent example of fixed positive ions and mobile electrons, we can define the plasma frequency here in terms of the electrons only: where we have used the geometric mean number density in the numerical evaluation; $m_e$ and $\epsilon_0$ are the electron rest mass and electric constant, respectively."
 The simple assumption of such a strongly anisotropic conducting flux tube has major implications., The simple assumption of such a strongly anisotropic conducting flux tube has major implications.
 The electron dynamics in the interior can be treated essentially as one-dimensional. since the electron momentum parallel to the magnetic field greatly exceeds that perpendicular to it: hence in modelling the electron distributions. and deriving the Fermi energy as a substitute for the surface work function. a one-dimensional treatment will be a good approximation.," The electron dynamics in the interior can be treated essentially as one-dimensional, since the electron momentum parallel to the magnetic field greatly exceeds that perpendicular to it; hence in modelling the electron distributions, and deriving the Fermi energy as a substitute for the surface work function, a one-dimensional treatment will be a good approximation."
" Moreover. since cross-tield transport is inhibited. —ye role of the Landau levels in the interior is diminished: in the non-relativistic formulation of the electron motion in a uniform strong magnetic field /5 (Sokolov&Ternov1986). the electron energy 5 is given by where w,—cDm, is the cyclotron frequency. m, is the electron rest mass and n=O.1.2.... is the principal quantum number for the quantised electron orbit in the plane perpendicular to the magnetic field."," Moreover, since cross-field transport is inhibited, the role of the Landau levels in the interior is diminished: in the non-relativistic formulation of the electron motion in a uniform strong magnetic field $B$ \citep{sokolov}, the electron energy $\varepsilon$ is given by where $\omega_c=eB/m_e$ is the cyclotron frequency, $m_e$ is the electron rest mass and $n=0,1,2,...$ is the principal quantum number for the quantised electron orbit in the plane perpendicular to the magnetic field."
 The radius # of orbit of the perpendicular motion of the electron can be expressed (in the same relativistic limit) as Sokolov&Ternov(1986) The mean orbital radius associated with the Landau ground state is given by in other words. ὁ=η0). in Eq. (3).," The radius $R$ of orbit of the perpendicular motion of the electron can be expressed (in the same non-relativistic limit) as \citet{sokolov}
 The mean orbital radius associated with the Landau ground state is given by in other words, $\hat{\rho}=R(n=0)$, in Eq. \ref{rudermanrho}) ),"
 as already assumed., as already assumed.
 Note that the energy increment ὃς between Landau levels is where £ is given in Tesla., Note that the energy increment $\delta \varepsilon$ between Landau levels is where $B$ is given in Tesla.
" Hence for a typical pulsar magnetic field of 107 T. Landau levels are separated by ~11.5keV. implying that there is negligible population of the higher Landau levels if thermal excitation is the only mechanism. given that the typical surface temperature of a pulsar is <10""K tin energetic terms. «l00eV) cHaberl2007:Kargaltsev&PavlovBogdanovetal.2006)."," Hence for a typical pulsar magnetic field of $10^8$ T, Landau levels are separated by $\sim 11.5$ keV, implying that there is negligible population of the higher Landau levels if thermal excitation is the only mechanism, given that the typical surface temperature of a pulsar is $<10^6$ K (in energetic terms, $< 100$ eV) \citep{2007Ap&SS.308..181H,kargaltsev2007,2006ApJ...646.1104B}."
 This reinforces the merit in assuming that the electron momentum is largely parallel to the magnetic field. and lends credence to the argument that a one-dimensional statistical treatment captures the essential physics.," This reinforces the merit in assuming that the electron momentum is largely parallel to the magnetic field, and lends credence to the argument that a one-dimensional statistical treatment captures the essential physics."
 Finally. although calculations involving the Landau levels are quantum in nature. they are not relativistic ¢though the generalisation is possible).," Finally, although calculations involving the Landau levels are quantum in nature, they are not relativistic (though the generalisation is possible)."
 For the moment. we will defer the detailed discussion about the need for a relativistic treatment to the Appendix.," For the moment, we will defer the detailed discussion about the need for a relativistic treatment to the Appendix."
 Ingeneral. the distribution function for electrons in the presence of a magnetic field. £ is really the Fermi-Dirac distribution. {ου where « is the energy. j/ is the chemical potential. sry is the magnetic moment of the electron. and. 7 is the temperature.," Ingeneral, the distribution function for electrons in the presence of a magnetic field $B$ is really the Fermi-Dirac distribution, $f_{FD}$ , where $\epsilon$ is the energy, $\mu$ is the chemical potential, $\mu_B$ is the magnetic moment of the electron, and $T$ is the temperature."
 In the limit 7»0. gi-cp. the Fermi energy. and since jgD~GhelmEgi for 2~I07T. we can assume that the electrons are spin-aligned in the lowest energy configuration. and so this term can be neglected.," In the limit $T\rightarrow 0$, $\mu \rightarrow \epsilon_F$, the Fermi energy, and since $\mu_B B\sim 6\, {\mbox keV}\gg k_BT$ for $B\sim 10^8$ T, we can assume that the electrons are spin-aligned in the lowest energy configuration, and so this term can be neglected."
 Hence we have For temperatures such that Agyi. the distribution is therefore basically a step function. with all energy levels equally occupied up to jr. and none of the higher ones occupied.," Hence we have For temperatures such that $k_BT \ll \mu$, the distribution is therefore basically a step function, with all energy levels equally occupied up to $\mu$, and none of the higher ones occupied."
 Ruderman(1971) calculated the Fermi energy for the simple I-D case. motivated by the restricted motion of the electrons imposed by the enormous magnetic field strengths in the pulsar interior.," \citet{1971PhRvL..27.1306R} calculated the Fermi energy for the simple 1-D case, motivated by the restricted motion of the electrons imposed by the enormous magnetic field strengths in the pulsar interior."
 The reason for calculating the Fermi energy is that c;- is an excellent guide to the work function of the surface. that is. the potential barrier which must be surmounted before interior particles can escape to the exterior.," The reason for calculating the Fermi energy is that $\epsilon_F$ is an excellent guide to the work function of the surface, that is, the potential barrier which must be surmounted before interior particles can escape to the exterior."
 Assuming that the mean electron energy is far below the Fermi temperature (so that the step-function nature of the Fermi distribution can be assumed). for NV electrons in the population. and fp=«cp is the Fermi energy in the limit of 7«⋅ ," Assuming that the mean electron energy is far below the Fermi temperature (so that the step-function nature of the Fermi distribution can be assumed), for $N$ electrons in the population, where $g(\epsilon)$ is the density of states for the electron gas, and $\mu = \epsilon_F$ is the Fermi energy in the limit of $T \ll T_F$."
↕∶⋯⊾⋔∁∩⋂∁−↳∐∣∏∁⋂⊰↥⋯⊤∙∣∣∁∣∁∁⊓⊾∢⋯∙⋮↾⋡∙∣⊰⋅∙↙∣↿∖∕⋅⋅⊐↲∕⋅⋅∶↕∠−∣∏↲∕⋅⋅⋅ where £ is the characteristic scale-length of the problem. and we have suppressed the normal degeneracy factor 2. given the assumption.," For the one-dimensional electron gas, $g(k)\mbox{d}k= [L/(2\pi)]\mbox{d}k$ , where $L$ is the characteristic scale-length of the problem, and we have suppressed the normal degeneracy factor $2$ , given the spin-alignment assumption."
 In this case. the integration yields where we should interpret ;V/L as the line-density of electrons.," In this case, the integration yields where we should interpret $N/L$ as the line-density of electrons."
 Assuming a uniform density approximation within the, Assuming a uniform density approximation within the
"contribution functions 9»,. Comprising Ary gee. On.de and nsquer. May then be combined with a model for the star formation history of the thin dise 9(/) to establish the current birth-rate. merger rate and number of DDs.","contribution functions $\delta n_{\ast}$, comprising $\delta n_{\ast,\rm new}$ , $\delta n_{\ast,\rm dd}$ and $\delta n_{\ast,\rm mer}$, may then be combined with a model for the star formation history of the thin disc $S(t)$ to establish the current birth-rate, merger rate and number of DDs."
" From above. we have 0n,(4N) to be the SF contribution at time /. to the number per unit SF rate at time /.). integrated over an interval οἱ, "," From above, we have $\delta n_{\ast}(\Delta)$ to be the SF contribution at time $t_{\rm sf}$ to the number per unit SF rate at time $t_{\rm sf}$, integrated over an interval $\delta t_{\rm sf}$."
"Hence 6,=On,f/Olyzz/Oby, is the sample contribution function per unit SF rate per unit time at time /.;."," Hence $\dot{C_{\ast}} = \partial n_{\ast}/\partial t_{\rm sf} 
\approx \delta n_{\ast}/\delta t_{\rm sf}$ is the sample contribution function per unit SF rate per unit time at time $t_{\rm sf}$."
 To obtain total numbers in a real thin disc. we must multiply by the thin-dise SF rate to obtain the total contribution rates: C also reflects the distribution of age of the DDs.," To obtain total numbers in a real thin disc, we must multiply by the thin-disc SF rate to obtain the total contribution rates: $\dot{C}$ also reflects the distribution of age of the DDs."
" For example. if the thin-disc SF rate is οί). star formation at /.,=0 will contribute on.(aise)fof(0) DDs with age faisc: star formation at/,,=1 Gyr will contribute O77...)(aise12/954:(1) DDs with age fais1 Gyr. and so on."," For example, if the thin-disc SF rate is $S(t)$ , star formation at $t_{\rm sf}=0$ will contribute $\delta n_{{\ast}}(t_{\rm disc})/\delta t_{\rm sf} \cdot S(0)$ DDs with age $t_{\rm disc}$; star formation at $t_{\rm sf}=1$ Gyr will contribute $\delta n_{{\rm ast}}(t_{\rm disc}-1)/\delta t_{\rm sf} \cdot S(1)$ DDs with age $t_{\rm disc}-1$ Gyr, and so on."
" Since we know from f refeq,dollhatstarormaltionallimct; contributes CLa) DDs at thin dise age {μις we detine a rate contribution function to be the contribution from star formation at /.; to the number rate at time /4;,.."," Since we know from \\ref{eq_cdot} that star formation at time $t_{\rm sf}$ contributes $\dot{C}(t_{\rm disc}-t_{\rm sf})$ DDs at thin disc age $t_{\rm disc}$, we define a rate contribution function to be the contribution from star formation at $t_{\rm sf}$ to the number rate at time $t_{\rm disc}$."
 The integral of the rate contribution functiontells us the birth rate and the merger rate of DDs., The integral of the rate contribution functiontells us the birth rate and the merger rate of DDs.
" We detine n(/) to be the total number of DDs at thin dise age /. where » may represent new-born ni. merged my, or existing naa DDs."," We define $n(t)$ to be the total number of DDs at thin disc age $t$, where $n$ may represent new-born $n_{\rm new}$, merged $n_{\rm mer}$ or existing $n_{\rm dd}$ DDs."
" Star formation from /.4 to /.|07, will generate umDIAM DDs with age fainAa.", Star formation from $t_{\rm sf}$ to $t_{\rm sf}+\delta t_{\rm sf}$ will generate $\dot{C}\cdot \delta t_{\rm sf}$ DDs with age $t_{\rm disc}-t_{\rm sf}$ .
 Hence. the overall number of new-born. alive or merged DDs at /=ἐς is Then we are able to calculate the number rate (μις) of DDs from the contribution function €' where 7? represents the birth rate v or merger rate c.," Hence, the overall number of new-born, alive or merged DDs at $t = t_{\rm disc}$ is Then we are able to calculate the number rate $\dot{n}(t_{\rm disc})$ of DDs from the contribution function $\ddot{C}$ where $\dot{n}$ represents the birth rate $\nu$ or merger rate $\zeta$."
 We will give the details of these functions in the present simulation in 32.4.., We will give the details of these functions in the present simulation in \ref{sec_sfrDD}.
 Furthermore. since we know the overall rate of change in the number DDs v(/)ο. we ean also calculate the total number of DDs in the thin dise at time fice Gra(tise )) by the integral Consequently. we have two different methods to compute the current number of DDs in the thin disc.," Furthermore, since we know the overall rate of change in the number DDs $\nu(t)-\zeta(t)$, we can also calculate the total number of DDs in the thin disc at time $t_{\rm disc}$ $n_{\rm dd}(t_{\rm disc})$ ) by the integral Consequently, we have two different methods to compute the current number of DDs in the thin disc."
" refeq, imberlrepresentsthesumofcontribulionsf romceachindividualSPepo re", \\ref{eq_number1} represents the sum of contributions from each individual SF epochto the total number by counting which DDs exist at the current epoch.
fequaumber2representstheintegralofthebirth raleminusthemerger rale.ornclibirlhrate.overlheentireS E historyo f ," \\ref{eq_number2} represents the integral of the birth-rate minus the merger-rate, or nett birth rate, over the entire SF history of the galaxy."
"theg the evaluation of the sum in refeq, imberlgivesstighllyhighernumbersthanfq. "," The two methods should give the same result but, due to the limited grid in $t_{\rm sf}$, the evaluation of the sum in \\ref{eq_number1} gives slightly higher numbers than \\ref{eq_number2}. ."
dnthepresentsimulationwithquasi exponentials thedif ferencesarel and foi CO|LHe COrate.|CO. andNcALg| NDDs. 57a.respectively.," In the present simulation with quasi-exponential SF rate, the differences are, and for He+He, CO+He, CO+CO, and ONeMg+X DDs, respectively."
"We list the time variables. numbers (rates). contribution functions and their relation inthe thin dise and our simulation in reftab,ariables..","We list the time variables, numbers (rates), contribution functions and their relation inthe thin disc and our simulation in \\ref{tab_variables}. ."
" The SF rate is assumed to be given by the quasi-exponential function 7=9Gyr (2)... ↰∢ which produces∙ z 3.5 AJ."" yr. whereat thecurrent epoch."," The SF rate is assumed to be given by the quasi-exponential function where$\tau=9$ Gyr \citep{Yu10}, , which produces $\approx$ 3.5 $M_{\odot}$ $^{-1}$ atthe current epoch."
 This is consistent with ?.., This is consistent with \citet{Diehl06}. .
" The contribution function for each starting epoch (/.,) 1s", The contribution function for each starting epoch $t_{\rm sf}$ ) is
the radius. the deeretion lass loss associated with a required level of angiar monieutui loss depends crucially on the outer radius for Viscous coupliie of the disk. and can be siguificarlv less than the spherical. winud-like iaass loss conuuon voassuned in evolutionary calculaions.,"the radius, the decretion mass loss associated with a required level of angular momentum loss depends crucially on the outer radius for viscous coupling of the disk, and can be significantly less than the spherical, wind-like mass loss commonly assumed in evolutionary calculations."
 We discuss the ]ylivsical processes tiat affect the outer disk raclius. iuchding thermal disk outflow. and abation of the disk maeral via a lne-driveu wind iuduce by the stars radiation.," We discuss the physical processes that affect the outer disk radius, including thermal disk outflow, and ablation of the disk material via a line-driven wind induced by the star's radiation."
 We present paraneterized scaliug laws for taking account of decretiou«isk dass loss in stellar evolution codes. including how hese are affectoc by inetallicitv. or by presence witLin a cloT.e hinary αποον a deuse custer.," We present parameterized scaling laws for taking account of decretion-disk mass loss in stellar evolution codes, including how these are affected by metallicity, or by presence within a close binary and/or a dense cluster."
 Effects simular to those discised here should also be present im accretion disks dirng star formation. aud may play an iuportant role in shaping the cistribution of roation speeds on the ZANIS.," Effects similar to those discussed here should also be present in accretion disks during star formation, and may play an important role in shaping the distribution of rotation speeds on the ZAMS."
(Jorjen. Ikaluajs. BBingech 2000: Darazza. Bingecli. JJevjen 2002: Lisker et al.,"(Jerjen, Kalnajs, Binggeli 2000; Barazza, Binggeli, Jerjen 2002; Lisker et al."
 2006a. bj.," 2006a, b)."
 These galaxies constitute a siguificaut fraction of bright dEs iu the Vireo cluster (Lisker et al., These galaxies constitute a significant fraction of bright dEs in the Virgo cluster (Lisker et al.
 2007)., 2007).
 Their properties wight be related to recent or ongoing star formation activities and distinct environmental effects., Their properties might be related to recent or ongoing star formation activities and distinct environmental effects.
 The discovery of these objects hiuts that the carly-tyvpe dwarf galaxies are heterogeneous objects. which originated fou various channels of evolutionary scenarios (see Lisker 2000 for a review).," The discovery of these objects hints that the early-type dwarf galaxies are heterogeneous objects, which originated from various channels of evolutionary scenarios (see Lisker 2009 for a review)."
 Tere. we present uew UV CAIRs of carly-type dwart galaxies in the Virgo cluster using extensive GALEN UV photometric data in combination with SDSS data.," Here, we present new UV CMRs of early-type dwarf galaxies in the Virgo cluster using extensive GALEX UV photometric data in combination with SDSS data."
 Our goal is to study. whether the various subclasses of early-type dwarf galaxies show different sequences in UV CMBs related to their star formation aud evolutionary histories., Our goal is to study whether the various subclasses of early-type dwarf galaxies show different sequences in UV CMRs related to their star formation and evolutionary histories.
 We used UV images from the CALEN Release 3 (GR3) dataset., We used UV images from the GALEX Release 3 (GR3) dataset.
 GALENX observed the Vireo cluster as part of the All-sky huagiug Survey (AIS). Nearby Calaxy Survey (NGS). and Deep Tagine Survey (DIS) in two UV xuads Eu-ultraviolet (FUV: 1750À)) and new-ultrasijolet (CNUV: 2750A)).," GALEX observed the Virgo cluster as part of the All-sky Imaging Survey (AIS), Nearby Galaxy Survey (NGS), and Deep Imaging Survey (DIS) in two UV bands: far-ultraviolet (FUV; $-$ ) and near-ultraviolet (NUV; $-$ )."
 GALEN inuaged 97 fields of Virgo cluster coveriug a total ~ S2 deg?., GALEX imaged 97 fields of Virgo cluster covering a total $\sim$ 82 $^2$.
 The depth of each field varies in accordauce with its survey mode: 16 NCS. fields 3.000. FUV~1.500s). SO ATS fields CNUV. FUV~100s). aud 1 DIS field (NUV~22.0008).," The depth of each field varies in accordance with its survey mode: 16 NGS fields $\sim$ 3,000s, $\sim$ 1,500s), 80 AIS fields (NUV, $\sim$ 100s), and 1 DIS field $\sim$ 22,000s)."
 Most NCS fields (12 of 16) cover the regions within augular distance of2 degree from the AIS7., Most NGS fields (12 of 16) cover the regions within angular distance of 2 degree from the M87.
 Using SExtractor (Bertin AArnouts 1906). we performed photometry for all detected objects," Using SExtractor (Bertin Arnouts 1996), we performed photometry for all detected objects."
 For this. we required fluxes at least lo above the sky noise.," For this, we required fluxes at least $\sigma$ above the sky noise."
 We adopted ALAG_AUTO(total) as the source magnitude., We adopted $\_$ AUTO(total) as the source magnitude.
 Flix calibrations were applied to bring the final photometry iuto the AB magnitude system (Oke 1990)., Flux calibrations were applied to bring the final photometry into the AB magnitude system (Oke 1990).
 The typical errors are 0.10 mag aud OTI mas iu the NUV and FUV. respectively.," The typical errors are 0.10 mag and 0.14 mag in the NUV and FUV, respectively."
 We take advantage of the comprehensive sample of certain or possible cluster embers classified as dE and dwarf lenticular (0450) galaxies in the Vireo Cluster Catalog (VCC) of Binegecli et al. (, We take advantage of the comprehensive sample of certain or possible cluster members classified as dE and dwarf lenticular (dS0) galaxies in the Virgo Cluster Catalog (VCC) of Binggeli et al. (
1985).,1985).
 Iu addition. we include 11 leutieular galaxies (SOs) of the VCC with optical magnitudes similar to dS0.," In addition, we include 11 lenticular galaxies (S0s) of the VCC with optical magnitudes similar to dS0."
 The cross-identification between 7714 VCC early-type chwart ealaxies aud GALEN photomery results in 193 aud 59 ealaxies in the NUW aud ΕΙΝ band. respectively.," The cross-identification between 774 VCC early-type dwarf galaxies and GALEX photometry results in 193 and 59 galaxies in the NUV and FUV band, respectively."
 All matched objects were visually iispected and we retained objects with clear detection., All matched objects were visually inspected and we retained objects with clear detection.
" NCS fields reach limiting magnitudes of  23.0 mae int1ο NUV aud FUV,. while AIS ones reach ~ 22.0 mae."," NGS fields reach limiting magnitudes of $\sim$ 23.0 mag in the NUV and FUV, while AIS ones reach $\sim$ 22.0 mag."
 A] FUV-detected. galaxics are also detected. in the NUN, All FUV-detected galaxies are also detected in the NUV.
 The resulting sample includes fainter dwarf galaxies compared to previous UV studies using the CALEN luterual Release (IR1.0) (Doselli ct al., The resulting sample includes fainter dwarf galaxies compared to previous UV studies using the GALEX Internal Release (IR1.0) (Boselli et al.
 2005)., 2005).
 We secured galaxies down to mp  20 mag., We secured galaxies down to $_{B}$ $\sim$ 20 mag.
 GALEN UV data have beeu combined with SDSS r-baud data frou SDSS Data Release 5 (DR5)., GALEX UV data have been combined with SDSS r-band data from SDSS Data Release 5 (DR5).
 The SDSS photometric pipeline fails to measure accurately the local sky flux around Vireo dEs aud thus the total magnitude (see Lisker ot al., The SDSS photometric pipeline fails to measure accurately the local sky flux around Virgo dEs and thus the total magnitude (see Lisker et al.
 2007 for the details)., 2007 for the details).
 Therefore. we performed our own sky subtraction and photometric measurement. following the procedure of Lisker et al. (," Therefore, we performed our own sky subtraction and photometric measurement, following the procedure of Lisker et al. ("
2007).,2007).
 Only forceround Calactic extinction correction for cach galaxy is applied (Schlegel ct al., Only foreground Galactic extinction correction for each galaxy is applied (Schlegel et al.
 1998)., 1998).
 We use the reddening law of Cardelli et al. (, We use the reddening law of Cardelli et al. (
"1989) to derive the following: Rye =s.90. ειν =s.16. aud R,.=2.72.","1989) to derive the following: $_{NUV}$ =8.90, $_{FUV}$ =8.16, and $_{r}$ =2.72."
 We adopt a Vireo cluster distance of 15.9 Mpc. aa distance modulus AL=31.01 mae (Craham ot al.," We adopt a Virgo cluster distance of 15.9 Mpc, a distance modulus $-$ M=31.01 mag (Graham et al."
 1999)., 1999).
 Tn Figure l. we preseut optical (Fie.," In Figure 1, we present optical (Fig."
 18). NUV (Fie.," 1a), NUV (Fig."
 1b). aud ΕΝ (Fie lc) CAIRs for dEs (red circles) and SOs (vellow circles).," 1b), and FUV (Fig 1c) CMRs for dEs (red circles) and dS0s (yellow circles)."
 Of galaxies classified as dS0s. a substantial fraction corresponds to dEs with disk substructures (stars. Lisker et al.," Of galaxies classified as dS0s, a substantial fraction corresponds to dEs with disk substructures (stars, Lisker et al."
 2006a) or blue centers (triangles: Lisker et al., 2006a) or blue centers (triangles; Lisker et al.
 2006b)., 2006b).
 Note that. in what follows. we refer to dSOs and peculiar dEs (disk substructure or blue ceuter) collectively as dS0s.," Note that, in what follows, we refer to dS0s and peculiar dEs (disk substructure or blue center) collectively as dS0s."
 We also include blue compact dwiuf galaxies (BCDs. squares) drawn from the VCC. for comparison purposes.," We also include blue compact dwarf galaxies (BCDs, squares) drawn from the VCC, for comparison purposes."
 UV CARs follow the general trend of the optical CMB. Le. early-type dwart galaxies become progressively bluer with decreasing optical huuinositv.," UV CMRs follow the general trend of the optical CMR, i.e., early-type dwarf galaxies become progressively bluer with decreasing optical luminosity."
 Towever. the UV colors span a much wider rangethan the optical CAIR. owing to the wide baseline of UV to optical colors: while gr ouly spans a range of ~0.6 mag. or aud + varies up to [.5 mae aud 6.0 mae. respectively.," However, the UV colors span a much wider rangethan the optical CMR, owing to the wide baseline of UV to optical colors: while $g-r$ only spans a range of $\sim$ 0.6 mag, $-r$ and $-r$ varies up to 4.5 mag and 6.0 mag, respectively."
 The most interesting feature in our UV CAIRs is that dS0s form a tielt sequence which is clearly distinct from that of normal dEs., The most interesting feature in our UV CMRs is that dS0s form a tight sequence which is clearly distinct from that of normal dEs.
 In UV. CAIRs. dS0s follow a steeper sequence than dEs (dotted Lue in Fig.," In UV CMRs, dS0s follow a steeper sequence than dEs (dotted line in Fig."
 la-c eives the mean of dS0s)., 1a-c gives the mean of dS0s).
 Aleamwhile. the optical CAIR of dSOs (see Fie.," Meanwhile, the optical CMR of dS0s (see Fig."
 la) is not ich different from that of normal dEs., 1a) is not much different from that of normal dEs.
 We note that DBoselli ct al. (, We note that Boselli et al. (
2005. 2008) were not able to observe such features in them UV CARs inainly due to them limited sample of dwarf ealaxies.,"2005, 2008) were not able to observe such features in their UV CMRs mainly due to their limited sample of dwarf galaxies."
 In addition. the faint eud of the dS0 sequence in UV CAIRs appears to be linked to the DCDs.," In addition, the faint end of the dS0 sequence in UV CMRs appears to be linked to the BCDs."
 Note hat some galaxies originally classified as BC'Ds in the VCC have a similar appearance like dEs with blue centers (Lisker ct al., Note that some galaxies originally classified as BCDs in the VCC have a similar appearance like dEs with blue centers (Lisker et al.
 2006b): the visual classification vetween dE with blue ceuter aud. BCD appears to have a sinooth transition., 2006b): the visual classification between dE with blue center and BCD appears to have a smooth transition.
 This is now confined by our UV CARs., This is now confirmed by our UV CMRs.
 Furthermore. several studies claimed that BCDs welt be potential progenitors of dEs (see Lisker 2009 aud references herein).," Furthermore, several studies claimed that BCDs might be potential progenitors of dEs (see Lisker 2009 and references therein)."
 Our UV CAIRs shown in Fie., Our UV CMRs shown in Fig.
 indicate that dSOs evidently have different stellar yopulation properties as compared to normal dEs., 1 indicate that dS0s evidently have different stellar population properties as compared to normal dEs.
 Since the UW flux is sensitive to young (= 1 Cyr} stellar populations. the bluer UV colors of dS0s at fixed muinosity inuplies that dS0s have experienced recent or ongoing star formation activities whereas dEs have becu relatively quiescent in the past few Cos.," Since the UV flux is sensitive to young $\lesssim$ 1 Gyr) stellar populations, the bluer UV colors of dS0s at fixed luminosity implies that dS0s have experienced recent or ongoing star formation activities whereas dEs have been relatively quiescent in the past few Gyrs."
 To coufi lis. we examined SDSS spectra aud available literature (Doselli et al.," To confirm this, we examined SDSS spectra and available literature (Boselli et al."
 2008: Michielsen et al., 2008; Michielsen et al.
 2008: Paudel et al., 2008; Paudel et al.
 2010) and found that the majority of dSOs show relatively strong Tea cinission and/or IL absorption ines., 2010) and found that the majority of dS0s show relatively strong $\alpha$ emission and/or $\beta$ absorption lines.
 Interestingly. dSOs showing Πα cussion lines are systematically less Iuninous aud have strong NUV. aud FUV fluxes.," Interestingly, dS0s showing $\alpha$ emission lines are systematically less luminous and have strong NUV and FUV fluxes."
" We found that oof 13 faint (M, > -16.9) dSO0s exhibit Πα eiiissiou lines with EW > 2 À.", We found that of 13 faint $M_{r}$ $>$ -16.9) dS0s exhibit $\alpha$ emission lines with EW $>$ 2 .
. Aeauwhile. dS0s that show stroug IL absorptions are prefercutially located in the lauinous," Meanwhile, dS0s that show strong $\beta$ absorptions are preferentially located in the luminous"
dependence in radius. compared. to the input. behavior.,"dependence in radius, compared to the input behavior."
 We present a quantitative discussion of the dilution in the magnitude of radial dependence in properties in the special case of a constant. enhancement ο for pairs separated by roores, We present a quantitative discussion of the dilution in the magnitude of radial dependence in properties in the special case of a constant enhancement $\epsilon$ for pairs separated by $r<r_c$.
 In this particular case the matching of one member ofan enhanced pair with an unenhanced galaxy in the same eroup gives an artificial enhancement O.le out to larec radii 2Sr. and matches of one member of an enhanced pair with a member of another very. distant enhanced. pair pulls down the value of the recovered enhancement. with the discrepaney between the input and recovered. enhancement being a function of the fraction of galaxies in close pairs and the value of the input enhancement.," In this particular case the matching of one member of an enhanced pair with an unenhanced galaxy in the same group gives an artificial enhancement $\sim 0.1 \epsilon$ out to large radii $\ga 5r_c$, and matches of one member of an enhanced pair with a member of another very distant enhanced pair pulls down the value of the recovered enhancement, with the discrepancy between the input and recovered enhancement being a function of the fraction of galaxies in close pairs and the value of the input enhancement."
 This systematic error is <10% for enhancements €.«d. but precision measurements should account for this effect.," This systematic error is $<10\%$ for enhancements $\epsilon < 4$, but precision measurements should account for this effect."
" We compare hese results with observations of SER enhancement. [rom he SDSS Lietal.(2008). hinding very similar behavior a significant enhancement at radii < Ükkpc and a weak enhancement out to more than kkpc. lending credibility o the notion that weak enhancement in SER seen out. to arge radii is an artifact of the use of weighted: correlation ""unction statistics."," We compare these results with observations of SFR enhancement from the SDSS \citet{li}, finding very similar behavior — a significant enhancement at radii $<40$ kpc and a weak enhancement out to more than kpc, lending credibility to the notion that weak enhancement in SFR seen out to large radii is an artifact of the use of weighted correlation function statistics."
 While we explored a particular case in his Letter. it is easy to see that the phenomenon is general.," While we explored a particular case in this Letter, it is easy to see that the phenomenon is general."
 Given this difference between input weights and those recovered by the weightec 2 point correlation function. one might ask if one shouldn't use a clillerent metboc to explore radial trends in. observables.," Given this difference between input weights and those recovered by the weighted 2 point correlation function, one might ask if one shouldn't use a different method to explore radial trends in observables."
 We would. argue that most different methods boil down to weighted 2 poin correlation functions implicitly anyway. and that one is stuck at least at the qualitative level with the cilferences between input and recovered weights that we have cliscusscc above.," We would argue that most different methods boil down to weighted 2 point correlation functions implicitly anyway, and that one is stuck at least at the qualitative level with the differences between input and recovered weights that we have discussed above."
 For example. partnoring projected pairs into cdilleren ‘pairs’ (ie. not matching every galaxy with every other galaxy) sulfers from two drawbacks: thisis still à projectec analysis. and many projected close pairs will be separated by significant distances along the line of sight: and second. one may choose the wrong galaxy to partner with. a particularly acute issue for triplets or groups of galaxies.," For example, partnering projected pairs into different 'pairs' (i.e., not matching every galaxy with every other galaxy) suffers from two drawbacks: this is still a projected analysis, and many projected close pairs will be separated by significant distances along the line of sight; and second, one may choose the wrong galaxy to partner with, a particularly acute issue for triplets or groups of galaxies."
 One can see that such a method will suller from à. similar supression of enhancement from the inclusion of non-pairs in the pair sample: of course. radial smearing is not possible in such a case. as there is only one radial bin.," One can see that such a method will suffer from a similar supression of enhancement from the inclusion of non-pairs in the pair sample; of course, radial smearing is not possible in such a case, as there is only one radial bin."
 We conclude that those wishing to quantitatively analyze weighted correlation functions (or related. observables) will need to account carefullv for this effect using an analvsis of simulated. mock catalogs., We conclude that those wishing to quantitatively analyze weighted correlation functions (or related observables) will need to account carefully for this effect using an analysis of simulated mock catalogs.
 We thank Cheng Li for sharing with us the electronic version of the results of their work., We thank Cheng Li for sharing with us the electronic version of the results of their work.
 aacknowledges the HeidelbergInternational Max. Planck Research School program., acknowledges the Heidelberg–International Max Planck Research School program.
"names/coordinates. their redshift z. and their linear polarization degree and angle. pj, and 6j.","names/coordinates, their redshift $z$, and their linear polarization degree and angle, $p_{\rm lin}$ and $\theta_{\rm lin}$."
 A compilation of other measurements of quasar optical circular. polarization is given in Table 3.., A compilation of other measurements of quasar optical circular polarization is given in Table \ref{tab:prevqso}.
 Unless indicated otherwise. these measurements were obtained in white light. e.. in the 3200-8800 oor 4000-8800 sspectral ranges. which roughly correspond to an effective wavelength of 6000A.," Unless indicated otherwise, these measurements were obtained in white light, i.e., in the 3200–8800 or 4000–8800 spectral ranges, which roughly correspond to an effective wavelength of 6000."
. When several estimates of either linear or circular polarization are available. only the value with the smallest uncertainty is considered.," When several estimates of either linear or circular polarization are available, only the value with the smallest uncertainty is considered."
 BL Lae objects. similar in many respects to highly polarized quasars (HPQs) (ο... Scarpa and Falomo 1997:: Fan et al. 2008)).," BL Lac objects, similar in many respects to highly polarized quasars (HPQs) (e.g., Scarpa and Falomo \cite{SCA97}; Fan et al. \cite{FAN08}) ),"
 are included., are included.
 Both BL Lac and HPQs belong to the blazar sub-group of active galactic nuclei (AGN)., Both BL Lac and HPQs belong to the blazar sub-group of active galactic nuclei (AGN).
 For BL Lac objects. the polarization is often strongly variable.," For BL Lac objects, the polarization is often strongly variable."
 We then adopt the circular polarization with the smallest uncertainty and. when quasi-simultaneous observations are available. the value of the linear polarization obtained as close as possible in time.," We then adopt the circular polarization with the smallest uncertainty and, when quasi-simultaneous observations are available, the value of the linear polarization obtained as close as possible in time."
 Otherwise we select a representative value of the linear polarization from the survey of Impey and Tapia (1990)), Otherwise we select a representative value of the linear polarization from the survey of Impey and Tapia \cite{IMP90}) ).
 The measurements reported in Tables 2. and 3.4 show that all quasars and BL Lac objects have null circular polarization (< 3 c) except two HPQs. 1256-229 and 2155-152. and one highly polarized BL Lac object. 0219-428.," The measurements reported in Tables \ref{tab:dataqso}
 and \ref{tab:prevqso} show that all quasars and BL Lac objects have null circular polarization $<$ 3 $\sigma$ ) except two HPQs, $-$ 229 and $-$ 152, and one highly polarized BL Lac object, $+$ 428."
 We first discuss the constraints provided by the majority of null detections on the photon-pseudoscalar mixing mechanism. and then the consequences of the three detections for blazar physics.," We first discuss the constraints provided by the majority of null detections on the photon-pseudoscalar mixing mechanism, and then the consequences of the three detections for blazar physics."
" Quasars with right ascension. between 11°20"" anc 14°30"" belong to the region of alignment Al defined i Hutsemékkers (1998)).", Quasars with right ascension between $^{\rm h}$ $^{\rm m}$ and $^{\rm h}$ $^{\rm m}$ belong to the region of alignment A1 defined in Hutsemékkers \cite{HUT98}) ).
 In this region of the sky. quasars with |«z<2.3 have their polarization angle preferentially 1 the range [1467-2267] (modulo 180°). while quasars with QO«z| have their polarization angle preferentially 1 the range [307-1207].," In this region of the sky, quasars with $1 < z < 2.3$ have their polarization angle preferentially in the range $\degr$ $\degr$ ] (modulo $\degr$ ), while quasars with $0 < z < 1$ have their polarization angle preferentially in the range $\degr$ $\degr$ ]."
" Assuming that the quasar intrinsic polarization vectors are randomly oriented. the additio of a small systematic linear polarization Apg,=—0.56€ at a fixed position angle can account for the observec alignments (Hutsemékkers et al. 2008::"," Assuming that the quasar intrinsic polarization vectors are randomly oriented, the addition of a small systematic linear polarization $\Delta p_{\rm lin} \simeq 0.5 \%$ at a fixed position angle can account for the observed alignments (Hutsemékkers et al. \cite{HUT08};"
 Appendix. Appendix A:))., Appendix \ref{sec:apa}) ).
 If photon-pseudoscalar mixing is responsible for this extra linear polarization. one expects. on average. that Perel=Apps0.5% (Appendix Appendix B:)).," If photon-pseudoscalar mixing is responsible for this extra linear polarization, one expects, on average, that $| p_{\rm circ}| \simeq
\Delta p_{\rm lin} \simeq 0.5 \%$ (Appendix \ref{sec:apb}) )."
 Because the light from most quasars is intrinsically linearly polarized to some extent and not circularly polarized. limits on any additional polarization from interactions along the line of sight cannot be derived from the measurement of the linear polarization degree. while. on the other hand. useful constraints can be derived from the measurement of circular polarization.," Because the light from most quasars is intrinsically linearly polarized to some extent and not circularly polarized, limits on any additional polarization from interactions along the line of sight cannot be derived from the measurement of the linear polarization degree, while, on the other hand, useful constraints can be derived from the measurement of circular polarization."
 Most of the thirteen quasars with z>1 located in region Al were found to have [peice]x0.25% (3c upper limit). which is definitely smaller than the expected value.," Most of the thirteen quasars with $z > 1$ located in region A1 were found to have $|p_{\rm circ}| \lesssim 0.25 \% $ $\sigma$ upper limit), which is definitely smaller than the expected value."
" Averaging over the thirteen objects. we infer that (pol)=0.035+0.016% after neglecting the sign. from which a stringent 3c upper limit on the cireular polarization of (p.i,€0.05% can be derived."," Averaging over the thirteen objects, we infer that $\langle |p_{\rm circ}|
\rangle = 0.035 \pm 0.016 \%$ after neglecting the sign, from which a stringent $\sigma$ upper limit on the circular polarization of $\langle |p_{\rm circ}| \rangle \leq 0.05\%$ can be derived."
 This limit is one order of magnitude smaller than the expected value [Perel=0.596.," This limit is one order of magnitude smaller than the expected value $|
p_{\rm circ}| \simeq 0.5 \%$."
 A similar result is obtained for the nine objects at z«I in that region., A similar result is obtained for the nine objects at $z < 1$ in that region.
 This result rules out the interpretation of the observed alignments in terms of photon-pseudoscalar mixing. at least in its simplest formulation.," This result rules out the interpretation of the observed alignments in terms of photon-pseudoscalar mixing, at least in its simplest formulation."
 A more complex treatment of the photon-pseudoscalar interaction is thus required to account for the observations (Payez et al. 2010a. 2010b))," A more complex treatment of the photon-pseudoscalar interaction is thus required to account for the observations (Payez et al. \cite{PAY10a,PAY10b}) )."
 Cireular polarization is detected at the 3c level in two HPQs: 1256-229 and 2155-152 (Table 2))., Circular polarization is detected at the $\sigma$ level in two HPQs: $-$ 229 and $-$ 152 (Table \ref{tab:dataqso}) ).
 On April 21. we had," On April 21, we had"
formation histories (SEIIS) to compare the evolution of stellar populations in the mid-IR with the evolution of ealaxy colors.,formation histories (SFHs) to compare the evolution of stellar populations in the mid-IR with the evolution of galaxy colors.
 We use the Marastou(2005) models. the Kroupa(2001) IME. solu metallicity. a TP-ACB A- band hpuumositv fraction that evolves as in Figure 1.. and the mic-IR € and M euseuible colors given above.," We use the \cite{maraston2005} models, the \cite{kroupa2001} IMF, solar metallicity, a TP-AGB $K$ -band luminosity fraction that evolves as in Figure \ref{fig:agbf}, and the mid-IR C and M ensemble colors given above."
 No dust components outside of those implicit in the colors of the Calactic TP-ACD stars have been added., No dust components outside of those implicit in the colors of the Galactic TP-AGB stars have been added.
 Several SEIIs have been constructed. with paraneters even in Table 1..," Several SFHs have been constructed, with parameters given in Table \ref{tab:models}. ."
 We use expoucutially declining SFIs. or r-miodoels. unmodified by having each model beein at n)=D. with an expoucutial rise of Cyr until a peak at redshift 1τν.," We use exponentially declining SFHs, or $\tau$ -models, modified by having each model begin at $z_0=5$, with an exponential rise of 1 Gyr until a peak at redshift $z_p$."
 The models explicitly terminate Vy timescales after lp., The models explicitly terminate $N_t$ timescales after $z_p$ .
" The models have been normalized to stellar masses rauging from 2«1019AZ, and 3«101AJ, at 2=0."," The models have been normalized to stellar masses ranging from $2\times 10^{10}M_\odot$ and $3\times
10^{11}M_\odot$ at $z=0$."
 Parameters were chosen to produce colors consistent with a diversity of blue aud red galaxies at the present epoch., Parameters were chosen to produce colors consistent with a diversity of blue and red galaxies at the present epoch.
 Iu FiguresOo 2((a-c) we compare the colors of the models to the galaxies in CDFS between 0.7<τςL1 (Wuvtsetal.2008) using the bicolor diagrams «.ye VS goτον BW.iu wea.gee anda.)(Rl) νο ο.on (u.g-t-dv. denote redslifted passbauds).," In Figures \ref{fig:u24}( (a-c) we compare the colors of the models to the galaxies in CDFS between $0.7 < z < 1.1$ \citep{wuyts2008} using the bicolor diagrams $u_z-g_z$ vs $g_z-z_z$, $K_z-[24]$ vs $u_z-g_z$, and $u_z-[24]$ vs $g_z-z_z$, $u_zg_zz_zK_z$ denote redshifted passbands)."
 Dlue triangles indicate times when logSSER=10. aud red triangles when logeSSFRxLO. where SFR refers to on-going star formation rates.," Blue triangles indicate times when $\log {\rm SSFR} >
-10$, and red triangles when $\log {\rm SSFR} \le -10$, where SFR refers to on-going star formation rates."
 The extinction of starlight bv Ay-=1 (Calzettictal.2000) is shown by the red arrow., The extinction of starlight by $A_V=1$ \citep{calzetti2000} is shown by the red arrow.
 With uo additional tuning. these SFIS mimic both the blue star forming sequence aud thered quicscent sequence. while simuultaueouslv reproducing the correlations of 2 lau enission with optical colors.," With no additional tuning, these SFHs mimic both the blue star forming sequence and thered quiescent sequence, while simultaneously reproducing the correlations of $24\mu$ m emission with optical colors."
" Figure 2((d) shows that the simple models reproduce the correlation between 12,22 huuinosity aud SFRs of Chary&Elbaz(2001).. but ouly when we average the SFR over the 1.5 Cy prior to the epoch(s) of observation. Chary&Elbaz(2001)."," Figure \ref{fig:u24}( (d) shows that the simple models reproduce the correlation between $12\mu$ m luminosity and SFRs of \cite{chary2001}, but only when we average the SFR over the 1.5 Gyr prior to the epoch(s) of observation. \cite{chary2001},"
. aud others. have calibrated the underlvius SFR as a function of nid-IR. luuinesity and. though our models reproduce this correlation. the timescale probed by this relation is mach longer than has been assumed in the past.," and others, have calibrated the underlying SFR as a function of mid-IR luminosity and, though our models reproduce this correlation, the timescale probed by this relation is much longer than has been assumed in the past."
 In other words. the mid-IR is explicitly seusitive to star formation over the timescales that galaxies produce populations of TP-ACGD C stars. or 1.5 Cyr (confirmuinetheearlierresultsofSalimctal. 2004))..," In other words, the mid-IR is explicitly sensitive to star formation over the timescales that galaxies produce populations of TP-AGB C stars, or 1.5 Gyr \citep[confirming the earlier results of][]{salim2009}. ."
" ""Together these results also imply that the relationship between rates of on-going star formation and mid-IR fluxes will be complicated by the detailed SFUs within a 1.5 Car windows.", Together these results also imply that the relationship between rates of on-going star formation and mid-IR fluxes will be complicated by the detailed SFHs within a 1.5 Gyr windows.
 Bursts that occur at 2=1.5 and decay with 7=1 Cyr. still produce substantial mid-IR fluxes at ;=1. resulting in SFRs 2.3 higher than actual on-going rates.," Bursts that occur at $z=1.5$ and decay with $\tau=1$ Gyr, still produce substantial mid-IR fluxes at $z=1$, resulting in SFRs $2.3\times$ higher than actual on-going rates."
 For 7=0.5 Car. the factor is 6.1.," For $\tau=0.5$ Gyr, the factor is $6.4$."
 Using the ~3 Car exponential timescale for the decline of the star formation rate density of the universe at late times iuplies that the mic-IR is an over-estimate bv at least50%., Using the $\sim 3$ Gyr exponential timescale for the decline of the star formation rate density of the universe at late times implies that the mid-IR is an over-estimate by at least.
". Taken a step further. post-starburst and ""ereen valley” sealaxies may simply be huuinous m the mid-IR because TP-AGB C stars coutinue to appear long after the cessation of major star formation activity."," Taken a step further, post-starburst and “green valley” galaxies may simply be luminous in the mid-IR because TP-AGB C stars continue to appear long after the cessation of major star formation activity."
 Calculating the mupact on the star formation rate density ultimately requires knowing the frequency. duration. and iutensity of major mass building eveuts.," Calculating the impact on the star formation rate density ultimately requires knowing the frequency, duration, and intensity of major mass building events."
 Given the unknown duty cycles of major star formine events. mid-IR-based star formation rates of individual ealaxies at 2=1 should be treated with skepticisim at a level of at least a factor of two. with additional uncertainties in star formation rate densities.," Given the unknown duty cycles of major star forming events, mid-IR-based star formation rates of individual galaxies at $z=1$ should be treated with skepticism at a level of at least a factor of two, with additional uncertainties in star formation rate densities."
 Our models have strong implications for the origins of unid-IR eiissiou im nearby. resolved. svstems.," Our models have strong implications for the origins of mid-IR emission in nearby, resolved systems."
 Hore we conrpare data on the nearby galaxy M8SI with our model's inplied correlations of the mid-IR with (1) Iuninositv at Jv. ancl (2) the relative amount of star formation in the xevious 1.5 Civr of evolution.," Here we compare data on the nearby galaxy M81 with our model's implied correlations of the mid-IR with (1) luminosity at $K$, and (2) the relative amount of star formation in the previous 1.5 Gyr of evolution."
" SDSS u iud 2\TASS A, nuages are shown in Fieures 3((a} and (b).", SDSS $u$ and 2MASS $K_s$ images are shown in Figures \ref{fig:M81}( (a) and (b).
 Binnine these to increase the S/N ratios oer data point. we show color-color diagrams for poiuts iu the galaxy down to pus=20 mag per aresec? in (c) and (cd).," Binning these to increase the $S/N$ ratios per data point, we show color-color diagrams for points in the galaxy down to $\mu_K=20$ mag per $^2$ in (c) and (d)."
 Our sinooth SEIIs at late times ave shown by the hick black lines., Our smooth SFHs at late times are shown by the thick black lines.
 Colors indicate galaxy radius: Azx1.5 win (red). L.5<HR«3 un (green). 9zxHRx5 miu (blue). aud A75 minu (violet).," Colors indicate galaxy radius: $R\le 1.5$ min (red), $1.5 < R<3$ min (green), $3 \le R\le5$ min (blue), and $R>
5$ min (violet)."
 For simplicity. we assiuue »oiuts ouly fall redward of these models iw give gt vecause of extinction and thus derive a map of A across AIS1.," For simplicity, we assume points only fall redward of these models in $u-g$ vs $g-z$ because of extinction and thus derive a map of $A_V$ across M81."
 These extinctions allow us to correct wy aud inter he ratio So)/Sy at cach position iu the galaxy using Fig. A, These extinctions allow us to correct $u-g$ and infer the ratio $S_{24}/S_K$ at each position in the galaxy using Fig. \ref{fig:M81}( (
c).,c).
" We show the observed 21,420 map along with the resulting model in Figures fa) and 0).", We show the observed $24\mu$ m map along with the resulting model in Figures \ref{fig:M81b}( (a) and \ref{fig:M81b}( (b).
" Aside from the limiting S/N of the & and A, data. the agreement is good."," Aside from the limiting $S/N$ of the $u$ and $K_s$ data, the agreement is good."
 We also find similar results in μια but have uot included them owing to space cousideratious., We also find similar results in $8\mu$ m but have not included them owing to space considerations.
 Iu Fig. l(, In Fig. \ref{fig:M81b}( (
c} we show the eneircled fux deusities iu both {μαι and Span. and one cau directly see that the Iuninosity and structure of MSI is consistent with TP-ACGD origins.,"c) we show the encircled flux densities in both $24\mu$ m and $8\mu$ m, and one can directly see that the luminosity and structure of M81 is consistent with TP-AGB origins."
 Within Ac3 απο]. the simple model is missing ~20% of the flux. but eiven uncertaitics in usine vg color as a proxy for age. uncertain extinetion correctious. and unaecouuted metallicity effects. we cannot rule out oadditional contributionsfrou interstellar cirus.," Within $R<3$ arcmin, the simple model is missing $\sim 20\%$ of the flux, but given uncertainties in using $u-g$ color as a proxy for age, uncertain extinction corrections, and unaccounted metallicity effects, we cannot rule out additional contributionsfrom interstellar cirrus."
 Iu reeions ofintense star formation. which are known to be dust eushrouded. the model also underproduces the mid-fluxes. but such regious do uot comprise the bulk of AISTs luminosity.," In regions ofintense star formation, which are known to be dust enshrouded, the model also underproduces the mid-IRfluxes, but such regions do not comprise the bulk of M81's luminosity."
 We conclude that the extended. diffuse imud-IR Cluission noted by IWemnicuttetal.(2009) arises frou the stellar populations of the galaxy.," We conclude that the extended, diffuse mid-IR emission noted by \cite{kennicutt2009} arises from the stellar populations of the galaxy."
 This result is consistent with the analysis of M33 by Verleyetal. (2009).. who cluploved a more lianited set of mmodels aud. argued that," This result is consistent with the analysis of M33 by \cite{verley2009}, , who employed a more limited set of models and argued that"
Magnetic fields accompany stars from the cradle to the grave: they have been detected in hot molecular cores (2).. they are known to be responsible for the electromagnetic emission of pulsars (?) and they also have long been detected in other stellar remnants such as white dwarfs (?)..,"Magnetic fields accompany stars from the cradle to the grave: they have been detected in hot molecular cores \citep{girart_magnetic_2009}, they are known to be responsible for the electromagnetic emission of pulsars \citep{ferrario_origin_2008}
 and they also have long been detected in other stellar remnants such as white dwarfs \citep{kemp_discovery_1970}."
 Magnetic fields influence diverse physical processes. such as mass accretion and loss. stellar rotation or elemental diffusion. that critically affect the evolution of their host stars.," Magnetic fields influence diverse physical processes, such as mass accretion and loss, stellar rotation or elemental diffusion, that critically affect the evolution of their host stars."
 And yet we lack a proper explanation of their origin. and our understanding of their evolution along the HR diagram is still fragmentary.," And yet we lack a proper explanation of their origin, and our understanding of their evolution along the HR diagram is still fragmentary."
 Outside our Sun. the vast majority of the direct information (ie. excluding indirect indexes of magnetic activity such as X-ray emission) we possess on stellar magnetic fields comes from the exploitation of the various observational features associated with the Zeeman effect.," Outside our Sun, the vast majority of the direct information (i.e. excluding indirect indexes of magnetic activity such as X-ray emission) we possess on stellar magnetic fields comes from the exploitation of the various observational features associated with the Zeeman effect."
 These appear in intensity (line broadening) and in polarized light (as signatures in linear and circular polarization)., These appear in intensity (line broadening) and in polarized light (as signatures in linear and circular polarization).
 Magnetic line broadening is very weak even for strong fields. and competes with other processes such as thermal and rotational broadening.," Magnetic line broadening is very weak even for strong fields, and competes with other processes such as thermal and rotational broadening."
 Polarization measurements. on the other hand are much richer in. information and sensitive to weaker fields (of a few G. according to ?)) although they often require the use of specialized instrumentation such as Balmer-line Zeeman analysers (?) or high resolution echelle spectropolarimeters (as those developed by ? or ?)).," Polarization measurements, on the other hand are much richer in information and sensitive to weaker fields (of a few G, according to \citealp{donati_magnetic_2009}) ) although they often require the use of specialized instrumentation such as Balmer-line Zeeman analysers \citep{angel_magnetic_1970}
 or high resolution echelle spectropolarimeters (as those developed by \citealp{semel_zeeman-doppler_1993} or \citealp{donati_espadons:_2003}) )."
 But these polarimetric instruments also ope the door to diagnostics based upon other physical phenomena also affecting polarization and dependent on magnetic fields., But these polarimetric instruments also open the door to diagnostics based upon other physical phenomena also affecting polarization and dependent on magnetic fields.
 With this paper we aim to provide the theoretical background to a new tool for the detection of even weaker magnetic fields. based on the measurement of the Hanle effect. that will complement in sensitivity and information content the existent techniques.," With this paper we aim to provide the theoretical background to a new tool for the detection of even weaker magnetic fields, based on the measurement of the Hanle effect, that will complement in sensitivity and information content the existent techniques."
 Resonance scattering polarization is the result of an anisotropic illumination. of emitting atoms., Resonance scattering polarization is the result of an anisotropic illumination of emitting atoms.
 Spectral lines formed in a stellar atmosphere can show resonance scattering polarization if their region of formation is sufficiently high for the radiation field to be anisotropic., Spectral lines formed in a stellar atmosphere can show resonance scattering polarization if their region of formation is sufficiently high for the radiation field to be anisotropic.
 Limb-darkening contributes to increase the anisotropy., Limb-darkening contributes to increase the anisotropy.
 The emitted light is linearly polarized. and its degree of polarization depends on the scattering angle.," The emitted light is linearly polarized, and its degree of polarization depends on the scattering angle."
 In the classical approximation. the polarization will be zero in forward scattering and maximum at 90 degrees scattering.," In the classical approximation, the polarization will be zero in forward scattering and maximum at 90 degrees scattering."
 Resonance scattering is however a quantum phenomenon and the classical view provides only a rough approximation to the actual degree of polarization. though one that serves the purpose of illustrating the maim issue with the stellar observation of resonance scattering polarization.," Resonance scattering is however a quantum phenomenon and the classical view provides only a rough approximation to the actual degree of polarization, though one that serves the purpose of illustrating the main issue with the stellar observation of resonance scattering polarization."
 The linear polarization emitted will be maximum at the limb of the stellar dise. and zero at the center., The linear polarization emitted will be maximum at the limb of the stellar disc and zero at the center.
 From pure symmetry considerations. the direction of polarization will be tangent to the stellar limb at every position angle.," From pure symmetry considerations, the direction of polarization will be tangent to the stellar limb at every position angle."
 As we integrate over all position angles. the resultant polarization will be zero if the star presents a spherical aspect.," As we integrate over all position angles, the resultant polarization will be zero if the star presents a spherical aspect."
 Rotationally deformated stars. non-spherical stellar envelopes or winds constitute examples in which the spherical symmetry has been broken and the integral over all the emitting points may end up being different from zero.," Rotationally deformated stars, non-spherical stellar envelopes or winds constitute examples in which the spherical symmetry has been broken and the integral over all the emitting points may end up being different from zero."
 These cases have been extensively studied in the past by Ignace and collaborators (222?)..," These cases have been extensively studied in the past by Ignace and collaborators \citep{ignace_hanle_2001,ignace_scattering_2008, ignace_scattering_2009, ignace_circumstellar_2008}."
 But here we want to concentrate on the case of stellar photospheres with spherical symmetry., But here we want to concentrate on the case of stellar photospheres with spherical symmetry.
 And with that aim we turn our attention to the fact that resonance scattering polarization may also be modified by magnetic fields., And with that aim we turn our attention to the fact that resonance scattering polarization may also be modified by magnetic fields.
 This is the so-called Hanle effect., This is the so-called Hanle effect.
 It is commonly used in solar physics to measure magnetic fields in. prominences (?) and in the quiet solar photosphere (??)..," It is commonly used in solar physics to measure magnetic fields in prominences \citep{casini_magnetic_2003} and in the quiet solar photosphere \citep{stenflo_hanle_1982,faurobert_investigation_2001}."
 Generally speaking. the Hanle effect induces two primary modifications into resonance scattering. polarization arising from a single scattering event: it depolarizes the emitted light and rotates its plane of polarization.," Generally speaking, the Hanle effect induces two primary modifications into resonance scattering polarization arising from a single scattering event: it depolarizes the emitted light and rotates its plane of polarization."
 The amount of depolarization and rotation will depend on the strength of the field. but also on the geometry of the three distinctive directions present in the problem: the direction of preferential illumination of the atom (usually the local vertical). the magnetic field and the line of sight.," The amount of depolarization and rotation will depend on the strength of the field, but also on the geometry of the three distinctive directions present in the problem: the direction of preferential illumination of the atom (usually the local vertical), the magnetic field and the line of sight."
 Calculating the polarization in a spectral line from a nonresolved star requires then the addition of all the scattering events in its atmosphere as the line-of-sight changes [ direction. respect to the two other directions., Calculating the polarization in a spectral line from a nonresolved star requires then the addition of all the scattering events in its atmosphere as the line-of-sight changes in direction respect to the two other directions.
 The theory describing those dependencies has been completely developed, The theory describing those dependencies has been completely developed
simulated cluster.,simulated cluster.
 The 0.59.5 keV spectra are created by interpolating on a reference table of isothermal plana enudssion spectra to find the contribution from cach gas particle. and then sumunine these contributions to obtain the complete spectrum.," The $0.5-9.5$ keV spectra are created by interpolating on a reference table of isothermal plasma emission spectra to find the contribution from each gas particle, and then summing these contributions to obtain the complete spectrum."
 The procedure is the same as that outlined iu rofsecinockex for creating mock Fe Ίνα line spectra. except that the table of reference spectra for interpolation is eenerated using the MERAL plasima eiission code (Mewoe. Ixaastra ποσαil 1995) aud the spectral resolution is 150 eV per bin.," The procedure is the same as that outlined in \\ref{sec:mockex} for creating mock Fe $\alpha$ line spectra, except that the table of reference spectra for interpolation is generated using the MEKAL plasma emission code (Mewe, Kaastra Liedahl 1995) and the spectral resolution is 150 eV per bin."
 The best-fit spectral temperature is determined by minumuizues the chi-square of the residuals eenecrated by differencing the complete 0.5 keV spectrum of the siulation with isothermal plasima spectra created using MEIAL., The best-fit spectral temperature is determined by minimizing the chi-square of the residuals generated by differencing the complete $0.5-9.5$ keV spectrum of the simulation with isothermal plasma spectra created using MEKAL.
 The solid line in Figure 6 shows the cumnulative frequency distrihttion of the maxima velocity eradieut among the six pairs of cach fou-poiuting mosaic., The solid line in Figure \ref{fig:allshift} shows the cumulative frequency distribution of the maximum velocity gradient among the six pairs of each four-pointing mosaic.
 The fraction of cluster projections in the sample of 1.836 with a aNd normalized velocity difference larger than some value. is well fit by The uuuber of cluster projections in our sample with a aN normalized velocity difference larger thin half the sound speed for the cluster is 111. or approximately of the samydle.," The fraction of cluster projections in the sample of 1,836 with a maximum normalized velocity difference larger than some value $x$ is well fit by The number of cluster projections in our sample with a maximum normalized velocity difference larger than half the sound speed for the cluster is 111, or approximately of the sample."
 The total umuber of splittings out of the |1.016 measured to be huger than 0.5e; is 200. or approximately," The total number of splittings out of the 11,016 measured to be larger than $0.5c_{s}$ is 200, or approximately."
 The Likelihood of hieh Mach umuber splittings falls off dramatically. as (Nefe;)f.," The likelihood of high Mach number splittings falls off dramatically, as $(\Delta v/c_s)^{-4}$."
 The lack of very lüeh Mach collisions is expected from the arguments given in equatious (1)) and (2)) above., The lack of very high Mach collisions is expected from the arguments given in equations \ref{eq:cs}) ) and \ref{eq:vinf}) ) above.
" One anticipates (gr a few ve, because larger Mach uunbers could not be eenerated bw hierarchical clustering driven by gravity.", One anticipates $v_{\rm inf} \lta$ a few $\times c_s$ because larger Mach numbers could not be generated by hierarchical clustering driven by gravity.
 Our mock spectral measurements are consistent with this expectation., Our mock spectral measurements are consistent with this expectation.
 Note that the quoted value of the souud speed always refers to the dominant member of a mereine pair., Note that the quoted value of the sound speed always refers to the dominant member of a merging pair.
 With respect to ος of the sinaller member. high Mach nuunuber collisions are certainly possible.," With respect to $c_s$ of the smaller member, high Mach number collisions are certainly possible."
" But the measured “broad-beam temperature. and sound speed. of the πιοος svstemi will always be driven by the larger member, aud thus the data preseuted in Figure 6 are appropriate for comparison with observation."," But the measured “broad-beam” temperature, and sound speed, of the merging system will always be driven by the larger member, and thus the data presented in Figure \ref{fig:allshift} are appropriate for comparison with observation."
 QO.liu It is iiportaut o recognize that even though all chisters have been noved to a fiducial redshift of :=04 to construct iuocdA observations. we have used clusters recovered from a simulated sample at several different output redshifts ranging from ;=0.510 to :=0.," 0.1in It is important to recognize that even though all clusters have been moved to a fiducial redshift of $z=0.1$ to construct mock observations, we have used clusters recovered from a simulated sample at several different output redshifts ranging from $z = 0.540$ to $z = 0$."
 It is therefore n:ural to ask if the frequency of large velocity eracicuts depends ou the epoch of observation of the cluster sauple., It is therefore natural to ask if the frequency of large velocity gradients depends on the epoch of observation of the cluster sample.
 To address this question. we have coustructed the cunmiulative frequency distribution of the maxima observed normalized velocity eradieut for three subsamples erouped by simulation output redshift.," To address this question, we have constructed the cumulative frequency distribution of the maximum observed normalized velocity gradient for three subsamples grouped by simulation output redshift."
 The results are showi iun Fiewe 7.., The results are shown in Figure \ref{fig:newoldshift}.
 The IKohuogorov-σον (Is-S) test (5e.cay. Press et al.," The Kolmogorov-Smirnov (K-S) test (see, Press et al."
 1992) returns a likelihood that the hieh redshift aud middle redshift zubsauiples folow the same distribution. à likelihood. that the low aud middle redshift subsamples follow the same distzjbution. aud au likelihood that the hieh aud low reeshift stbsamples ollow the same distribution.," 1992) returns a likelihood that the high redshift and middle redshift subsamples follow the same distribution, a likelihood that the low and middle redshift subsamples follow the same distribution, and an likelihood that the high and low redshift subsamples follow the same distribution."
 Another question to consider is whether the size of theAstro-E2 FOV reative to the clusters size plays a role iu the frequency of Iarge velocity splittings observed., Another question to consider is whether the size of the FOV relative to the cluster's size plays a role in the frequency of large velocity splittings observed.
 We address this by coustructiug the cumulative frequency distribution of the maxiimu observed normalized velocity eradieut for two subsauies erouped bx he plivsical size of the cluster (recall that all clusters are placed at the same fiducial redshift for observation. so that plivsical size corresponds clirectly to aieular size).," We address this by constructing the cumulative frequency distribution of the maximum observed normalized velocity gradient for two subsamples grouped by the physical size of the cluster (recall that all clusters are placed at the same fiducial redshift for observation, so that physical size corresponds directly to angular size)."
 Clusters with au rogo larger than 1.16 Mpc (the median value for our sample) iie up the large custer subsample. while clusters with royy<1.16 Alpe form the small cluster subsample.," Clusters with an $r_{200}$ larger than 1.46 Mpc (the median value for our sample) make up the large cluster subsample, while clusters with $r_{200} < 1.46$ Mpc form the small cluster subsample."
" The resulting distributiois are shown in Fieure ὃν,", The resulting distributions are shown in Figure \ref{fig:bigsmallshift}.
 The Kk-s test gives a likelihood that both subsamples follow the same distributiol., The K-S test gives a likelihood that both subsamples follow the same distribution.
 0.1iu For purposes of illustration. we highheht the cluster which exhibits the maxim velocity eradieut: cluster uuniber 2 at output redshift 0.222 in y-axis projection.," 0.1in For purposes of illustration, we highlight the cluster which exhibits the maximum velocity gradient: cluster number 2 at output redshift 0.222 in $y$ -axis projection."
" This projection vields a maxi rormalized velocity eradicut of l.17 ος, ", This projection yields a maximum normalized velocity gradient of 1.47 $c_{s}$ .
Data relevant to that cluster are compiled iu Figures 9--13.., Data relevant to that cluster are compiled in Figures \ref{fig:splspec}- \ref{fig:spltemp}.
 Fieve 9 shows Poisson realizations of the four-poiut mosaic spectra created usiueg the procedure outlined iu rofsecinockex aud erouped using the procedure explained πι retsec:velerad.., Figure \ref{fig:splspec} shows Poisson realizations of the four-point mosaic spectra created using the procedure outlined in \\ref{sec:mockex} and grouped using the procedure explained in \\ref{sec:velgrad}.
 These spectra show that the top two quadrauts of our observing pattern are πιοτος relative to the bottoni two., These spectra show that the top two quadrants of our observing pattern are blueshifted relative to the bottom two.
 This accurately represents the nuderling motion ¢Mf the cluster. as can be seen frou Figure 10. which shows the perfect flux spectra generated from the simulation overlaid with the BAPEC £ts to the spectra of Figure 9.. ingÜ.four-pointliu," This accurately represents the underlying motion of the cluster, as can be seen from Figure \ref{fig:persplspec} which shows the perfect flux spectra generated from the simulation overlaid with the BAPEC fits to the spectra of Figure \ref{fig:splspec}."
 spectraΟτι The advantage of using simulalous is that we can exanune the underlying cause of lis observed velocity structure., 0.1in 0.1in The advantage of using simulations is that we can examine the underlying cause of this observed velocity structure.
 Figure 11 shows the ¢eusitv-weiehted. LOS velocitymap of the eas im cluster 2 im a region 2rogg on a side.," Figure \ref{fig:splvel}
 shows the density-weighted, LOS velocitymap of the gas in cluster 2 in a region $2 r_{200}$ on a side."
 A strong vertical eradienut i1projected velocity is, A strong vertical gradient inprojected velocity is
It has direct analogs iu both SN 2000 aud SN 20091p in NGC 7259 2011).. specifically in terms of the inferred expausiou velocities at eruption aud of the elt curve behavior.,"It has direct analogs in both SN 2000ch and SN 2009ip in NGC 7259 , specifically in terms of the inferred expansion velocities at eruption and of the light curve behavior."
 The recent. more powerful revival of SN 2000ch displays “muusually” high velocities (FWHALD) of L5002800 kim 72010).," The recent, more powerful revival of SN 2000ch displays “unusually” high velocities (FWHM) of 1500–2800 km $^{-1}$."
". SN 2009ip shows blueshifted. absorption at 30005000 km ο, which speculate for SN 20091p could be due to a fast blast wave. which occurred quasi-contemiporaneouslv with the origin of the slower ejecta,"," SN 2009ip shows blueshifted absorption at 3000--5000 km $^{-1}$, which speculate for SN 2009ip could be due to a fast blast wave, which occurred quasi-contemporaneously with the origin of the slower ejecta."
" SN 2000ch exhibits multiple P. Cveui absorption coniponents, with profile edges up to 30003500 kins |."," SN 2000ch exhibits multiple P Cygni absorption components, with profile edges up to 3000–3500 km $^{-1}$."
 A sustained high-luninosity pre-cruption state was secu for both SNe 2000ch aud 2009Ip: ον 2000ch was at AMgc10.7 mae prior to the 2000 cruption2001).. and SN 20091p had a pre-cruption Iuuünosity of My=~10 mae2010)..," A sustained high-luminosity pre-eruption state was seen for both SNe 2000ch and 2009ip; SN 2000ch was at $M_R\simeq -10.7$ mag prior to the 2000 eruption, and SN 2009ip had a pre-eruption luminosity of $M_V\simeq -10$ mag."
" Althoneh not vearly the My,z12 mag brightuess of SN 1961V. th. SNe 2000ch and 20091p. therefore. both may also jive been im a super-Eddinetouthe phase prior to their eiaut eruptions."," Although not nearly the $M_{\rm pg}\approx -12$ mag brightness of SN 1961V, both SNe 2000ch and 2009ip, therefore, both may also have been in a super-Eddington phase prior to their giant eruptions."
 Even though lue widths were different. it is interesting to note that the Πα line profiles. iu articular. of SN LOGLV and SN 2000ch7).. lear miaxiumun of the 2000 eruption. were very simular a sharp drop-off to the blue wing aud extended wing to he red.," Even though the line widths were different, it is interesting to note that the $\alpha$ line profiles, in particular, of SN 1961V and SN 2000ch, near maximum of the 2000 eruption, were very similar — a sharp drop-off to the blue wing and extended wing to the red."
" The Πα emnissiou line in 2002 for prole Object""n7/SN 1961V also showed a similar asvuuuetric | we cluphlasize that this profile had a very simular shape as the mach broader line profile for SN L9GLV in 1962 as shown by Zwickv))."," The $\alpha$ emission line in 2002 for Object 7/SN 1961V also showed a similar asymmetric profile (and, we emphasize that this profile had a very similar shape as the much broader line profile for SN 1961V in 1962, as shown by )."
 A possible explanation could be the effects of dust extinction in the expanding ejecta. although we have shown that the extinction from the ejecta is likely relatively modest for SN 1961V. A detailed analysis of this effect should be explored. although we consider this to be bevoud the scope of this paper.," A possible explanation could be the effects of dust extinction in the expanding ejecta, although we have shown that the extinction from the ejecta is likely relatively modest for SN 1961V. A detailed analysis of this effect should be explored, although we consider this to be beyond the scope of this paper."
 We do agree with and(2011).. however. that the “undulations” in SN LOGIV's post-masimaun liebt curve may well have ariseu roni theblast wave overtaking previouslyejected shells : qnatter ahead of the shock.," We do agree with and, however, that the “undulations” in SN 1961V's post-maximum light curve may well have arisen from the blast wave overtaking previously-ejected shells of matter ahead of the shock."
 We speculate here that he star was already in a sustained. eruptive outburst xior to 1960 and that the onset of the super-outburst. which peaked in hunuinositv iu 1961 December. couk vossibly have been due to the interaction of the fast-noving (~2000 kin ly. dense. massive shell with the oe-existiug. slower. less dense mass loss.," We speculate here that the star was already in a sustained, eruptive outburst prior to 1960 and that the onset of the super-outburst, which peaked in luminosity in 1961 December, could possibly have been due to the interaction of the fast-moving $\sim$ 2000 km $^{-1}$ ), dense, massive shell with the pre-existing, slower, less dense mass loss."
 À potoeutia analog is the behavior of the SN Tn 1991NV in NCC 1011 modeled. the lieh huninosity. sustained plateau. aud sudden drop-off of this SN as he interaction of a fast (21500 kau 5 lys dense shel interacting with a slower. less deuse shell.," A potential analog is the behavior of the SN IIn 1994W in NGC 4041 — modeled the high luminosity, sustained plateau, and sudden drop-off of this SN as the interaction of a fast $\gtrsim 1500$ km $^{-1}$ ), dense shell interacting with a slower, less dense shell."
" Furthermore. th. the brief and more sustained plateaus in the SN 1961V elt curve could have arisen from the interaction ofthe fast blast wave with various regnunues of previously ejected matter. or to periods of partial recombination in the expanding ejecta, analogous to the recombination wave in SN ILP ejecta."," Furthermore, both the brief and more sustained plateaus in the SN 1961V light curve could have arisen from the interaction of the fast blast wave with various regimes of previously ejected matter, or to periods of partial recombination in the expanding ejecta, analogous to the recombination wave in SN II-P ejecta."
 Alternatively. these plateaus could also have been due to subsequent lesser eruptions by the star (Ihuuphirevs ct al. 1999)).," Alternatively, these plateaus could also have been due to subsequent lesser eruptions by the star (Humphreys et al. )."
 The fast-moving massiveshell radiated for mauv vears after the outburst. albeit more faintly," The fast-moving massiveshell radiated for many years after the super-outburst, albeit more faintly."
" detected the broad enmuüssiou-line component at Fi,2.2.10 cre cu7s + in 1986.", detected the broad emission-line component at $F_{{\rm H}\alpha} \simeq 2.2 \times 10^{-16}$ erg $^{-2}$ $^{-1}$ in 1986.
" We cau set a limit on detection of this component in the HST/STIS spectrum from 2002 at Fu,<3«101 erg ? | (sec Figure 3)]).", We can set a limit on detection of this component in the /STIS spectrum from 2002 at $F_{{\rm H}\alpha} < 3 \times 10^{-16}$ erg $^{-2}$ $^{-1}$ (see Figure \ref{figspec}) ).
 It is correct to point out the similarities in the variety of SN impostor aud SN Tn properties., It is correct to point out the similarities in the variety of SN impostor and SN IIn properties.
 The two are very likely intimately intertwined. as we now kuow that at least one SN IIu arose from a SN impostor2009).," The two are very likely intimately intertwined, as we now know that at least one SN IIn arose from a SN impostor."
. The SN Tn are also a diverse class of objects (if the terii “class” is truly applicable in the case of stich heterogeneitv). aud it is still not clear low many SNe Iu have. in fact. really been imnupostors.," The SN IIn are also a diverse class of objects (if the term “class” is truly applicable in the case of such heterogeneity), and it is still not clear how many SNe IIn have, in fact, really been impostors."
 For instance. SN 1991W itself may be au nmipostor2009).," For instance, SN 1994W itself may be an impostor."
. Obvioushe we have extrapolated fairly extravagautlv from two pliotomietrie measurements of Object 7 from recent data.," Obviously, we have extrapolated fairly extravagantly from two photometric measurements of Object 7 from recent data."
 We have had to assume that the colors for the star from 1991 are applicable to 2008 as well., We have had to assume that the colors for the star from 1991 are applicable to 2008 as well.
 What is ultimately vane is a set of deep. iultibaud optical aud uear-IR observatious of the SN 1961V cuviromment using the modernHST with the Wide Field Camera 3. which would vastly improve upou the pre-furbishinent WE/PC-1 images audthe motley assortineout of WEPC2 aud unfiltered STIS image data analyzed to date.," What is ultimately required is a set of deep, multiband optical and near-IR observations of the SN 1961V environment using the modern with the Wide Field Camera 3, which would vastly improve upon the pre-furbishment WF/PC-1 images andthe motley assortment of WFPC2 and unfiltered STIS image data analyzed to date."
 Such future observations would ouly require a rather modest iuvestiieut ofHST time to image in DVRIJII at S/N.z10 would require oulv 3 orbits., Such future observations would only require a rather modest investment of time --- to image in $BVRIJH$ at $S/N\gtrsim 10$ would require only 3 orbits.
 Looking bevondHST. observatious with theTelescope. particularly with the ABB. Tastrmuent (MIRI. would reveal the actual dust cussion from the surviving star.," Looking beyond, observations with the, particularly with the Mid-IR Instrument (MIRI), would reveal the actual dust emission from the surviving star."
 speculationThis object has clearly garnered much atteution aud Over the decades aud continues to provide us with invaluable insights iuto the evolution of the most massive stars., This object has clearly garnered much attention and speculation over the decades and continues to provide us with invaluable insights into the evolution of the most massive stars.
 With these space-based data. the definitive nature of the SN 1961V precursor may well be established. once aud for all.," With these space-based data, the definitive nature of the SN 1961V precursor may well be established once and for all."
" Finally, NCC 1058 should coutiuue to be regularly monitored by SN searches in nearby galaxies."," Finally, NGC 1058 should continue to be regularly monitored by SN searches in nearby galaxies."
 For Objecti Tas the SN 1961V. survivor. we nmueht expect. nic as was the case for SN 2006jcaar2007).. that the will explode as the SN that we believe other authors have erroncously coucluded has already occurred.," For Object 7 as the SN 1961V survivor, we might expect, much as was the case for SN 2006jc, that the star will explode as the SN that we believe other authors have erroneously concluded has already occurred."
 The super-outburst from the 1960s could well be the forerunner of a core-collapse event., The super-outburst from the 1960s could well be the forerunner of a core-collapse event.
 It is possible that the star will explode as a οολ. hydrogei-rich SN. Hu. such as SN 200G6ev2007).. or as a more helime1 SN Ton. such as SN 2006102011).," It is possible that the star will explode as a high-luminosity, hydrogen-rich SN IIn, such as SN 2006gy, or as a more helium-rich SN Ibn, such as SN 2006jc."
. This work is based iu part on archival data obtained with theTelescope. which is operated by the Jet Propulsion Laboratory. California Lhustitute of Technology under a contract with NASA.," This work is based in part on archival data obtained with the, which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA."
 We thank Roberta Ihuuphlrevs. for her coments. aud the referee. whose reconmucndations helped improve the manuscript.," We thank Roberta Humphreys, for her comments, and the referee, whose recommendations helped improve the manuscript."
" We also thauk Chris Itochauelk for correcting us on our use of ""7 in the DUSTY modeling. VLA.. IIST.. Spitzer."," We also thank Chris Kochanek for correcting us on our use of $\tau$ ” in the DUSTY modeling. , , ."
to check uunuerical effects.,to check numerical effects.
 Tn all cases. the simulates volumes correspond to a cubic box of a comoving 10 Mpc hot side leusth.," In all cases, the simulated volumes correspond to a cubic box of a comoving 10 Mpc $h^{-1}$ side length."
 The particle masses for the dark an initial gas components are given in Table 1.., The particle masses for the dark and initial gas components are given in Table \ref{tab:simus}.
 Simulation $320 could only reach +z2 due to high computationa costs., Simulation S320 could only reach $z \approx 2$ due to high computational costs.
 By analysing the sTFR and bTFR in $230. $320 aud SLIGO. we check our results for nunerical effects.," By analysing the sTFR and bTFR in S230, S320 and S160, we check our results for numerical effects."
 The simnulatious have been performed by using a version ofCADGLET-3. an update of optimized or massively parallel simulations of lightly inhomogencous systems (Springel&ILeruquist2003:Springel2005).," The simulations have been performed by using a version of, an update of optimized for massively parallel simulations of highly inhomogeneous systems \citep[][]{sh03, springel2005}."
.. This version of includes the multiphase model or the interstellar ποπα (ISM) aud the SN. feedback scheme of Sceanunapiecoetal.(2005.2006).," This version of includes the multiphase model for the interstellar medium (ISM) and the SN feedback scheme of \citet{scan05, scan06}."
. We run he same iuitial condition with ($230) and without SN eedback (S230NF) in order to quantify the effects of SN-induced ealactic winds., We run the same initial condition with (S230) and without SN feedback (S230NF) in order to quantify the effects of SN-induced galactic winds.
 The SN feedback scheme adopted im this work considers both Type II and Type Ia SNe for the chemical and enerev production., The SN feedback scheme adopted in this work considers both Type II and Type Ia SNe for the chemical and energy production.
 We adopt 0.7«10?5 ere per SN event., We adopt $0.7 \times 10^{51}$ erg per SN event.
 The chemical evolution model used iu this code is the one developed by Mosconietal.(2001) and. later on. adapted by Scannapiecoetal.(2005) orGADGET-2.," The chemical evolution model used in this code is the one developed by \citet{mos01} and, later on, adapted by \citet{scan05} for."
 This model assumes the imstantancous recveling approximation (IRA) forΧΙΙ., This model assumes the instantaneous recycling approximation (IRA) for.
" Lifetimes for he progenitors of SNIa are randomly selected in the range 103,107] vr."," Lifetimes for the progenitors of SNIa are randomly selected in the range $[10^8, 10^9]$ yr."
 The chemical vields for SNII are given bv Woosley&Weaver(1995) while those of SNIa correspoiuk o the W7 model of Thieleiianuetal.(1993).," The chemical yields for SNII are given by \citet{WW95}
 while those of SNIa correspond to the W7 model of \citet{thiel93}."
. The SN feedback model is grafted outo a umItiphase nodel specially designed to muprove the description of he ISM. allowing the coexistence of diffuse and dense eas phases.," The SN feedback model is grafted onto a multiphase model specially designed to improve the description of the ISM, allowing the coexistence of diffuse and dense gas phases."
 Within this new framework. the injection of cherey and reavy Clements mto differeut components of he ISM cau be more realistically treated leading to a more effective production of galactic winds.," Within this new framework, the injection of energy and heavy elements into different components of the ISM can be more realistically treated leading to a more effective production of galactic winds."
" The ejecB ΟΠΟΙΟΥ: is distributed into and managed by differentlythe so-callec cold (temperature Z«T, where T5=ὃν104 K anc density. ρOp.. where pe is202 T<qa10.7%ecin.2)3 and hot (otherwise) ISM components.", The ejected energy is distributed into and managed differently by the so-called cold (temperature $T < T_c $ where $ T_c = 8\times 10^4$ K and density $\rho > 0.1 \rho_{\rm c}$ where $\rho_{\rm c} $ is $7 \times 10^{-26} {\rm g \ cm^{-3}}$ ) and hot (otherwise) ISM components.
 The hot phase thermalizes oeistantancously the energy while the cold phase builds up reservoir until it accumulates enough οπου to raise ie entropy of the eas particle to match he value of its own sturounding hot cuviroument., The hot phase thermalizes instantaneously the energy while the cold phase builds up a reservoir until it accumulates enough energy to raise the entropy of the gas particle to match the value of its own surrounding hot environment.
 The properties of 1e hot aud cold eas componcuts of cach gas particle are estimated locally without usine auv global properties of je systems., The properties of the hot and cold gas components of each gas particle are estimated locally without using any global properties of the systems.
 The fraction of SN energy distributed iuto 1¢ cold phase is eiven by the feedback parameter e., The fraction of SN energy distributed into the cold phase is given by the feedback parameter $\epsilon_c$.
" The ejection and distribution of chemical elements is couple o the cuerey procedure so that the fraction of metals muuped iuto the cold aud hot phases are also given by e, in these simulations.", The ejection and distribution of chemical elements is coupled to the energy procedure so that the fraction of metals pumped into the cold and hot phases are also given by $\epsilon_c$ in these simulations.
 We adopt e.—0.5 which have been ound by Seaunapiecoctal.(2008) to best reproduce a disc galaxy iu simulations of a Milkyv-Waxy type halo., We adopt $\epsilon_c =0.5$ which have been found by \citet{scan08} to best reproduce a disc galaxy in simulations of a Milky-Way type halo.
 Virialized structures are selected from the general uass distribution by using a standard fricuds-of+tricuds echuique., Virialized structures are selected from the general mass distribution by using a standard friends-of-friends technique.
 The substructures residing within a eiven vinalized halo are then individualized with the SUBFIND algoritlin of Spriugeletal.(2001) to build up ealaxy catalogues a different redshifts., The substructures residing within a given virialized halo are then individualized with the SUBFIND algorithm of \citet{springel01} to build up galaxy catalogues at different redshifts.
 Note that. x defuition. a substructure cau correspond either tothe central galaxy or a satellite svsteii within a given halo.," Note that, by definition, a substructure can correspond either tothe central galaxy or a satellite system within a given halo."
 Iu order to characterize the siuulated galaxies. we defiue the barvouic radius (H4) as the one that cucloses 83 per ceut of the xuvons associated to cach substructure.," In order to characterize the simulated galaxies, we define the baryonic radius $R_{\rm bar}$ ) as the one that encloses 83 per cent of the baryons associated to each substructure."
 Tn the case of S160. S230 and S230NF. for all the linear reeressions. we ouly consider those simulated galaxies defined bv more than 2<107 particles within Ria: which is equivalent to lave stella masses larger than QU AI. lat.," In the case of S160, S230 and S230NF, for all the linear regressions, we only consider those simulated galaxies defined by more than $2 \times 10^{3}$ particles within $R_{\rm bar}$, which is equivalent to have stellar masses larger than $10^9$ $_\odot$ $^{-1}$."
 Tn S230. Mills-Waw. type galaxies at 2= are resolved with approximately 107 total particles within Rag.," In S230, Milky-Way type galaxies at $z = 0$ are resolved with approximately $10^{5}$ total particles within $R_{\rm bar}$."
" A similar procedure was carried out for the lugh resolution simulation $320. where Milkv-Waxy. type systems are already resolved with more than 10? particles within Aya, at 2=2.0."," A similar procedure was carried out for the high resolution simulation S320, where Milky-Way type systems are already resolved with more than $10^{5}$ particles within $R_{\rm bar}$ at $z = 2.0$."
 In $320. the smallest simulated ealaxies we considered for calculatious lave 10! particles within Ray.," In S320, the smallest simulated galaxies we considered for calculations have $10^{4}$ particles within $R_{\rm bar}$."
" The properties of the simulated galaxies such as stellar Wass, barvonie lass and rotation curves are estimated within HB "," The properties of the simulated galaxies such as stellar mass, baryonic mass and rotation curves are estimated within $R_{\rm bar}$."
We define as dise svsteius those which have Wore than 75 per ceut of their gas componcut on a rotationally supported disc structure by usine the coudition c/V.«I to select them (where σ aud V. are the velocity dispersion aud the tangential velocity compoucut. respectively).," We define as disc systems those which have more than 75 per cent of their gas component on a rotationally supported disc structure by using the condition $\sigma/V 
< 1$ to select them (where $\sigma$ and $V$ are the velocity dispersion and the tangential velocity component, respectively)."
 We acknowledee the fact that. at 2=0. most of our galaxies contaius aree stellar bulges aud thick stellar disces. beiug more consistent with carly type spirals.," We acknowledge the fact that, at $z=0$, most of our galaxies contains large stellar bulges and thick stellar discs, being more consistent with early type spirals."
 Nevertheless. the easeous disc components are very well-defined aud trace remarkably well the poteutial well of their host haloes as can clearly be appreciated in Fig. l..," Nevertheless, the gaseous disc components are very well-defined and trace remarkably well the potential well of their host haloes as can clearly be appreciated in Fig. \ref{fig:rot_curv}. ."
 Rotation curves are estimated by using the tangential velocity of gas particles ou the plane perpeudicular to their total augular momentum., Rotation curves are estimated by using the tangential velocity of gas particles on the plane perpendicular to their total angular momentum.
 For these systems. taugenutial velocity constitutes a good represcutation of the potential," For these systems, tangential velocity constitutes a good representation of the potential"
nearby orbits around the ealaxyv.,nearby orbits around the galaxy.
 The effect of adding vaudomly orbiting dark matter sub-halos on highly idealized star streams has been studied previously (hataYoon.Johnston&Ποσο 2010).. Παπιο that the streams were folded. chopped and heated to about oover a Hubble time.," The effect of adding randomly orbiting dark matter sub-halos on highly idealized star streams has been studied previously \citep{Ibata:02,SGV:08,StarStreams,YJH:10}, finding that the streams were folded, chopped and heated to about over a Hubble time."
 For the examination of the expected degree of huupiuess of star streams we need a more realistic inodel stream., For the examination of the expected degree of lumpiness of star streams we need a more realistic model stream.
 The association of elobular clusters with the NW= stream (IIuxorctal.2008:Mackeyetal.2010) indicates that a dwarf ealaxy. likely AndXNXVII. is the source of the stream.," The association of globular clusters with the NW stream \citep{Huxor:08,Mackey:10} indicates that a dwarf galaxy, likely AndXXVII, is the source of the stream."
 The study of the effects of dark matter sub-halos ou he stream is mhbereutlv statistical since we are unsure ο What deeree the visible stars aud eas eive a complete census of the sub-halos. as hielliehted iu the celebratec wissing satellite problem (sivpinctal.1999:Moore 19993.," The study of the effects of dark matter sub-halos on the stream is inherently statistical since we are unsure to what degree the visible stars and gas give a complete census of the sub-halos, as highlighted in the celebrated missing satellite problem \citep{Klypin:99,Moore:99}."
. A detailed match to the orbit of the NW stream i:S rot required for this very basic assesinent of the action o sub-halos ou a stream., A detailed match to the orbit of the NW stream is not required for this very basic assessment of the action of sub-halos on a stream.
 The details of the stream creation xocess have relatively little to do with the subsequeu sub-halo interactions with the stream., The details of the stream creation process have relatively little to do with the subsequent sub-halo interactions with the stream.
 Our test particle stream originates from particles orbiting i a constau uass Plununer sphere to which particles iu the core reeion are eraduallv given velocities that boost them out into the region where fides can carry thon away., Our test particle stream originates from particles orbiting in a constant mass Plummer sphere to which particles in the core region are gradually given velocities that boost them out into the region where tides can carry them away.
 Future studies will report a full suite of selt-exavitatiug simulations., Future studies will report a full suite of self-gravitating simulations.
 The simulation uses ai galactie potential with a spherical NEW halo potential scaled to the results of the Aquarius simulation (Springeletal.2008)., The simulation uses a galactic potential with a spherical NFW halo potential scaled to the results of the Aquarius simulation \citep{Aquarius}.
. The rotation curve of M31 is somewhat higher than the Milkyv-Way. but bevoud 30 kpe mass modeling finds that the two ealaxies are very simular (Carignanetal.2006).," The rotation curve of M31 is somewhat higher than the Milky-Way, but beyond 30 kpc mass modeling finds that the two galaxies are very similar \citep{Carignan:06}."
. For simplicity and comparability we therefore adopt the same disk-bulee potential for the disk aud bulge as Johuston(1998). which has a AMlvamoto-Nagai disk potentia (Miviuuoto&Nagai1975). and a nuclear bulge modele with a Plununier sphere., For simplicity and comparability we therefore adopt the same disk-bulge potential for the disk and bulge as \citet{Johnston:98} which has a Miyamoto-Nagai disk potential \citep{MN:75} and a nuclear bulge modeled with a Plummer sphere.
" The sub-lhialos are modoled as a collection of Plinuner spheres following the distribution in niases, orbits and internal structure of the Sprimecetal.(2008). simulations."," The sub-halos are modeled as a collection of Plummer spheres following the distribution in masses, orbits and internal structure of the \citet{Aquarius} simulations."
 The star stream particles are evolved in the combined poteutials of the backeroun ealaxv and orbiting sub-halos., The star stream particles are evolved in the combined potentials of the background galaxy and orbiting sub-halos.
 We use time steps of 0.11 Myr. or about LO? ina IIibble time. to ensure tha the quickly moving particles are integrated properly over the stall scale potentials of the sub-hialos.," We use time steps of 0.14 Myr, or about $10^5$ in a Hubble time, to ensure that the quickly moving particles are integrated properly over the small scale potentials of the sub-halos."
 The simulatious start with the Pluuunuer sphere 109AL. progenitor located at c= 100 kpe from the center iu the plane of the disk. with y=:0.," The simulations start with the Plummer sphere $10^6 \msun$ progenitor located at $x=$ 100 kpc from the center in the plane of the disk, with $y=z=0$."
 The initial velocity is chosen to be cutirely tanecutial perpeudicular to the plane of the disk with an aneular momentum of about of the circular value at that radius., The initial velocity is chosen to be entirely tangential perpendicular to the plane of the disk with an angular momentum of about of the circular value at that radius.
 In. the absence of sib-lialos there are no density variations in the simulated star streams., In the absence of sub-halos there are no density variations in the simulated star streams.
 M31 contains ucarly 30 kuowu dwart galaxies., M31 contains nearly 30 known dwarf galaxies.
 To what deeree could these csvarfs. along with their dark-halos. cause the deusity variations we are incasurine?," To what degree could these dwarfs, along with their dark-halos, cause the density variations we are measuring?"
 For mstauce. what is the effect of the heaviest 5 sub-halos alone?," For instance, what is the effect of the heaviest 5 sub-halos alone?"
 Figure 9 shows the c y plane projection of the stream in the presence of 0. 5. 100. and 1000 sub-halos as drawn from the AJb mass distribution.," Figure \ref{fig_Nsub_xy} shows the $x-y$ plane projection of the stream in the presence of 0, 5, 100, and 1000 sub-halos as drawn from the $M^{-1.9}$ mass distribution."
 Iucludiug the 5 most massive, Including the 5 most massive
radial profiles. extended sources such as galaxies or close doubles were readily identified by significant differences in derived photometry depending ou aperture size.,"radial profiles, extended sources such as galaxies or close doubles were readily identified by significant differences in derived photometry depending on aperture size."
 This effect verified the slight clongation of 2\LASS 2952., This effect verified the slight elongation of 2MASS $-$ 2952.
 All other T dwart targets Gucludiug the two close sources in the 2MASS 2739 field) have photometry in cach aperture consistent with the formal mucertaiutics., All other T dwarf targets (including the two close sources in the 2MASS $-$ 2739 field) have photometry in each aperture consistent with the formal uncertainties.
 We adopt the 3-pixel aperture imaenitudes for poiut sources (optimizing the signal-to-noise ratio). except for the second source in the 2MASS 2739 field. where we select a 2-pixel aperture to munimize the contribution of the brighter nearby source: aud extended sources. iucludiug 2MASS 2952. where we select 5-pixcl aperture magnitudes to minimize aperture corrections.," We adopt the 3-pixel aperture magnitudes for point sources (optimizing the signal-to-noise ratio), except for the second source in the 2MASS $-$ 2739 field, where we select a 2-pixel aperture to minimize the contribution of the brighter nearby source; and extended sources, including 2MASS $-$ 2952, where we select 5-pixel aperture magnitudes to minimize aperture corrections."
 UST WPFC2 and 2MASS J-band inaenitudes and colors for our T dwarf targets and Gliese (Cioliowskictal.1998:Legeettet1999). are listed in Table 3.," HST WPFC2 and 2MASS J-band magnitudes and colors for our T dwarf targets and Gliese \citep{gol98,leg99} are listed in Table 3."
 Figure 3Pa plots Faliw magnitude VOrSUs FSIIW FLORAL color for all sources identified in the ten WPFC?2 datasets. aloug with data for Cliese 2297 Single point sources aud target objects are plotted as solid circles. while extended sources (i.c.. galaxies) are plotted as open circles.," Figure 3 plots F814W magnitude versus $-$ F1042M color for all sources identified in the ten WPFC2 datasets, along with data for Gliese 229B. Single point sources and target objects are plotted as solid circles, while extended sources (i.e., galaxies) are plotted as open circles."
 Primary T dwarf targets are individually abelled. all of which are 23 maeuituces redder than 1ο backeround stellar aud galactic sources. again due o the red wing of the pressure-broadened I& I doublet.," Primary T dwarf targets are individually labelled, all of which are 2–3 magnitudes redder than the background stellar and galactic sources, again due to the red wing of the pressure-broadened K I doublet."
 Both sources at the position of 2MIASS 2739 lie at red colors. nuüplviug that both are T dwarfs.," Both sources at the position of 2MASS $-$ 2739 lie at red colors, implying that both are T dwarfs."
" Dased on the estimated surface deusitv of T dwarfs detectable w 2MASS. 8.L\10 ! 7 (Bureasseretal.2002d).. which we extrapolate to a limiting J imaguitude of 17 (the i»pareut J magnitude of 2\TASS 2739B: see below). he probability of two relatively bright T dawarfs randomly ving within —18"" of each other (the approximate search radius ou the PC chip) is T "," Based on the estimated surface density of T dwarfs detectable by 2MASS, $\times$ $^{-4}$ $^{-2}$ \citep{me02}, which we extrapolate to a limiting J magnitude of 17 (the apparent J magnitude of 2MASS $-$ 2739B; see below), the probability of two relatively bright T dwarfs randomly lying within $\sim$ $\arcsec$ of each other (the approximate search radius on the PC chip) is $\times$ $^{-7}$."
We therefore coufkcutly claim companionship for these two objects based ou their xoxindtv and unique colors., We therefore confidently claim companionship for these two objects based on their proximity and unique colors.
 By the same argument. the wo sources at the position of 2MASS 2352 are also companion T dwarfs. based ou the red color of their combined light.," By the same argument, the two sources at the position of 2MASS $-$ 2352 are also companion T dwarfs, based on the red color of their combined light."
 Hereafter. we refer to these two svstenis ax 2MASS 2739AD aud 2MAÀSS 1531. 2352AD.," Hereafter, we refer to these two systems as 2MASS $-$ 2739AB and 2MASS $-$ 2352AB."
 Figure L| plots the . FI012M. versus ESIIW J color-color diagram for the observed T dwarfs aud. Clicse 229B. Note that the colors of single targets follow a fairly linear trend: Because 2MLASS 2739 is uuresolved by 2\LASS. we determined J-band component magnitudes from the colmbined light magnitude. J = 15.22+0.05. aud the band fux ratio. musing 1l aud the photometry listed in Table 3.," Figure 4 plots the $-$ F1042M versus $-$ J color-color diagram for the observed T dwarfs and Gliese 229B. Note that the colors of single targets follow a fairly linear trend: Because 2MASS $-$ 2739 is unresolved by 2MASS, we determined J-band component magnitudes from the combined light magnitude, J = $\pm$ 0.05, and the J-band flux ratio, using 1 and the photometry listed in Table 3."
 The J colors for these two objects both lie 70.15 mae below the linear fit traced by the single stars. but are consistent within the photometric uucertaüuties.," The $-$ J colors for these two objects both lie $\sim$ 0.15 mag below the linear fit traced by the single stars, but are consistent within the photometric uncertainties."
 The combined light ΑΝ J color of 2\TASS 2952AB is also below the single star locus. but in this case it is probably because the object is mareiually resolved iu the WPFC? images.," The combined light $-$ J color of 2MASS $-$ 2952AB is also below the single star locus, but in this case it is probably because the object is marginally resolved in the WPFC2 images."
 Ou the other hand. 2MÁSS 0311 is sleltly redder in JJ color than expected. although by no more than 2o.," On the other hand, 2MASS $-$ 0311 is slightly redder in $-$ J color than expected, although by no more than $\sigma$."
 Both | F1012M and J colors are generally redder for the later-tvpe T dwarts. with the former being particularly scusitive to spectral type.," Both $-$ F1042M and $-$ J colors are generally redder for the later-type T dwarfs, with the former being particularly sensitive to spectral type."
 One notable exception is the T6.5 enmission-liue dwarf 2MLASS 1237|6526 (Bureasserctal.2000a).. which has the reddest FLOL2AL color in the sample (see 65.3).," One notable exception is the T6.5 emission-line dwarf 2MASS 1237+6526 \citep{me00b}, which has the reddest $-$ F1042M color in the sample (see $\S$ 5.3)."
" Ou the other hand. F1012M J colors generally decrease for later spectral types. likely due to increased Ποο aud CIE, absorption around 1.25 jan (Burgasseretal.2002d0)."," On the other hand, $-$ J colors generally decrease for later spectral types, likely due to increased $_2$ O and $_4$ absorption around 1.25 $\micron$ \citep{me02}."
". Iu order to derive separatious and flux ratios for our two T dwarf binaries. and search for füut conrpanionus around the other target sources. we performed pout spread function (PSF) subtraction ou all of our primary targets,"," In order to derive separations and flux ratios for our two T dwarf binaries, and search for faint companions around the other target sources, we performed point spread function (PSF) subtraction on all of our primary targets."
 Our techuique was as follows: first. we extracted subimages of all appareutlv sinele poiut sources from the PC chip images of all ten datasets; a total of 22 sources in FalWW and 11 in FIOL2AL. These included some of the target objects. although care was taken to exclude any point sources with bad pixels near the source peak.," Our technique was as follows: first, we extracted subimages of all apparently single point sources from the PC chip images of all ten datasets, a total of 22 sources in F814W and 11 in F1042M. These included some of the target objects, although care was taken to exclude any point sources with bad pixels near the source peak."
 We then subtracted two-dimensional Gaussian fits to the PSFs from the images: typical residuals were consistently =10 of the original source peak., We then subtracted two-dimensional Gaussian fits to the PSFs from the images; typical residuals were consistently $\lesssim 10$ of the original source peak.
" Finally, we averaged these CGaussian-subtracted images. scaled by the fit maxima. to produce a single PSF residual image for cach filter."," Finally, we averaged these Gaussian-subtracted images, scaled by the fit maximum, to produce a single PSF residual image for each filter."
 For each of our target sources. we searched for fait conpauionus usine an iterative κ reduction routine.," For each of our target sources, we searched for faint companions using an iterative ${\chi}^2$ reduction routine."
 Model inages were coustructed by combining two PSF residual nuages with two Cien surfaces having the same FWIIM as the PSF fits described above. each scaled to separate componcut fluxes.," Model images were constructed by combining two PSF residual images with two Gaussian surfaces having the same FWHM as the PSF fits described above, each scaled to separate component fluxes."
 For 2\TASS 2739AB and 2MASS 2952AB. initial guesses were based on the approximate positions and fux ratios from the aperture photometry (we assuned 2ATASS 2952AB to he separated by 1 pixel alone cach axis as an initial eucss).," For 2MASS $-$ 2739AB and 2MASS $-$ 2952AB, initial guesses were based on the approximate positions and flux ratios from the aperture photometry (we assumed 2MASS $-$ 2952AB to be separated by 1 pixel along each axis as an initial guess)."
 Our routine then iteratively searched for the optimal solution to the primary position. secondary position. xunary flux. and secondary fux. iu that order. by shifting he component positions in steps of 0.1 pixels aud scaling he fluxes in steps of (0.01 mae).," Our routine then iteratively searched for the optimal solution to the primary position, secondary position, primary flux, and secondary flux, in that order, by shifting the component positions in steps of 0.1 pixels and scaling the fluxes in steps of (0.01 mag)."
 If the secondary Hux was scaled below 1 count or separations below 0.5 yincls were reached. then the object was considered a sinele xnt source.," If the secondary flux was scaled below 1 count or separations below 0.5 pixels were reached, then the object was considered a single point source."
 Otherwise. the routine derived. separations. vosition angles. and flux ratios for the optimal binary solutiou.," Otherwise, the routine derived separations, position angles, and flux ratios for the optimal binary solution."
 For all of the appareutlv sinele targets. we followed up lis process by fitting a single PSF residual plus Caussiau o the image aud then searchiug bv eve for amy obvious counterparts.," For all of the apparently single targets, we followed up this process by fitting a single PSF residual plus Gaussian to the image and then searching by eye for any obvious counterparts."
 We then used the sae binary search routine or cach inage with 20 random companion initial positions., We then used the same binary search routine for each image with 20 random companion initial positions.
 If uo companion brighter than the S/N = 7 detection iuits (approximately 25.5 mag at ESLIW and 19.9 mag, If no companion brighter than the S/N = 7 detection limits (approximately 25.5 mag at F814W and 19.9 mag
For alinost 30 vears. close double neutron star (DNS) Μπα svstenis have heen kuownu to exist iu the Calaxy as a sniall subset of the observed radio pulsar population (Tulse Tavlor 1975: Wolszezan 1991).,"For almost 30 years, close double neutron star (DNS) binary systems have been known to exist in the Galaxy as a small subset of the observed radio pulsar population (Hulse Taylor 1975; Wolszczan 1991)."
 These svsteuis ose orbital energv due to the emission of eravitational waves (Tavlor Weisberg 19809. 2003: Stairs ct 11995): the associated orbital in-spiral contiuues until he binary system coalesces. resulting im oa burst of eravitational waves.," These systems lose orbital energy due to the emission of gravitational waves (Taylor Weisberg 1989, 2003; Stairs et 1998); the associated orbital in-spiral continues until the binary system coalesces, resulting in a burst of gravitational waves."
 DNS nespirals are prime targets Or gravitational-wave detection by the erouncd-based interferometers Laser Iuterterometer CvavitationalWave Observatory (LIGO: Abraimovici et 11992). GEO (Dauzinann ct 11995). and VIRGO (Caron et 11997).," DNS in-spirals are prime targets for gravitational-wave detection by the ground-based interferometers Laser Interferometer Gravitational-Wave Observatory (LIGO; Abramovici et 1992), GEO (Danzmann et 1995), and VIRGO (Caron et 1997)."
 Eveut rate estimates ave very important for the development of eravitationalewave interferometers (Thorne Cutler 2002)., Event rate estimates are very important for the development of gravitational-wave interferometers (Thorne Cutler 2002).
 They are based ou estimates of Galactic rates and their extrapolation throughout a survey volume (Finn 2001). eiven the source streneth and iustrunient seusitivitv.," They are based on estimates of Galactic rates and their extrapolation throughout a survey volume (Finn 2001), given the source strength and instrument sensitivity."
 For DNS biuaes. Galactic rate estimates have been obtained using two very different methods.," For DNS binaries, Galactic rate estimates have been obtained using two very different methods."
 One is purely theoretical and involves models of binary evolution calibrated usually to the observationallv determined supernova rate for the Galaxy., One is purely theoretical and involves models of binary evolution calibrated usually to the observationally determined supernova rate for the Galaxy.
 The other. more clupirical. approach is based on the plysical properties of the close DNS biumies known iu the Galactic field and modeling of radio pulsar survey selection effects.," The other, more empirical, approach is based on the physical properties of the close DNS binaries known in the Galactic field and modeling of radio pulsar survey selection effects."
 For a review and detail of both these approaches. see EKalogera et ((2001. hereafter INST) aud references therein.," For a review and details of both these approaches, see Kalogera et (2001, hereafter KNST) and references therein."
 The enipirical method has generally provided us with better constraints on the coalescence rate (IRNST). although the mucertaiuty still exceeds two orders of magnitude.," The empirical method has generally provided us with better constraints on the coalescence rate (KNST), although the uncertainty still exceeds two orders of magnitude."
 This is primarily due to (1) the verv small umber (oulv two until recently) of close DNSs known in the Galactic field with merecr times shorter than a UWubble time aud (2) the Huplicit assmuption that this small sample is a good represcutation of the total Galactic population ΝΤ)., This is primarily due to (1) the very small number (only two until recently) of close DNSs known in the Galactic field with merger times shorter than a Hubble time and (2) the implicit assumption that this small sample is a good representation of the total Galactic population (KNST).
 Two recent developments make it appropriate to revisit the DNS inerger rate caleulations., Two recent developments make it appropriate to revisit the DNS merger rate calculations.
 First. the discovery of the 2.1 hr DNS binary PSR J07373039 in a large-area survey using the Parkes radio telescope (Bureay ct 22003) briugs the nuniber of known DNS svstems to merece in the Calactic Seld to three.," First, the discovery of the 2.4 hr DNS binary PSR J0737–3039 in a large-area survey using the Parkes radio telescope (Burgay et 2003) brings the number of known DNS systems to merge in the Galactic field to three."
 With an orbital period of only 2.1 hr. J0737.3039 will coalesce iu ouly S5 My. a factor of 3.5 shorter than the merecr time of PSR Bl9l3|16.," With an orbital period of only 2.4 hr, J0737–3039 will coalesce in only 85 Myr, a factor of 3.5 shorter than the merger time of PSR B1913+16."
 This imuneciately hints towards a possible significant increase of the coalescence rate (Durgay ct 22003)., This immediately hints towards a possible significant increase of the coalescence rate (Burgay et 2003).
" Second. a novel statistical method has been developed by να, EIalogera Lorimer (2003."," Second, a novel statistical method has been developed by Kim, Kalogera Lorimer (2003,"
We thank G. Handler. P. 1. Amado and C. Jordi for useful discussions.,"We thank G. Handler, P. J. Amado and C. Jordi for useful discussions."
 The referee. M. Bazot. is thanked for insightful comments that led to the improvement of the paper.," The referee, M. Bazot, is thanked for insightful comments that led to the improvement of the paper."
 Data were partially obtained by J. Martin with the Joan Oró Telescope (TIO) of the Montsee Astronomical Observatory (OAdUM). which is owned by the Consorei del Montsec and operated by the Institute for Space Studies of Catalonia (IEEC).," Data were partially obtained by J. Martin with the Joan Oró Telescope (TJO) of the Montsec Astronomical Observatory (OAdM), which is owned by the Consorci del Montsec and operated by the Institute for Space Studies of Catalonia (IEEC)."
. This research has made use of the Exoplanet Transit Database thttp://var.astro.cz/ETD)., This research has made use of the Exoplanet Transit Database (http://var.astro.cz/ETD).
the profiles are so steep. that we cannot measure a reliable minimum of curvature (75).,"the profiles are so steep, that we cannot measure a reliable minimum of curvature $r_b$ )."
 The King fit for these cases is a bad match for the entire radial extent. so. even though one can formally obtain a value for 74; and r4. neither of them provide meaningful information about the density profile.," The King fit for these cases is a bad match for the entire radial extent, so, even though one can formally obtain a value for $r_{ck}$ and $r_{ch}$, neither of them provide meaningful information about the density profile."
 For the cases in which we have three close snapshots. we notice that the deviation between the different radial measurements is of order for rp. for r4. and for r4. but the deviation between the three different types of core radii is larger.," For the cases in which we have three close snapshots, we notice that the deviation between the different radial measurements is of order for $r_b$, for $r_{ch}$, and for $r_{ck}$, but the deviation between the three different types of core radii is larger."
 The central surface brightness slope is obtained by calculating the derivative of the smooth profile inside the core radius., The central surface brightness slope is obtained by calculating the derivative of the smooth profile inside the core radius.
 This derivative is constant for r—rp., This derivative is constant for $r<r_b$.
 It is worth mentioning that the value is the same when we measure the slope of a linear fit to the photometric points in the same region., It is worth mentioning that the value is the same when we measure the slope of a linear fit to the photometric points in the same region.
 For the couple of very concentrated cases. models mlt12.5 and mltl6.0. where we cannot reliably measure a break radius. we take the central values of the derivative as the slope.," For the couple of very concentrated cases, models m1t12.5 and m1t16.0, where we cannot reliably measure a break radius, we take the central values of the derivative as the slope."
 If we try to use completeness uncorrected profiles instead of light profiles the value for rj. 75 and r4 does not change much. since it is the shape of the profile inside the core radius that changes. but not the turnover radius.," If we try to use completeness uncorrected profiles instead of light profiles the value for $r_h$, $r_b$ and $r_{ck}$ does not change much, since it is the shape of the profile inside the core radius that changes, but not the turnover radius."
" 7,4, on the other hand suffers a larger change since the value of the central density is lower.", $r_{ch}$ on the other hand suffers a larger change since the value of the central density is lower.
 Obviously. the value of the central slope is very different (flatter in general).," Obviously, the value of the central slope is very different (flatter in general)."
 If we try to construct a star count profile using only those stars that are detected with close to completeness. there are too few stars left and the profile becomes too noisy in the center to make any meaningful measurements.," If we try to construct a star count profile using only those stars that are detected with close to completeness, there are too few stars left and the profile becomes too noisy in the center to make any meaningful measurements."
 Fig., Fig.
 5 shows the fit of single-mass King profiles to model m3t. which contains stellar-mass black holes.," 5 shows the fit of single-mass King profiles to model m3t, which contains stellar-mass black holes."
 It can be seen that the fits are significantly more noisy in the center than those for models mlt and m2t. which is most likely due to the more stochastic heating of the cluster by a few black holes as compared to à core of neutron stars and white dwarts.," It can be seen that the fits are significantly more noisy in the center than those for models m1t and m2t, which is most likely due to the more stochastic heating of the cluster by a few black holes as compared to a core of neutron stars and white dwarfs."
 Table 2 shows that the derived photometric parameters are nevertheless still within the range seen for those of clusters without stellar-mass black holes. in. particular the central surface brightness slopes are still all below -0.12.," Table 2 shows that the derived photometric parameters are nevertheless still within the range seen for those of clusters without stellar-mass black holes, in particular the central surface brightness slopes are still all below -0.12."
 Once we have central surface brightness slopes and ος measurements for every modeled cluster we proceed to plot each point on a slope versus 7/7; plane., Once we have central surface brightness slopes and $r_c/r_h$ measurements for every modeled cluster we proceed to plot each point on a slope versus $r_c/r_h$ plane.
 We create a plane for each of the three measured radii., We create a plane for each of the three measured radii.
" We find that using 7; or rg gives very similar results. while using r,; does not give meaningful constraints for clusters without flat central light profiles. so we exclude this quantity from further analysis."," We find that using $r_{ck}$ or $r_{b}$ gives very similar results, while using $r_{rh}$ does not give meaningful constraints for clusters without flat central light profiles, so we exclude this quantity from further analysis."
 In Figures 6 and 7 we show the location of our models on the slope versus η and 54/7; planes respectively., In Figures 6 and 7 we show the location of our models on the slope versus $r_b/r_h$ and $r_{ck}/r_h$ planes respectively.
 The models span a range of central slopes from 0.18 to -1.00. but the only models that have slopes steeper than -0.5 are those that have achieved core collapse. while the steepest slope for a model containing an IMBH is -0.45.," The models span a range of central slopes from 0.18 to -1.00, but the only models that have slopes steeper than -0.5 are those that have achieved core collapse, while the steepest slope for a model containing an IMBH is -0.45."
 As shown in Figs 6 and 7. there are two models containing an IMBH that present a flat central core (model mb4t9.0 and mb4t11.5). otherwise. only the models containing intermediate-mass black holes show shallow central cusps.," As shown in Figs 6 and 7, there are two models containing an IMBH that present a flat central core (model mb4t9.0 and mb4t11.5), otherwise, only the models containing intermediate-mass black holes show shallow central cusps."
 Models without IMBHs show either a flat central slope. or steepcentral cusps.," Models without IMBHs show either a flat central slope, or steepcentral cusps."
" Regarding the rs/r, ratio. the cases that haven't reached core-collapse and started from a King model with Wo=7 lie within a narrow range between 0.15 and 0.35 and there is no clear distinction between these cases and those containing IMBHs in this respect."," Regarding the $r_b/r_h$ ratio, the cases that haven't reached core-collapse and started from a King model with $W_0=7$ lie within a narrow range between 0.15 and 0.35 and there is no clear distinction between these cases and those containing IMBHs in this respect."
" The cases that clearly separate towards large r,./7; are those that started from King models with Wo2 5.", The cases that clearly separate towards large $r_c/r_h$ are those that started from King models with $W_0=5$ .
 The models, The models
the LITRAN 2008 database by extrapolating the intensities using Equation 3 to the temperatures of the recorded spectra.,the HITRAN 2008 database by extrapolating the intensities using Equation 3 to the temperatures of the recorded spectra.
 An error in (he calibrated intensity of perhaps a factor of two is suggested for our line lists., An error in the calibrated intensity of perhaps a factor of two is suggested for our line lists.
 Although this seems large. emission intensities are notoriously difficult to calibrate (Nassar&Bernath2003).," Although this seems large, emission intensities are notoriously difficult to calibrate \citep{nassar03}."
. We have accounted for (he instrument response by recording a blackbody spectrum and correcting the intensities with the instrument response function., We have accounted for the instrument response by recording a blackbody spectrum and correcting the intensities with the instrument response function.
 The most notable corrections were obvious towards the edge of each spectral region (see Figure 4))., The most notable corrections were obvious towards the edge of each spectral region (see Figure \ref{fig4}) ).
 Dlending of lines also causes errors in line intensiües and in the empirical lower state energy., Blending of lines also causes errors in line intensities and in the empirical lower state energy.
 These blended lines cause problems when matching our observations with HITRAN and make il difficult to identify the contribution of each line to the observed peak., These blended lines cause problems when matching our observations with HITRAN and make it difficult to identify the contribution of each line to the observed peak.
 We have tried to reduce our intensitv calibration error bv comparing as many spectral lines with IUTRAN lines as possible., We have tried to reduce our intensity calibration error by comparing as many spectral lines with HITRAN lines as possible.
 Each comparison gives an intensity calibration factor and after outliers have been removed a general [actor can be obtained., Each comparison gives an intensity calibration factor and after outliers have been removed a general factor can be obtained.
 The temperature of the experiment was accurate to within £10 Ix but this only applies to the central portion of the ΑΟ. tube which is surrounded by the furnace., The temperature of the experiment was accurate to within $\pm$ 10 K but this only applies to the central portion of the $_{2}$ $_{3}$ tube which is surrounded by the furnace.
 There is therefore a temperature gradient within the AlSO4 tube which affects the shape of some lines as discussed by (2003)., There is therefore a temperature gradient within the $_{2}$ $_{3}$ tube which affects the shape of some lines as discussed by \citet{nassar03}.
. This elfect can be observed in the enission spectra as we see absorption of the low fundamental NIL; lines due to cooler gas towards the tube ends change to emission as the temperature of the tube increases (see Figure 9))., This effect can be observed in the emission spectra as we see absorption of the low fundamental $_{3}$ lines due to cooler gas towards the tube ends change to emission as the temperature of the tube increases (see Figure \ref{fig9}) ).
Case A or Binass trauster takes place.,Case A or B mass transfer takes place.
 The donor mass is αμα. compared with that for the eiant. so its Roche lobe will oulv be ~20% of that of the giant. with Roche coutact established when the giant begius ITe-shell burning: ie. the iitial separation will be a;1200. (Brownctal.20010).," The donor mass is small compared with that for the giant, so its Roche lobe will only be $\sim20\%$ of that of the giant, with Roche contact established when the giant begins He-shell burning; i.e. the initial separation will be $a_i\sim1200\rsun$ \citep{Bro01b}."
".. Now. initially, we expect the hypernova beat aud NRF (sinetic} energies to be about equal. frou equipartition."," Now, initially, we expect the hypernova heat and XRF (kinetic) energies to be about equal, from equipartition."
 However. the N-ravs have to produce rau pressure work to clear the wav through the He star for the jet. aud this takes up most of the kinetic enerev.," However, the X-rays have to produce ram pressure work to clear the way through the He star for the jet, and this takes up most of the kinetic energy."
 The heat energy. which is transformed iuto kinetic energy. of the supernova is about 5 bethes for SN2008D and 2 bethes for SN2006aj.," The heat energy, which is transformed into kinetic energy, of the supernova is about 5 bethes for SN2008D and 2 bethes for SN2006aj."
 Using Leeotal.(2002) we can find the mass of the donor (secondary star) that will eive SN2008D 2.5 tines more augular momentum energy than SN2006a]., Using \citet{Lee02} we can find the mass of the donor (secondary star) that will give SN2008D $2.5$ times more angular momentum energy than SN2006aj.
 Using the relation between the Πο core to the star My=O.08(MeganefA.bYM. Leeetal.(2002). found that the separation following common envelope evolution was (ait) where AZ; is the donor (secondary star} mass., Using the relation between the He core to the star $ M_{\rm He}=0.08(M_{\rm Giant}/\msun)^{1.45}\msun $ \citet{Lee02} found that the separation following common envelope evolution was a_i where $M_d$ is the donor (secondary star) mass.
 Frou Isepler we have the preexplosion periodο” we take Mosa ↴∖∣↴↴∣and Ay.M. =LOAL..to be the same for SN2006aj aud SN2008D (see Sec. ?7?)).," From Kepler we have the preexplosion period Since we take $M_{\rm Giant}$ and $M_{\rm He}=4.6\msun$ to be the same for SN2006aj and SN2008D (see Sec. \ref{Expl}) ),"
 we can easily estimate the ratio of orbital rotation rates (Ou yetech , we can easily estimate the ratio of orbital rotation rates $\Omega_{\rm orbital}$ ): = .
"The extractable spin cucrevj in Dlaudford-Zuajok is Mpuet5) where e, is the dimeusionless spin parameter given by a,=JieGMügzIuQueGAR aud fla.))=1 02)..(6) ", The extractable spin energy in Blandford-Znajek is c^2 where $a_\star$ is the dimensionless spin parameter given by $a_\star = J_{\rm BH} c/GM_{\rm BH}^2 \approx I_{\rm He}\Omega_{\rm He} c/GM_{\rm BH}^2$ and ) = 1 -.
ere we asstuneyall that the angular mnonientuni ds conserved durius the collapse from Πο star to DII. neelecting the (1nall) mass left in the disk. some of which will be lost iu the explosion.," Here we assume that the angular momentum is conserved during the collapse from He star to BH, neglecting the (small) mass left in the disk, some of which will be lost in the explosion."
 For low a. fla.)=a2/s.," For low $a_\star$, $f(a_\star) \cong a_\star^2 /8$."
 We therefore take the ecnerey as proportional to Oi., We therefore take the energy as proportional to $\Omega_{\rm He}^2$ .
 Dx assundue the tidal locking between the orbital period and the spin period of Πο star (Leeetal.2002).. one cau take Oy.zOng.," By assuming the tidal locking between the orbital period and the spin period of He star \citep{Lee02}, one can take $\Omega_{\rm He} \approx \Omega_{\rm orbital}$."
 This then. ooOeives a donor mass of OAL... for SN2008D. It is now amore than 20 vears since the explosion of SN1987À. Nothing has been seen of it.," This, then, gives a donor mass of $\sim 6.8\msun$ for SN2008D. It is now more than 20 years since the explosion of SN1987A. Nothing has been seen of it."
 Brown&Weineartucr(1991) wrote down an aualvtical scenario showing that the compact object went iuto a DII. the mass of which (Bethe&Brown1995) was shown to be x1.5GAZ. from the 7.5% ΤΟΝΙ production.," \citet{Bro94} wrote down an analytical scenario showing that the compact object went into a BH, the mass of which \citep{Bet95} was shown to be $\leq1.56\msun$ from the $7.5 \%$ $^{56}$ Ni production."
 This calculation involved a 39002LOO kan separation distance (between matter that fell back aud matter that went to infinity). but the deusitv was low at that point. so the DII ass Was mseustive to the separation.," This calculation involved a $3900\pm400$ km separation distance (between matter that fell back and matter that went to infinity), but the density was low at that point, so the BH mass was insensitive to the separation."
" The assunptiou of Bethe&Brown(1995) that the couipact object was a DII wasstrengthened by the Chevalier(1989) work. which showed that after ouly ~1 vear SNI987À should be observed with a huninosity ~Lear=lbs107 eres to were a neutron star present, whereas the actual luminosity was ἐν10° eres &.|; two orders of magnitude less."," The assumption of \citet{Bet95} that the compact object was a BH wasstrengthened by the \citet{Che89} work, which showed that after only $\sim1$ year SN1987A should be observed with a luminosity $\sim L_{Edd}=4\times10^{38}$ ergs $^{-1}$ were a neutron star present, whereas the actual luminosity was $4\times10^{36}$ ergs $^{-1}$, two orders of magnitude less."
 A DIL was calculated to contribute at the level of 105107 eres s| (Brown&Weineartucr1991)., A BH was calculated to contribute at the level of $10^{34}-10^{35}$ ergs $^{-1}$ \citep{Bro94}.
. The difference could come from radioactivitv of the clouds., The difference could come from radioactivity of the clouds.
 πραπσα accretion: 1.6. accretion at a rate faster than Eddiustou. was enmiploved in the Brown&νοeartucr(1991) worl:as well as by Chevalier(1989).," Hypercritical accretion; i.e., accretion at a rate faster than Eddington, was employed in the \citet{Bro94} workas well as by \citet{Che89}."
. The excess radiation euecrgv was carried off by neutrinos., The excess radiation energy was carried off by neutrinos.
 Recently a clear proof that hyperentical accretion was necessary in the evolution of the binary M32. 7 was even by MorenoMéndez.etal.(2008)., Recently a clear proof that hypercritical accretion was necessary in the evolution of the binary M33 $-$ 7 was given by \citet{Mor08}.
.. The prescut-day binary with period 3.15 days would have broken up by loss of mass soon after the explosion which formed the DII had lypercritical accretion not taken place., The present-day binary with period $3.45$ days would have broken up by loss of mass soon after the explosion which formed the BH had hypercritical accretion not taken place.
" πηρααπσα accretion iuto the DIT of N33 X. 7 was required,", Hypercritical accretion into the BH of M33 $-$ 7 was required.
 ID αμα cases hwpererifieal accretion may not be possible because of the huge amount of augular moment which wast be present. or other reasons. but it is clear that im some cases livpereritical accretion is possible.," In many cases, hypercritical accretion may not be possible because of the large amount of angular momentum which must be present, or other reasons, but it is clear that in some cases hypercritical accretion is possible."
 Tn fact. many cases of Doudi acerction do involve Lypercritical values. as in the Brown&Wein- work.," In fact, many cases of Bondi accretion do involve hypercritical values, as in the \citet{Bro94} work."
 Now. the conunon envelope evolutionin the binary progenitor of SN2008D mist. like those of other GRBs (Brownoetal. 2007). be of type L: ie. the Ile burning must be finished.before the livdroseu envelope is removed.," Now, the common envelope evolutionin the binary progenitor of SN2008D must, like those of other GRBs \citep{Bro07}, , be of type $_c$ ; i.e., the He burning must be finishedbefore the hydrogen envelope is removed."
 We have shown that the DIT results from au, We have shown that the BH results from an
fields ecnerated bv liveτονμπας lotions can be opologically lou-trivial aud thus prone to pressure-divenu or current-driven iustabililos (SCC. 0.8. Lougaretti 2008 ‘or review).,"fields generated by hydrodynamic motions can be topologically non-trivial and thus prone to pressure-driven or current-driven instabilities (see, e.g., Longaretti 2008 for review)."
 This problem is well studied iu the context of experimenS Ol1 controled thermonuclear fusion (sec. e.g.. Bateman 1978) mx ras been discussed. in relation ο jets bv a nunber of athors (see. e.g Eichler 1993. Appl 1996 Appl et al.," This problem is well studied in the context of experiments on controlled thermonuclear fusion (see, e.g., Bateman 1978) and has been discussed in relation to jets by a number of authors (see, e.g., Eichler 1993, Appl 1996, Appl et al."
 2001V Lerv et al.," 2000, Lery et al."
 2000)., 2000).
 A linear stalüjlitv aalysis of sT1pqmiagnuetosonic jets has been 201’orled ly Ap ple al. (, A linear stability analysis of supermagnetosonic jets has been performed by Appl et al. (
2000) for different magnetic confieurations 1n‘Ladi15 a force-free field.,2000) for different magnetic configurations including a force-free field.
" It has been shown that the cuumen-(lriven lustahilities can occur iu hne axial fied for various profies of the azimuthal field even if these components are comparable,", It has been shown that the current-driven instabilities can occur in the axial field for various profiles of the azimuthal field even if these components are comparable.
" The 1OL-ποια. deveoplment of the curreut-«rive1 instability has con, analysed Lery et al. (", The non-linear development of the current-driven instability has been analysed by Lery et al. (
20KWO). who found hat his instability can nmodifv t1C nmüagnetic structure of a jet redistribitius the cuirent densiY iu the 1Mer Xu,"2000), who found that this instability can modify the magnetic structure of a jet redistributing the current density in the inner part."
 ~The current-driven πιστα]ülitv of relativistic jets aud erious in toroidal magnetic fields has been considered Beechuan (1ΩςO8). who obaine that the doimiuaut lusability iu this case are the làuk (n 1) aud pinch (in= () inodes.," The current-driven instability of relativistic jets and plerions in toroidal magnetic fields has been considered by Begelman (1998), who obtained that the dominant instability in this case are the kink $m=1$ ) and pinch $m=0$ ) modes."
 The kink. mode generally dominates. lus destroviug the concentric feld structure;," The kink mode generally dominates, thus destroying the concentric field structure."
 Apart from he cureut-driven instabilities. the pressure-driven ones caused x the thermal pressure eracieut can also occur imn jets.," Apart from the current-driven instabilities, the pressure-driven ones caused by the thermal pressure gradient can also occur in jets."
 The modes. correspouding to these instabilities. are radially localized aud characterized by high waveuuubers.," The modes, corresponding to these instabilities, are radially localized and characterized by high wavenumbers."
 Likely. hese iiodes are responsible for geucratiug MIID urbuleice in the ]et core (I&ersale. Lougaretti. Pelletier 2000).," Likely, these modes are responsible for generating MHD turbulence in the jet core (Kersale, Longaretti, Pelletier 2000)."
 The presare-driven instabilities are well studied in laboratorv piich configurations as well., The pressure-driven instabilities are well studied in laboratory pinch configurations as well.
 Robinsou (1971) considers he stabiitv of τ1ο pinch with a large ratio of the gas aud magnetic pressure usine the energv oxinciple aid fuds that staülitv is »ossdlble if currents are ocated outside the aad dlastua column., Robinson (1971) considers the stability of the pinch with a large ratio of the gas and magnetic pressure using the energy principle and finds that stability is possible if currents are located outside the main plasma column.
 The criterion of pressure-drivei dnstabiitics in cevlindrical ecolctry las been «erived bv Loue:weti (20:3)., The criterion of pressure-driven instabilities in cylindrical geometry has been derived by Longaretti (2003).
 This criterion is related to the Alfvéunic nodes. which usually require ess restricine conditions for lustahility and can even be unstable if Suvdiuu's criterio1 of stability is satisfied.," This criterion is related to the Alfvénnic modes, which usually require less restricting conditions for instability and can even be unstable if Suydam's criterion of stability is satisfied."
 Note that πιοΊσα] siuulatious often support the idea that maguetic jets should be 1ustable ancl can generate turnmleut notions causes by mstabilities., Note that numerical simulations often support the idea that magnetic jets should be unstable and can generate turbulent motions caused by instabilities.
 For instance. Lory Frauk (2000) found that the iustabiities seen in thei jet slinulations develo) with a swvavekΙστ] aud eyowh time hat are well matched by a Inear stability allaIvsis.," For instance, Lery Frank (2000) found that the instabilities seen in their jet simulations develop with a wavelength and growth time that are well matched by a linear stability analysis."
 Reativistic iunlations of extragalacic jets by Leisimann et al. (, Relativistic simulations of extragalactic jets by Leismann et al. (
2005) aud Roca-Sogorh et al. (,2005) and Roca-Sogorb et al. (
2008) also clearvy show that the various inreguavitics hat develop iu he jjet flow can be interpreted as ATWD iustabiities.,2008) also clearly show that the various irregularities that develop in the jet flow can be interpreted as MHD instabilities.
" Our study focuses on the stability. of jets with a subthermal maejetic field where t16 αςacetic cherey Is OWOL han the thermal οποιον of particOs,", Our study focuses on the stability of jets with a subthermal magnetic field where the magnetic energy is lower than the thermal energy of particles.
 This kind of 1naenetic fiek can be generated. for mstaucoe. by the ulmleut dvuaiuo action or bv hvdrodyviuuauic 1uotions (stretching) in tre process of jet propagalon.," This kind of magnetic field can be generated, for instance, by the turbulent dynamo action or by hydrodynamic motions (stretching) in the process of jet propagation."
 We show hat stabiitv properties o: jefs with a subthermal field eum be essentialv different from those with a lughly supertrermmal force-free magnetic field as was considered. Or exine. by Appl et al. (," We show that stability properties of jets with a subthermal field can be essentially different from those with a highly superthermal force-free magnetic field as was considered, for example, by Appl et al. ("
2000).,2000).
 Iu articular. lüeher azuuthal inodes with n»>1 can have tthe highest growhi rat u varkuice with the supert1011111 case.," In particular, higher azimuthal modes with $m\gg1$ can have the highest growth rate at variance with the superthermal case."
 In our jet Moclel. 1th. destabilizing factors - the pressure eraclicit and clectric current - are presented simultaneously. aud he iustabilitv occurs uuder the coubiuec influence of bohi hese factors.," In our jet model, both destabilizing factors - the pressure gradient and electric current - are presented simultaneously, and the instability occurs under the combined influence of both these factors."
" ""Therefore. the iustabilitv considered has a mined pressure- and current-drivΠλ natire."," Therefore, the instability considered has a mixed pressure- and current-driven nature."
 The paper is organized as folQWsS., The paper is organized as follows.
 Section 2 contiIs he derivation of the relevant equations. aud Sect.," Section 2 contains the derivation of the relevant equations, and Sect."
 3 shows he numerical results., 3 shows the numerical results.
 Conclusions are preseuted in Sect., Conclusions are presented in Sect.
 1., 4.
 We cousider a very simplified model asstuine hat the je is an infutelv loue stationary cvliudrical outflow ancl its xopasation through the züubieut medinm is modelled by a sequeice of quasi-equilibrimm states., We consider a very simplified model assuming that the jet is an infinitely long stationary cylindrical outflow and its propagation through the ambient medium is modelled by a sequence of quasi-equilibrium states.
" For the sake of snplicitv. it is often assuned that the velocity oft plasma witim a jet. V. does not ¢αραιά on coordinates (seo, Ce. ApX 1996. Appl et al."," For the sake of simplicity, it is often assumed that the velocity of plasma within a jet, $V$, does not depend on coordinates (see, e.g., Appl 1996, Appl et al."
 2000 Lery et al.," 2000, Lery et al."
 2000). and we wil adopt the same assuiplon lu oursπαν.," 2000), and we will adopt the same assumption in our study."
 Tusabilities of he magnetic configuraticuns associated to the electric Clrrent are basically absolue mmstabilities. ic. they erow. but do not xopagate.," Instabilities of the magnetic configurations associated to the electric current are basically absolute instabilities, i.e. they grow, but do not propagate."
 We suppose that tUs is the case also iu he rest fine of the jet. and unstable )orturbations are therefore simply adyeced with the flow at thejjet volcity (sec. e.g.àY Appl et al.," We suppose that this is the case also in the rest frame of the jet, and unstable perturbations are therefore simply advected with the flow at the jet velocity (see, e.g., Appl et al."
 2000)., 2000).
 Therefore. we treat the stability properties in the rest frame of he jet.," Therefore, we treat the stability properties in the rest frame of the jet."
 We explore the evlindrical coordinates (s. 47. 2) with the nut vectors (Ex. €.. €i).," We explore the cylindrical coordinates $s$ , $\varphi$ , $z$ ) with the unit vectors $\vec{e}_{s}$, $\vec{e}_{\varphi}$, $\vec{e}_{z}$ )."
 The naenetic field Is ASSTuued to be axisviuinietric with a non-vanishiug albd y-compoucut., The magnetic field is assumed to be axisymmetric with a non-vanishing $z$ - and$\varphi$ -component.
The azimuthal field desends ou the,The azimuthal field depends on the
energies lower or higher than the break.,energies lower or higher than the break.
 We considered the LECS aud MECS detectors. which have a much. higher statistics than the PDS. aud calculated. the count rates in four different energy bands: 0.12.0. 0.1LO. 2.010 aud 5.010 keV. for the two observations.," We considered the LECS and MECS detectors, which have a much higher statistics than the PDS, and calculated the count rates in four different energy bands: 0.1–2.0, 0.1–4.0, 2.0–10 and 5.0–10 keV, for the two observations."
 The values for the May. observation are: 0.077τε 0.002. 0.086+0.002. 0.050d0.002. 0.011-ε0.001.," The values for the May observation are: $0.077 \pm 0.002$ , $0.086 \pm 0.002$ , $0.050 \pm 0.002$, $0.014 \pm 0.001$."
 For the June observation we have: 0.050+0.003. 0.059+0.002. 0.010+=O.00L. 0.01340.001.," For the June observation we have: $0.050 \pm 0.003$, $0.059 \pm 0.002$, $0.040 \pm 0.001$, $0.013 \pm 0.001$."
 Thus. on a monthly time scale. the amount of variability iu the energy baud 0.1-10 keV seeuis to be ereater at softer energies.," Thus, on a monthly time scale, the amount of variability in the energy band 0.1-10 keV seems to be greater at softer energies."
 Tn the Mav observation rapid Xray variability of about a factor of three in £:.5 hours was clearly detected. but only at energies smaller than 31 keV. coufirmine a hieher amount of variabilitv at energies below the break.," In the May observation rapid X–ray variability of about a factor of three in 4–5 hours was clearly detected, but only at energies smaller than 3–4 keV, confirming a higher amount of variability at energies below the break."
 This can be seen frou the light curves of rofüe:le: in the 0.1]1 keV band the flux increased by a factor ~3 just after the starting of the observation and reached the maxinuun level at about 30h., This can be seen from the light curves of \\ref{fig:lc}: in the 0.1–4 keV band the flux increased by a factor $\sim$ 3 just after the starting of the observation and reached the maximum level at about 30h.
 This level was mnautained for about 23 hours aud then the couut rate declined to ~ 0.06 +. comparable to the level ucasured at the beginning of the observation.," This level was maintained for about 2–3 hours and then the count rate declined to $\sim$ 0.06 $^{-1}$, comparable to the level measured at the beginning of the observation."
 Above 1 keV this variability. if at all present. is much less xonounced.," Above 4 keV this variability, if at all present, is much less pronounced."
" Note that our 26 liuüt. in the baud 110 τον, corresponds to a variability of1054."," Note that our $3\, \sigma$ limit, in the band 4–10 keV, corresponds to a variability of."
.. Thus. at hieh eneredes. the source is much less variable than below 1 seV. We extracted LECS and MECS spectra during the Hare (from the third to the ninthi points of he Nταν ight curve shown in Fig.22) aud outside the flare aud erforiued the spectral analvsis.," Thus, at high energies, the source is much less variable than below 4 keV. We extracted LECS and MECS spectra during the flare (from the third to the ninth points of the X–ray light curve shown in 2) and outside the flare and performed the spectral analysis."
 Again. in both cases a )ower law did not fit the data aud a DPL model was recessary.," Again, in both cases a power law did not fit the data and a BPL model was necessary."
 The first spectral index is steeper during the dare (Ty=2.7£0.06 vs 2.1£0.15 outside the flax, The first spectral index is steeper during the flare $\Gamma_1 = 2.7 \pm 0.06$ vs $2.4 \pm 0.15$ outside the flare).
 The break secs to move at Neher energies (best fif values are Ll and 3.5 keV. respectively). although the wo values are consistent inside the confidence errors ‘or three parameters of interest.," The break seems to move at higher energies (best fit values are 4.4 and 3.5 keV, respectively), although the two values are consistent inside the confidence errors for three parameters of interest."
 The second spectral iudex does not change at all., The second spectral index does not change at all.
 Thus. also the fast variability that we detected curing the Max observation. suggests that he break moves at higher energies when the source flux Increases.," Thus, also the fast variability that we detected during the May observation, suggests that the break moves at higher energies when the source flux increases."
 Tn the Juue observation we did not detect significant variability. neither at high nor at low energies.," In the June observation we did not detect significant variability, neither at high nor at low energies."
" Optical photometry of ON 231 during the BeppoSAX volutines was performed with some telescopes in Italy. in the standard bandpasses Johuson D. V aud Cousins R. L operated by the Perugia and Torino Observatories aud w the Istituto Astronomico of University ""La Sapieuzi in Roma."," Optical photometry of ON 231 during the SAX pointings was performed with some telescopes in Italy, in the standard bandpasses Johnson B, V and Cousins R, I, operated by the Perugia and Torino Observatories and by the Istituto Astronomico of University “La Sapienza"" in Roma."
 The main results of the optical observations diving the great. 1998 outburst of ON 231 were already resented by Massaro et al. (, The main results of the optical observations during the great 1998 outburst of ON 231 were already presented by Massaro et al. (
1999).,1999).
 A detailed description of the instrumeutation and data reduction. together with a colplete data list up to 1998 June 9 cau be retrieved from the article bv Tosti et al. (," A detailed description of the instrumentation and data reduction, together with a complete data list up to 1998 June 9 can be retrieved from the article by Tosti et al. ("
1999).,1999).
 The mean V. B aud E magnitude are eiven in Table 1.," The mean V, $_{\rm c}$ and $_{\rm c}$ magnitude are given in Table 1."
 From these data we also evaluated the optical (energv) spectral iudex (assuming Ay= 0.19) which was found equal to 1.2140.08 for all observations., From these data we also evaluated the optical (energy) spectral index (assuming $A_V = 0.19$ ) which was found equal to $1.24 \pm 0.08$ for all observations.
 Iu reffüe:optical we show the optical light curve of ON 231 iu the R band from the cud of April to about the end of June with the data obtained at the three observing sites., In \\ref{fig:optical} we show the optical light curve of ON 231 in the R band from the end of April to about the end of June with the data obtained at the three observing sites.
 The times of the two Σταν observations are marked., The times of the two X–ray observations are marked.
 From this light curve we can see that the R magnitude in the period between the two BeppoSAX poiutiugs was in the interval 13.0) 13.5: the source remained quite bright but at a 11ean level £ünter than that of ereat burst of the - lof April., From this light curve we can see that the R magnitude in the period between the two $Beppo$ SAX pointings was in the interval 13.0 – 13.5: the source remained quite bright but at a mean level fainter than that of great burst of the end of April.
 In May and June the aneular distance of ON 231 from the Sun was simall aud we were able to perform. our optical observations oulv for few hours: iu particular. the observations of May. were only at the beginniug aud at the eud of the BeppoSAN pointing aud tle missed tle “flare” observed in the soft NXravs (see 22).," In May and June the angular distance of ON 231 from the Sun was small and we were able to perform our optical observations only for few hours: in particular, the observations of May were only at the beginning and at the end of the $Beppo$ SAX pointing and then missed the “flare” observed in the soft X–rays (see 2)."
 In June. the weather couditious allowed to observe ON 231 oulv at the beginning of the BeppoSAX poiutiug.," In June, the weather conditions allowed to observe ON 231 only at the beginning of the $Beppo$ SAX pointing."
 Iu weshow the spectral energv distribution (SED) of ON 231. iucludiug our sinultauecous Xrav and optical data.," In \\ref{fig:sed} weshow the spectral energy distribution (SED) of ON 231, including our simultaneous X–ray and optical data."
 The SED clearly shows that in the, The SED clearly shows that in the
beyond the well studied clusters Fornax and Virgo.,beyond the well studied clusters Fornax and Virgo.
" In this paper, we present a spectroscopic census of compact objects in the core region of the Hydrall galaxy cluster (Abell 1060)."," In this paper, we present a spectroscopic census of compact objects in the core region of the I galaxy cluster (Abell 1060)."
" II is well suited for a search for UCDs, since the cluster centre is dominated by the prominent cD galaxy NGC 3311, which exhibits a very pronounced diffuse light component and an extremely rich globular cluster system (????).. "," I is well suited for a search for UCDs, since the cluster centre is dominated by the prominent cD galaxy NGC 3311, which exhibits a very pronounced diffuse light component and an extremely rich globular cluster system \citep{1977ApJ...212..317V, 1995AJ....109.1033M, 2005A&A...438..103M, 2008ApJ...681.1233W}."
"Our aim is to investigate the bright end of the GCLF, where UCDs are expected to be found, and the globular cluster system of the two central cluster galaxies NGC 3311 and NGC 3300."," Our aim is to investigate the bright end of the GCLF, where UCDs are expected to be found, and the globular cluster system of the two central cluster galaxies NGC 3311 and NGC 3309."
" For this, we analyse two spectroscopic surveys, which were carried out with the VIsible MultiObject Spectrograph (VIMOS,?) mounted on UT3 at the VLT."," For this, we analyse two spectroscopic surveys, which were carried out with the VIsible MultiObject Spectrograph \citep[VIMOS,][]{2003SPIE.4841.1670L} mounted on UT3 at the VLT."
" One survey explicitly targets at UCD candidates (ESO observing programme 082.B-0680, PI: I. Misgeld), the other one targets at fainter sources, mainly GC candidates (ESO observing programme 076.B-0154, PI: T. Richtler)."," One survey explicitly targets at UCD candidates (ESO observing programme 082.B-0680, PI: I. Misgeld), the other one targets at fainter sources, mainly GC candidates (ESO observing programme 076.B-0154, PI: T. Richtler)."
 The significance of the data presented here for the dynamics of NGC 3311 is discussed in a parallel contribution (?).., The significance of the data presented here for the dynamics of NGC 3311 is discussed in a parallel contribution \citep{2011arXiv1103.2053R}.
" Throughout this paper we adopt a Hydrall distance modulus of (m—M)=33.37 mag, which is the mean value from different studies (see?,andreferencestherein).."," Throughout this paper we adopt a I distance modulus of $(m-M)=33.37$ mag, which is the mean value from different studies \citep[see][and references therein]{2005A&A...438..103M}."
 This corresponds to a physical scale of 229 pc/arcsec at 47.2 Mpc., This corresponds to a physical scale of 229 pc/arcsec at $47.2$ Mpc.
 VIMOS allows the simultaneous observation of 4 quadrants in one telescope pointing., VIMOS allows the simultaneous observation of 4 quadrants in one telescope pointing.
" Each quadrant is of dimension 7’x8’, with a gap of about 2’ between the quadrants."," Each quadrant is of dimension $7'\times 8'$, with a gap of about $2'$ between the quadrants."
" For the UCD survey, we placed four multi-object spectroscopy (MOS) pointings around NGC 3311, the central cD galaxy of the Π cluster (pointings Nr."," For the UCD survey, we placed four multi-object spectroscopy (MOS) pointings around NGC 3311, the central cD galaxy of the I cluster (pointings Nr."
 1—4 in Fig. 1))., 1–4 in Fig. \ref{fig:fields}) ).
 Each MOS pointing was observed with two different slit masks which were created with the VIMOS mask creation software VMMPS., Each MOS pointing was observed with two different slit masks which were created with the VIMOS mask creation software VMMPS.
 Pointing Nr., Pointing Nr.
 | was already observed with one slit mask in 2007 as part of our previous observing programme 076.B-0293 (see ? for details)., 1 was already observed with one slit mask in 2007 as part of our previous observing programme 076.B-0293 (see \cite{2008A&A...486..697M} for details).
" For reasons of consistency, we include the results from this run into the following analyses."," For reasons of consistency, we include the results from this run into the following analyses."
" For the new UCD survey, this pointing was re-observed with one additional slit mask."," For the new UCD survey, this pointing was re-observed with one additional slit mask."
 Table 1 lists all observations analysed in this paper., Table \ref{tab:obslog} lists all observations analysed in this paper.
 The candidates for pointings Nr., The candidates for pointings Nr.
 1 and Nr., 1 and Nr.
" 2 were selected as described in ?,, i.e. being unresolved in the VIMOS V- and R-band pre-images, and restricted in apparent magnitude and colour to 19.2«V22.7 mag and 0.48«V—R0.93 mag."," 2 were selected as described in \cite{2008A&A...486..697M}, i.e. being unresolved in the VIMOS $V$ - and $R$ -band pre-images, and restricted in apparent magnitude and colour to $19.2<V<22.7$ mag and $0.48<V-R<0.93$ mag."
 The UCD candidates for the new MOS pointings Nr., The UCD candidates for the new MOS pointings Nr.
 3 and Nr., 3 and Nr.
" 4 were again selected from VIMOS pre-imaging in V and R, however in a slightly different manner."," 4 were again selected from VIMOS pre-imaging in $V$ and $R$, however in a slightly different manner."
 Figure 2 shows exemplarily for pointing Nr., Figure \ref{fig:ucdselection} shows exemplarily for pointing Nr.
" 4 all SExtractor (?) detections in the four quadrants, and the UCD candidates that were selected by the following requirements:"," 4 all SExtractor \citep{1996A&AS..117..393B} detections in the four quadrants, and the UCD candidates that were selected by the following requirements:"
These results imply that in F stars even relatively weak (oroidal fields will cause instability (hat should largely wipe out the differential rotation (nonlinear caleulations would be needed {ο test this conclusion).,These results imply that in F stars even relatively weak toroidal fields will cause instability that should largely wipe out the differential rotation (nonlinear calculations would be needed to test this conclusion).
 This inference implies that substantial differential rotation would be very hard to maintain in (he (achocline of an F star. particularly if it is of antisolar ivpe.," This inference implies that substantial differential rotation would be very hard to maintain in the tachocline of an F star, particularly if it is of antisolar type."
 Since F star convection zones are (hin aud (heir tachoclines are not [ar below (heir photospheres. we inler (his instability could severely limit the amplitude of surface differential rotation in F stars.," Since F star convection zones are thin and their tachoclines are not far below their photospheres, we infer this instability could severely limit the amplitude of surface differential rotation in F stars."
 Figure 7 displavs growth rates for overshoot (frames a).b)) tachoclines of IX-sGus. again for disturbances of both svuumetiries about (he equator.," Figure 7 displays growth rates for overshoot (frames a),b)) tachoclines of K-stars, again for disturbances of both symmetries about the equator."
 We see that in the overshoot case. (he result is qualitatively similar to Chat for G stars.," We see that in the overshoot case, the result is qualitatively similar to that for G stars."
 For weak field only antisolar differential rotations lead (o instability lor low peak field in the toroidal band., For weak field only antisolar differential rotations lead to instability for low peak field in the toroidal band.
 Instability occurs [or somewhat lower toroidal field for all differential rotations. because the effective gravity G in Ix-star overshoot tachoclines is about that for G stars.," Instability occurs for somewhat lower toroidal field for all differential rotations, because the effective gravity $G$ in K-star overshoot tachoclines is about that for G stars."
 Therefore in overshoot tachoclines for all three classes of stars. antisolar differential rotations with bancled toroidal fields are unstable for much smaller peak toroidal fields than are solar (wpe differential rotations.," Therefore in overshoot tachoclines for all three classes of stars, antisolar differential rotations with banded toroidal fields are unstable for much smaller peak toroidal fields than are solar type differential rotations."
production of resonance photous per unit volume (in excess of those produced by the primeval plasma) is ft = (1). where yp is the number density of lLydrogen nuclei. fit)=a@fa is the expansion rate. and ἐν ix a free paralcter.,"production of resonance photons per unit volume (in excess of those produced by the primeval plasma) is /dt = H(t), where $n_{\rm H}$ is the number density of hydrogen nuclei, $H(t)=\dot a/a$ is the expansion rate, and $\epsilon _{\alpha}$ is a free parameter."
 The computation of the ionization historv bv Seageretal. (2000) is reacülv adjusted to take account of this new source term if it is approximately homogeneous., The computation of the ionization history by \cite{SeaSasSco00} (2000) is readily adjusted to take account of this new source term if it is approximately homogeneous.
" The results iu Figure 1 assume the IHubble parameter is h=0 dm units of LOO lan + 4. the barvou deusity parameter is Q5?=0.02 (Tytleretal. 2000) and the total matter density parameter is O,,=0.25."," The results in Figure 1 assume the Hubble parameter is $h=0.7$ in units of $100$ km $^{-1}$ $^{-1}$, the baryon density parameter is $\Omega _\ba h^2=0.02$ \cite{Tytler} 2000) and the total matter density parameter is $\Omega _\mat= 0.25$."
" The ionization history is quite simular at Q,,=0.1.", The ionization history is quite similar at $\Omega _\mat=0.4$.
 The optical depth for Thomson scattering subsequeut to redshift 2 is if the fractional ionization is constant at ο at redshift less than z.," The optical depth for Thomson scattering subsequent to redshift $z$ is = 63 x ( ) ( ) 	 ( 	 ( z , if the fractional ionization is constant at $x$ at redshift less than $z$."
 Figure 1 shows that the delaved recombination through the redshift 2. where 7 passes through unitv is about as fast relative to the expansion rate as in the standard recombination model., Figure 1 shows that the delayed recombination through the redshift $z_*$ where $\tau$ passes through unity is about as fast relative to the expansion rate as in the standard recombination model.
 Furthermore the decrease in +. itself is approximately Sources of photons mav also produce iouizine radiatiou., Furthermore the decrease in $z_{*}$ itself is approximately Sources of photons may also produce ionizing radiation.
" Since the rate of recombination of fully ionized barvous at the cosmic nean density is faster than the rate of expansion the ionization. ."" may be approximated bv the equilibrimim equation ane: H.(L) The definition of the parameter ei follows equation (2)). and o is the recombination cocficicut for principal quanti numbers 9&2."," Since the rate of recombination of fully ionized baryons at the cosmic mean density is faster than the rate of expansion the ionization, $x$ may be approximated by the equilibrium equation x^2 H. The definition of the parameter $\epsilon _{\rm i}$ follows equation \ref{eq:source}) ), and $\alpha$ is the recombination coefficient for principal quantum numbers $n\geq 2$."
 At this ionization the optical depth for Thomson scatterius is Figure 2 shows iu inore detail the effect of the production of ionizing photons ou the ionization history., At this ionization the optical depth for Thomson scattering is ( ( ( ( z. Figure 2 shows in more detail the effect of the production of ionizing photons on the ionization history.
" Ife, >1 the slow decrease in the optical depth through 7~1 would remove the first peak iu the anisotropy power spectrum. an effect the measurements indicate is unacceptable."," If $\epsilon _{\rm i} \gsim 1$ the slow decrease in the optical depth through $\tau\sim 1$ would remove the first peak in the anisotropy power spectrum, an effect the measurements indicate is unacceptable."
 Sources of photons may also add euergyw to the CXMB by inverse Compton scattering. but if the energy added is comparable to the energy iu photous the effect on the y-paraieter is small.," Sources of photons may also add energy to the CMB by inverse Compton scattering, but if the energy added is comparable to the energy in photons the effect on the $y$ -parameter is small."
" Iu the adiabatic CDAL model the ionization history and the cosinological parameters fix the CAIB anisotropy power spectrum: the results in Figure 2 for the cosinologicallv flat model with the parameters in Figure 1. aud in Figure 3 for an open model with the cosmological parameters 04,= 0.6. Q4—0. 5=0.7. Οι=0.02 are computed using a code based on White&Scott (1996)."," In the adiabatic CDM model the ionization history and the cosmological parameters fix the CMB anisotropy power spectrum; the results in Figure 2 for the cosmologically flat model with the parameters in Figure 1, and in Figure 3 for an open model with the cosmological parameters $\Omega_\mat=0.6$ , $\Omega_{\Lambda}=0$, $h=0.7$, $\Omega_\ba h^{2}=0.02$ are computed using a code based on \cite{WhiSco96} (1996)."
" The shift iu the angular wavenumber A, at the peak is noteworthy because7,is used to iter the space curvature.", The shift in the angular wavenumber $l_1$ at the peak is noteworthy because$l_1$is used to infer the space curvature.
" A coneral expression for its value in adiabatic models is (Hu&Sugiviuna. 1995. with (420.736,) where"," A general expression for its value in adiabatic models is \cite{HuSug95} 1995, with $\ell_1 \approx 0.73 \ell_p$ ) where"
"where hy,«€k< hy. hy corresponds to the viscous scale of the fhüd while ; is linked with the scale of the resistive cascade transler.","where $k_\nu<k<k_\eta$ , $k_\nu$ corresponds to the viscous scale of the fluid while $k_\eta$ is linked with the scale of the resistive cascade transfer."
 We choose {ΑΛ} as an exponential-drop form., We choose $f(k/k_\eta)$ as an exponential-drop form.
 The magnetic field amplified bx the turbulence spectrum las been described by (2004.2006).," The magnetic field amplified by the turbulence spectrum has been described by \citet{niemiec04, niemiec06}."
. We obtain the amplified magnetic field as: In general. Eq.(2) presented as a power-law wilh a cutoff at high wave nmunber is universal for (he fluid dvnamo turbulence. whatever the radiation field is.," We obtain the amplified magnetic field as: In general, Eq.(2) presented as a power-law with a cutoff at high wave number is universal for the fluid dynamo turbulence, whatever the radiation field is."
 The A(q) in Eq.(1) can be linked by the magnetic field as A(q)=Cy(0B7(q)) where Ct is the normalization number.," The $K(\textbf{q})$ in Eq.(1) can be linked by the magnetic field as $K(\textbf{q})=C_0\langle\delta
B^2(q)\rangle$ where $C_0$ is the normalization number."
 Therefore. this turbulent approach for obtaining magnetic field is the developments in the framework of current. DSR. theory.A," Therefore, this turbulent approach for obtaining magnetic field is the developments in the framework of current DSR theory.,"
.. the nearest galaxy. was sketched [rom (he observational view (Israel1998).," the nearest galaxy, was sketched from the observational view \citep{israel98}."
. In particular. the knot in the jet has been detected in radio. X-rav (llarceastleetal.2003:ναοἱ2003:Kataokaοἱal.2006) and infrared (larcdeastle.INraft&Worrall2006) bands.," In particular, the knot in the jet has been detected in radio, X-ray \citep{hardcastle03,kraft03,kataoka06} and infrared \citep{hardcastle06} bands."
 With these observations. this object provides a multi-band spectrum to constrain the radiation mechanisms and the models of particle acceleration.," With these observations, this object provides a multi-band spectrum to constrain the radiation mechanisms and the models of particle acceleration."
" The central density of the knot in is n=3.7x10το? (Kraftetal.2003).. the correlation length of the random magnetic field is estimated by —I0em where fy=οτρ, is the skin depth. while the size of the knot is less (than 10 pe (Ilardeastleetal.2003)."," The central density of the knot in is $n=3.7\times
10^{-2}cm^{-3}$ \citep{kraft03}, the correlation length of the random magnetic field is estimated by $l_{cor}\sim(0.1-1)l_{sk}\sim 10^5-10^6 cm$ where $l_{sk}=c/w_{pe}$ is the skin depth, while the size of the knot is less than $10$ pc \citep{hardcastle03}."
. The flare points and complicated light curves (Llarcdeastle.lxraft&Worrall2006) indicate the disturbed effects of the irregular magnetic fields., The flare points and complicated light curves \citep{hardcastle06} indicate the disturbed effects of the irregular magnetic fields.
 These small-scale random inhomogeneities give us the opportunity to caleulate the emission using perturbative DSR., These small-scale random inhomogeneities give us the opportunity to calculate the emission using perturbative DSR.
 We insert Eq.(2) to Ex.(1) and caleulate imunericallv. we set (he turbulent spectrum a=1.45.," We insert Eq.(2) to Eq.(1) and calculate numerically, we set the turbulent spectrum $\alpha=1.45$."
 The electron energy. distribution αλανx is assumed as s=3.3.," The electron energy distribution $dN/d\gamma
\propto\gamma ^{-s}$ is assumed as $s=3.3$."
 The bulk Lorenz [actor is I— 12., The bulk Lorenz factor is $\Gamma=12$ .
" The range of & for turbulent spectrum calculation can be estimated by &/,=pl* where the Prandtl number is D.710T!/n~10!! for the warm medium in the knot of (Schekochihin&Cowlev2007)."," The range of $k$ for turbulent spectrum calculation can be estimated by $k_\eta/k_\nu =P_r^{1/2}$, where the Prandtl number is $P_r\sim 10^{-5}T^4/n\sim 10^{14}$ for the warm medium in the knot of \citep{schekochihin07}."
. The final result. with (he comparison to the observational data is shown in Fig., The final result with the comparison to the observational data is shown in Fig.
 l., 1.
 Thus. we use the single grossturbulent spectrum to reproduce (he multi-band emission. with its drop-olf point properly shown in the X-ray band.," Thus, we use the single grossturbulent spectrum to reproduce the multi-band emission, with its drop-off point properly shown in the X-ray band."
 From the datafitting. we find that the relativistic electrons with," From the datafitting, we find that the relativistic electrons with"
rather than the linear development of a non-axisvmmetric counterpart of the parametric instability.,rather than the linear development of a non-axisymmetric counterpart of the parametric instability.
 Figure 5 shows a colour coded image of density on slices through the model in the 4 plane at z=0 (top). the v> plane at y=0 (middle) and the gy2 plane at w=0 (bottom).," Figure 5 shows a colour coded image of density on slices through the model in the $x-y$ plane at $z = 0$ (top), the $x-z$ plane at $y = 0$ (middle) and the $y-z$ plane at $x = 0$ (bottom)."
 Black is highest density. blue Lowest.," Black is highest density, blue lowest."
 The slices are taken late in the evolution. at /280Q+.," The slices are taken late in the evolution, at $t = 80 \Omega^{-1}$."
 Density variations are visible because compressive waves are strongly excited., Density variations are visible because compressive waves are strongly excited.
 The extended. sharp features are shocks.," The extended, sharp features are shocks."
 The ramis., The r.m.s.
 variation in surface density is £0N7NM=0.04., variation in surface density is $\<\delta\Sigma^2\>^{1/2}/\<\Sigma\> = 0.04$.
 We have explored. the οσο of cach of the main. mocel parameters on the development of the parametric instability and its non-linear outcome., We have explored the effect of each of the main model parameters on the development of the parametric instability and its non-linear outcome.
 A full list of relevant mocels. with model parameters. is given in Table 1.," A full list of relevant models, with model parameters, is given in Table 1."
 Run 1 is the fiducial model., Run 1 is the fiducial model.
 One concern in formulating a numerical model such as this is whether an artificial aspeet of the boundary conclitions controls the outcome., One concern in formulating a numerical model such as this is whether an artificial aspect of the boundary conditions controls the outcome.
 In this respect. the azimuthal and radial boundary conditions are somewhat less worrisome han the vertical boundary. conditions: the former restrict he scale. of structure that can develop to the size of the vox. while the latter introduces a reflection. of outgoing waves that would otherwise dissipate in the dise atmosphere (although there could be a sharp boundary between a hot disc atmosphere and the body of the disc that would. also ρωσίσο rellections. albeit from a [ree rather than fixed »ouncdarv).," In this respect, the azimuthal and radial boundary conditions are somewhat less worrisome than the vertical boundary conditions; the former restrict the scale of structure that can develop to the size of the box, while the latter introduces a reflection of outgoing waves that would otherwise dissipate in the disc atmosphere (although there could be a sharp boundary between a hot disc atmosphere and the body of the disc that would also produce reflections, albeit from a free rather than fixed boundary)."
a reduction in the number of low luminosity galaxies.,a reduction in the number of low luminosity galaxies.
 Upon merging. the stars anc cold. gas of a satellite galaxy. (an accreting galaxy) are added to the reservoir of the central galaxy (called -Ceontrals’. henceforth) of the parent halo.," Upon merging, the stars and cold gas of a satellite galaxy (an accreting galaxy) are added to the reservoir of the central galaxy (called `Centrals', henceforth) of the parent halo."
 SAMSs have reprocuced a range of galactic observables. inelucling colours. luminosities. anc mass functions.," SAMs have reproduced a range of galactic observables, including colours, luminosities, and mass functions."
 SAMs come in several Uavours. and. although the codes share many similar features as outlined above. they also diller in the wav in whieh certain processes. relating to barvonic physics. are implemented: (eg... treatment of supernovae and AGN feedback).," SAMs come in several flavours, and, although the codes share many similar features as outlined above, they also differ in the way in which certain processes, relating to baryonic physics, are implemented (e.g., treatment of supernovae and AGN feedback)."
 These lead different SAMs to produce dillerent. solutions to the problem. of galaxy formation., These lead different SAMs to produce different solutions to the problem of galaxy formation.
 Some of these dillerences have been explored at length. in the literature. via direct. Comparison with both empirical field and efuster galaxy luminosity functions. which are the ol galaxy environments. (22??7)..," Some of these differences have been explored at length in the literature, via direct comparison with both empirical field and cluster galaxy luminosity functions, which are the of galaxy environments \citep{Hatton2003, Mo2004, Gonzalez2005, Bower2006, Croton2006}."
 For example. ? found that the 7. and. ? models. give different trends for the temporal evolution of galaxy merger rates based on close pair counting.," For example, \citet{Mateus2008} found that the \citet{Bower2006} and \citet{DeLucia2006} models give different trends for the temporal evolution of galaxy merger rates based on close pair counting."
 7. suggest that the ? and 2? models reach dillerent. conclusions regarding the rate of chance/ alignment in low velocity dispersion compact eroups., \citet{DiazGimenez2008} suggest that the \citet{Bower2006} and \citet{DeLucia2006} models reach different conclusions regarding the rate of chance alignment in low velocity dispersion compact groups.
 Recent examples of problems encountered. by. the SAM approach include the excess of low-mass red galaxies. as identified by 2.. ancl 2...," Recent examples of problems encountered by the SAM approach include the excess of low-mass red galaxies, as identified by \citet{Weinmann2006}, and \citet{Baldry2006}."
 A comprehensive review of the SAM approach can be found in ?.., A comprehensive review of the SAM approach can be found in \citet{Baugh2006}.
 What has been explored. thus far. at least in any formal sense. is the impact of these barvonic physics prescriptions upon the resulting luminosity and stellar mass functions for the most.comenon of environments. that of galaxy groups.," What has been explored, thus far, at least in any formal sense, is the impact of these baryonic physics prescriptions upon the resulting luminosity and stellar mass functions for the most of environments, that of galaxy groups."
 Lt is to this aim that our current. study is [ocused., It is to this aim that our current study is focused.
 Galaxy groups are environments where galactic evolution is happening at a high rate due to the Iow velocity dispersion of groups., Galaxy groups are environments where galactic evolution is happening at a high rate due to the low velocity dispersion of groups.
 This means means that galaxy-galaxy interactions are more likely than in clusters., This means means that galaxy-galaxy interactions are more likely than in clusters.
 In this paper. we examine the outputs of four widelv-used SAMs applied to the Millennium ?.. in order to quantify the impact of barvonic physics prescriptions upon the resulting compact and loose group luminosity functions.," In this paper, we examine the outputs of four widely-used SAMs applied to the Millennium \citet{Springel2005}, in order to quantify the impact of baryonic physics prescriptions upon the resulting compact and loose group luminosity functions."
 Two of the models which we examine will be collectively referred. to as the “Durham models”. being those of 7.. (D-BBOG). and ? Οδ). whieh is an updated: version of 1212060. with a more sophisticated treatment of rani pressure1). stripping.," Two of the models which we examine will be collectively referred to as the “Durham models"", being those of \citet{Bower2006}, B06), and \citet{Font2008} F08), which is an updated version of B06, with a more sophisticated treatment of ram pressure stripping."
" We also analyse two ""Munich. models”. being those of ? (ALDDOG hereafter). and ?. (ALBBOT). which clilfers from ALDDOG mainly in the supernova feedback recipes."," We also analyse two “Munich models"", being those of \citet{DeLucia2006} D06 hereafter), and \citet{Bertone2007} B07), which differs from D06 mainly in the supernova feedback recipes."
 A related moclel by ?.. of which ALDDOG is a clirect descendant. is also referred to in our stucly.," A related model by \citet{Croton2006}, of which D06 is a direct descendant, is also referred to in our study."
 After outlining our galaxy group cataloguing procedure. constructed. using a classical f[riends-of-friends: approach 2). we examine systematically the predicted distributions of luminosity. ancl first-to-second. rank magnitude gap Lor both compact anc loose groups of galaxies. for cach of the SAAIsS under. consideration. 3).," After outlining our galaxy group cataloguing procedure, constructed using a classical friends-of-friends approach 2), we examine systematically the predicted distributions of luminosity, and first-to-second rank magnitude gap for both compact and loose groups of galaxies, for each of the SAMs under consideration 3)."
 We analyse the Luminosity distribution. of galaxy groups in the cillerent models so that the next. generation of SXMs can improve the implementation of galaxy formation physics., We analyse the luminosity distribution of galaxy groups in the different models so that the next generation of SAMs can improve the implementation of galaxy formation physics.
 The SAMs used in our analysis employ the merger. trees associated with the Millennium Simulation (7) a large N-body simulation corresponding to a significant volume of the visible Universe. and. generated. using the WAIAP Year 1 cosmology (2).," The SAMs used in our analysis employ the merger trees associated with the Millennium Simulation \citep{Springel2005} a large N-body simulation corresponding to a significant volume of the visible Universe, and generated using the WMAP Year 1 cosmology \citep{Spergel2003}."
"? Lhe simulation used 2160? particles in a periodic box of side length 500.+ Alpe. gravitational softening of tkpe. and individual particle masses of 10"" Alo: 64 outputs exist within the Millennium database. ranging from redshift z—127 to 2=0."," The simulation used $2160^3$ particles in a periodic box of side length $h^{-1}$ Mpc, gravitational softening of $^{-1}$ kpc, and individual particle masses of $\times$ $^8$ $_\odot$; 64 outputs exist within the Millennium database, ranging from redshift $z$ =127 to $z$ =0."
 The simulation was post-processed using ao Friends-ol-Eriencds (Fok) algorithm (?).. in order to identify density peaks. and then SUBEIND (7). was emploved to identify substructure ancl split spuriously joined haloes.," The simulation was post-processed using a Friends-of-Friends (FoF) algorithm \citep{Geller1983}, in order to identify density peaks, and then SUBFIND \citep{Springel2001} was employed to identify substructure and split spuriously joined haloes."
" This information was then used to build merger trees for the dark matter haloes. onto which the SAMSs are ""mapped""."," This information was then used to build merger trees for the dark matter haloes, onto which the SAMs are “mapped”."
 3elore embarking on a discussion. of the. predicted luminosity. functions resulting from the use of. the aforementioned. SAAS applied. to the Millennium. merger trees. Ἡ ds important (o sumumarise brielly the. defining characteristics associated with cach of the primary SAAIs emplovecl here.," Before embarking on a discussion of the predicted luminosity functions resulting from the use of the aforementioned SAMs applied to the Millennium merger trees, it is important to summarise briefly the defining characteristics associated with each of the primary SAMs employed here."
 We will highlight the dilferent ways in which the codes create merger trees. the wav in which galaxy positions are defined. the implementation of satellite disruption and accretion. and the way in which supernova and AGN feedback are implemented.," We will highlight the different ways in which the codes create merger trees, the way in which galaxy positions are defined, the implementation of satellite disruption and accretion, and the way in which supernova and AGN feedback are implemented."
" In the Durham models. merger trees are produced. in a manner which follows that of ὃν, and the properties of these trees are described in ?.."," In the Durham models, merger trees are produced in a manner which follows that of \citet{Helly2003}, and the properties of these trees are described in \citet{Harker2006}."
 These mocdels account for ostensibly separate haloes which are joined by a bridge of dark matter and hence can be erroneously put in a single halo by Fol algorithms. anc also account. for haloes which are only temporarily joined.," These models account for ostensibly separate haloes which are joined by a bridge of dark matter and hence can be erroneously put in a single halo by FoF algorithms, and also account for haloes which are only temporarily joined."
 Accounting for these effects. results in a halo catalogue containing more haloes than in the original Fok catalogue., Accounting for these effects results in a halo catalogue containing more haloes than in the original FoF catalogue.
 Phe merger trees are then constructed from these catalogues by Following subhalocs [rom carly times to late times., The merger trees are then constructed from these catalogues by following subhaloes from early times to late times.
 We note that the merger trees were constructed independently of those in 2.., We note that the merger trees were constructed independently of those in \citet{Springel2005}.
 The merging of galaxies. and Lifetime of satellite galaxies. are derived. using the method. presented. in ?.. which is considerably more sophisticated than the method used in 2..," The merging of galaxies, and lifetime of satellite galaxies, are derived using the method presented in \citet{Benson2002}, which is considerably more sophisticated than the method used in \citet{Cole2000}."
 When dark haloes merge. a new combined clark halo is formed. and the largest of the galaxies contained within is assumed to be the central galaxy. whilst all other ealaxiecs within the halo are satellites.," When dark haloes merge, a new combined dark halo is formed, and the largest of the galaxies contained within is assumed to be the central galaxy, whilst all other galaxies within the halo are satellites."
 Satellites are then evolved. under the combined. cllects of dynamical friction. and tidal stripping.," Satellites are then evolved under the combined effects of dynamical friction, and tidal stripping."
 These cllects are mocdelled analytically., These effects are modelled analytically.
 The initial orbital energy. and. angular momentum. of the satellite upon merging are specified.," The initial orbital energy, and angular momentum, of the satellite upon merging are specified."
" Phe orbital energy is set using a constant value of ας)ον, = 0.5. representative of the median binding energy of satellites. while the orbital cllipticity. is chosen to be between 0.1 and. 1.0 at random."," The orbital energy is set using a constant value of $r_c(E)/R_{vir}$ = 0.5, representative of the median binding energy of satellites, while the orbital ellipticity, is chosen to be between 0.1 and 1.0 at random."
 Given these parameters. the apocentric distance is found. and the orbit equations are integrated. at that. point.," Given these parameters, the apocentric distance is found, and the orbit equations are integrated at that point."
 The host and satellite haloes are all assumed. to. have NEW, The host and satellite haloes are all assumed to have NFW
which is indeed the case. and indicates the validity of our method.,"which is indeed the case, and indicates the validity of our method."
 Applving this technique to the five radio galaxies without detected: nuclear sources. we derive lower limits o the nuclear extinction.," Applying this technique to the five radio galaxies without detected nuclear sources, we derive lower limits to the nuclear extinction."
 The non-detections of compact sources in 3€ 42 and 3€ 153 do not rule out. unobscured nuclei with any significance. since both these sources have aint emission line Duxes and therefore are expected to have quite faint nuclei.," The non-detections of compact sources in 3C 42 and 3C 153 do not rule out unobscured nuclei with any significance, since both these sources have faint emission line fluxes and therefore are expected to have quite faint nuclei."
" For the other three galaxies we determine he following 30 limits: ob,O4"" [or 3€ OS: dpL317 or 3€ 171: and chy245"" for 3€ 192.", For the other three galaxies we determine the following $3\sigma$ limits: $A_V > 74^m$ for 3C 98; $A_V > 37^m$ for 3C 171; and $A_V > 45^m$ for 3C 192.
 Note that these imits are clerived from the non-detections at M-band (where our sensitivity to highly obseured nuclei is greatest) and are herefore independent of the J and. A-band fits., Note that these limits are derived from the non-detections at $M$ -band (where our sensitivity to highly obscured nuclei is greatest) and are therefore independent of the $J$ and $K$ -band fits.
 The high extinction towards the nucleus of 3€ OS therefore. clearly ecludes à A -band nucleus brighter than the limit we quote in Table 3.., The high extinction towards the nucleus of 3C 98 therefore clearly precludes a $K$ -band nucleus brighter than the limit we quote in Table \ref{tab:fitres}.
 The core dominance parameter. 2 (also called the core-to-obe ratio). is a wiclely-used orientation. indicator (Orr Browne 1982) anc we are therefore capable of determining he nuclear extinction to our radio galaxies as a function of viewing angle.," The core dominance parameter, $R$ (also called the core-to-lobe ratio), is a widely-used orientation indicator (Orr Browne 1982) and we are therefore capable of determining the nuclear extinction to our radio galaxies as a function of viewing angle."
 Simpson (19942. 1996) proposed analysing a large sample of radio galaxies in this way to distinguish )etween. dillerent. geometries. for the obscuring material. which partly provided the motivation for the study described vere.," Simpson (1994a, 1996) proposed analysing a large sample of radio galaxies in this way to distinguish between different geometries for the obscuring material, which partly provided the motivation for the study described here."
 The value o£ 2 is usually determined at GCGlLIz. and he properties of our sources at this frequency are listed in ‘Table Al of the Appendix.," The value of $R$ is usually determined at GHz, and the properties of our sources at this frequency are listed in Table \ref{tab:cores} of the Appendix."
 We omit 3C 84 since it does not possess the characteristic FRILL radio morphology., We omit 3C 84 since it does not possess the characteristic II radio morphology.
 The values of the nuclear extinction derived: earlier are plotted against log/? in Fig. 13.., The values of the nuclear extinction derived earlier are plotted against $\log R$ in Fig. \ref{fig:correl}.
 Using a generalized Ixendall's rank correlation statistic (Isobe et 110986). we can reject the hypothesis that ye is uncorrelated with # at better than conlidence.even if 3€ 234 is excluded from the analysis.," Using a generalized Kendall's rank correlation statistic (Isobe et 1986), we can reject the hypothesis that $A_V$ is uncorrelated with $R$ at better than confidence,even if 3C 234 is excluded from the analysis."
 The nuclear extinction therefore increases with viewing angle aas I decreases) and. suggests a [lattened. distribution for the obscuring material., The nuclear extinction therefore increases with viewing angle as $R$ decreases) and suggests a flattened distribution for the obscuring material.
 lenoring density inhomogencities. the obscuring materias geometry is defined by ον(0). which we can derive from ly(2?) if we can transform the observed. core dominance parameter. 2. to a viewing angle. 6.," Ignoring density inhomogeneities, the obscuring material's geometry is defined by $A_V(\theta)$ , which we can derive from $A_V(R)$ if we can transform the observed core dominance parameter, $R$, to a viewing angle, $\theta$."
" These two quantities are related by (Orr Browne 1982). where ep—R(90"") and is the velocity of the beamed core component relative to the speed of light."," These two quantities are related by (Orr Browne 1982), where $R_{\rm T} \equiv R(90\degr)$ and $\beta$ is the velocity of the beamed core component relative to the speed of light."
 We adopt 7=0.99 (Orr Browne 1982). although its exact value is unimportant except at small values of 8. which are not relevant to our studs of radio galaxies.," We adopt $\beta = 0.99$ (Orr Browne 1982), although its exact value is unimportant except at small values of $\theta$, which are not relevant to our study of radio galaxies."
 Yo convert [rom A to 8. it is necessary to know the value of Ry.," To convert from $R$ to $\theta$, it is necessary to know the value of $R_{\rm T}$."
 Orr Browne determined p=0.024 (rom a sample of BCL. quasars. but they assumed that these objects were rancomls oriented with respect to the line of sight.," Orr Browne determined $R_{\rm T} = 0.024$ from a sample of 3CR quasars, but they assumed that these objects were randomly oriented with respect to the line of sight."
 Since it is now believed that quasars are preferentially pointed towards us. Orr Jowne's value of ép will be an overestimate.," Since it is now believed that quasars are preferentially pointed towards us, Orr Browne's value of $R_{\rm T}$ will be an overestimate."
 We therefore. recetermine Ay using both quasars ancl FRILL radio galaxies [rom Laine et ((1983) with z«O43. although: we exclude ὃς 236 since i possesses à steep-spectrum radio core.," We therefore redetermine $R_{\rm T}$ using both quasars and II radio galaxies from Laing et (1983) with $z<0.43$, although we exclude 3C 236 since it possesses a steep-spectrum radio core."
 As described in the Xppendix. a good fit to the data is obtained with (logRp)2NC.2.54.0.51).," As described in the Appendix, a good fit to the data is obtained with $P(\log R_{\rm T}) =
{\sf N}(-2.54,0.51)$."
 This is consistent with the distribution derived by Simpson from the radio galaxies alone. and with estimates mace from other samples of radio galaxies MMorganti ct 11997).," This is consistent with the distribution derived by Simpson from the radio galaxies alone, and with estimates made from other samples of radio galaxies Morganti et 1997)."
 Since we have only determined the probability distribution. for fp. ancl not its actual value for each radio galaxy. the observed core dominance parameter. f. is transformed into a probability distribution for the viewing angle. 8.," Since we have only determined the probability distribution for $R_{\rm T}$, and not its actual value for each radio galaxy, the observed core dominance parameter, $R$ , is transformed into a probability distribution for the viewing angle, $\theta$."
 This transformation is described in the Appendix., This transformation is described in the Appendix.
 We list the viewing angles for the radio galaxies in Table 6 and plot the cross-section through the torus in Fig. 12.., We list the viewing angles for the radio galaxies in Table \ref{tab:theta} and plot the cross-section through the torus in Fig. \ref{fig:torus}.
 lt is immediately clear from this analysis that our inability to constrain the angle at which we are viewing each object is a major limitation to the ellectiveness of this technique., It is immediately clear from this analysis that our inability to constrain the angle at which we are viewing each object is a major limitation to the effectiveness of this technique.
 Doppler boosting only produces a fourfolel increase in the observed. Luminosity of the central component for ϐz50° (the viewing angle which is believed. to separate quasars from radio galaxies at low redshift: L94. Simpson 1998a. and see also Table 6)). barely enough to produce a signal over the factor of three scatter in fp.," Doppler boosting only produces a fourfold increase in the observed luminosity of the central component for $\theta \approx 50\degr$ (the viewing angle which is believed to separate quasars from radio galaxies at low redshift; L94, Simpson 1998a, and see also Table \ref{tab:theta}) ), barely enough to produce a signal over the factor of three scatter in $R_{\rm T}$ ."
 Since core dominance isbelieved to be the best available orientation indicator. it is clear that à much larger sample of radio galaxies will beneeded to produce a useful torus map.," Since core dominance isbelieved to be the best available orientation indicator, it is clear that a much larger sample of radio galaxies will beneeded to produce a useful torus map."
Astrophysical accretion disks are able to evolve. because angular momentum is extracted from Lluid elements and. transporteck outward.,Astrophysical accretion disks are able to evolve because angular momentum is extracted from fluid elements and transported outward.
 This. is cllected bv the oesence of nonvanishingὃν racdial-azimuthal components. of the Maxwell ancl Reynolds. stress. tensors. produced. by maenetohvdrodynamic. (MIID) turbulence driven. by. the magnetorotational instability (AIRD) (Balbus&Lawley 1998).," This is effected by the presence of nonvanishing radial-azimuthal components of the Maxwell and Reynolds stress tensors, produced by magnetohydrodynamic (MHD) turbulence driven by the magnetorotational instability (MRI) \citep{bh98}."
. As there is no analytic theory of MIID. turbulence at hand (nor is there one in sight). large-scale. numerical simulation has been the main avenue of progress toward unelerstaiding Its propertics.," As there is no analytic theory of MHD turbulence at hand (nor is there one in sight), large-scale numerical simulation has been the main avenue of progress toward understanding its properties."
 Many numerical studies make use of the local “shearing ον. approximation (Llawley.Cióunmie&Balbus—1995)., Many numerical studies make use of the local “shearing box” approximation \citep{hgb95}.
. ‘The shearing box is an invaluable tool for studying local Dow cdvnamies in detail. and for resolving turbulent Dow with the argest possible dynamical range.," The shearing box is an invaluable tool for studying local flow dynamics in detail, and for resolving turbulent flow with the largest possible dynamical range."
 MILD turbulence. like all ruc turbulence. should be chaotic. as quantified. formally »w à measured positive Lvapunov exponent.," MHD turbulence, like all true turbulence, should be chaotic, as quantified formally by a measured positive Lyapunov exponent."
 What is less clear. but of great astrophysical significance. is whether ong term Low averages are even well-defined.," What is less clear, but of great astrophysical significance, is whether long term flow averages are even well-defined."
 To put. the question most starkly. imagine macroscopically identical disks. with Iluid. perturbations that vary by a tiny amount.," To put the question most starkly, imagine macroscopically identical disks, with fluid perturbations that vary by a tiny amount."
 The fine scale description of their internal turbulence will surely differ. but will quantities such as the stress tensor components converge to the same values in the long term?," The fine scale description of their internal turbulence will surely differ, but will quantities such as the stress tensor components converge to the same values in the long term?"
 This question goes directly to the heart of the standard à cisk formalism (Shakura&Sunvaev1973). which assumes that clisk transport may be described by a spatially constant or slowly varying a parameter. (, This question goes directly to the heart of the standard $\alpha$ disk formalism \citep{ss73} which assumes that disk transport may be described by a spatially constant or slowly varying $\alpha$ parameter. (
The quantity à is defined as the ratio of radial-azimuthal component of the stress tensor Zp. to the gas. or gas plus radiation. pressure.),"The quantity $\alpha$ is defined as the ratio of radial-azimuthal component of the stress tensor $T_{R\phi}$ to the gas, or gas plus radiation, pressure.)"
 How. well supported is this assumption?, How well supported is this assumption?
 This paper begins to study. these complex. issues. by examining the chaotic nature of the AHID turbulence., This paper begins to study these complex issues by examining the chaotic nature of the MHD turbulence.
 The presentation is organized. as follows., The presentation is organized as follows.
 In. 82 we brielly review the shearing box., In 2 we briefly review the shearing box.
 In. $33 we present the results of experiments designed to reveal how the measured properties of turbulent. flow are related. to both computational and physical input parameters., In 3 we present the results of experiments designed to reveal how the measured properties of turbulent flow are related to both computational and physical input parameters.
 In. S44. we carry out a series of experiments that demonstrate qualitatively that the MIID turbulence is chaotic. anc in 855 this is quantified by computing the Lyapunov exponents for a set of simulations.," In 4, we carry out a series of experiments that demonstrate qualitatively that the MHD turbulence is chaotic, and in 5 this is quantified by computing the Lyapunov exponents for a set of simulations."
 Our conclusions are summarized in 866., Our conclusions are summarized in 6.
 The shearing box system. described in Llawley.Coum-mic&Balbus (1995).. is designed. to represent a very local section of an accretion disk. viewed in corotating coordinates with angular frequency OQ.," The shearing box system, described in \cite{hgb95}, is designed to represent a very local section of an accretion disk, viewed in corotating coordinates with angular frequency $\Omega$."
 Starting with the full set of dynamical equations in evlindrical coordinates. the equations are locally expanded about a fiducial evlindrical radius 2. with (dursαμ.dz) corresponding to evlindrical coordinates (d.edo.dz).," Starting with the full set of dynamical equations in cylindrical coordinates, the equations are locally expanded about a fiducial cylindrical radius $R$, with $(dx, dy, dz)$ corresponding to cylindrical coordinates $(dR,
Rd\phi, dz)$."
 “Phe computational domain is then a Cartesian box. but with the rotational inertial forces (Coriolis and. centrifugal) retained.," The computational domain is then a Cartesian box, but with the rotational inertial forces (Coriolis and centrifugal) retained."
 Phe centrifugal. force nearly balances eravity. leaving a remnant tidal force linear in .c.," The centrifugal force nearly balances gravity, leaving a remnant tidal force linear in $x$."
 All other forces are directly retained., All other forces are directly retained.
 For this svstem. the ideal ALLID equations of motion," For this system, the ideal MHD equations of motion"
to it's radius via y©R/ 120A ,to it's radius via $\gamma\approx120\Delta{}R/R$ ).
It should also be noted that these assume the Cowling R).approximation and neglect self-gravity of the density perturbations., It should also be noted that these assume the Cowling approximation and neglect self-gravity of the density perturbations.
" {Ushomirskyetall(2000) showed that including self-gravity can increase the quadrupole calculations by between 25-200 per cent, and similarly found that self gravity can affect results by factors of between 0.5-3."," \citet{Ushomirsky:2000} showed that including self-gravity can increase the quadrupole calculations by between 25–200 per cent, and similarly \citet{Haskell:2006} found that self gravity can affect results by factors of between 0.5–3."
 For the millisecond recycled pulsars spin-down arguments alone tell us that their quadrupoles must be relatively small (< 10°°kgmm7?)., For the millisecond recycled pulsars spin-down arguments alone tell us that their quadrupoles must be relatively small $\lesssim 10^{30}$ $^2$ ).
" Such a quadrupole would be obtainable with any (see below) meaning that if detected they are not helpful differentiating between theories, although multiple detections could build up useful statistics on their properties and limits on their internal magnetic fields."," Such a quadrupole would be obtainable with any (see below) meaning that if detected they are not helpful differentiating between theories, although multiple detections could build up useful statistics on their properties and limits on their internal magnetic fields."
 Here we will review some of the work presented by [Owen](2005) regarding maximum sustainable quadrupoles for a variety of stellarEoS., Here we will review some of the work presented by \citet{Owen:2005} regarding maximum sustainable quadrupoles for a variety of stellar.
". For stars made from normal neutron star matter (neutrons, protons and electrons) provide a detailed model of the quadrupole (see Eqn."," For stars made from neutron star matter (neutrons, protons and electrons) \citet{Ushomirsky:2000} provide a detailed model of the quadrupole (see Eqn."
 69)., 69).
" applies standard numbers in this definition (and corrects the definition of the shear modulus to be 4x10?ergcm ὃ, or 2.5x10 ffm 3) to give where (co.i) is an averaged strain of 0.1, Rio is the radius in units of 10kkm, and Mi. is the mass in units of 1.4Μο."," \citet{Owen:2005} applies standard numbers in this definition (and corrects the definition of the shear modulus to be $4\ee{29}\,{\rm
erg}\,{\rm cm}^{-3}$ , or $2.5\ee{-4}$ $^{-3}$ ) to give where $\langle\sigma_{0.1}\rangle$ is an averaged strain of $0.1$, $R_{10}$ is the radius in units of km, and $M_{1.4}$ is the mass in units of $1.4\,M_{\odot}$."
 Uncertainties in the star's mass will only affect this estimate by small amounts ggiven and observational bounds on the mass between theoretical]~1—2.5Mo the quadrupole will only vary within about a factor of three from 0.5-1.5.," Uncertainties in the star's mass will only affect this estimate by small amounts given and observational bounds on the mass between $\sim 1-2.5\,M_{\odot}$ the quadrupole will only vary within about a factor of three from 0.5–1.5."
" However, for the radius, with its far larger exponent, small differences can give a larger range of possible quadrupoles."," However, for the radius, with its far larger exponent, small differences can give a larger range of possible quadrupoles."
 If we take a theoretical range from kkm then this can change the quadrupole by about anorder of magnitude., If we take a theoretical range from km then this can change the quadrupole by about anorder of magnitude.
 The most massive stars will also havethe, The most massive stars will also havethe
"The Chandra N-ray ceutrokl position of LES 19271651 is B.A.(2000)19527919.61"".Dec.(20)=65°335 Lae”. which is iu excclleut aereeieut with the optical position (c.f.","The Chandra X-ray centroid position of 1ES 1927+654 is $\rm R.A.(2000) = 19^h 27^m 19.61^s, Dec.(2000) = 65^{\circ}33^{\prime} 54.86^{\prime\prime}$ , which is in excellent agreement with the optical position (c.f."
 Fig., Fig.
 9)., 9).
 The vositional accuracy 1s about one aresec., The positional accuracy is about one arcsec.
 The uuprecedeuted positional accuracy of Chaudra confrius the identification of the stronely variable X-ray source with the distant ealaxy., The unprecedented positional accuracy of Chandra confirms the identification of the strongly variable X-ray source with the distant galaxy.
 All optically bright objects in Fig., All optically bright objects in Fig.
 9 (labeled as 2-6) have beeu spectroscopically identified as late C or carly EK stars., 9 (labeled as 2-6) have been spectroscopically identified as late G or early K stars.
 This rules out anv siguificant contribution of then to the X-ray flux of LES 1927|65L., This rules out any significant contribution of them to the X-ray flux of 1ES 1927+654.
" The positional accuracy of ROSAT is less sensitive than Chandra. however. the centroid position of LES 1927|651 in the ROSAT All-Sky Survey of RÀ(2000) = 19527919,2*x LB. Dec.(2000) = 657:5s""+20"" is consistent with the Chandra position."," The positional accuracy of ROSAT is less sensitive than Chandra, however, the centroid position of 1ES 1927+654 in the ROSAT All-Sky Survey of R.A.(2000) = $\rm 19^h27^m19.2^s \pm 1.3^s$ , Dec.(2000) = $\rm 65^{\circ}33^{\prime}58^{\prime\prime} \pm 20^{\prime\prime}$ is consistent with the Chandra position."
 Iun the following we coustrün the timing propertics obtained from the ROSAT AI-Skv. Survey. ROSAT pointed aud Chandra observations.," In the following we constrain the timing properties obtained from the ROSAT All-Sky Survey, ROSAT pointed and Chandra observations."
 The plotted error bars in the light curves correspond to 10 in the Poisson regie (cf, The plotted error bars in the light curves correspond to 1 $\rm \sigma$ in the Poisson regime (c.f.
 Ctehyels 19560)., Gehrels 1986).
 As a conservative approach we have calculated the total errors of the counts using the relation: 1.0|(counts0.75)., As a conservative approach we have calculated the total errors of the counts using the relation: $\rm 1.0 + \sqrt{(counts\ +\ 0.75)}$.
 LES 1927|65 Lwas observed durius the ROSAT 1uiui-survey for about 5 days between 1990 July 11 aud 16 with a total exposure time of 251 seconds., 1ES 1927+654 was observed during the ROSAT `mini-survey' for about 5 days between 1990 July 11 and 16 with a total exposure time of 254 seconds.
 During the normal survey scan operations. LES 1927|651 was observed for about 11 days between 1990 December 11 and 21.," During the normal survey scan operations, 1ES 1927+654 was observed for about 11 days between 1990 December 11 and 21."
 Fig., Fig.
 1 shows the PSPC survev light curve of LES 1927|651., 1 shows the PSPC survey light curve of 1ES 1927+654.
 The lef panel refers to the iuiSurvey” observations in July 1990 aud the right paucl eives the count rate variations durus the survey scan observations in December 1990., The left panel refers to the `mini-survey' observations in July 1990 and the right panel gives the count rate variations during the survey scan observations in December 1990.
 During the miui-survev he paths of LES 19271651 through the PSPC detector asted only between 5.6 aud 7.8 seconds iud the source passed he PSPC detector L9 times., During the mini-survey the paths of 1ES 1927+654 through the PSPC detector lasted only between 5.6 and 7.8 seconds and the source passed the PSPC detector 49 times.
 During the December observations the source passed the PSPC detector 113 ines and the exposure tines of the iudividual scans rauge )etxeeen 5.6 aud 26.1 seconds., During the December observations the source passed the PSPC detector 143 times and the exposure times of the individual scans range between 5.6 and 26.1 seconds.
 Stumune up all this of LES 19271651 through the PSPC detector during all survey observations. results in a otal exposure time of 3200 seconds.," Summing up all paths of 1ES 1927+654 through the PSPC detector during all survey observations, results in a total exposure time of 3200 seconds."
 Most interestingly are he mnusually laree amplitude and persistent variability. naking this object the second radio-quict ACN showine histype of behavior. the first being IRAS 132213809," Most interestingly are the unusually large amplitude and persistent variability, making this object the second radio-quiet AGN showing thistype of behavior, the first being IRAS 13224–3809"
Iu all inodels tιο adopted radial distribution of the total field streneth :uid cosmic ray electron density was set to vield an exponeuial total power disk with a racial scale leneth ry (Sect.,In all models the adopted radial distribution of the total field strength and cosmic ray electron density was set to yield an exponential total power disk with a radial scale length $r_0$ (Sect.
 L1)., 4.1).
 The intrinsic deerce of polarization was rising linearly from py in the centre to po im the disk outskirts. ry.," The intrinsic degree of polarization was rising linearly from $p_1$ in the centre to $p_2$ in the disk outskirts. $r_0$,"
 pi and po were adjusted to vield the best qualitative aerecmeut of the models with observations., $p_1$ and $p_2$ were adjusted to yield the best qualitative agreement of the models with observations.
 The best results presented in Fig., The best results presented in Fig.
 9ad are as follows:, 9a–d are as follows:
deviation of the zeroth shapelet. a 2-D circular Gaussian.,"deviation of the zeroth shapelet, a 2-D circular Gaussian."
 Then an image |/? is the sum of the shapelets with appropriate coefficients: and a lensed image is the result of applying various operators to the source: where the terms are for convergence. rotation. shear. |-flexion. 3-flexion. twist and turn respectively.," Then an image $|f\rangle$ is the sum of the shapelets with appropriate coefficients: and a lensed image is the result of applying various operators to the source: where the terms are for convergence, rotation, shear, 1-flexion, 3-flexion, twist and turn respectively."
 We wish to discover what these operators are in terms of the ladder operators which aet on, We wish to discover what these operators are in terms of the ladder operators which act on
with tilted rings using the task inAIPS.,with tilted rings using the task in.
" The beam size in this map is 24.5""x17.1"". so we used wwide rings stepped everyd"," The beam size in this map is $\times$, so we used wide rings stepped every."
eWe began by fitting the entire velocity field. (he approaching side only. and the receding onlv and allowing all parameters to vary.," We began by fitting the entire velocity field, the approaching side only, and the receding side only and allowing all parameters to vary."
 Generally speaking the approaching side was harder to fit Chan the receding side or both halves together., Generally speaking the approaching side was harder to fit than the receding side or both halves together.
 We [ound that the center and systemic velocity were quite stable from ring to ring ancl among the three solutions. so we determined the average from the solution to the entire field and fixed those parameters.," We found that the center and systemic velocity were quite stable from ring to ring and among the three solutions, so we determined the average from the solution to the entire field and fixed those parameters."
" The kinematic center is 7 28"" 17.2°+0.4°. 44.4"" (2000). ancl is marked as the large X in Figure 13.."," The kinematic center is $^h$ $^m$ $^s$$\pm$ $^s$, $\pm$ (J2000), and is marked as the large X in Figure \ref{fig:vel}."
 The kinematic center is —0.35. 45.4 {from the center of the optical bar (83.1.1)).," The kinematic center is $-0.35^s$ , $+5.4$ from the center of the optical bar \ref{sec:bar}) )."
 The svstemic velocity was found to be 35541 Ll., The systemic velocity was found to be $\pm$ 1.
 This is the same as values found by Simpson Gottesman (2000: 35640.4 1)) [rom VLA observations and by Stil Israel (2002: 355-1 ')) from WSRT observations., This is the same as values found by Simpson Gottesman (2000; $\pm$ 0.4 ) from VLA observations and by Stil Israel (2002; $\pm$ 1 ) from WSRT observations.
 We then fixed the center and svstemic velocity and fit the velocity field again., We then fixed the center and systemic velocity and fit the velocity field again.
 The variation of the position angle with radius and among the three velocity [ield fits was small. so we lixed the position angle al 2942:3.," The variation of the position angle with radius and among the three velocity field fits was small, so we fixed the position angle at $\pm$."
. This value for the position angle is (he same as that found by Stl Israel (2964 J. and it is ddifferent from the position anele of the optical bar.," This value for the position angle is the same as that found by Stil Israel $\pm$ ), and it is different from the position angle of the optical bar."
 The average position angle is shown as the solid straight line in Figure 13.. and (he variation with radius is shown in the middle panel of Figure 23..," The average position angle is shown as the solid straight line in Figure \ref{fig:vel}, and the variation with radius is shown in the middle panel of Figure \ref{fig:rot}."
 We then fixed the position angle and refit the velocity field., We then fixed the position angle and refit the velocity field.
 The variations in the inclination with the center. svstemic velocity. and position angle fixecl are [αν small.," The variations in the inclination with the center, systemic velocity, and position angle fixed are fairly small."
 ILowever. if a warp is present. the inclination need not be (he same throughout the disk.," However, if a warp is present, the inclination need not be the same throughout the disk."
" Therefore. we adopted an average inclination of 42255* [for the disk interior to a radius of60"".. where the S-clistortion becomes visible in Figure Devond"," Therefore, we adopted an average inclination of $\pm5$ for the disk interior to a radius of, where the S-distortion becomes visible in Figure \ref{fig:vel}."
" 60"".. the inclination determined [or each ring was used in determining the final rotation speed at that radius."," Beyond , the inclination determined for each ring was used in determining the final rotation speed at that radius."
 The variation of inclination with radius is shown in the bottom panel of Figure 23.. and the final rotation curve is shown in the top panel.," The variation of inclination with radius is shown in the bottom panel of Figure \ref{fig:rot}, and the final rotation curve is shown in the top panel."
 We show (he rotation curve lor fits to the receding and approaching halves separately and for the fit to the entire velocity field., We show the rotation curve for fits to the receding and approaching halves separately and for the fit to the entire velocity field.
 The rotation curve in Figure 23. is relatively normal., The rotation curve in Figure \ref{fig:rot} is relatively normal.
 It rises rapidlv in (he center and begins to gently um over around a radius of ((800 pc)., It rises rapidly in the center and begins to gently turn over around a radius of (800 pc).
" By (the rotation speed appears to level ο,", By the rotation speed appears to level off.
 At a radius of ((2.93 kpc) there is an abrupt rise (o a higher rotation speed in the approaching half of the galaxy. clearly caused by. a corresponding drop inthe inclination angle., At a radius of (2.93 kpc) there is an abrupt rise to a higher rotation speed in the approaching half of the galaxy clearly caused by a corresponding drop inthe inclination angle.
 Otherwise. the," Otherwise, the"
time for unsaturated stars brighter than 13th magnitude.,time for unsaturated stars brighter than 13th magnitude.
 We approach target selection by computing. for everv KICclassified star in the field. the radius of the siiallest planet detectable at the 7.1-signma level (threshold at which we expect less (han one statistical false-positive) over the mission lifetime.," We approach target selection by computing, for every KIC-classified star in the field, the radius of the smallest planet detectable at the 7.1-sigma level (threshold at which we expect less than one statistical false-positive) over the mission lifetime."
" The total SNI is the ratio of the transit depth (which depends on the ratio of the planet to star surface area) to the total noise. 2;,4. in the folded and binned lisht curve."," The total SNR is the ratio of the transit depth (which depends on the ratio of the planet to star surface area) to the total noise, $\sigma_{tot}$, in the folded and binned light curve."
 The calculation requires knowledge of the stellar parameters as well as the instrument performance., The calculation requires knowledge of the stellar parameters as well as the instrument performance.
" The per-cadence noise is modeled and scaled by. 1/V; where \,, is the number of transits observed over the 3.5-vear mission duration and by 1/Nui, where Nit is Khe number of 30-minute saniples per transit event (o give σι.", The per-cadence noise is modeled and scaled by $1/\sqrt{N_{tr}}$ where $N_{tr}$ is the number of transits observed over the 3.5-year mission duration and by $1/\sqrt{N_{sample}}$ where $N_{sample}$ is the number of 30-minute samples per transit event to give $\sigma_{tot}$.
" The number of transits depends on (he orbital period for a given stellar mass. M,. and semi-major axis. d. while (he number of samples per transit depends on the transit duration (/;.) which. assuming a circular orbit. is given by: where /y is the central transit duration."," The number of transits depends on the orbital period for a given stellar mass, $M_*$, and semi-major axis, $a$, while the number of samples per transit depends on the transit duration $t_{tr}$ ) which, assuming a circular orbit, is given by: where $t_0$ is the central transit duration."
 It is scaled by w/4 to give the mean transit duration for stars randomly distributed in inclination., It is scaled by $\pi/4$ to give the mean transit duration for stars randomly distributed in inclination.
" The mininun detectable planet radius. 725,5. Is computed at three semi-major axes: 1) the inner radius of the habitable zone (HZ). 2) half that distance. and 3) five stellar radii."," The minimum detectable planet radius, $R_{p,min}$, is computed at three semi-major axes: 1) the inner radius of the habitable zone (HZ), 2) half that distance, and 3) five stellar radii."
 A planet is not considered detectable unless the total SNR exceeds 7.1-sigma and at least three transits occur over the 3.5-vear mission lifetime., A planet is not considered detectable unless the total SNR exceeds 7.1-sigma and at least three transits occur over the 3.5-year mission lifetime.
" We use (he standard solar-svstem inner HZ radius of IxXasting.Whitmire.&Revnolds(1992) (0.95 AU) and scale it by the ratio of the stellar luminosity (computed [rom the 7;;; and £2, archived in the KIC) to that of the Sun.", We use the standard solar-system inner HZ radius of \citet{hz} (0.95 AU) and scale it by the ratio of the stellar luminosity (computed from the $T_{eff}$ and $R_*$ archived in the KIC) to that of the Sun.
Surveying the radio sky at low frequencies Cz300 MIIZ) is a unique tool for investigating many questions related to the formation aud evolution of massive galaxies. quasars and clusters of galaxies (e.g.?)..,"Surveying the radio sky at low frequencies $\lesssim 300$ MHz) is a unique tool for investigating many questions related to the formation and evolution of massive galaxies, quasars and clusters of galaxies \citep[e.g.,][]{miley2008}."
 Low-frequency racio observations benefit frou the steepness of radio spectra of various types of cosmic radio sources. such as massive IHzhRCs (high-redshift radio galaxies: redshift ;2 2) aud diffuse halo relic cutission iu nearby galaxw clusters (2< 0.1).," Low-frequency radio observations benefit from the steepness of radio spectra of various types of cosmic radio sources, such as massive HzRGs (high-redshift radio galaxies; redshift $z \gtrsim 2$ ) and diffuse halo relic emission in nearby galaxy clusters $z \lesssim 0.1$ )."
 IIZRCis are amonest the most massive galaxies iu the carly Universe (e.g...?).. usually located in forming galaxy clusters with total masses of more than 1015 7)..," HzRGs are amongst the most massive galaxies in the early Universe \citep[e.g.,][]{miley2008}, usually located in forming galaxy clusters with total masses of more than $10^{14}_{}$ \citep[e.g.,][]{venemans2007}."
" The most cficient way of finding IIZRCs is to focus on USS (ultra-steep spectrun: 5,xp""a withaX 1) radio sources (??).."," The most efficient way of finding HzRGs is to focus on USS (ultra-steep spectrum; $S_{\nu} \propto \nu^{\alpha}$ with $\alpha \lesssim -1$ ) radio sources \citep{rottgering1997,debreuck2002}."
 This was reinforced by ? who showed that the radio spectra of WzRGs in general do not show spectral curvature. but are straight.," This was reinforced by \citet{klamer2006} who showed that the radio spectra of HzRGs in general do not show spectral curvature, but are straight."
 The USS selection criteria appear to hold down to very low flux levels (6.9.. ?)..," The USS selection criteria appear to hold down to very low flux levels \citep[e.g.,][]{afonso2011}."
 Concentrating on the faiutest sources frou surveys made at the lowest frequencies is therefore au obvious wav of pushing the distance linüt for WzRCs bevoud the present highestο redshift of TN J0921-2201 at 2=5.1 (?) and probing massive ealaxy formation iuto the epoch of relouization., Concentrating on the faintest sources from surveys made at the lowest frequencies is therefore an obvious way of pushing the distance limit for HzRGs beyond the present highest redshift of TN J0924-2201 at $z = 5.1$ \citep{vanbreugel1999} and probing massive galaxy formation into the epoch of reionization.
 Galaxy clusters containing diffuse radio sources appear to have laree Nav lDunünosifies aud galaxy velocity dispersions (e.g.7). which are thought to be characteristics of cluster merger activity (6.8...TP.," Galaxy clusters containing diffuse radio sources appear to have large X-ray luminosities and galaxy velocity dispersions \citep[e.g.,][]{hanisch1982}, which are thought to be characteristics of cluster merger activity \citep[e.g.,][]{giovannini2000,kempner2001}."
 Svuchrotron halos aud relies provide unique diagnostics for studving the magnetic field. plasma distribution aud eas notions within clusters. important inputs to models of cluster evolution (e.g...2)..," Synchrotron halos and relics provide unique diagnostics for studying the magnetic field, plasma distribution and gas motions within clusters, important inputs to models of cluster evolution \citep[e.g.,][]{feretti2004}."
 Cluster svuchrotron. enissiou is known to be related to the N-rav gas aud pinpoints shocks in the gas., Cluster synchrotron emission is known to be related to the X-ray gas and pinpoints shocks in the gas.
 Further. cluster radio cussion usually has steep radio spectra (a«—1). the radiatiug electrons are old aud can provide fossil records of the cluster history (e.g...T)..," Further, cluster radio emission usually has steep radio spectra $\alpha < -1$ ), the radiating electrons are old and can provide fossil records of the cluster history \citep[e.g.,][]{miley1980}."
 Several low-frequency survevs have been performed m the past. such as the Caunbridge surveys 3€. 1C. 6C aud TC at 159. 178. 151 aud again 151 MIIEz. respectively (0271777). the UTR-2 sky survey between- 10-25 MITZ (?). the VLSS at 71 MIIz (2). aud the ougoiuz MRT sky survey at 151.5 ΑΠ (e.g.?Y.," Several low-frequency surveys have been performed in the past, such as the Cambridge surveys 3C, 4C, 6C and 7C at 159, 178, 151 and again 151 MHz, respectively \citep{edge1959,bennett1962,pilkington1965,gower1967,hales1988,hales2007}, , the UTR-2 sky survey between 10-25 MHz \citep{braude2002}, the VLSS at 74 MHz \citep{cohen2007} and the ongoing MRT sky survey at 151.5 MHz \citep[e.g.,][]{pandey2007}."
 These SUPVOVS abe Iuited im sensitivity aud angular resolutio- nainlv due to man-made REL ionospheric phase distortions and wide-field inaeims problems.," These surveys are limited in sensitivity and angular resolution, mainly due to man-made RFI, ionospheric phase distortions and wide-field imaging problems."
" Recent developments iu data reduction techniques make it possible to perform. deeper surveys (=50 Ly of the knw-frequency skv at higher resolution ( 30"").", Recent developments in data reduction techniques make it possible to perform deeper surveys $\lesssim 50$ ) of the low-frequency sky at higher resolution $\lesssim 30\arcsec$ ).
 One telescope that senificautlv improved his situation is the CAIRT., One telescope that significantly improved this situation is the GMRT.
" A few deep. single-pointing surveys at 153 ΛΠΙ (οἱ,22?) have been performed. vielding noise levels between 0.7-2 and resolutions between20-30""."," A few deep, single-pointing surveys at 153 MHz \citep[e.g.,][]{ishwara2007,sirothia2009,ishwara2010} have been performed, yielding noise levels between 0.7-2 and resolutions between."
" Aud the is a new. ongoing 153 MIIZ GAIRT sky survey. ainied at covering the full northern sky. down o DEC>BOP ata ~20"" resolution iud à 7.9 noise."," And the is a new, ongoing 153 MHz GMRT sky survey, aimed at covering the full northern sky down to $\dec{} > -30\degs$ at a $\sim 20\arcsec$ resolution and a $7-9$ noise."
 Iu this article we preseut deep. high-resolution GMRT observations at 153 MIIz of the NOAO field.," In this article we present deep, high-resolution GMRT observations at 153 MHz of the NOAO field."
 The field is a large (9square degree) northern field that has been targeted by survevs spanning the eutire clectromaguctic spectrum., The field is a large $\sim 9$square degree) northern field that has been targeted by surveys spanning the entire electromagnetic spectrum.
 This field has been extensively surveved with radio telescopes inchiding the WSRT at Lt GIIz (2).. the VLA at 325 MIIz (?2).. and will be complemented with deep 71 MIIzZ EVLA observations.," This field has been extensively surveyed with radio telescopes including the WSRT at 1.4 GHz \citep{devries2002}, the VLA at 325 MHz \citep{croft2008}, and will be complemented with deep 74 MHz EVLA observations."
 The large northern NDWES survey (7). provided 6 colour nuages (By RETIN) to very fait optical and. NIR flux limits.," The large northern NDWFS survey \citep{jannuzi1999} provided 6 colour images $B^{}_{W} \, R \, I \, J \, H \, K$ ) to very faint optical and NIR flux limits."
 Additional. deeper NIR images in JNe are available from the FLAMENsurvey (?).. while additional Lhaud maages are available frou the :Dootes campaigu," Additional, deeper NIR images in $J \, K^{}_{S}$ are available from the FLAMEXsurvey \citep{elston2006}, , while additional $z$ -band images are available from the $z$ Bootes campaign"
"the SMBH may have varying angular momentum, which can shift suddenly as massive clumps of gas develop and move through the disk.","the SMBH may have varying angular momentum, which can shift suddenly as massive clumps of gas develop and move through the disk."
 The properties of the gas that is ultimately accreted may then determine the spin and subsequently the mode of feedback produced by the SMBH., The properties of the gas that is ultimately accreted may then determine the spin and subsequently the mode of feedback produced by the SMBH.
" We have studied the transport of gas in the circumnuclear region of a disk galaxy within a cosmological simulation at different redshifts, for different SMBH masses, and for a run including an approximation of optically thick cooling."," We have studied the transport of gas in the circumnuclear region of a disk galaxy within a cosmological simulation at different redshifts, for different SMBH masses, and for a run including an approximation of optically thick cooling."
" The mass accretion rate is not steady, but fluctuates randomly and substantially, the accretion rate through the circumnuclear disk being almost as often negative as positive."," The mass accretion rate is not steady, but fluctuates randomly and substantially, the accretion rate through the circumnuclear disk being almost as often negative as positive."
" This result is consistent with that of ?,, who find a large amount of variation in the instantaneous accretion rates in their galaxy simulations on scales <1kpc."," This result is consistent with that of \citet{HopkinsQuataert09}, who find a large amount of variation in the instantaneous accretion rates in their galaxy simulations on scales $< 1 \dim{kpc}$."
 We find that there is no preferred timescale for accretion over the course of the million years spanned by each of the simulations., We find that there is no preferred timescale for accretion over the course of the $\sim$ million years spanned by each of the simulations.
" The flat slope of the Fourier transform of the accretion rate characterizes the fluctuations as a function of timescale, revealing the stochastic nature of accretion in the simulations."," The flat slope of the Fourier transform of the accretion rate characterizes the fluctuations as a function of timescale, revealing the stochastic nature of accretion in the simulations."
" This complex and chaotic behavior is apparent at each of the three redshifts explored in detail here: z=3, 4, and 6, as well as in z=4 simulations containing black holes with larger masses, and the z=4 run including optically thick cooling."," This complex and chaotic behavior is apparent at each of the three redshifts explored in detail here: $z=3$, $4$, and $6$, as well as in $z=4$ simulations containing black holes with larger masses, and the $z=4$ run including optically thick cooling."
" The dynamic and turbulent nature of the simulated circumnuclear disk is not well modeled by Bondi accretion, even when using a modified prescription that takes into account the vorticity and turbulent properties of the gas."," The dynamic and turbulent nature of the simulated circumnuclear disk is not well modeled by Bondi accretion, even when using a modified prescription that takes into account the vorticity and turbulent properties of the gas."
 Bondi prescriptions do not take into account the effect of the disk’s self-gravity., Bondi prescriptions do not take into account the effect of the disk's self-gravity.
" Additionally, the modified Bondi accretion rates, estimated from the properties of the disk in the highest-resolution part of the simulation (where the density rises steeply with decreasing radius), are highly super-Eddington on the smallest scales a radiative efficiency of 0.1)."," Additionally, the modified Bondi accretion rates, estimated from the properties of the disk in the highest-resolution part of the simulation (where the density rises steeply with decreasing radius), are highly super-Eddington on the smallest scales (assuming a radiative efficiency of $0.1$ )."
" As the Eddington(assuming rate provides an upper limit for the accretion rate in the presence of radiative feedback from the SMBH, highly super-Eddington rates are not likely to endure in nature."," As the Eddington rate provides an upper limit for the accretion rate in the presence of radiative feedback from the SMBH, highly super-Eddington rates are not likely to endure in nature."
 The Eddington rate (or a few times the Eddington rate) is set as an upper limit to the accretion rate in many of the simulations that employ Bondi type prescriptions to model accretion ????)..," The Eddington rate (or a few times the Eddington rate) is set as an upper limit to the accretion rate in many of the simulations that employ Bondi type prescriptions to model accretion \citep[e.g.,][]{Springeletal05a, DiMatteo05, Lietal07b, DiMatteo08}."
" On scales corresponding to the spatial resolution(e.g., of those simulations (2100pc), the accretion rates predicted by the modified Bondi prescription in the present simulations are closer to the Eddington limit than they are at smaller scales."," On scales corresponding to the spatial resolution of those simulations $\gtrsim 100 \dim{pc}$ ), the accretion rates predicted by the modified Bondi prescription in the present simulations are closer to the Eddington limit than they are at smaller scales."
" However, black holes in other simulations spend the majority of time accreting well below this limit, at substantially sub-Eddington rates."," However, black holes in other simulations spend the majority of time accreting well below this limit, at substantially sub-Eddington rates."
" The difference between the rates determined here and those of other simulations is even larger when comparing with prescriptions that multiply the Bondi accretion rate by a large factor to approximate the effects of the small scale physics, since no such factor has been included in our calculations dis-cussionoftheparametero ???).."," The difference between the rates determined here and those of other simulations is even larger when comparing with prescriptions that multiply the Bondi accretion rate by a large factor to approximate the effects of the small scale physics, since no such factor has been included in our calculations \citep[see discussion of the parameter
 $\alpha$][]{BoothSchaye09, JohanssonBN09, JohanssonNB09}."
" However, it(see is not straightforward to make a direct comparison between accretion rates in the present simulations and the rates in other simulations that contain prescriptions for AGN feedback."," However, it is not straightforward to make a direct comparison between accretion rates in the present simulations and the rates in other simulations that contain prescriptions for AGN feedback."
" As shown in galaxy merger simulations (e.g., ?7), the presence of AGN feedback regulates black hole growth by forcing gas out of the circumnuclear region."," As shown in galaxy merger simulations \citep[e.g.,][]{Springeletal05a,
 Debuhretal09}, the presence of AGN feedback regulates black hole growth by forcing gas out of the circumnuclear region."
 Future work incorporating AGN feedback into the present simulations will address this issue., Future work incorporating AGN feedback into the present simulations will address this issue.
" The absence of AGN feedback in our simulations may result in an excessively dense circumnuclear gas disk, which corresponds to large, super-Eddington accretion rates within the Bondi prescription."," The absence of AGN feedback in our simulations may result in an excessively dense circumnuclear gas disk, which corresponds to large, super-Eddington accretion rates within the Bondi prescription."
" Allowing the black hole particle to grow in situ in our simulations, or using a more physically motivated recipe for star formation in the zoom-in simulation would further change the distribution of mass in the circumnuclear gas disk."," Allowing the black hole particle to grow in situ in our simulations, or using a more physically motivated recipe for star formation in the zoom-in simulation would further change the distribution of mass in the circumnuclear gas disk."
" The circumnuclear disk is self-gravitating, almost certainly behaving outside the Bondi regime, even with the modifications of ?.."," The circumnuclear disk is self-gravitating, almost certainly behaving outside the Bondi regime, even with the modifications of \citet{Krumholzetal06}."
" This result reinforces the need for high-resolution simulations incorporating detailed gas dynamics and radiative processes, in order to truly model the complicated dynamics on small scales, which ultimately govern accretion onto SMBHs."," This result reinforces the need for high-resolution simulations incorporating detailed gas dynamics and radiative processes, in order to truly model the complicated dynamics on small scales, which ultimately govern accretion onto SMBHs."
 The chaotic behavior of the disk may be consistent with models suggesting that stochastic accretion of molecular clouds from the circumnuclear region of, The chaotic behavior of the disk may be consistent with models suggesting that stochastic accretion of molecular clouds from the circumnuclear region of
"floor level. the S,f,Lx relationis not.","floor level, the $S_{\nu,arc}/f_{\nu}-L_X$ relation is not."
 Fitting all 15 clusters for which we have estimates of both the Iuninosityv aud SZ effect flux deusity. we fiud a best-fit entropy. floor level of Ay=310!2 keV eur.," Fitting all 15 clusters for which we have estimates of both the luminosity and SZ effect flux density, we find a best-fit entropy floor level of $K_0 = 310^{+70}_{-70}$ keV $^2$."
 However. the fit is not a good one. as is evident from the residuals plotted iu Figure 7 aud the calculated reduced-\? (4Z=3L31/11— 127).," However, the fit is not a good one, as is evident from the residuals plotted in Figure 7 and the calculated $\chi^2$ $\chi^2_{\nu} = 34.34/14 = 4.27$ )."
 The two massive cooling flow clusters. AlS35 and RAJL3175-1115 are obvious outliers, The two massive cooling flow clusters A1835 and RXJ1347.5-1145 are obvious outliers.
 Iguormg these two clusters. we obtain Ay=38515) keV eu? (26 error bars) and a significantly improved (AZ=13.79/12 1.15).," Ignoring these two clusters, we obtain $K_0 = 
385^{+75}_{-70}$ keV $^2$ $2\sigma$ error bars) and a significantly improved fit $\chi^2_{\nu} = 13.79/12 = 1.15$ )."
 This best-fit value of Avy is cousisteut with the results of 83.2 aud $3.3 and also with N-rav observations of nearby massive clusters., This best-fit value of $K_0$ is consistent with the results of 3.2 and 3.3 and also with X-ray observations of nearby massive clusters.
" Splitting the sample iuto two redshift bius (<0.3 and > 0.3). we also fud there to be uo difference in the cutropy floors of ""nearby and ""distaut ealaxy clusters."," Splitting the sample into two redshift bins $< 0.3$ and $> 0.3$ ), we also find there to be no difference in the entropy floors of “nearby” and “distant” galaxy clusters."
 This is tlie same as was found for the Searedfedo relation.," This is the same as was found for the $S_{\nu,arc}/f_{\nu}-y_0$ relation."
 Every single SZ effect scaling relation that we have exanuned is consistent with or requires a high value for the eutropv floor level. Avy.," 	 Every single SZ effect scaling relation that we have examined is consistent with or requires a high value for the entropy floor level, $K_0$."
" Iu fact. several of the trends. such asthe ywPy. yy—Mírsgo). and Si,fego xelations. rule out the standard sclfsimilay model at niu signa."," In fact, several of the trends, such as the $y_0-T_X$, $y_0-M(r_{500})$, and $S_{\nu,arc}/f_{\nu}-y_0$ relations, rule out the standard self-similar model at many sigma."
 Neither of the relations show any convincing evidence for strong evolution in νο out to the limit to which our sample extends (2~ 0.7)., Neither of the relations show any convincing evidence for strong evolution in $K_0$ out to the limit to which our sample extends $z \sim 0.7$ ).
 It is interestingthat the estimates of Ay from the various relations do not always agree., It is interesting that the estimates of $K_0$ from the various relations do not always agree.
" For example. the best-fit eutropv fHoors from the yoPy and Si,/f,Lx treuds are consistent with results frou studies of X-ray scaling relations of nearby massive clusters (οιο,, Babul et al."," For example, the best-fit entropy floors from the $y_0-T_X$ and $S_{\nu,arc}/f_{\nu}-T_X$ trends are consistent with results from studies of X-ray scaling relations of nearby massive clusters (e.g., Babul et al."
" 2002) iid the results of our SZ effect-Innimosity relations but are mareially lower than the results from our S,4,./f,;Yo iul yyM(rsoo) relations."," 2002) and the results of our SZ effect-luminosity relations but are marginally lower than the results from our $S_{\nu,arc}/f_{\nu}-y_0$ and $y_0-M(r_{500})$ relations."
 A conservative estimate of theπο value of Ay. however. iust. fall iu between the results of each of the individual relations: i.c.. 300 keV cue <AyXGOO keV ens.," A conservative estimate of the value of $K_0$, however, must fall in between the results of each of the individual relations; i.e., $300$ keV $^2$ $\lesssim K_0 \lesssim 600$ keV $^2$."
 This is clearly illustrated iu Fieme 58 through a plot of A47 vs. Ny for the relations we have examined (A4?=\?hp where ης is the 4? for the hest-fit power-law model for cach of the scaling relations)., This is clearly illustrated in Figure 8 through a plot of $\Delta \chi^2$ vs. $K_0$ for the relations we have examined $\Delta \chi^2 \equiv \chi^2 - \chi^2_{BF}$ where $\chi^2_{BF}$ is the $\chi^2$ for the best-fit power-law model for each of the scaling relations).
 A naive simultaueous fit to all of the relations. ieuoriug correlated variables and errors. vields Ry=bo!on keV cu? level). which is remarkably simular to that derived solely from X-ray data (c.f.," A naive simultaneous fit to all of the relations, ignoring correlated variables and errors, yields $K_0 = 430^{+60}_{-55}$ keV $^2$ level), which is remarkably similar to that derived solely from X-ray data (c.f."
 Babul al., Babul et al.
 2002)., 2002).
 At present. it is unclear why some of the scaling relations do not converge on the same value of Ay.," At present, it is unclear why some of the scaling relations do not converge on the same value of $K_0$."
 A more detailed ialysis of this would require talking into account all of the observational and analysis biases (associated with both N-ray aud SZ effect). which is bevoud the scope this paper.," A more detailed analysis of this would require taking into account all of the observational and analysis biases (associated with both X-ray and SZ effect), which is beyond the scope of this paper."
 We expect that it will be possible to get much amore firm handle on these differeuces im the near future., We expect that it will be possible to get a much more firm handle on these differences in the near future.
 First. the ummber of high redshift clusters observed through the SZ effect is increasingly rapidly (sec Reese et al.," First, the number of high redshift clusters observed through the SZ effect is increasingly rapidly (see Reese et al."
 2002) and with it comes improved statistics., 2002) and with it comes improved statistics.
 Second. and perhaps more important. a nuniber of new experiments (or substantial upgrades to existing oues) are already uncer construction aud will ereatly improve the quality of the SZ effect observations.," Second, and perhaps more important, a number of new experiments (or substantial upgrades to existing ones) are already under construction and will greatly improve the quality of the SZ effect observations."
 For example. the bandwidths of the future aud the upgradedOVRO array are expected to be nearly an order of magnitude larger than that of curent interferometers and. as such. will lead to substantial improvements iu the signal-to-noise ratios of SZ effect data.," For example, the bandwidths of the future and the upgraded array are expected to be nearly an order of magnitude larger than that of current interferometers and, as such, will lead to substantial improvements in the signal-to-noise ratios of SZ effect data."
 Tighter constraints on the SZ effect surface brightuess profiles of clusters will then be possible and. in turn. more stringent lanits cau be placed ou the eutropy distributions of these clusters.," Tighter constraints on the SZ effect surface brightness profiles of clusters will then be possible and, in turn, more stringent limits can be placed on the entropy distributions of these clusters."
 Indeed. we demoustrate below that observations with the aud the upgradedOVRO QO.liu array will allow one to coustrain the amount of excess entropy im clusters all the way out to 2~ aud. best of all. without the need for any N-rav results.," Indeed, we demonstrate below that observations with the and the upgraded 0.1in array will allow one to constrain the amount of excess entropy in clusters all the way out to $z \sim 2$ and, best of all, without the need for any X-ray results."
 lt was briefly discussed in 83.1 that current SZ effect data alone cannot tightly constrain the three paramcters of the surface briehtuess | model., 	 It was briefly discussed in 3.1 that current SZ effect data alone cannot tightly constrain the three parameters of the surface brightness $\beta$ model.
 A large degeueracy is present in the shape paraueters. .§ and 0. (ce... Carlstrom et al.," A large degeneracy is present in the shape parameters, $\beta$ and $\theta_c$ (e.g., Carlstrom et al."
 1996: Caeeo et al., 1996; Grego et al.
 2000: 2001)., 2000; 2001).
" A uunuber of authors have dealt with this problem bv using the values of 9 and 0, obtained from modcling theπι surface brightuess of the cluster (e.g. Patel et al."," A number of authors have dealt with this problem by using the values of $\beta$ and $\theta_c$ obtained from modeling the surface brightness of the cluster (e.g., Patel et al."
 2000: Crainge et al., 2000; Grainge et al.
 2002a: 2002b: LaRoque ct al., 2002a; 2002b; LaRoque et al.
 2003)., 2003).
 In the case of low/intermediate redshift clusters. N-rav observations provide tighter constraints on these piruneters than do SZ effect observations.," In the case of low/intermediate redshift clusters, X-ray observations provide tighter constraints on these parameters than do SZ effect observations."
" Ποπονα, a truly A-vayv-independeut probe of the ICAL requires that oulv SZ effect data be used in the analysis."," However, a truly X-ray-independent probe of the ICM requires that only SZ effect data be used in the analysis."
 By using a joint niaxinuun-likelihood fit to both the X-ray aud SZ effect surface brieltucsses of clusters. Reese et al. (," By using a joint maximum-likelihood fit to both the X-ray and SZ effect surface brightnesses of clusters, Reese et al. ("
2000: 2002) found a compromise between these two scenarios.,2000; 2002) found a compromise between these two scenarios.
 Pushing the analysis of the ICAL to ligher redshifts than cousidered by Reese et al. (, Pushing the analysis of the ICM to higher redshifts than considered by Reese et al. (
2000: 2002). however. will likely brine us iuto a regine that is uniquely accessible to,"2000; 2002), however, will likely bring us into a regime that is uniquely accessible to"
classification of galaxies with respect to their global. unobscured star-formation activity by means of the DI colour.,"classification of galaxies with respect to their global, unobscured star-formation activity by means of the $B-R$ colour."
 Near-IR photometry was extracted from the 2MASS database(2).. oroviding J. ff. and band photometry for all cluster members.," Near-IR photometry was extracted from the 2MASS database\citep{Skrutskie06}, providing $J$, $H$, and band photometry for all cluster members."
 We used the magnitude values from the Extended Source Catalogue (XSC) where available: where the objects were not present in his catalog. the Point Source Catalogue (PSC) was used instead.," We used the magnitude values from the Extended Source Catalogue (XSC) where available; where the objects were not present in this catalog, the Point Source Catalogue (PSC) was used instead."
 Undetected galaxies were assigned an upper magnitude limit consistent with the 2MASS limits., Undetected galaxies were assigned an upper magnitude limit consistent with the 2MASS limits.
GALEX near- and. far-UV shotometry was obtained from the Nearby Galaxy Survey (NGS) in he GR4/5 data release., near- and far-UV photometry was obtained from the Nearby Galaxy Survey (NGS) in the GR4/5 data release.
 Where no significant UV flux was detected. we assigned an upper limit consistent with the NGS limits in the field of A3112.," Where no significant UV flux was detected, we assigned an upper limit consistent with the NGS limits in the field of A3112."
 All optical and near-IR magnitudes were converted o the AB system., All optical and near-IR magnitudes were converted to the AB system.
 Optical cluster members are identified using the technique presented in ?.., Optical cluster members are identified using the technique presented in \citet{Biviano06}.
 We identify 146 dynamically bound optical cluster members in the field observed with BLAST. scattered across the cluster area from its core to a maximum distance of 3.4 5.+ Mpc (at the cluster redshift).," We identify 146 dynamically bound optical cluster members in the field observed with BLAST, scattered across the cluster area from its core to a maximum distance of 3.4 $h^{-1}$ Mpc (at the cluster redshift)."
 We derive a dynamical mass of (4.7 + 0.6) I0AL. within {ους 1.79 b+ Mpe is the radius where the overdensity of the cluster with respect to the cosmic background density exceeds 200)., We derive a dynamical mass of (4.7 $\pm$ 0.6) $\times$ $^{14} M_{\odot}$ within = 1.79 $h^{-1}$ Mpc is the radius where the overdensity of the cluster with respect to the cosmic background density exceeds 200).
 This value and the cluster X-ray luminosity of 4.2. 10 WL. 101 L. o (2) identify A3112 as an intermediate mass system., This value and the cluster X-ray luminosity of 4.2 $\times$ $^{37}$ W (1.1 $\times$ $^{11}$ $_{\odot}$ ) \citealt{Boehringer04}) ) identify A3112 as an intermediate mass system.
 We fit the cluster red sequence (RS) in the (2 /7) vs. plane., We fit the cluster red sequence (RS) in the $B-R$ ) vs. plane.
 This allows for galaxy classification to be carried out independently with respect to stellar mass (traced. by the magnitude) and to the unobscured. star-formation activity (whose signature can be identified in the £2// colour). thus minimizing any residual colour term in the colour-magnitude= plane.," This allows for galaxy classification to be carried out independently with respect to stellar mass (traced by the magnitude) and to the unobscured star-formation activity (whose signature can be identified in the $B-R$ colour), thus minimizing any residual colour term in the colour-magnitude plane."
 We fit the RS through a recursive 3o-clipping algorithm. which converges to the tit: Figure 2. shows the cluster colour-magnitude diagram.," We fit the RS through a recursive $\sigma$ -clipping algorithm, which converges to the fit: Figure \ref{redseq} shows the cluster colour-magnitude diagram."
 We assume as a reference for the obtained by ? (converted o the AB system) on a large sample of galaxies from 2MASS, We assume as a reference for the obtained by \citet{Cole01} (converted to the AB system) on a large sample of galaxies from 2MASS.
 Out of the 146 identified cluster members. 99 lie along the RS. while 21 of them populate the colour-magnitude plane downwards he RS (see Figure 2).," Out of the 146 identified cluster members, 99 lie along the RS, while 21 of them populate the colour-magnitude plane downwards the RS (see Figure \ref{redseq}) )."
 Interestingly. a similar number of cluster members (26) lie upwards the RS.," Interestingly, a similar number of cluster members (26) lie upwards the RS."
 These very red galaxies could in principle be either voung and dusty or very old evolved galaxies whose dust reservoir is completely depleted., These very red galaxies could in principle be either young and dusty or very old evolved galaxies whose dust reservoir is completely depleted.
 BLAST observations are a powerful tool to solve this degeneracy without the need for optical spectroscopy. since sub-mm emission Is a direct probe of dust.," BLAST observations are a powerful tool to solve this degeneracy without the need for optical spectroscopy, since sub-mm emission is a direct probe of dust."
 We derive the unobscured SFR of each cluster member fromGALEX broadband photometry. using the approach deseribed by ?..," We derive the unobscured SFR of each cluster member from broadband photometry, using the approach described by \citet{Schiminovich05}."
 On average. cluster galaxies have negligible or very small LAL. +) SFRs.," On average, cluster galaxies have negligible or very small $< 1$ ) SFRs."
 However. 15 cluster members (i.e. about of our sample) show moderate SFRs (25 4).," However, 15 cluster members (i.e. about of our sample) show moderate SFRs $\ga 5$ )."
 We also calculate the stellar mass of cluster members from photometry using the same recipe provided by ?.., We also calculate the stellar mass of cluster members from photometry using the same recipe provided by \citet{Arnouts07}.
 We assume the relation for active/blue galaxies (parameter set | in Arnouts et al., We assume the relation for active/blue galaxies (parameter set 1 in Arnouts et al.
 2007) for galaxies below the RS. and the relation for quiescent/red galaxies for (parameter set 2) for galaxies along and above the RS.," 2007) for galaxies below the RS, and the relation for quiescent/red galaxies for (parameter set 2) for galaxies along and above the RS."
 We obtain stellar masses across two orders of magnitude. from 7«.107 for the smallest galaxies in our sample. to LS«.107 for the central galaxy.," We obtain stellar masses across two orders of magnitude, from $7\times10^{8}$ for the smallest galaxies in our sample, to $1.8\times10^{10}$ for the central galaxy."
 We stack the BLAST flux density maps on the cluster members catalogue to assess the mean flux density in the 3 BLAST bands., We stack the BLAST flux density maps on the cluster members catalogue to assess the mean flux density in the 3 BLAST bands.
 We obtain stacked values of 16.6-£2.5. 6.13:1.9. and 1.52: 1.3 mJy at 250. 350. andmicron. respectively.," We obtain stacked values of $\pm$ 2.5, $\pm$ 1.9, and $\pm$ 1.3 mJy at 250, 350, and, respectively."
 This converts. to a mean SFR. of Q4 per cluster member and a total. SFR. of 584 for the whole sample of cluster members., This converts to a mean SFR of 0.4 per cluster member and a total SFR of 58.4 for the whole sample of cluster members.
" We thus calculate a specific SFR. ΡΕ=SER""(ALi10M.)12.433.4vr. +."," We thus calculate a specific SFR, $\Sigma\rmn{SFR} = \rmn{SFR}^{\rmn{tot}}/(\rmn{M}_{\rmn{dyn}}/10^{14} \rmn{M}_{\odot}) = 12.4 \pm 3.4~\rmn{yr}^{-1}$ ."
 This is in very good agreement with/ the relation found by ? (Figure 3z cf., This is in very good agreement with the relation found by \citet{Cowie04} (Figure \ref{specsfr}; cf.
 also ? and 2»)., also \citealt{Geach06} and \citealt{Haines09b}) ).
 Far-infrared. spectral energy distributions (SEDs hereafter) have been fit to cluster members identified as BLAST counterparts. to help identify their nature.," Far-infrared spectral energy distributions (SEDs hereafter) have been fit to cluster members identified as BLAST counterparts, to help identify their nature."
 The direct association of optical objects with sub-mm sources is usually far from trivial. mainly due to the large beam size in the sub-mm.," The direct association of optical objects with sub-mm sources is usually far from trivial, mainly due to the large beam size in the sub-mm."
 Ideally. radio observations would be required to pinpoint the precise position to be matched with optical catalogues (2:: 29).," Ideally, radio observations would be required to pinpoint the precise position to be matched with optical catalogues \citealt{Dye09}; \citealt{Ivison10}) )."
 However. we notice that in the field of A3112. in each case that a robust 5a) source is detected. an optical cluster member is present within |-σ of the positional uncertainty from the source peak.," However, we notice that in the field of A3112, in each case that a robust $\geq 5\sigma$ ) source is detected, an optical cluster member is present within $\sigma$ of the positional uncertainty from the source peak."
 Moreover. these BLAST sources are all found to be brighter at than at 350 ormicron.. suggesting that they originate from low-redshift galaxies.," Moreover, these BLAST sources are all found to be brighter at than at 350 or, suggesting that they originate from low-redshift galaxies."
 As shown later in Section 3.2.. these sources are found to have low temperatures (7< 20KK). consistent with being quiescent star-formers at the cluster redshift.," As shown later in Section \ref{indsources}, these sources are found to have low temperatures $T<20$ K), consistent with being quiescent star-formers at the cluster redshift."
 Moreover. for these sources a single counterpart is usually detected within the positional uncertainty. ruling out the presence of other low-z galaxies not associated to the cluster that could contribute to the sub-mm signal.," Moreover, for these sources a single counterpart is usually detected within the positional uncertainty, ruling out the presence of other low-z galaxies not associated to the cluster that could contribute to the sub-mm signal."
 We thus conclude that for the scopes of this work. when these criteria are met (i.e. robust detection of a BLAST source and presence of a single optical counterpart within the positional uncertainty). association of optical cluster members to BLAST sources can be considered robust.," We thus conclude that for the scopes of this work, when these criteria are met (i.e. robust detection of a BLAST source and presence of a single optical counterpart within the positional uncertainty), association of optical cluster members to BLAST sources can be considered robust."
 In addition to 3c detections atmicron.. we also include sources with a —4c detection both at 250 andmicron.. to increase the number of contirmed counterparts while still maintaining a criterion of robustness.," In addition to $\sigma$ detections at, we also include sources with a $>4\sigma$ detection both at 250 and, to increase the number of confirmed counterparts while still maintaining a criterion of robustness."
 We thus select tive galaxies. shown in Figure + and whose data appear in Table |.," We thus select five galaxies, shown in Figure \ref{cmsources} and whose data appear in Table 1."
 Of the tive selected galaxies. JJO3|700-441.605 is also the source IRAS 03152-4427.," Of the five selected galaxies, J031700–441605 is also the source IRAS 03152–4427."
 Several other galaxies are in good positional mateh with BLAST sources. however they are either not robustly detected (Le. « do) at BLAST wavelengths. not cluster members or missing a spectroscopic redshift altogether.," Several other galaxies are in good positional match with BLAST sources, however they are either not robustly detected (i.e. $< 4\sigma$ ) at BLAST wavelengths, not cluster members or missing a spectroscopic redshift altogether."
 We do not include these galaxies in our analysis to avoid biasing our results., We do not include these galaxies in our analysis to avoid biasing our results.
 SEDs are fitted using the same method explained and used in 9 taking into account filter response curves. calibration uncertainties and correlations between the BLAST maps (2).," SEDs are fitted using the same method explained and used in \citet{Chapin08}, , taking into account filter response curves, calibration uncertainties and correlations between the BLAST maps \citealt{Truch09}) )."
 Since we have only a modest range of FIR/sub-mm wavelengths (the three BLAST bands). we do not fit the dust emissivity index ὐ G.e. the slope of the moditied blackbody}: instead we fix it to 2.," Since we have only a modest range of FIR/sub-mm wavelengths (the three BLAST bands), we do not fit the dust emissivity index $\beta$ (i.e. the slope of the modified blackbody); instead we fix it to 2,"
into LAINBs. with another due to unresolved LAINBs aud ouly of the ciuissiou due to the interstellar eas (Sarazin.win.&Breeman2000).,"into LMXBs, with another due to unresolved LMXBs and only of the emission due to the interstellar gas \citep*{Irwin00}."
. Ou the other haud. the bulk of the emission in the brightest ellipticals is from the hot ISAL," On the other hand, the bulk of the emission in the brightest ellipticals is from the hot ISM."
 Because both the gas coutent aud the uunber of LAINBs of a galaxy should be related to its total mass. it is not surprising that we observe a tight Ly/—0 relation despite these physical differences.," Because both the gas content and the number of LMXBs of a galaxy should be related to its total mass, it is not surprising that we observe a tight $\lx - \sigma$ relation despite these physical differences."
 Tere we attempt to adjust the Zx/—0 relation for differences iu the contribution of the galaxy ISAL to the total N-vav luminosity., Here we attempt to adjust the $\lx - \sigma$ relation for differences in the contribution of the galaxy ISM to the total X-ray luminosity.
 We asstune that the total N-rav Cluission fraction from the ISAL fisay. (1) is a function of the X-ray to optical emission ratio. Lx/Ly. aud (2) is anchored at by NGC 1697 and at by NGC 5011. the brightest uncoutauinated galaxy in our salple. where the emission is almost cutirely from the hot ISM (Buote2000).," We assume that the total X-ray emission fraction from the ISM, $\fism$, (1) is a function of the X-ray to optical emission ratio, $\lx/\lb$, and (2) is anchored at by NGC 4697 and at by NGC 5044, the brightest uncontaminated galaxy in our sample, where the emission is almost entirely from the hot ISM \citep{Buote00}."
. Usine the Zx/Lj data in Exkridecetal. (1995).. these assumptions viek Exkiridegeetal.(1995) observe a significant correlation between the N-ray luminosity and X-ray το optical Cluission ratio: Lx/Lpxyear," Using the $\lx/\lb$ data in \cite{Eskridge95a}, these assumptions yield \cite{Eskridge95a} observe a significant correlation between the X-ray luminosity and X-ray to optical emission ratio: $\lx/\lb \propto
\lx^{0.56\pm0.04}$."
 Combining this result with equation (1)) aud our Lx0 fit. we find We conclude that the variation iu the gas content of elliptical galaxies has only a iuild effect ou the galaxy Lxσ relation. steepenius it within the measured uncertaiities.," Combining this result with equation \ref{eq:fism}) ) and our $\lx - \sigma$ fit, we find We conclude that the variation in the gas content of elliptical galaxies has only a mild effect on the galaxy $\lx - \sigma$ relation, steepening it within the measured uncertainties."
 Clusters of galaxies and clliptical galaxies form a continuous. well-defined relation in the Ly o@ plane.," Clusters of galaxies and elliptical galaxies form a continuous, well-defined relation in the $\lx - \sigma$ plane."
" The best-fit power laws have the form ὃνX6"". with ;)=LLNS aud m=πω, respectively. intersecting at σ=330 lanο. Ly=107 oes|."," The best-fit power laws have the form $\lx \propto \sigma^m$, with $m =
4.4^{+0.7}_{-0.3}$ and $m = 10.2^{+4.1}_{-1.6}$ respectively, intersecting at $\sigma = 330$ km, $\lx = 10^{43}$ erg."
 The steepening of the ὃς60 relation from clusters to individual galaxies supports models where the gascous medi is preheated by supernova explosions or mereiug shocks. aud is consistent with the observed LxTF aud 0.T relations for galaxies aud svstcus of galaxies.," The steepening of the $\lx - \sigma$ relation from clusters to individual galaxies supports models where the gaseous medium is preheated by supernova explosions or merging shocks, and is consistent with the observed $\lx - T$ and $\sigma - T$ relations for galaxies and systems of galaxies."
 The systematic variation iu the gas coutent of elliptical ealaxies has a neclieible effect on these results., The systematic variation in the gas content of elliptical galaxies has a negligible effect on these results.
 The scatter inthe Lx/—0 relation is suaallest at the scale of objects which are more likely to have reached dynamical equilibrium rieh clusters of galaxies and individual ellipticals., The scatter in the $\lx - \sigma$ relation is smallest at the scale of objects which are more likely to have reached dynamical equilibrium—rich clusters of galaxies and individual ellipticals.
 Poor groups of galaxies have the largest scatter. an indication that uuresolved. embedded X-ray. sources or a nonequilibrium galaxy velocity distributiou affect the integrated properties of these svstenis.," Poor groups of galaxies have the largest scatter, an indication that unresolved, embedded X-ray sources or a nonequilibrium galaxy velocity distribution affect the integrated properties of these systems."
 We thauk the anouvimous referee for useful coments., We thank the anonymous referee for useful comments.
 This research has beeu supported by the Smithsonian Tustitution., This research has been supported by the Smithsonian Institution.
‘Technology. funded by the National Aeronautics and Space Administration and the National Science Foundation.,"Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation."
"0.6"" can correspond to ::0.5 kkpe. sullicient to map also a small spiral.","$''$ can correspond to $\lsim$ kpc, sufficient to map also a small spiral."
 The benefits of gravitational lensing are complemented by Integral Field Spectroscopy (which produces a contiguousvelociliy map at each point in the target galaxy)., The benefits of gravitational lensing are complemented by Integral Field Spectroscopy (which produces a contiguous map at each point in the target galaxy).
 This allows a clean decoupling of the spatial and spectral information. thus eliminating the problems arising from their mixing in traditional long-slit observations.," This allows a clean decoupling of the spatial and spectral information, thus eliminating the problems arising from their mixing in traditional long-slit observations."
 Lt is therefore much. easier to identifv and study. galaxies. with regular(bi-svmametric) velocity fields., It is therefore much easier to identify and study galaxies with regular (bi-symmetric) velocity fields.
 In this paper. we present a cetailed study of four rotation curves extracted from disk: galaxies which have been observed through the cores of massive galaxy. cluster lenses.," In this paper, we present a detailed study of four rotation curves extracted from disk galaxies which have been observed through the cores of massive galaxy cluster lenses."
 These targets are taken [rom the recent work of Swinbanketal.(2003.2006)..," These targets are taken from the recent work of \citet{Swinbank03,Swinbank06a}."
 They were observed with the Genmini-North Multi-Object Spectrograph Integral Field. Unit (GMOSI1EU., They were observed with the Gemini-North Multi-Object Spectrograph Integral Field Unit (GMOS.
. We concentrate on the galaxy clynamics as traced by the OujAA3726.1.3728.8A comission line. doublet., We concentrate on the galaxy dynamics as traced by the $\lambda\lambda$ emission line doublet.
 The LIEU data provide a map of the ealaxy’s velocity field in sky. co-ordinates., The IFU data provide a map of the galaxy's velocity field in sky co-ordinates.
 To interpret this field. the magnification ancl distortion. caused by the eravitational lensing elfect is removed using detailed mocels of the cluster lenses (see Smithetal.(2005).. Ixneibetal. (1996).. Smith(2002). for details).," To interpret this field the magnification and distortion caused by the gravitational lensing effect is removed using detailed models of the cluster lenses (see \citet{Smith05}, \citet{Kneib96}, \citet{Smith02Th} for details)."
 The primary constraints on the lens models are the positions ancl redshifts of speetroscopically confirmed. gravitational arcs in each cluster., The primary constraints on the lens models are the positions and redshifts of spectroscopically confirmed gravitational arcs in each cluster.
 The source plane velocity. fields. of four. systems which display regular. (hi-svnunetric) rotational velocity fields rresembling rotating disks. were reduced to one-dimensional rotation curves from which the asvmptotic terminal velocity. was extracted and compared. with the ealaxy luminosity (Swinbanketal.2003.2006)," The source plane velocity fields of four systems which display regular (bi-symmetric) rotational velocity fields resembling rotating disks, were reduced to one-dimensional rotation curves from which the asymptotic terminal velocity was extracted and compared with the galaxy luminosity \citep{Swinbank03,Swinbank06a}."
 The key advantage of using gravitational lensing to boost the images ol distant galaxies is that we are less biases towards the most luminous galaxies., The key advantage of using gravitational lensing to boost the images of distant galaxies is that we are less biases towards the most luminous galaxies.
 Whilst observational information on the clistribution of the disks in galaxies at these carly times would be welleome. such observations will have to wait for luture instrumentation ALMA).," Whilst observational information on the distribution of the disks in galaxies at these early times would be wellcome, such observations will have to wait for future instrumentation ALMA)."
 In this paper we use nebular emission lines to. probe the kinematic of the galaxies., In this paper we use nebular emission lines to probe the kinematic of the galaxies.
 We extract. one-dimensional rotation curves from the velocity fields. to infer the distribution of stellar and dark matter components., We extract one-dimensional rotation curves from the velocity fields to infer the distribution of stellar and dark matter components.
 Finally. we compare our results with similarly luminous disk galaxies in the local Universe.," Finally, we compare our results with similarly luminous disk galaxies in the local Universe."
 Phrough-out this paper we use a cosmology with Ly=T2kms+. Qo=0.3 and Ay=0.7. fy=13.3Cyr.," Through-out this paper we use a cosmology with $H_{0}=72\kms$, $\Omega_{0}=0.3$ and $\Lambda_{0}=0.7$, $t_0=13.7 \ Gyr$."
 Our sample comes from. observations of six. gravitational ares in Swinbankctal., Our sample comes from observations of six gravitational arcs in \cite{Swinbank06a}.
).. In order to avoid. possible biases. the targets were selected only to be representative of galaxies in the distant. Universe and no attempt was made to select galaxies with relaxed late-twpe morphology.," In order to avoid possible biases, the targets were selected only to be representative of galaxies in the distant Universe and no attempt was made to select galaxies with relaxed late-type morphology."
 We did. however. require that ares were resolved in both spatial dimensions so that a two dimensional velocity field could be extracted from the HEU data.," We did, however, require that arcs were resolved in both spatial dimensions so that a two dimensional velocity field could be extracted from the IFU data."
 This restricted our selection to galaxies with moderate magnification., This restricted our selection to galaxies with moderate magnification.
 From the sample of six galaxies. four galaxies appear to have (relaxed). bi-svnunetric velocity fields with [ate-tvpe morphologies anc colours.," From the sample of six galaxies, four galaxies appear to have (relaxed) bi-symmetric velocity fields with late-type morphologies and colours."
 The rotation curves from these four galaxies appear regular and we therefore restrict our analysis to these ares., The rotation curves from these four galaxies appear regular and we therefore restrict our analysis to these arcs.
 We stress that the morphology. colours ancl velocity fields of the four galaxies in this sample all strongly suggest these galaxies are Consistent with late type spirals (see Swinbanketal. (2006))).," We stress that the morphology, colours and velocity fields of the four galaxies in this sample all strongly suggest these galaxies are consistent with late type spirals (see \cite{Swinbank06a}) )."
 From our optical/near-infrared. imaging. we constrain the spectral energy distribution (SED) of each galaxy.," From our optical/near-infrared imaging, we constrain the spectral energy distribution (SED) of each galaxy."
 Since the ares usually lic with a [ew ares-seconcds of nearby. bright cluster galaxies. we calculate the magnitude of the ares in various pass-bands by masking the are and interpolating the light [rom the nearby cluster members.," Since the arcs usually lie with a few arcs-seconds of nearby bright cluster galaxies, we calculate the magnitude of the arcs in various pass-bands by masking the arc and interpolating the light from the nearby cluster members."
 The background light is then removed. ancl surface photometry in different bancs is obtained., The background light is then removed and surface photometry in different bands is obtained.
 Using the cluster mass models the ares are reconstructed. το the source-plane anc the geometry ancl clisk-scale parameters of the disks are measured., Using the cluster mass models the arcs are reconstructed to the source-plane and the geometry and disk-scale parameters of the disks are measured.
 This is achieved. by fitting ellipses to an isophote of the galaxy image using a modified version of the routine which [its an exponential profile to the. two-dimensional light distribution., This is achieved by fitting ellipses to an isophote of the galaxy image using a modified version of the routine which fits an exponential profile to the two-dimensional light distribution.
 From this. the ellipticity. the inclination and luminosities and the disk scale lengths are obtained (see Table 2 and 32 in Swinbanketal. (2006))).," From this, the ellipticity, the inclination and luminosities and the disk scale lengths are obtained (see Table 2 and 3 in \cite{Swinbank06a}) )."
 ‘These latter are also reported below in Table 1, These latter are also reported below in Table 1.
 In Fig., In Fig.
 1 weshow the one dimensional rotation curves of the galaxies in our sample., \ref{fig:rot_curves} we show the one dimensional rotation curves of the galaxies in our sample.
 These are extracted by sampling the velocity field. along the major axis cross section., These are extracted by sampling the velocity field along the major axis cross section.
 The point in the velocity is defined using the center of the galaxy in the reconstructed source plane image., The zero-point in the velocity is defined using the center of the galaxy in the reconstructed source plane image.
 The error bars for the velocities are derived. from the formal 30 uncertainty in the velocity arising from Gaussian. profile fits to the Or] emission in cach averaged. pixel of the datacube., The error bars for the velocities are derived from the formal $3\sigma$ uncertainty in the velocity arising from Gaussian profile fits to the ] emission in each averaged pixel of the datacube.
 For, For
UD 199142 ↻⊔↴∖↸⊔⊔⋠↕↴∖⋅↸⊔∏⊔⊓⋮↴∖↴⊓⋅∪∐∶↴∙⊾∫⇀↕⊓⊺∩≺∖∖⊀≚⋜∏⋝↴∖↴∪↥⋅↻⊓∪∐⋖⋀∖↕⋜↧↑∐↕≺∏↕≼↧⋜∐↘↽↕↴∖↴↸∖↑⋜↧↕∙↓⋂∩⋅↱⊐∶and HD ∐↸∖⋜∐⋅↴⋝∙↖⇁∙↸⊳≺⊢⋯∪↖↽↕∐∶↴⋁↴∖↴↑⋜∐⋅↴∖↴↴⋝∙↖⇁↖⇁⋜⋯≼∐∖∐⊀≚∐↸⊳↨↘↽↸∖↥⋅↸∖↑⋜↧↕∙≺⊇∩∩∩∶358022 w,"HD 199143 and HD 358623 were presented as young, nearby, co-moving stars by van den Ancker et al. ("
"ere vdpresented. as vonne AON),",2000; henceforth vdA00).
 A0O). ΠΟ199112 is at a distance of 17.7 d 2.1pcas measured by Iüpparcos., HD 199143 is at a distance of $47.7 \pm 2.4$ pc as measured by Hipparcos.
" Because ΠΟ 1991 E ialic LID:358623‘o3 iare onlv 6five iare min: apiapart ffrom cach“ ∪↑↕∐∖↥⋅⋜⋯≺↧⋝∪↑∐↴∖↴∐∪↖↖↽⋜↧↸⊳↕↖↽↕↑⋅↖↽⋖⋜↧⋅↖↽∪∏↑∐⋃≼∐↸⊳⋜↧↑∪↥⋅⋝⋜⋯≼↧↑∐↸∖⋅⋅ ⋅⋅ sale proper motion.∙ vdAO0 suesested that they form. a (siuall. but possibly larger) voung nearby moving group (Capricornus). similar to the TorA. Tuc. TW να, and P Pic moving sroups"," Because HD 199143 and HD 358623 are only five arc min apart from each other and both show activity (a youth indicator) and the same proper motion, vdA00 suggested that they form a (small, but possibly larger) young nearby moving group (Capricornius), similar to the HorA, Tuc, TW Hya, and $\beta$ Pic moving groups."
 ΠΏ 199113 has similar UV space motion as the Tuc and TW να stars (vdA00: Zuckerman Webb 2000)., HD 199143 has similar $UVW$ space motion as the Tuc and TW Hya stars (vdA00; Zuckerman Webb 2000).
 Four more member candidates were presented by vau den Aucker et al. (, Four more member candidates were presented by van den Ancker et al. (
2001: honceforth vdAOL) selected. within 5° around UD 1990110 by stroug ROSAT X-rav cussion aud. partly. by proper motion.,"2001; henceforth vdA01) selected within $5^{\circ}$ around HD 199143 by strong ROSAT X-ray emission and, partly, by proper motion."
 It would be very important to find more members to this new assoclation. uot ouly to study the formation aud mass function of these new young nearby groups. but also because such vouneg nearby stars are very well suited for ≼∐↥⋅↸∖↸⊳↑↕⋯⋜↧∶↴∙⊾↕∐∶↴⋁↴∖↴↸∖⋜∐⋅↸⊳∐↸∖↴∖↴∪⋡↴∖∏⊢↴∖↴∖↕⋜," It would be very important to find more members to this new association, not only to study the formation and mass function of these new young nearby groups, but also because such young nearby stars are very well suited for direct imaging searches of sub-stellar companions."
∐⋅↸⊳∪∐∏≻⋜∐∐∪∐↴∖↴∙ ∐↕≻↽∩≝⊔↓∶⊔⋜↧↕↴∖↴∪↸⊳⋜↧∐↸∖≼↕≧↕≻↕⊺↴∢∔⊔⊤⋜⋯≼≋⊀≚≼≓≽↕⊓∶≩∩≺∖∖≝⊔ ∐⋜↧↴∖↴↴∖↴⋉∖↸⊳⊓⋅⋜↧↕↑⋅↖↴⋉∖⇪≺∖∖⋖∐≺∏↨↘↽∙∖↽≋⊔↕↑∐≓⋀∖↕∪∪↥⋅↸∖↕∩≺∖∖≺∖∖∶↖↽≼∟≚∩↭ ⋜⋯≼↧≼∐↴∖↴↻↕⋜↧⋅↖↽↴∖↴⋜⋯∪⋯⋜↧↕∪∏↴∖↴∏∏⋅⋜⊢↖↽↕∪↕↸∖⇈↸∖∐∐↴∖↴↴∖↴↕∪∐⋅≼⊲≀↕∐∐∶↴∙," HD 199143 (also called $-17^{\circ}6127$ and SAO 163989) has spectral type F8 (Houk Smith-Moore 1988; vdA00) and displays anomalous ultra-violett emission, Ca H K emission, and fast rotation (vdA00)."
⊾↕⊔↧⋅↖↽∐⋜↧⋯↕↸⊳↥⋅⋜⋯∶↴∙⊾↸∖↕∐∪↥⋅≼∐∖↥⋅↑∪≼∐∖↑↸∖↸⊳↑↕⋟⋜↧↕∐↑↸⊳∪∐∏≻⋜⊔↕∪∐↴∖↴⋅ ∙∖↽↕↘⊽∖⊔↕↴∖↴↴∖↴↕∪∐∙⋜⋯≼↧↕≯⋜↧↴∖↴↑↥⋅∪↑⋜↧↕∪∐≺↖⇁≺∟≚∩∣⋝⋅⊀∐↴∖↴∪∙∐↕≻↓⋜∐⊔↸∖↕⋅↖⇁↕∐↑∐↸∖∐≓↴⋝⋜⊔≼⊔∐↕≻↸∖↸∷⊇∩∩∩⋅⋅↧∏↕∙↖↽⊇∩∩↕∙⋜⋯≼↕≻↸∖↸⊳∙ ↕≝↭∐∶≩↴∖↴∐∪↖↖↽↴∖↴⋏∖⊽≓⋜⋯≼↧≼↽≥⊣⋜⋯≼⊓∖⊼↸⊳↸∖↴∖∷∖↴⋖↖↽≺∟≚∣⊔⋜↧↴∖↴∖↖↽↸∖∐≀↧↴∖↴⊇∩∩↕⋜⋯≼⊔∐↑∐↸∖⋅↧≓⋜⊔≼∐↘⊽≓⋝⋜⋯≼↧↴∖↴↕∐⋅↧∏↽⋪≽∩∩↕∖↴↻↸∖↸⊳↨↘↽↕↸∖⋜⊔≼↧ ∐⊰⊀≚≋⊔∕∣∣⊔↸∖⊼↸⊳↸∖↴∖↴↴∖↴↸∖∐∐↴∖↴↴∖↴↕∪∐∙↴⋝∏↑↖↽↸∖↥⋅⋅↖↽↕∪↖↖↽↿∏∏⋉∖↥⋅∐∐∐↑↴∖↴↓⋃↥⋅⋯⋜↧↕∐⊰↕⋯⋜↧∩⋝↕∐∩⋝⋝∙∑⊽≺∏⋃∩∐↸∖⋜∐⋅↴⋝↖⊽∖⋞∐∖↕∐↘↸∖∐↕⋗ in the other TRAS bands (GdAOO0). so that this star shows moderate. but uot strong infrared (IR) excess emission.," Also, HD 199143 shows N- and Q-band excess (vdA01) as well as IRAS $12 \mu m$ excess emission, but very low upper limits in the other IRAS bands (vdA00), so that this star shows moderate, but not strong infrared (IR) excess emission."
" Ποπονα, vdAO0 argue that all its features could be explained by a faint T-Tauri-like companion. which produces itself the UV and IR excess einissiou aud whose eireuustellar material accretes outo ID 199113 aud thereby spins wp the primary."," However, vdA00 argue that all its features could be explained by a faint T-Tauri-like companion, which produces itself the UV and IR excess emission and whose circumstellar material accretes onto HD 199143 and thereby spins up the primary."
 Mora et al. (, Mora et al. (
2001) measured a rotational velocity of ο3n;=15548 kan/s. TID ο.358623Kr (also called 1776128 and AZ Cap) has spectral with Io enissin. strong flaring. and heuceforth,"2001) measured a rotational velocity of $v \cdot \sin i = 155 \pm 8$ km/s. HD 358623 (also called $-17^{\circ}6128$ and AZ Cap) has spectral type K7-M0 with $\alpha$ emission, strong flaring, and strong Li absorption (Mathioudakis et al."
vd as well as N- and Q-band excess (vdAOL). all NUM for a T Tauri star.," 1995; vdA00), as well as N- and Q-band excess (vdA01), all typical for a T Tauri star."
" The Tycho proper motion of TD 358623 Ga,=F943 mas/vr aud ys=6343 mas/vr) is idautical to that of. IID ↽↽∙199113 Gi,=59.24:≓∶↕∙↕⋯⋜↕↴∖↴∣⋅∏⋅ and p—61.55dE0.85 mas/vr).", The Tycho proper motion of HD 358623 $\mu _{\alpha} = 59 \pm 3$ mas/yr and $\mu _{\delta} = -63 \pm 3$ mas/yr) is identical to that of HD 199143 $\mu _{\alpha} = 59.2 \pm 1.1$ mas/yr and $\mu _{\delta} = -61.55 \pm 0.85$ mas/yr).
 Recently. i. al. (," Recently, Zuckerman et al. ("
2001) arened that both IID 100110 andZuckenan IID 3586 are actually part of the 9 Pic moving eroup.,2001) argued that both HD 199143 and HD 358623 are actually part of the $\beta$ Pic moving group.
" Tn λίαν 2001. Javawardhana Ὀταπάσκο (2001: henceforth JBOL) observed the two MD iu J I with the AO system, ADONIS at the ESO thes23.61 telescope on La Silla,"," In May 2001, Jayawardhana Brandeker (2001; henceforth JB01) observed the two stars in J K with the AO system ADONIS at the ESO 3.6m telescope on La Silla."
" Near cach of the two stars, detected one companion candidate."," Near each of the two stars, they detected one companion candidate."
 The close aud faint object near IID 199113 is red CFA=Ll mae) aud. hence. either sub-stellar or the (reddened) companion expected wv vdAOO0. whose circumstellar material could explain he anomalous features of the pennany IID 199113.," The close and faint object near HD 199143 is red $J-K=1.4$ mag) and, hence, either sub-stellar or the (reddened) companion expected by vdA00, whose circumstellar material could explain the anomalous features of the primary HD 199143."
 The conipauion candidate near WD358623 is less than 2 mag auter than the prinary in J IK (JDOI) aud could be an A\Ltype stellar companion., The companion candidate near HD 358623 is less than 2 mag fainter than the primary in J K (JB01) and could be an M-type stellar companion.
 ↖↖⊽↸∖∪↴⋝↴∖↴↸∖↥⋅↖⇁↸∖≼↧↑∐↸∖↑↖↖⇁∪↴∖↴↑⋜∐⋅↴∖↴↖↖↽↕↑∐∐∶↴∙⊾∐↴∖↴↸∖∐↴∖↴↕↑↕↖↽↕↑⋅↖↽⋜⊔≼↧ 1911," We observed the two stars with high sensitivity and high dynamic range in order to detect faint companions, namely in the H-band in Dec. 2000, July 2001, and Dec. 2001 and in the J- and K-bands in July 2001 (speckle and normal IR imaging)."
10 and HD358623 are well-suited for direct imaging of sub-stellar companions. both brown dwarfs aud eiat. plaucts. because young sub-stellar objects are still relatively bright (¢.g. Burrows ct al.," Young nearby stars like HD 199143 and HD 358623 are well-suited for direct imaging of sub-stellar companions, both brown dwarfs and giant planets, because young sub-stellar objects are still relatively bright (e.g. Burrows et al."
 1997). so that they are less difficult to detect in the PSF wing of a wich brighter star.," 1997), so that they are less difficult to detect in the PSF wing of a much brighter star."
 Sec. c.g. Lowrance et al. (," See, e.g., Lowrance et al. ("
1999. 2000). Neuhauuser et al. (,"1999, 2000), Neuhäuuser et al. ("
20000). 2nd. Corenther et al. (,"2000b), and Guenther et al. ("
2001) for imaging aud spectroscopy of brown cavarf companions of the voung stars TWA-5 and WR 7329 iu the TW Ίνα and Tue associations.,2001) for imaging and spectroscopy of brown dwarf companions of the young stars TWA-5 and HR 7329 in the TW Hya and Tuc associations.
 The brown dwuf near TWA-5 was the first sub-stellar companion around a preanaiu sequence star confirmed. by both proper motion and spectroscopy. and also the first," The brown dwarf near TWA-5 was the first sub-stellar companion around a pre-main sequence star confirmed by both proper motion and spectroscopy, and also the first"
The value of & is numerically estimated as 1.41.6 for Tvpe I bursts 1984).. and 1.72.0 for accretion disks (Shimura&Takahara1995).,"The value of $\kappa$ is numerically estimated as 1.4–1.6 for Type I bursts \citep{ebisuzaki_hard}, and 1.7–2.0 for accretion disks \citep{shimura_hard}. ."
". If we adopt &=1.7. the observed soft-component parameters of ATi, 1.8 keV and rin~d km vields kT~ 1.1 keV and rh~ 12 km."," If we adopt $\kappa = 1.7$, the observed soft-component parameters of $kT_{\rm in} \sim$ 1.8 keV and $r_{\rm in} \sim 4$ km yields $kT^{\rm eff}_{\rm in} \sim$ 1.1 keV and $r^{\rm eff}_{\rm in} \sim$ 12 km."
 Thus. the estimated true radius becomes larger than the NS radius of 10. km.," Thus, the estimated true radius becomes larger than the NS radius of 10 km."
" Moreover. the value of 7llἩ d8 Close to the radius of last stable orbit in terms ofgeneral relativitv. 342, = 12.4 km. where R,=2GA/c? is the Schwarzschild radius. C is the gravitational constant. M is the NS mass. and e is the light speed."," Moreover, the value of $r^{\rm eff}_{\rm in}$ is close to the radius of last stable orbit in terms ofgeneral relativity, $3 R_{\rm s}$ = 12.4 km, where $R_{\rm s} \equiv 2GM/c^{2}$ is the Schwarzschild radius, $G$ is the gravitational constant, $M$ is the NS mass, and $c$ is the light speed."
 As to the BB component. ATyg~ 2.7 keV and rg 12 km vields Τιμ~ L5 keV and rit~ 2.7 km. assuming &e 1.5 The estimated Te is close to the local Ecldington temperature (2.0 keV) of a 1.4 M. NS. suggesting that the BB emission arises [rom a region on the NS surface.," As to the BB component, $kT_{\rm BB} \sim$ 2.7 keV and $r_{\rm BB} \sim$ 1.2 km yields $kT^{\rm eff}_{\rm BB} \sim$ 1.8 keV and $r^{\rm eff}_{\rm BB} \sim$ 2.7 km, assuming $\kappa \sim$ 1.5 The estimated $kT^{\rm eff}_{\rm BB}$ is close to the local Eddington temperature (2.0 keV) of a 1.4 $M_{\odot}$ NS, suggesting that the BB emission arises from a region on the NS surface."
 In addition. rtl is sunaller (han 10 km. when assuming isotropic emission from a spherical source.," In addition, $r^{\rm eff}_{\rm BB}$ is smaller than 10 km, when assuming isotropic emission from a spherical source."
 Therefore. as previously suggested by Mitsudaetal.(1984).. the BB component can be regarded as being emitted from an equatorial zone of the NS. where the accretion disk contacts the surlace.," Therefore, as previously suggested by \citet{mitsuda_z}, the BB component can be regarded as being emitted from an equatorial zone of the NS, where the accretion disk contacts the surface."
 From the above spectral analysis. it has been confirmed (hat (he Eastern (AICD+BB+Gan) model successfully reproduces the spectra in the upper-banana state. ancl vields physically reasonable interpretations.," From the above spectral analysis, it has been confirmed that the Eastern (MCD+BB+Gau) model successfully reproduces the spectra in the upper-banana state, and yields physically reasonable interpretations."
 we applied the AICD+BB+Gan model to the 95 spectra in the upper-banana state. and obtained 2/d.o.L.," we applied the MCD+BB+Gau model to the 95 spectra in the upper-banana state, and obtained $\chi^2$ /d.o.f."
 of <1.4 for all of them., of $< 1.4$ for all of them.
 Figure 6 summarizes the relation among (he disk bolometric luminosity Lai. Lhe BB bolometric Iumninosity. [or isotropic emission Lpp. and their sum Li=LacEpp. as well as (he temperatures and radii.," Figure \ref{fig:spec_1608_all1} summarizes the relation among the disk bolometric luminosity $L_{\rm disk}$, the BB bolometric luminosity for isotropic emission $L_{\rm BB}$, and their sum $L_{\rm tot} \equiv L_{\rm disk} + L_{\rm BB}$, as well as the temperatures and radii."
 Here. Lai; is caleulated assuming à [ace-on disk (i.e.. the inclination angle /= 0°) as wherethe first factor of 2 means emission from the two sides of the disk. σ is the Slelan-Bollzimann constant. and Z(r) isthe disk temperature al the radius r.," Here, $L_{\rm disk}$ is calculated assuming a face-on disk (i.e., the inclination angle $i = 0\arcdeg$ ) as wherethe first factor of 2 means emission from the two sides of the disk, $\sigma$ is the Stefan-Boltzmann constant, and $T(r)$ isthe disk temperature at the radius $r$ ."
" In Figures 6. (a). both Lag, and Lpp are seen to increase as £44, increases [rom 1x107 to 4x10"" erg !."," In Figures \ref{fig:spec_1608_all1} (a), both $L_{\rm disk}$ and $L_{\rm BB}$ are seen to increase as $L_{\rm tot}$ increases from $1 \times 10^{37}$ to $4 \times 10^{37}$ erg $^{-1}$ ."
 However. a closer inspection reveals thatLai; varies more steeply than," However, a closer inspection reveals that$L_{\rm disk}$ varies more steeply than"
varies wilh luminosity in this source.,varies with luminosity in this source.
 We note that the narrow iron Ίνα line width: varied significantly−↽−∙ between. (wo individual−−− exposures:. from: 509020202026 km lin −⋅ 2000 to 1690⋅423729 km !1 m 2002., We note that the narrow iron $\alpha$ line width varied significantly between two individual exposures; from $5090^{+2020}_{-2030}$ km $^{-1}$ in 2000 to $1690^{+1290}_{-1690}$ km $^{-1}$ in 2002.
" The line intensity also decreased [rom 3.4τιx10 photons 7 1 (o 2.202x10? photons ? !. Meanwhile the continuum luminosity (2.0 10.0 keV) increased from 1.5x107 erese ! to 1.9x10” ereseD |,", The line intensity also decreased from $3.4^{+1.5}_{-1.1}\times10^{-5}$ photons $^{-2}$ $^{-1}$ to $2.2^{+0.6}_{-0.7}\times10^{-5}$ photons $^{-2}$ $^{-1}$ Meanwhile the continuum luminosity (2.0 – 10.0 keV) increased from $1.5\times10^{43}$ ergs $^{-1}$ to $1.9\times10^{43}$ ergs $^{-1}$.
 This suggestsex a variable orieinex of ihe narrow iron Ka line., This suggests a variable origin of the narrow iron $\alpha$ line.
 The line width presented in Table 2 is dominated by the second observation with longer exposure time., The line width presented in Table 2 is dominated by the second observation with longer exposure time.
 If simply taking the line width from the first exposure. we can obtain a black hole mass four times higher. well consistent with the best-fit lines in Fig.," If simply taking the line width from the first exposure, we can obtain a black hole mass four times higher, well consistent with the best-fit lines in Fig."
 1 ancl 2., 1 and 2.
 For (he remaining sources will multiple available ILEZTG. exposures. no narrow iron Ka line variation was found to be significant.," For the remaining sources with multiple available HETG exposures, no narrow iron $\alpha$ line variation was found to be significant."
 While the correlation between Mq ancl Mg is statistically insignificant (at à confidence level of excluding NGC! 5548). we argue that this mav be attributed to the large uncertainties in the measurements of M because of the large errorbars in the iron Ix line widths.," While the correlation between $M_{T}$ and $M_{B}$ is statistically insignificant (at a confidence level of excluding NGC 5548), we argue that this may be attributed to the large uncertainties in the measurements of $M_{T}$ because of the large errorbars in the iron K line widths."
 In Fig., In Fig.
 1 and 2 we can see that the large scattering of data points from the best-fit lines are mainly due to the large uneertainties in (he measurements of iron Ίνα line width., 1 and 2 we can see that the large scattering of data points from the best-fit lines are mainly due to the large uncertainties in the measurements of iron $\alpha$ line width.
 The scattering of data points in Fie., The scattering of data points in Fig.
 1 can be measured by the standard deviation of log(My/M y). which is 0.50 for ten sources and 0.38 with NGC 5548 excluded.," 1 can be measured by the standard deviation of $M_T/M_B$ ), which is 0.50 for ten sources and 0.38 with NGC 5548 excluded."
 This is comparable to the tvpical lo uncertainty of Mg/ logCfp) which is ~ 0.35., This is comparable to the typical $\sigma$ uncertainty of $M_T/f_T$ ) which is $\sim$ 0.35.
 To verily the reliability of this new technique to weigh SAIBIL. more data points and better measurements of iron Ka line widths are required.," To verify the reliability of this new technique to weigh SMBH, more data points and better measurements of iron $\alpha$ line widths are required."
 Given the diffieulty in obtaining lenethilv WETG observations with (he required S/N to constrain the iron line wiclth. we have lo awail {he next generation of X-ray observatories that are able to measure the iron Ix. line al hieher spectral resolutions (i.e. of the order 100 kim/s) with calorimeter-based detectors.," Given the difficulty in obtaining lengthily HETG observations with the required S/N to constrain the iron line width, we have to await the next generation of X-ray observatories that are able to measure the iron K line at higher spectral resolutions (i.e. of the order 100 km/s) with calorimeter-based detectors."
 Belore that. we need future X-ray observations to verily the origins of the narrow iron [xa line by better resolving the line profile ancl X-ray reverberationanapping.," Before that, we need future X-ray observations to verify the origins of the narrow iron $\alpha$ line by better resolving the line profile and X-ray reverberation-mapping."
 The work is supported by The Chinese NSF through NSFCLOT73010 and NSFC 10325312., The work is supported by The Chinese NSF through NSFC10773010 and NSFC 10825312.
 We would like to thank Dr. Wei Zheng for helpful comments and his careful review of the manuscript., We would like to thank Dr. Wei Zheng for helpful comments and his careful review of the manuscript.
 JAW thanks Dr. Tingeti Wang and Matt. Malkan for discussions., JXW thanks Dr. Tinggui Wang and Matt Malkan for discussions.
Jiang acknowledges support from the “Chuang Xin Foundation operated bv the Graduate School of USTC.,"Jiang acknowledges support from the ""Chuang Xin"" Foundation operated by the Graduate School of USTC."
in the EF of that part of the run. centred on 500 s and with amplitude 6.3 mamag.,"in the FT of that part of the run, centred on 500 s and with amplitude 6.3 mmag."
 This run gives 2 = 21.6., This run gives $R$ = 21.6.
 In run 86599 part (LL) there are two DNOs in the EE at 23.41 s and 11.01 s. The latter is a first. harmonic. though again there is no signal at the fundamental.," In run S6599 part (II) there are two DNOs in the FT – at 23.41 s and 11.01 s. The latter is a first harmonic, though again there is no signal at the fundamental."
 The fundamental beats with 23.41 s at a period of 368 s. There is no signal at this. putative. Q?O period in the ET. but we note that 368/22.04 gives 2 = 16.7.," The fundamental beats with 23.41 s at a period of 368 s. There is no signal at this, putative, QPO period in the FT, but we note that 368/22.04 gives $R$ = 16.7."
 ltun 86660 has a double DNO that has a beat at 281 s: the observed. QPO is near 214 s. The observed A! — 13.1., Run S6660 has a double DNO that has a beat at 281 s; the observed QPO is near 214 s. The observed $R$ = 13.1.
 Runs 86570 and 86580 give observed values of /? = 14.6 and R= 16.2 respectively., Runs S6570 and S6580 give observed values of $R$ = 14.6 and $R$ = 16.2 respectively.
 ltuns 56555 anc 86634 contained. apparent harnionics that are. probably beats with the integration lengths., Runs S6555 and S6634 contained apparent harmonics that are probably beats with the integration lengths.
 The true periods are given in footnotes to Table 2., The true periods are given in footnotes to Table 2.
 CN Ori was observed on 2002 December 29 during outburst., CN Ori was observed on 2002 December 29 during outburst.
 A double DNO was visible in the first  1 hr of the light curve with peaks at 12.10 s and. 11.23 5s. Phe beat. period between these two periodicities is 156.6 s: there is no sign in the EP of a peak at this period., A double DNO was visible in the first $\sim$ 1 hr of the light curve with peaks at 12.10 s and 11.23 s. The beat period between these two periodicities is 156.6 s; there is no sign in the FT of a peak at this period.
 Vhis run gives /? = 13.9., This run gives $R$ = 13.9.
 We observed WX Livi following an outburst in September 2001. when it had. almost returned. to quiescence.," We observed WX Hyi following an outburst in September 2001, when it had almost returned to quiescence."
 In. this run (S6248) strong QPOs at 185 s are visible (see Fig. 3))., In this run (S6248) strong QPOs at 185 s are visible (see Fig. \ref{lc6248}) ).
 These QPOs remained coherent for ~ 10 eveles., These QPOs remained coherent for $\sim$ 10 cycles.
 At the same time. DNOs are apparent in the EE at 19.4 s (amplitude 3.8 mmag).," At the same time, DNOs are apparent in the FT at 19.4 s (amplitude 3.8 mmag)."
 This gives R= 9.5., This gives $R$ = 9.5.
 QPOs at 191: s were also observed. during another run of WX Livi in July 2002 (run 56463). but will be reported in detail elsewhere.," QPOs at 191 s were also observed during another run of WX Hyi in July 2002 (run S6463), but will be reported in detail elsewhere."
 Optical DNOs with periods from 19.4 s to 28.0 s have been seen in OY Car at the end. of superoutburst. (Schoembs 1986). and 18 s DNOs have been observed with the LIST. also at the end of superoutburst (Marsh Horne 1998).," Optical DNOs with periods from 19.4 s to 28.0 s have been seen in OY Car at the end of superoutburst (Schoembs 1986), and 18 s DNOs have been observed with the HST, also at the end of superoutburst (Marsh Horne 1998)."
 No simultaneous DNOs and QPOs have hitherto been detected., No simultaneous DNOs and QPOs have hitherto been detected.
 We have extensive coverage of the February 2003 superoutburst of OY Car. but list in Table 1: only the runs that are relevant to the current discussion. which are near maximum light and obtained on the same night. with an interruption between them.," We have extensive coverage of the February 2003 superoutburst of OY Car, but list in Table 1 only the runs that are relevant to the current discussion, which are near maximum light and obtained on the same night with an interruption between them."
 Run 56722 shows a DNO at 17.62 s and QPOs at 281 s: later that night run 86724 shows a DNO at 17.79 s and a QPO initially at 338 s which later changed to 297 s. The phase diagrams shown in Fig., Run S6722 shows a DNO at 17.62 s and QPOs at 281 s; later that night run S6724 shows a DNO at 17.79 s and a QPO initially at 338 s which later changed to 297 s. The phase diagrams shown in Fig.
 4 show a correlation between the behaviour of the DNOs and QPOs., \ref{oc6722} show a correlation between the behaviour of the DNOs and QPOs.
 Values of /? = 15.9 and 19.0 are given by these data., Values of $R$ = 15.9 and 19.0 are given by these data.
 Z Cha was observed during the February 2000 outburst (run S6061. κου Table 1) and a distinct DNO at 25.15 s was seen in the EF.," Z Cha was observed during the February 2000 outburst (run S6061, see Table 1) and a distinct DNO at 25.15 s was seen in the FT."
 Phe FP of the prewhitened. light curve (of the first 1.5 hr of run 86061) is shown in Fig. 5.., The FT of the prewhitened light curve (of the first 1.5 hr of run S6061) is shown in Fig. \ref{ftzcha}.
 In this section a distinct QPO signal at 585 s is present., In this section a distinct QPO signal at 585 s is present.
 This gives /?zm 23.5., This gives $R \approx$ 23.3.
shape.,shape.
 It is more relevant when er.. in which case our results can only be taken as illustrative.," It is more relevant when $a \sim r_{\rm c}$, in which case our results can only be taken as illustrative."
 It remains then only to trace the center of the cavity with distance and azimuth in the orbital plane to completely define the spiral interaction region through the WR wind., It remains then only to trace the center of the cavity with distance and azimuth in the orbital plane to completely define the spiral interaction region through the WR wind.
 A cross-section of the spiral pattern is basically a ‘shadow’ of the wind collision that advances through the WR wind at constant radial expansion., A cross-section of the spiral pattern is basically a `shadow' of the wind collision that advances through the WR wind at constant radial expansion.
 We simply need an expression for the star's location around the orbit with phase to determine an equation of motion for this ‘shadow’., We simply need an expression for the star's location around the orbit with phase to determine an equation of motion for this `shadow'.
 Such a relation is derivable from Kepler's laws., Such a relation is derivable from Kepler's laws.
 At any given phase. the cross-section center advances radially according to Conservation of angular momentum £ provides a relation for the star location: with the specitic angular momentum given by for M the summed mass of the two stars.," At any given phase, the cross-section center advances radially according to Conservation of angular momentum ${\cal L}$ provides a relation for the star location: with the specific angular momentum given by for $M$ the summed mass of the two stars."
 Defining an angular velocity w=2z/[ for period P. using Kepler's third law. and combining the three preceding equations. a differential equation for the cross-section center can be derived: where a convenient scaling parameter we call the ‘wrapping length’ my 18 introduced: The wrapping length is related to the pitch angle of the spiral shape.," Defining an angular velocity $\omega = 2\pi/P$ for period $P$, using Kepler's third law, and combining the three preceding equations, a differential equation for the cross-section center can be derived: where a convenient scaling parameter we call the `wrapping length' $r_{\rm w}$ is introduced: The wrapping length is related to the pitch angle of the spiral shape."
 Since ro is a scale for the emission of the line. it is natural to characterize models by the ratio Parefre=Pf... where fo=refesx indicating the numberof wrappings per critical radius crossing time.," Since $r_{\rm c}$ is a scale for the emission of the line, it is natural to characterize models by the ratio $2\pi r_{\rm
w}/r_{\rm c} = P/t_{\rm c}$, where $t_{\rm c} = r_{\rm c}/\vinf$ indicating the number of wrappings per critical radius crossing time."
 If the wind flow time across the critical radius is much longer than 7. the spiral will have many circuits over that scale: but if the orbital period is long. the spiral is essentially a cone over the span of a critical radius.," If the wind flow time across the critical radius is much longer than $P$, the spiral will have many circuits over that scale; but if the orbital period is long, the spiral is essentially a cone over the span of a critical radius."
 Before tackling the case of general orbits. it is instructive to consider the extremely long period binaries for which the bow shock geometry is asymptotically conical in shape. having no spiral curvature.," Before tackling the case of general orbits, it is instructive to consider the extremely long period binaries for which the bow shock geometry is asymptotically conical in shape, having no spiral curvature."
" We will refer to this limit as the ""conical (or linear) bow shock.", We will refer to this limit as the `conical' (or 'linear') bow shock.
 In the approximation of negligible wrapping of the spiral. the cavity and compressed layer are cones centered on the line of centers for the two stars.," In the approximation of negligible wrapping of the spiral, the cavity and compressed layer are cones centered on the line of centers for the two stars."
 The isovelocity zones are also cones., The isovelocity zones are also cones.
 An important point is that we assume the flow in the compressed laver is radial and has the same speed as the WR terminal speed., An important point is that we assume the flow in the compressed layer is radial and has the same speed as the WR terminal speed.
 This is a reasonable approximation for an adiabatic shock and a strong WR wind (see Tuthill 22008)., This is a reasonable approximation for an adiabatic shock and a strong WR wind (see Tuthill 2008).
 These isovelocity cones are centered on the observer's of-sight. and so are inclined to that of the CWIR.," These isovelocity cones are centered on the observer's line-of-sight, and so are inclined to that of the CWIR."
 What is interesting is that the intersection of the interaction region with the isovelocity cones is a fixed pattern with radius., What is interesting is that the intersection of the interaction region with the isovelocity cones is a fixed pattern with radius.
 Consider a spherical shell., Consider a spherical shell.
 The cross-section of the isovelocity zones are rings., The cross-section of the isovelocity zones are rings.
 That of the interaction region is a ring also which. without loss of generality. is assumed to lie in the .r-z plane.," That of the interaction region is a ring also which, without loss of generality, is assumed to lie in the $x$ $z$ plane."
 It is straightforward to find the crossing points between the two rings in terms of the azimuthal angle ay for the observer (see Fig. 25., It is straightforward to find the crossing points between the two rings in terms of the azimuthal angle $\alpha_0$ for the observer (see Fig. \ref{fig2}) ).
" If the cavity center is at @.—904. the implicit solution for ay is t, is the observed normalized velocity shift in the line and te is the value for the isovelocity zone for the cavity axis."," If the cavity center is at $\theta_{\rm c} = 90^\circ - i$, the implicit solution for $\alpha_0$ is $w_{\rm z}$ is the observed normalized velocity shift in the line and $w_{\rm c}$ is the value for the isovelocity zone for the cavity axis."
" The same relation can be used for 3” and a, to determine the crossing points between an isovelocity ring on the shell and the circular boundary of the compression layer.", The same relation can be used for $\beta'$ and $\alpha_0'$ to determine the crossing points between an isovelocity ring on the shell and the circular boundary of the compression layer.
" The key is that oo and aj, are constants with radius.", The key is that $\alpha_0$ and $\alpha_0'$ are constants with radius.
 There are several special cases that are notable., There are several special cases that are notable.
 If viewed pole- intersections only occur for ϐτν90°7 and 0«90°p ," If viewed pole-on, intersections only occur for $\theta >90^\circ - \beta'$ and $\theta
<90^\circ + \beta'$."
When viewed edge-on. the axis of the interaction region coincides with the z-axis. in which case there is no emission for 0.«.7. and emission from the compressed laver is exclusively from 9«8< y.," When viewed edge-on, the axis of the interaction region coincides with the $z$ -axis, in which case there is no emission for $\theta<\beta$, and emission from the compressed layer is exclusively from $\beta<\theta<\beta'$ ."
 For emission from the compression region. the density is enhanced by a constant factor of + in our treatment.," For emission from the compression region, the density is enhanced by a constant factor of 4 in our treatment."
" In terms of the emission per unit solid angle. (LL,/(£2. the integration along a hypothetical radial that lies entirely within the compression layer will be 8 times greater than for one in a purely spherical wind."," In terms of the emission per unit solid angle, $dL_\nu/d\Omega$, the integration along a hypothetical radial that lies entirely within the compression layer will be 8 times greater than for one in a purely spherical wind."
 Of course. the compression layer has a solid angle extent that is 1/4 that of the cavity.," Of course, the compression layer has a solid angle extent that is 1/4 that of the cavity."
 In effect. the wind collision redistributes mass in a sector of WR flow. and there is a net gain in line emission above what that thesector would have produced if it were undisturbed.," In effect, the wind collision redistributes mass in a sector of the WR flow, and there is a net gain in line emission above what that sector would have produced if it were undisturbed."
 The wind collision leads in essence to a globally stuctured clump., The wind collision leads in essence to a globally stuctured clump.
 The important point is that one should not expect CWIRs to conserve flux in the forbidden line as compared to a spherical wind., The important point is that one should not expect CWIRs to conserve flux in the forbidden line as compared to a spherical wind.
 Also. the CWIR does not extend down to the photosphere of," Also, the CWIR does not extend down to the photosphere of"
reason for this is a combination of the better and. more modern cross sections which we used and of the additional processes included in the calculation such as the transitions through the 2s level of HH. We compare in detail our results with those obtained by SVSS5 in Fig 2.,reason for this is a combination of the better and more modern cross sections which we used and of the additional processes included in the calculation such as the transitions through the $2s$ level of H. We compare in detail our results with those obtained by SVS85 in Fig 2.
 While for small values of wr. the curves are similar it is evident that the differences become substantial for ο20.1 We have presented. an updated: calculation of the energy cascade arising from a primary clectron with energy in the range (3.10 keV) predicted for one of the most popular dark matter particle candidates. ie. sterile neutrinos.," While for small values of $x_e$ the curves are similar it is evident that the differences become substantial for $x_e \simgt > 0.1$ We have presented an updated calculation of the energy cascade arising from a primary electron with energy in the range $3-10$ keV) predicted for one of the most popular dark matter particle candidates, i.e. sterile neutrinos."
 We have computed the fractional energy deposition into ionizations. excitations and heating to a new level of detail and followed the fate of individual photons to be able to distinguish between Lya radiation and continuum photons with energies under 10.2 eV. As mentioned. previously in this work. Lye radiation allocts the eas in several wavs.," We have computed the fractional energy deposition into ionizations, excitations and heating to a new level of detail and followed the fate of individual photons to be able to distinguish between $\alpha$ radiation and continuum photons with energies under 10.2 eV. As mentioned previously in this work, $\alpha$ radiation affects the gas in several ways."
 H has a thermal elect on the matter. with a heating or cooling effect. depending on the nature of the photons.," It has a thermal effect on the matter, with a heating or cooling effect depending on the nature of the photons."
 Line or injected Lya photons cool the gas. while photons between the Lyo and resonances that redshift to 10.2 eV. Lya photons) act as a heat source for the gas.," Line or $injected$ $\alpha$ photons cool the gas, while photons between the $\alpha$ and $\beta$ resonances that redshift to 10.2 eV $\alpha$ photons) act as a heat source for the gas."
 A Lya background is. also responsible for the Wouthuvsen-Field process. which directly alfects the physics of the 21 em line radiation from neutral LE and can make it visible in emission or absorption against the CMD.," A $\alpha$ background is also responsible for the Wouthuysen-Field process, which directly affects the physics of the 21 cm line radiation from neutral H and can make it visible in emission or absorption against the CMB."
 This aspect is important because 21 em observations of the high redshift Universe will be performed in the near future by next generation low frequency racio interferometers such as LOFAR., This aspect is important because 21 cm observations of the high redshift Universe will be performed in the near future by next generation low frequency radio interferometers such as LOFAR.
 We included in our calculations the only mechanisms hat could produce Lyso radiation. recombinations and free-lree interactions with ions.," We included in our calculations the only mechanisms that could produce $\alpha$ radiation, recombinations and free-free interactions with ions."
 Both processes are more probable as the ionized fraction increases. but at the same time the cross section for cleetron-cleetron collisions becomes dominant. so we found hat both these channels are practically negligible ancl that electrons injected in a highlv ionized gas are thermalized refore they can produce continuum photons.," Both processes are more probable as the ionized fraction increases, but at the same time the cross section for electron-electron collisions becomes dominant, so we found that both these channels are practically negligible and that electrons injected in a highly ionized gas are thermalized before they can produce continuum photons."
 We expect that the same calculations performed. for relativistic electrons. could. produce interesting results in his sense. also taking into account that processes such as inverse-C'ompton on CALB photons would become important and produce continuum radiation.," We expect that the same calculations performed for relativistic electrons could produce interesting results in this sense, also taking into account that processes such as inverse-Compton on CMB photons would become important and produce continuum radiation."
 This could be a useful extension to this work and could be applied to study the cllects of Light Dark Matter. decays/annihilations in the energy range around  LO MeV., This could be a useful extension to this work and could be applied to study the effects of Light Dark Matter decays/annihilations in the energy range around $\sim $ 10 MeV.
the structures.,the structures.
 The above figures indicate (hat this mechanism is al plav even in cases where (he initial phase relations are uncorrelated., The above figures indicate that this mechanism is at play even in cases where the initial phase relations are uncorrelated.
 In the damping reeime presented above. circularly symmetric structures in density. current and magnetic fields readilv form and persist for many. Alfvénn times. until disrupted by mergers wilh other structures of similar amplitude.," In the damping regime presented above, circularly symmetric structures in density, current and magnetic fields readily form and persist for many Alfvénn times, until disrupted by mergers with other structures of similar amplitude."
 It is possible to define. for each circular structure. an effective separatrix that distinguishes it [rom surrounding turbulence and “sheets” (that exist between structures. [," It is possible to define, for each circular structure, an effective separatrix that distinguishes it from surrounding turbulence and large-amplitude “sheets” that exist between structures. ["
see. e.g.. the magnetic field contours at latertimes in refbmag-uncorrelated-contour..],"see, e.g., the magnetic field contours at latertimes in \\ref{bmag-uncorrelated-contour}. .]"
 The density field has significant gradients in both the regions surrounding the structure and within the structures themselves., The density field has significant gradients in both the regions surrounding the structure and within the structures themselves.
 The ability to separate these circular structures from the background sheets and (turbulence is determined by the magnitudes — relative and absolute — of the damping parameters., The ability to separate these circular structures from the background sheets and turbulence is determined by the magnitudes – relative and absolute – of the damping parameters.
 Larger damping values erode the small-spatial-scale structures (ο a greater extent and. if large enough. disrupt the structure persistence mechanism (hat. for a fixed diameter. depends on a sullicientlv large amplitude current filament to generate a sufficiently large racially sheared magnetic field.," Larger damping values erode the small-spatial-scale structures to a greater extent and, if large enough, disrupt the structure persistence mechanism that, for a fixed diameter, depends on a sufficiently large amplitude current filament to generate a sufficiently large radially sheared magnetic field."
 The preceding results were for a damping regime where g/jc1. an intermediate regime.," The preceding results were for a damping regime where $\eta / \mu \sim 1$, an intermediate regime."
 Numerical solutions with jo=0 and 5 small explore the regime where )/j—0., Numerical solutions with $\mu = 0$ and $\eta$ small explore the regime where $\eta / \mu \rightarrow 0$.
 In this regime. which is opposite (he regime used in Craddock et al..," In this regime, which is opposite the regime used in Craddock et al.,"
 circularly. svimetric current and magnetic structures are not as prevalent. rather. sheet-like structures dominate (he large amplitude fluctuations.," circularly symmetric current and magnetic structures are not as prevalent, rather, sheet-like structures dominate the large amplitude fluctuations."
 Current and magnetic field gradients are strongly dampect. and the characterise length scales in these fields are larger.," Current and magnetic field gradients are strongly damped, and the characteristic length scales in these fields are larger."
 Contours of density for a numerical solution with ji.—0 are shown in relfig:densitv-zero-nni.., Contours of density for a numerical solution with $\mu = 0$ are shown in \\ref{fig:density-zero-mu}. .
 Visual comparison wilh contours for runs with smaller damping parameters refdendat-uncorrelated-contour.. where 7)= jj) indicate a preponderance of sheets in the je=0 case. at the expense of cireularlv-svimnietrie structures as seen above.," Visual comparison with contours for runs with smaller damping parameters \\ref{dendat-uncorrelated-contour}, where $\eta = \mu$ ) indicate a preponderance of sheets in the $\mu = 0$ case, at the expense of circularly-symmetric structures as seen above."
 All damping is in ap any current filament that would otherwise form is unable (ο preserve its small-scale. large amplitude characteristics before being resislively damped.," All damping is in $\eta$; any current filament that would otherwise form is unable to preserve its small-scale, large amplitude characteristics before being resistively damped."
 Inspection of the current and |B] contours for the same numerical solution reffig:current-zero-mu. and 13]] reveal broader profiles and relatively few circular current and magnetic field structures with a well-defined separatrix as in the small j case., Inspection of the current and $|B|$ contours for the same numerical solution \\ref{fig:current-zero-mu} and \ref{fig:bmag-zero-mu}] ] reveal broader profiles and relatively few circular current and magnetic field structures with a well-defined separatrix as in the small $\eta$ case.
 Since (here is no diffusive damping. gradients in electron density are able to persist. aud electron density structures generally follow the same structures in the current and magnetic fields.," Since there is no diffusive damping, gradients in electron density are able to persist, and electron density structures generally follow the same structures in the current and magnetic fields."
 ]vurtosis excess measurements for the po=0 numerical solutions vield mean values consistent with the +=jc numerical solutions. as seen in relfig:zero-mm-kurtosis..," Kurtosis excess measurements for the $\mu = 0$ numerical solutions yield mean values consistent with the $\eta = \mu$ numerical solutions, as seen in \\ref{fig:zero-mu-kurtosis}. ."
 Magnetic field strength andelectron density statistics are predominantly, Magnetic field strength andelectron density statistics are predominantly
To obtain a realistic period distribution. we use the period distribution (in log|P|) from the MACIIO sample (Alcocketal.1999) and the OGLE sample (Udalskietal.L999b) as input to generate a period distribution that matches the observed distribution.,"To obtain a realistic period distribution, we use the period distribution (in $\log[P]$ ) from the MACHO sample \citep{alc99} and the OGLE sample \citep{uda99b} as input to generate a period distribution that matches the observed distribution."
 It is well known that the Cepheid P-L relation has au intrinsic dispersion duc to he finite width of the iustability strip., It is well known that the Cepheid P-L relation has an intrinsic dispersion due to the finite width of the instability strip.
 We model his intrinsic dispersion as a Gaussian distribution with &=0.23 mae centered at zero., We model this intrinsic dispersion as a Gaussian distribution with $\sigma=0.23$ mag centered at zero.
 In addition to tlje intrinsic dispersion. we also add a Gaussian error of σ=0.05 mae to represent pliotoimietric errors.," In addition to the intrinsic dispersion, we also add a Gaussian error of $\sigma=0.05$ mag to represent photometric errors."
 These two Cassiani errors are then added in quadrature to the eeucrated P-L relations using the above equations and our period distribution., These two Gaussian errors are then added in quadrature to the generated P-L relations using the above equations and our period distribution.
 We plot out the simulated P-L relatious in Fieure 1.., We plot out the simulated P-L relations in Figure \ref{figsimu1}.
 These are similar to the published LAIC P-L relation (e.g.Udalskietal.1999a)., These are similar to the published LMC P-L relation \citep[e.g.][]{uda99a}.
. By lookiie at these P-L relatious. it is very difficult to distinguish the nonlinear and linear P-L relations (see Appeidix A for the answer).," By looking at these P-L relations, it is very difficult to distinguish the nonlinear and linear P-L relations (see Appendix A for the answer)."
 There are two reasons that male the nonlinear P-L relaion difficul to visualize., There are two reasons that make the nonlinear P-L relation difficult to visualize.
 Firstly. the existence of intrinsic dispersion dominates the total dispersion of the relation.," Firstly, the existence of intrinsic dispersion dominates the total dispersion of the relation."
 Secoudlv. the uonlinearity of the P-L relation is shallow. or the break is not a sharp or steep break that will be easy to visuaize.," Secondly, the nonlinearity of the P-L relation is shallow, or the break is not a sharp or steep break that will be easy to visualize."
 A shallow break of the P-L relaion would be. for example. that the sope variation betweeu the long ane short period slopes is roughly. 20% or less.," A shallow break of the P-L relation would be, for example, that the slope variation between the long and short period slopes is roughly $20$ or less."
 To illustrate these effects we plot another two siuulated P-L reations in Figure >. oue of them has a sharp/steep break aud another oue does not have iutriusije dispersio1i., To illustrate these effects we plot another two simulated P-L relations in Figure \ref{figsimu2}: one of them has a sharp/steep break and another one does not have intrinsic dispersion.
 The nonlinearity of the P-L rela1ος in this figure is more appareut than the P-L relatious given in Fietre l.., The nonlinearity of the P-L relations in this figure is more apparent than the P-L relations given in Figure \ref{figsimu1}.
 Based ou the above demonstration. how then cau we be confident about detecting the existence of a nonlinearv du the P-L relation. if any?," Based on the above demonstration, how then can we be confident about detecting the existence of a nonlinearity in the P-L relation, if any?"
 The aaswer is that we need to use someanalisis to detect the hidden nonlinearity., The answer is that we need to use some to detect the hidden nonlinearity.
 One ¢of the statisical tests that we ορίου in our analysis is f F-test which cau be fouid m many statistical tesxts (c.g..Weisberg1980).," One of the statistical tests that we employ in our analysis is the $F$ -test which can be found in many statistical texts \citep[e.g.,][]{wei80}."
. The F-test has been applied the OGLE data (ναυτ&Necow2001.2006) aid the MACΠΟ data (Necoweal.2005) aud both datase return a significant resul for the nonlinearity for the V-bai LAIC P-L relation (sce the F-test results in t Appendix. A for the P-L relation in Figure 1)).," The $F$ -test has been applied to the OGLE data \citep{kan04,kan06} and the MACHO data \citep{nge05} and both datasets return a significant result for the nonlinearity for the $V$ -band LMC P-L relation (see the $F$ -test results in the Appendix A for the P-L relation in Figure \ref{figsimu1}) )."
" To demoustrate that the F-test can return a reliable resi. we repeat the ""smmulatioi that was done in Fig rel any inies acl build up he clisribution of the F-tes results."," To demonstrate that the $F$ -test can return a reliable result, we repeat the “simulation” that was done in Figure \ref{figsimu1} many times and build up the distribution of the $F$ -test results."
 The resulting histograms for both of the intrinsically linear aud nonlinear siulated P-L relatio1s are shown in Figure Mi3.., The resulting histograms for both of the intrinsically linear and nonlinear simulated P-L relations are shown in Figure \ref{figfhist}.
" It can be clearly seen from this figure that the F-test will retWh a significant (100 per ceut of the time) aud a non-significant (95 per cent of the time) result whe ithe P-L relation is iutriusic nonlinear and iur. respectively,"," It can be clearly seen from this figure that the $F$ -test will return a significant (100 per cent of the time) and a non-significant (95 per cent of the time) result when the P-L relation is intrinsic nonlinear and linear, respectively."
 Other tests that mavbe apply to test aud detect the )onlinear P-L relation include. for example. the nou-paraietric regression as outlined iu Necowetal.(2005).," Other tests that maybe apply to test and detect the nonlinear P-L relation include, for example, the non-parametric regression as outlined in \citet{nge05}."
 Cureutly perhaps the best LMC Cepheid simples are from the OGLE aud MACTIO projects., Currently perhaps the best LMC Cepheid samples are from the OGLE and MACHO projects.
 They are the “best” in terms of the umber of Cepheids aud the quality of the photometric data (for example. small photometric errors aud lavee nuuber of data points per light curves).," They are the ""best"" in terms of the number of Cepheids and the quality of the photometric data (for example, small photometric errors and large number of data points per light curves)."
 Even though both samples show a nonlinear P-L relation as detected in Tanuuuaun&Reindl(2002).. I&àubur&Necow(2001) and al. (20053.. both samples lack Cepheids with log(P)>1.5 (due to the saturation of CCD).," Even though both samples show a nonlinear P-L relation as detected in \citet{tam02}, \citet{kan04} and \citet{nge05}, both samples lack Cepheids with $\log(P)>1.5$ (due to the saturation of CCD)."
 The lack of longer period Cepheids. together with the (overall) ziiallez number of long period Cepheids. is another criticism," The lack of longer period Cepheids, together with the (overall) smaller number of long period Cepheids, is another criticism"
rings.,rings.
 We used or this matter. regatling to plauet-noon systems. the results of (2006).. where tje authors th‘ough numerical simulaious obtain semi empirical expressious for the selinajor axis miaxiniunm ald miuimuu that a satellite in orbit of a glaut extrasolar planet may have asa [uction of the stelar and planetary paratjeters.," We used for this matter, regarding to planet-moon systems, the results of \cite{Domingos2006}, where the authors through numerical simulations obtain semi empirical expressions for the semi-major axis maximum and minimum that a satellite in orbit of a giant extrasolar planet may have as a function of the stellar and planetary parameters."
 Domingosetal.(2006) also estimates the tani.in mass of a satellite sucl that its orbit is stable., \cite{Domingos2006} also estimates the maximum mass of a satellite such that its orbit is stable.
 An interesting result is that planets with very ¢ose in orbits to their host star cau ouly 10ld Moons with very sinall masses. but more clistaut plaets nay have stable moots with masses even larger than tla of the Earth.," An interesting result is that planets with very close in orbits to their host star can only hold moons with very small masses, but more distant planets may have stable moons with masses even larger than that of the Earth."
 For ex:€uuple. at a dist:uice of 0221 AU from its host sta1. with an orbital period of 39.5 cl. way harbor a satellite of ip to 1.5 .," For example, at a distance of 0.224 AU from its host star, with an orbital period of 39.8 d, may harbor a satellite of up to 1.5 $_\oplus$."
 Further away plalets. such as HD 9278s. αἱ approximaely 1 AU [rom its star. allows for a satellite witha manimun mass of 1x10! ," Further away planets, such as HD 92788, at approximately 1 AU from its star, allows for a satellite witha maximum mass of $1 \times 10^4$ $_\oplus$."
The transitiug extrasolar planets witl the longest periods observed so ar are CoRoT-9b (95.27 «d). HD 30606 (111.31 d) aud Ixepler-11 e (118.37 d).," The transiting extrasolar planets with the longest periods observed so far are CoRoT-9b (95.27 d), HD 80606 (114.34 d) and Kepler-11 g (118.37 d)."
 Thus. these planet:« uay harbor a moon with 1nass siuila “or even larger than Eart1 that may be detectable from tle application of the present method to CoRoT or Ixepler lightceurves.," Thus, these planets may harbor a moon with mass similar or even larger than Earth, that may be detectable from the application of the present method to CoRoT or Kepler lightcurves."
 Figure 9 shows two examples of lighteurves obtained from our inodel., Figure \ref{fig:planetas_sem_lua} shows two examples of lightcurves obtained from our model.
 The figure ou the left. 2(a).. is for the transit of a planet like HD 209158b (Soutliworth (2010))). whereas the figure on the right. 2(b).. is for a planet similar to ColtoT-2b (Alonsoetal.(200 ))).," The figure on the left, \ref{fig:planetas_sem_lua_a}, is for the transit of a planet like HD 209458b \cite{Southworth2010}) ), whereas the figure on the right, \ref{fig:planetas_sem_lua_b}, , is for a planet similar to CoRoT-2b \cite{Alonso2008}) )."
linear regression fit logCA;)=D»logCGvy).,linear regression fit $\log(A_i)=D_2 \log(x_i)$.
 We find that that the 4 datapoints for each of the 12 cases exhibit a linear relationship. which proves the fractality of the avalanche areas.," We find that that the 4 datapoints for each of the 12 cases exhibit a linear relationship, which proves the fractality of the avalanche areas."
 The average fractal dimension of the 12 timesteps shown in Fig., The average fractal dimension of the 12 timesteps shown in Fig.
 | and 2 is D5=143x0.17., 1 and 2 is $D_2 = 1.43 \pm 0.17$.
 We measure Now the fractal dimension D». of the instantaneous energy dissipation volume in the 2-D avalanche for all 700 time steps of its. duration. shown for 12 time instants in Fig.," We measure now the fractal dimension $D_2$ of the instantaneous energy dissipation volume in the 2-D avalanche for all 700 time steps of its duration, shown for 12 time instants in Fig."
 1., 1.
 The unstable nodes (signifying instantaneous energy dissipation) are counted in each time step. which vield a number for the fractal volume or area A(t)= Vs(D. while the size x of the encompassing box is determined from the area of the time-integrated avalanche. i.e.. (5)=Yat). which yields the time evolution of the fractal dimension Da(t)=log|V»(0]/log[G0] CEq.," The unstable nodes (signifying instantaneous energy dissipation) are counted in each time step, which yield a number for the fractal volume or area $A(t)=V_2(t)$ , while the size $x$ of the encompassing box is determined from the area of the time-integrated avalanche, i.e., $x(t)=\sqrt{a(t)}$, which yields the time evolution of the fractal dimension $D_2(t) = \log[V_2(t)]/\log[x(t)]$ (Eq."
 5) as a function of time. shown in the top right panel in Fig.," 5) as a function of time, shown in the top right panel in Fig."
 3., 3.
 The fractal dimension D»(f) fluctuates around a constant mean value of D»=1.45€0.13. which is close to the arithmetic mean of the minimum dimension Doin*l| and maximum Euclidean limit Dojo.=2. Le. (D2)-(Dain+Drnacd/2=3/2.," The fractal dimension $D_2(t)$ fluctuates around a constant mean value of $D_2 = 1.45 \pm 0.13$, which is close to the arithmetic mean of the minimum dimension $D_{2,min} \approx 1$ and maximum Euclidean limit $D_{2,max}=2$, i.e. $\langle D_2 \rangle \approx (D_{2,min}+D_{2,max})/2=3/2$."
 This corroborates our second major assumption that the instantaneous volume of energy dissipation is fractal. and that the fractal dimension can be approximated by a mean (time-independent and size-independent) constant during the evolution of avalanches. in the statistical average.," This corroborates our second major assumption that the instantaneous volume of energy dissipation is fractal, and that the fractal dimension can be approximated by a mean (time-independent and size-independent) constant during the evolution of avalanches, in the statistical average."
 If we moreover define a mean energy dissipation rate quantum (AE) per unstable node. which ts indeed almost a constant for a cellular automaton model near the critical state. we expect a scaling of the instantaneous dissipation rate (or flux) 1) that is proportional to the instantaneous dissipation volume Vs (with Eq.," If we moreover define a mean energy dissipation rate quantum $\langle \Delta E \rangle$ per unstable node, which is indeed almost a constant for a cellular automaton model near the critical state, we expect a scaling of the instantaneous dissipation rate (or flux) $f(t)$ that is proportional to the instantaneous dissipation volume $V_S$ (with Eq."
 6). Combiningέ this with the diffusive expansion. of the boundary xt£)&7? (Eq.," 6), Combining this with the diffusive expansion of the boundary $x(t) \propto t^{1/2}$ (Eq."
 1). we can then predict the average time evolution of the energy dissipation rate 1)2de(r)/dt. Integrating Eq. (," 1), we can then predict the average time evolution of the energy dissipation rate $f(t)=de(t)/dt$, Integrating Eq. ("
8) 1n time. we obtain the time evolution of the total dissipated energy. e(r). Hence. for our 2-D avalanche (with D»= 3/2) we expect an evolution of e(r)er7. Which indeed closely matches the actually simulated cellular automaton case. as we see in Fig.,"8) in time, we obtain the time evolution of the total dissipated energy, $e(t)$, Hence, for our 2-D avalanche (with $D_2=3/2$ ) we expect an evolution of $e(t) \propto t^{(7/4)}$, which indeed closely matches the actually simulated cellular automaton case, as we see in Fig."
 3 (bottom left panel)., 3 (bottom left panel).
 The time evolution of the energy dissipation rate is shown 11 Fig., The time evolution of the energy dissipation rate is shown in Fig.
 3 (top left panel). which fluctuates strongly during the entire avalanche. but follows in the statistical average the predicted evolution de(r)/drx1227=PT for Dy=3/2.," 3 (top left panel), which fluctuates strongly during the entire avalanche, but follows in the statistical average the predicted evolution $de(t)/dt \propto t^{D_2/2} = t^{(3/4)}$ for $D_2\approx 3/2$."
 Note that our analytical expressions of the time evolution of avalanches. such as the linear size (7) (Eq.," Note that our analytical expressions of the time evolution of avalanches, such as the linear size $x(t)$ (Eq."
 1). the instantaneous energy dissipation rate f(t) (Eq.," 1), the instantaneous energy dissipation rate $f(t)$ (Eq."
 7. 8). or the total dissipated energy ο(1) (Eq.," 7, 8), or the total dissipated energy $e(t)$ (Eq."
 9). do not predict the specific evolution of a single avalanche event. but rather the statistical expectation value of a large ensemble of avalanches. similar to the statistical nature of the diffusive random walk model (Eq.," 9), do not predict the specific evolution of a single avalanche event, but rather the statistical expectation value of a large ensemble of avalanches, similar to the statistical nature of the diffusive random walk model (Eq."
 1)., 1).
 The time evolution of the instantaneous energy dissipation rate f(1) fluctuates strongly. as it can be seen in for the largest avalanche simulated 1n a cellular automaton model (Fig.," The time evolution of the instantaneous energy dissipation rate $f(t)$ fluctuates strongly, as it can be seen in for the largest avalanche simulated in a cellular automaton model (Fig."
 3. top left panel).," 3, top left panel)."
 We might estimate the peak values that can be obtained statistically (after a time duration ¢) from the optimum conditions when the fractal filling factor of the avalanche reaches a near-Euclidean filling. 1.e.. in the limit of DyS.," We might estimate the peak values that can be obtained statistically (after a time duration $t$ ) from the optimum conditions when the fractal filling factor of the avalanche reaches a near-Euclidean filling, i.e., in the limit of $D_S \mapsto S$."
 Replacing the fractal dimension Ds by the Euclidean limit S in Eqs., Replacing the fractal dimension $D_S$ by the Euclidean limit $S$ in Eqs.
 7 and 8 yields then (as an upper limit) an expectation value for the peak ptf). Denoting the energy dissipation rate in. the statistical average after time ¢=Τ with with F=f(rT). the peak energy dissipation rate with P=p(tT). and the total energy of the avalanche with E.=e(fT). it follows from Eqs. (8-," 7 and 8 yields then (as an upper limit) an expectation value for the peak $p(t)$ , Denoting the energy dissipation rate in the statistical average after time $t=T$ with with $F=f(t=T)$ , the peak energy dissipation rate with $P=p(t=T)$, and the total energy of the avalanche with $E=e(t=T)$, it follows from Eqs. (8-10)"
" that E«FT=PPS’T, and we expect then the following correlations between the three parameters E. F. P and T for an ensemble of avalanches. For instance. for à 2-D avalanche with an average fractal dimension of Ds=3/2 we expect the following two correlations. EoT/7. FοΤ1, and P.xT! (see Fig."," that $E \propto F T = P^{D_S/S} T$, and we expect then the following correlations between the three parameters $E$, $F$, $P$ and $T$ for an ensemble of avalanches, For instance, for a 2-D avalanche with an average fractal dimension of $D_2=3/2$ we expect the following two correlations, $E \propto T^{7/4}$, $F \propto T^{3/4}$, and $P \propto T^1$ (see Fig."
 3)., 3).
 The powerlaw indices for the correlated parameters are listed for the three Euclidean dimensions S$=1.2.3 separately in Table I.," The powerlaw indices for the correlated parameters are listed for the three Euclidean dimensions $S=1,2,3$ separately in Table 1."
 Considering the probability of an avalanche with volume V. the statistical likelihood simply scales reciprocally to the volume size V. if avalanches are equally likely in every space location of auniform volume Vo of a system in a (self-organized) eritical state.," Considering the probability of an avalanche with volume $V$, the statistical likelihood simply scales reciprocally to the volume size $V$, if avalanches are equally likely in every space location of a uniform volume $V_0$ of a system in a (self-organized) critical state."
 This is illustrated in Fig. (, This is illustrated in Fig. (
4).,4).
 For the 1-D Euclidean space. a=| avalanche can happen with the maximum size L=Lo of the system (top left). Ξ2 avalanches with the half size L=Lo/2. orn24 avalanches for a quarter size L=Lo/4.," For the 1-D Euclidean space, $n=1$ avalanche can happen with the maximum size $L=L_0$ of the system (top left), $n=2$ avalanches with the half size $L=L_0/2$, or $n=4$ avalanches for a quarter size $L=L_0/4$."
 For the 2-D Euclidean space. the number of possible avalanches that can be fit into the total area Ao of the system isn=| for A=Αρ =2224 forA=Αρ/2. or n—2+=16 for A=Ao/4 (second row).," For the 2-D Euclidean space, the number of possible avalanches that can be fit into the total area $A_0$ of the system is $n=1$ for $A=A_0$, $n=2^2=4$ for $A=A_0/2$, or $n=2^4=16$ for $A=A_0/4$ (second row)."
 For the 3-D Euclidean space we have. correspondingly. ?=| for V2Vy. i=2?8 for cubes of half size L=Lo/2. and 1=4°64 for quarter-size cubes with L=Lo/4 (bottom row).," For the 3-D Euclidean space we have, correspondingly, $n=1$ for $V=V_0$, $n=2^3=8$ for cubes of half size $L=L_0/2$, and $n=4^3=64$ for quarter-size cubes with $L=L_0/4$ (bottom row)."
 So. generalizing to $=1.2.3 dimensions. we canexpress the probability for an avalanche of size L and volume Vs=L as. This simple probability argument 1$ based on the assumption that the number or occurrence frequency of avalanches is equally likelythroughout the system. so it assumes à homogeneous distribution of critical states across the entire system.," So, generalizing to $S=1,2,3$ dimensions, we canexpress the probability for an avalanche of size $L$ and volume $V_S=L^S$ as, This simple probability argument is based on the assumption that the number or occurrence frequency of avalanches is equally likelythroughout the system, so it assumes a homogeneous distribution of critical states across the entire system."
 The oceurrence frequency distribution of length scales. N(L)«L (Eq.," The occurrence frequency distribution of length scales, $N(L) \propto L^{-S}$ (Eq."
 12). serves as a primary distribution function from whichall other occurrence frequency distribution," 12), serves as a primary distribution function from whichall other occurrence frequency distribution"
emission. away from the phase centre.,emission away from the phase centre.
 To reconstruct an image. the assumption that any variation in the Lringe amplitude: wit1i hour angle isR due to the interferometerR⋅ response to the source structure only is made.," To reconstruct an image, the assumption that any variation in the fringe amplitude with hour angle is due to the interferometer response to the source structure only is made."
 However. this is violated if the source varies within the time needed for aperture synthesis.," However, this is violated if the source varies within the time needed for aperture synthesis."
 For our observations. a direct reconstruction of the source results in many artifacts including jet-like emission. [rom a central. core.," For our observations, a direct reconstruction of the source results in many artifacts including jet-like emission from a central core."
 The variability of the source is shown in refuv ariationswhichplolsthemeasured fliragainstbaselinelenglhoruvspacing., The variability of the source is shown in \\ref{uv_variations} which plots the measured flux against baseline length or $uv$ spacing.
Oncecansccthallhesourceishighlgeariableoverallbaselinedisl , One can see that the source is highly variable over all baseline distances and no accurate reconstruction of the source brightness distribution can be obtained.
The plot shown in reluy .arialionsdocsallowsomequantaliveevaluation, The plot shown in \\ref{uv_variations} does allow some quantative evaluation.
 Aresolredsource wouldshowadecreascin measured {litewil pinere," A resolved source would show a decrease in measured flux with increasing $uv$ spacing, whereas during a flare the measured flux is approximately constant over all $uv$ separations."
dsin guy Spacing., In 3 the measured flux is high at the longest baselines suggesting that the source is unresolved.
 Wheres at Ὁ Cllz has an angular size of less than TO mas., A source that is unresolved at a $uv$ spacing of 3.5 $\lambda$ at 5 GHz has an angular size of less than 70 mas.
 This is consistent with a scatter-broadened. size of Cvgnus X-3.2 which has a strong dependence on frequency (Wilkinson. Naravan Spencer 1904) anc has been measured at 5 Cillz to be 2PO30 mas (Aliocluszewski et 22010].," This is consistent with a scatter-broadened size of Cygnus X-3, which has a strong dependence on frequency (Wilkinson, Narayan Spencer 1994) and has been measured at 5 GHz to be $\simeq 20-30$ mas (Mioduszewski et 2000)."
 For these observations the success of the MEBRLIN array is not in its imaging capabiliies. but its phoometry.," For these observations the success of the MERLIN array is not in its imaging capabilities, but its photometry."
 Figs 4-9 show photometry for all six C-band epocis., Figs \ref{photometry_1}- \ref{photometry_6} show photometry for all six C-band epochs.
 Note that in these figures the verical scales vary and the zero is not included., Note that in these figures the vertical scales vary and the zero is not included.
" Vertical lines in all hese figures indicate the time at which X-rav. minimums occ""urs using the ephermeris by Matz et ((1996).", Vertical lines in all these figures indicate the time at which X-ray minimum occurs using the ephermeris by Matz et (1996).
 Data have been average«bL into time bins of 2.0-4.0, Data have been averaged into time bins of 2.0-4.0
Cosmic shear surveys offer a unique aud unbiased view on the wav matter cluscr at cosmological scales aud can then serve as a mean to explore the details of he eravitational iustabiliics.,Cosmic shear surveys offer a unique and unbiased view on the way matter cluster at cosmological scales and can then serve as a mean to explore the details of the gravitational instabilities.
 In particular the statistical xoperties of the shear fied. in particular their veh order correlation fictions. are expeced to reflect thee of the uatter density field. (sce 3ellier 1999).," In particular the statistical properties of the shear field, in particular their high order correlation functions, are expected to reflect those of the matter density field (see Mellier 1999)."
" The me:Γονπο, of correlaticn functions iu the cosniüe shear sitrvevs has heu been recognized as a mca1 to break the »urameter degeneracy )etwoeen the desity parameter of the Universe and σς tha leasturements of the shear powxY spectra xovide for (Bernardeau e al.", The measurement of correlation functions in the cosmic shear surveys has then been recognized as a mean to break the parameter degeneracy between the density parameter of the Universe and $\sigma_8$ that measurements of the shear power spectra provide for (Bernardeau et al.
 1997. Jain Sejak 1997) or a wav to test the eravitv law at cosmiological scales (Bernardeat 2001).," 1997, Jain Seljak 1997) or a way to test the gravity law at cosmological scales (Bernardeau 2004)."
 Matter correlation fictions have Όσοι explored extensively in different regine., Matter correlation functions have been explored extensively in different regime.
 Areasonable uucderstaucdiie of their behaviors have been obtained in the quasilinear regiae from perturbation theorv techniques id iuto the nonlinear regiue from phenomenological yproaches (sec review of Bernarcdean οἳ d., A reasonable understanding of their behaviors have been obtained in the quasilinear regime from perturbation theory techniques and into the nonlinear regime from phenomenological approaches (see review of Bernardeau et al.
 2002)., 2002).
 ecentlv a senüanalvtie technique based on the halo -rodel (Seljak 200. Ma Fry 2000. Scoccimarra et al.," Recently a semianalytic technique based on the halo model (Seljak 2000, Ma Fry 2000, Scoccimarro et al."
 2001. see Coorav 9ιο] 2002 for a receut review) las attract «a lot of ateutiou because it ca1 provide accurate predictions for fje ealaxy or matter correlation xoperties.," 2001, see Cooray Sheth 2002 for a recent review) has attracted a lot of attention because it can provide accurate predictions for the galaxy or matter correlation properties."
 So far however most of these ticoretical approaches have ¢lealt with the matter denusitv field or wit1 the couvereeice fiek., So far however most of these theoretical approaches have dealt with the matter density field or with the convergence field.
 The later is closely related to he density field. beiug a simple projection of i. but the actual observational situatic Lis nore cunibersoue.," The later is closely related to the density field, being a simple projection of it, but the actual observational situation is more cumbersome."
 What is ivectly measured istI shear field (through galaxy shape nueasurements. που Allier 1999 for a detailed review on the obscervationa techniques) and it reveals difücult to build reliable xojected. density maps.," What is directly measured is the shear field (through galaxy shape measurements, see Mellier 1999 for a detailed review on the observational techniques) and it reveals difficult to build reliable projected density maps."
 It forces us to explore iore «leeply the ligh-order correlatiou patterns., It forces us to explore more deeply the high-order correlation patterns.
 Those. because of their ecometrical nature. are more intricate fiui that of the convergence maps.," Those, because of their geometrical nature, are more intricate than that of the convergence maps."
 In particular compCX relatious are expected between the «correlation components because both of pseudo-vectOr απο of those and because oue expects vanishius D modes in the shear fied.," In particular complex relations are expected between the correlation components because both of pseudo-vector nature of those and because one expects vanishing ""B"" modes in the shear field."
 As a results shear correlation cocficicuts depeid lia coniplicated way on the basis on which they are computed. have frequeut sien changes. ete. (," As a results shear correlation coefficients depend in a complicated way on the basis on which they are computed, have frequent sign changes, etc. ("
see Schucider aui Lombardi 2003. for au oxhaustive exploration of these properties).,"see Schneider and Lombardi 2003, for an exhaustive exploration of these properties)."
 It. makes t10 construction of iuehods for nmeasuiug the shear three-point function difficult., It makes the construction of methods for measuring the shear three-point function difficult.
 Attempts however have been made to detect the shear or aperture mass high order correlation functiows (Bernarcdeau et al., Attempts however have been made to detect the shear or aperture mass high order correlation functions (Bernardeau et al.
 2603. Pen ( al.," 2003, Pen et al."
 2003. Jarvis et al.," 2003, Jarvis et al."
 2001)., 2004).
 Alhotwh these methods can give robust results. they iav be far from optimal aud therefore rot completely saisfactorv.," Although these methods can give robust results, they may be far from optimal and therefore not completely satisfactory."
 One aiui of this o»vper is fo provide better foundations for the design of jew. ietliods or neasunrueg shear threc-poiut functions., One aim of this paper is to provide better foundations for the design of new methods for measuring shear three-point functions.
 Iu lis paox the focus wil be put on the onc-halo ποσο case for the description of the natter correlation VOPCLies., In this paper the focus will be put on the one-halo model case for the description of the matter correlation properties.
 The idea is not however to build an accurate nodel for the nass distribution it to mild a model good chough to reproduce the generic ecomevical properties of he shear correlation patterus., The idea is not however to build an accurate model for the mass distribution but to build a model good enough to reproduce the generic geometrical properties of the shear correlation patterns.
 The 1-iio model. with a )OWOY aw density profile. is a good caididate for such a ask being simple cnough to allow coudete computations of the correlation functious.," The 1-halo model, with a power law density profile, is a good candidate for such a task being simple enough to allow complete computations of the correlation functions."
 The paOY js divided as ollows., The paper is divided as follows.
 The second section is devote to a presentation of the mathematical tools applied to t16 One-halo model in the third section., The second section is devoted to a presentation of the mathematical tools applied to the one-halo model in the third section.
 The fourth section gives some insights ou the results that have been obtained., The fourth section gives some insights on the results that have been obtained.
 Wwjat we are interested in are the statistical properties of the either the projected deusity field o(r). the couvergence field &(r) aud the 2-componcut shear field (51.52).," What we are interested in are the statistical properties of the either the projected density field $\phi(\vr)$, the convergence field $\kappa(\vr)$ and the 2-component shear field $(\gamma_{1},\gamma_{2})$."
" In the folowing the plane wave approximation is used. as usual. sO that the convergence aud shear field) are all obtained through derivative operators applied to the projected potential. where r is the augular position of the poiut ou the kv and a aud b are the point coordinates,"," In the following the plane wave approximation is used, as usual, so that the convergence and shear field are all obtained through derivative operators applied to the projected potential, where $\vr$ is the angular position of the point on the sky and $a$ and $b$ are the point coordinates."
where Ly is the present-day. D-band luminosity in units of Ls. (Lp—84QULs. for ST: Gavazzi et al.,where $L_{\rm B}$ is the present-day B-band luminosity in units of $L_{{\rm B}\odot}$ $L_{\rm B} = 8.4\times10^{10} L_{{\rm B}\odot}$ for 87; Gavazzi et al.
 2005) and £45 is the age of the stellar population in units of 15 Civr he formula is valid in the range from ~0.5 to over 15 Cyr)., 2005) and $t_{15}$ is the age of the stellar population in units of 15 Gyr (the formula is valid in the range from $\sim$ 0.5 to over 15 Gyr).
 Integrating this equation under the assumption that re current stellar population is 10.5 Gyr old. (formed. at >= 2.1) we obtain a gas mass contribution from stellar =vinds of 1.104.AZ. during the past LO Cyr.," Integrating this equation under the assumption that the current stellar population is 10.5 Gyr old (formed at $z=2.1$ ), we obtain a gas mass contribution from stellar winds of $1\times10^{11}~M_{\odot}$ during the past 10 Gyr."
" Assuming ju the material from which the current stellar population of M 87 forme was pre-cnrichecl to conservatively Za)1.5 Solar. with a οἱο abundance ratio of 1.5 Solar. the otal mass of Si returned to the ISM/ICM, by the stellar winds is 4.3Q0 AJ.."," Assuming that the material from which the current stellar population of M 87 formed was pre-enriched to conservatively $Z_{\rm Si}\sim0.5$ Solar, with a Si/Fe abundance ratio of 1.5 Solar, the total mass of Si returned to the ISM/ICM by the stellar winds is $4.3\times10^7~M_{\odot}$."
 The total mass of Fe returned. is 4.8«107Al., The total mass of Fe returned is $4.8\times10^7~M_{\odot}$.
" Under these assumptions. the total mass of Si produced. by stellar winds in excess of a οἱο ratio of 1 Solar is L4.10""Αι."," Under these assumptions, the total mass of Si produced by stellar winds in excess of a Si/Fe ratio of 1 Solar is $1.4\times10^7~M_{\odot}$."
" ""πο observed. total Si mass in excess to a Lat profile with Si/Fe-1 Solar around. 87 is 3.6«10"".AL...", The observed total Si mass in excess to a flat profile with Si/Fe=1 Solar around 87 is $3.6\times10^6~M_{\odot}$.
 Pherefore. despite all the uncertainties in the estimates of the metal mass loss. the excess Si observed arouncl M 8T could most likely be produced by stellar winds.," Therefore, despite all the uncertainties in the estimates of the metal mass loss, the excess Si observed around M 87 could most likely be produced by stellar winds."
 Because the initial starbursts. that enriched the material from which the current stellar population formed. produced predominantly SNoc products. and the Meg» index indicates that the stellar population of S87 is enriched. to more that 1 Solar (Ixobavashi Arimoto 1999. Matsushita οἱ al.," Because the initial starbursts, that enriched the material from which the current stellar population formed, produced predominantly $_{\rm CC}$ products, and the $_2$ index indicates that the stellar population of 87 is enriched to more that 1 Solar (Kobayashi Arimoto 1999, Matsushita et al."
 2003) this scenario can plausibly produce centrally peaked abundance proliles of λος products., 2003) this scenario can plausibly produce centrally peaked abundance profiles of $_{\rm CC}$ products.
 Another possible mechanism contributing to the observed centrally peaked distribution of SNe products is strong carly enrichment of the lowest entropy N-ray. emitting gas and inellicient mixing of this material with the surrounding ICM., Another possible mechanism contributing to the observed centrally peaked distribution of $_{\rm CC}$ products is strong early enrichment of the lowest entropy X-ray emitting gas and inefficient mixing of this material with the surrounding ICM.
 If the lowest entropy. X-ray. emitting gas currently seen in the Virgo Cluster core was at high redshift located in the environments of massive galaxies during their epoch of maximum. star formation. then this material may have become enriched. significantly by SNc« products.," If the lowest entropy X-ray emitting gas currently seen in the Virgo Cluster core was at high redshift located in the environments of massive galaxies during their epoch of maximum star formation, then this material may have become enriched significantly by $_{\rm CC}$ products."
 As the cluster. formed. this low entropy SN enriched. eas will naturally sink ane accumulate at the base of the cluster potential.," As the cluster formed, this low entropy $_{\rm CC}$ enriched gas will naturally sink and accumulate at the base of the cluster potential."
 Assuming that it does not become well mixed with the surrounding ICM as it does so and it does not cool out of the hot phase. this may Lead to the observed peak in metal abundances.," Assuming that it does not become well mixed with the surrounding ICM as it does so and it does not cool out of the hot phase, this may lead to the observed peak in metal abundances."
 We explore other possible explanations for the observed abundance ratio profiles., We explore other possible explanations for the observed abundance ratio profiles.
" Each of these mechanisms predicts a central enhancement in the οἱFe. S/Ee. Απο, and Ca/lc ratios and each of them might. to some degree. contribute to the observed. racial trends."," Each of these mechanisms predicts a central enhancement in the Si/Fe, S/Fe, Ar/Fe, and Ca/Fe ratios and each of them might, to some degree, contribute to the observed radial trends."
 AX stellar LAIR. which is latter (has a smaller à in Equation 2. therefore. producing more massive stars) in the central regions of the cluster would produce a central increase of Si-eroup elements.," A stellar IMF, which is flatter (has a smaller $\alpha$ in Equation 2, therefore producing more massive stars) in the central regions of the cluster would produce a central increase of Si-group elements."
 The ratios of chemical elements produced by SNoc ave a strong function of the mass of the progenitor., The ratios of chemical elements produced by ${\rm SN_{CC}}$ are a strong function of the mass of the progenitor.
 To examine the cllect of the EME on the predicted abundance ratios. we vary its slope a.," To examine the effect of the IMF on the predicted abundance ratios, we vary its slope $\alpha$ ."
 Fie., Fig.
 6 shows the predicted abundance ratios assuming a steepening IMIE as a function of radius and a racially constant relative fraction of SNIa. f=0.15.," \ref{fig:alpha} shows the predicted abundance ratios assuming a steepening IMF as a function of radius and a radially constant relative fraction of ${\rm SN\;Ia}$, $f=0.15$."
 This fraction was chosen to lie within the range suggested by the Si/Le abundance ratio profile and it only alfects the normalization of the predicted. profiles., This fraction was chosen to lie within the range suggested by the Si/Fe abundance ratio profile and it only affects the normalization of the predicted profiles.
 The explanation of the observed range of values in the radial profiles of the Sifke and S/Lle ratios by a radial trend. in the EME would. require extremely steep EME at larger radii., The explanation of the observed range of values in the radial profiles of the Si/Fe and S/Fe ratios by a radial trend in the IMF would require extremely steep IMF at larger radii.
 Moreover. this scenario would produce. very. large central increases of the Nese ancl Alefbe ratios. which we would clearly detect even given the systematic uncertainties in the Ne anc Mg abundance determinations.," Moreover, this scenario would produce very large central increases of the Ne/Fe and Mg/Fe ratios, which we would clearly detect even given the systematic uncertainties in the Ne and Mg abundance determinations."
 While we cannot rule out a small radial trend in the stellar IME. it cannot be responsible for the large observedranges in the abundance ratios.," While we cannot rule out a small radial trend in the stellar IMF, it cannot be responsible for the large observedranges in the abundance ratios."
In Seleznev οἱ al. (,In Seleznev et al. (
2010). we combined optical photometry with 2MÀSS data (Skrutskie et 22006). and focused our attention mainly on the structure of Trumpler 20.,"2010), we combined optical photometry with 2MASS data (Skrutskie et 2006), and focused our attention mainly on the structure of Trumpler 20."
 Detailed star count analvsis revealed (hat the cluster has a regular shape and an angular diameter of LO arcmin. confirming Trumplers estimate based on a visual inspection.," Detailed star count analysis revealed that the cluster has a regular shape and an angular diameter of 10 arcmin, confirming Trumpler's estimate based on a visual inspection."
 As shown in Fig., As shown in Fig.
 7 of Selezuev et ((2010). the radial clensitv profile is smooth. but the cluster shows a hole in its nominal center.," 7 of Seleznev et (2010), the radial density profile is smooth, but the cluster shows a hole in its nominal center."
 Assuming solar metallicitv. we found a reddening consistent with the one derived bv PlIa08. but a smaller distance of 2.9 kpc. for an age Οἱ 1.5 Gyr.," Assuming solar metallicity, we found a reddening consistent with the one derived by Pla08, but a smaller distance of 2.9 kpc, for an age of 1.5 Gyr."
 Metallicitv. together with an insullicient color baseline. may explain these slightly different In an attempt to better characterize this interesting cluster. in 2009 we acquired new deep photometry.," Metallicity, together with an insufficient color baseline, may explain these slightly different In an attempt to better characterize this interesting cluster, in 2009 we acquired new deep photometry."
 The description ancl interpretation of (his photometric material is the subject of this paper., The description and interpretation of this photometric material is the subject of this paper.
 We basically aimed at putting the cluster parameters on a firmer base. and tried to establish whether the blue sequence. erroneously indicated as the main sequence of Trumpler 20 by MeSwain Gies (2005). is composed bx field stars or by cluster As can be seen in Fig.," We basically aimed at putting the cluster parameters on a firmer base, and tried to establish whether the blue sequence, erroneously indicated as the main sequence of Trumpler 20 by McSwain Gies (2005), is composed by field stars or by cluster As can be seen in Fig."
 1. made from a 900 see J-hancl exposure. Trumpler 20 is barely visible in a very dense stellar [ield. which complicates the interpretation of its CMD (see below).," 1, made from a 900 sec $I$ -band exposure, Trumpler 20 is barely visible in a very dense stellar field, which complicates the interpretation of its CMD (see below)."
 The field shown in Fig., The field shown in Fig.
 1 is 20 arcinin on a side: North is at the top. aud (he East io the left.," 1 is 20 arcmin on a side; North is at the top, and the East to the left."
shocks occur in the material ejected in a GRB and are expected to be magnetized.,shocks occur in the material ejected in a GRB and are expected to be magnetized.
" The geometry is also such that the shocks will be perpendicular, i.e., the magnetic field will be perpendicular to the velocity vector, or parallel to the shock front."," The geometry is also such that the shocks will be perpendicular, i.e., the magnetic field will be perpendicular to the velocity vector, or parallel to the shock front."
" We have analyzed such shocks, assuming that a fraction e, of the gas thermal energy in the shocked gas goes into electrons and that this energy is entirely radiated in prompt radiation."," We have analyzed such shocks, assuming that a fraction $\epsilon_e$ of the gas thermal energy in the shocked gas goes into electrons and that this energy is entirely radiated in prompt radiation."
" We consider two values of e&, viz., €=0.2,"," We consider two values of $\epsilon_e$ , viz., $\epsilon_e=0.2$,"
" which we consider to be a reasonable estimate, and ε,=1, which is highly optimistic."," which we consider to be a reasonable estimate, and $\epsilon_e=1$, which is highly optimistic."
" Our calculations indicate that, once o exceeds about 0.1, the efficiency of thermalization begins to fall noticeably, and that the drop becomes quite precipitous once c>1 (Figs. [I], D)."," Our calculations indicate that, once $\sigma$ exceeds about 0.1, the efficiency of thermalization begins to fall noticeably, and that the drop becomes quite precipitous once $\sigma>1$ (Figs. \ref{fig1}, \ref{fig2}) )."
" GRB observations indicate that the prompt y-ray emission is quite efficient, with the efficiency parameter e, (defined in eq. [2p "," GRB observations indicate that the prompt $\gamma$-ray emission is quite efficient, with the efficiency parameter $\epsilon_\gamma$ (defined in eq. \ref{egamma}) )"
being typically of order 0.5 or larger (Table[I))., being typically of order 0.5 or larger (Table \ref{tab1}) ).
" On the other hand, not a single GRB has o<0.1, as needed to obtain such high efficiency in a cold magnetized shock, and half our sample has σ>1, where radiative efficiency is very poor."," On the other hand, not a single GRB has $\sigma<0.1$, as needed to obtain such high efficiency in a cold magnetized shock, and half our sample has $\sigma>1$, where radiative efficiency is very poor."
" The implication is that GRB prompt emission cannot be produced by either internal shocks or the reverse shock, if jets are cold and magnetically accelerated."," The implication is that GRB prompt emission cannot be produced by either internal shocks or the reverse shock, if jets are cold and magnetically accelerated."
 This conclusion is hard to avoid., This conclusion is hard to avoid.
" Even with very optimistic assumptions, e.g., all the thermal energy goes into electrons (e,=1, which might happen if the jet is made entirely of electrons and positrons), and is immediately radiated in y-rays, the calculated efficiency is far below what is needed to explain the observations."," Even with very optimistic assumptions, e.g., all the thermal energy goes into electrons $\epsilon_e=1$, which might happen if the jet is made entirely of electrons and positrons), and is immediately radiated in $\gamma$ -rays, the calculated efficiency is far below what is needed to explain the observations."
" We consider here several possible resolutions of this puzzle, none of which is very One possibility is to satisfactory]associate the prompt emission with the forward shock, which is very weakly magnetized (c« 1) and therefore converts a large fraction of the jet kinetic energy into thermal energy."," We consider here several possible resolutions of this puzzle, none of which is very One possibility is to associate the prompt emission with the forward shock, which is very weakly magnetized $\sigma\ll1$ ) and therefore converts a large fraction of the jet kinetic energy into thermal energy."
" This alone is not enough since the thermal energy must then be radiated with greater than efficiency in order to explain the observed values of e,.", This alone is not enough since the thermal energy must then be radiated with greater than efficiency in order to explain the observed values of $\epsilon_\gamma$.
" Therefore, nearly all the thermal energy should go into electrons (e;~ 1), which is very unlikely for the electron-proton plasma we expect to be present in the forward shock."," Therefore, nearly all the thermal energy should go into electrons $\epsilon_e\sim1$ ), which is very unlikely for the electron-proton plasma we expect to be present in the forward shock."
" In any case, the forward shock has been convincingly associated [Piran|with 2005;afterglow emissionZhang|(2007}; and references therein), and it does not seem likely that the same region will also produce the prompt emission."," In any case, the forward shock has been convincingly associated with afterglow emission; and references therein), and it does not seem likely that the same region will also produce the prompt emission."
 A second possibility is that much of the magnetic energy in a GRB shock is somehow converted to particle thermal energy., A second possibility is that much of the magnetic energy in a GRB shock is somehow converted to particle thermal energy.
" That is, when σ is large and most of the energy density in the gas is in the form of magnetic energy, there is a mechanism whereby this energy is converted to particle energy."," That is, when $\sigma$ is large and most of the energy density in the post-shock gas is in the form of magnetic energy, there is a mechanism whereby this energy is converted to particle energy."
" A scenario where this can happen is if the pre-shock gas is ""striped"" as in current models of EY&Kir dissipation001.Lust in the magnetized wind of pulsarsIO.", A scenario where this can happen is if the pre-shock gas is “striped” as in current models of energy dissipation in the magnetized wind of pulsars.
 A striped morphol(Gras iis not obvious fora GRB jet (but see[|McKinney |densky[2010))., A striped morphology is not obvious for a GRB jet (but see ).
" However, if it is present, we do expect a substantia&Uz] fraction "" the magnetic energy to be dissipated in the shock."," However, if it is present, we do expect a substantial fraction of the magnetic energy to be dissipated in the shock."
" Figure B] shows results for a hypothetical model in which we assume that, in addition to a fraction e,=0.2 of the gas thermal enthalpy, of the magnetic energy is radiated."," Figure \ref{fig3} shows results for a hypothetical model in which we assume that, in addition to a fraction $\epsilon_e=0.2$ of the gas thermal enthalpy, of the magnetic energy is radiated."
 This model does explain the GRB observations but at the price of making a very extreme (and theoretically unsupported) assumption., This model does explain the GRB observations but at the price of making a very extreme (and theoretically unsupported) assumption.
 We do not endorse this model but present it merely as a way to emphasize how difficult it is to explain the radiative efficiency of GRB prompt emission., We do not endorse this model but present it merely as a way to emphasize how difficult it is to explain the radiative efficiency of GRB prompt emission.
" A third possibility is that the magnetic energy is dissipated, not through a shock, but through some other “current-driven"" mechanism such as reconnection."," A third possibility is that the magnetic energy is dissipated, not through a shock, but through some other ``current-driven'' mechanism such as reconnection."
" Poynting-dominated magnetically accelerated jets are fairly stable onceX are ultra-relativistic (e.g., 2009)) and are unlikely to have Tchekhovskoy|[Narayan,Li& fluctuations that might drive reconnection."," Poynting-dominated magnetically accelerated jets are fairly stable once they are ultra-relativistic (e.g., ) and are unlikely to have large-amplitude fluctuations that might drive reconnection."
" However,large-amplitude it is conceivable that these jets lose their stability once they reach a large radius e.g., the deceleration radius where the jet meets the external 010),medium and begins to slow down."," However, it is conceivable that these jets lose their stability once they reach a large radius, e.g., the deceleration radius where the jet meets the external medium and begins to slow down."
 Whether the instability would be powerful enough to drive wholesale reconnection and convert most of the magnetic energy into particle energy is an open question., Whether the instability would be powerful enough to drive wholesale reconnection and convert most of the magnetic energy into particle energy is an open question.
 As Fig., As Fig.
"B] shows, something like this is needed if one is to explain the data."," \ref{fig3} shows, something like this is needed if one is to explain the data."
" Another possibility is that our assumption of cold gas, whose acceleration is entirely by magnetic means, is incorrect."," Another possibility is that our assumption of cold gas, whose acceleration is entirely by magnetic means, is incorrect."
 relativistic MHD simulations of magnetized jets indicate that these( jets develop a kink [Obergaulinger|/2008}instability which [Moll][2009)might lead to dissipation., Non-relativistic MHD simulations of magnetized jets indicate that these jets develop a kink instability which might lead to dissipation.
 We could then have a scenario in which the jet starts off magnetically dominated at the base but quickly dissipates its magnetic energy into heat while the jet is still non- or quasi-relativistic., We could then have a scenario in which the jet starts off magnetically dominated at the base but quickly dissipates its magnetic energy into heat while the jet is still non- or quasi-relativistic.
 Further acceleration of the jet is then driven by the thermal pressure of the heated gas., Further acceleration of the jet is then driven by the thermal pressure of the heated gas.
" Thus, we no longer have a magnetically driven jet, but something akin to the standard fireball model of a GRB."," Thus, we no longer have a magnetically driven jet, but something akin to the standard fireball model of a GRB."
" Clearly, the calculations presented here, which are restricted to cold magnetized gas, are not relevant for such a model."," Clearly, the calculations presented here, which are restricted to cold magnetized gas, are not relevant for such a model."
" Finally, it is possible that the prompt emission in GRBs is not produced in the jet at a large distance from the progenitor, but rather in the photospheric region where the jet ejecta first become [σοιtransparent."," Finally, it is possible that the prompt emission in GRBs is not produced in the jet at a large distance from the progenitor, but rather in the photospheric region where the jet ejecta first become transparent."
 esasModels of Kc aform have been developed ancand it is claimed ththat they produce prompt y- emission DOTwith high isradiative efficiency and with the correct spectrum neni2011)).," Models of this form have been developed and it is claimed that they produce prompt $\gamma$ -ray emission with high radiative efficiency and with the correct spectrum (e.g., )."
" (e.g.,MagneticPe'er fields& may Ryde|2011]play arole in photospheric models (Uzdensky but the role of shocks is unclear."," Magnetic fields may play arole in photospheric models , but the role of shocks is unclear."
" Our analysis &is not McKinneyapplicable to |2010),,these models.", Our analysis is not applicable to these models.
 RN and AT were supported in part by NASA grant NNX11AE16G, RN and AT were supported in part by NASA grant NNX11AE16G
of the feeding zone is only due to planet accretion.,of the feeding zone is only due to planet accretion.
 Since no mechanisms for the dissipation of the gaseous component of the nebula were modelled. the variation of the volume gas density of the feeding zone is due only to the formation of the envelope.," Since no mechanisms for the dissipation of the gaseous component of the nebula were modelled, the variation of the volume gas density of the feeding zone is due only to the formation of the envelope."
 We note that this is an idealised situation where the protoplanet probably has the largest amount of available material to feed itself., We note that this is an idealised situation where the protoplanet probably has the largest amount of available material to feed itself.
 We found that. in spite of the favourable conditions for mass accretion of our model. for protoplanetary dises with densities lower than that of à 6 MMSN. the formation process could not be completed according to the timescales imposed by the observations of circumstellar dises (lower than 107 yr) in either of the cases considered for the calculation of Λο.," We found that, in spite of the favourable conditions for mass accretion of our model, for protoplanetary discs with densities lower than that of a 6 MMSN, the formation process could not be completed according to the timescales imposed by the observations of circumstellar discs (lower than $10^7$ yr) in either of the cases considered for the calculation of $R_\mathrm{eff}$."
 The results for a disc of 6 MMSN are depicted in Fig. 5.., The results for a disc of 6 MMSN are depicted in Fig. \ref{comp1}.
 The upper panel (Fig., The upper panel (Fig.
" 5 a) shows the evolution of the core and envelope mass when ignoring for the protoplanet capture effective radius the presence of the atmosphere (R5, caleulated according to Eq. (11))).", \ref{comp1} ) shows the evolution of the core and envelope mass when ignoring for the protoplanet capture effective radius the presence of the atmosphere $R^*_\mathrm{eff}$ calculated according to Eq. \ref{eq:reff}) )).
 The complete formation of a Jupiter-mass object takes a bit over 17 My and the final mass of the core is = 28 Ma (note that. in our model. all accreted solids are deposited onto the core).," The complete formation of a Jupiter–mass object takes a bit over 17 My and the final mass of the core is $\simeq$ 28 $\mathrm{M_{\oplus}}$ (note that, in our model, all accreted solids are deposited onto the core)."
 However. when including the atmospheric gas drag. the timescale turns out to be 12 My (still over the limiting 10 My) while the mass of the core increases to 60 Ma (see Fig.," However, when including the atmospheric gas drag, the timescale turns out to be 12 My (still over the limiting 10 My) while the mass of the core increases to 60 $\mathrm{M_{\oplus}}$ (see Fig."
 5 b)., \ref{comp1} ).
 This means that. in this case. the effect of the gas drag of the atmosphere reduces the formation time in about30%.. but also affects the final mass of the core. which is increased a factor of 2," This means that, in this case, the effect of the gas drag of the atmosphere reduces the formation time in about, but also affects the final mass of the core, which is increased a factor of 2."
 Although a core of ~10Μ.. (currently an acceptable value for Jupiter's core mass. Saumon Guillot 2004)) is formed in 6.5My in the second simulation. the runaway collapse of the gaseous envelope occurs ~5 My later.," Although a core of $\sim 10 \; \mathrm{M_{\oplus}}$ (currently an acceptable value for Jupiter's core mass, Saumon Guillot \cite{guillot}) ) is formed in $\sim \, \mathrm{6.5 \; My}$ in the second simulation, the runaway collapse of the gaseous envelope occurs $ \sim 5$ My later."
 As seen from Eq. (10)).," As seen from Eq. \ref{eq:accrete}) ),"
 the solids accretion rate is directly proportional to the solids surface density and the fact that the feeding zone is far from being depleted when this mass ts achieved (see Fig. 6)).," the solids accretion rate is directly proportional to the solids surface density and the fact that the feeding zone is far from being depleted when this mass is achieved (see Fig. \ref{density}) ),"
 allows, allows
each other if the attraction-repulsion mdex is larger or sanaller than 1 respectively.,each other if the attraction-repulsion index is larger or smaller than 1 respectively.
 iFrom Table 58 we can deduce that: Tn Section 5.2.2. we remarked that the brightest stars im the sample agree with the brightest luminosity for cach eroup population (see figure 3)). Thusconc, >From Table \ref{tab_repul} we can deduce that: In Section \ref{sec_lumbias} we remarked that the brightest stars in the sample agree with the brightest luminosity for each group population (see figure \ref{fig_lumbias}) ).
erned., Thus.
 Our calibratious show tvat the upper liwit in [Kk huninosity o| the OD »pulatiou (vyὅσις)δι mae.), Our calibrations show that the upper limit in K luminosity of the OD population $(K_0-3\sigma_K) = -8.1$ mag.)
 is fainter than that of the D population ((AySN)=9.| uae.]," is fainter than that of the D population $(K_0-3\sigma_K) =
-9.4$ mag.)"
 as SCCLL iu Table 2.., as seen in Table \ref{tab_estiK}.
 This confirms the dependence of he upper indt of the ACB on «ρω , This confirms the dependence of the upper limit of the AGB on ${\cal M}_{ms}$.
Willson (1980) has described a schematic evolution ou the ACB related to the iarzass-oss rate. its acceleration by the pulsations aud probably he induced dust formation.," Willson (1980) has described a schematic evolution on the AGB related to the mass-loss rate, its acceleration by the pulsations and probably the induced dust formation."
 She fouud a difference m solar uuuosities of ~(L3L/L; where stars of solar abuudauce and Mj. equal to 1.5 aud 1 M: leave the ACB.," She found a difference in solar luminosities of $\sim0.3 L/L_{\sun}$ where stars of solar abundance and ${\cal
M}_{ms}$ equal to 1.5 and 1 ${\cal M}_{\sun}$ leave the AGB."
 Our result is of the same order., Our result is of the same order.
 Using available HIPPARCOS data we apply the LM algoritlin to improve the Duunmositv calibrations in visible. near-intrared and infrared wavelength ranges aud to eet information about the star and the circmustellar envelope.," Using available HIPPARCOS data we apply the LM algorithm to improve the luminosity calibrations in visible, near-infrared and infrared wavelength ranges and to get information about the star and the circumstellar envelope."
 According to the ealactic population related to müfial mass sud iaetalliciv of the stars and to the ciretuustellar envelope thickness and expansion. several eroups of LPVs are obtained: bright (BD) and disk (diskl) galactic 20211atioji with bright and expanding envelope. not so volne and massive disk population (disk2) divided iuto 2 eTOlps: one with thin cuvelope (1) and the other wi ha xieht and expanding envelope (b).," According to the galactic population – related to initial mass and metallicity of the stars – and to the circumstellar envelope thickness and expansion, several groups of LPVs are obtained: bright (BD) and disk (disk1) galactic population with bright and expanding envelope, not so young and massive disk population (disk2) divided into 2 groups: one with thin envelope (f) and the other with a bright and expanding envelope (b)."
 A similar separation according to euvelope properties is found for the old disk (OD) population., A similar separation according to envelope properties is found for the old disk (OD) population.
 At least some LPVs are found to beloug to extended disk (ED) Our results deduced from kinematic properties confirm that the ACB evolution depends on the initial mass of the progenitor i the main sequence., At least some LPVs are found to belong to extended disk (ED) Our results deduced from kinematic properties confirm that the AGB evolution depends on the initial mass of the progenitor in the main sequence.
 This agrees with the comparison of color-magnitude diagrams using our estimated individual bhunuimositioes with theoretical evolutionary tracks., This agrees with the comparison of color-magnitude diagrams using our estimated individual luminosities with theoretical evolutionary tracks.
 According to the assigue ealactic »pulationu we can Oogive rangesOo of ageOo aud of he lower lit nein sequence mass for each star of our sample., According to the assigned galactic population we can give ranges of age and of the lower limit main sequence mass for each star of our sample.
" The upper limit of the ACB also depends on M,,.."," The upper limit of the AGB also depends on ${\cal
M}_{ms}$."
" Tic clifferenee of the values fouvl in Ix Iunuimositv limits are COLsistent with Willsous schemaic model related to the tnass loss rate and its acceleraion bv the pulsations: ""Sars evolve up the AGB with ouly moderate mass loss: at T,~3000/0 Mira pulsation commences. driving f1ο mass loss rate up by at least a actor 107."," The difference of the values found in K luminosity limits are consistent with Willson's schematic model related to the mass loss rate and its acceleration by the pulsations: ""Stars evolve up the AGB with only moderate mass loss; at $T_e \sim 3000K$ Mira pulsation commences, driving the mass loss rate up by at least a factor 10""."
 The induced dust formation is followed bv thie stabilization of the Ix DIuniuositv after the carbon euriclent., The induced dust formation is followed by the stabilization of the K luminosity after the carbon enrichment.
 The ultimate ai of this work ds fo estimate individual EK. 12 aud 25 absolute maguitudes given.," The ultimate aim of this work is to estimate individual K, 12 and 25 absolute magnitudes given,"
brightness profiles) are all stored in XML format and placed at the data website (http://abyss.uoregon.edu/-—js/Isb),brightness profiles) are all stored in XML format and placed at the data website $\sim$ js/lsb).
 In addition. the data website coutaius the scripts (written in the Python computer language) which are used to convert raw telescope values iuto astronomical meaniugful parameters.," In addition, the data website contains the scripts (written in the Python computer language) which are used to convert raw telescope values into astronomical meaningful parameters."
 These well commented scripts allow the user to follow all the details for data reduction. rather than attempting to extract the procedures from the published text.," These well commented scripts allow the user to follow all the details for data reduction, rather than attempting to extract the procedures from the published text."
 Many of the calibrating values (e.g. Galactic extinction. CMB distance) are obtained over the network (e.g. NED). and those scripts are also found at the website.," Many of the calibrating values (e.g. Galactic extinction, CMB distance) are obtained over the network (e.g. NED), and those scripts are also found at the website."
 Iu addition. we compare our values with galaxies in common from other studies.," In addition, we compare our values with galaxies in common from other studies."
 However. certain parameters. such as clistance. have cliauged since the original studies were published.," However, certain parameters, such as distance, have changed since the original studies were published."
 Thus. this scripts procedures coutain all the information to couvert other datasets iuto a common framework for comparison to our data.," Thus, this script's procedures contain all the information to convert other datasets into a common framework for comparison to our data."
 An additional challengeOm is to visually present the data for a largee raugeOm of egalaxy. sizes ancl morphology., An additional challenge is to visually present the data for a large range of galaxy sizes and morphology.
 For it is the spatial color aud inteusity information that will address many of the star formation issues., For it is the spatial color and intensity information that will address many of the star formation issues.
 Structural information is summarized by surface brightuess proliles. which are displayed for all the galaxies at the data website.," Structural information is summarized by surface brightness profiles, which are displayed for all the galaxies at the data website."
 The image tuformation (appearance. Ha aud color maps) are sumiuarized in a fashion shown in Figure 1 (with the whole sample found at the data website).," The image information (appearance, $\alpha$ and color maps) are summarized in a fashion shown in Figure 1 (with the whole sample found at the data website)."
 This visual summary includes two grayscale images (on the left at high coutrast. ou the right at low contrast with nearby stars removed). a two color (B— V) map (blue is B-V=0.0. red is B—V= 1.0). a high contrast Ha map. the £—V color profile and list of the galaxys structural parameters.," This visual summary includes two grayscale images (on the left at high contrast, on the right at low contrast with nearby stars removed), a two color $B-V$ ) map (blue is $B-V=0.0$, red is $B-V=1.0$ ), a high contrast $\alpha$ map, the $B-V$ color profile and list of the galaxy's structural parameters."
 Note that absolute values are based on distauces taken from NED (NASA's Extragalactic Database) using the concordance model (i.e. NED's cosmology-corrected. distance)., Note that absolute values are based on distances taken from NED (NASA's Extragalactic Database) using the concordance model (i.e. NED's cosmology-corrected distance).
 All redshifts were based ou 21-ci HI measurements (Eder Schombert 2000)., All redshifts were based on 21-cm HI measurements (Eder Schombert 2000).
 For nearby objects in the Hunter Elineereen (2006) aud van Zee (2001) samples. redshift iudependeut distauces (e.g. Cepheids) from NED were used where available.," For nearby objects in the Hunter Elmegreen (2006) and van Zee (2001) samples, redshift independent distances (e.g. Cepheids) from NED were used where available."
 Total magnitudes and integrated colors used the cleaned frames where the cleaned areas are re-filled with estimated intensities from the fitted ellipses., Total magnitudes and integrated colors used the cleaned frames where the cleaned areas are re-filled with estimated intensities from the fitted ellipses.
 While this is uot perfectly accurate [or irregularly shaped galaxies. the filled regions rarely contributed more than the total light of a galaxy.," While this is not perfectly accurate for irregularly shaped galaxies, the filled regions rarely contributed more than the total light of a galaxy."
 Total maenitudese were determined usiugOm asyinptotic fits to the aperture photometry (see Schombert 2007)., Total magnitudes were determined using asymptotic fits to the aperture photometry (see Schombert 2007).
 Rather than using curves of growth. (which. are ill-defined [or LSB galaxies). these fits were mace to (1) the raw pixel sumauued values. (2) the intensities calculated. from the fitted ellipses. (3) extrapolation of luminosity from exponential fits to the surface photometry.," Rather than using curves of growth (which are ill-defined for LSB galaxies), these fits were made to (1) the raw pixel summed values, (2) the intensities calculated from the fitted ellipses, (3) extrapolation of luminosity from exponential fits to the surface photometry."
 For LSB galaxies. a larger fraction of their luminosity is found iu their halo regions compared to HSB," For LSB galaxies, a larger fraction of their luminosity is found in their halo regions compared to HSB"
vackeround aud the detection threshold are already kuown. aud thus it is possible to state precisely the intensity Ay at which the source will be detected at a certain probabilitv.,"background and the detection threshold are already known, and thus it is possible to state precisely the intensity $\lamS$ at which the source will be detected at a certain probability."
" We may set à certam mininmn xobabilitv. Jg of detecting a ""bright"" source by setting the exposure time long enough so that amy source with inteusitv ereater than a certain pre-specified cutoff has probability yyy, or more of being detected."," We may set a certain minimum probability, $\beta_{\rm min}$ of detecting a “bright” source by setting the exposure time long enough so that any source with intensity greater than a certain pre-specified cutoff has probability $\beta_{\rm min}$ or more of being detected."
" Conversely. we cau determine how bright a source must be in order to have probability yyy, or more of cine detected with a given exposure time."," Conversely, we can determine how bright a source must be in order to have probability $\beta_{\rm min}$ or more of being detected with a given exposure time."
 This allows us to define an upper lait on the source intensity * setting a Ημ probability of detecting the source., This allows us to define an upper limit on the source intensity by setting a minimum probability of detecting the source.
 This latter calculation is the topic of 3.1. and he basis of our definition of au upper linüt.," This latter calculation is the topic of \ref{s:def}
 and the basis of our definition of an upper limit."
 Power calculations are generally used to determine the minimum exposure time required to eusure a ΠΠ probability of source detection (see Appendix Bj}., Power calculations are generally used to determine the minimum exposure time required to ensure a minimum probability of source detection (see Appendix \ref{a:ul-pow}) ).
 In rofsilimn we use them to construct upper nmnaits., In \\ref{s:ulim} we use them to construct upper limits.
 Iu this section. we develop a clear statistical definition of au upper huit that (1) is based on principles. Gi) depends only ou the method of detection. (ii) does not depend on prior or outside knowledge about the source intensity. (1€) correspouds to precise probability statements. aud (v) is internally self-consistent in that all values of the intensity below the upper limit are less likely to be detected at the specified Tvpe-I error rate aud values above are more likely to be detected.," In this section, we develop a clear statistical definition of an upper limit that (i) is based on well-defined principles, (ii) depends only on the method of detection, (iii) does not depend on prior or outside knowledge about the source intensity, (iv) corresponds to precise probability statements, and (v) is internally self-consistent in that all values of the intensity below the upper limit are less likely to be detected at the specified Type-I error rate and values above are more likely to be detected."
 Iu astronomy upper lianits are inextricably bound to source detection: by an upper luit. au astrononier luealis or conversely. Uulike a confidence interval. the upper lait depeuds directly ou the detection process aud in particular ou the mmaxinuun probability of a false detection aud the minimi power of the test. that is on à and yin respectively.," In astronomy upper limits are inextricably bound to source detection: by an upper limit, an astronomer means or conversely, Unlike a confidence interval, the upper limit depends directly on the detection process and in particular on the maximum probability of a false detection and the minimum power of the test, that is on $\alpha$ and $\beta_{\rm min}$ respectively."
 In this way. au upper luit incorporates both the probabilities of a Type Tanda Type II error.," In this way, an upper limit incorporates both the probabilities of a Type I and a Type II error."
" Formally, we define the upper limit. G(o.yin) to be tle smallest As such that Conmunonly used values for Jj, throughout statistics are 0.8 and 0.9."," Formally, we define the upper limit, ${\ulim}(\alpha,
\beta_{\rm min})$ to be the smallest $\lamS$ such that Commonly used values for $\beta_{\rm min}$ throughout statistics are 0.8 and 0.9."
 Tf μαι21. (ανug) ropreseuts the intensity of a source that is unlikely to eo undetected. aud we can conclude that an undetected source is unlikely to have intensity ercater than 6a. yin).," If $\beta_{\rm min} \approx1$, $\ulim(\alpha, \beta_{\rm min})$ represents the intensity of a source that is unlikely to go undetected, and we can conclude that an undetected source is unlikely to have intensity greater than $\ulim(\alpha, \beta_{\rm min})$ ."
Accretion on to supermassive black holes (SAIBUs) located in the centre of active galaxies provides a significant contribution to the energy irradiated over cosmic times.,Accretion on to supermassive black holes (SMBHs) located in the centre of active galaxies provides a significant contribution to the energy irradiated over cosmic times.
 The spectral shape of (he X-rav background and ils progressive resolution into individual sources indicate that most active galactie nuclei (AGN) are heavily obseured by large column densities of dust and gas (e.g. Fabian Iwasawa 1999: Gilli. Comastri Iasinger 2007).," The spectral shape of the X-ray background and its progressive resolution into individual sources indicate that most active galactic nuclei (AGN) are heavily obscured by large column densities of dust and gas (e.g. Fabian Iwasawa 1999; Gilli, Comastri Hasinger 2007)."
 According to the AGN unilication model (Antonucci 1993). the differences observed in the optical spectra of AGN can be ascribed to the presence of a dusty torus surrounding the central engine: in nearly [ace-on objects. classified as (wpe 1. favourable lines of sight allow the exploration of (he very inner regions and the detection of broad emission lines on top of a slrong optical/ultraviolet (UV) continuum.," According to the AGN unification model (Antonucci 1993), the differences observed in the optical spectra of AGN can be ascribed to the presence of a dusty torus surrounding the central engine: in nearly face-on objects, classified as type 1, favourable lines of sight allow the exploration of the very inner regions and the detection of broad emission lines on top of a strong optical/ultraviolet (UV) continuum."
 On the contrary. such spectral features are absent whenever (he svinmetry axis of the svstem lies close to the plane of the skv and the dusty sereen blocks the direct nuclear light. so that only the high-ionization narrow lines originating from (he outer regions are visible in (wpe 2 objects as signatures of the underlving accretion activity.," On the contrary, such spectral features are absent whenever the symmetry axis of the system lies close to the plane of the sky and the dusty screen blocks the direct nuclear light, so that only the high-ionization narrow lines originating from the outer regions are visible in type 2 objects as signatures of the underlying accretion activity."
 As the dust affects the optical spectral properties ancl classification. the amount of eas along the line of sight suppresses the X-ray emission through photoelectric absorption and Compton scattering.," As the dust affects the optical spectral properties and classification, the amount of gas along the line of sight suppresses the X-ray emission through photoelectric absorption and Compton scattering."
 Compton-thick sources (i.e. (hose with VyZ10?! cm7) are difficult to unveil al high redshilt (2~1 3) even with the deepest N-ray. surveys (e.g. Alexander οἱ al., Compton-thick sources (i.e. those with $N_\rmn{H} \ga 10^{24}$ $^{-2}$ ) are difficult to unveil at high redshift $z \sim 1$ –3) even with the deepest X-ray surveys (e.g. Alexander et al.
 2003)., 2003).
 None the less. the absorbed optical to soft X-ray primary radiation is reprocessed by Che intervening material and re-emitted at longer wavelengths. driving a significant luminosity in (he mid- and far-infrared (IR).," None the less, the absorbed optical to soft X-ray primary radiation is reprocessed by the intervening material and re-emitted at longer wavelengths, driving a significant luminosity in the mid- and far-infrared (IR)."
 Indeed. compelling evidence for the existence around z~2 of a vast population of Compton-thick AGN among the IR galaxies has been found. by selecting through various criteria those sources showing excess mid-IR enussion with respect to the predictions relative to the star formation component alone (Dadcdi et al.," Indeed, compelling evidence for the existence around $z \sim 2$ of a vast population of Compton-thick AGN among the IR galaxies has been found, by selecting through various criteria those sources showing excess mid-IR emission with respect to the predictions relative to the star formation component alone (Daddi et al."
 2007: Fiore et al., 2007; Fiore et al.
 2008: Treister et al., 2008; Treister et al.
 2009: Dauer οἱ al., 2009; Bauer et al.
 2010)., 2010).
 The local counterparts of the IR. svstems harbouring the most obscured nuclear activity ab high redshift are the so-called Ultraluminous infrared galaxies (ULIRGs. LOM L....). which rival opticallv-bright quasars as the most powerful sources in the nearby Universe with their huge mid- ancl Du-IR. emission. due (o the dust reprocessing of radiation (Sanders Mirabel 1996).," The local counterparts of the IR systems harbouring the most obscured nuclear activity at high redshift are the so-called Ultraluminous infrared galaxies (ULIRGs, $L_\rmn{IR} \sim L_\rmn{bol} > 10^{12} L_{\sun}$ ), which rival optically-bright quasars as the most powerful sources in the nearby Universe with their huge mid- and far-IR emission, due to the dust reprocessing of higher-frequency radiation (Sanders Mirabel 1996)."
 It is now well-established that the hidden source of the primary radiation field inside ULIBRGs is a combination of extreme star, It is now well-established that the hidden source of the primary radiation field inside ULIRGs is a combination of extreme star
" ίσιο, (Blaudford&Davue1982."," \citep[e.g.,][]{ba07}. \citep[][hereafter BP82]{bp82},"
 of the disk wind uxxlel is that the wind effücieutlv renioves aneular moment from the disk material. which could explain he strong inferred link between accretion aud outflow* phenomena iu protostars (6.8.Ikóniel&Salimeronu20 11).," of the disk wind model is that the wind efficiently removes angular momentum from the disk material, which could explain the strong inferred link between accretion and outflow phenomena in protostars \citep[e.g.,][]{ks11}."
. Several previous sewianalytic studies have matched solutions of the οιations of non-ileal MIID that deseri wealshy 101ized. magnetized accretion disk. and solutionsa of the equations of cold. ideal ATID for; a polvtropic⋅ fiid that deseribe a DPS2-tvpe magnetocentiifugal wind that removes all the disks excess angular mocitu.," Several previous semianalytic studies have matched solutions of the equations of non-ideal MHD that describe a weakly ionized, magnetized accretion disk, and solutions of the equations of cold, ideal MHD for a polytropic fluid that describe a BP82-type magnetocentrifugal wind that removes all the disk's excess angular momentum."
 These models focused on a radially localized portion of the disk (e.g. Wardle&Ikónigl 1993.. hereaftcY WER93: Sahucronetal.2007.. hereafter SINOT: Saliicrouetal 2011... hereafter SRWIL1). or on a global disk model (e.9.. IXónielL989:: Li 1996.. hereafter LOG: Ferreira1997.. hereafter E97) based ou the same assuniption of ποαιαν iu spherical radius that underlies the BPs? wind model.," These models focused on a radially localized portion of the disk (e.g., \citealt{wk93}, hereafter WK93; \citealt{skw07}, hereafter SKW07; \citealt{skw11}, , hereafter SKW11), or on a global disk model (e.g., \citealt{k89}; \citealt{li96}, hereafter L96; \citealt{f97}, hereafter F97) based on the same assumption of self-similarity in spherical radius that underlies the BP82 wind model."
 Another approach is presentec in Campbell(2003.2005)... where the thinness of the disk is used to Justify solutions for the disk structure that are separable in the radial aud vertical coordinates: these solutions are matched toa visothermal wind.," Another approach is presented in \citet{ca03, ca05}, where the thinness of the disk is used to justify solutions for the disk structure that are separable in the radial and vertical coordinates; these solutions are matched to an isothermal wind."
" A key parameter in determining whether a disk can launch a imagnuetccentrifugal wind is the field line inclination angele at the disk surface B,./D. where DB, aud Be. are the radia Land vertical field components at the disk surface (subscript s)."," A key parameter in determining whether a disk can launch a magnetocentrifugal wind is the field line inclination angle at the disk surface $B_{r,{\rm s}}/B_{z,{\rm s}}$, where $B_{r,{\rm s}}$ and $B_{z,{\rm s}}$ are the radial and vertical field components at the disk surface (subscript `s')."
 This inclinaion angle is determiued by the fnx distribution along the disk surface aud can only be calcilated im a self-consisteut fashion ina elobal trcatineut (Ocibie&Livio2001.hereafter OLOL).., This inclination angle is determined by the flux distribution along the disk surface and can only be calculated in a self-consistent fashion ina global treatment \citep[][hereafter OL01]{ol01}. .
 A second key parameter describing the interaction of, A second key parameter describing the interaction of
This research has made use of data obtained from the satellite. à collaborative mission between the space agencies of Japan (JAXA) and the USA (NASA).,"This research has made use of data obtained from the satellite, a collaborative mission between the space agencies of Japan (JAXA) and the USA (NASA)."
The estimate of the scattering efficiency (12) implies that the intensity. (rausler is more significant at lareer radio luminosities. shorter periods. and weaker magnetic field strengths.,"The estimate of the scattering efficiency (12) implies that the intensity transfer is more significant at larger radio luminosities, shorter periods, and weaker magnetic field strengths."
 The IPs are indeed met in the pulsars with periods 2<0.6 s (Manchester&Lyne1917)., The IPs are indeed met in the pulsars with periods $P\la 0.6$ s \citep{ml77}.
. Aloreover. the population of normal short-period pulsars. 2?~0.1 s. is generally characterized bv larger radio Iuminosities than that of the long-period ones.," Moreover, the population of normal short-period pulsars, $P\sim 0.1$ s, is generally characterized by larger radio luminosities than that of the long-period ones."
" As for the millisecond pulsars. (heir luminosities are somewhat less (Ixranmeretal.19983).. but very short periods. P?~1—10 nis. and weak magnetic fields. D,~LOS—10? G. favor even larger scattering efficiencies."," As for the millisecond pulsars, their luminosities are somewhat less \citep{wiel99}, but very short periods, $P\sim 1-10$ ms, and weak magnetic fields, $B_\star\sim 10^8-10^9$ G, favor even larger scattering efficiencies."
 Note that the pulsars with IPs ave indeed more abundant in the population of the millisecond pulsars., Note that the pulsars with IPs are indeed more abundant in the population of the millisecond pulsars.
 Our model of LP formation as a result of induced scattering of the MP implies peculiar polarization properties of the scattered component., Our model of IP formation as a result of induced scattering of the MP implies peculiar polarization properties of the scattered component.
 In contrast to Che longitudinal scattering. when the intensiv mav be efficiently (ranslerred only between (he photon states with the ordinary. polarization and the scattered component is characterized bv the complete linear polarization. the transverse scattering involves both orthogonal polarizations ancl the situation is more complicated.," In contrast to the longitudinal scattering, when the intensity may be efficiently transferred only between the photon states with the ordinary polarization and the scattered component is characterized by the complete linear polarization, the transverse scattering involves both orthogonal polarizations and the situation is more complicated."
 For different channels of the scattering. the efficiency of intensity transfer. differs by the [actor g. which is generally of order unity.," For different channels of the scattering, the efficiency of intensity transfer differs by the factor $g^{ij}$, which is generally of order unity."
 In. case of intense scattering (see eq.[3]). the difference in g and I for various channels nav play a sienificant role. and the intensity transfer in one of the channels may substantially dominate (hat in the others. so that the scattered component max be strongly polarized.," In case of intense scattering (see eq.[8]), the difference in $g^{ij}$ and $I_\nu^{(0)}$ for various channels may play a significant role, and the intensity transfer in one of the channels may substantially dominate that in the others, so that the scattered component may be strongly polarized."
 Note that the observed IPs are tvpically characterized bv higher percentage of linear polarization than the AMPs (e.g.Rankin&Rathnasree1997:Weltevredeοἱal. 2007).. with the giant IPs showing almost complete linear polarization (Eilek&Hankins2007).," Note that the observed IPs are typically characterized by higher percentage of linear polarization than the MPs \citep[e.g.][]{rr97,welt07}, , with the giant IPs showing almost complete linear polarization \citep{eh07}."
. Our model also suggests a specific behavior of the position angle of lmear polarization in the IP emission., Our model also suggests a specific behavior of the position angle of linear polarization in the IP emission.
 The position angle of (he scattered radiation is determined by the orientation of the kyx b-plane in the scattering region aud (therefore should somewhat differ from that of the MP., The position angle of the scattered radiation is determined by the orientation of the ${\bf k_1}\times {\bf b}$ -plane in the scattering region and therefore should somewhat differ from that of the MP.
 Besides that. the MP. ancl IP may be dominated by different polarization noces. in which case the position angle of the IP is additionally shifted by 90°.," Besides that, the MP and IP may be dominated by different polarization modes, in which case the position angle of the IP is additionally shifted by $90^\circ$."
 As the scattering reeion lies in the outer magnetosphlere. in the area covered by the radio beam (he magnetic lield is almost uniform and hence the position angle should remain practically unchanged across the LP.," As the scattering region lies in the outer magnetosphere, in the area covered by the radio beam the magnetic field is almost uniform and hence the position angle should remain practically unchanged across the IP."
 All this is in line with the observational data 2007)..," All this is in line with the observational data \citep[e.g.][]{rr97,mh98,welt07}.."
“LOUls. rapidly reducing the Jeans mass by factors of 10100 and thereby triggeringCoco» starbursts (Rees 1989).,"clouds, rapidly reducing the Jeans mass by factors of 10--100 and thereby triggering starbursts (Rees 1989)."
 Even if los of the eas is in a suele phase. rapid cooling behiud the vow shock can triggeroo star formation (Daly 1990).," Even if most of the gas is in a single phase, rapid cooling behind the bow shock can trigger star formation (Daly 1990)."
 The lobe-induced star formation would clearly be couccutrated arolud the site of the active galaxy. thereby naturally introducing bias in the distribution of star forming sites.," The lobe-induced star formation would clearly be concentrated around the site of the active galaxy, thereby naturally introducing bias in the distribution of star forming sites."
 Crokshi (1997) has suggested that radio sources at high redsüft (2«2 <3). powered by accretion of protogalactic lat¢yal outo preexisting black holes. asseiibled their host cllipical galaxies via radio lobe mduced starbursts.," Chokshi (1997) has suggested that radio sources at high redshift $2 < z < 3$ ), powered by accretion of protogalactic material onto preexisting black holes, assembled their host elliptical galaxies via radio lobe induced starbursts."
 She argued for such an origin of the entire population of massive ellipticals seen at the present epoch., She argued for such an origin of the entire population of massive ellipticals seen at the present epoch.
 Tere our focus is on quantitatively assessing if radio sources could have mace au inpact ou the cutive star/ealaxy formation process on the elobal scale., Here our focus is on quantitatively assessing if radio sources could have made an impact on the entire star/galaxy formation process on the global scale.
 keeping a conservaive bias. we have ouly considered FR II lobes aud therefore used a value for ®(:=2.5) which is less than a teuth of the value used by Chokshi.," Keeping a conservative bias, we have only considered FR II lobes and therefore used a value for $\Phi(z=2.5)$ which is less than a tenth of the value used by Chokshi."
" Tuspired by recent models of raclo sonrce evolution aud cosmic structure formation. we hewe taken into account a number of additional factors. which vield sieuificaut evels of effective volume coverage atained by radio galaxy lobes diving the cosinic era of pc""dk radio source production."," Inspired by recent models of radio source evolution and cosmic structure formation, we have taken into account a number of additional factors, which yield significant levels of effective volume coverage attained by radio galaxy lobes during the cosmic era of peak radio source production."
" While we have focused our atteutiou on the “qtasar OY it is clear that f, for radio galaxies at i23 wotld be vet sunaller: lewee p and their fractional volume coverage may not decliue for 2X even if the quasar population was SDIUWCT. as deduced by Shaver et ((1998)."," While we have focused our attention on the “quasar era” it is clear that $f_d$ for radio galaxies at $z > 3$ would be yet smaller; hence $\rho$ and their fractional volume coverage may not decline for $z > 3$, even if the quasar population was sparser, as deduced by Shaver et (1998)."
 But the data are inadequate to rule out very slow declines at :>Mol 5(0.8.. Jarvis Rawlings 2000).," But the data are inadequate to rule out very slow declines at $z > 3$ (e.g., Jarvis Rawlings 2000)."
" Thus. even at those very carly epochs. radio sources nav have contributed substanutiallv to he formation of galaxies. which have receutlv been cis'overed. from IB. aud. sub-nuu survevs (οι, Steidel et 1999: Blain et 11999: Archibald et 22001)."," Thus, even at those very early epochs, radio sources may have contributed substantially to the formation of galaxies, which have recently been discovered from IR and sub-mm surveys (e.g., Steidel et 1999; Blain et 1999; Archibald et 2001)."
 Au interesting corollary of our picture is that the racdio lolxss could efficicutly seed with maeuetic feld a large porion of the cosiic web DDaly Loeb 1990)., An interesting corollary of our picture is that the radio lobes could efficiently seed with magnetic field a large portion of the cosmic web Daly Loeb 1990).
 From. a (Table 1) we estimate au equipartition magnetic field int he filaments to be ~1075 C. This relatively stroug fiek is du accord with the recent estimate for the cosmic wel of fikunecuts based. on a more realistic interpretation of rotation measure data (Ryu. hang Dieruiun 1998).," From $u$ (Table 1) we estimate an equipartition magnetic field in the filaments to be $\sim10^{-8}$ G. This relatively strong field is in accord with the recent estimate for the cosmic web of filaments based on a more realistic interpretation of rotation measure data (Ryu, Kang Biermann 1998)."
 We have ignored the relatively small overpressured radio obes associated with the weaker. albeit more abundant. FR I sources.," We have ignored the relatively small overpressured radio lobes associated with the weaker, albeit more abundant, FR I sources."
" We have also neglected the explicit growth of τος dimensional istabilities which will afflict even very xwverful jets trying to propagate to Mpe distances (6.9.. IIooda Wiita 1998): however. under these circumstances he jet advance is likely to resemble the ""dentist dil scenario of Scheucr (1982). so while the hotspot emission nav weaken. the lobes ean coutinue to inflate aud expaud."," We have also neglected the explicit growth of three dimensional instabilities which will afflict even very powerful jets trying to propagate to Mpc distances (e.g., Hooda Wiita 1998); however, under these circumstances the jet advance is likely to resemble the “dentist drill” scenario of Scheuer (1982), so while the hotspot emission may weaken, the lobes can continue to inflate and expand."
" Both of these effects would teud to further reduce the value of f, aud thereby increase our estimates for 6.", Both of these effects would tend to further reduce the value of $f_d$ and thereby increase our estimates for $\zeta$.
 However. recurrent periods of activity iu individual galaxies. even if lov add up to ~5«105 xy. should inflate iualler total volunes.," However, recurrent periods of activity in individual galaxies, even if they add up to $\sim 5 \times 10^8$ yr, should inflate smaller total volumes."
 These details will be explored in future work., These details will be explored in future work.
 We thank Vasant Kulkarni. Arun Aanealam and Rajaram. Nitvananda for helpful comuneuts.," We thank Vasant Kulkarni, Arun Mangalam and Rajaram Nityananda for helpful comments."
" PJW is erateful for support from Research Program Enhancement funds at GST,", PJW is grateful for support from Research Program Enhancement funds at GSU.
Most of the team members (many referenced above) are captured in Figure 27.,Most of the team members (many referenced above) are captured in Figure 27.
 Special roles were played by the individuals depicted in Figure 28 and 29., Special roles were played by the individuals depicted in Figure 28 and 29.
" Other notable contributions were made by John Graham, Nancy Silbermann, Randy Phelps, Daya Rawson, Fabio Bresolin, Lucas Macri, Bob Hill, Kim Sebo, Paul Harding, Anne Turner, Han Ming Sheng, Shaun Hughes, Charles Prosser, John Huchra, Holland Ford, and Garth Illingworth."," Other notable contributions were made by John Graham, Nancy Silbermann, Randy Phelps, Daya Rawson, Fabio Bresolin, Lucas Macri, Bob Hill, Kim Sebo, Paul Harding, Anne Turner, Han Ming Sheng, Shaun Hughes, Charles Prosser, John Huchra, Holland Ford, and Garth Illingworth."
" Jim Gunn, Sandra Faber and John Hoessel were instrument team liaisons."," Jim Gunn, Sandra Faber and John Hoessel were instrument team liaisons."
" The team drew on work from a large number of individuals, including Brent Tully, Riccardo Giovanelli, Mario Hamuy, Mark Phillips, Bob Schommer, Martha Haynes, John Tonry, Adam Riess, Bob Kirshner, Brian Schmidt, Gustav Tammann, Allan Sandage, Mike Pierce, John Blakeslee, George Jacoby, Robin Ciardullo, Sandra Faber, Donald Lynden-Bell, Gary Wegner, David Burstein, Alan Dressler, Roberto Terlevich, Roger Davies and Gerard de Vaucouleurs."," The team drew on work from a large number of individuals, including Brent Tully, Riccardo Giovanelli, Mario Hamuy, Mark Phillips, Bob Schommer, Martha Haynes, John Tonry, Adam Riess, Bob Kirshner, Brian Schmidt, Gustav Tammann, Allan Sandage, Mike Pierce, John Blakeslee, George Jacoby, Robin Ciardullo, Sandra Faber, Donald Lynden-Bell, Gary Wegner, David Burstein, Alan Dressler, Roberto Terlevich, Roger Davies and Gerard de Vaucouleurs."
A similar result was found by Crotonοἱal.(2005) analvsing the variation of the of the LFs of galaxies in the 2dEGB5 with the environment.,A similar result was found by \citet{croton} analysing the variation of the of the LFs of galaxies in the 2dFGRS with the environment.
 They study the dependence of the LF's with the density contrast estimated within 8h.!Mpe sphere observing a smooth variation of the Schechter parameters in density environments ranging from voids to clusters., They study the dependence of the LFs with the density contrast estimated within $8 \mpc$ sphere observing a smooth variation of the Schechter parameters in density environments ranging from voids to clusters.
 It should be taken into account that (his parameter ean not be directly related with group masses since the virial mass describes a closer environment than the corresponding to 85.!Mpe density contrast. even so. their results shows the same trends (han the described in the previous paragraph.," It should be taken into account that this parameter can not be directly related with group masses since the virial mass describes a closer environment than the corresponding to $8 \mpc$ density contrast, even so, their results shows the same trends than the described in the previous paragraph."
 Our resulis means thal. as svsteni mass increases. (he characteristic luminositv of ealaxies increases.," Our results means that, as system mass increases, the characteristic luminosity of galaxies increases."
" hegarding the steepening of the faint end slope will mass. at least. (wo possibilities arise: an important fraction of bright. Moi,<—18. galaxies gets brighter. then the ‘knee’ of the Schechter function. becomes less pronounced ancl (his gives a sleeper a. or. there are some physical mechanisms that increase the number of faint. Moi, --18. ealaxies."," Regarding the steepening of the faint end slope with mass, at least two possibilities arise: an important fraction of bright, $M_{\rb}\lesssim-18$, galaxies gets brighter, then the `knee' of the Schechter function becomes less pronounced and this gives a steeper $\alpha$, or, there are some physical mechanisms that increase the number of faint, $M_{\rb}\gtrsim-18$, galaxies."
 Therelore. (here exist some processes that enhance galaxy. brightness for bright ealaxies and possibly some other processes (hat increase the number of Dant. galaxies.," Therefore, there exist some processes that enhance galaxy brightness for bright galaxies and possibly some other processes that increase the number of faint galaxies."
 The effect of (ese processes becomes more noticeable [or massive svstems., The effect of these processes becomes more noticeable for massive systems.
 Merging and galactic cannibalism are likely to be responsible of producing brighter galaxies., Merging and galactic cannibalism are likely to be responsible of producing brighter galaxies.
 As the result of a tidal interaction between (wo galaxies. the massive counterpart can get. brighter while the less massive ciminishes its Iuminositv.," As the result of a tidal interaction between two galaxies, the massive counterpart can get brighter while the less massive diminishes its luminosity."
 On the other haad. processes involving the interaction between galaxies ancl (he intra-svstem environment. such as ram pressure. are important Lor massive svstems.," On the other hand, processes involving the interaction between galaxies and the intra-system environment, such as ram pressure, are important for massive systems."
 It results in the loss of gas in less bound galaxies. drastically reducing theslar lormation.," It results in the loss of gas in less bound galaxies, drastically reducing thestar formation."
 Ina previous work. Stratevaetal.(2001). found that (he color distribution of galaxies can be approximated by a bimodal function. ie. bv (he sum of (wo normal Gaussian Iunctions.," In a previous work, \citet{strat01} found that the color distribution of galaxies can be approximated by a bimodal function, i.e. by the sum of two normal Gaussian functions."
 This behavior can be explained by two different formation processes which generate (wo ealaxy populations with different average colors., This behavior can be explained by two different formation processes which generate two galaxy populations with different average colors.
 The most common choice is to adopt the u—r color to split the galaxy distribution into two different populations., The most common choice is to adopt the $u-r$ color to split the galaxy distribution into two different populations.
 There are several works in the literature that use this color distribution to distinguish between (wo galaxy populations., There are several works in the literature that use this color distribution to distinguish between two galaxy populations.
 Recently. Baldryοἱal.(2004) have shown that it can not be chosen an unique color divider point since this point depends on absolute magnitude.," Recently, \citet{baldry03} have shown that it can not be chosen an unique color divider point since this point depends on absolute magnitude."
" So. in order to divide the sample of galaxies in eroups into two different populations we have parametrized the relation between the color divider point and the absolute magnitude in the ""tr band."," So, in order to divide the sample of galaxies in groups into two different populations we have parametrized the relation between the color divider point and the absolute magnitude in the $\rb$ band."
 To do so. we firstly use the AIGS and split it into absolute magnitude bins of width 0.5.," To do so, we firstly use the MGS and split it into absolute magnitude bins of width $0.5$ ."
 For, For
Together with our ACS study. this constrains the separations of CFIIET-PI-23 to be smaller than 5.4 AU and that of CFIET-PI-25 to be smaller than ~5.4 13 AU while that of should be less than 13 AU (see Figure 1)).,"Together with our ACS study, this constrains the separations of CFHT-Pl-23 to be smaller than 5.4 AU and that of CFHT-Pl-25 to be smaller than $\sim$ 5.4–13 AU while that of CFHT-Pl-21 should be less than 13 AU (see Figure \ref{limit_detection_all}) )."
 Spectroscopic studies would be currently the only wav to test the possibility that these objects are binaries., Spectroscopic studies would be currently the only way to test the possibility that these objects are binaries.
 Table 4. summarizes this analvsis., Table \ref{binary_candidates} summarizes this analysis.
 Our sample of bona-fide brown dwarls Pleiades members include 15 objects., Our sample of bona-fide brown dwarfs Pleiades members include 15 objects.
 Two of them were peviouslv known binaries. aud should therefore be excluded. from the statistics.," Two of them were peviously known binaries, and should therefore be excluded from the statistics."
 This eives an observed visual binary aw vol <7.7% Dor separations greater than 5.4 AU and primary masses between 0.030m0.065 MNM..., This gives an observed visual binary frequency of $<$ for separations greater than 5.4 AU and primary masses between 0.030–0.065 $_{\sun}$.
 The binary frequency is defined here as (he number ol binaries divided bv the of objects in the sample., The binary frequency is defined here as the number of binaries divided by the total number of objects in the sample.
 Upper limit uncertainty is derived as explained in(2003)., Upper limit uncertainty is derived as explained in.
. noticed that the primaries of the only (wo binaries resolved with WEDPC? are brighter (han /=18.5 mag. suggesting breaking the statistical analvsis in (wo bins of magnitudes.," noticed that the primaries of the only two binaries resolved with WFPC2 are brighter than $I$ =18.5 mag, suggesting breaking the statistical analysis in two bins of magnitudes."
 In (he first bin. between 5J< 18.5 mae corresponding to <0.065 \L.. they reported a frequency of 22. ΕΣ among a sample ol 9 objects.," In the first bin, between $<I<$ 18.5 mag corresponding to $<M<$ 0.065 $_{\sun}$, they reported a binary frequency of $^{+19}_{-8}$, with 2 binaries among a sample of 9 objects."
 In the same magnitude bin. and over the same separation range (>7 12 AU. we have 6 new objects and 0 new binary.," In the same magnitude bin, and over the same separation range $>$ 7–12 AU, we have 6 new objects and 0 new binary."
 The combination of the two results gives a total of 2 binaries over 15 objects. leading to a refined binary frequency of n," The combination of the two results gives a total of 2 binaries over 15 objects, leading to a refined binary frequency of $^{+13.7}_{-4.3}$."
uIn the second magnitude bin. between 18.5«/ «21.0 corresponding to 0.035<A «0.055 M... reported 0binary. among; a total of 6 objects.," In the second magnitude bin, between $<I<$ 21.0 corresponding to $<M<$ 0.055 $_{\sun}$, reported 0binary among a total of 6 objects."
 Ii the same magnitude bin and over the same separation range (>712 AU. we report5 new objects and 0 new binary.," In the same magnitude bin and over the same separation range $>$ 7–12 AU, we report 5 new objects and 0 new binary."
 The combination of the (wo results gives à total of0 binary over 11 objects. leading to a refined limit on the visual binary frequency of fii.—9.14..," The combination of the two results gives a total of 0 binary over 11 objects, leading to a refined limit on the visual binary frequency of $f_{vis} <$."
 In the new separation range (hat we were able to investigate with - between AU (for the brightest objects only. 17.7<£ «18.5 mag or 0.055<M. n«0.065 M... see Fig. 1)).," In the new separation range that we were able to investigate with ACS, between 5.4--7.0 AU (for the brightest objects only, $<I<$ 18.5 mag or $<M<$ 0.065 $_{\sun}$, see Fig. \ref{limit_detection_all}) ),"
 we report Q binaries among a LoLal of 6 objects. leading to a limit on visual binary [requenev of [ω«16.7... consistent with that reported in the separation range between 12 AU for the same range of masses.," we report 0 binaries among a total of 6 objects, leading to a limit on the visual binary frequency of $f_{vis} <$, consistent with that reported in the separation range between 7–12 AU for the same range of masses."
" To summarize.we obtain (he following MON in (he separation range 75.4 AU ""nmand in the range of mass between 0.055«PM «0.065 M... we report a visual binary o fu.=5 <16.7%.."," To summarize,we obtain the following binary frequencies: in the separation range $>$ 5.4--7.0 AU and in the range of mass between $<M<$ 0.065 $_{\sun}$ , we report a visual binary frequency of $f_{vis} = \frac{0}{6}<$ ."
 In the mion range 27-12 AU and in the mass range, In the separation range $>$ 7-12 AU and in the mass range
effects like temperature. metallicity. rotation. ete.,"effects like temperature, metallicity, rotation, etc."
 as well. these parameters can be determined from molecular bands. which can resolve the degeneracy between gravity and other parameters.," as well, these parameters can be determined from molecular bands, which can resolve the degeneracy between gravity and other parameters."
 In high resolution spectra. several features are available to constrain atmospheric parameters simultaneously.," In high resolution spectra, several features are available to constrain atmospheric parameters simultaneously."
 Thus. the determination of gravity from the pressure broadened wings can be expected to be much more accurate than comparing color ratios from low resolution spectra.," Thus, the determination of gravity from the pressure broadened wings can be expected to be much more accurate than comparing color ratios from low resolution spectra."
 High resolution optical spectra of M dwarfs were shown by (1998).. but no high resolution data showing the full optical spectrum in L dwarts or cooler were made available.," High resolution optical spectra of M dwarfs were shown by , but no high resolution data showing the full optical spectrum in L dwarfs or cooler were made available."
 Some individual features in high resolution L dwarf spectra were investigated by 2002)., Some individual features in high resolution L dwarf spectra were investigated by .
 In this paper. we present an atlas of high resolution. high signal to noise spectra in the red and near-IR spectral range for three L and an early T dwarf system (2200€Tay1200 KK).," In this paper, we present an atlas of high resolution, high signal to noise spectra in the red and near-IR spectral range for three L and an early T dwarf system $2200 \la T_{\rm eff} \la 1200$ K)."
 We also compare a set of the most recent model calculations to the data., We also compare a set of the most recent model calculations to the data.
 For the full wavelength region. we show the spectral features of ultra-cool L and early T dwarfs at high resolution. and we make a first attempt to identify the shortcomings and successes of our current model calculations.," For the full wavelength region, we show the spectral features of ultra-cool L and early T dwarfs at high resolution, and we make a first attempt to identify the shortcomings and successes of our current model calculations."
 We present a high resolution spectral atlas of four very low mass objects of spectral types between LO and ΤΙ., We present a high resolution spectral atlas of four very low mass objects of spectral types between L0 and T1.
 Name. spectral type. J-magnitude. and exposure times of the objects are given in reftab:observations..," Name, spectral type, $J$ -magnitude, and exposure times of the objects are given in \\ref{tab:observations}."
 The signal to noise ratio (SNR) of the spectra varies over the wavelength region according to the object's spectral energy distribution and detector efficiency. it is Well over 20 in most of the region in the L dwarfs. so that the dense molecular absorption features are well discernible from the noise.," The signal to noise ratio (SNR) of the spectra varies over the wavelength region according to the object's spectral energy distribution and detector efficiency, it is well over 20 in most of the region in the L dwarfs, so that the dense molecular absorption features are well discernible from the noise."
 In reffig:atlas pall. weshowrhe fullspectrao fall fourtargets.," In \\ref{fig:atlas_full}, we show the full spectra of all four targets."
InthetoppahbekpredlsoguafacdealrapdcadufüTURAYd Iv rorating BOV star(alsoliste Wthatweobservedwiththe same setuptoidenti fvtellui lto," In the top panel, we also provide the spectrum of a rapidly rotating B9V star (also listed in ) that we observed with the same setup to identify telluric lines due to absorption of Earth's atmosphere."
l lweprovidethedetaileds pectralatlaswithidenti fi, In \\ref{fig:atlas1} to \ref{fig:atlas10} we provide the detailed spectral atlas with identifications of the most prominent absorption features.
cat," In all plots, synthetic spectra chosen to match the object's effective temperature are overplotted."
ioi models., We discuss the models in \\ref{sect:models}.
 Data were obtained with the UVES spectrograph at ESO/VLT service mode during April and Μαν. 2006.," Data were obtained with the UVES spectrograph at ESO/VLT in service mode during April and May, 2006."
 UVES was operated in dichroic mode using both the blue and the red arm., UVES was operated in dichroic mode using both the blue and the red arm.
 Because of the red colour of L dwarf spectra. the blue instrument arm contains very little flux if any. but it covers yyeveral hydrogen lines that are interesting during flares.," Because of the red colour of L dwarf spectra, the blue instrument arm contains very little flux if any, but it covers several hydrogen lines that are interesting during flares."
 For this pectral atlas. we only consider the red arm that was configured in à non-standard setting centered at 830nnm.," For this spectral atlas, we only consider the red arm that was configured in a non-standard setting centered at nm."
 This setting covers the wavelength region 6400 —AA.. it contains Ha and the FeH Wing-Ford band that is very useful for spectral analysis in late-type dwarfs2006a).," This setting covers the wavelength region 6400 –, it contains $\alpha$ and the FeH Wing-Ford band that is very useful for spectral analysis in late-type dwarfs."
. Between the two CCDs of the red arm. the spectra have a gap from ttoAA.," Between the two CCDs of the red arm, the spectra have a gap from to."
. The Na doublet at llies just blueward of the gap., The Na doublet at lies just blueward of the gap.
 The spectra were taken at a slit width of 172 yielding a resolving power of R~33000.," The spectra were taken at a slit width of 2 yielding a resolving power of $R \sim 33\,000$."
 Data were reduced using the MIDAS-based ESO-pipeline for UVES data., Data were reduced using the MIDAS-based ESO-pipeline for UVES data.
 Bias-subtraction. division by a flatfield-lamp spectrum. and wavelength calibration follow standard routines.," Bias-subtraction, division by a flatfield-lamp spectrum, and wavelength calibration follow standard routines."
 We did not remove telluric lines for our spectral atlas. but we show a spectrum of a tellurie standard star for comparison.," We did not remove telluric lines for our spectral atlas, but we show a spectrum of a telluric standard star for comparison."
 Theoretical models have been calculated using the general-purpose stellar atmosphere code version 15.2., Theoretical models have been calculated using the general-purpose stellar atmosphere code version 15.2.
 Details of the numerical methods are given in(1999)., Details of the numerical methods are given in.
. In this work we use a setup of the microphysics that gives the currently best fits to observed spectra of M. L. and T dwarts for the low Zr regime and that also updates the microphysics used in the GAIA model grid2006).," In this work we use a setup of the microphysics that gives the currently best fits to observed spectra of M, L, and T dwarfs for the low $T_{\rm eff}$ regime and that also updates the microphysics used in the GAIA model grid."
. The water lines are taken from the calculations of(200601: this list gives the best overall fit to the water bands over a wide temperature range., The water lines are taken from the calculations of; this list gives the best overall fit to the water bands over a wide temperature range.
 TiO lines are taken from for similar reasons., TiO lines are taken from for similar reasons.
 The treatment of opacities and the equation of state (EOS) ts similar to the one described in detail in.(2001).. with extensions and modifications described below (HITRAN:: Plez. Bernath. priv.comm.).," The treatment of opacities and the equation of state (EOS) is similar to the one described in detail in, with extensions and modifications described below (HITRAN; Plez, Bernath, priv.comm.)."
 One of the most important recent Improvements of cool stellar atmosphere models is the availability of new atomic line profile data based on accurate inter-atomic potentials., One of the most important recent improvements of cool stellar atmosphere models is the availability of new atomic line profile data based on accurate inter-atomic potentials.
 The calculations presented here include detailed and depth dependent line profiles for each of the DI and D2 transitions, The calculations presented here include detailed and depth dependent line profiles for each of the D1 and D2 transitions
form the shear estimators.,form the shear estimators.
 Combining the above two reasons. we find it unlikely to form CSEs when a PSE is present.," Combining the above two reasons, we find it unlikely to form CSEs when a PSF is present."
" The mathematical details of the above statements are given in Appendix ο As searching for optimal shear estimators is actively ongoing nowadays (Llevmansetal.2006:Massey.2007:Bri-dleetal.2009. 201011. it is important to realize that CSLEs (""conventional shear estimators.” bv which we mean the shear estimators that are mace of just one number from a galaxy image for each shear component) are hard to use in practice due to their unavoidable complex forms even in the absence of the PSE (simpler forms. such as the quadrupole moments. are biased estimators. as shown in 2.1)."," The mathematical details of the above statements are given in Appendix C. As searching for optimal shear estimators is actively ongoing nowadays \citealt{heymans06,massey07,bridle09,bridle10}) ), it is important to realize that CSEs (“conventional shear estimators,” by which we mean the shear estimators that are made of just one number from a galaxy image for each shear component) are hard to use in practice due to their unavoidable complex forms even in the absence of the PSF (simpler forms, such as the quadrupole moments, are biased estimators, as shown in 2.1)."
 ‘Therefore. existing shear estimators of the conventional tvpe must quantify the bias factor. when estimating the shear. which can be achieved numerically (see.e.g... Erben et al.," Therefore, existing shear estimators of the conventional type must quantify the bias factor when estimating the shear, which can be achieved numerically (see, Erben et al."
 2001. Bacon οἱ al.," 2001, Bacon et al."
 2001. or most recently. Hevmansetal.2006:Masseyet2007:Bridle 2010)) or estimated analytically shear susceptibility in KSB Waiser et al.," 2001, or most recently, \citealt{heymans06,massey07,bridle10}) ) or estimated analytically, shear susceptibility in KSB [Kaiser et al."
 1995] and derived methods. or responsivity factor in lernstein Jarvis 2002 and similar methods). although most people have been mainly. focusing on the systematic errors caused by the photon noise and the PSE.," 1995] and derived methods, or responsivity factor in Bernstein Jarvis 2002 and similar methods), although most people have been mainly focusing on the systematic errors caused by the photon noise and the PSF."
 However. to achieve percent or even sub-percent level accuracy in cosmic shear measurements. it does not seem enough to completely rely on numerical tests using computer-generated: galaxies of limited. morphology richness. or approximate analytical methods.," However, to achieve percent or even sub-percent level accuracy in cosmic shear measurements, it does not seem enough to completely rely on numerical tests using computer-generated galaxies of limited morphology richness, or approximate analytical methods."
 Unfortunately. in the presence of PSE. most ofthe existing shear measurement methods are too complicated or oo mocdel-dependent (Voigt&Bridle2010:Bernstein 2010)) o allow for an accurate analytic analysis of the svstematic errors in their shear estimators.," Unfortunately, in the presence of PSF, most of the existing shear measurement methods are too complicated or too model-dependent \citealt{vb10,bernstein10}) ) to allow for an accurate analytic analysis of the systematic errors in their shear estimators."
 Phe method. of ZOS (sec also Zhang2O10a ως the reatment of photon noise and the pixelation ellect) is easily amenable to the corrections described in eq.(10)). and can also account for the PSE correction.," The method of Z08 (see also \citealt{zhang10a} for the treatment of photon noise and the pixelation effect) is easily amenable to the corrections described in \ref{q5}) ), and can also account for the PSF correction."
 Not only is it simple. out. also well defined: regardless of. the morphologies of galaxies and the PSE.," Not only is it simple, but also well defined regardless of the morphologies of galaxies and the PSF."
 We show here how to properly use his method. (instead. of using it as σος) to recover the cosmic shear in an unbiased. way., We show here how to properly use this method (instead of using it as CSEs) to recover the cosmic shear in an unbiased way.
 The basic idea of ZOS is to use the spatial derivatives of 1ο galaxy surface brightness field to measure the cosmic garears., The basic idea of Z08 is to use the spatial derivatives of the galaxy surface brightness field to measure the cosmic shears.
 Lt relies on the fact that gravitational lensing clocs =100 onky distort the overall shape of the object. but. also =eocally modlifics the anisotropy of the gradient. field of je surface brightness.," It relies on the fact that gravitational lensing does not only distort the overall shape of the object, but also locally modifies the anisotropy of the gradient field of the surface brightness."
 As it allows for using the shape information from galaxy substructures. the method of 205 “an potentially improve on the signal-to-noise ratio of the gaΊσα measurements.," As it allows for using the shape information from galaxy substructures, the method of Z08 can potentially improve on the signal-to-noise ratio of the shear measurements."
 lt is shown in ZOS that the shear measurement should be carried out in the Fourier space. in which anv PSE can be transformed. into the desired. isotropic. Caussian [orm through multiplications. and the spatial derivatives of the surface brightness field can be easily measured.," It is shown in Z08 that the shear measurement should be carried out in the Fourier space, in which any PSF can be transformed into the desired isotropic Gaussian form through multiplications, and the spatial derivatives of the surface brightness field can be easily measured."
 The cosmic shear can be estimated using the following relations: where dis the scale radius of the isotropic Gaussian PSE Ws. which is defined as: fo is the surface brightness field.," The cosmic shear can be estimated using the following relations: where $\beta$ is the scale radius of the isotropic Gaussian PSF $W_{\beta}$, which is defined as: $f_O$ is the surface brightness field."
 0; denotes 0/007., $\partial_i$ denotes $\partial /\partial x_i$.
 Xs shown in Appendix D. the method of 205 cllectively utilizes the quadrupole moments in the Fourier space to measure the cosmic shears.," As shown in Appendix D, the method of Z08 effectively utilizes the quadrupole moments in the Fourier space to measure the cosmic shears."
 Now. here is an important point: in order to implement this method. we must make it clear what we mean bv the angular brackets in eq.(38)).," Now, here is an important point: in order to implement this method, we must make it clear what we mean by the angular brackets in \ref{shear12PSF}) )."
 First. we need to measure the derivatives of the surface brightness ancl average them. within a single galaxy.," First, we need to measure the derivatives of the surface brightness and average them within a single galaxy."
 Let us denote this averaging by ον. and write: Of course. these are still extremely noisy as they use only one galaxy.," Let us denote this averaging by $\langle\rangle_g$, and write: Of course, these are still extremely noisy as they use only one galaxy."
 The question is then. “how clo we average these quantities over many galaxies to obtain an unbiased estimator of the shears?”," The question is then, “how do we average these quantities over many galaxies to obtain an unbiased estimator of the shears?”"
 If one uses these quantities as if they were the CSEs. then one would simply average them over many galaxies.," If one uses these quantities as if they were the CSEs, then one would simply average them over many galaxies."
" llowever. this will produce a biased estimator: where 3, and d2 are the ensemble averages of functions of multipole moments of the galaxy images in Fourier space. and ©, denotes the ensemble average over many galaxies."," However, this will produce a biased estimator: where $\delta_1$ and $\delta_2$ are the ensemble averages of functions of multipole moments of the galaxy images in Fourier space, and $\langle\rangle_{en}$ denotes the ensemble average over many galaxies."
 The derivation ofthe forms of δι and 9» is given in Appendix D. δι and 9» are generally. nonzero and dependent on the galaxy morphology., The derivation of the forms of $\delta_1$ and $\delta_2$ is given in Appendix D. $\delta_1$ and $\delta_2$ are generally nonzero and dependent on the galaxy morphology.
 Insteack we need to take the ensemble averages of the numerator ancl the denominator separately first. ancl then divide them to obtain an unbiased. estimator:," Instead, we need to take the ensemble averages of the numerator and the denominator separately first, and then divide them to obtain an unbiased estimator:"
Some possible precession scenarios are sununarized in Table 2..,Some possible precession scenarios are summarized in Table \ref{table:pulsargw}.
" Hf we attribute persistent X-ray pulsations to magnetic f[unnelling onto a polar hot spot. or to a magnetically anisotropic atmospheric opacity. then the angle between and must be large. leading (to precession wilh a large wobble angle. which would presumably be damped on short üime-scales unless il is driven (ef,"," If we attribute persistent X-ray pulsations to magnetic funnelling onto a polar hot spot, or to a magnetically anisotropic atmospheric opacity, then the angle between and must be large, leading to precession with a large wobble angle, which would presumably be damped on short time-scales unless it is driven (cf."
 Chandler wobble)., Chandler wobble).
" Such a pulsar emits gravitational waves at a [recuency near f, (offset by the body-Irame precessionfrequency) and 2/,.", Such a pulsar emits gravitational waves at a frequency near $f_*$ (offset by the body-frame precessionfrequency) and $2f_*$.
 However. the relative orientations of µ.ο). and e4 are determined when the crust of the newly born neutron star crvstallizes alter birth and subsequently by accretion torques.," However, the relative orientations of , and $\vv{e}_{3}$ are determined when the crust of the newly born neutron star crystallizes after birth and subsequently by accretion torques."
 This is discussed in detail bv. Melatos(2000)., This is discussed in detail by \citet{mel00a}.
. If viscous dissipation in the fluid star forces to align with before evvstallization. and if ihe svimmmetry axis of the crust when it ervstallizes is alongQ. then e4 (of the ervstalline crust. plus the subsequently accreted mountain).poo and are all parallel and there is no precession (nor. indeed. pulsation).," If viscous dissipation in the fluid star forces to align with before crystallization, and if the symmetry axis of the crust when it crystallizes is along, then $\vv{e}_3$ (of the crystalline crust plus the subsequently accreted mountain), and are all parallel and there is no precession (nor, indeed, pulsation)."
 But if (he crust crystallizes before has time to alien withpe. then ο and are not necessarily aligned. (depending on the relative size of the crystalline ancl pre-accrelion magnetic delormation) and the star does precess.," But if the crust crystallizes before has time to align with, then $\vv{e}_3$ and are not necessarily aligned (depending on the relative size of the crystalline and pre-accretion magnetic deformation) and the star does precess."
" Moreover. this conclusion does not change when a mountain is subsequently accreted alongpe: (he new ο, (nearly. but not exactly. parallel to 44) is still misaligned with in general."," Moreover, this conclusion does not change when a mountain is subsequently accreted along; the new $\vv{e}_3$ (nearly, but not exactly, parallel to ) is still misaligned with in general."
" Gravitational waves are emitted al f, and 2/,.", Gravitational waves are emitted at $f_*$ and $2f_*$.
 Of course. internal dissipation alter crystallization (and. indeed. cluring accretion) may force to align with ey (ef Earth).," Of course, internal dissipation after crystallization (and, indeed, during accretion) may force to align with $\vv{e}_3$ (cf."
F? If this occurs. the precession stops and (he gravitational wave signal at f. disappears.," $^{,}$ If this occurs, the precession stops and the gravitational wave signal at $f_*$ disappears."
" The smaller signal al 2/, persists if the star is triaxial (almost certainly (vue lor any realistic magnetic mountain. even though we do not calculate (he (riaxialitv explicitly in this paper) but disappears if the star is biaxial (which is unlikely)."," The smaller signal at $2f_*$ persists if the star is triaxial (almost certainly true for any realistic magnetic mountain, even though we do not calculate the triaxiality explicitly in this paper) but disappears if the star is biaxial (which is unlikely)."
 To compute the polarization waveforms will precession included. one may employ the small-wobble-anele expansion Lor a nearly spherical star derived by Zimmermann(1980) and extended to quadratic order by VanDenBroeck(2005).," To compute the polarization waveforms with precession included, one may employ the small-wobble-angle expansion for a nearly spherical star derived by \citet{zim80}
 and extended to quadratic order by \citet{van05}."
. This calculation lies outside the scope of this paper but constitutes important fiture work., This calculation lies outside the scope of this paper but constitutes important future work.
 Recent coherent. multi-interferometer searches for continuous gravitational waves from nonaxisvmmeltre pulsars appear to have focused on the signal at 2/.. to the exclusion of the signal at...," Recent coherent, multi-interferometer searches for continuous gravitational waves from nonaxisymmetric pulsars appear to have focused on the signal at $2f_*$, to the exclusion of the signal at $f_*$."
 Examples include the $1 science run of the LIGO and GEO 600 detectors. which was used to place an upper limit e<2.9x10.! on the ellipticity of the radio millisecond pulsar J1939+2134 (TheLIGOScientifieCollaboration:D.Abbottetal. 2004b).. andthe $2 science runof the three LIGO I detectors (two 4-km arms and one ?-kin arm). which," Examples include the S1 science run of the LIGO and GEO 600 detectors, which was used to place an upper limit $\epsilon\leq 2.9\times 10^{-4}$ on the ellipticity of the radio millisecond pulsar $+$ 2134 \citep{lig04a}, , andthe S2 science runof the three LIGO I detectors (two 4-km arms and one 2-km arm), which"
no emission lines).,no emission lines).
 A significant number of the objects classitied as AGN based on their emission-line ratios overlap the starforming population in this plane., A significant number of the objects classified as AGN based on their emission–line ratios overlap the star--forming population in this plane.
 This is interpreted as meaning that these are radio—quiet AGN whose radio emission is due to star formation — the problem identitied above., This is interpreted as meaning that these are radio–quiet AGN whose radio emission is due to star formation – the problem identified above.
 The dotted line on this plot shows the GGyr exponential star formation model from the top panel., The dotted line on this plot shows the Gyr exponential star formation model from the top panel.
" The solid line. 0.225 above this in D,(4000). is the proposed division between radio-loud AGN (above the line. plottec as diamonds) and star-forming galaxies (below the line. plotted as crosses)."," The solid line, 0.225 above this in $D_n(4000)$, is the proposed division between radio-loud AGN (above the line, plotted as diamonds) and star–forming galaxies (below the line, plotted as crosses)."
 This cut-off value was chosen to be most consistent with other methods that could have been adopted for AGN-starburs separation. as illustrated in the later panels.," This cut–off value was chosen to be most consistent with other methods that could have been adopted for AGN–starburst separation, as illustrated in the later panels."
 Using this cut-off. 2215 radio sources are classified as radio-loud AGN. and 497 as star-forming.," Using this cut-off, 2215 radio sources are classified as radio–loud AGN, and 497 as star–forming."
" Note that the plots only show the subset of these a redshifts with 0.03<20.1. to avoid overcrowding the plot and to allow a comparison with emission-line diagnostic methods: the higher redshift sources fill out more of the plane at larger values of Liou,/Ad,. and contirm that the location of the proposed cut a those values is appropriate."," Note that the plots only show the subset of these at redshifts with $0.03 \le z \le
0.1$, to avoid overcrowding the plot and to allow a comparison with emission–line diagnostic methods; the higher redshift sources fill out more of the plane at larger values of $L_{\rm 1.4GHz} / M_*$, and confirm that the location of the proposed cut at those values is appropriate."
 The middle right panel shows the BPT emission line diagnostic diagram., The middle right panel shows the BPT emission line diagnostic diagram.
 It can be seen that the AGN-starburs separation defined above (ie., It can be seen that the AGN–starburst separation defined above (ie.
 diamonds versus crosses) also makes good sense in this plot: (1) the “composite” galaxies that lie close to the star forming galaxy locus are largely classified as starbursts. whilst those nearer to the AGN locus are predominantly classitied as radio-loud AGN: (ii) almost all of the LINERS are classitied as radio-loud AGN: (ii) the Seyferts close to the LINER region are mostly classified as radio-loud. whilst those with lower [NIT] 6583 / Ho ratios are a mixture of the two classes: (v) the three star forming galaxies now classified as radio-loud AGN all lie near the boundary with composites.," diamonds versus crosses) also makes good sense in this plot: (i) the `composite' galaxies that lie close to the star forming galaxy locus are largely classified as starbursts, whilst those nearer to the AGN locus are predominantly classified as radio–loud AGN; (ii) almost all of the LINERS are classified as radio–loud AGN; (iii) the Seyferts close to the LINER region are mostly classified as radio-loud, whilst those with lower [NII] 6583 / $\alpha$ ratios are a mixture of the two classes; (iv) the three star forming galaxies now classified as radio-loud AGN all lie near the boundary with composites."
 The lower left panel shows the Ha /H:? line ratio as a function of galaxy stellar mass., The lower left panel shows the $\alpha$ / $\beta$ line ratio as a function of galaxy stellar mass.
 The Ha / H:7 line ratio is an approximate measure of dust-reddening: the dotted line shows the expected value for zero reddening., The $\alpha$ / $\beta$ line ratio is an approximate measure of dust–reddening; the dotted line shows the expected value for zero reddening.
 Star forming galaxies form a tight relation between these parameters. with more massive galaxies being more heavily reddened (cf.," Star forming galaxies form a tight relation between these parameters, with more massive galaxies being more heavily reddened (cf."
" Figure 6 of Brinchmann Radio-loud AGN deviate from this locus. in the sense of having less reddening (due to less star formation and hence less dust) at a given stellar mass: this diagram indicates that the classification division adopted for 2,(42000) versus Li46g/M. works well."," Figure 6 of Brinchmann \nocite{bri04a}
 Radio–loud AGN deviate from this locus, in the sense of having less reddening (due to less star formation and hence less dust) at a given stellar mass; this diagram indicates that the classification division adopted for $D_n(4000)$ versus $L_{\rm 1.4GHz} / M_*$ works well."
" The final panel shows the distribution of the galaxies in the {ΟΙπυυτ Versus Lic, plane."," The final panel shows the distribution of the galaxies in the $L_{\rm
[OIII]~5007}$ versus $L_{\rm 1.4 GHz}$ plane."
 This relation was considered as a way to separate radio-loud AGN and star-forming galaxies: indeed. it can be seen that for the LINERS and the galaxies without emission lines the division agrees very well with that adopted.," This relation was considered as a way to separate radio–loud AGN and star-forming galaxies; indeed, it can be seen that for the LINERS and the galaxies without emission lines the division agrees very well with that adopted."
 However. many of the Seyferts and composites lie on the relation detined by the star-forming galaxies in this plane. but are considerably offset from the star forming locus in all of the other plots.," However, many of the Seyferts and composites lie on the relation defined by the star–forming galaxies in this plane, but are considerably offset from the star forming locus in all of the other plots."
 It is for this reason that the final classification was not based upon this relation., It is for this reason that the final classification was not based upon this relation.
" These plots demonstrate the reliability of the AGN-starburst separation using the 2,,(4000) versus Lic,/Ad. relation: through comparison of the locations of galaxies on different diagnostics. it is estimated that &1% of objects will have been misclassified."," These plots demonstrate the reliability of the AGN–starburst separation using the $D_n(4000)$ versus $L_{\rm 1.4GHz} / M_*$ relation: through comparison of the locations of galaxies on different diagnostics, it is estimated that $\lta 1$ of objects will have been misclassified."
" The 2,(4000) versus L446g(AL. relation was also used to estimate and to correct for the star formation contribution to the radio luminosity of galaxies classified as radio—loud AGN: for each of these galaxies the ""star formation! radio luminosity corresponding its bbreak strength. as estimated by the 3GGyr exponential star formation track ¢the dotted line in the middle left panel). was subtracted to obtain a corrected AGN radio luminosity."," The $D_n(4000)$ versus $L_{\rm 1.4GHz} / M_*$ relation was also used to estimate and to correct for the star formation contribution to the radio luminosity of galaxies classified as radio--loud AGN: for each of these galaxies the `star formation' radio luminosity corresponding its break strength, as estimated by the Gyr exponential star formation track (the dotted line in the middle left panel), was subtracted to obtain a corrected AGN radio luminosity."
 In no case was this correction larger than[5(., In no case was this correction larger than.
. The radio-loud AGN in the sample exhibit a variety of optical properties: some are classified as optical AGN based upon their emission lines while others are optically inactive., The radio–loud AGN in the sample exhibit a variety of optical properties; some are classified as optical AGN based upon their emission lines while others are optically inactive.
 Figure 10 shows the cumulative fractions of the different radio source types as a function of redshift., Figure \ref{cumfracs} shows the cumulative fractions of the different radio source types as a function of redshift.
 Out to redshifts 2~0.1. the relative numbers of radio-loud AGN with and without emission lines are roughly similar.," Out to redshifts $z \sim 0.1$, the relative numbers of radio–loud AGN with and without emission lines are roughly similar."
 At higher redshifts the proportion of emission-line AGN decreases rapidly: this is because emission lines such as [OTT] 5007 become increasing difficult to detect at higher redshift (only lines brighter than ~1077L. can be detected at += 0.1). both because of the increased distance and because the larger physical size of the spectroscopic fibres means that a larger fraction of starlight from the host galaxy is included.," At higher redshifts the proportion of emission-line AGN decreases rapidly; this is because emission lines such as [OIII] 5007 become increasing difficult to detect at higher redshift (only lines brighter than $\sim
10^{5.8} L_{\odot}$ can be detected at $z =0.1$ ), both because of the increased distance and because the larger physical size of the spectroscopic fibres means that a larger fraction of starlight from the host galaxy is included."
 This makes it more difficult to pick out the weaker nuclear lines., This makes it more difficult to pick out the weaker nuclear lines.
 The local radio luminosity function was derived both for radio—loud AGN and radio-emitting star-forming galaxies out to redshift 0.3., The local radio luminosity function was derived both for radio--loud AGN and radio–emitting star–forming galaxies out to redshift 0.3.
 These were caleulated in the standard way using the 1/Vines method (2: 2).. where Vines was calculated using the upper and lower redshift limits determined by the joint radio and optica selection criteria. namely a radio cut-off of SmmJy and optica cut-offs of 14.5.<r«17.77.," These were calculated in the standard way using the $1/V_{\rm max}$ method \cite{sch68b,con89}, , where $V_{\rm max}$ was calculated using the upper and lower redshift limits determined by the joint radio and optical selection criteria, namely a radio cut–off of mJy and optical cut–offs of $14.5 < r < 17.77$."
 An accurate calculation of the exact area of sky within the overlap region of the SDSS DR? and the FIRST survey is not simple., An accurate calculation of the exact area of sky within the overlap region of the SDSS DR2 and the FIRST survey is not simple.
 The absolute normalisation of the derivedradio luminosity function has thus been set by normalising, The absolute normalisation of the derivedradio luminosity function has thus been set by normalising
relations also hold between q. O? and O'.,"relations also hold between $q$ , $\Theta^2$ and $\Theta^{\prime}$."
 Given that. one should distinguish between accelerated expansion with simply —1<q«0 and that with OÓ» 0.," Given that, one should distinguish between accelerated expansion with simply $-1<\tilde{q}<0$ and that with $\dot{\tilde{\Theta}}>0$ ."
" We may therefore view —1<q«0 aud O0 (equivalently d« —1) as the couditious for ""weakly aud ""strongly! accelerated. expausiou respectively.", We may therefore view $-1<\tilde{q}<0$ and $\dot{\tilde{\Theta}}>0$ (equivalently $\tilde{q}<-1$ ) as the conditions for `weakly' and `strongly' accelerated expansion respectively.
 Then. it is important to recoguise that. as long as we only require d to lie in the (-1.0) range. the [-acceleration term in Eqs.," Then, it is important to recognise that, as long as we only require $\tilde{q}$ to lie in the (-1,0) range, the 4-acceleration term in Eqs."
 (3bb) aud (obb) does not need to dominate the side of these expressions., \ref{eq:Rays1}b b) and \ref{eq:Rays2}b b) does not need to dominate the right-hand side of these expressions.
 This implies that peculiar motious can lead to weakly accelerated expausion within the limits of the linear (the aluiost-FRW) approximation., This implies that peculiar motions can lead to weakly accelerated expansion within the limits of the linear (the almost-FRW) approximation.
 Given that. we will focus on the —1«q0 case for the rest of this letter.," Given that, we will focus on the $-1<\tilde{q}<0$ case for the rest of this letter."
 Note that the supernovae results put the deceleration parameter close to —0.5 (Turner&Riess2002:etal2001).," Note that the supernovae results put the deceleration parameter close to $-0.5$ \citep{TR,Retal2}."
. Let us now cousider au extended spatial region (4) — see Fig. 2..," Let us now consider an extended spatial region $A$ ) – see Fig. \ref{fig:pvel},"
 which largely. complies with the FRW syuunetries aud expands with the Hubble flow. but is still endowed with a bulk ;»eculiar velocity field that ‘adds’ to the background expausiou (ie. with )> 0).," which largely complies with the FRW symmetries and expands with the Hubble flow, but is still endowed with a bulk peculiar velocity field that `adds' to the background expansion (i.e. with $\vartheta>0$ )."
 Typical observers inskle (4) have peculiar velocities close to the mean bulk flow of the patch., Typical observers inside $A$ ) have peculiar velocities close to the mean bulk flow of the patch.
 To linear order iu Uo. the deceleration parameter for those observers obeys Eq. (7)).," To linear order in $v_a$, the deceleration parameter for those observers obeys Eq. \ref{eq:tq2}) )."
 The simplest case correspouds ο 30/0?~Q. which occurs when ) varies veryslowly with time (forexample).," The simplest case corresponds to $3\dot{\vartheta}/\tilde{\Theta}^2\simeq0$, which occurs when $\vartheta$ varies veryslowly with time (forexample)."
 Then. when the Hubble expansion dominates the kinematies. 7/0<1 and a straightforward Taylor expansion 'educes Eq. (7))," Then, when the Hubble expansion dominates the kinematics, $\vartheta/\Theta\ll1$ and a straightforward Taylor expansion reduces Eq. \ref{eq:tq2}) )"
 to, to
and 3.53 jam emission bands in cireumstellar media of Ae/Be IIerbig stars IID 97048 and Elias 1 show convincing presence of nanodiamnonds (Guiloisetal.1999).,and 3.53 $\mu m $ emission bands in circumstellar media of Ae/Be Herbig stars HD 97048 and Elias 1 show convincing presence of nanodiamonds \citep{guillois99}.
. VanNerkhovenelal.(2002) attribute these bands to C-IE stretehing in hydrogenated nanocdiamond. as distinct from the 3.3 yam PAIL feature.," \citet{kerckhoven02} attribute these bands to C-H stretching in hydrogenated nanodiamond, as distinct from the 3.3 $\mu$ m PAH feature."
 The 3.47 san feature in absorption toward a number of proto-stars is attributed to the tertiary. ΟΠ stretching mode in diamond like structures CAllaanandolaetal.1992)., The 3.47 $\mu m $ feature in absorption toward a number of proto-stars is attributed to the tertiary C-H stretching mode in diamond like structures \citep{allamandola92}.
. Spectra of diamondoid molecules (Piralietal.2007) show that nanodiamonds a few nanometre in size could be responsible for the 3.53 and 3.43 pam enission lines and smaller diamondoids give the 3.47 jan absorption feature., Spectra of diamondoid molecules \citep{pirali07} show that nanodiamonds a few nanometre in size could be responsible for the 3.53 and 3.43 $\mu$ m emission lines and smaller diamondoids give the 3.47 $\mu$ m absorption feature.
 Cosmic nanocdiamondsare also detected in primitive carbonaceous meteorites οἱ presolar origin (Lewisetal.1957:Daulton1996:Dai2002:Garai2006).," Cosmic nanodiamondsare also detected in primitive carbonaceous meteorites of presolar origin \citep{lewis87, daulton96, dai02, garai06}."
. In fact. nanodiamonds are considered (to be (he most abundant presolar component in meteorites (Anders&Zinner1993:," In fact, nanodiamonds are considered to be the most abundant presolar component in meteorites \citep{anders93, zinner98}."
1993).. Jonesetal.(2004) studied Co—/7 stretching mode of nanocdiamoncds extracted from Orgueil meteorite and observed tlie above mentioned IR bands., \citet{jones04} studied $C-H$ stretching mode of nanodiamonds extracted from Orgueil meteorite and observed the above mentioned IR bands.
 If the ISAM nanodiamonds are not hydrogenated their detection is hard al.2002) and they could be more abundant than estimated by the observations ol infrared C'—Lf bands (cleDiegoetal.2007)., If the ISM nanodiamonds are not hydrogenated their detection is hard \citep{kerckhoven02} and they could be more abundant than estimated by the observations of infrared $C-H$ bands \citep{dedeigo07}.
. It is. therefore. important to incorporate nanodiaumnonds in UV extinction models [or which their independent scattering and extinction properties need to be understood.," It is, therefore, important to incorporate nanodiamonds in UV extinction models for which their independent scattering and extinction properties need to be understood."
 The ex(ünetlion properties of nanodiamond dust have been reported (Mutschkeetal.2004) for spherical shape and the far-UV break of spectral enerev in quasars is attributed to nanodiamond dust (Dinetteοἱal.2005.2006).," The extinction properties of nanodiamond dust have been reported \citep{mutschke04} for spherical shape and the far-UV break of spectral energy in quasars is attributed to nanodiamond dust \citep{binette05, binette06}."
. In this communication extinction properties of nanodiamond grains of different. ellipsoidal shapes and sizes are reported., In this communication extinction properties of nanodiamond grains of different ellipsoidal shapes and sizes are reported.
 To study the effect of nanociamond within graphite extinction efficiencies are also reported for nanociamond-eraphite as core-mantle erains., To study the effect of nanodiamond within graphite extinction efficiencies are also reported for nanodiamond-graphite as core-mantle grains.
 An extinction eurve modeling is proposed including nanocdiamond as a component., An extinction curve modeling is proposed including nanodiamond as a component.
 Various aspects of evolution of Carbon in the ISAT have been discussed in literature (Dorschener&Salama 1993).," Various aspects of evolution of Carbon in the ISM have been discussed in literature \citep{dorschner95, henning98}."
. It is generally asstunecl that the ISM carbon is primarily Ivdrogenatecl Amorphous Carbon (IAC) that transforms to graphite and diamond like structures in the presence of UV radiation field (Li&Greenberg 2002).., It is generally assumed that the ISM carbon is primarily Hydrogenated Amorphous Carbon (HAC) that transforms to graphite and diamond like structures in the presence of UV radiation field \citep{ligrn02}. .
 Regions with low UV radiations. such as dense clouds and giant star atmospheres. eraphitic," Regions with low UV radiations, such as dense clouds and giant star atmospheres, graphitic"
The plan of the paper ts as follows.,The plan of the paper is as follows.
 In ations. datareduction. phoronget combiningHS Mn)," In \\ref{sec:obs_dr_phot} we describe the observations, data reduction, photometry and completeness analysis."
" UR) aysd hie distanceofi refsec:obsur,liotwedescribetheobserv.trgby.color magnitudediagram( CM emd). starcountsprofiles(s profile).surfacebrightnesspro file(s surfacebrightness)mandmetallicitygradient(s f))."," Next, we present results for the distance of NGC 7793 as estimated from the tip of the red giant branch (TRGB, \\ref{sec:trgb}) ), color-magnitude diagram (CMD, \\ref{sec:cmd}) ), star counts profiles \\ref{sec:profile}) ), surface brightness profile \\ref{sec:surfacebrightness}) ) and metallicity gradient \\ref{sec:mdf}) )."
Discussionandconclusions followins discussion., Discussion and conclusions follow in \\ref{sec:discussion}.
 The data were obtained using the Gemini Multi Object Spectrograph (GMOS) on the Gemini South telescope over three nights in 2005 August as a part of the program GS-2005B-Q-4., The data were obtained using the Gemini Multi Object Spectrograph (GMOS) on the Gemini South telescope over three nights in 2005 August as a part of the program GS-2005B-Q-4.
 Deep σ΄ and i’ images of two major axis fields on each side of the galaxy were taken: the locations of the fields (SE and NW) are shown in Figure 1.., Deep $g'$ and $i'$ images of two major axis fields on each side of the galaxy were taken; the locations of the fields (SE and NW) are shown in Figure \ref{fields}.
 GMOS field of view is 5.5 on a side. (, GMOS field of view is $5'.5$ on a side. (
At the distance of NGC 7793 (3.61 Mpe. refsec:trgb)). 1 corresponds to 1.05 kpe.),"At the distance of NGC 7793 (3.61 Mpc, \\ref{sec:trgb}) ), $1'$ corresponds to $1.05$ kpc.)"
" The average FWHM of the data is 0”.6 (SE) and 07.8 (NW) in ¢’. and 0"".5 (SE) and 0”.7 (NW) in / band."," The average FWHM of the data is $0''.6$ (SE) and $0''.8$ (NW) in $g'$, and $0''.5$ (SE) and $0''.7$ (NW) in $i'$ band."
 To reduce the data we employed the standard IRAF/Gemini routines which included (1) bias subtraction and flat fielding (qizeduce).(nD (for / data only) creating the master fringe frame from the individual reduced frames ) and single (n) mosaicking of individual GMOS CCDs into a reference frame c)). and (1v) combining the dithered exposures into a final image (imeoadd))," To reduce the data we employed the standard IRAF/Gemini routines which included (i) bias subtraction and flat fielding ), (ii) (for $i'$ data only) creating the master fringe frame from the individual reduced frames ) and subtracting it from the individual images ), (iii) mosaicking of individual GMOS CCDs into a single reference frame ), and (iv) combining the dithered exposures into a final image )."
 We obtained 13«600 s exposures in g’ and 22«600 s exposures in // band per field. bringing total on-source exposure time to 11.7 hours.," We obtained $13\times600$ $s$ exposures in $g'$ and $22\times600$ $s$ exposures in $i'$ band per field, bringing total on-source exposure time to $11.7$ hours."
 The data for the SE field were taken during the nights of 2005 Aug O9UT (hereafter: first night) and 2005 Aug IOUT (hereafter: second night)., The data for the SE field were taken during the nights of 2005 Aug 09UT (hereafter: first night) and 2005 Aug 10UT (hereafter: second night).
 Only5 (out of 13) ¢’-band and 21 (out of 22) /-band images were observed on the first night and the observing log indicated that a thin cloud might have affected i’-band observations., Only 5 (out of 13) $g'$ -band and 21 (out of 22) $i'$ -band images were observed on the first night and the observing log indicated that a thin cloud might have affected $i'$ -band observations.
 In addition. only one standard star field observation was recorded.," In addition, only one standard star field observation was recorded."
 Remaining science images of SE field. as well as three standard stars fields were observed the following night.," Remaining science images of SE field, as well as three standard stars fields were observed the following night."
 The bulk of the data of the NW field was collected the night of 2005 Aug 11UT (12 e'-band and 21 /-band images: hereafter: third night)., The bulk of the data of the NW field was collected the night of 2005 Aug 11UT (12 $g'$ -band and 21 $i'$ -band images; hereafter: third night).
 However. no photometric standard stars were observed that night.," However, no photometric standard stars were observed that night."
" The remaining science frames (one in each of the bands) were observed the previous night under photometric conditions,", The remaining science frames (one in each of the bands) were observed the previous night under photometric conditions.
 Initial analysis of the photometry revealed a suspicious discrepancy in /-band magnitude distribution between the two fields., Initial analysis of the photometry revealed a suspicious discrepancy in $i'$ -band magnitude distribution between the two fields.
 In correspondence with the Gemini. staff it was confirmed that this was most likely due to the non-photometric conditions on the night of 2005 Aug O9UT. when the majority of the science frames of the SE field were taken.," In correspondence with the Gemini staff it was confirmed that this was most likely due to the non-photometric conditions on the night of 2005 Aug 09UT, when the majority of the science frames of the SE field were taken."
 Accounting for this. and the fact that the photometric standard stars observation were only taken on the second night of the run. we decided to proceed in the following manner: - SE field. /-band: combine 21 images taken on the first night and compare photometry of this deep image with the photometry extracted from the single image observed on the second night. -," Accounting for this, and the fact that the photometric standard stars observation were only taken on the second night of the run, we decided to proceed in the following manner: - SE field, $i'$ -band: combine 21 images taken on the first night and compare photometry of this deep image with the photometry extracted from the single image observed on the second night. -"
 SE field. ¢’-band: combine separately 5 images observed on the first. and 8 images taken on the second night and compare the photometry between the two images. -," SE field, $g'$ -band: combine separately 5 images observed on the first, and 8 images taken on the second night and compare the photometry between the two images. -"
 NW field. /-band: compare the photometry extracted from the yai!deep qoumimageαμ createdsy by WRPhI 21 images takenp on NL. second night. -," NW field, $i'$ -band: compare the photometry extracted from the deep image created by combining 21 images taken on the third night of the run with the single image taken on the second night. -"
 NW field. ¢’-band: similarly to the /-band case. compare a combined deep image created from the 12 exposures taken on the third night. with the single image taken on the second night of the run.," NW field, $g'$ -band: similarly to the $i'$ -band case, compare a combined deep image created from the 12 exposures taken on the third night, with the single image taken on the second night of the run."
 In the following sections. we will refer to the (combinations of) images taken on the second night of the run as calibration images and to the ones observed on the first and third night as final images.," In the following sections, we will refer to the (combinations of) images taken on the second night of the run as calibration images and to the ones observed on the first and third night as final images."
 To extract stellar photometry we used the standalone version of DAOPHOT and ALLSTAR packages (?).., To extract stellar photometry we used the standalone version of DAOPHOT and ALLSTAR packages \citep{stetson87}.
 Following the initial runs of and routines. which were used to catalog objects in the image and measure their aperture photometry. we proceeded to determine the point spread function (PSF) for each image.," Following the initial runs of and routines, which were used to catalog objects in the image and measure their aperture photometry, we proceeded to determine the point spread function (PSF) for each image."
 Depending on the filter and the field. 80—220 moderately bright isolated stars in each field were selected as PSF stars and used to iteratively compute the PSE.," Depending on the filter and the field, $80-220$ moderately bright isolated stars in each field were selected as PSF stars and used to iteratively compute the PSF."
" The PSF stars were ""hand-picked"" and their radial. contour and mesh profiles were visually examined within the IRAF/DAOPHOT package."," The PSF stars were “hand-picked” and their radial, contour and mesh profiles were visually examined within the IRAF/DAOPHOT package."
 The calculated point spread function was used to subtract the PSF stars from the original image: the positions of the subtracted PSF stars were inspected again and the PSF stars which did not subtract cleanly were excluded from the PSF calculation., The calculated point spread function was used to subtract the PSF stars from the original image; the positions of the subtracted PSF stars were inspected again and the PSF stars which did not subtract cleanly were excluded from the PSF calculation.
 In addition. stars with subtraction errors which differed more than 3c from the mean value were also excluded.," In addition, stars with subtraction errors which differed more than $3\sigma$ from the mean value were also excluded."
 The next iteration of the point spread function was calculated using images in which. within the fitting radius of each PSF star. all but PSF stars have been subtracted.," The next iteration of the point spread function was calculated using images in which, within the fitting radius of each PSF star, all but PSF stars have been subtracted."
 This was followed with yet another visual inspection within IRAF/DAOPHOT as described above., This was followed with yet another visual inspection within IRAF/DAOPHOT as described above.
 The whole procedure was repeated once more to derive the final PSF., The whole procedure was repeated once more to derive the final PSF.
 Finally. ALLSTAR was used to fit the calculated PSF to all stars in the object catalogs and determine their photometry," Finally, ALLSTAR was used to fit the calculated PSF to all stars in the object catalogs and determine their photometry."
 Comparison of the final and calibration images revealed the following., Comparison of the final and calibration images revealed the following.
 In the /-band. we found the difference in photometry extracted from the calibrated and final images," In the $i'$ -band, we found the difference in photometry extracted from the calibrated and final images"
We also cousider planets with nuw20;1 that planet formation theories suggest mieht still be mainly rocky bodies that have not uude'eoue substautial growth via gas accretion.,"We also consider planets with $m < 20
M_\oplus$ that planet formation theories suggest might still be mainly rocky bodies that have not undergone substantial growth via gas accretion."
 Note that this category would include Uranus aud Neptne as well as the terrestrial planets in our solar systei., Note that this category would include Uranus and Neptune as well as the terrestrial planets in our solar system.
 Fiially. we also present results for planets o“all masses. bi these are still limited to 111uw10A; due to our choice of the planet inass fuictio1.," Finally, we also present results for planets of all masses, but these are still limited to $m < 10 M_J$ due to our choice of the planet mass function."
 This categoΝ would iuclude all the planets ii otr nOar system as well as of the presettly SHOWLL extrasoar planets., This category would include all the planets in our solar system as well as of the presently known extrasolar planets.
 In table 3.+) we present the number of planets which a‘e detected or characterized in ot sliiulations for all planets (top). planets wih mass less 1lali 20:Vl finicldlle). and. planets wit nass less than 34M (bottom).," In table \ref{TableStatsAll} we present the number of planets which are detected or characterized in our simulations for all planets (top), planets with mass less than $20 M_\oplus$ (middle), and planets with mass less than $3 M_\oplus$ (bottom)."
 The dilerent columus provide t Lts ol simulations with variot ulssion parameters., The different columns provide the results of simulations with various mission parameters.
 The rauges provkled represent colfic intervals both in this table an hroughout this paper., The ranges provided represent confidence intervals both in this table and throughout this paper.
 These «onfidence intervals reflect oily ical uncertainties due to the ando realizajon of the mass-perio distribution (1). not uities in the clistribution itself.," These confidence intervals reflect only statistical uncertainties due to the random realization of the mass-period distribution (1), not uncertainties in the distribution itself."
 In 'e[HistogramCG‘id we show tlje likeihood of findiug a give1 LULLaber of planets., In \\ref{HistogramGrid} we show the likelihood of finding a given number of planets.
 Tje. differei columus cousider planets wih different maximur masses., The different columns consider planets with different maximum masses.
 The top our rows are for a SIM survey with 1 jras single iieasureme oxecision., The top four rows are for a SIM survey with 1 $\mu$ as single measurement precision.
" The to2 row is for cletecine a platet. the secold row is for measuring the mass aud orbi parameters wit1 aceuracy. he third row is for measuring tle mnasses with accuracy. a the fourth row is [or measuring the masses aucl orbital paramete""s with accuracy."," The top row is for detecting a planet, the second row is for measuring the mass and orbital parameters with accuracy, the third row is for measuring the masses with accuracy, and the fourth row is for measuring the masses and orbital parameters with accuracy."
 The bot )iwO rows ale [ty a radial velocity survey of the same stars with: siugle measurement pr‘ision., The bottom two rows are for a radial velocity survey of the same stars with $3$ single measurement precision.
 The next o bottom row is fkx detecting the planet. aud th bottom row is for measuring tle lasses alle lo‘bital parameters.," The next to bottom row is for detecting the planet, and the bottom row is for measuring the masses and orbital parameters."
 The solic lites are for five-year surveys aud the dotted lines are for LO vear surveys., The solid lines are for five-year surveys and the dotted lines are for 10 year surveys.
 We couc«cle that a SIM survey of 120 stars al ljas precision is expected to detect ~214-T planets over| [ive years OF 338 planets over teu years., We conclude that a SIM survey of 120 stars at $1\mu$ as precision is expected to detect $\sim24\pm7$ planets over five years or $\sim33\pm8$ planets over ten years.
 The five-year survey would measure the masses aid orbis of 164-6 of these planets with accuracy aud ~13d-6 planets with accuracy., The five-year survey would measure the masses and orbits of $\sim16\pm6$ of these planets with accuracy and $\sim13\pm6$ planets with accuracy.
 However. most of these planes are relatively jissive.," However, most of these planets are relatively massive."
 If we restrict ourselves to planets with mass €34M.. then even the ter-veal Survey vVOLd ouly detect. ~54-3 planets and would probably not measure aly masses or o‘bits to accuracy (see Table 2).," If we restrict ourselves to planets with mass $\le3M_\oplus$, then even the ten-year survey would only detect $\sim5\pm3$ planets and would probably not measure any masses or orbits to accuracy (see Table 2)."
 In 'e[HistogramMaidssious we explore the ellect o ‘varying tL Ussion j»arameters., In \\ref{HistogramMissions} we explore the effect of varying the mission parameters.
 The solid liue is for a mission with 1 pas single neasurenient acctracy. the k dashed line for 1.E µας. the dotted line or 2 gas.," The solid line is for a mission with 1 $\mu$ as single measurement accuracy, the long dashed line for 1.4 $\mu$ as, the dotted line for 2 $\mu$ as."
 The thick lines a'e for a five-vear mission aL e thiu ines are for a ten-vear mission., The thick lines are for a five-year mission and the thin lines are for a ten-year mission.
 The upper panel shows the uumber of planets detected :| the other panels show the number of jxanets for which masses €aid orbits are determiued., The upper panel shows the number of planets detected and the other panels show the number of planets for which masses and orbits are determined.
 T eft paiels are for all planets. and the isht panels are for planets wit hon<20M.," The left panels are for all planets, and the right panels are for planets with $m \le 20 M_\oplus$."
 Note that imore plajets Of all inasses are fouud by uissious targeting a larger —umber of stars at lower preciSnu however. such missious are much less sensitive to the low-1nass terestrial planets that may be 1ici inte'esting.," Note that more planets of all masses are found by missions targeting a larger number of stars at lower precision; however, such missions are much less sensitive to the low-mass terrestrial planets that may be most interesting."
 In Fies., In Figs.
 { aud 5 we slot the cumulative number of planets fouid below a given mass., \ref{CumlativeLevels} and \ref{CumlativeMissions} we plot the cumulative number of planets found below a given mass.
 In Fig., In Fig.
(seeMiller&Branch1990).,\citep[see][]{miller90}.
. Our conclusion is that ον100061 was not a very high mass star and very likely had an initial mass of less than 3M..., Our conclusion is that SN1999gi was not a very high mass star and very likely had an initial mass of less than $^{+3}_{-2}$ $_{\odot}$.
 The well maintained. and easily accessible HIST. archive has made (his project leasible ancl. in the future. will allow (he investigation of SNe sitesbefore explosion to be investigated in a svstematic way.," The well maintained, and easily accessible HST archive has made this project feasible and, in the future, will allow the investigation of SNe sites explosion to be investigated in a systematic way."
 We have a 110 SNAP project that will bring the number of Iate-tvpe galaxies (within a distance of ~17 MAIpe) with WFDPC?2 2 or 3-colour photometry (o 72350., We have a 10 SNAP project that will bring the number of late-type galaxies (within a distance of $\sim$ Mpc) with WFPC2 2 or 3-colour photometry to $\sim$ 350.
 This will allow the sites of future core-collapse 5Ne in (these galaxies to be imaged prior to explosion and will extend the present work lo a more statistically meaningful sample., This will allow the sites of future core-collapse SNe in these galaxies to be imaged prior to explosion and will extend the present work to a more statistically meaningful sample.
 The advent of Virtual Observatory initiatives both in Europe and the US (e.g. ASTROVIRTEL) will make (his (wpe of project even easier io manage. and allow very. [ast reaction (to events where either limits can be set on the progenitor or in the event that a candidate star is identified.," The advent of Virtual Observatory initiatives both in Europe and the US (e.g. ) will make this type of project even easier to manage, and allow very fast reaction to events where either limits can be set on the progenitor or in the event that a candidate star is identified."
 SIS. NT and CMF acknowledge support from PPARC. CAT thanks Churchill College for a fellowship.," SJS, NT and CMF acknowledge support from PPARC, CAT thanks Churchill College for a fellowship."
 We (hank the initiative al ESO/ST-ECF for new software development lor searching IIST/ESO archives., We thank the initiative at ESO/ST-ECF for new software development for searching HST/ESO archives.
 We acknowledge A. Filippenko ancl the team ol IST SNAP 8602 for waiving the proprietary period of their data., We acknowledge A. Filippenko and the team of HST SNAP 8602 for waiving the proprietary period of their data.
For these two cases we also give the final. pericentre distance distributions in Fig. 13.,For these two cases we also give the final pericentre distance distributions in Fig. $13$.
 In the low inclination case we see that particles from extension. B can. plunge to pericentre distances of 0.2., In the low inclination case we see that particles from extension B can plunge to pericentre distances of $0.2$.
 KLSS proposed. that these particles could. explain the existence of an inner warp in the scattered [light dustdisc of 3 Pie at ~50au (Burrows et al., KLSS proposed that these particles could explain the existence of an inner 'warp' in the scattered light dustdisc of $\beta$ Pic at $\sim$ (Burrows et al.
 1995. Alouillet ct al.," 1995, Mouillet et al."
 1997)., 1997).
 Wecan see from Lig. 13.," Wecan see from Fig. $13$,"
 that for the higher inclination encounter. extension D particles have significantly higher perturbecl pericentre distances (down to about O.7: or —2002au)).," that for the higher inclination encounter, extension B particles have significantly higher perturbed pericentre distances (down to about $0.7$; or $\sim$ )."
 This is a direct. consequence of the lower eccentricities produced. at comparable semimajor axes in extension B for the two cases., This is a direct consequence of the lower eccentricities produced at comparable semimajor axes in extension B for the two cases.
 Thus the minimum pericentre distance is minimised in coplanar cases., Thus the minimum pericentre distance is minimised in coplanar cases.
 C'orrespondinglv. larger minimum poericentre distancesare also charateristic of hyperbolic encounters.," Correspondingly, larger minimum pericentre distancesare also charateristic of hyperbolic encounters."
 Fig., Fig.
 14 gives the final eccentricity ancl pericentre. distributions for a hvperbolic encounter with ο=2 and ;=30, $14$ gives the final eccentricity and pericentre distributions for a hyperbolic encounter with $e=2$ and $i=30$.
 Η the explanation of the inner warp suggested. by IKLSS is confirmed then this also supports the need for a low inclination ancl relative velocity encounter., If the explanation of the inner warp suggested by KLSS is confirmed then this also supports the need for a low inclination and relative velocity encounter.
 As can be seen in Fig., As can be seen in Fig.
 4 the close ἠν-Ών of a dise of xwticles by a perturbing star can result in the very. close approach of some of the disc particles to the perturber., $4$ the close fly-by of a disc of particles by a perturbing star can result in the very close approach of some of the disc particles to the perturber.
 Since he unperturbed. disc does not extend. all the way out to »ericentre. this occurs by particles streaming through the vicinity of the instantaneous Lagrange Point between the wo stars. about the time of closest approach.," Since the unperturbed disc does not extend all the way out to pericentre, this occurs by particles streaming through the vicinity of the instantaneous Lagrange Point between the two stars, about the time of closest approach."
 In the case hat particles become captured by the perturber the captureelliciency is generally low (see also Hall ct al., In the case that particles become captured by the perturber the captureefficiency is generally low (see also Hall et al.
 1996)., 1996).
 Table 1 gives the percentage of initial dise particles that are captured w the perturber for the mocdels discussed above. and from. it we can see tha rw lower eccentricitv. ancl inclination encounters are required. in order to effect capture at all.," Table $1$ gives the percentage of initial disc particles that are captured by the perturber for the models discussed above, and from it we can see that the lower eccentricity and inclination encounters are required, in order to effect capture at all."
 For the model parameters used by IKLSS. the percentage of captured. particles is 10. per cent of the initial particle number. but note that if the initial clise were allowed Oo extend. to. pericentre. this figure could be fractionally arger (Hall et al.," For the model parameters used by KLSS, the percentage of captured particles is $\sim$ 10 per cent of the initial particle number, but note that if the initial disc were allowed to extend to pericentre this figure could be fractionally larger (Hall et al."
 1996)., 1996).
 In the case of 3 Pic. considering he maximal parent body disc of Backman Paresce (1993). the captured material could. therefore represent. up o about 10 earth. masses of planetesimals which would subsequently orbit the perturber and. produce a scattered ight signature similar to Veea-like sources.," In the case of $\beta$ Pic, considering the maximal parent body disc of Backman Paresce (1993), the captured material could therefore represent up to about $10^3$ earth masses of planetesimals which would subsequently orbit the perturber and produce a scattered light signature similar to Vega-like sources."
 This would not however uniquely identify a perturber candidate since approximately 15 per cent of main sequence stars of all types are known to have such dises (Backman Cillett 1987. Aumann 19858). but given the encounter parameters we find here. it seems likely that a perturber candidate should have this signature.," This would not however uniquely identify a perturber candidate since approximately 15 per cent of main sequence stars of all types are known to have such discs (Backman Gillett 1987, Aumann 1988), but given the encounter parameters we find here, it seems likely that a perturber candidate should have this signature."
 None the less we max find erude approximations for the orbital properties of the captured. planetesimals., None the less we may find crude approximations for the orbital properties of the captured planetesimals.
 We shall make an analogy with the theory of mass transfer in semi-detached: binaries. in which the captured matter orbits the secondary with the specific angular momentum of relative motion at the Lagrange Point (see Frank. Wine Raine 1992).," We shall make an analogy with the theory of mass transfer in semi-detached binaries, in which the captured matter orbits the secondary with the specific angular momentum of relative motion at the Lagrange Point (see Frank, King Raine 1992)."
" Here we deduce that if a particle in the outermost parts of the disc is captured. close το the perturber's pericentre. then it will orbit the perturber with specific angular monentunm: where 2, is the initial outer radius of the disc and b is the separation of the secondary from the Lagrange Point at the instant of pericentre passage. approximated by: In the above we have taken the circular. velocity. of a particle Iving on the binary axis relative to the perturber at pericentre for the input particle velocity."," Here we deduce that if a particle in the outermost parts of the disc is captured close to the perturber's pericentre, then it will orbit the perturber with specific angular momentum: where $R_{\rm o}$ is the initial outer radius of the disc and $b$ is the separation of the secondary from the Lagrange Point at the instant of pericentre passage, approximated by: In the above we have taken the circular velocity of a particle lying on the binary axis relative to the perturber at pericentre for the input particle velocity."
 Although the instantaneous Lagrange Point is located well within the envelope of the initial disc. the rapid. eccentricity. changes in the dise prior to particle transfer cause compression of the disc such that the outer dise. particles pass through the vicinity of the Lagrange Point with approximately their initial velocities (e.g. see Fig.," Although the instantaneous Lagrange Point is located well within the envelope of the initial disc, the rapid eccentricity changes in the disc prior to particle transfer cause compression of the disc such that the outer disc particles pass through the vicinity of the Lagrange Point with approximately their initial velocities (e.g. see Fig."
 4)., $4$ ).
 With respect to the perturber. the specific angular momentum of the captured: particle is: νοΔΙα1et). where the characteristic semimajor axis ancl eccentricity with respect to the secondary are respectively a ancl e," With respect to the perturber, the specific angular momentum of the captured particle is: $\sqrt{GM_{\rm s}a'(1-e'^2)}$, where the characteristic semimajor axis and eccentricity with respect to the secondary are respectively $a'$ and $e'$."
 llence we have: Thus for a model with e= Loy= 0.3. and gq= 2.6. we find αι67)— 0.3.," Hence we have: Thus for a model with $e=1$ , $\mu=0.3$ , and $q=2.6$ , we find $a'(1-e'^2)\sim0.3$ ."
 This equation docs not. apply when the relative velocity of the perturber and disc particles, This equation does not apply when the relative velocity of the perturber and disc particles
A basic tenet. of modern cosmology is the idea that the present large-scale structure the Universe originated by the eravitational growth of small matter inhomogencities.,A basic tenet of modern cosmology is the idea that the present large-scale structure the Universe originated by the gravitational growth of small matter inhomogeneities.
 “Phese initial density [uctuations are thought to be imprinted in à universe dominated by collisionless dark matter at very high redshifts., These initial density fluctuations are thought to be imprinted in a universe dominated by collisionless dark matter at very high redshifts.
 Their distribution of amplitudes with spatial scale depends ultimately both on the nature of this collisionless matter and on the physical processes operating prior to the epoch of recombination., Their distribution of amplitudes with spatial scale depends ultimately both on the nature of this collisionless matter and on the physical processes operating prior to the epoch of recombination.
 A family of these generic models are the moderately-sucesstull. hierarchical. cosmogonies. which suppose that the variance of initial Fluctuations decreases with scale.," A family of these generic models are the moderately-sucessfull hierarchical cosmogonies, which suppose that the variance of initial fluctuations decreases with scale."
 This means that small structures are the first to collapse and that galaxies. groups and clusters are formed by the merging of non-linear. objects into. larger and larger units.," This means that small structures are the first to collapse and that galaxies, groups and clusters are formed by the merging of non-linear objects into larger and larger units."
 Fhis merging sequence can be visualized as a hierarchical tree with the thickness of its branches rellecting the mass ratio of the objects involved. in the merging (Lacey Cole 1993)., This merging sequence can be visualized as a hierarchical tree with the thickness of its branches reflecting the mass ratio of the objects involved in the merging (Lacey Cole 1993).
 1£ we imagine time running from the top of the tree. the main trunk would. represent the final object. while its past merging history would. be represented. schematically by. the ramification of this trunk into small branches. representing accretion of small sub-Iumps. and by the splitting into branches of comparable thickness when merging of sub-clumps of comparable size OCCULS.," If we imagine time running from the top of the tree, the main trunk would represent the final object, while its past merging history would be represented schematically by the ramification of this trunk into small branches, representing accretion of small sub-lumps, and by the splitting into branches of comparable thickness when merging of sub-clumps of comparable size occurs."
 ‘The linear growth of the density field is well-unclerstood. but. collapsed objects. or “dark halos’. are highly non-lincar gravitational structures whose dynamical evolution is difficult to trace.," The linear growth of the density field is well-understood, but collapsed objects, or `dark halos', are highly non-linear gravitational structures whose dynamical evolution is difficult to trace."
 Some progress can be made by the clirect numerical integration of the equations of motion in N-body simulations. but these are limited in cdvnamic range and are very time-consuming.," Some progress can be made by the direct numerical integration of the equations of motion in N-body simulations, but these are limited in dynamic range and are very time-consuming."
 Theoretical models are usually based on the analytic. top-hat model of Gunn Gott (1972).," Theoretical models are usually based on the analytic, top-hat model of Gunn Gott (1972)."
 Spherical overdensities in a critical density universe reach a maximum size when their linear overdensity reaches 1.06. then recollapse ancl virialize at an overdensity of approximately 6.=1.69.," Spherical overdensities in a critical density universe reach a maximum size when their linear overdensity reaches 1.06, then recollapse and virialize at an overdensity of approximately $\delta_c=1.69$."
 Unfortunately real halos are neither uniform. nor spherically-svnimetric so that. their collapse times scatter about the predicted: value., Unfortunately real halos are neither uniform nor spherically-symmetric so that their collapse times scatter about the predicted value.
 In cosmology we are seldom interested. in the specific nature of one individual halo. but. rather in the statistical properties of the whole population.," In cosmology we are seldom interested in the specific nature of one individual halo, but rather in the statistical properties of the whole population."
 The analytical approach to this problem. was ploneered by Press Schechter (1974: hereafter PS)., The analytical approach to this problem was pioneered by Press Schechter (1974; hereafter PS).
 To estimate what proportion of the Universe which is contained in structures of mass AZ at. τος z. the density field. is first smoothed with a top-hat filter of radius A. where Ad=4/3zp4?* and p is the mean density of the Universe.," To estimate what proportion of the Universe which is contained in structures of mass $M$ at redshift $z$, the density field is first smoothed with a top-hat filter of radius $R$, where $M=4/3\pi\overline{\rho}R^3$ and $\overline{\rho}$ is the mean density of the Universe."
 CAL.2) is then defined to be the fractional," $F(M,z)$ is then defined to be the fractional"
coherent stun of A raudonm plasors loses the phase information aud results in the formation of speckles iu secing-limited images with a visibleTR telescope.,coherent sum of $R$ random phasors loses the phase information and results in the formation of speckles in seeing-limited images with a visible/IR telescope.
 NRM-interferometiy solves this problem. by discarding lieht with a pupil mask designed so that each baseliue is uuique (R= 1). which mates the extraction of the phase possible.," NRM-interferometry solves this problem, by discarding light with a pupil mask designed so that each baseline is unique $R=1$ ), which makes the extraction of the phase possible."
 The phases alone. being corrupted by residual OPDs. are of restricted interest.," The phases alone, being corrupted by residual OPDs, are of restricted interest."
 It is however possible to conibine them to form what is kuown as closure-phase (Jeuuisou1958). that is the sun of three phases ucasured by baselines forming a closed triangle.," It is however possible to combine them to form what is known as closure-phase \citep{1958MNRAS.118..276J}, that is the sum of three phases measured by baselines forming a closed triangle."
| This remarkable interferometric quantity (cf., This remarkable interferometric quantity (cf.
 the introduction o closure phase by Monuier (20001) exhibits a compelling property: it rejects all residual pupil-plaue phase errors., the introduction to closure phase by \citet{2000plbs.conf..203M}) ) exhibits a compelling property: it rejects all residual pupil-plane phase errors.
 Moreover. because it is determined frou he analysis of the final science detector aud uot ou a separate ari wavefront sensor. it is also ininunue to non-common path errors between the wavefront sensor and he scieuce camera.," Moreover, because it is determined from the analysis of the final science detector and not on a separate arm wavefront sensor, it is also immune to non-common path errors between the wavefront sensor and the science camera."
" Ouce extracted and calibrated. the closure-phases cau hen be compared to a parametric model for instance of a binary star. to confirin or infirm the presence of a conipanion around a given source. while uncertainties xovide contrast detection (νο, seusitivitv) lits."," Once extracted and calibrated, the closure-phases can then be compared to a parametric model, for instance of a binary star, to confirm or infirm the presence of a companion around a given source, while uncertainties provide contrast detection (i.e. sensitivity) limits."
 This approach was successfully used by (Llovdetal.2006:2008:Martinacheetal. 2009).. who typically report sensitivity of 5-6 maguitudes in the near iufrared at separations raugiue frou 0.5 to 1 A/D.," This approach was successfully used by \citep{2006ApJ...650L.131L,
 2007ApJ...661..496M, 2008ApJ...678..463I, 2008ApJ...679..762K,
 2009ApJ...695.1183M}, who typically report sensitivity of 5-6 magnitudes in the near infrared at separations ranging from 0.5 to 4 $\lambda/D$."
 This paper aus at eeucraliziug the notion of closure-phase. aud shows that closure-pliase like quantities. 1.6. sharing the same property of iudepeudoence to pupil-plaue phase errors. can be constructed even in the case of redundant apertures.," This paper aims at generalizing the notion of closure-phase, and shows that closure-phase like quantities, i.e. sharing the same property of independence to pupil-plane phase errors, can be constructed even in the case of redundant apertures."
 Whether contiguous (ie. sinele-dish) or not (d.e. iuterferoimetzic).- the 2D pupil of au imagine svsteni cau be discretized iuto a finite collection of Α΄ elementary sub-apertures.," Whether contiguous (i.e. single-dish) or not (i.e. interferometric), the 2D pupil of an imaging system can be discretized into a finite collection of $N$ elementary sub-apertures."
" One of these clemeutary sub-apertures taken as zero-phnase reference. the pupil-plaue phase of a coherent poiut-like lieht source can be written as a NO leeonrponenut vector ο,"," One of these elementary sub-apertures taken as zero-phase reference, the pupil-plane phase of a coherent point-like light source can be written as a $N-1$ -component vector $\varphi$."
 Caven that the image. or interferogram. of this source is sufficicutly sampled. then in the Fourier plane (a.a.," Given that the image, or interferogram, of this source is sufficiently sampled, then in the Fourier plane (a.k.a."
 (Cu.0)- plane in interferometry) one will be able to sample up to AL phases. where Af is a function of the pupil geometry oulv.," $(u,v)$ -plane in interferometry) one will be able to sample up to $M$ phases, where $M$ is a function of the pupil geometry only."
 For a nouaceduudaut array inade of N elementary sub-apertures. the nuuber of sampled (ανο). phases is maximum Af=(2)," For a non-redundant array made of $N$ elementary sub-apertures, the number of sampled $(u,v)$ phases is maximum $M = (^N_2)$."
" The BHue nunber of sub-apertures organized m a reduudaut array, for instance following a regular erid. produces sienificautly less distinct (ανο) sample points as each point receives the contribution of several pairs of sub-apertures."," The same number of sub-apertures organized in a redundant array, for instance following a regular grid, produces significantly less distinct $(u,v)$ sample points as each point receives the contribution of several pairs of sub-apertures."
 Iu mist cases. since cach point receives the sin of several random phasors. both phase aud amplitude are lost and cannot be simply retrieved: this results in the formation of speckles.," In most cases, since each point receives the sum of several random phasors, both phase and amplitude are lost and cannot be simply retrieved: this results in the formation of speckles."
 However. if the Strehl is ligh enough. the complex amplitude associated to the iustriuental pliase in one point of the pupil. 24. can be approxiniated by eff!z1|Agg," However, if the Strehl is high enough, the complex amplitude associated to the instrumental phase in one point of the pupil, $\varphi_k$ , can be approximated by $e^{i\varphi_k} \approx 1 +
i\varphi_k$."
 Direct. application of the approach is therefore for now. restricted to diffractiou-Blmited optical aud mid-IR telescopes ike OST (cf.," Direct application of the approach is therefore for now, restricted to diffraction-limited optical and mid-IR telescopes like HST (cf."
 Section 3)). but should also prove relevant o the upcoming generation of extreme AQ svstenis.," Section \ref{sec:hst}) ), but should also prove relevant to the upcoming generation of extreme AO systems."
 Given that the proposed approximation holds. while observing a point source. the uuknowu (instrumental) yhase distribution iu the pupil y can he related to the yhases € measured in the Fourier plane with a single jucar operator.," Given that the proposed approximation holds, while observing a point source, the unknown (instrumental) phase distribution in the pupil $\varphi$ can be related to the phases $\Phi$ measured in the Fourier plane with a single linear operator."
 To build au intuitive understaudiug of his relation. let us consider the following scenarios: To reproduce this behavior. the following linear model will be used: where 9 represents the M-comiponeut Fourier plane phase vector. Roa AL« diagonal matrix whose diagonal clemeuts code the reduudancy of the baselines. and A veprescuts a AL.(NV1) transfer matrix. whose properties form the core of the discussion of this work.," To build an intuitive understanding of this relation, let us consider the following scenarios: To reproduce this behavior, the following linear model will be used: where $\Phi$ represents the $M$ -component Fourier plane phase vector, $\mathbf{R}$ a $M \times M$ diagonal matrix whose diagonal elements code the redundancy of the baselines, and $\mathbf{A}$ represents a $M \times (N-1)$ transfer matrix, whose properties form the core of the discussion of this work."
 To be complete. the model should also include the phase information intrinsic to the observed source. represented by the terii ® that simply adds on top of the instrmucutal phase.," To be complete, the model should also include the phase information intrinsic to the observed source, represented by the term $\Phi_O$ that simply adds on top of the instrumental phase."
 One can theu iiultiply bothsides of the equation by the matrix R. so that it becomes:, One can then multiply bothsides of the equation by the matrix $\mathbf{R}$ so that it becomes:
where rZh and 7? are the sonic points of atomic hydrogen ancl protons respectively. η and s are corresponding number density and. velocity.,"where $r_{c}^{h}$ and $r_{c}^{p}$ are the sonic points of atomic hydrogen and protons respectively, $n$ and $u$ are corresponding number density and velocity."
 The mass loss rate of M—9x1010 &/s obtained by applying the solution over the entire planetary surface is higher (han that of M=3x1010 ος obtained by Murrav-Clay. et al. (," The mass loss rate of $\dot{M}=9\times
10^{10}$ g/s obtained by applying the solution over the entire planetary surface is higher than that of $\dot{M}=3\times 10^{10}$ g/s obtained by Murray-Clay et al. ("
2009). but. both of them accord approximately with Chat of VMO3 in observation.,"2009), but both of them accord approximately with that of VM03 in observation."
" To fit the observed. profile of Lya. IxX10 assumed that the mean temperature of thermosphere is 7=5000—LOOOOIX and the upper boundary is located at. A72.9/2, where the number density is n=2.6x10*em"," To fit the observed profile of $Ly\alpha$, K10 assumed that the mean temperature of thermosphere is $T=8000-10000$ K and the upper boundary is located at $R \sim 2.9R_{p}$ where the number density is $n=2.6\times 10^{7}
cm^{-3}$."
" Our calculation results show that the particle number density at the radius (2~2.91,) is n=5xLOPem7."," Our calculation results show that the particle number density at the radius $R \sim 2.9R_{p}$ ) is $n=5\times 10^{6}
cm^{-3}$."
 A significant dillerence between their model and ours is that the assumption of hyvdrostatie equilibrium in their models., A significant difference between their model and ours is that the assumption of hydrostatic equilibrium in their models.
" Our results show that the sonic points of 77 and ff ave at 2.572, and 3.67R,. respectively."," Our results show that the sonic points of $H$ and $H^{+}$ are at $R_{p}$ and $R_{p}$, respectively."
" It means that the assumption of hydrostatic equilibrium is not unacceptable in the region range from 142, to I.", It means that the assumption of hydrostatic equilibrium is not unacceptable in the region range from $R_{p}$ to $R_{p}$.
 llowever. the number density distribution could be different due to the difference in plivsieal detail.," However, the number density distribution could be different due to the difference in physical detail."
" For example. our results that about hydrogen is ionized at 2.9/2, do not support (he assumption of IX10 that the atmosphere is mostly ionized above 2.9/2,."," For example, our results that about hydrogen is ionized at $R_{p}$ do not support the assumption of K10 that the atmosphere is mostly ionized above $R_{p}$."
 In addition. in (he assumption of hydrostatic equilibrium the profile of number density is flatter (han (hat of hvdrodyniamies. which can lead to hieh optic depth in the wings of line.," In addition, in the assumption of hydrostatic equilibrium the profile of number density is flatter than that of hydrodynamics, which can lead to high optic depth in the wings of line."
 It is convenient to define the mass loss rates of neutral hydrogen and protons as Our results indicate that the mass loss rates of neutral hydrogen ancl protons are 3.4x LOMe/s and 5.6x 10!e/s. respectively.," It is convenient to define the mass loss rates of neutral hydrogen and protons as Our results indicate that the mass loss rates of neutral hydrogen and protons are $3.4\times 10^{10}$ g/s and $5.6\times 10^{10}$ g/s, respectively."
 To fit the observations of ILD 209453b. (wo scenarios can supply a satisfactory fit.," To fit the observations of HD 209458b, two scenarios can supply a satisfactory fit."
 In thee first case. thermal hydrogen atoratoms arere enough to be enoughused to fit fitthe Ivman alpha transittransi profile so that the energetic atoms are not necessary.," In the first case, thermal hydrogen atoms are enough to be used to fit the lyman alpha transit profile so that the energetic atoms are not necessary."
 In the second case. superthermal (hot) hydrogen atoms are required in order to fit the observations if depleted thermal," In the second case, superthermal (hot) hydrogen atoms are required in order to fit the observations if depleted thermal"
although we do not use these in our analysis.,although we do not use these in our analysis.
" These new observations are placed in context with literature data for ULIRGs, SMGs and local of disk "," These new observations are placed in context with literature data for ULIRGs, SMGs and local samples of disk galaxies."
"In order to investigate the sampleslocation of these galaxies.populations of normal high-z galaxies in the gas mass versus SFR plane, either for the integrated properties or for the surface densities, a crucial ingredient is, again, the aco conversion factor."," In order to investigate the location of these populations of normal $z$ galaxies in the gas mass versus SFR plane, either for the integrated properties or for the surface densities, a crucial ingredient is, again, the $\alpha_{\rm CO}$ conversion factor."
" Comparing the dynamical and stellar mass estimates, D10 derive a high aco=3.6+0.8 Ms (K km s! ρε) for the BzK galaxies, quite similar to that for localο) spirals (aco= 4.6)."," Comparing the dynamical and stellar mass estimates, D10 derive a high $\alpha_{CO}=3.6\pm0.8$ $M_\odot$ (K km $^{-1}$ $^2$ $^{-1}$ for the BzK galaxies, quite similar to that for local spirals $\alpha_{CO}=4.6$ )."
" This is not unexpected, given the evidence that the z1.5 near-IR selected galaxies appear to be high redshift analogs of local disks with enhanced gas content (seee.g.,dis-Tacconietal.2010,andlaterinthis letter).."," This is not unexpected, given the evidence that the $z\sim1.5$ near-IR selected galaxies appear to be high redshift analogs of local disks with enhanced gas content \citep[see e.g., discussions in ][Tacconi et al.\ 2010, and later in this letter]{dad08,dad10,dan09}. ."
" In the following, we adopt this value of aco=3.6 for the z= 0.5-2.5 normal and the ‘consensus’ value for the other populations (aco=4.6 for local aco=0.8 for local (U)LIRGs and distant SMGs/QSOs), spirals,and explore the consequences for the relation between gas masses and IR luminosities/SFRs."," In the following, we adopt this value of $\alpha_{CO}=3.6$ for the $z=0.5$ –2.5 normal and the `consensus' value for the other populations $\alpha_{CO}=4.6$ for local spirals, $\alpha_{CO}=0.8$ for local (U)LIRGs and distant SMGs/QSOs), and explore the consequences for the relation between gas masses and IR luminosities/SFRs."
 Fig., Fig.
 1 is equivalent to Fig., \ref{fig:Mgas_scat} is equivalent to Fig.
" 13 in DIO, after replacing Lig with My."," 13 in D10, after replacing $L'_{\rm
CO}$ with $M_{\rm H2}$."
 The right panel shows the ratio of Lm to My2 plotted versus Lg., The right panel shows the ratio of $L_{\rm IR}$ to $M_{\rm H2}$ plotted versus $L_{\rm IR}$.
 The implied gas consumption timescales (τρις=Mu2/SFR; right panel of Fig. 1)), The implied gas consumption timescales $\tau_{\rm gas} = M_{\rm H2}/SFR$; right panel of Fig. \ref{fig:Mgas_scat}) )
" are 0.3-0.8 Gyr for the BzK about 23 times that for and over one order of galaxies?,,magnitude smaller forlocal spirals,(U)LIRGs and distant SMGs."," are 0.3–0.8 Gyr for the BzK, about 2–3 times that for spirals, and over one order of magnitude smaller forlocal (U)LIRGs and distant SMGs."
" In a simple picture, this finding can"," In a simple picture, this finding can"
the plasma cloud is traversecl approximately orthogonally. as in Section 4 above.,"the plasma cloud is traversed approximately orthogonally, as in Section 4 above."
 Echoes of giant pulses from the Crab pulsar. with delays of 50 - 1060 yes ancl clurations of hours to some days have oen observed. by Crossley ct al(2007).. ancl interpreted using a geometrical analysis similar to ours.," Echoes of giant pulses from the Crab pulsar, with delays of 50 - 100 $\mu$ s and durations of hours to some days have been observed by Crossley et al, and interpreted using a geometrical analysis similar to ours."
 These echoes were attributed to a plasma cloud closer to the pulsar. and obablv within the cüffuse svachrotron nebula.," These echoes were attributed to a plasma cloud closer to the pulsar, and probably within the diffuse synchrotron nebula."
 Remarkably he scale of this structure and that of the filament whose cHeets we have observed are closely similar. despite. the different locations in the inner and outer parts of the nebula: roth are around one astronomical unit.," Remarkably the scale of this structure and that of the filament whose effects we have observed are closely similar, despite the different locations in the inner and outer parts of the nebula; both are around one astronomical unit."
 Bhat et al attributed slowly varving scattering of the Crab pulsar observed. at. 1400 MIIz to small-scale ilamentary structure in the nebula., Bhat et al attributed slowly varying scattering of the Crab pulsar observed at 1400 MHz to small-scale filamentary structure in the nebula.
 IXuzmin et al., Kuzmin et al.
 ound a close correlation between the incidence of scattering at. 100. MlIz and changes in dispersion measure of the Crab pulsar. on à time scale of some months.," found a close correlation between the incidence of scattering at 100 MHz and changes in dispersion measure of the Crab pulsar, on a time scale of some months."
 Further observations at Jodrell Bank. and earlier work by Rankin and Counselman and by Isaacman ancl Rankin(lO77).. suggest that these variations are continuous. and not related to the discrete events under discussion.," Further observations at Jodrell Bank, and earlier work by Rankin and Counselman and by Isaacman and Rankin, suggest that these variations are continuous, and not related to the discrete events under discussion."
 Ixuzmin et al., Kuzmin et al.
 do however suggest that the source of the variable component of the dispersion measure is within the Crab nebula. and that it again has a linear scale of around one astronomical unit.," do however suggest that the source of the variable component of the dispersion measure is within the Crab nebula, and that it again has a linear scale of around one astronomical unit."
 In all three events recorded with sullicient. resolution the delay is observed to decrease to. zero. ancl subsequentIv increase in a near parabolic form., In all three events recorded with sufficient resolution the delay is observed to decrease to zero and subsequently increase in a near parabolic form.
" ""This is interpreted as the two edges of a filament crossing the line of sight.", This is interpreted as the two edges of a filament crossing the line of sight.
 In the 1997 event there appears to be a relatively [lat profile of electron content across the cloud. but we may interpret the phenomenon generally as a filament with. diameter around 3⋅Lo1l m with: a total linc-of-sight'⋅⋪ electron content around 3107 m7.," In the 1997 event there appears to be a relatively flat profile of electron content across the cloud, but we may interpret the phenomenon generally as a filament with diameter around $3\times 10^{11}$ m with a total line-of-sight electron content around $3\times 10^{21}$ $^{-2}$."
" The electron density would then be of. order. 1027ᾗ 7. ""nLe. 107 em"," The electron density would then be of order $10^{10}$ $^{-3}$, i.e. $10^4$ $^{-3}$."
 Direct observation of such filaments by their emission or absorption is a rather remote possibility: milliaresecond: angular resolution would »o required. in contrast to the 100 milliaresecond resolution ol the LIST observations of filamentary structure in the outer vats of the nebula (Llester ct al1995).," Direct observation of such filaments by their emission or absorption is a rather remote possibility; milliarcsecond angular resolution would be required, in contrast to the 100 milliarcsecond resolution of the HST observations of filamentary structure in the outer parts of the nebula (Hester et al."
. ‘The rarity of these events suggests that the Crab Nebula is only sparsely filled with such filaments., The rarity of these events suggests that the Crab Nebula is only sparsely filled with such filaments.
 Lf a typical ilament takes several days to cross the line of sight. and he interval between such events is several vears. we can envisage a nebula containing only a few thousand such ilaments. spaced apart by some hundreds of their diameters and located. only in the outer regions.," If a typical filament takes several days to cross the line of sight, and the interval between such events is several years, we can envisage a nebula containing only a few thousand such filaments, spaced apart by some hundreds of their diameters and located only in the outer regions."
 The filaments bear no obvious relation to the well-known visible filaments. and do not contribute significantly to the overall mass of the Nebula.," The filaments bear no obvious relation to the well-known visible filaments, and do not contribute significantly to the overall mass of the Nebula."
 We thank the referee. for helpful suggestions on. the presentation of this paper., We thank the referee for helpful suggestions on the presentation of this paper.
-lau,-1cm
"and Bg are the azimuthal and radial magnetic fields, respectively.","and $B_R$ are the azimuthal and radial magnetic fields, respectively."
 A=90° and 270° correspond to the azimuthal unreconnected sectored heliosheath magnetic fields., $\lambda = 90^\circ$ and $270^\circ$ correspond to the azimuthal unreconnected sectored heliosheath magnetic fields.
 Deviation of A from 90° and 270° indicates some process is distorting the sectored field., Deviation of $\lambda$ from $90^\circ$ and $270^\circ$ indicates some process is distorting the sectored field.
" data show the distribution of A is peaked in the two azimuthal directions, A=90° and 270° (Opheretal. 2011)."," data show the distribution of $\lambda$ is peaked in the two azimuthal directions, $\lambda = 90^\circ$ and $270^\circ$ \citep{Opher11}."
". These peaks are significantly broader in the heliosheath than upstream, indicating that reconnection or another mechanism is disturbing the heliosheath field."," These peaks are significantly broader in the heliosheath than upstream, indicating that reconnection or another mechanism is disturbing the heliosheath field."
 The observed distribution of is consistent with that found in high-@ simulations(Opheretal.2011)., The observed distribution of $\lambda$ is consistent with that found in $\beta$ \citep{Opher11}.
". Since the islands are elongated, the magnetic fields tend to remain primarily in the azimuthal direction even well after the islands begin to interact with each other."," Since the islands are elongated, the magnetic fields tend to remain primarily in the azimuthal direction even well after the islands begin to interact with each other."
" Round islands, such as would be expected from an MHD model or a low f kinetic model, are not consistent with observations since they produce much broader A distributions."," Round islands, such as would be expected from an MHD model or a low $\beta$ kinetic model, are not consistent with observations since they produce much broader $\lambda$ distributions."
" Thus, MHD reconnection (Lazarian&Opher2009) in the heliosheath seems to be ruled out."," Thus, MHD reconnection \citep{Lazarian09} in the heliosheath seems to be ruled out."
" Shown in reflambdacompare is the distribution of A from the simulations at 6=0.2 refjzbeta((a)), and 6=4.8 refjzbeta((c)) at t= "," Shown in \\ref{lambdacompare} is the distribution of $\lambda$ from the simulations at $\beta=0.2$ \\ref{jzbeta}( (a)), and $\beta=4.8$ \\ref{jzbeta}( (c)) at $t=110 \Omega_{\text{ci}}^{-1}$."
"The high f simulation which has elongated islands 11005"".retains the two peaks at A=90? and A=270°.", The high $\beta$ simulation which has elongated islands retains the two peaks at $\lambda=90^\circ$ and $\lambda=270^\circ$.
" The long islands have a larger magnetic field in the azimuthal direction than the radial, resulting in peaks in the A distribution, but the shorter islands become round having a magnetic field with similar strength in both directions, resulting in a broad distribution in A."," The long islands have a larger magnetic field in the azimuthal direction than the radial, resulting in peaks in the $\lambda$ distribution, but the shorter islands become round having a magnetic field with similar strength in both directions, resulting in a broad distribution in $\lambda$."
 The loss of tension in a finite 8 plasma prevents the complete release of magnetic energy that would be expected in an MHD model., The loss of tension in a finite $\beta$ plasma prevents the complete release of magnetic energy that would be expected in an MHD model.
 A complete understanding of the 6 dependence of magnetic islands is essential in order to obtain reliable signatures that can be compared with data., A complete understanding of the $\beta$ dependence of magnetic islands is essential in order to obtain reliable signatures that can be compared with data.
 In this work there was no out-of-plane guide magnetic field., In this work there was no out-of-plane guide magnetic field.
" In the heliospheric current sheet, the magnetic field rotates from one direction to the other keeping a constant magnitude rather than passing through zero (Smith2001).."," In the heliospheric current sheet, the magnetic field rotates from one direction to the other keeping a constant magnitude rather than passing through zero \citep{Smith01}."
 A guide field would cause the center of the islands to have a much lower f since the magnetic field does not go to zero., A guide field would cause the center of the islands to have a much lower $\beta$ since the magnetic field does not go to zero.
" Because of this magnetic field, we would not expect the Weibel instability to develop."," Because of this magnetic field, we would not expect the Weibel instability to develop."
" In real systems there is frequently a guide field, so this would be worth further investigation."," In real systems there is frequently a guide field, so this would be worth further investigation."
" In astrophysical accretion disks, reconnection plays a role in determining the saturation of the magnetorotational instability (MRI) (Sanoetal.2004)."," In astrophysical accretion disks, reconnection plays a role in determining the saturation of the magnetorotational instability (MRI) \citep{Sano04}."
. The saturation of MRI is strongly dependent on the dissipation of the magnetic field due to reconnection., The saturation of MRI is strongly dependent on the dissipation of the magnetic field due to reconnection.
" For the high ϐ in accretion disks, suppression of the most strongly growing small islands may significantly impact the saturation of the MRI."," For the high $\beta$ in accretion disks, suppression of the most strongly growing small islands may significantly impact the saturation of the MRI."
" Since 58 is typically larger than 100 in these structures, the only surviving islands would be so long that it is likely that much of the magnetic free energy would not be dissipated."," Since $\beta$ is typically larger than $100$ in these structures, the only surviving islands would be so long that it is likely that much of the magnetic free energy would not be dissipated."
" Further, since the MRI requires magnetic tension, the absence of tension could limit the development of the instability."," Further, since the MRI requires magnetic tension, the absence of tension could limit the development of the instability."
" Sharmaetal.(2006) perform a simulation showing an enhancement of the growth of MRI due to anisotropies with P,>, which enhances the magnetic tension, caused by µ conservation as a magnetic field develops."," \cite{Sharma06} perform a simulation showing an enhancement of the growth of MRI due to anisotropies with $P_\perp >
P_\parallel$, which enhances the magnetic tension, caused by $\mu$ conservation as a magnetic field develops."
" They do not capture the physics of reconnection and Fermi acceleration in magnetic islands that would generate anisotropies with P,<Pj, which removes magnetic tension."," They do not capture the physics of reconnection and Fermi acceleration in magnetic islands that would generate anisotropies with $P_\perp < P_\parallel$, which removes magnetic tension."
" These two competing sources of anisotropy, both affect the tension and thus the growth of the MRI."," These two competing sources of anisotropy, both affect the tension and thus the growth of the MRI."
 The relative importance of these mechanisms needs to be explored., The relative importance of these mechanisms needs to be explored.
" Reconnection at high 5, although relatively rare in the terrestrial magnetosphere, is also found in the magnetosphere of Saturn (Mastersetal.2011)."," Reconnection at high $\beta$, although relatively rare in the terrestrial magnetosphere, is also found in the magnetosphere of Saturn \citep{Masters11}."
. Magnetic islands were discovered in a region where ( is larger than 10., Magnetic islands were discovered in a region where $\beta$ is larger than 10.
 The 6 dependence of the growth of finite-sized magnetic islands may lead to a better understanding of these findings., The $\beta$ dependence of the growth of finite-sized magnetic islands may lead to a better understanding of these findings.
" Since the development of elongated islands requires only moderate f, we expect to see the development of longer islands than expected in lower (6 systems such as the magnetosphere."," Since the development of elongated islands requires only moderate $\beta$, we expect to see the development of longer islands than expected in lower $\beta$ systems such as the magnetosphere."
" In contrast to Karimabadietal. (2005),, these longer islands can grow to a large enough size to play a role in magnetospheric dynamics."," In contrast to \cite{Karimabadi05}, these longer islands can grow to a large enough size to play a role in magnetospheric dynamics."
 Since the B of the magnetosphere is not exceptionally large it is unlikely that the persisting anisotropy is enough to keep the islands from eventually becoming round., Since the $\beta$ of the magnetosphere is not exceptionally large it is unlikely that the persisting anisotropy is enough to keep the islands from eventually becoming round.
 The computations were performed at the National Energy Research Scientific Computing Center., The computations were performed at the National Energy Research Scientific Computing Center.
" 1,1 Top"," 1,1 Top"
1.5. 3.7. 9.0 and 37mJv respectively. arising from quiescent dust. at. about SOOIN. or a power law with a = 3.,"1.5, 3.7, 9.0 and 37mJy respectively, arising from quiescent dust at about 800K or a power law with $\alpha$ = –3."
 llis deduction is consistent with the results found here. ic. that the fourth component has fy = 8 and £j = 34 mJy.," His deduction is consistent with the results found here, i.e. that the fourth component has $F_K$ = 8 and $F_L$ = 34 mJy."
 The present method gives no information as to ££; ancl fy as they are tacitly taken to be zero but. if the source is cust at SOOWK. we have seen that the fluxes at these wavelengths will be small.," The present method gives no information as to $F_J$ and $F_H$ as they are tacitly taken to be zero but, if the source is dust at 800K, we have seen that the fluxes at these wavelengths will be small."
 This object appears heavily obscurecl in. visible light. and its variable component is significantly redder than average., This object appears heavily obscured in visible light and its variable component is significantly redder than average.
 There is some evidence for a clelay between J and L of 200-E100 clavs., There is some evidence for a delay between $J$ and $L$ of $\pm$ 100 days.
 A laree visual range was found for this galaxy by Winkler et al (1992)., A large visual range was found for this galaxy by Winkler et al (1992).
 The archetype S2 galaxy 11068 has been. discussed in cletail by Glass (1995).," The archetype S2 galaxy, 1068 has been discussed in detail by Glass (1995)."
 The 47ff colour of its variable component is not well-determined. but the ffA and dyL colours are by far the reddest of the sample.," The $J-H$ colour of its variable component is not well-determined, but the $H-K$ and $K-L$ colours are by far the reddest of the sample."
 A detailed. discussion of the event around JL 2447000. as observed at many wavelengths from the x-ray. to the Lk. was given by Daribaud et al (1992).," A detailed discussion of the event around JD 2447000, as observed at many wavelengths from the x-ray to the IR, was given by Baribaud et al (1992)."
 X time lag of 2 + 1 months was found between the UV. and the LR., A time lag of 2 $\pm$ 1 months was found between the UV and the IR.
 This result was criticised bx Oknvanskij Horne (2001). who find that the delay is consistent with 0 and is less than 904.," This result was criticised by Oknyanskij Horne (2001), who find that the delay is consistent with 0 and is less than 20d."
 Lebofskv Rieke (SO) reported a decline in the A Dux of 1120 from levels of G471 mJv. that had. been observed in 1970.1972 by Penston et al (1974). to ~24 mJv in LOTS.," Lebofsky Rieke (1980) reported a decline in the $K$ flux of 120 from levels of 64–71 mJy, that had been observed in 1970–1972 by Penston et al (1974), to $\sim$ 24 mJy in 1978."
 This decline took at least three vears., This decline took at least three years.
 In the present work the (not cereddened) A Dux varied from 32 to 47 mv., In the present work the (not dereddened) $K$ flux varied from 32 to 47 mJy.
 Only three galaxies in the present sample have shown such large changes., Only three galaxies in the present sample have shown such large changes.
 However. the case for 1120 seems to be well corroborated and is almost certainly real.," However, the case for 120 seems to be well corroborated and is almost certainly real."
 Phe Penston et al and Lebolsky Ricke values are plotted. with the present data in Fig 6 as crosses., The Penston et al and Lebofsky Rieke values are plotted with the present data in Fig 6 as crosses.
 The fuses tend to lie quite close to the regression lines shown except at £L. where the Penston L values seem too bright.," The fluxes tend to lie quite close to the regression lines shown except at $L$, where the Penston $L$ values seem too bright."
 However. ie standard errors of his measurements were quite hig=," However, the standard errors of his measurements were quite high."
 Long-term D light curves of 1120 have been presented by Hagen-Thorn ct al (1997) and Clements οἱ al (1995) in which a decline over the vears L973 to 1978 is clearly seen.," Long-term $B$ light curves of 120 have been presented by Hagen-Thorn et al (1997) and Clements et al (1995), in which a decline over the years 1973 to 1978 is clearly seen."
 A cross-correlation analysis between J and £ shows that, A cross-correlation analysis between $J$ and $L$ shows that
Discrete objects are identified within the 1.5.ο) data cube as a closed surface such that all values are greater than or equal to a siugular threshold of auteuna temperature.,"Discrete objects are identified within the $T(l,b,v)$ data cube as a closed surface such that all values are greater than or equal to a singular threshold of antenna temperature."
 The three dimensional pixels (hereafter. voxels) are contiguous within the volume.," The three dimensional pixels (hereafter, voxels) are contiguous within the volume."
 For a given angular position. (7;.b;). a minium of 2 contiguous chauncls are required to exceed the threshold.," For a given angular position, $l_i,b_i$ ), a minimum of 2 contiguous channels are required to exceed the threshold."
 Iu practice. the program fuds a seed voxel above the threshold aud then recursively checks neigliboriug channels aud positions to build up au object.," In practice, the program finds a seed voxel above the threshold and then recursively checks neighboring channels and positions to build up an object."
 Once checked. the voxel is flagged so it would not be checked again.," Once checked, the voxel is flagged so it would not be checked again."
 A minium of 5 aneular pixels are required for an object to be included iu the final catalog., A minimum of 5 angular pixels are required for an object to be included in the final catalog.
 An object is comprised of N augular pixels with cach pixel i. contributing P; spectroscopic chamnels.," An object is comprised of N angular pixels with each pixel, i, contributing $P_i$ spectroscopic channels."
" A ceutroid position (/,..5... 0.) is calculated from the intensity weighted mcan position within the image. A kinematic distance. D. to the object is obtained by assuming a flat rotation curve where The associated zlealactocentric radius; R. aud scale height.o z. are To parameterize the internal motions within au object. we calculate the equivalent width from the composite spectrum of the object."," A centroid position $l_c,b_c,v_c$ ) is calculated from the intensity weighted mean position within the image, A kinematic distance, D, to the object is obtained by assuming a flat rotation curve where The associated galactocentric radius, R, and scale height, z, are To parameterize the internal motions within an object, we calculate the equivalent width from the composite spectrum of the object."
" where and D, aud P,,,, ave the minima aud maxima spectroscopic contributing channels over all the pixels.", where and $P_{min}$ and $P_{max}$ are the minimum and maximum spectroscopic contributing channels over all the pixels.
 Ac isan approximation to the full width half maxima line width of a centrally peaked spectrum., ${\delta}v$ is an approximation to the full width half maximum line width of a centrally peaked spectrum.
 It includes motions along the line of sight as measured by the width of individual line profiles and more macroscopic, It includes motions along the line of sight as measured by the width of individual line profiles and more macroscopic
Figure 5 for the weak field antisolar case shows an even more complex perturbation pattern.,Figure 5 for the weak field antisolar case shows an even more complex perturbation pattern.
" Here the flow again (frame b)) has a tendency to be geostrophic, with counterclockwise flow around the low fluid pressure and clockwise around the high."," Here the flow again (frame b)) has a tendency to be geostrophic, with counterclockwise flow around the low fluid pressure and clockwise around the high."
 This happens because the magnetic field is too weak to force the flow to do otherwise., This happens because the magnetic field is too weak to force the flow to do otherwise.
 Now the perturbation field peak vectors tend to coincide with the peaks in fluid pressure., Now the perturbation field peak vectors tend to coincide with the peaks in fluid pressure.
" At this low field, hydrodynamics is more dominant everywhere."," At this low field, hydrodynamics is more dominant everywhere."
 The energy for instability in this case is coming primarily from the differential rotation., The energy for instability in this case is coming primarily from the differential rotation.
" The tilt in the velocity vectors is such that flow toward the pole has a strong component (in the rotating frame) opposite to the direction of rotation, flow toward the equator, a component in the direction of rotation."," The tilt in the velocity vectors is such that flow toward the pole has a strong component (in the rotating frame) opposite to the direction of rotation, flow toward the equator, a component in the direction of rotation."
 These tilts imply a Reynolds, These tilts imply a Reynolds
 140.2.,$\pm$ 0.2.
 We therefore constrain the D baud magnitude to 22L8., We therefore constrain the B band magnitude to $\ga$ 24.8.
 We see no evidence for a background ealaxyv: the region ds relatively uncrowded. as it is ~ 1! from the M31. bulge. aud the detection μπιτ is D « 28.," We see no evidence for a background galaxy; the region is relatively uncrowded, as it is $\sim$ $'$ from the M31 bulge, and the detection limit is B $<$ 28."
 There is no evidence for a counterpart in the 2\LASS All Sky Catalog (Skrutskieetal.2006).. hence. J0012.3|1115 cannot be associated with a late type star iu our adaxy.," There is no evidence for a counterpart in the 2MASS All Sky Catalog \citep{skrutskie2006}, hence J0042.3+4115 cannot be associated with a late type star in our Galaxy."
 We conclude that it is located in MOI., We conclude that it is located in M31.
 The distance modulus for M31 —21.5. aud we can estimate Ap by using the empirical relations Ay ~ Ng/lss10 atom em 7? (Predehl&Schuutt 1995).. aud E(D-V) ~ Ay /3.," The distance modulus for M31 $\sim$ 24.5, and we can estimate $A_{\rm B}$ by using the empirical relations $A_{\rm V}$ $\sim$ $N_{\rm H}$ $\times 10^{21}$ atom cm $^{-2}$ \citep{predehl95}, and E(B-V) $\sim$ $A_{\rm V}$ /3."
 The colin density varied significauth: between observations. hence the variable compoucut was probably internalto the system.," The column density varied significantly between observations, hence the variable component was probably internalto the system."
 Since the donor is unlikely to suffer lis extra absorption. we assume ΑΙ = 1022 atom 2 (see below). aud Ap = 0.7.," Since the donor is unlikely to suffer this extra absorption, we assume $N_{\rm H}$ = $\times$ $^{21}$ atom $^{-2}$ (see below), and $A_{\rm B}$ = 0.7."
 Therefore My 2 OL , Therefore $M_{\rm B}$ $\ga$ $-$ 0.4.
The known counterparts of high mass Nav binaries (IINEXDs) in the SAIC have apparent V πιμις. -in the range 13 Say mds and BV iu the range 029 < D-V x 0.06 (sece.g.Coeetal.2005:Antoniou 2009).," The known counterparts of high mass X-ray binaries (HMXBs) in the SMC have apparent V magnitudes in the range 13 $\la$ $m_{\rm V}$ $\la$ 18, and $B-V$ in the range $-0.32$ $\le$ B-V $\le$ 0.06 \citep[see e.g.][]{coe05,antoniou09}."
". For a distance of ~60 kpc. this equates to 6 S Mp = 1. all brighter than our threshold of 3j 2 0.1,"," For a distance of $\sim$60 kpc, this equates to $-$ 6 $\la$ $M_{\rm B}$ $\la$ $-1$, all brighter than our threshold of $M_{\rm B}$ $\ga$ $-$ 0.4."
" The three kuown BIL UAINBs are Cyeuus X- LMC€ X-1 aud LAIC κο,"," The three known BH HMXBs are Cygnus X-1, LMC X-1 and LMC X-3."
 Cyveuus. NX-1 has a counterpart with AA = 6.5 (Walborn1972) and OV = 0.8 (Ililtuer1956)., Cygnus X-1 has a counterpart with $M_{\rm V}$ = $-$ 6.5 \citep{walborn72} and $-$ V = 0.8 \citep{hiltner56}.
. The counterpart to LMC X-1 has magnitude V = L1.60-0.02 and BV = O0.1740.08 (Oroszetal.2009): hence Mp  — L2 for a distance of 50 kpc., The counterpart to LMC X-1 has magnitude V = $\pm$ 0.02 and $-$ V = $\pm$ 0.08 \citep{orosz09}; hence $M_{\rm B}$ $\sim$ $-$ 4.2 for a distance of 50 kpc.
 LALC Νο has a D — LF couuterpar (seee.g.Drocksopp 2001).. and Ap ~ 1.5: this is — 8c brighter than the brightest star withiu the ellipse.," LMC X-3 has a B $\sim$ 17 counterpart \citep[see e.g.][]{brocksopp01}, and $M_{\rm B}$ $\sim$ $-$ 1.5; this is $\sim$ $\sigma$ brighter than the brightest star within the ellipse."
 JO012.3|15 is therefore most likely to be a low mass X-ray binary (LAINB)., J0042.3+4115 is therefore most likely to be a low mass X-ray binary (LMXB).
 We present the ~12 vear 0.310 keV huninositv liehteurve of J0012.3|L115 created from the SI ACIS observations in Fig. 2::, We present the $\sim$ 12 year 0.3–10 keV luminosity lightcurve of J0042.3+4115 created from the 84 ACIS observations in Fig. \ref{acislc};
" circles muuurk lumunositfios from freely-fitted bright spectra. while crosses represent faint spectra where we assume Ny = 1404107 atom cm 7, and D = LA."," circles mark luminosities from freely-fitted bright spectra, while crosses represent faint spectra where we assume $N_{\rm H}$ = $\times$ $^{21}$ atom cm $^{-2}$, and $\Gamma$ = 1.5."
 Uncertainties are quoted at a la level., Uncertainties are quoted at a $\sigma$ level.
" The lightcirve is extremely variable. with the luminosity viuviug over ~0.5 34107 ore i,"," The lightcurve is extremely variable, with the luminosity varying over $\sim$ $\times$ $^{38}$ erg $^{-1}$."
 We note that the spectral fits to all bright observations are cousistent with a constaut P. although Ny varied by a factor —5: the faint observatious may be up to iues brighter.," We note that the spectral fits to all bright observations are consistent with a constant $\Gamma$ , although $N_{\rm H}$ varied by a factor $\sim$ 5; the faint observations may be up to times brighter."
 RXJO0012.311115. appears to be persistently bright., J0042.3+4115 appears to be persistently bright.
 By contrast. most Calactic black hole LAINBS ave trausieut.," By contrast, most Galactic black hole LMXBS are transient."
 One exception is CRS 19151105: a 7 vear RNTE/ASM Lehtcurve of 1915|105 showed it to be persisteutlv bright (MeClintock&Remillard2006)., One exception is GRS 1915+105; a 7 year RXTE/ASM lightcurve of 1915+105 showed it to be persistently bright \citep{mr06}.
. Another possible exception is GRS 1758-258: it is thought to be a Galactic LAINB. but its true nature is not confirmed due to the lieh degree of absorption (scec.g.Munoz-Axjcillaetal.2010.audrefer-enceswitlin) We also examined the short term variability of JO0012.311115 during the long NAIENewton observation.," Another possible exception is GRS 1758-258; it is thought to be a Galactic LMXB, but its true nature is not confirmed due to the high degree of absorption \citep[see e.g.][ and references within]{munoz_arjonilla10}
 We also examined the short term variability of J0042.3+4115 during the long XMM-Newton observation."
 We prescut the 0.310 keV EPIC-pu intensity liehtewmve for J0012.3|£115. in Fig.o 3.," We present the 0.3–10 keV EPIC-pn intensity lightcurve for J0042.3+4115 in Fig. \ref{xmmlc},"
 along with the background lehtcurve ii erey for comparison., along with the background lightcurve in grey for comparison.
 The intensity varices bv a factor 2 (lo deviation) du «10 ks. hence the enüssion is dominated bv a single source.," The intensity varies by a factor 2 $\sigma$ deviation) in $<$ 10 ks, hence the emission is dominated by a single source."
 The probability of J0012.3]1115) consisting of anultiple bright variable sources is very low. especially since it is not associated with any elobular cluster.," The probability of J0042.3+4115 consisting of multiple bright variable sources is very low, especially since it is not associated with any globular cluster."
 The longest ACTS observation of JO012.3|1115 was ODSID1575. an ACIS-S observation with a ~ 10 ks exposure time: the net source spectra coutained 7690 photons.," The longest ACIS observation of J0042.3+4115 was OBSID1575, an ACIS-S observation with a $\sim$ 40 ks exposure time; the net source spectrum contained 7690 photons."
 An on-axis source with lis intensity would be iu danger of pile-up: rowever. J0012.3|1115 was ~ 1 off-axis. aud he photons were spread over a large number of jxel« (2100).," An on-axis source with this intensity would be in danger of pile-up; however, J0042.3+4115 was $\sim$ $'$ off-axis, and the photons were spread over a large number of pixels $>$ 100)."
" Each incoming photon is assessed wits impact on a 3x3 array of ACIS pixels ""good"" photons are detected in only 2 of the 9 jxels. while cosmic ravs etc."," Each incoming photon is assessed by its impact on a 3x3 array of ACIS pixels ; “good” photons are detected in only 2 of the 9 pixels, while cosmic rays etc."
 are detected mi 23 or nore (Davis 2001).., are detected in 3 or more \citep{davis01}. .
 We therefore estinated the xobabilitv of pile up from the brightest pair of nels: this pair accunulated NOT photons over ~38 ks. or oue photon every —11 frames.," We therefore estimated the probability of pile up from the brightest pair of pixels; this pair accumulated 807 photons over $\sim$ 38 ks, or one photon every $\sim$ 14 frames."
 Hence. we conclude that pile up is uulikelvy to have Όσοι sienificaut.," Hence, we conclude that pile up is unlikely to have been significant."
 The 0.37.0 keV. spectrum of JO0012.3|1115 diving observation OBSID1575 is welldescribed, The 0.3–7.0 keV spectrum of J0042.3+4115 during observation OBSID1575 is welldescribed
contamination from gas such as C5 at 5141.,contamination from gas such as $C_{2}$ at 5141.
A... We therefore only ealeulate the dust production in J band., We therefore only calculate the dust production in $I$ band.
 The 7 band radial profile of C/2007 N3 (Lulin) is shown in Fig. 10.., The $I$ band radial profile of C/2007 N3 (Lulin) is shown in Fig. \ref{fig:iradial_prof}.
 To estimate the rate of dust production in comet C/2007 N23 (Lulin). we utilize the Afp quantity introduced by ÀHearn(1984).," To estimate the rate of dust production in comet C/2007 N3 (Lulin), we utilize the $Af\rho$ quantity introduced by \citet{Ahearn84}."
".. This quantity serves as a proxy for dust production and when the cometary coma is in steady state. the value for AAfp is an aperture independent parameter. where 1 is the Bond Albedo. f is the filling factor of the coma. m... is the apparent solar magnitude. Meamc Is the measured cometary magnitude. p is the linear radius of the aperture at the comet's position (cm) and rj, and A are the heliocentric and geocentric distances measured in AU and em. respectively."," This quantity serves as a proxy for dust production and when the cometary coma is in steady state, the value for $Af \rho$ is an aperture independent parameter, where $A$ is the Bond Albedo, $f$ is the filling factor of the coma, $m_{\odot}$ is the apparent solar magnitude, $m_{comet}$ is the measured cometary magnitude, $\rho$ is the linear radius of the aperture at the comet's position (cm) and $r_{h}$ and $\Delta$ are the heliocentric and geocentric distances measured in AU and cm, respectively."
" Cometary magnitudes are observed to follow similar phase angle effects as asteroids: (herelore we also apply the phase angle correction OF ρα.=O)=mo,(A)-Ca where a is the phase angle in degrees and C is correction factor of 0.03 magnitudes per degree. (he mean of the correction factors derived by Meechetal.(1987)."," Cometary magnitudes are observed to follow similar phase angle effects as asteroids; therefore we also apply the phase angle correction of $m_{comet}(\alpha \; = 0) \; = m_{comet} \; (\alpha) - C \alpha$ where $\alpha$ is the phase angle in degrees and C is correction factor of 0.03 magnitudes per degree, the mean of the correction factors derived by \citet{Meech87}."
. Figure LL illustrates the progression of Af as a funcion of p aaxd Table 2. reports values of Afp al a selection of distances from the comet photocenter.," Figure \ref{fig:afrhoIband} illustrates the progression of $Af \rho$ as a function of $\rho$ and Table \ref{tab:afr_tab}
 reports values of $Af \rho$ at a selection of distances from the comet photocenter."
 Comet C/2007 N23 (Lulin) was sufficiently distant at the epoch of our observations that we did not have the spatial resolution to map changes in polarization across the coma., Comet C/2007 N3 (Lulin) was sufficiently distant at the epoch of our observations that we did not have the spatial resolution to map changes in polarization across the coma.
 Thus it is unknown whether or not there was any significant variation in polarization with coma morphology., Thus it is unknown whether or not there was any significant variation in polarization with coma morphology.
 Comet C/1995 O1 (IIale-Dopp). for example. had a high surface brightness jet that showed distinctly greater Iractional polarization in the NIB. than the," Comet C/1995 O1 (Hale-Bopp), for example, had a high surface brightness jet that showed distinctly greater fractional polarization in the NIR than the"
should be interpreted as follows.,should be interpreted as follows.
 if FAP > 107. tf 1077« FAPx 10? and if FAP« 107.," if FAP $\,>\,$ $^{-3}$ , if $^{-3}\le\,$ $\le\,$ $^{-5}$ and if $\,<\,$ $^{-5}$."
 The smallest FAP obtained for HgMn star is 0.08., The smallest FAP obtained for HgMn star is 0.08.
 Thus. none of the measurements indicate the presence of a magnetic signal.," Thus, none of the measurements indicate the presence of a magnetic signal."
 A visual examination of each LSD Stokes V profile also do not suggest a magnetic field detection., A visual examination of each LSD Stokes $V$ profile also do not suggest a magnetic field detection.
 To make sure that the LSD circular polarization. profiles were not affected by a spurious polarization. we analysed LSD null spectra at each phase.," To make sure that the LSD circular polarization profiles were not affected by a spurious polarization, we analysed LSD null spectra at each phase."
 The aand FAP measurements were done in the same way as for LSD Stokes V profiles., The and FAP measurements were done in the same way as for LSD Stokes $V$ profiles.
 The eerrors for the null spectra are fully consistent with those inferred from the circular polarization profiles., The errors for the null spectra are fully consistent with those inferred from the circular polarization profiles.
 The absence of signal in the null spectrum means that our scientific data is not visibly affected by significant spurious polarization., The absence of signal in the null spectrum means that our scientific data is not visibly affected by significant spurious polarization.
" Due to the orbital motion. the relative shift of the spectral lines of the components in the composite spectrum varies from zero to «200Εν, which can be seen from the LSD / profiles in Fig. |.."," Due to the orbital motion, the relative shift of the spectral lines of the components in the composite spectrum varies from zero to $\sim$ 200, which can be seen from the LSD $I$ profiles in Fig. \ref{LSD}."
 In addition to this. the primary component shows an intrinsic line profile variability.," In addition to this, the primary component shows an intrinsic line profile variability."
 Since one of the main aims of this study ts to investigate line profile variability in 66 Ert. it is Important to separate the effect of the spectral line blending due to the orbital motion from an intrinsic variability.," Since one of the main aims of this study is to investigate line profile variability in 66 Eri, it is important to separate the effect of the spectral line blending due to the orbital motion from an intrinsic variability."
 To separate different variability effects. we employ the procedure of spectral disentangling described by ?., To separate different variability effects we employ the procedure of spectral disentangling described by \citet{Folsom:2010}.
 It combines information from all orbital phases and vields radial velocities (RV) for both components. their average separated spectra and standard deviation in the reference frame of each component.," It combines information from all orbital phases and yields radial velocities (RV) for both components, their average separated spectra and standard deviation in the reference frame of each component."
 Fig., Fig.
 3 shows an example of spectral disentangling in the region 4355-4380 econtaining several variable lines., \ref{sdplot} shows an example of spectral disentangling in the region 4355–4380 containing several variable lines.
 The spectral disentangling procedure provided a new set of high-precision RV measurements for both components of 66 Eri., The spectral disentangling procedure provided a new set of high-precision RV measurements for both components of 66 Eri.
 These data. presented in Table 2.. have typical error bars of 0.1-0.2kms7!.," These data, presented in Table \ref{tab2}, have typical error bars of 0.1–0.2."
. We combined our RVs with the velocities published by ?.. ??.. and ?.. deriving improved orbital parameters of the system.," We combined our RVs with the velocities published by \citet{Young:1976}, \citet{Yuschenko:1999, Yuschenko:2001}, and \citet{Catanzaro:2004}, deriving improved orbital parameters of the system."
 The new orbital elements are listed in Table 3..3.. while Fig.," The new orbital elements are listed in Table \ref{tab3}, while Fig."
 4. compares the respective predicted RV curves with the actual measurements., \ref{orvs} compares the respective predicted RV curves with the actual measurements.
 The standard deviation ofthe orbital fit is 2.5 ffor the primary and 2.8 ffor the secondary., The standard deviation ofthe orbital fit is 2.5 for the primary and 2.8 for the secondary.
 Compared to the previous orbital analysis by ?.. we significantly improved the accuracy of the orbitalperiod and of the velocity amplitudes. obtaining a mass ratio with the precision better than 1%..," Compared to the previous orbital analysis by \citet{Catanzaro:2004}, we significantly improved the accuracy of the orbitalperiod and of the velocity amplitudes, obtaining a mass ratio with the precision better than ."
spectrograph (Gillet et al. 1994)).,spectrograph (Gillet et al. \cite{Gill94}) ).
 Light passing through aoa circular entrance aperture then encounters a modified Bowen-Walraven image slicer (Walraven. 1972)). whose 5 slices of 076 each are imaged onto a 2048x1024 EEV CCD with 13.5 pm pixels.," Light passing through a 3"" circular entrance aperture then encounters a modified Bowen-Walraven image slicer (Walraven \cite{Walr72}) ), whose 5 slices of 0""6 each are imaged onto a 2048x1024 EEV CCD with 13.5 $\mu$ m pixels."
 To gain in sensitivity. all the corresponding lines of the CCD were summed before read-out. producing a single line spectrum as output.," To gain in sensitivity, all the corresponding lines of the CCD were summed before read-out, producing a single line spectrum as output."
 However as a consequence. the possibility of identifying and cleaning cosmic rays hits before final reduction disappears.," However as a consequence, the possibility of identifying and cleaning cosmic rays hits before final reduction disappears."
 The spectra were reduced following standard procedures: bias and flat-field corrections. and wavelength calibration using a thorium-argon internal lamp.," The spectra were reduced following standard procedures: bias and flat-field corrections, and wavelength calibration using a thorium-argon internal lamp."
 In view of the small spectral range covered and used. no spectral response correction was performed.," In view of the small spectral range covered and used, no spectral response correction was performed."
 Many of the observations (but not all) were done in service mode. and used a 1200 I/mm grating giving a dispersion of 7.6À per mm. and a spectral resolution of 0.32 A (0.10 per pixel).," Many of the observations (but not all) were done in service mode, and used a 1200 l/mm grating giving a dispersion of $\AA$ per mm, and a spectral resolution of 0.32 $\AA$ (0.10 per pixel)."
" Typical individual exposure times are 30. minutes. but the sequencing of observations. and phase coverage is irregular. a tribute to be payed to the service mode operation,"," Typical individual exposure times are 30 minutes, but the sequencing of observations, and phase coverage is irregular, a tribute to be payed to the service mode operation."
 The details of observations are given in Table 2.., The details of observations are given in Table \ref{ObsSpec}.
 An exemple of a high-resolution spectrum ts given in Fig. 3.., An exemple of a high-resolution spectrum is given in Fig. \ref{high}.
 A few. low dispersion spectra were obtained towards the end of the campaign. to check the general aspect of the object.," A few, low dispersion spectra were obtained towards the end of the campaign, to check the general aspect of the object."
 We used the OHP 1.93m telescope in December 2007. with the Carelec spectrograph and a 300 I/mm grating giving 1.8 A per pixel and a 6.5 A resolution with the 2” slit used.," We used the OHP 1.93m telescope in December 2007, with the Carelec spectrograph and a 300 l/mm grating giving 1.8 $\AA$ per pixel and a 6.5 $\AA$ resolution with the 2"" slit used."
 The same setting was used again in December 2008., The same setting was used again in December 2008.
 In June 2008. we used the IDS at the INT 2.5m telescope in La Palma: there. a 630 I/mm grating gave 0.9 A per pixel and 2.7 A resolution with a 175 slit.," In June 2008, we used the IDS at the INT 2.5m telescope in La Palma: there, a 630 l/mm grating gave 0.9 $\AA$ per pixel and 2.7 $\AA$ resolution with a 1""5 slit."
 Those spectra were reduced with standard procedures. including the use of standard star observations to correct for the wavelength dependant spectral response.," Those spectra were reduced with standard procedures, including the use of standard star observations to correct for the wavelength dependant spectral response."
 In the case of the INT however. only the central part of the spectrum can be exploited due to strong vignetting.," In the case of the INT however, only the central part of the spectrum can be exploited due to strong vignetting."
 Summation has been made over the full He extent along the slit and the spectra are displayed in Fig. 4.., Summation has been made over the full $\alpha$ extent along the slit and the spectra are displayed in Fig. \ref{low}.
" As can be seen from Fig. 2.,"," As can be seen from Fig. \ref{CCD},"
 daily light curves of HR Del show night to night variations and also aperiodic stochastic variations. that is so called flickering.," daily light curves of HR Del show night to night variations and also aperiodic stochastic variations, that is so called flickering."
 The CCD data. because they contain long time series of observations at similar epochs. were used to search," The CCD data, because they contain long time series of observations at similar epochs, were used to search"
wide wavelength range is made possible by the use of an atmospheric dispersion compensator (ADC) within the 24) instrument.,wide wavelength range is made possible by the use of an atmospheric dispersion compensator (ADC) within the 2dF instrument.
 Lach spectrum. is visually assigned. a redshift quality Dag Q which ranges from Q=1 (unreliable) to Q—5 (highest quality)., Each spectrum is visually assigned a redshift quality flag $Q$ which ranges from $Q=1$ (unreliable) to $Q=5$ (highest quality).
" The spectra are not Dux calibrated and thus consist of a sequence of ""counts! as a function of wavelength.", The spectra are not flux calibrated and thus consist of a sequence of `counts' as a function of wavelength.
 The ας is described in detail in Colless et ((2001. 2003) and the database may be accessed online al//msowww.," The 2dFGRS is described in detail in Colless et (2001, 2003) and the database may be accessed online at."
anu.edu.au/2dFGRS/. Our sample selection is based. on the 2dEGIUS spectral line catalogue. prepared. by lan Lewis., Our sample selection is based on the 2dFGRS spectral line catalogue prepared by Ian Lewis.
 In. this Section we briefly summarize the generation. of the spectral line catalogue: for Lull details see Lewis ct ((2002)., In this Section we briefly summarize the generation of the spectral line catalogue; for full details see Lewis et (2002).
. After removal of the continuum by subtracting the median over windows of width 133.X. Lewis et {fitted up to twenty absorption or emission lines. corresponding to standard galaxy spectral features.," After removal of the continuum by subtracting the median over windows of width $133 \ang$, Lewis et fitted up to twenty absorption or emission lines, corresponding to standard galaxy spectral features."
 The line profiles were assumed to be Gaussian. parameterized. by an amplitude and width.," The line profiles were assumed to be Gaussian, parameterized by an amplitude and width."
 The wavelength. spacings of the line centres were fixed at their known laboratory values. with a variable overall offset to accommodate redshifting.," The wavelength spacings of the line centres were fixed at their known laboratory values, with a variable overall offset to accommodate redshifting."
 Ehe quality of cach line fit was Classified by a Uae determined. by the rms. residuals. ranging from ϐ (bad fit) to 5 (good fit). and a signal-to- parameter was computed for each line (relative to the continuum).," The quality of each line fit was classified by a flag determined by the rms residuals, ranging from 0 (bad fit) to 5 (good fit), and a signal-to-noise parameter was computed for each line (relative to the continuum)."
 Where possible. equivalent. widths were then deduced: using the fitted. line flux. ancl the value. of.the continuum [lux in the local 133.X window.," Where possible, equivalent widths were then deduced using the fitted line flux and the value ofthe continuum flux in the local $133 \ang$ window."
 This does. not require absolute [ux calibration of the spectra. although we must assume that there is no significant acelitive error in the continuum due to elfects such as scattered. light.," This does not require absolute flux calibration of the spectra, although we must assume that there is no significant additive error in the continuum due to effects such as scattered light."
 We corrected. all equivalent: widths for cosmological ellects by dividing by a factor (1|2). where z is the galaxy reclshilt.," We corrected all equivalent widths for cosmological effects by dividing by a factor $(1+z)$, where $z$ is the galaxy redshift."
 Galaxies exhibit a continuum of properties. and. thus the choice of selection criteria. for a specific sub-class is somewhat arbitrary., Galaxies exhibit a continuum of properties and thus the choice of selection criteria for a specific sub-class is somewhat arbitrary.
 Zablucloll ct ((1996) performed the first. environmentallv-unbiased: selection of I2]X. galaxies. obtained from the Las Campanas Redshift Survey (LCTUS).," Zabludoff et (1996) performed the first environmentally-unbiased selection of E+A galaxies, obtained from the Las Campanas Redshift Survey (LCRS)."
 Their sample was defined by requiring the equivalent width of Ol] 3727 emission to be less than 2.5X. and the average of the Aequivalent widths of the Balmer lines. 119. I5 and LL3 to exceed 5.5A in absorption.," Their sample was defined by requiring the equivalent width of [OII] $3727 \ang$ emission to be less than $2.5 \ang$, and the average of the equivalent widths of the Balmer lines $\delta$, $\gamma$ and $\beta$ to exceed $5.5 \ang$ in absorption."
 These criteria are strict. selecting an extreme class of objects corresponding to 2 per cent. (21711113) of LORS galaxies.," These criteria are strict, selecting an extreme class of objects corresponding to 0.2 per cent (21/11113) of LCRS galaxies."
 Zablucloll et oonlv considered spectra possessing à signal-to-noise ratio exceeding S0 in the continua about the L9. Le and. 117 ines.," Zabludoff et only considered spectra possessing a signal-to-noise ratio exceeding $8.0$ in the continua about the $\delta$, $\gamma$ and $\beta$ lines."
 We based our I2]A galaxy. sample selection criteria on hose of Zabludolf. et.al... but with several adjustments.," We based our E+A galaxy sample selection criteria on those of Zabludoff et, but with several adjustments."
 Firstly. the 2dPGBS line [fits catalogue. (Section 2.2)) xwameterizes the quality of the fit to each spectral line using a dillerent method to that of Zablucdolletale: thus we cannot employ. an identical selection criterion as regards signal- ratio.," Firstly, the 2dFGRS line fits catalogue (Section \ref{seclinefit}) ) parameterizes the quality of the fit to each spectral line using a different method to that of Zabludoff et; thus we cannot employ an identical selection criterion as regards signal-to-noise ratio."
 In our analysis we considered. an equivalent width measurement to be reliable if the signal-to-noise xwameter of the line exceeded 1.0 and the flag parameter of the line was equal to 4 or 5 (these tags are classified as a eood' fit)., In our analysis we considered an equivalent width measurement to be reliable if the signal-to-noise parameter of the line exceeded $1.0$ and the flag parameter of the line was equal to 4 or 5 (these flags are classified as a `good' fit).
 Note that a ‘signal-to-noise parameter equal to 1.0 is in fact a high-quality detection: this parameter is defined as the mean signal-to-noise ratio of the resolution elements of the line. averaged over three lincwidths.," Note that a `signal-to-noise parameter' equal to $1.0$ is in fact a high-quality detection: this parameter is defined as the mean signal-to-noise ratio of the resolution elements of the line, averaged over three line-widths."
 The choice of a minimum value of 1.0 is fairly arbitrary. but serves to select an extreme class of galaxies as required.," The choice of a minimum value of $1.0$ is fairly arbitrary, but serves to select an extreme class of galaxies as required."
 Furthermore. rather than using the average of Balmer equivalent widths. we introduced a weighting scheme.," Furthermore, rather than using the average of Balmer equivalent widths, we introduced a weighting scheme."
 The relative equivalent: widths of the Balmer absorption lines (11051) in a given galaxy spectrum. are determined: partly » fundamental atomic physics anc are hence expected o displav some level of correlation., The relative equivalent widths of the Balmer absorption lines $\delta\gamma\beta$ ) in a given galaxy spectrum are determined partly by fundamental atomic physics and are hence expected to display some level of correlation.
 We fitted: empirical inear relations to the distributions of (LI 118) and (LI3.119) equivalent widths for objects with reliable measurements of hese lines in absorption (see for more details of our fitting procedure)., We fitted empirical linear relations to the distributions of $\gamma$ $\delta$ ) and $\beta$ $\delta$ ) equivalent widths for objects with reliable measurements of these lines in absorption (see \\ref{fighghd} for more details of our fitting procedure).
 We hereby derived empirical best-fitting correlations: where all equivalent widths are measured in X in absorption., We thereby derived empirical best-fitting correlations: where all equivalent widths are measured in $\ang$ in absorption.
" We used these linear fitting formulae to convert 11:3 ancl Le equivalent widths to ""effective 119 values.", We used these linear fitting formulae to convert $\beta$ and $\gamma$ equivalent widths to `effective' $\delta$ values.
 For each spectrum we averaged these values for the Ld-3 absorption lines., For each spectrum we averaged these values for the $\delta\gamma\beta$ absorption lines.
 reffiehehd: displays the scatter plot for the case of (LI 119)., \\ref{fighghd} displays the scatter plot for the case of $\gamma$ $\delta$ ).
 We selected catalogues of LE|A galaxies using two different methods: this allowed: us to ascertain the effects of the selection. criteria on the properties of the sample., We selected catalogues of E+A galaxies using two different methods; this allowed us to ascertain the effects of the selection criteria on the properties of the sample.
" The first selection method was based on the average of the weighted Balmer ""effective L9 equivalent. widths described above. the value of which was required to exceed 5.5X in absorption."," The first selection method was based on the average of the weighted Balmer `effective $\delta$ ' equivalent widths described above, the value of which was required to exceed $5.5
\ang$ in absorption."
 The second selection was based solely on the 119 equivalent width. which was required to exceed 5.5A.," The second selection was based solely on the $\delta$ equivalent width, which was required to exceed $5.5 \ang$ ."
 We emphasize again that as there is no sign of bimodality in the sample. the choice of the value 5.5A is fairly arbitrary.," We emphasize again that as there is no sign of bimodality in the sample, the choice of the value $5.5 \ang$ is fairly arbitrary."
 ΑΗ IE|A objects were required to have no detection of OL] 3727X emission., All E+A objects were required to have no detection of [OII] $3727 \ang$ emission.
 Non-detection was defined: either by an, Non-detection was defined either by an
LMC in RA aud Dec) as [ree parameters. we can obtain the tilt ancl the angle of the line of nodes if he Cepheids ou average lie in a plane.,"LMC in RA and Dec) as free parameters, we can obtain the tilt and the angle of the line of nodes if the Cepheids on average lie in a plane."
 The top left aud bottom right plots show the distribution of he points when viewed from orthogoual directious in the plane of the sky., The top left and bottom right plots show the distribution of the points when viewed from orthogonal directions in the plane of the sky.
 Empty circles represent he Cepheids that are brighter than the average (Le. they lie above the mean PL relation). and illed circles show those that are fainter (μαι the average (below the meau PL relation).," Empty circles represent the Cepheids that are brighter than the average (i.e. they lie above the mean PL relation), and filled circles show those that are fainter than the average (below the mean PL relation)."
 In this igure the reference coordinate system las been rotated by 50° so that the line of nodes of the LMC is parallel with the w-anis., In this figure the reference coordinate system has been rotated by $^{\circ}$ so that the line of nodes of the LMC is parallel with the $x$ –axis.
 In this plot. it is clear that the Cepheics in the bottom half tend to ye fainter than the PL. hence further away. while those in the top half teud to be systematically wiehter. hence closer than average.," In this plot, it is clear that the Cepheids in the bottom half tend to be fainter than the PL, hence further away, while those in the top half tend to be systematically brighter, hence closer than average."
 The simplest interpretation is tha re LAC is in fact tilted with respect to the plane of the sky., The simplest interpretation is that the LMC is in fact tilted with respect to the plane of the sky.
 By tilting the LMC by 28° relative to the plane of the sky we cau miuimize the width of the histogram in the top right corner of Fig. 6.., By tilting the LMC by $28^{\circ}$ relative to the plane of the sky we can minimize the width of the histogram in the top right corner of Fig. \ref{fig:tilt_plot}.
 This is in good agreement with the results of POL. aud will be the subject of a more complete discussion of the data at a later time.," This is in good agreement with the results of P04, and will be the subject of a more complete discussion of the data at a later time."
 We believe that the variations in the [3.6]—[1.5] color. both at mean light and throughout the pulsation cycle. are due to CO absorption in the 1.5 pam baud.," We believe that the variations in the $[3.6]-[4.5]$ color, both at mean light and throughout the pulsation cycle, are due to CO absorption in the 4.5 $\mu$ m band."
 We do not see any evidence of extended euission surrounding the Cepleicds in our images., We do not see any evidence of extended emission surrounding the Cepheids in our images.
 This is cousisteut with the results of Marengoetal.(2010a.b) aud Barmbyetal.(2011) who found evideuce for circuumstellar emissiou in the longer wavelength IRAC bands. but nothing at 3.6 or L5 yan. Marengoetal.(2010a) notes that the [3.6]2[1.5] color of the Cepheids is incdistinguishable from their non-variable control stars. auc is therefore caused by au iutriusic feature of stars of this spectral type. regardless of whether or not they are Cepheids.," This is consistent with the results of \citet{2010ApJ...709..120M, 2010ApJ...725.2392M} and \citet{2011AJ....141...42B} who found evidence for circumstellar emission in the longer wavelength IRAC bands, but nothing at 3.6 or 4.5 $\mu$ m. \citet{2010ApJ...709..120M} notes that the $[3.6]-[4.5]$ color of the Cepheids is indistinguishable from their non–variable control stars, and is therefore caused by an intrinsic feature of stars of this spectral type, regardless of whether or not they are Cepheids."
 This rules out circumstellar envelopes aud mass-loss as the source of the feature. leaving only the CO baudheact.," This rules out circumstellar envelopes and mass–loss as the source of the feature, leaving only the CO bandhead."
 The possibility of a period-color (PC) relationship at mid-infrared) wavelengths was correctly noted by Marengoetal.(2010a)., The possibility of a period–color (PC) relationship at mid–infrared wavelengths was correctly noted by \citet{2010ApJ...709..120M}.
. However. their inagnuitudes (aud therefore colors) were measured at only a sinele epoch. introducing large scatter into the PC relatiou. as is shown iu their figure 5.," However, their magnitudes (and therefore colors) were measured at only a single epoch, introducing large scatter into the PC relation, as is shown in their figure 5."
 Figure 7 shows the relationship between period and [3.6]—[1.5] color for our sample., Figure \ref{fig:pc_relation} shows the relationship between period and $[3.6]-[4.5]$ color for our sample.
 The period-color relation was fit using Cepheids with 1€logP?1.5. aud is fouud to be The LMC Cepheids clearly exhibit a period-color relation in this period range.," The period–color relation was fit using Cepheids with $1 \leq \log P \leq 1.8$, and is found to be The LMC Cepheids clearly exhibit a period–color relation in this period range."
 The staudu deviation around the relation is 0.018 mag., The standard deviation around the relation is $\pm 0.018$ mag.
 The relation appears to invert for tle longest—period (logP?> 2) Cepheids., The relation appears to invert for the longest—period $\log P > 2$ ) Cepheids.
 Iguoriug the logP?>2 sample. the loug period Cepheids are brighter aud," Ignoring the $\log P > 2$ sample, the long period Cepheids are brighter and"
"""Phe Fornax. chvarl⋅ spheroidal. is. a dark matter dominated. satellite orbiting the Milky Way.",The Fornax dwarf spheroidal is a dark matter dominated satellite orbiting the Milky Way.
 Lt has five globular clusεξ£ hat are at a projected. distance. from. the centre of ⋅⋅1.60. 1.05. )43. 0.24 and kkpe as well as further substructure at à projected distance of κκρο 2005).," It has five globular clusters that are at a projected distance from the centre of 1.60, 1.05, 0.43, 0.24 and kpc as well as further substructure at a projected distance of kpc ."
. EThese star clusters move withinDi. a dense background. of dark matter and. should therefore⋅ ⋡⋖⋅⋜↧↓∎⋯∙↿⋯⇂⋡∙∖⇁∠⇂∙∖⇁↓↥⋜↧↓↕↓↕≼⇍⋜↧⇂⇂⋅↓⋅↕≼⇍⇂↕∢⋟↓↥⊳≼⇍⋜⋯⊳∖⊲↓⊔⋏∙≟↥↓↥⋖⋅⊔↓⋯⇜∢⋅ energy and spiral to the centre of the galaxy.," These star clusters move within a dense background of dark matter and should therefore be affected by dynamical friction, causing them to lose energy and spiral to the centre of the galaxy."
 We will show ater that. if eqsFornax has a cosmologically. consistent. density. distribution∢∢⊀ of dark matter. the orbital. cecay timescale. of hese objects from their current positions is ͵Z; GCwr.," We will show later that, if Fornax has a cosmologically consistent density distribution of dark matter, the orbital decay timescale of these objects from their current positions is $\lsim$ Gyr."
 This is. much shorter than the age of. the host galaxy. presenting. us with. the puzzle of⋅ why these five⋅ elobulars have not merged ogether at the centre forming a single nucleus1976).," This is much shorter than the age of the host galaxy, presenting us with the puzzle of why these five globulars have not merged together at the centre forming a single nucleus."
. Several. groups have studied. the originu of nuclei 2.in galaxies: e.g. Lotz ct ((2001) carried. out Monte. Carlo simulations. which show that some. but not all. of the nuclei ob dwarf elliptical galaxies could indeed have formed through coalescence of their.. e@lobular clusters.," Several groups have studied the origin of nuclei in galaxies: e.g. Lotz et (2001) carried out Monte Carlo simulations, which show that some, but not all, of the nuclei of dwarf elliptical galaxies could indeed have formed through coalescence of their globular clusters."
 Aclditionallyu they observed several dl galaxies and found out that within the inner few scale lengths. their sample appeared to be depleted of ⋅⋠bright clusters.," Additionally they observed several dE galaxies and found out that within the inner few scale lengths, their sample appeared to be depleted of bright clusters."
 Ob anc ⋠∙((2000). used. numerical. . ⊳∖↓⊔↓⊔↓⋜∐↓∪⊔⊳∖⋯⊳∖↓↕∪∖∖⋎⇂↓⋯⇂↓↓⊔⇂∖∖⊽⋜⊔⋅⇂⋏∙≟⋜↧↓⋜∟∖⊓⊾⊳∖∖∖⋎↓↿↓↥↓⋅∢⋅↓⋜⊔↓∖⇁∢⋅↓∙∖⇁ . . : . . weak external tidal perturbations. dvnamical friction. can ead to significant orbital decay of globular clusters and the ormation of compact nuclei within a Hubble timescale.," Oh and (2000) used numerical simulations to show that in dwarf galaxies with relatively weak external tidal perturbations, dynamical friction can lead to significant orbital decay of globular clusters and the formation of compact nuclei within a Hubble timescale."
 Oh. Lin. and lücher((2000) gave two possible. models . ∪↓⋅↿⇂↥⋖⋅∪∣⋡≱∖⋖⋅↓⋅∖⇁⋖⋅∠⇂⊳∖↓≻⋜⊔⋯↓∠↓⊳∖↿↓⋅↓∣⋡⋯↓∪⊔∪⇂↓⊲∪↓⋅⊔⋜∟∖⋏∙≟↓∪∣⋡⊔↓⋜⊔⋅≱∖⋡.," Oh, Lin and (2000) gave two possible models for the observed spatial distribution of Fornax globulars."
 ... ⋅∖ One possibilityvn they proposed. is. that. the clark matter consists. of massive. black holes which. transfer. energy. to he elobulars. preventing them from sinking to the centre of⋅ the galaxy.," One possibility they proposed is that the dark matter consists of massive black holes which transfer energy to the globulars, preventing them from sinking to the centre of the galaxy."
 Another possibilityaun they investigated. was to »xostulate a strong tidal interaction between the Milky Way and Fornax. which. also could injectuu energy. into. their. orbits. and the central core of. the dSph., Another possibility they investigated was to postulate a strong tidal interaction between the Milky Way and Fornax which also could inject energy into their orbits and the central core of the dSph.
 ...This latter idea: is. probably ruled out due to the proper motion observations of Fornax which. suggest it 24is already. at. closest approach on an extended orbit which never takes it close to the Milky Was., This latter idea is probably ruled out due to the proper motion observations of Fornax which suggest it is already at closest approach on an extended orbit which never takes it close to the Milky Way.
 Llere we investigate another possibility. for the lack of. a nucleus in. Fornax.. namely that the central dark matter distribution⋠⊀. has a. very shallow cusp or core which dramatically increases the dynamical friction sinking timescale1998)..," Here we investigate another possibility for the lack of a nucleus in Fornax, namely that the central dark matter distribution has a very shallow cusp or core which dramatically increases the dynamical friction sinking timescale."
 This would be, This would be
Lt is possible to derive a more general expression [or the DE if we assume that it depends on ¢through Q=5ον where { is a scaling radius.,"It is possible to derive a more general expression for the DF if we assume that it depends on $\varepsilon$ through $Q=\varepsilon-L_z^2/(2R_a^2)$ , where $R_a$ is a scaling radius."
 Suppose that the svstem has only stars with €Q20. so f((Q.L:)=0 for Q<0.," Suppose that the system has only stars with $Q>0$, so $f(Q,L_z)=0$ for $Q\leq0$."
" Here. Q eas Rh,ox."," Here, $Q\rightarrow\varepsilon$ as $R_a\rightarrow\infty$."
 The fundamental equation can be written. in terms of (Q. as where f(Q.L.) is the even part of f((Q.L.)..," The fundamental equation can be written, in terms of $Q$, as where $f_{+}(Q,L_z)$ is the even part of $f(Q,L_z)$."
" So. Following a similar procedure than in section 2.1.. one can find that a DE of the form corresponds to a mass density of the form fora,»1/2. where a,€le."," So, following a similar procedure than in section \ref{form1}, one can find that a DF of the form corresponds to a mass density of the form for $\alpha_n>-1/2$, where $\alpha_n\in\mathbb{R}$."
" Now. if we sum over all posible values of 2. we obtain the general expression corresponding to a density of the form with 2,»0 and a,71/2."," Now, if we sum over all posible values of $R_a$ we obtain the general expression corresponding to a density of the form with $R_a>0$ and $\alpha_n>-1/2$."
 ]nasystem in which the gravitational potential has no upper bound. it is not possible to celine correctly the relative potential V. and the relative energy. z. because the scape energy of the svstem is x.," In a system in which the gravitational potential has no upper bound, it is not possible to define correctly the relative potential $\Psi$ and the relative energy $\varepsilon$, because the scape energy of the system is $\infty$."
" For this reason. we shall write the fundamental equation in terms of ££ and &. and. we will suppose that the DE can be written as fora,©»1/2. and that the density is given by fora,&1/2."," For this reason, we shall write the fundamental equation in terms of $E$ and $\Phi$, and we will suppose that the DF can be written as for $\alpha_n > -1/2$, and that the density is given by for $\alpha_n > -1/2$."
" Thus then. by integrating with respect to L.. follows that Now. if we assume that for all j¢.0,|1/2). then and so we obtain ""Therefore. the distribution function is fora, &1/2."," Thus then, by integrating with respect to $L_z$, follows that Now, if we assume that for all $j\in(0,\alpha_n + 1/2)$, then and so we obtain Therefore, the distribution function is for $\alpha_n > - 1/2$ ."
" On the other hand. we can assume that the density has the more general form fora, &1/2."," On the other hand, we can assume that the density has the more general form for $\alpha_n>-1/2$."
" So. the corresponding DE will be fora,z1/2 and Q defined as Q=E|Lz/(47)"," So, the corresponding DF will be for $\alpha_n>-1/2$ and $Q$ defined as $Q=E+L_z^2/(2R_a^2)$."
" Now. if we sum over all the posible values of Ry. we can obtain thegeneralization corresponding to a density of the form with A,> Oanda,&»1/2."," Now, if we sum over all the posible values of $R_a$, we can obtain thegeneralization corresponding to a density of the form with $R_a > 0$ and $\alpha_n > -1/2$."
 The formalism. sketched above can also be used directly in the case of [at systems., The formalism sketched above can also be used directly in the case of flat systems.
 Note that in the method introcucecl bv Jiang&Ossipkov(2007) it was not possible. since the fundamental equation could. not be solved using the Abel integral equation.," Note that in the method introduced by \cite{jiang} it was not possible, since the fundamental equation could not be solved using the Abel integral equation."
 Now. we will proceed. similarly to the tridimensional case. finding the DEs for different kinds ofdensities.," Now, we will proceed similarly to the tridimensional case, finding the DFs for different kinds ofdensities."
 Then. we will also study the case of models with divergent gravitational potential.," Then, we will also study the case of models with divergent gravitational potential."
 As in the tridimensional case. first we suppose that So. by inverting (2)) with respect to L.. we obtain," As in the tridimensional case, first we suppose that So, by integrating\ref{inta3}) ) with respect to $L_z$ , we obtain"
shearing instability (KHI).,shearing instability (KHI).
 The KHI is triggered when the velocity gradient between dust-rich gas at the midplane and dust-poor gas at altitude becomes too large., The KHI is triggered when the velocity gradient between dust-rich gas at the midplane and dust-poor gas at altitude becomes too large.
" Barring gravitational instability, dust should settle to a state that is marginally stable against the KHI."," Barring gravitational instability, dust should settle to a state that is marginally stable against the KHI."
" The question of whether gravitational instability is viable translates into the question of whether the state that is marginally stable to the KHI has Ho2Ho,/Toomre (this is a necessary but not sufficient criterion for the formation of planetesimals by gravitational collapse; see footnote 5))."," The question of whether gravitational instability is viable translates into the question of whether the state that is marginally stable to the KHI has $\mu_0 \gtrsim \mu_{\rm 0,Toomre}$ (this is a necessary but not sufficient criterion for the formation of planetesimals by gravitational collapse; see footnote \ref{foot:slow}) )."
" In this paper, we sought out such marginally stable states by numerical simulation."," In this paper, we sought out such marginally stable states by numerical simulation."
 Starting with dust well mixed with gas at either bulk solar or supersolar metallicity we allowed dust to settle vertically until dynamical instabilities prevented the midplane density from increasing further.," Starting with dust well mixed with gas at either bulk solar or supersolar metallicity, we allowed dust to settle vertically until dynamical instabilities prevented the midplane density from increasing further."
" We tracked the approach to the marginally stable state using a combination of a 1D settling code and a 3D shearing box code, working in the limit that particles are small enough not to excite streaming instabilities."," We tracked the approach to the marginally stable state using a combination of a 1D settling code and a 3D shearing box code, working in the limit that particles are small enough not to excite streaming instabilities."
" All the instabilities that afflicted our dust layer originated at the layer's edges, where dust density gradients were steepest."," All the instabilities that afflicted our dust layer originated at the layer's edges, where dust density gradients were steepest."
" We found evidence for two kinds of instabilities: the usual KHI driven by vertical shear, and the Rayleigh-Taylor instability (RTI) driven by the weight of piled-up dust."," We found evidence for two kinds of instabilities: the usual KHI driven by vertical shear, and the Rayleigh-Taylor instability (RTI) driven by the weight of piled-up dust."
" These instabilities were mostly confined to the dust layer's top and bottom surfaces, leaving dust near the midplane free to settle but occasionally speeding up the accumulation of solids by transferring dust from pileups downward."," These instabilities were mostly confined to the dust layer's top and bottom surfaces, leaving dust near the midplane free to settle but occasionally speeding up the accumulation of solids by transferring dust from pileups downward."
 The midplane density stopped increasing when the dust layer became so thin that instabilities at the edges threatened to overturn the entire layer., The midplane density stopped increasing when the dust layer became so thin that instabilities at the edges threatened to overturn the entire layer.
" Using our standard procedure of refsec:method,, we attained maximum dust-to-gas ratios of µρ&2.45 and 20.3 for the casesof solar and 4x solar bulk metallicity, respectively (Figures 5 and 9))."," Using our standard procedure of \\ref{sec:method}, we attained maximum dust-to-gas ratios of $\mu_0 \approx 2.45$ and $20.3$ for the casesof solar and $4\times$ solar bulk metallicity, respectively (Figures \ref{fig:solar19101930} and \ref{fig:mr2122}) )."
 These values are lower limits because in our standard procedure dust particles at the layer’s top and bottom faces keep settling until they excite instabilities so vigorous that dust at the midplane is stirred up., These values are lower limits because in our standard procedure dust particles at the layer's top and bottom faces keep settling until they excite instabilities so vigorous that dust at the midplane is stirred up.
" In reality, dust at the layer’s edges may reach a state of marginal stability and stop settling, leaving dust near the midplane free to settle further."," In reality, dust at the layer's edges may reach a state of marginal stability and stop settling, leaving dust near the midplane free to settle further."
" We modified our procedure in refssec:weight to try to account for this effect, reaching μο7:2.9 and 26.4 for the two metallicity cases (Figures 10 and 11))."," We modified our procedure in \\ref{ssec:weight} to try to account for this effect, reaching $\mu_0 \approx 2.9$ and $26.4$ for the two metallicity cases (Figures \ref{fig:solarwin} and \ref{fig:mrwin}) )."
 These values are still lower limits because our simulations omit self-gravity., These values are still lower limits because our simulations omit self-gravity.
" But the correction for self-gravity should be small for the solar metallicity disk, on the order of (~2.9/34)."," But the correction for self-gravity should be small for the solar metallicity disk, on the order of $\sim 2.9/34$ )."
" For our supersolar metallicity disk, the correction for self-gravity might be on the order of unity (~26.4/34)—although it might also be much higher, as Sekiya(1998) and Youdin&Shu(2002) showed that vertical self-gravity can yield a singularity in pig."," For our supersolar metallicity disk, the correction for self-gravity might be on the order of unity $\sim 26.4/34$ )—although it might also be much higher, as \citet{sekiya98} and \citet{youdinshu02}
 showed that vertical self-gravity can yield a singularity in $\mu_0$."
" We conclude that a minimum-mass disk of bulk (height-integrated) solar metallicity orbiting a solar-mass star cannot form planetesimals by self-gravity alone: even neglecting turbulence intrinsic to gas, the KHI would force the midplane dust density to fall short of the Toomre density by about an order of magnitude."," We conclude that a minimum-mass disk of bulk (height-integrated) solar metallicity orbiting a solar-mass star cannot form planetesimals by self-gravity alone: even neglecting turbulence intrinsic to gas, the KHI would force the midplane dust density to fall short of the Toomre density by about an order of magnitude."
 Our results make clear what changes to the circumstellar environment would be needed for self-gravity to prevail., Our results make clear what changes to the circumstellar environment would be needed for self-gravity to prevail.
" 'To attain the Toomre density in à minimum-mass gas disk, the bulk metallicity would need to be enhanced over solar by a factor of a few <4."," To attain the Toomre density in a minimum-mass gas disk, the bulk metallicity would need to be enhanced over solar by a factor of a few $\lesssim 4$."
" For disks with total mass (gas plus dust) greater than that of the minimum-mass solar nebula, the required degree of metal enrichment would be lower."," For disks with total mass (gas plus dust) greater than that of the minimum-mass solar nebula, the required degree of metal enrichment would be lower."
" Our results agree with those of the prescriptive model of Weidenschilling(2006),, who found that the density of mm:-sized particles (το~0.001) at r=3 AU in a disk for which pg=1.6xgem? (Fz 1.3) and Xa/X,e0.015 (solar metallicity)107? fell short of the Toomre density by about a factor of 10."," Our results agree with those of the prescriptive model of \citet{weiden06}, who found that the density of mm-sized particles $\taus \sim 0.001$ ) at $r = 3$ AU in a disk for which $\rhog = 1.6
\times 10^{-9} \gm \cm^{-3}$ $F \approx 1.3$ ) and $\Sigmad/\Sigmag
\approx 0.015$ (solar metallicity) fell short of the Toomre density by about a factor of 10."
" When the bulk metallicity 34/35 increased to 0.054, the Toomre density was exceeded by 8, factor of 3."," When the bulk metallicity $\Sigmad/\Sigmag$ increased to $0.054$, the Toomre density was exceeded by a factor of 3."
" In Paper I, as in previous works (Sekiya1998;Youdin&Shu2002;Youdin&Chiang 2004),, all dust profiles were assumed to have spatially constant Richardson numbers Ri."," In Paper I, as in previous works \citep{sekiya98,youdinshu02,youdinchiang04}, all dust profiles were assumed to have spatially constant Richardson numbers $Ri$."
" The dust profiles we have computed are free of this assumption, whose validity we can now test."," The dust profiles we have computed are free of this assumption, whose validity we can now test."
" We calculate Ri(z) for our marginally stable states, derived under both standard refsec:method)) andmodified refssec:weight)) procedures."," We calculate $Ri(z)$ for our marginally stable states, derived under both standard \\ref{sec:method}) ) andmodified \\ref{ssec:weight}) ) procedures."
" To compute the numerator (Brunt frequency) of Ri in equation (4)) we use the horizontally averaged dust-to-gas ratio (ju(z)), computing derivatives using centered differences and assuming the gas to obey a Gaussian density profile footnote 9))."," To compute the numerator (Brunt frequency) of $Ri$ in equation \ref{eqn:richardson}) ), we use the horizontally averaged dust-to-gas ratio $\langle \mu(z) \rangle$, computing derivatives using centered differences and assuming the gas to obey a Gaussian density profile (see footnote \ref{foot:muchado}) )."
" To compute the denominator (vertical shearing(see of Ri, we also use inserting it into equationrate) (5)) and computing (u(z)),therefrom the velocity derivative."," To compute the denominator (vertical shearing rate) of $Ri$ , we also use $\langle
\mu(z) \rangle$ , inserting it into equation \ref{eqn:vphi}) ) and computing therefrom the velocity derivative."
 Of course we could also compute, Of course we could also compute
"The Schaye(2004) model assumes that all cold clouds form stars, but as we have seen in this paper, this is probably an oversimplification.","The \citet{schaye04} model assumes that all cold clouds form stars, but as we have seen in this paper, this is probably an oversimplification."
" In a more recent paper, Krumholz,Leroy&McKee(2011) look in more detail at the chemistry and thermodynamics of cold clouds in the ISM."," In a more recent paper, \citet{klm11} look in more detail at the chemistry and thermodynamics of cold clouds in the ISM."
" They use simple 1D cloud models that assume chemical and thermal equilibrium to explore a range of different cloud densities and visual extinctions, and show that in these models, the transition from atomic to molecular hydrogen is well correlated with a further sharp drop in the equilibrium gas temperature."," They use simple 1D cloud models that assume chemical and thermal equilibrium to explore a range of different cloud densities and visual extinctions, and show that in these models, the transition from atomic to molecular hydrogen is well correlated with a further sharp drop in the equilibrium gas temperature."
 This correlation is not a result of H» cooling., This correlation is not a result of $_{2}$ cooling.
" Rather, it occurs because the conditions required in order to attain a low gas temperature — high densities to boost Ct cooling, and efficient dust shielding to suppress photoelectric heating — are similar to those required to produce a high equilibrium H» fraction."," Rather, it occurs because the conditions required in order to attain a low gas temperature – high densities to boost $^{+}$ cooling, and efficient dust shielding to suppress photoelectric heating – are similar to those required to produce a high equilibrium $_{2}$ fraction."
" They then argue that star formation is strongly correlated with regions of cold gas, owing to the T?/? temperature dependence of the Bonnor-Ebert mass scale, which makes gravitational fragmentation much easier to bring about in cold gas than in warm gas."," They then argue that star formation is strongly correlated with regions of cold gas, owing to the $T^{3/2}$ temperature dependence of the Bonnor-Ebert mass scale, which makes gravitational fragmentation much easier to bring about in cold gas than in warm gas."
" In both of these models, the correlation between Hz and star formation comes about because the H» traces (but does not cause) the regions where the thermal pressure is low enough to allow stars to form."," In both of these models, the correlation between $_{2}$ and star formation comes about because the $_{2}$ traces (but does not cause) the regions where the thermal pressure is low enough to allow stars to form."
 The results from our present study provide strong support for this picture., The results from our present study provide strong support for this picture.
" They show that Ho cooling plays an insignificant role in determining the cloud temperature, that the differences between the temperatures of clouds cooled solely by Ct or by a mix of Ct and CO are very similar, and that the key factor enabling star formation within the clouds is the shielding of the interstellar radiation field by dust."," They show that $_{2}$ cooling plays an insignificant role in determining the cloud temperature, that the differences between the temperatures of clouds cooled solely by $^{+}$ or by a mix of $^{+}$ and CO are very similar, and that the key factor enabling star formation within the clouds is the shielding of the interstellar radiation field by dust."
" In the absence of this shielding, the temperature of the gas remains high, star formation is strongly suppressed, and the Hz abundance is very small."," In the absence of this shielding, the temperature of the gas remains high, star formation is strongly suppressed, and the $_{2}$ abundance is very small."
" In this study, we have investigated whether or not the formation of molecular gas is a prerequisite for star formation."," In this study, we have investigated whether or not the formation of molecular gas is a prerequisite for star formation."
" We have performed simulations using several different chemical models: one in which the gas is assumed to remain atomic throughout, a second in which H» formation is included, but CO formation is not, and a third which follows both Hz and CO formation."," We have performed simulations using several different chemical models: one in which the gas is assumed to remain atomic throughout, a second in which $_{2}$ formation is included, but CO formation is not, and a third which follows both $_{2}$ and CO formation."
 We find only minor differences in the nature and rate of star formation in these simulations., We find only minor differences in the nature and rate of star formation in these simulations.
" In contrast, disabling the effects of dust shielding has a very strong effect: the gas temperature does not fall much below 100 K and the formation of stars is strongly suppressed."," In contrast, disabling the effects of dust shielding has a very strong effect: the gas temperature does not fall much below 100 K and the formation of stars is strongly suppressed."
" We infer from these results that the observational correlation between H» and star formation is not a causal relationship: Hz and CO are not required for star formation, and the fact that we find a good correlation between the H» surface density and the star formation rate surface density simply reflects the fact that both are correlated with some third factor."," We infer from these results that the observational correlation between $_{2}$ and star formation is not a causal relationship: $_{2}$ and CO are not required for star formation, and the fact that we find a good correlation between the $_{2}$ surface density and the star formation rate surface density simply reflects the fact that both are correlated with some third factor."
" Our results suggest that the key factor is the ability of the clouds to shield themselves effectively against the interstellar radiation field: clouds that are too diffuse to shield themselves do not cool and hence form few, if any stars."," Our results suggest that the key factor is the ability of the clouds to shield themselves effectively against the interstellar radiation field: clouds that are too diffuse to shield themselves do not cool and hence form few, if any stars."
" Since effective shielding of the UV background is also required in order to form large abundances of He or CO (Gloveretal.2010;Glover&MacLow2011),, this naturally leads to a correlation between molecular gas and star formation without the necessity for a direct causal link between them."," Since effective shielding of the UV background is also required in order to form large abundances of $_{2}$ or CO \citep{g10,gm11}, this naturally leads to a correlation between molecular gas and star formation without the necessity for a direct causal link between them."
" Our current results do not allow us to establish whether the column density of dust required to provide effective shielding is independent of the cloud properties, or a function of the mean density of the gas; this will be addressed in future work."," Our current results do not allow us to establish whether the column density of dust required to provide effective shielding is independent of the cloud properties, or a function of the mean density of the gas; this will be addressed in future work."
" Finally, it is interesting to speculate about the possible observational consequences of this result."," Finally, it is interesting to speculate about the possible observational consequences of this result."
 One possible way of testing this model would be to look for regions in which ongoing star formation is not accompanied by significant amounts of molecular gas., One possible way of testing this model would be to look for regions in which ongoing star formation is not accompanied by significant amounts of molecular gas.
" If molecular gas is required for star formation, then it would be very difficult to explain the existence of such regions, whereas they are easily accommodated within our model."," If molecular gas is required for star formation, then it would be very difficult to explain the existence of such regions, whereas they are easily accommodated within our model."
" Unfortunately, such regions are likely to be rare, since they require the molecular gas fraction to be far out of equilibrium, and as our models show, high molecular fractions can be reached within a single free-fall given typical Galactic conditions."," Unfortunately, such regions are likely to be rare, since they require the molecular gas fraction to be far out of equilibrium, and as our models show, high molecular fractions can be reached within a single free-fall given typical Galactic conditions."
" If our results hold at lower metallicities (which is a reasonable assumption, but one which must be tested by future simulations), then one promising place to look for such regions would be within low metallicity star-forming dwarf galaxies such as I Zw 18 or DDO 154, since in these systems the characteristic chemical timescales will be much longer."," If our results hold at lower metallicities (which is a reasonable assumption, but one which must be tested by future simulations), then one promising place to look for such regions would be within low metallicity star-forming dwarf galaxies such as I Zw 18 or DDO 154, since in these systems the characteristic chemical timescales will be much longer."
" Indeed, efforts to date to detect CO within these galaxies have been unsuccessful"," Indeed, efforts to date to detect CO within these galaxies have been unsuccessful"
Several deep survevs have iow heen carried out at a wavelength of 850 jin using t1ο Submillimeter Comunon User Bolometer Array (SCUBA) camera ou the James Clerk Maxwell Telescope.,Several deep surveys have now been carried out at a wavelength of 850 $\mu$ m using the Submillimeter Common User Bolometer Array (SCUBA) camera on the James Clerk Maxwell Telescope.
 These survevs have led to the identification of a sample of subnuu sources with fiux densi ↕↸∖↴∖↴↕∐↑∐↸∖↥⋅⋜↧∐∶↴⋁↸∖⊇↑∪∐∣⋯⋅Jy at 850 san with a surface ⋅ ⋅≻⋅ ≺∐∖↕↴∖↴↕∙↖↽∪↕∿↓∩∩∩≺∐∖∶↴⋁−, These surveys have led to the identification of a sample of submm sources with flux densities in the range 2 to 10 mJy at 850 $\mu$ m with a surface density of $\sim$ 1000 $^{-2}$.
∙≼∶↕↖↽↸∖∐ that the SCUBA resolution is relatively poor aud that there are roughlygb 20 optical ealaxies down to R baud magnitude of 26 out to a redshift of Lin the SCUBA cau. definite optical identification of cleected πατι sources has no been possible.," Given that the SCUBA resolution is relatively poor and that there are roughly 20 optical galaxies down to R band magnitude of 26 out to a redshift of 4 in the SCUBA beam, definite optical identification of detected submm sources has not been possible."
 Uneler the assunption that the πΠ source population is at redshifts ereaer than  1. IIughes ct al. (," Under the assumption that the submm source population is at redshifts greater than $\sim$ 1, Hughes et al. ("
1998) icentified submua «xourees in the Hubble Deep Field (IIDE: Williams oet al.,1998) identified submm sources in the Hubble Deep Field (HDF; Williams et al.
 1996) with sealaxies iu the redshift range of 2.5 to l1., 1996) with galaxies in the redshift range of 2.5 to 4.
 The implied starformation rate in this redshift range based on the subnuu fiux densities was order of an maguitude ercater than what was previously calculated using optical. ultraviolet aud infrared cata.," The implied starformation rate in this redshift range based on the submm flux densities was order of an magnitude greater than what was previously calculated using optical, ultraviolet and infrared data."
 Receutly. subi counterparts in he IIDE were questioned by Richards (1998) based on uew 1.1 CGIIz radio counterparts to these subnuu sources.," Recently, submm counterparts in the HDF were questioned by Richards (1998) based on new 1.4 GHz radio counterparts to these submm sources."
 These radio identifications suggestOO that the opical counterparts to most of the IDF πι sources aro at redshifts lower than what were previously suggested by Uueghes et al. (, These radio identifications suggest that the optical counterparts to most of the HDF submm sources are at redshifts lower than what were previously suggested by Hughes et al. (
1998).,1998).
 Such a low redshift distribuion dramatically changes the previous claim for a substantially higher starformation rate at redshifts ereater than ~ 2., Such a low redshift distribution dramatically changes the previous claim for a substantially higher starformation rate at redshifts greater than $\sim$ 2.
 Based on spectroscopic redshifts of subuumu sources detected by Eales et al. (, Based on spectroscopic redshifts of submm sources detected by Eales et al. (
1998) in the fields coutaiuiug previous Canada-France-Redshitt Survey (CERS). Lilly et al. (,"1998) in the fields containing previous Canada-France-Redshift Survey (CFRS), Lilly et al. ("
1998) concluded that nxmt of the πα sources are at redshifts less than ~ 1.,1998) concluded that most of the submm sources are at redshifts less than $\sim$ 1.
 Such a low redshift distribution is also compatible with opical counterparts based on archival nibble Space Telesc'ope observations for subuua sources detected towards HHOrdaxv clusters (Sunudl et al., Such a low redshift distribution is also compatible with optical counterparts based on archival Hubble Space Telescope observations for submm sources detected towards galaxy clusters (Smail et al.
 L998a: hereafter S98)., 1998a; hereafter S98).
 We reer the reader to Simail et al. (, We refer the reader to Smail et al. (
1998b) for a recent review on published deep SCUBA surveys at S500 guns These surveys dachide the IIDE (IIughes et al.,1998b) for a recent review on published deep SCUBA surveys at 850 $\mu$ m. These surveys include the HDF (Hughes et al.
 1998). CERS fields (Eales et al.," 1998), CFRS fields (Eales et al."
 1998). the Lockman hole and Iawai Survey Fields (Barger ct al.," 1998), the Lockman hole and Hawaii Survey Fields (Barger et al."
 1998). aud leusiug clusters (S122dl et al.," 1998), and lensing clusters (Smail et al."
 1997: S98)., 1997; S98).
 Based on a combined anaysis of the subnuu aud far-infrared source counts combined with measured values for the backeround iuteusities at millinieter. subiuiu. aud far-infrared wavelengths. Blain ct al. (," Based on a combined analysis of the submm and far-infrared source counts combined with measured values for the background intensities at millimeter, submm, and far-infrared wavelengths, Blain et al. ("
1998) sugeested that of the 850 pan sources are at redshifts below 3.8 aud 8.2.,1998) suggested that of the 850 $\mu$ m sources are at redshifts below 3.8 and 8.2.
" The same analysis also concluded that there is no )eak iu he starformation rate between redshifts of 1 aud 2, as previously suggested by the optical and ultraviolet data. but rather the starformation increases as (1|:)! ill a redshift of ~ 1. and remains coustaut thereafter."," The same analysis also concluded that there is no peak in the starformation rate between redshifts of 1 and 2, as previously suggested by the optical and ultraviolet data, but rather the starformation increases as $(1+z)^4$ till a redshift of $\sim 1$ , and remains constant thereafter."
 If uost of the subi sources :we at Ligh redshifts (+= 1). heu deep su1n wavelength surveys should begin to recover instances of eravitaticμιαν leused πα sources. as the probability for lensing increases with redshift.," If most of the submm sources are at high redshifts $z \gtrsim 4$ ), then deep submm wavelength surveys should begin to recover instances of gravitationally lensed submm sources, as the probability for lensing increases with redshift."
 If he redshift distribution of background aud foreground sources are known. the uuuber of lensed sources in a giveu παολ Call )o uxed to constrain cosmological world models. especially the cosinological constant (e.8.. Turner et al.," If the redshift distribution of background and foreground sources are known, the number of lensed sources in a given survey can be used to constrain cosmological world models, especially the cosmological constant (e.g., Turner et al."
 1990)., 1990).
 If the background source redshift distribution is Tuknown. ensed source statistics ca be used to study backeroux source redshifts using prior knowledge ou the cosmolocical worldmocl and foreground lenses.," If the background source redshift distribution is unknown, lensed source statistics can be used to study background source redshifts using prior knowledge on the cosmological worldmodel and foreground lenses."
stable).,stable).
 aw>0 also satisfies this condition. but à star cannot be spun up rapidly enough to allow the appearance of the CFS instability. because it easily reaches its mass-shedding limit.," $\alpha > 0$ also satisfies this condition, but a star cannot be spun up rapidly enough to allow the appearance of the CFS instability, because it easily reaches its mass-shedding limit."
 We now apply the new rotation law to construct equilibrium configurations of differentially rotating neutron stars and study their dependence on o., We now apply the new rotation law to construct equilibrium configurations of differentially rotating neutron stars and study their dependence on $\alpha$.
" Each configuration is defined by five parameters: the axis ratio 7,/r;. the polytropic index N. the maximum density Pye. and the two parameters of the rotation law. Ro and a."," Each configuration is defined by five parameters: the axis ratio $r_p/r_e$, the polytropic index $N$ , the maximum density $ \rho_{max}$ and the two parameters of the rotation law, $R_0$ and $\alpha$."
 We construct sequences of axisymmetric and differentially rotating objects using the code discussed in ?.., 		 We construct sequences of axisymmetric and differentially rotating objects using the code discussed in \citet{Komatsu1989a}.
 The code iteratively solves Einstein’s equation and the first integral of motion for a stationary fluid configuration., The code iteratively solves Einstein's equation and the first integral of motion for a stationary fluid configuration.
 For all computation we used a grid with 600 points in the r— direction and 300 in the 8— direction., For all computation we used a grid with 600 points in the $r-$ direction and 300 in the $\theta-$ direction.
 The radial grid is set up in such a way that the inner uniformly-distributed 300 grid points just cover the whole star (on the equator the 300th point from the origin always corresponds to the surface of the star)., The radial grid is set up in such a way that the inner uniformly-distributed 300 grid points just cover the whole star (on the equator the 300th point from the origin always corresponds to the surface of the star).
" Outside the star we adopt the ""compactified"" coordinate as in 2.. to take into account the exact boundary condition at the radial infinity."," Outside the star we adopt the “compactified"" coordinate as in \citet{Cook1992}, to take into account the exact boundary condition at the radial infinity."
" For a given EOS. a functional of the rotation profile and maximum density. the code requires information on ""how rapidly” the star is rotating."," For a given EOS, a functional of the rotation profile and maximum density, the code requires information on ""how rapidly"" the star is rotating."
 To this end. it is more convenient to specify a parameter that measures the deformation induced by the rotation rather than the angular momentum or the rotational frequency.," To this end, it is more convenient to specify a parameter that measures the deformation induced by the rotation rather than the angular momentum or the rotational frequency."
 We follow ? in fixing the ratio of the polar coordinate radius of the star to the equatorial radius., We follow \citet{Komatsu1989a} in fixing the ratio of the polar coordinate radius of the star to the equatorial radius.
 The physical parameters of rotation as well as other physical quantities are then computed., The physical parameters of rotation as well as other physical quantities are then computed.
 In the current study we use a polytropic equation of state. with the index N=| to model neutron stars. Typical neutron star masses and radi are recovered when we set Ξ100 in geometrized units.," In the current study we use a polytropic equation of state, with the index $N=1$ to model neutron stars, Typical neutron star masses and radi are recovered when we set $\kappa=100$ in geometrized units."
 We fix this parameter for all the sequences to have a crude model of the nuclear equation of state for neutron matter., We fix this parameter for all the sequences to have a crude model of the nuclear equation of state for neutron matter.
 In a subsequent paper we will investigate the dependence of the space of configurations on the EOS. using realistic cold and finite-temperature EOSs.," In a subsequent paper we will investigate the dependence of the space of configurations on the EOS, using realistic cold and finite-temperature EOSs."
 To obtain an equilibrium model. we fix the parameters of the rotation profile. a and Ro. then choose the maximum density may and the coordinate axis. ratio.," To obtain an equilibrium model, we fix the parameters of the rotation profile, $\alpha$ and $R_0$, then choose the maximum density $\rho_{\rm max}$ and the coordinate axis ratio."
 In. our. code this set of parameters uniquely determines an equilibrium configuration. whose physical characteristics such as mass. compactness and angular momentum. angular frequency at the centre are computed once the solution is obtained.," In our code this set of parameters uniquely determines an equilibrium configuration, whose physical characteristics such as mass, compactness and angular momentum, angular frequency at the centre are computed once the solution is obtained."
 Rest mass and gravitational mass are computed by using the standard formula (see e.g. ?)), Rest mass and gravitational mass are computed by using the standard formula (see e.g. \citet{Bardeen1970}) ).
 An important measure of rotation. the 7/|W]| parameter. is introduced as in. 2..," An important measure of rotation, the $T/|W|$ parameter, is introduced as in \citet{Komatsu1989a}."
 This is used both in Newtonian and general relativistic studies of rotating stars and defined as the ratio. of rotational. kinetic energy to gravitationalbinding energy (see ? for details)., This is used both in Newtonian and general relativistic studies of rotating stars and defined as the ratio of rotational kinetic energy to gravitationalbinding energy (see \citet{Komatsu1989a} for details).
 It characterises the overall strength. of rotation of the star., It characterises the overall strength of rotation of the star.
" Classical studies suggest that when 7/]W|~0.14. bar-shaped equilibria bifurcate (into “Jacobi” or ""Dedekind"" type equilibrium sequences) and 7/]W|~0.27 marks the onset of dynamical instability of axisymmetric configurations (2).."," Classical studies suggest that when $T/|W|\sim 0.14$, bar-shaped equilibria bifurcate (into ""Jacobi"" or ""Dedekind"" type equilibrium sequences) and $T/|W|\sim 0.27$ marks the onset of dynamical instability of axisymmetric configurations \citep{Tassoul1978}."
 In general relativity numerical simulations point to a rather lower limit. 7/|W]~0.25 (2)..," In general relativity numerical simulations point to a rather lower limit, $T/|W|\sim 0.25$ \citep{Manca2007}."
 For a given rotation profile and a maximum density. we start from a non-rotating model (the polar-to-equatorial axis ratio is equal to unity). and decrease the ratio to obtain stars with increasingly rapid rotation.," For a given rotation profile and a maximum density, we start from a non-rotating model (the polar-to-equatorial axis ratio is equal to unity), and decrease the ratio to obtain stars with increasingly rapid rotation."
 We terminate the sequence if one of the following conditions is satisfied: 1) ΤΙΜΗ=0.14., We terminate the sequence if one of the following conditions is satisfied: 1) $T/|W| = 0.14$.
 This is the classical criterion at which CFS instability or viscous instability sets in for a bar-shaped deformation (the actual critical point depends weakly on both the equation of state and degree of differential rotation (2)))., This is the classical criterion at which CFS instability or viscous instability sets in for a bar-shaped deformation (the actual critical point depends weakly on both the equation of state and degree of differential rotation \citep{Karino2002}) ).
 2) Mass-shedding limit., 2) Mass-shedding limit.
 The last condition is reached when the angular frequency of matter at the equatorial surface comes close to local Keplerian frequency and a further spin-up of a star leads to shedding of mass., The last condition is reached when the angular frequency of matter at the equatorial surface comes close to local Keplerian frequency and a further spin-up of a star leads to shedding of mass.
 Beyond this point it is not possible to construct equilibrium configurations., Beyond this point it is not possible to construct equilibrium configurations.
 3) Topology change., 3) Topology change.
 When the degree of differential rotation is large the maximum density may move away from the rotation axis., When the degree of differential rotation is large the maximum density may move away from the rotation axis.
 When the value of the axis ratio reaches zero. the star develops a hole on the rotation axis.," When the value of the axis ratio reaches zero, the star develops a hole on the rotation axis."
 The equilibrium sequence may be continued beyond this point. but we are not interested in this toroidal shape configuration as a model of a neutron star.," The equilibrium sequence may be continued beyond this point, but we are not interested in this toroidal shape configuration as a model of a neutron star."
 Concerning the last point above. we should note that the structure of the parameterspace is quite complex. as has been analyzed by ?..," Concerning the last point above, we should note that the structure of the parameterspace is quite complex, as has been analyzed by \citet{Ansorg2009}. ."
 The toroidal and the spheroidal configurations form disjoint families of solutions separated by a mass, The toroidal and the spheroidal configurations form disjoint families of solutions separated by a mass
Recently. there ws been a rapid growth in the number of extra-solar planets identified (Vogt et al.,"Recently, there has been a rapid growth in the number of extra-solar planets identified (Vogt et al."
 2000: Marcy et al., 2000; Marcy et al.
 2000)., 2000).
 Driven bw technological advances. most have been fou by the identification of a ‘Doppler rellexὃν rough more novel techniques. such as planetary occulation (Charbonneau 2000). are also proving fruitful.," Driven by technological advances, most have been found by the identification of a `Doppler reflex', although more novel techniques, such as planetary occultation (Charbonneau 2000), are also proving fruitful."
 Collier Cameron et al. (, Collier Cameron et al. (
1999) claim to have directly detected the salieit reflected. from the planet orbiting 7 Boottis (althe)uegh see Charbonneau ct al.,1999) claim to have directly detected the starlight reflected from the planet orbiting $\tau$ Boöttis (although see Charbonneau et al.
 1999)., 1999).
 While it How appears that this 7 3o0ttis measure has not been confirmed in [οἱOWUL» observations. the identification of planets due to relected starlight has a firm theoretical foundation (Suclarsky et al.," While it now appears that this $\tau$ Boöttis measure has not been confirmed in follow-up observations, the identification of planets due to reflected starlight has a firm theoretical foundation (Sudarsky et al."
 2000)., 2000).
 All these techniques locus on stars in the vicinity. of the sun. over a region of several tens of parsecs.," All these techniques focus on stars in the vicinity of the sun, over a region of several tens of parsecs."
 At Larger distances. however. planets can be detected. orbiting the compact objects responsible for gravitationally microlensing stars in the Galactic. ίσο and Alagellanic Clouds via their perturbative inlluence on he microlensing light curve (Manmbsganss 1997).," At larger distances, however, planets can be detected orbiting the compact objects responsible for gravitationally microlensing stars in the Galactic Bulge and Magellanic Clouds via their perturbative influence on the microlensing light curve (Wambsganss 1997)."
 More recently. Cuall Gaudi (2000) and Lewis Ibata (2000)(hereafter LIP000) have considered instead. the detection of planes orbiting the microlensed sources.," More recently, Graff Gaudi (2000) and Lewis Ibata (2000)(hereafter LI2000) have considered instead the detection of planets orbiting the microlensed sources."
" Using the models for “ho Jupiter"" type planets as a basis for their studies. thes* groups. demonstrated that the small fraction of light. relected [rom the planet (uplo101L.) can be significan⋠⋠⋅Iv magnified. resulting in an observable ~1 per cent deviaion in the microlensing licht. curve."," Using the models for `hot Jupiter' type planets as a basis for their studies, these groups demonstrated that the small fraction of light reflected from the planet $(up~to \times10^{-4}L_*)$ can be significantly magnified, resulting in an observable $\sim1$ per cent deviation in the microlensing light curve."
 LI2000 also demonstraed how the monitoring of polarization through a microlensing event can probe the composition of the planetary atmos»here., LI2000 also demonstrated how the monitoring of polarization through a microlensing event can probe the composition of the planetary atmosphere.
P=4641.0% at a position angle of 35+I’. statistically consistent with the foreground value.,"$P = 4.6 \pm 1.0\%$ at a position angle of $35 \pm
1\degr$, statistically consistent with the foreground value."
 The intrinsic polarization of the light of C1. if any. must be lower than1%.," The intrinsic polarization of the light of C1, if any, must be lower than."
. Hence. our data suggest that the source is not polarized. which ts consistent with stellar light emitted isotropically from a supergiant star.," Hence, our data suggest that the source is not polarized, which is consistent with stellar light emitted isotropically from a supergiant star."
 Using optical and NIR images. spectra and polarimetry. we have searched for the counterpart of the high-energy sourceJ16283-4838.," Using optical and NIR images, spectra and polarimetry, we have searched for the counterpart of the high-energy source."
. We have found three candidates inside theSwift error circle of the source. which ts consistent with the expected number of chance superpositions.," We have found three candidates inside the error circle of the source, which is consistent with the expected number of chance superpositions."
 However. several pieces of evidence suggest that the brightest one J16281083-4838560)) Is the correct counterpart to the high energy source.," However, several pieces of evidence suggest that the brightest one ) is the correct counterpart to the high energy source."
 This source. coincident with a MIR GLIMPSE source G335.3268+00.1016)) exhibits NIR spectral features that are typical of late-O or early-B supergiant stars.," This source, coincident with a MIR GLIMPSE source ) exhibits NIR spectral features that are typical of late-O or early-B supergiant stars."
 Moreover. the combined NIR-MIR SED of the 2MASS and GLIMPSE sources is most closely fitted by an absorbed black body of luminosity and temperature consistent with these stellar types. and with an absorption in full agreement with that measured in X-rays forJ16283—4838.," Moreover, the combined NIR–MIR SED of the 2MASS and GLIMPSE sources is most closely fitted by an absorbed black body of luminosity and temperature consistent with these stellar types, and with an absorption in full agreement with that measured in X-rays for."
. The 2MASS source also displayed a steady luminosity decrease during April. 18-28. 2005. a few days after the X-ray source flare of April 7-10 and variations in its absorption during April 14-15.," The 2MASS source also displayed a steady luminosity decrease during April 18–28, 2005, a few days after the X-ray source flare of April 7–10 and variations in its absorption during April 14–15."
 Hence. we infer that our results imply thatJ16281083—4838560..G335.3268+00.1016.. and are the same source.," Hence, we infer that our results imply that, and are the same source."
 Given the association discussed above. our data strongly imply that is a Galactic. high-mass X-ray binary. as suspected by Beckmann et al. (2005)).," Given the association discussed above, our data strongly imply that is a Galactic high-mass X-ray binary, as suspected by Beckmann et al. \cite{Bec05}) )."
 Our classification of the donor in this system as a late-O or early- blue supereiant. m addition to our photometry displaying a SED consistent with a high-mass stellar source in the Galaxy. with an extinction close to that derived from X-ray observations. makes the classification of highly secure.," Our classification of the donor in this system as a late-O or early-B blue supergiant, in addition to our photometry displaying a SED consistent with a high-mass stellar source in the Galaxy, with an extinction close to that derived from X-ray observations, makes the classification of highly secure."
 Our data cannot help us determine the nature of the aecretor. however. as discussed by Beckmann et al. (2005)).," Our data cannot help us determine the nature of the accretor, however, as discussed by Beckmann et al. \cite{Bec05}) ),"
 this source being similar to those in the class of highly-absorbed HMXBs discovered byINTEGRAL. such as (Filliatre Chaty 2004.. see also Chaty et al. 2008))," this source being similar to those in the class of highly-absorbed HMXBs discovered by, such as (Filliatre Chaty \cite{Fil04}, , see also Chaty et al. \cite{Cha08}) )"
 or (Rodriguez et al. 2005))., or (Rodriguez et al. \cite{Rdr05}) ).
 Most systems in this class have been shown to contain neutron stars às accretors., Most systems in this class have been shown to contain neutron stars as accretors.
 We note that our distance estimate changes the value of the source luminosity considerably. with respect to that estimated by Beckmann et al. (2005)).," We note that our distance estimate changes the value of the source luminosity considerably, with respect to that estimated by Beckmann et al. \cite{Bec05}) )."
" For our 13.6-21.6 kpe range. the luminosity during the flare would have been in the range L=10799777eres7!, while in quiescence it would have been L=10°97’epes7!, "," For our 13.6–21.6 kpc range, the luminosity during the flare would have been in the range $L = 10^{36.8-37.2}\,\mathrm{erg \, s}^{-1}$, while in quiescence it would have been $L = 10^{35.5-35.9}\,\mathrm{erg \, s}^{-1}$."
These values are far higher than those derived by Beckmann et al. (2005)).," These values are far higher than those derived by Beckmann et al. \cite{Bec05}) ),"
 but still consistent with a neutron star accretor., but still consistent with a neutron star accretor.
 However. the possibility of a black hole aceretor cannot be ruled out by the available data.," However, the possibility of a black hole accretor cannot be ruled out by the available data."
 The origin of the absorption in this system ts another interesting point., The origin of the absorption in this system is another interesting point.
 The variability in the X-ray absorption implies that this is caused by a circumstellar medium., The variability in the X-ray absorption implies that this is caused by a circumstellar medium.
 A strong. variable stellar wind from the early-type donor would be a natural explanation. as pointed out by Beckmann et al. (2005)).," A strong, variable stellar wind from the early-type donor would be a natural explanation, as pointed out by Beckmann et al. \cite{Bec05}) )."
 Our results suggest that the NIR and X-ray absorption are related. since the absorption obtained from our fit to the NIR-MIR SED (A=28.9 magnitudes on April 28. 2005) translates into a hydrogen column density of 0.52x107 em. similar to that obtained by Beckmann et al. (2005))," Our results suggest that the NIR and X-ray absorption are related, since the absorption obtained from our fit to the NIR--MIR SED $A_V =
28.9$ magnitudes on April 28, 2005) translates into a hydrogen column density of $0.52 \times 10^{23}$ $^{-2}$, similar to that obtained by Beckmann et al. \cite{Bec05}) )"
 by fitting the X-ray spectra of the source on April 13 and April 15. 2005 (of 0.6 and 0.4x1077 cm™. respectively).," by fitting the X-ray spectra of the source on April 13 and April 15, 2005 (of 0.6 and $0.4 \times 10^{23}$ $^{-2}$, respectively)."
 This would point to an extended medium in which both the primary and the donor would be embedded., This would point to an extended medium in which both the primary and the donor would be embedded.
 Both the X-ray absorption and NIR luminosity interestingly exhibit variations on timescales of days., Both the X-ray absorption and NIR luminosity interestingly exhibit variations on timescales of days.
 The latter could be attributed within this picture to absorption variations. although no simultaneous X-ray and NIR data are available to test this suggestion by searching for correlations between both absorption values.," The latter could be attributed within this picture to absorption variations, although no simultaneous X-ray and NIR data are available to test this suggestion by searching for correlations between both absorption values."
" If this picture 1s correct. the contrasting behavior of the J-band luminosity on the one hand. and H—-A, luminosity on the other remains intriguing."," If this picture is correct, the contrasting behavior of the $J$ -band luminosity on the one hand, and $H$ $K_{\mathrm s}$ luminosity on the other remains intriguing."
 Emission at longer wavelengths (MIR-FIR). correlated with NIR/X-ray absorption. that has a tail reaching the NIR. would be a possible explanation of this behavior.," Emission at longer wavelengths (MIR–FIR), correlated with NIR/X-ray absorption, that has a tail reaching the NIR, would be a possible explanation of this behavior."
" In this case. the J-band variations may be controlled by the absorption of the system. while those in H and K, bands could be more strongly dependent on the emission."," In this case, the $J$ -band variations may be controlled by the absorption of the system, while those in $H$ and $K_{\mathrm s}$ bands could be more strongly dependent on the emission."
 Warm circumstellar dust in the absorber medium that reprocesses the absorbed light may produce the proposed MIR-FIR radiation., Warm circumstellar dust in the absorber medium that reprocesses the absorbed light may produce the proposed MIR–FIR radiation.
 Unfortunately our data are insufficient to perform a quantitative test of this hypothesis., Unfortunately our data are insufficient to perform a quantitative test of this hypothesis.
 Follow-up observations of the flare and post-flare behavior of the source in the NIR and MIR ranges. achievable for example with instruments such as SOFI at NTT and VISIR at VLT (e.g.. Rahoui et al. 2008) ," Follow-up observations of the flare and post-flare behavior of the source in the NIR and MIR ranges, achievable for example with instruments such as SOFI at NTT and VISIR at VLT (e.g., Rahoui et al. \cite{Rah08}) )"
would be interesting to address this point., would be interesting to address this point.
 Undoubtedly. additional observations of this source are needed to revealthe particular mechanism responsible for the accretion in this class of X-ray binaries.," Undoubtedly, additional observations of this source are needed to revealthe particular mechanism responsible for the accretion in this class of high-mass X-ray binaries."
conclusions are weakened somewhat with at most about 20 per cent of the optical emission associated with the X-ray source.,conclusions are weakened somewhat with at most about 20 per cent of the optical emission associated with the X-ray source.
" Any significant reprocessing of primary soft X-rays into the optical waveband occurs on scales greater than 100072, The lack of optical variability is consistent with observations of less extremely X-ray variable Seyfert | galaxies such as NGC 4051 (Done et al 1990).", Any significant reprocessing of primary soft X-rays into the optical waveband occurs on scales greater than $1000R_{\rm s}$ The lack of optical variability is consistent with observations of less extremely X-ray variable Seyfert 1 galaxies such as NGC 4051 (Done et al 1990).
 AJY thanks PPARC for support., AJY thanks PPARC for support.
 ACF and CSC thank the Royal Society., ACF and CSC thank the Royal Society.
the Nllt/optical/UV luminosity is and the ΑΗΕΙ luminosity is The NIRfopticalfUVY luminosity given here is really a lower-limit since we have assumed the minimum possible value for the reddening.,the NIR/optical/UV luminosity is and the MIR/FIR luminosity is The NIR/optical/UV luminosity given here is really a lower-limit since we have assumed the minimum possible value for the reddening.
 These waveband groups have been chosen on the basis of physical origin., These waveband groups have been chosen on the basis of physical origin.
 Phe οταν (ie. ~2.1015Hz and above) emission is thought to be produced bv non-thermal processes (e.g. Comptonization) in a hot corona associated with the inner regions of an accretion disk., The $\gamma$ -ray (i.e. $\sim 2\times 10^{16}\Hz$ and above) emission is thought to be produced by non-thermal processes (e.g. Comptonization) in a hot corona associated with the inner regions of an accretion disk.
 Phe NlIlt/optical/UV (~1074.104° LZ) emissions have plausible origins as thermal emission from the optically-thick accretion disk material., The NIR/optical/UV $\sim 10^{14}-10^{16}\Hz$ ) emissions have plausible origins as thermal emission from the optically-thick accretion disk material.
 ΕΣ (~Lot?Lot Hz) emission is likely to be thermal emission from warm or hot dust. associated with the dusty warm absorber and. putative molecular torus., The MIR/FIR $\sim 10^{12}-10^{14}\Hz$ ) emission is likely to be thermal emission from warm or hot dust associated with the dusty warm absorber and putative molecular torus.
 Here we address the implications of the relative magnitudes of these luminosities for the energeties of the source., Here we address the implications of the relative magnitudes of these luminosities for the energetics of the source.
 First. we will discuss some theoretical expectations.," First, we will discuss some theoretical expectations."
 We will assume a pure black hole model for the AGN emission. Le. we will assume no contribution {ο the observed. XCGN emission. from. a nuclear star-cluster or starburst.," We will assume a pure black hole model for the AGN emission, i.e. we will assume no contribution to the observed `AGN' emission from a nuclear star-cluster or starburst."
 As mentioned in the Introduction. it is believed that the inner aceretion clisk possesses à hot optically- corona responsible for the non-thermal />-ray emission.," As mentioned in the Introduction, it is believed that the inner accretion disk possesses a hot optically-thin corona responsible for the non-thermal $\gamma$ -ray emission."
 Coronal models coupled with spectral constraints imply that a large fraction of the energy that is (locally) dissipated in the aceretion disk is transported into. the corona. possibly in a magnetic form. before being radiated.," Coronal models coupled with spectral constraints imply that a large fraction of the energy that is (locally) dissipated in the accretion disk is transported into the corona, possibly in a magnetic form, before being radiated."
 The dominant radiation process is thought to be inverse Compton scattering of soft thermal (optical/UV) photons rom the accretion disk., The dominant radiation process is thought to be inverse Compton scattering of soft thermal (optical/UV) photons from the accretion disk.
 The emission of the optical/UV seed οποίος is probably driven by high-energy. irradiation from he corona. thereby completing a self-sustaining feedback.," The emission of the optical/UV seed photons is probably driven by high-energy irradiation from the corona, thereby completing a self-sustaining feedback."
 Suppose that the corona covers the entire disk surface and that almost all of the accretion energy is released within he corona leading to the N-rav/25-ray. power-law emission., Suppose that the corona covers the entire disk surface and that almost all of the accretion energy is released within the corona leading to the $\gamma$ -ray power-law emission.
 Approximately half of the primary high-energy. photons will strike the accretion disk., Approximately half of the primary high-energy photons will strike the accretion disk.
" Approximately half of the lux that strikes the clisk will be thermalized and re-racdiated at optical/UV. wavelengths. with the remaining half being ""rellected? (ic. the photons undergo Compton backseattering or excite X-rav. fluorescence)."," Approximately half of the flux that strikes the disk will be thermalized and re-radiated at optical/UV wavelengths, with the remaining half being `reflected' (i.e. the photons undergo Compton backscattering or excite X-ray fluorescence)."
 Thus. this scenario. would predict where AO~1/3.," Thus, this scenario would predict where $\Lambda\sim 1/3$."
" Observationally, we infer there to be significantly more Nllt/optical/UV. emission than this. Ao2ld (where approximate equality corresponds to. the case where the reddening takes its minimum allowed. value. £(BV)20.61)."," Observationally, we infer there to be significantly more NIR/optical/UV emission than this, $\Lambda\approxgt 1$ (where approximate equality corresponds to the case where the reddening takes its minimum allowed value, $E(B-V)=0.61$ )."
 There are several possible interpretations., There are several possible interpretations.
 First. only a fraction of the (locally) cissipated energy may be transported. into the corona.," First, only a fraction of the (locally) dissipated energy may be transported into the corona."
 However. it is dillicult to reconcile this with the X-ray spectrum given current coronal models (e.@.. Llaarcdt Maraschi 1991).," However, it is difficult to reconcile this with the X-ray spectrum given current coronal models (e.g., Haardt Maraschi 1991)."
 Secondly. there may be another optical/UV source in addition to the accretion disk such as a powerful nuclear starburst.," Secondly, there may be another optical/UV source in addition to the accretion disk such as a powerful nuclear starburst."
 This is difficult to reconcile with the fact that the optical continuum shown in Fig., This is difficult to reconcile with the fact that the optical continuum shown in Fig.
 2a appears featureless and. reddened to the same degree as the BLR., 2a appears featureless and reddened to the same degree as the BLR.
 Lastly. and most likely. the corona may not cover the whole disk.," Lastly, and most likely, the corona may not cover the whole disk."
 It may. be patehy or only exist in the innermost regions of the disk., It may be patchy or only exist in the innermost regions of the disk.
 The regions of the accretion disk without an active corona would still produce optical/UV. emission. via thermal emission. resulting from viscous dissipation., The regions of the accretion disk without an active corona would still produce optical/UV emission via thermal emission resulting from viscous dissipation.
 For the minimal reddening case. £(D1)=0.61. the MIGUEL. luminosity is comparable with luminosity in the whole of the rest of the spectrum.," For the minimal reddening case, $E(B-V)=0.61$, the MIR/FIR luminosity is comparable with luminosity in the whole of the rest of the spectrum."
 Within the clust-reprocessing paradigm. this is a troublesome result to understand unless the covering fraction of the dusty material is almost unity or the primary emission. is anisotropic (with more primary radiation being emitted: towards the clusty reprocessing material than towards us).," Within the dust-reprocessing paradigm, this is a troublesome result to understand unless the covering fraction of the dusty material is almost unity or the primary emission is anisotropic (with more primary radiation being emitted towards the dusty reprocessing material than towards us)."
 A covering raction of unity is implausible given our understanding of he geometry of a Sevfert nucleus., A covering fraction of unity is implausible given our understanding of the geometry of a Seyfert nucleus.
 Llowever. if we suppose hat E(BV)>0.61. then the Hit/optical/UV. luminosity can greatly exceed the above value thereby. alleviating the xoblem of the MIIU/ELdR production.," However, if we suppose that $E(B-V)>0.61$, then the IR/optical/UV luminosity can greatly exceed the above value thereby alleviating the problem of the MIR/FIR production."
 We have presented a multiwaveband: study of the Sevífert l ealaxy 6-30-15. including previously unpublished optical data from the ANT. and UV. data fromfC.," We have presented a multiwaveband study of the Seyfert 1 galaxy $-$ 6-30-15, including previously unpublished optical data from the AAT, and UV data from."
 Our compilation of data. spanning 6 decades of frequency. has allowed: us to. examine reprocessing mechanisms ancl the geometry of this svstem.," Our compilation of data, spanning 6 decades of frequency, has allowed us to examine reprocessing mechanisms and the geometry of this system."
 The optical line ancl continuum emission. both show 1e elfects of dust extinction., The optical line and continuum emission both show the effects of dust extinction.
 The reddening inferred. [rom Balmer line studies lies in the range (D.Y)—0.61.1.09., The reddening inferred from Balmer line studies lies in the range $E(B-V)=0.61-1.09$.
 ο.üven Chis reddening. we would expect the UV emission from re source to be less than observed.," Given this reddening, we would expect the UV emission from the source to be less than observed."
 Vhe fact that we cdo etect a UV. continuum ancl broad 1A1549 line can be meconciled with a typical Sevfert spectrum if 1.5 per cent of 1e intrinsic (i.e. dereddened) source spectrum is scattered around the matter responsible for the extinction and into our line of sight., The fact that we do detect a UV continuum and broad $\lambda 1549$ line can be reconciled with a typical Seyfert spectrum if 1–5 per cent of the intrinsic (i.e. dereddened) source spectrum is scattered around the matter responsible for the extinction and into our line of sight.
 UV spectropolarimetey will be required to est this hypothesis., UV spectropolarimetry will be required to test this hypothesis.
 The X-ray spectrum of this Sevfert. nucleus. clearly reveals a warn. absorber but little of the cold. (neutral) absorption that would be expected to accompany the dust responsible for the optical/UV. reddening., The X-ray spectrum of this Seyfert nucleus clearly reveals a warm absorber but little of the cold (neutral) absorption that would be expected to accompany the dust responsible for the optical/UV reddening.
 To reconcile the X-ray absorption with the optical reddening we postulate that the dust resides in the warm absorber., To reconcile the X-ray absorption with the optical reddening we postulate that the dust resides in the warm absorber.
 Detailed. X-ray studies have shown the warm absorber to be comprised of, Detailed X-ray studies have shown the warm absorber to be comprised of
should apply to the cloud sample in Ingallsetal.(2002).,should apply to the cloud sample in \citet{ingalls02}.
. Bakes Ticleus found. however. that the predicted heating rate could be doubled if the exponent of the erain size distribution was decreased. from -3.5 to -1.0.," Bakes Tielens found, however, that the predicted heating rate could be doubled if the exponent of the grain size distribution was decreased from -3.5 to -4.0."
 Since Ay aud FIR intensity depend on large erains aud the heating mainly on PÁIIs the derived efficiency € is model dependent., Since $A_{\rm V}$ and FIR intensity depend on large grains and the heating mainly on PAHs the derived efficiency $\epsilon$ is model dependent.
 Iu this paper we have used the dust model of LiDraine (2001)., In this paper we have used the dust model of \citet{li01}.
. Weingartuer&Draiue(20015) based their studies on the same dust nodel aud cousidered further cüffereut size distributions discussed in Weineartuer&Draine(2001a)., \citet{wd134} based their studies on the same dust model and considered further different size distributions discussed in \citet{wd548}.
. For cold neutral inediuu (fF ~LOOKIS) and. size distributions consistent with the diffuse cloud extinction law. Ry ~3.1. their predictions for the photoelectric heating rate are close to the values given by Bakes&Ticlens(1991).," For cold neutral medium $T\sim$ K) and size distributions consistent with the diffuse cloud extinction law, $R_{\rm V}\sim$ 3.1, their predictions for the photoelectric heating rate are close to the values given by \citet{bakes94}."
. The results depend on the carbon abundance which is limited by extinction measurements to values below ~6«10/7 carbon atoms per IL nucleus (Weinegartnuer&Draine2001a.b:Li 2001).," The results depend on the carbon abundance which is limited by extinction measurements to values below $\sim6\times 10^{-5}$ carbon atoms per H nucleus \citep{wd548,
wd134, li01}."
. The models of Li&Draine(2001) aud Weineartucr&Draine(20018) favoured carbon abundances close to this upper Dut and the resulting rate of the photoelectric heating ix some above the value eiven by Bakes Ticlens (Weingartucr&Draine, The models of \citet{li01} and \citet{wd548} favoured carbon abundances close to this upper limit and the resulting rate of the photoelectric heating is some above the value given by Bakes Tielens \citep{wd134}.
2001)).. Habartetal.(2001). derived values of € for the efficiency. of the shotoclectric heating across the cloud L1721.," \citet{habart01} derived values of $\epsilon\,$ for the efficiency of the photoelectric heating across the cloud L1721."
 Compared with the lugalls et al., Compared with the Ingalls et al.
" sample. he cloud has higher visual extinction. “ly~375, and. due to the proximity of a D2 star. it is subjected to a stronger radiation field. \25yy."," sample, the cloud has higher visual extinction, $A_{\rm
V}\sim3^{m}$, and, due to the proximity of a B2 star, it is subjected to a stronger radiation field, $\chi\ga5 \chi_0$."
 By adopting the cust model of Désert(1990).. Tlabart et al.," By adopting the dust model of \citet{desert90}, Habart et al."
 Were able to derive cficiencies of the plotoclectric cluission separately for PATIL. very. siiall evain and ]luee eran compoucuts.," were able to derive efficiencies of the photoelectric emission separately for PAH, very small grain and large grain components."
 The erived efficiencies were ~3% for PAIR. ~! for very small eras and 0.1 for large grains.," The derived efficiencies were $\sim 3$ for PAHs, $\sim$ for very small grains and $\sim$ for large grains."
 Part of the observed variation was attributed to changes iu the abundance of the dust components., Part of the observed variation was attributed to changes in the abundance of the dust components.
 The clouds in the Ingalls sample have lower visual extinction. and abundance variations are expected το be correspondingly simaller.," The clouds in the Ingalls sample have lower visual extinction, and abundance variations are expected to be correspondingly smaller."
 Another source of uncertainty is the balance between the cohuun censity aud the streneth of the racdiatiou field., Another source of uncertainty is the balance between the column density and the strength of the radiation field.
 As ciscussed above. if a stronger radiation Ποια or a smaller cohuun density were adopted iu the models. the calculated ratio Zegi/(efgg) would increase aud the derived value of ε decrease.," As discussed above, if a stronger radiation field or a smaller column density were adopted in the models, the calculated ratio $I_{\rm CII}/(\epsilon\,I_{\rm FIR})$ would increase and the derived value of $\epsilon$ decrease."
 According to Fig. Ἐν," According to Fig. \ref{fig:map.y},"
 the ratio feg/tefgig) increases up to above its average value when moving from the cloud ceuter o the cloud edges. where the radiation field is not attenuated.," the ratio $I_{\rm CII}/(\epsilon I_{\rm FIR})$ increases up to above its average value when moving from the cloud center to the cloud edges, where the radiation field is not attenuated."
 Therefore. if the clouds had sienificautly lower extinction. the cfiicicucy of the photoelectric heating could be lower by the sune amount.," Therefore, if the clouds had significantly lower extinction, the efficiency of the photoelectric heating could be lower by the same amount."
 We modified the model € bv reducing its column deusitv by a factor of three aud by uultiplving the intensity of the external radiation field bv a factor of two., We modified the model $C$ by reducing its column density by a factor of three and by multiplying the intensity of the external radiation field by a factor of two.
 The estimated average efficiency. of the plotoclectric heating decreased youn 410.7 to 2.25.107. ie. only by22.," The estimated average efficiency of the photoelectric heating decreased from $\times 10^{-2}$ to $\times 10^{-2}$, i.e. only by."
 Based ou III aud molecular line data the cohuun densities are inmost of the observed clouds within a factor of two from the average column density of the models., Based on HI and molecular line data the column densities are in most of the observed clouds within a factor of two from the average column density of the models.
 Iu this paper we have used for the intensity of the local ISRF values giveu by Mezecretal(1982). anc Mathisetal.(1983)., In this paper we have used for the intensity of the local ISRF values given by \citet{mezger82} and \citet{mathis83}.
. According to Draine(1978) and Parravanoctal.(2003) the actual ISRF could jo up to ~T0% stronger., According to \citet{draine78} and \citet{parravano03} the actual ISRF could be up to $\sim$ stronger.
 However. the difference is verv unlikely o be a factor of two.," However, the difference is very unlikely to be a factor of two."
 The actual errors caused by the πουτααν of the column density aud iuteusitv values is therefore less than., The actual errors caused by the uncertainty of the column density and intensity values is therefore less than.
. Compared with Ingallsctal.(2002) our estimate of the photoolectriie heatiug efficiency is xualler bv one thi., Compared with \cite{ingalls02} our estimate of the photoelectric heating efficiency is smaller by one third.
 Alost of the difference is due to a difference dn the predicte FIR intensity., Most of the difference is due to a difference in the predicted FIR intensity.
 For example. for a model with optical depth 41.0 imas through the cloud Ingalls et al.," For example, for a model with optical depth $A_{\rm V}$ =1.0 mag through the cloud Ingalls et al."
 obtained a LOO) yan surface brightness of slightly more than |., obtained a 100 $\mu$ m surface brightness of slightly more than $^{-1}$.
 For a homogeneous. spherically svnunetric cloud with equal optical depth we obtain a surface briglituess of «9.5 sr.|.," For a homogeneous, spherically symmetric cloud with equal optical depth we obtain a surface brightness of $\sim$ $^{-1}$."
 This is close to what Bernardetal.(1992). obtained for a sinular cloud 1uodel using the dust model of Désert(1990)., This is close to what \citet{bernard92} obtained for a similar cloud model using the dust model of \citet{desert90}.
. The difference between our result aud Ingalls et al., The difference between our result and Ingalls et al.
 cannot be due to model geometry., cannot be due to model geometry.
 One. would expectmore emissiou (higher Jey) frou a three oc.nensional cloud heated from all directions than from a plane parallel cloud heated ou two surfaces oulv., One would expect emission (higher $I_{\rm FIR}$ ) from a three dimensional cloud heated from all directions than from a plane parallel cloud heated on two surfaces only.
 The most likely explanation for the high FIR intensiticsi- obtaimed by Iugallsetal.(2002) is heir asstuuption of thermal equilibriun., The most likely explanation for the high FIR intensities obtained by \citet{ingalls02} is their assumption of thermal equilibrium.
 This means that all grains are coustautly at temperatures close to 9011 and almost all absorbed euergy ds, This means that all grains are constantly at temperatures close to K and almost all absorbed energy is
and the coherent radio emission from planets.,and the coherent radio emission from planets.
" The recent observations of the Auroral Ixilometric Radiation from the terrestrial magnetosphere and the new interpretation on the basis of (he ""tangent plane beaming model eave the opportunity to formulate a new model forVir.. where the emission is auroral-tvpe. emitted tangentially to the auroral circles."," The recent observations of the Auroral Kilometric Radiation from the terrestrial magnetosphere and the new interpretation on the basis of the ""tangent plane beaming model"" gave the opportunity to formulate a new model for, where the emission is ""auroral-type"", emitted tangentially to the auroral circles."
 The analvsis of the dynamical spectra permitted us to clearly see that the pulses occurred at slishtlv different times inside (he frequency band., The analysis of the dynamical spectra permitted us to clearly see that the pulses occurred at slightly different times inside the frequency band.
 In the Iramework of the new model. this could be due to relractive effects due to the propagation of the radiation inside a denser magnetized plasma surrounding the star in the magnetic equatorial belt.," In the framework of the new model, this could be due to refractive effects due to the propagation of the radiation inside a denser magnetized plasma surrounding the star in the magnetic equatorial belt."
 This is a further indication of the existence of a cold torus”. which also acts as an absorber of the evrosvachrotron continuous emission at centimeter wavelengths.," This is a further indication of the existence of a ""cold torus"", which also acts as an absorber of the gyrosynchrotron continuous emission at centimeter wavelengths."
 In the near future the EVLA will increase its maximum bandwidth up to 2 Giz., In the near future the EVLA will increase its maximum bandwidth up to 2 GHz.
 This will allow us to extend the dynamical spectra in a broader spectral region ancl (ο better deline the low and high limits of the cvelotvon maser., This will allow us to extend the dynamical spectra in a broader spectral region and to better define the low and high limits of the cyclotron maser.
 The time visibility of the peaks as a function of the frequency will allow us to study aid model wilh great. precision the propagation of the radiation in (he magnetospheric plasma surrounding the star., The time visibility of the peaks as a function of the frequency will allow us to study and model with great precision the propagation of the radiation in the magnetospheric plasma surrounding the star.
"(e.g. stellar evolutionary tracks, IMFs, binary fractions) to estimate stellar population parameters from the spectra and M/L ratios from these parameters.","(e.g. stellar evolutionary tracks, IMFs, binary fractions) to estimate stellar population parameters from the spectra and M/L ratios from these parameters."
 Most ingredients are the same for thePEGASE.HR and models., Most ingredients are the same for the and models.
" Even though stellar libraries differ, the M/L ratios of the two sets match in the V-band."," Even though stellar libraries differ, the M/L ratios of the two sets match in the $V$ -band."
" At the same time, using different models (e.g. ?)) for the M/L ratio estimates would require to use them as well for the determination of stellar population parameters with the full spectral fitting."," At the same time, using different models (e.g. \citealp{BC03a}) ) for the M/L ratio estimates would require to use them as well for the determination of stellar population parameters with the full spectral fitting."
" However, fitting low resolution SSP models against our data in a narrow spectral range of the FLAMES ΗΠΟΘ setup would not allow us to make any sensible estimates of age and metallicity."," However, fitting low resolution SSP models against our data in a narrow spectral range of the FLAMES HR09 setup would not allow us to make any sensible estimates of age and metallicity."
 The uncertainties of the stellar population parameters range from 0.03 dex in [Fe/H] and 15 per cent in age for Γ-19 (UCD 3) to >0.3 dex in metallicity and totally uncertain age for the faintest representatives of our sample such as F-62., The uncertainties of the stellar population parameters range from 0.03 dex in $[$ $]$ and 15 per cent in age for $F$ $19$ (UCD 3) to $>$ 0.3 dex in metallicity and totally uncertain age for the faintest representatives of our sample such as $F$ $62$.
" Generally, there is a clear correlation between the quality of age determination and the overall metallicity of a galaxy, which can be easily explained as in more metal-rich objects absorption lines are stronger, thus better constraining the fitting procedure for a given mean signal-to-noise ratio in the continuum."," Generally, there is a clear correlation between the quality of age determination and the overall metallicity of a galaxy, which can be easily explained as in more metal-rich objects absorption lines are stronger, thus better constraining the fitting procedure for a given mean signal-to-noise ratio in the continuum."
" Thanks to the high spectral resolution of our data and, therefore a well sampled line-of-sight velocity distribution in most UCDs, the velocity dispersion — metallicity degeneracy (seeSection1.3.1in?,fordetails) intrinsic to the full spectral fitting in the pixel space makes very little effect on the obtained measurements of velocity dispersion."," Thanks to the high spectral resolution of our data and, therefore a well sampled line-of-sight velocity distribution in most UCDs, the velocity dispersion – metallicity degeneracy \citep[see Section~1.3.1 in][for
details]{Chilingarian06} intrinsic to the full spectral fitting in the pixel space makes very little effect on the obtained measurements of velocity dispersion."
" Hence, even in cases where the metallicity measurements have very large uncertainties due to low signal-to-noise ratios, the velocity dispersions still remain well determined."," Hence, even in cases where the metallicity measurements have very large uncertainties due to low signal-to-noise ratios, the velocity dispersions still remain well determined."
" Our velocity dispersion values sometimes differ significantly from those obtained by ? (see Fig. 7)),"," Our velocity dispersion values sometimes differ significantly from those obtained by \citet{Mieske+08} (see Fig. \ref{figsigsig}) ),"
" therefore their results of dynamical modelling, i.e. aperture corrections, central and global velocity dispersions, and, consequently, dynamical mass-to-light ratios have to be corrected."," therefore their results of dynamical modelling, i.e. aperture corrections, central and global velocity dispersions, and, consequently, dynamical mass-to-light ratios have to be corrected."
"We repeated the dynamical modelling in exactly the same way as in ?? using new velocity dispersion estimates and structural properties from ? for 13 UCDs, and the photometric properties of F-2 and F-8 presented above.","We repeated the dynamical modelling in exactly the same way as in \citet{Hilker+07,Mieske+08} using new velocity dispersion estimates and structural properties from \citet{Mieske+08} for 13 UCDs, and the photometric properties of $F$ $2$ and $F$ $8$ presented above."
" Using dynamical and stellar mass-to-light ratios, we estimate the dark matter content of 14 UCDs in our sample as ((M/L)ayav— (M/L)«v)/(M/L)ayn,v. The"," Using dynamical and stellar mass-to-light ratios, we estimate the dark matter content of 14 UCDs in our sample as $((M/L)_{\mathrm{dyn,}V} -
(M/L)_{*V}) / (M/L)_{\mathrm{dyn,}V}$ The"
five-vear release of the delata and compare with both Gaussian and non-zero ssamples.,five-year release of the data and compare with both Gaussian and non-zero samples.
 Ehe results of the null Gaussian test are compared with those of Eriksenetal.(2004) for the first-vear ddata. and then we use the skeleton estimator to compute a likelihood estimate forfyL.," The results of the null Gaussian test are compared with those of \citet{Eriksen_etal_2004} for the first-year data, and then we use the skeleton estimator to compute a likelihood estimate for."
. This paper is organised as follows., This paper is organised as follows.
 In Section 2.. we carry out numerical studies on the CAB local skeleton. including the skeleton statistics utilised in ouranalysis (Section 2.1)) and the test of unbiasedness and convergeney of fyp--likelihood led by skeleton estimator from. noise-free Á[xz--simulations (Section 2.2)).," In Section \ref{sec_method}, we carry out numerical studies on the CMB local skeleton, including the skeleton statistics utilised in ouranalysis (Section \ref{subsec_sta}) ) and the test of unbiasedness and convergency of -likelihood led by skeleton estimator from noise-free -simulations (Section \ref{subsec_nulltest}) )."
 3.l presents an overview of the dedata ancl the instrumental properties that should be encoded. into our simulations to make an unbiasecl comparison and parameter estimation., \ref{subsec_wmap_data} presents an overview of the data and the instrumental properties that should be encoded into our simulations to make an unbiased comparison and parameter estimation.
 Section 3.2. describes the process of computing the estimator and further analysis from both the observed cata ancl simulations having consistent instrumental properties and skv-coverage., Section \ref{subsec_analysis} describes the process of computing the estimator and further analysis from both the observed data and simulations having consistent instrumental properties and sky-coverage.
 Results are reported in Section 4. including the analysis and discussion of a Gaussian frequentist test (Section 4.1)) and ÁÍxpz--estimations (4.2)).," Results are reported in Section \ref{sec_results}, including the analysis and discussion of a Gaussian frequentist test (Section \ref{subsec_gauss_res}) ) and -estimations \ref{subsec_fnl_res}) )."
 Finally. we present our conclusions in Section 5..," Finally, we present our conclusions in Section \ref{sec_conclusions}."
 According to the approximation mace by Novikov.Colombi&Doré (2006).. the local skeleton on a smooth 2D sphere pir). traces those points where the gradient. of p is the eigenvector of the corresponding Llessian matrix.," According to the approximation made by \citet{Novikov_etal_2006}, the local skeleton on a smooth 2D sphere $\rho(\vecr)$, traces those points where the gradient of $\rho$ is the eigenvector of the corresponding Hessian matrix."
 That is. it satisfies the characteristic equation with A (Àj>As: As ) the eigenvalues. where #Ho=píüriür; is the Wessian matrix at positionr.," That is, it satisfies the characteristic equation with $\lambda$ $\lambda_1>\lambda_2$; $\lambda_2<0$ ) the eigenvalues, where $\mathcal{H}\equiv\partial^2\rho/\partial
r_i\partial r_j$ is the Hessian matrix at position."
. Identicallv with Iriksenetal.(2004).. we do not specify the condition of eigenvalues of the local linear system.," Identically with \citet{Eriksen_etal_2004}, we do not specify the condition of eigenvalues of the local linear system."
 In other words. the skeleton in our analysis isconsidered as the set of underlying zero-contour lines of the realisation wherep; and p;; denote the first and second derivatives of ptr) in two ort directions.  and gy.," In other words, the skeleton in our analysis isconsidered as the set of underlying zero-contour lines of the realisation where$\rho_i$ and $\rho_{ij}$ denote the first and second derivatives of $\rho(\vecr)$ in two orthogonal directions, $x$ and $y$."
" As for the CAB temperature hogonalfield.Z(). the ""skeleton. map! à is re-expressed as where the semicolons denote the covariant derivatives and the definite expression of them can be found. in Schmalzing&Gorski(2002)."," As for the CMB temperature field $T(\vecn)$, the `skeleton map' $\mathcal{S}$ is re-expressed as where the semicolons denote the covariant derivatives and the definite expression of them can be found in \citet{Schmalzing_etal_2002}."
. The method for tracing the local skeleton in the LIEALDPix scheme has been reviewed in detail by Eriksenal. (2004)., The method for tracing the local skeleton in the HEALPix scheme has been reviewed in detail by \citet{Eriksen_etal_2004}.
". In Appenclix νι we seek to optimise the method by applying the cubic spline interpolation for estimating the underlving positions of skeleton""knots! on the pixelised sphere."," In Appendix \ref{sec_app_1}, we seek to optimise the method by applying the cubic spline interpolation for estimating the underlying positions of skeleton`knots' on the pixelised sphere."
 The resulting skeleton statistics. are introduced and tested for their applicability to non-Gaussian signal detection and. eestimation., The resulting skeleton statistics are introduced and tested for their applicability to non-Gaussian signal detection and estimation.
 In this work. the CMD temperature realisation intended for skeleton analysis. 7(7). is first normalised as. The standard. deviation σ is computed over the vali region of realisation after application of an adequate smoothing process (Section 3.2)).," In this work, the CMB temperature realisation intended for skeleton analysis, $T(\vecn)$, is first normalised as, The standard deviation $\sigma$ is computed over the valid region of realisation after application of an adequate smoothing process (Section \ref{subsec_analysis}) )."
 We utilise the skeleton length. distribution function of the normalised temperature thresholds 7. asà probe of non-Caussianity and to construct an estimator ofνι.," We utilise the skeleton length distribution function of the normalised temperature thresholds $\nu$, asa probe of non-Gaussianity and to construct an estimator of."
 As with any probability. density function. there are two types of distributions quantifving the skeleton length. the dillerentia pat and the cumulative one where the normalisation [actor Liaw=f°db) is the total length.," As with any probability density function, there are two types of distributions quantifying the skeleton length, the differential pdf and the cumulative one where the normalisation factor $L_{\rm tot} =
\int^{+\infty}_{\nu=-\infty}\,dL(\nu)$ is the total length."
 These two functions are equivalent ancl should. lead to consistent results., These two functions are equivalent and should lead to consistent results.
 In the first investigation of the statistical properties of the skeleton length in the cata (Eriksenetal.2004). Ihe cumulativeformi was utilised and compared with the predictions of a Gaussian model.," In the first investigation of the statistical properties of the skeleton length in the data \citep{Eriksen_etal_2004}, the cumulativeform was utilised and compared with the predictions of a Gaussian model."
 Ln our analysis. both the cillerential ancl cumulative functions are computed.," In our analysis, both the differential and cumulative functions are computed."
 We study the signature of the local-type non-Caussianity as a [function of oon the skeleton length distributions. ο) and. ον).," We study the signature of the local-type non-Gaussianity as a function of on the skeleton length distributions, $\mathcal{L}_d(\nu)$ and $\mathcal{L}_a(\nu)$."
 As a necessary precursor to. fyp--estimation. we establish that our estimators [cad to an unbiased and sullicientIy converged ÁÍxL--likelihood by analysing noise-freefull-sky realisations with a non-Gaussian signal component.," As a necessary precursor to -estimation, we establish that our estimators lead to an unbiased and sufficiently converged -likelihood by analysing noise-freefull-sky realisations with a non-Gaussian signal component."
 The test is based on simulations of the CALBanisotropy as a function ofκι., The test is based on simulations of the CMBanisotropy as a function of.
".. We adopt thealgorithm proposed. by Liguori.Matarrese&Moscardini(2003):Liguorietal.(2007) ancl recently improved by Elsner&Wandelt(2000). t0. simulate a set of⋅ Gaussian∢⊀ realisations⊀ 6 (e0;,,) withη corresponding. non-Gaussian components (alt))."," We adopt thealgorithm proposed by \citet{Liguori_etal_2003, Liguori_etal_2007} and recently improved by \citet{Elsner_etal_2009} to simulate a set of Gaussian realisations $a^{\rm G}_{\ell m}$ ) with corresponding non-Gaussian components $a^{\rm NG}_{\ell m}$ )."
 The cosmological parameters acopted for the ssimiulations are those determined. [or ar WALAP55 best-fit ACDAL model (Ixomatsuetal.2009)., The cosmological parameters adopted for the simulations are those determined for the 5 best-fit $\Lambda$ CDM model \citep{Komatsu_etal_2009}.
". Specifically. the following parameters are o.= (742.047 0.1090. Q,A7= 0.02273. A""aadopted:(hy=0.002\Mpe+)241 "". h= 0.719. =0 j and τς0.0 "," Specifically, the following parameters are adopted: $\Omega_{\Lambda}=0.742$ , $\Omega_{c}h^2=0.1099$ , $\Omega_{b}h^2=0.02273$ , $\Delta_{\mathcal{R}}^2(k_0=0.002 \rm Mpc^{-1})=2.41\times10^{-9}$ , $h=0.719$ , $n_s=0.963$ , and $\tau=0.087$ ."
There are a total of 2500 simulated fal. Poppet aNOYE pairs in this test that include power up to a maximum multipole fas= 1024.," There are a total of 2500 simulated $a^{\rm G}_{\ell m}$ , $a^{\rm
NG}_{\ell m}$ pairs in this test that include power up to a maximum multipole $\ell_{\rm max} = 1024$ ."
" Pixclised skvmaps with different vvalues are therefore obtained following the relation where b, is a Gaussian beam transfer. function. with", Pixelised skymaps with different values are therefore obtained following the relation where $b_{\ell}$ is a Gaussian beam transfer function with
during the latter part of the pre-overlap cra.,during the latter part of the pre-overlap era.
 The aim of this paper is to investigate the modification of the 21-cm power spectrum. by. quasars during the epoch of reionisation., The aim of this paper is to investigate the modification of the 21-cm power spectrum by quasars during the epoch of reionisation.
 Our results suggest that detailed: simulations ancl reionisation models will need to consider quasar contribution to 21-cm power spectra when interpreting future observations., Our results suggest that detailed simulations and reionisation models will need to consider quasar contribution to 21-cm power spectra when interpreting future observations.
 This paper is organised as follows: we begin in Section 2 by describing the inclusion of stellar reionisation within a semi-numerical scheme to produce realistic Ductuations in the ionisecl gas distribution. here we also describe the method by which we populate our simulation field. with quasars: in Section 3. we dicuss the choice of parameter space in which we explore the effect. of quasars on. the ionisation state of the LGAL: Section 4. describes the statistical signatures used to characterise reionisation: our results. including their epoch dependence. are. presented. in Section 5: we diseuss our conclusions and their consequences or redshilted 21-cm power spectrum measurements in Section 6..," This paper is organised as follows: we begin in Section \ref{Semi-numerical ionisation model} by describing the inclusion of stellar reionisation within a semi-numerical scheme to produce realistic fluctuations in the ionised gas distribution, here we also describe the method by which we populate our simulation field with quasars; in Section \ref{The quasar contribution to reionisation} we dicuss the choice of parameter space in which we explore the effect of quasars on the ionisation state of the IGM; Section \ref{Statistical signatures of reionisation} describes the statistical signatures used to characterise reionisation; our results, including their epoch dependence, are presented in Section \ref{Results}; we discuss our conclusions and their consequences for redshifted 21-cm power spectrum measurements in Section \ref{Discussion}."
" Throughout this paper we adopt the set of cosmological »wameters. determined by the (MALYP)) (2) for a Dat CDM universe: Qu=0. (dark matter and barvons): 24=0.73 (cosmological constant): ©,=0.046 (baryons): h=0.7 (Llubble constant): ης=1 (primordial spectrum. index): ax—0.5 (primordial spectrum normalisation).", Throughout this paper we adopt the set of cosmological parameters determined by the ) \citep{komatsu2008} for a flat $\Lambda$ CDM universe: $\Omega_{\rm m} = 0.27$ (dark matter and baryons); $\Omega_{\Lambda} = 0.73$ (cosmological constant); $\Omega_{\rm b} = 0.046$ (baryons); $h = 0.7$ (Hubble constant); $n_{\rm s} = 1$ (primordial spectrum index); $\sigma_8 = 0.8$ (primordial spectrum normalisation).
 All clistances are in comoving units unless stated otherwise., All distances are in comoving units unless stated otherwise.
 There are two contributors to the reionisation of the LAL that we consider here: stars ancl quasars., There are two contributors to the reionisation of the IGM that we consider here: stars and quasars.
 In. this section. we begin by summarising the features of our semi-numerical moclel for the reionisation of a three-dimensional volume of the LGAL by galaxies (Section 2.1)).," In this section, we begin by summarising the features of our semi-numerical model for the reionisation of a three-dimensional volume of the IGM by galaxies (Section \ref{stellarionisation}) )."
 Only a brief description is given herewe direct the reader to? for further details., Only a brief description is given here–we direct the reader to \cite{geil2008} for further details.
 We then discuss our method of populating a sample volume with quasars using a Monte Carlo algorithm (Section 2.2)) before describing the three-dimensional realisation of the ionisation state of the LGAL including the ionising influence of both gaars and quasars (Section 2.3))., We then discuss our method of populating a sample volume with quasars using a Monte Carlo algorithm (Section \ref{Quasar ionisation}) ) before describing the three-dimensional realisation of the ionisation state of the IGM including the ionising influence of both stars and quasars (Section \ref{Inclusion of quasars in the semi-numerical scheme}) ).
 We begin by simulating the linoar matter overcensity Ποια o(m.2)—βία.βρω1 inside a periodic. comoving. cubic region of volume V.=£. by caleulating the density contrast in Fourier space ok.2) corresponding to a ACDAL power spectrum (7). [linearly extrapolated to a specified redshift ," We begin by simulating the linear matter overdensity field $\delta(\xvec,z) \equiv \rho_{\rm m}(\xvec,z)/\bar{\rho}_{\rm m}-1$ inside a periodic, comoving, cubic region of volume $V = L^{3}$, by calculating the density contrast in Fourier space $\hat{\delta}(\kvec,z)$ corresponding to a $\Lambda$ CDM power spectrum \citep{eh1999} linearly extrapolated to a specified redshift $z$."
The semi-analvtie model used to compute the relation between the local dark matter overdensity and the ionisation state of the ICM. is. based. on the model. described. by 7T. and 7.., The semi-analytic model used to compute the relation between the local dark matter overdensity and the ionisation state of the IGM is based on the model described by \cite{wl2007} and \cite{wm2007}.
 Any model for the reionisation of the ICM must describe the relation between the emission of ionising photons by stars in galaxies and the ionisation state of the interealactic gas., Any model for the reionisation of the IGM must describe the relation between the emission of ionising photons by stars in galaxies and the ionisation state of the intergalactic gas.
 This relation is non-trivial as it depends on various internal parameters which may vary with galaxy mass., This relation is non-trivial as it depends on various internal parameters which may vary with galaxy mass.
 These parameters include the fraction of gas within galaxies that is converted into stars and accreting black holes. the spectrum of the ionising radiation and the escape fraction of ionising photons from the surrounding interstellar medium. as well as the ealactic halo and its immeciate infall region (see7.forareview)..," These parameters include the fraction of gas within galaxies that is converted into stars and accreting black holes, the spectrum of the ionising radiation and the escape fraction of ionising photons from the surrounding interstellar medium as well as the galactic halo and its immediate infall region \citep[see][for a review]{loeb2006}."
 This relation also depends on intergalactic physics., This relation also depends on intergalactic physics.
 In overdense regions of the IGM. galaxies will be over-abundant because simall-scale Hluctuations need to be of lower amplitude to form a galaxy when embedded: in a larger scale overdensity (?)..," In overdense regions of the IGM, galaxies will be over-abundant because small-scale fluctuations need to be of lower amplitude to form a galaxy when embedded in a larger scale overdensity \citep{mo1996}."
 On the other hand. the increase in the recombination rate in overdense regions counteracts this galaxy bias.," On the other hand, the increase in the recombination rate in overdense regions counteracts this galaxy bias."
 The process of reionisation also contains several lavers of feccback: radiative feedback heats the LGAL and. results in the suppression of low-mass galaxy formation which delays the completion of reionisation by lowering the local star formation rate., The process of reionisation also contains several layers of feedback: radiative feedback heats the IGM and results in the suppression of low-mass galaxy formation which delays the completion of reionisation by lowering the local star formation rate.
 Llowever. this ellect is counteracted in overdense regions by the biased formation of massive ealaxies.," However, this effect is counteracted in overdense regions by the biased formation of massive galaxies."
" The evolution of the ionisation fraction bv mass Qs, of a particular region of scale R with overdensity ὁμ (at redshift) 2) may be written as where IV, is the number of photons entering the LAL per barvon in galaxies. apy is the case-B recombination coelficient and C' is the clumping factor (which we assume. for simplicity. to be a constant value of 2)."," The evolution of the ionisation fraction by mass $Q_{\delta_R,R}$ of a particular region of scale $R$ with overdensity $\delta_R$ (at redshift $z$ ) may be written as where $N_{\rm ion}$ is the number of photons entering the IGM per baryon in galaxies, $\alpha_{\rm B}$ is the case-B recombination coefficient and $C$ is the clumping factor (which we assume, for simplicity, to be a constant value of 2)."
" The production rate of ionising photons in neutral regions is assumed to be proportional to the collapsed fraction Pi, of mass in halos above the minimum threshold mass for star formation (Αμ) whereas the minimum halo mass in ionised regions is limited. by the Jeans mass in an ionisecl IGM. (Miu)."," The production rate of ionising photons in neutral regions is assumed to be proportional to the collapsed fraction $F_{\rm col}$ of mass in halos above the minimum threshold mass for star formation $M_{\rm min}$ ), whereas the minimum halo mass in ionised regions is limited by the Jeans mass in an ionised IGM $M_{\rm ion}$ )."
" We assume Ai, Corresponds with a virial temperature of 103 IIS. representing the hydrogen cooling threshold. ancl Adj to correspond with a virial temperature of 10"" WIS. representing the mass below which infall [rom an ionised. LGAL is suppressed. (2).."," We assume $M_{\rm min}$ corresponds with a virial temperature of $10^4$ K, representing the hydrogen cooling threshold, and $M_{\rm ion}$ to correspond with a virial temperature of $10^5$ K, representing the mass below which infall from an ionised IGM is suppressed \citep{dijkstra2004a}."
" In. a region of comoving radius 2 and mean overdensity 0(2)=AL)(2)/Llean.) (specified at recshift z instead of the usual z= 0). we use the extended. Press-Scheehter model (2). to caleulate the relevant collapsed fraction. where erfe(.c) is the complimentary error function. στι is the variance of the overdensity Ποιά smoothed on a scale Rand o7, is the variance of the overdensity field smoothee on a scale Z4. corresponding to a mass scale οἱ Minin or Mi (both evaluated at recdshift z rather than at z= 0)."," In a region of comoving radius $R$ and mean overdensity $\delta(z)=\delta D_1(z)/D_1(z_{\rm obs})$ (specified at redshift $z$ instead of the usual $z = 0$ ), we use the extended Press-Schechter model \citep{bond1991} to calculate the relevant collapsed fraction, where $\mbox{erfc}(x)$ is the complimentary error function, $\sigma_R^2$ is the variance of the overdensity field smoothed on a scale $R$ and $\sigma^2_{\rm gal}$ is the variance of the overdensity field smoothed on a scale $R_{\rm gal}$, corresponding to a mass scale of $M_{\rm min}$ or $M_{\rm ion}$ (both evaluated at redshift $z$ rather than at $z = 0$ )."
 Equation (1)) may be integrated in time as a function of dg., Equation \ref{history}) ) may be integrated in time as a function of $\delta_R$.
 At a specified redshift this vields the filling fraction of ioniscd regions within the ICM. on various scales £& as a function. of overdensity., At a specified redshift this yields the filling fraction of ionised regions within the IGM on various scales $R$ as a function of overdensity.
 “Phis model. predicts. the sum of astrophwsical ellects. to. be. dominated: by galaxy bias. and that as a result. overdense regions are reionised first.," This model predicts the sum of astrophysical effects to be dominated by galaxy bias, and that as a result, overdense regions are reionised first."
" ""This leads to the growth of regions via a phase of percolation during which individual. regions overlap around clustered sources in overdense regions of the", This leads to the growth of regions via a phase of percolation during which individual regions overlap around clustered sources in overdense regions of the
sutiicicutly small ionization level. tiny eraius become the dominant charee carriers. and the non-ideal MIID diffusion cocfiicieuts behave very differently from the erain-free case.,"sufficiently small ionization level, tiny grains become the dominant charge carriers, and the non-ideal MHD diffusion coefficients behave very differently from the grain-free case."
 The Olunic conductivity is dominated by charged eraius rather than electrous when » exceeds about 1075..., The Ohmic conductivity is dominated by charged grains rather than electrons when $\bar{n}$ exceeds about $10^3n_e$.
 In the AD regime (strong maguctic field). Vall and AD cocfficicuts are stronely reduced by a factor of about μι)* relative to those in the Olunic regine Qveal magnetic feld). aud for sufficiently laree n/a. Tall dominated regime dininishes.," In the AD regime (strong magnetic field), Hall and AD coefficients are strongly reduced by a factor of about $(\bar{n}/n_e)^2$ relative to those in the Ohmic regime (weak magnetic field), and for sufficiently large $\bar{n}/n_e$, Hall dominated regime diminishes."
 We study the vole of tiny erains on the MBRI driven accretion in PPDs. aud find that novel behaviors occur when the tiny erains are suticicuthy abundant with span2100°. regardless of whether larger grains are xeseunt or not.," We study the role of tiny grains on the MRI driven accretion in PPDs, and find that novel behaviors occur when the tiny grains are sufficiently abundant with $x_{\rm PAH}\gtrsim10^{-9}$, regardless of whether larger grains are present or not."
 At the inner disk where accretion is avered. the predicted accretion rate iu the presence of inv eraius is oue to two orders of magnitude less than he erain-free case due to increased Olunic resistivity. but is similar to or higher than that with solar-abundauce Vigo erains.," At the inner disk where accretion is layered, the predicted accretion rate in the presence of tiny grains is one to two orders of magnitude less than the grain-free case due to increased Ohmic resistivity, but is similar to or higher than that with solar-abundance $0.1\mu$ m grains."
" A sharp increase in the predicted AL occurs at the transition radius rgag,c15 AU Gu the fiducial model) where the disk midplane becomes active. naking Olunic resistivity nrolevaut to the accretion rate."," A sharp increase in the predicted $\dot{M}$ occurs at the transition radius $r_{\rm trans}\approx15$ AU (in the fiducial model) where the disk midplane becomes active, making Ohmic resistivity irrelevant to the accretion rate."
 Quite unexpectedly. we find that at r-- inv eraius make acerction even more rapid than the erain-free case.," Quite unexpectedly, we find that at $r\gtrsim r_{\rm trans}$, tiny grains make accretion even more rapid than the grain-free case."
 Moreover. our predicted accretion rate increases with PAIT abundance.," Moreover, our predicted accretion rate increases with PAH abundance."
 These results are due to hat at large PAID abuudauce. ionizationrecombination valance makes s orders of maguitude larger thin p. and even excecds the eraim-free electron density ο at disk midplane.," These results are due to that at large PAH abundance, ionization-recombination balance makes $\bar{n}$ orders of magnitude larger than $n_e$, and even exceeds the grain-free electron density $n_{e0}$ at disk midplane."
" These facts prevent Olimic resistivity roni rapidly increasing as ""pag dacreascs. reduce the dissipation bv AD. thus facilitate the active laver to extend deeper iuto the disk midplane aud permut stronger MRI turbulence."," These facts prevent Ohmic resistivity from rapidly increasing as $x_{\rm PAH}$ increases, reduce the dissipation by AD, thus facilitate the active layer to extend deeper into the disk midplane and permit stronger MRI turbulence."
 Our results hiehlieht the importance of evaluating the full couductivity tensor in the calculation of the nou-ideal MIID diffusion cocticicuts rather than using the simple eraiu-free foriiulae (2))., Our results highlight the importance of evaluating the full conductivity tensor in the calculation of the non-ideal MHD diffusion coefficients rather than using the simple grain-free formulae \ref{eq:diff0}) ).
" We emphasize that the effects studied iu this paper mainly apply to tiny grains (=. 001,02). aud schen they are sufficicutly abundant GepagZ10 9)"," We emphasize that the effects studied in this paper mainly apply to tiny grains $\lesssim0.01\mu$ m), and when they are sufficiently abundant $x_{\rm PAH}\gtrsim10^{-9}$ )."
 For gius larger than 0.152. their abundance is at most 3.«410.72 per IT» molecule (for having 1% of mass). which is orders of magnitude smaller than 10.?.," For grains larger than $0.1\mu$ m, their abundance is at most $3\times10^{-12}$ per $_2$ molecule (for having $\%$ of mass), which is orders of magnitude smaller than $10^{-9}$."
 The reduction of AD cocfücient also exist for these relatively lareer eraius. as can be seen in the bottom panels of Figure 3 in (2011).. but its effect is πο more limited than the tiny erain case.," The reduction of AD coefficient also exist for these relatively larger grains, as can be seen in the bottom panels of Figure 3 in \citet{Bai11a}, but its effect is much more limited than the tiny grain case."
 When large exams aud tiny eraius coexist. the effect of large erains becomes ueeligible if repay210.9.," When large grains and tiny grains coexist, the effect of large grains becomes negligible if $x_{\rm PAH}>10^{-9}$."
 Although tiny grains strongly cuhauce PPD accretion in the outer disk. the situation at the inner disk is still siuilar to the case with O.ljan erains (Bai2011).. with predicted accretion rate unich less than the typical value of 10SAL. | as inferred from observations (ILutuinunctal.1998)..," Although tiny grains strongly enhance PPD accretion in the outer disk, the situation at the inner disk is still similar to the case with $0.1\mu$ m grains \citep{Bai11a}, with predicted accretion rate much less than the typical value of $10^{-8}M_{\odot}$ $^{-1}$ as inferred from observations \citep{Hartmann_etal98}. ."
 The receutle proposed far ultraviolet (PUV) ionization scenario docs uot provide aree accretion rate im the inner disk cither due to he small penetration depth of ΕΙΝ photons (PerezDecker&Cliang2011b)., The recently proposed far ultraviolet (FUV) ionization scenario does not provide large accretion rate in the inner disk either due to the small penetration depth of FUV photons \citep{PerezBeckerChiang11b}.
. Therefore. either additional ionization sources has to make the MBRI more efficient hau the XN-rawvs and FUVX photons (candidate may include euergetie protous from the protostars Clurner&Drake2009))). or additional mechanisni such as uagnetized wind (Sahnueronetal.2007) operates to xovide the augular moneutuni transport iu the inner cixk.," Therefore, either additional ionization sources has to make the MRI more efficient than the X-rays and FUV photons (candidate may include energetic protons from the protostars \citep{TurnerDrake09}) ), or additional mechanism such as magnetized wind \citep{Salmeron_etal07} operates to provide the angular momentum transport in the inner disk."
" Iu the case of trausitional disks characterized by mner roles or gaps (Calvetetal.2002:Espaillatct2007).. we note that the observationally inferred outer boundary of the holes or gaps is typically at a few τοις of AU (Ilughesetal.2009:ναι2009).. which is eenerallv greater than fray, du our models with PATIs."," In the case of transitional disks characterized by inner holes or gaps \citep{Calvet_etal02,Espaillat_etal07}, we note that the observationally inferred outer boundary of the holes or gaps is typically at a few tens of AU \citep{Hughes_etal09, Kim_etal09}, which is generally greater than $r_{\rm trans}$ in our models with PAHs."
" ""Therefore. the cuhancement of accretion bv tiny graius works effectively for transitional disks. aud N-ray driven MRI with PAIIS is able to feed the inner hole {σα at the (optimistic) rate of about 10SAL. Ἐν"," Therefore, the enhancement of accretion by tiny grains works effectively for transitional disks, and X-ray driven MRI with PAHs is able to feed the inner hole /gap at the (optimistic) rate of about $10^{-8}M_{\odot}$ $^{-1}$."
 This is sufficient to account for the observed accretion rate in transitional disks (Najitactal.2007:Sicilia-Aeuilaretal. 2010).. with the accreting gas fed. from the outer disk flowing through the hole / gap possibly guided by multiple plauets (Cliang&Aluray-Clav2007:Perez-Decker&Chiaug52011a:-Zhuotal. 2011).," This is sufficient to account for the observed accretion rate in transitional disks \citep{Najita_etal07,Sicilia_etal10}, with the accreting gas fed from the outer disk flowing through the hole / gap possibly guided by multiple planets \citep{CMC07,PerezBeckerChiang11,Zhu_etal11}."
. ιδιο thanks Jim Stone aud Jeremy Coocuan for carefully reading the manuscript with couuucuts. and Bruce Draine for useful discussions on PATIs.," X.-N.B thanks Jim Stone and Jeremy Goodman for carefully reading the manuscript with comments, and Bruce Draine for useful discussions on PAHs."
 Connuents from Daniel Perez-Becker aud the reterce. Eugene Chiang. are especially acknowledged which lead to several improvements to this work.," Comments from Daniel Perez-Becker and the referee, Eugene Chiang, are especially acknowledged which lead to several improvements to this work."
 This work is supported by NASA Ioeadquaters under the NASA Earth aud Space Science Fellowship Program. Ciraut NNNOQAQOOIL awarded to X.N.B. It has been shown iu Figure 1. and discussed im Section ??7. that near the transition radius rg Where the disk mudplane becomes active. the predictedaccretion rate AL increases sharply with radius. from well below the eraiu-free vate at r<<fran. to a factor of several higher at rofran.," This work is supported by NASA Headquaters under the NASA Earth and Space Science Fellowship Program Grant NNX09AQ90H awarded to X.N.B. It has been shown in Figure \ref{fig:acrate} and discussed in Section \ref{ssec:parameter} that near the transition radius $r_{\rm trans}$ where the disk midplane becomes active, the predictedaccretion rate $\dot{M}$ increases sharply with radius, from well below the grain-free rate at $r<r_{\rm trans}$ to a factor of several higher at $r>r_{\rm trans}$."
 We discuss the activation of the midplane by the MBI in this Appendix aud explain the sharp dependence of AL on disk radius near ria , We discuss the activation of the midplane by the MRI in this Appendix and explain the sharp dependence of $\dot{M}$ on disk radius near $r_{\rm trans}$ .
Figure AG shows the MRI permitted region iu our fiducial model at 10 and 16 AU between which lies the transition radius., Figure \ref{fig:transition} shows the MRI permitted region in our fiducial model at 10 and 16 AU between which lies the transition radius.
 We see from this plot that uch stronger magnetic field is permitted iu the disk midplane once it is activated. which is the cause of the bie jump in AM.," We see from this plot that much stronger magnetic field is permitted in the disk midplane once it is activated, which is the cause of the big jump in $\dot{M}$."
 Looking more closcly iuto the sharp transition. we find it is related to the dependence of the AD Elsasser uber Am on the maguetic field strength.," Looking more closely into the sharp transition, we find it is related to the dependence of the AD Elsasser number $Am$ on the magnetic field strength."
" We have shown in Figure 1. that 5j depends ou the magnetic field quadratically in weak (23, 1) aud strong (0;> 1) field regimesas conunonlv considered. but at the intexiiediate reeiue with j<jl< . ipa boehaves similarly as jo aud does not dependon the imaguetie field strength."," We have shown in Figure \ref{fig:model}
 that $\eta_A$ depends on the magnetic field quadratically in weak $\beta_e<1$ ) and strong $\beta_i>1$ ) field regimesas commonly considered, but at the intermediate regime with $\beta_i<1<\beta_e$ , $\eta_A$ behaves similarly as $\eta_O$ and does not dependon the magnetic field strength."
 Consequeuth. the," Consequently, the"
Iu seueral. we define the v; of an orgauisu as a continuous monotonous function of its parameters.,"In general, we define the $\chi_i$ of an organism as a continuous monotonous function of its parameters."
 Iu our particular case we define the fitness as the fuuction of the licht curve svuthesized from the orgauisuis parameters aud the observed light curve., In our particular case we define the fitness as the function of the light curve synthesized from the organisms parameters and the observed light curve.
" Since it is desirable that the fituess increases as the difference between the two light curves decreases, we define fituess as where sop. is the observed light curve containiusg AL points and s; is the Πο curve svuthesized from the organismi at exactly the same orbital phases preseut im Sole"," Since it is desirable that the fitness increases as the difference between the two light curves decreases, we define fitness as where $s_{\rm obs}$ is the observed light curve containing $M$ points and $s_i$ is the light curve synthesized from the organism $i$ at exactly the same orbital phases present in $s_{\rm obs}$."
 The GA starts with the random population of NV organisius which are sorted according to their fitness., The GA starts with the random population of $N$ organisms which are sorted according to their fitness.
" The miost-fit (better) half of thepopulation is sclected for reproduction. so that NYtb ""pareut pairs are randomly selected. (with better orgauisuis beime more probable to © selected than worse (less-fit) oreanisnis) and then two ""ehildren from each pair are created to replace the worse wif of the population."," The most-fit (better) half of thepopulation is selected for reproduction, so that $N/4$ “parent” pairs are randomly selected (with better organisms being more probable to be selected than worse (less-fit) organisms) and then two “children” from each pair are created to replace the worse half of the population."
" This ""reproduction process is formed analogously to the similar process in biology. i.c. the orgamisiis are ivided into Chromosomes aud then ie Chromosomes of the children are obtained from the Tromosonmes of the pareuts through process: fist child gets one part of the chromosome frou the first arent aud the second part from the second parent. while ie second child gets the first part from the second. aud 16 second part from the first parent."," This “reproduction” process is performed analogously to the similar process in biology, i.e. the organisms are divided into chromosomes and then the chromosomes of the children are obtained from the chromosomes of the parents through process: first child gets one part of the chromosome from the first parent and the second part from the second parent, while the second child gets the first part from the second and the second part from the first parent."
 This process converecs verv quickly to the nemrest al Πα., This process converges very quickly to the nearest local minimum.
" Tn order to avoid the ""stagnatioun of 16 population iu a local τή random ""mutatious are introduced. such as ""eopy-errors durius crossover. radon chauges of the individual genes (uunnubers). as well as the global unutatious such as the ""asteroid Lit”: a large uuber of the population is raduomly re-uitialized."," In order to avoid the “stagnation” of the population in a local minimum random “mutations” are introduced, such as “copy-errors” during crossover, random changes of the individual genes (numbers), as well as the global mutations such as the “asteroid hit”: a large number of the population is radnomly re-initialized."
 Our fitting process consists of two steps: This splitting of our method is necessary due to the limited computational resources., Our fitting process consists of two steps: This splitting of our method is necessary due to the limited computational resources.
 A inore general approach would involve au intrinsically lhrec-dinieusional disk geometry and would theu sunuultaucouslv minimize both the eecometrv and the temperature distribution., A more general approach would involve an intrinsically three-dimensional disk geometry and would then simultaneously minimize both the geometry and the temperature distribution.
 Towever. the nuunber of parameters that describe disk ecolmetry would be much larger than m our approach.," However, the number of parameters that describe disk geometry would be much larger than in our approach."
 Untortunately. these paraletcrs would only make a difference in a relatively siuall part of the leh curve lear the munimua. de. the amount of deviation from. he svuunetric shape.," Unfortunately, these parameters would only make a difference in a relatively small part of the light curve near the minima, i.e. the amount of deviation from the symmetric shape."
 Therefore. one would need to use a prohibitivelv laree number of orgauisuis with a uuch larger set of parameters to minimize the lig curve.," Therefore, one would need to use a prohibitively large number of organisms with a much larger set of parameters to minimize the light curve."
 Tusteacd. we Use Oll two-phase approach where he first phase can be thought of as the zeroth order hase (fitting of the ight curve with axisvuuuetric disk eniperature distribution aud an optional ho spot). whereas the second phase can be thought of as the first order correction (asviunetries dmn the disk temperature distribution introduce ireeularitics in the svuuuetric heht Curve Lua).," Instead, we use our two-phase approach where the first phase can be thought of as the zeroth order phase (fitting of the light curve with axisymmetric disk temperature distribution and an optional hot spot), whereas the second phase can be thought of as the first order correction (asymmetries in the disk temperature distribution introduce irregularities in the symmetric light curve minima)."
 We find this approach more practical at this time. due to the abovementionc: laited computational resources.," We find this approach more practical at this time, due to the abovementioned limited computational resources."
"abundances. we found a partial agreement with the observed. spectrum. for ,-=11200000 Ix. L—550 L. and o 1900 7.","abundances, we found a partial agreement with the observed spectrum for 000 K, L=550 $L_{\odot}$ and $_e$ = 1900 $^{-3}$."
 Important optical lines like4686A.. (4959A..5007A9). (6548A..6584A)) and. (6716N..6731.X)). are well reproduced. by this model. with discrepancies of or less.4471...A... 5," Important optical lines like, ), ) and ) are well reproduced by this model, with discrepancies of or less., ,"
412A.. ancl 5 11] ines agree with the observed. spectrum within ο., and [S ] lines agree with the observed spectrum within to.
 Other relatively intense lines such as 13729A)). Nell]3868A.. and sshow discrepancies of 10 with respect to 1e model," Other relatively intense lines such as ), ], and show discrepancies of to with respect to the model."
 Furthermore. the model. underestimates the intensities of the aand the lines by a factor of about 3.," Furthermore, the model underestimates the intensities of the and the lines by a factor of about 3."
 These lines are the keys [or he determination of the electron temperature., These lines are the keys for the determination of the electron temperature.
 Finally. the model underestimates Ni] aan Or] obv factors larger than 30.," Finally, the model underestimates ] and ] by factors larger than 30."
 Let us note. in addition. that his model requires a size for the core of 4.0 arcesec. twice he optical size observed.," Let us note, in addition, that this model requires a size for the core of 4.0 arcsec, twice the optical size observed."
 lt is then instructive to explore alternative scenarios., It is then instructive to explore alternative scenarios.
 Let us first note that in some PNe and related objects (see c.g. Corradi 1995). high aand line intensities have been interpreted. as the signature of very high core densities. as at Ny. lager than about 107 em5 the auroral aand 5755A)) to nebular aand 6583A)) line ratios are indicators of density rather than of temperature (Curzadvan 1970).," Let us first note that in some PNe and related objects (see e.g. Corradi 1995), high and line intensities have been interpreted as the signature of very high core densities, as at $N_e$ larger than about $^5$ $^{-3}$ the auroral and ) to nebular and ) line ratios are indicators of density rather than of temperature (Gurzadyan 1970)."
 For this reason. we have calculated: other models assuming much higher (albeit still constant) densities.," For this reason, we have calculated other models assuming much higher (albeit still constant) densities."
 As noted above. high core densities are implied by the radio size and tux CYaquist Ixwok 1990).," As noted above, high core densities are implied by the radio size and flux (Aaquist Kwok 1990)."
 CLOUDY models for the observed. radio core size. 0.25 arcsec. and such high densities (from 72)00 Ix up to 3.0 lem 7) show that both aand intensities can be now reproduced. but other. nebular lines. in. particular 3729A)). (6548A..6582A)). and. (6717N..6731A)). become now largely underestimated because of collisional quenching.," CLOUDY models for the observed radio core size, 0.25 arcsec, and such high densities (from 72000 K up to $3.0\times10^5$ $^{-3}$ ) show that both and intensities can be now reproduced, but other nebular lines, in particular ), ), and ), become now largely underestimated because of collisional quenching."
 A natural way to solve the problem might be to assume a strong density stratification in the core of Ix 4-47. with a very dense inner zone where aand aare mostly formed. and à lower density outer region where other important nebular lines are produced.," A natural way to solve the problem might be to assume a strong density stratification in the core of K 4-47, with a very dense inner zone where and are mostly formed, and a lower density outer region where other important nebular lines are produced."
 This idea should be tested by means of appropriate photoionization mocel: 3-D codes (like MIOCASSIN:an Ercolano et al., This idea should be tested by means of an appropriate photoionization model; 3-D codes (like MOCASSIN; Ercolano et al.
 2003) are much better suited than CLOUDY to deal with such extreme density. variations., 2003) are much better suited than CLOUDY to deal with such extreme density variations.
 In summary. we find that none of the constant density moclels is able to account. simultaneoulv. for all optical emission lines in theCore.," In summary, we find that none of the constant density models is able to account, simultaneouly, for all optical emission lines in the."
. In particular. the aand iintensities are strongly unclerstimated if the nebular density is the one derived empirically from the Ilines.," In particular, the and intensities are strongly understimated if the nebular density is the one derived empirically from the lines."
 A model with a strong density stratification could possibly oller a solution to the problem., A model with a strong density stratification could possibly offer a solution to the problem.
 The fact that we are not. able το provide an accurate representation of the sspectrum. also prevents us to determine the radiation escaping from the core and reaching the knots. and thus to attempt a reliable photoionization mocdellling of the latter.," The fact that we are not able to provide an accurate representation of the spectrum, also prevents us to determine the radiation escaping from the core and reaching the knots, and thus to attempt a reliable photoionization ling of the latter."
 A consistent photoionization modelling of the whole nebula (core|knots) would. also require a fully 3-D. modelling. that goes. beyond. the scopes of the present work.," A consistent photoionization modelling of the whole nebula (core+knots) would also require a fully 3-D modelling, that goes beyond the scopes of the present work."
 Given the evidence that the knots might be excited by shocks (Section., Given the evidence that the knots might be excited by shocks (Section.
 3.2). we instead attempt to describe their spectrum using existing shock moclels.," 3.2), we instead attempt to describe their spectrum using existing shock models."
 We have used the bow-shock models described in Raga ohm (1986) and Lartigan et al. (, We have used the bow-shock models described in Raga Bohm (1986) and Hartigan et al. (
LOST).,1987).
 We consider a bow shock with a functional form. τα=(αλ. where z is measured along the svmmetry axis. £r ds the cevlindrical radius. the parameter p determines the shape of the bow shock and the constant e determines its size (Beck οἱ al.," We consider a bow shock with a functional form, $z/a= (r/a)^p$, where $z$ is measured along the symmetry axis, $r$ is the cylindrical radius, the parameter $p$ determines the shape of the bow shock and the constant $a$ determines its size (Beck et al."
 )H)., 2004).
 The emission. from the bow-shock is modeled. as escribeck by Llartigan ct al. (, The emission from the bow-shock is modeled as described by Hartigan et al. (
LOST). being the geometry of the bow shock the parameter that determines the shock velocity.,"1987), being the geometry of the bow shock the parameter that determines the shock velocity."
 The plane-paralel shock models required. to predict the bow-shock emission line. ratios are obtained with the photoionization-shock code \LAPPINGS Ic., The plane-paralel shock models required to predict the bow-shock emission line ratios are obtained with the photoionization-shock code MAPPINGS Ic.
.. We have adopted a pre-shock density of 400 em7. that is within the range generally assumed. for stellar jets.," We have adopted a pre-shock density of 400 $^{-3}$, that is within the range generally assumed for stellar jets."
 The pre-shock magnetic field was taken to be negligible., The pre-shock magnetic field was taken to be negligible.
 We assumed clemmenttal abundances for He. C... N.. Ο. Ne. ο. and Ar to be within the range of “Pype-l PN values.," We assumed tal abundances for He, C, N, O, Ne, S, and Ar to be within the range of Type-I PN values."
 As for 10 preionization of the gas. local equilibrium. is assumed.," As for the preionization of the gas, local equilibrium is assumed."
 We consider the bow-shock velocity as a free parameter. aclopting a set of values from 50 to 300 km ," We consider the bow-shock velocity as a free parameter, adopting a set of values from 50 to 300 km $^{-1}$."
We have obtained the best fit to the observed. spectra for p=3., We have obtained the best fit to the observed spectra for $p$ =3.
 X summary of the results is presented in Figure 4 for a number of emission line ratios plotted as a function of6583A//lla., A summary of the results is presented in Figure \ref{bshock} for a number of emission line ratios plotted as a function of.
 Note that the later line ratio increases in strength as the shock velocity increases. and in the case of Ix 4-47 is matched by only the largest: shock velocities considered. somewhat larger than the estimate of 150 bby Corradi et al. (," Note that the later line ratio increases in strength as the shock velocity increases, and in the case of K 4-47 is matched by only the largest shock velocities considered, somewhat larger than the estimate of 150 by Corradi et al. ("
2000).,2000).
 For these velocities. the bow-shock models fit pretty. Νο the. πο ratios ΓΡ4072A//6725A.. and.755A... sensitive to8 the temperature in the recombination zone/5 where aand," For these velocities, the bow-shock models fit pretty well the line ratios $\equiv$, and, sensitive to the temperature in the recombination zone where and"
"and A,=884x1027.»c),2i"" kev .? Note that (he entropy of the eeas is initially constant at A,[n and then increases as a power law with index 1.28 as long as 2 remains constant in (he outer region (see Fig.",and $K_{o}=8.84\times10^{-7}\mu\mu_{e}^{2/3}Q_{o}^{-2/3}$ kev $^{-2}$ Note that the entropy of the gas is initially constant at $K_{o}$ and then increases as a power law with index 1.28 as long as $\beta$ remains constant in the outer region (see Fig.
 1)., 1).
 We emplhasize (hat inherent in equation (5) is (lie assumption that the entropy of the gas is (he same as the entropy of the dark matter aud (that as merging continues the increase in entropy is Che same for both components., We emphasize that inherent in equation (5) is the assumption that the entropy of the gas is the same as the entropy of the dark matter and that as merging continues the increase in entropy is the same for both components.
 Thus this value of IX must be a lower limit to the actual gas entropy. ancl as such it provides a floor on which gas physics processes (i.e. cooling. heating. astration etc.)," Thus this value of K must be a lower limit to the actual gas entropy and as such it provides a floor on which gas physics processes (i.e. cooling, heating, astration etc.)"
 can be plaved out., can be played out.
 The characteristics of a representative model (in this ease for the galaxy cluster AT639) are shown in Fig., The characteristics of a representative model (in this case for the galaxy cluster A1689) are shown in Fig.
 1., 1.
 Asa test of the model we apply it to three regimes of total mass: LSB galaxies. clusters of galaxies and cwarf spheroidal galaxies.," As a test of the model we apply it to three regimes of total mass: LSB galaxies, clusters of galaxies and dwarf spheroidal galaxies."
 llavashi et al. (, Hayashi et al. (
2004) have derived best fit rotation curves for a sample of LSB ealaxies using the NEW density prolile.,2004) have derived best fit rotation curves for a sample of LSB galaxies using the NFW density profile.
 They divided their fits into three categories., They divided their fits into three categories.
 The first ( class) provided good fits to (he observations., The first (A class) provided good fits to the observations.
 The second (D class) included galaxies which could not be satisfactorily fit with ACDALcompatible parameters., The second (B class) included galaxies which could not be satisfactorily fit with $\Lambda$ CDM-compatible parameters.
 Galaxies in the third group (C class) have irregular rotation curves., Galaxies in the third group (C class) have irregular rotation curves.
 Fig., Fig.
" 2 shows the fits of the circular velocity (GM,/7r)? of our model to four of the galaxies investigated by IIavashi et al.", 2 shows the fits of the circular velocity $_{r}/r)^{1/2}$ of our model to four of the galaxies investigated by Hayashi et al.
 The observational data is from AleGaugh et al., The observational data is from McGaugh et al.
 2001 and is available at http://www.astro.umd.edu/ ssm/data., 2001 and is available at http://www.astro.umd.edu/ ssm/data.
 Following Havashi et al., Following Hayashi et al.
 we let the smallest uncertainty in velocity be £5hinsee|., we let the smallest uncertainty in velocity be $\pm 5~ kmsec^{-1}$.
 The above model provides aclequate fits to both class A and class B samples., The above model provides adequate fits to both class A $and$ class B samples.
 Parameters for the class A galaxies (3.41x10.7.1.1.0.254. 1.92) for ESO2060140 and (1.2x107.1.83.0.110. 1.92) for F563-1 show sienilicantlyv higher central densities (and ως se 0.3) (han the D group galaxies (3.5x107.5.1.5.71LO 7.1.92) for ESOOS40411 and (1.68x107.6.0.8.28LO 7.1.92)," Parameters for the class A galaxies $3.41\times10^{-7},1.1,0.254,1.92$ ) for ESO2060140 and $1.2\times
10^{-7}
,1.83,0.110,1.92$ ) for F563-1 show significantly higher central densities (and $\beta_{max}$ $\sim0.3$ ) than the B group galaxies $3.5\times10^{-8},5.1,5.71\times10^{-3},1.92$ ) for ESO0840411 and $1.68\times10^{-8},6.0,8.28\times10^{-3},1.92$ )"
as the MWA develops.,as the MWA develops.
 As more tiles are added. significantly over conystrainiug the parameters of the array. a clirection clepeudent calibration scheme as described in ?.. with a more accurate weighting scheme incorporating the cliffereuces between tiles. will be applied tu the visibility doimaiu.," As more tiles are added, significantly over conystraining the parameters of the array, a direction dependent calibration scheme as described in \cite{mgw+08}, with a more accurate weighting scheme incorporating the differences between tiles, will be applied in the visibility domain."
 The 2x2 Jones matrix of a radio telescope is generally decomposed into: where G is the electroute gain. D represent the [eed errors. C is the configuration of the feed response. P is parallactie rotation aud F is Faraday rotation.," The 2x2 Jones matrix of a radio telescope is generally decomposed into: where $\gain$ is the electronic gain, $\dterms$ represent the feed errors, $\config$ is the configuration of the feed response, $\para$ is parallactic rotation and $\fara$ is Faraday rotation."
 We lave not attempted to correct [or Faraday rotation iu the experiment. the ramificatious of which are explored in 81.," We have not attempted to correct for Faraday rotation in the experiment, the ramifications of which are explored in \ref{sec:stokes}."
 Iu our application the dipoles do uot rotate relative to the source. but the projection of the dipoles changes ou the sky.," In our application the dipoles do not rotate relative to the source, but the projection of the dipoles changes on the sky."
 Where Jp is the dipole projection matrix given by L. D and H are latitude. declination and hour augle respectively.," Where $\project$ is the dipole projection matrix given by $L$, $D$ and $H$ are latitude, declination and hour angle respectively."
 In the calibration stage of the lunagineg pipeline (?) the Jones matrices of the individual anteuna elements are solved for. which essentially allows G aud D to be obtained. but they are incorporated in the fitted Joues matrix and not decomposed.," In the calibration stage of the imaging pipeline \citep{mgw+08} the Jones matrices of the individual antenna elements are solved for, which essentially allows $\gain$ and $\dterms$ to be obtained, but they are incorporated in the fitted Jones matrix and not decomposed."
 The 32T calibration scheme attempts to solve for the elements of the diagoual G matrix ancl the rest of the matrices are assumed to be the same for all tiles., The 32T calibration scheme attempts to solve for the elements of the diagonal $\gain$ matrix and the rest of the matrices are assumed to be the same for all tiles.
 Thus individual beams can be scaled. aud shifted (the elements are complex) but not chauged iu shape., Thus individual beams can be scaled and shifted (the elements are complex) but not changed in shape.
 This is required by the limited seusitivity of the 327 array., This is required by the limited sensitivity of the 32T array.
 The welght matrix must be constructed for every iuput sky pixel aud in the 32T RTS is at the begiuning of each ~3 minute integration., The weight matrix must be constructed for every input sky pixel and in the 32T RTS is pre-computed at the beginning of each $\sim$ 3 minute integration.
 For each pixel the image coordinates (£ and i’) are converted into a topocenirie hour angle anc declination., For each pixel the image coordinates $\ell^{\prime}$ and $m^\prime$ ) are converted into a topocentric hour angle and declination.
 In this process account has to be taken of the initial orthographicS projection. and the required1 spherical coordinates.," In this process account has to be taken of the initial orthographic projection, and the required spherical coordinates."
 The moclel of the beam is then formed as the stun of 16 dipoles with a phase delay commensurate with the required tile pointing centre., The model of the beam is then formed as the sum of 16 dipoles with a phase delay commensurate with the required tile pointing centre.
 The complex gain of the tile iu the desired pixel direction is then calculated and the Jones matrix for that pixel (Jp) formed., The complex gain of the tile in the desired pixel direction is then calculated and the Jones matrix for that pixel $ \jones_{pix}$ ) formed.
to replicate Ive Richter’s pu study with our more modern cata.,to replicate Iye Richter's \shortcite{ir85} study with our more modern data.
 We found .X(CDV)=0.72£0.18. identical to the canonical Milky Way value for Ay=3.1. and no reason to prefer By=2.5 over Ry=3.1 to describe the distribution of (6V3 against (5.," We found $X(UBV)=0.72\pm0.13$, identical to the canonical Milky Way value for $R_V=3.1$, and no reason to prefer $R_V=2.5$ over $R_V=3.1$ to describe the distribution of $\langle B-V\rangle$ against $\langle V\rangle$."
 While we thus find no evidence for radial variation in the M31. extinction law from GC colours. studies using other methods and classes of objects would be helpful to confirm our conclusions.," While we thus find no evidence for radial variation in the M31 extinction law from GC colours, studies using other methods and classes of objects would be helpful to confirm our conclusions."
 Aside from being more heavily-reddened. which we have argued to be a selection elfect. the brightest globular clusters in M31 are not particularly unusual.," Aside from being more heavily-reddened, which we have argued to be a selection effect, the brightest globular clusters in M31 are not particularly unusual."
 As noted above. they tend to be metal-rich: all have Fe/LI]=1. while the M31 median is Fe/H]=1.15 (Xurmbvetal.2000).," As noted above, they tend to be metal-rich; all have ${\rm [Fe/H]}\geq-1.1$, while the M31 median is ${\rm [Fe/H]}=1.15$ \cite{b00}."
 Djorgovski et shortceitedj97 measurecl velocity dispersions for 21 clusters including 000O01. 023078. and 225280: these three objects had the three highest velocity dispersions.," Djorgovski et \\shortcite{dj97} measured velocity dispersions for 21 clusters including 000–001, 023–078, and 225–280; these three objects had the three highest velocity dispersions."
 ALL three rave values of a.~25 kms +. indicating that they have 1e large masses which would be expected for such bright objects.," All three have values of ${\sigma}_v \sim 25$ km $^{-1}$, indicating that they have the large masses which would be expected for such bright objects."
 Phe cluster 000001. also known as Gl or Mavall LL. iw been the subject of several high-resolution imaging studies (Pritchet&vandenBereh1984:Richetal.1996:AMevlanetal. 2001).. all of which noted that it was quite lutened. with e=1.bfa-t2.," The cluster 000–001, also known as G1 or Mayall II, has been the subject of several high-resolution imaging studies \cite{pv84,ric96,mey01}, all of which noted that it was quite flattened, with $\epsilon=1-b/a \sim 0.2$."
 Mevlan οἱ shorteitemevOl find that. like the bright \lilky Way cluster w Con. 000001 shows evidence for a metallicity spread. ancl suggest that it may in fact be the core of a dwarf elliptical galaxy.," Meylan et \\shortcite{mey01} find that, like the bright Milky Way cluster $\omega$ Cen, 000–001 shows evidence for a metallicity spread, and suggest that it may in fact be the core of a dwarf elliptical galaxy."
 Llubble Space Telescope. observations of 225280 (Peecietal.1996:Stephens2001). show it to be a very metal-rich (Fe/H]~—(0.3. somewhat higher than the spectroscopic metallicity) but otherwise unremarkable cluster.," Hubble Space Telescope observations of 225–280 \cite{fp96,s01} show it to be a very metal-rich ${\rm [Fe/H]}\sim-0.3$, somewhat higher than the spectroscopic metallicity) but otherwise unremarkable cluster."
 The ellipticities of the other brightest. clusters. as measured by Staneva. Spassova Coley (1996)..ha range from 0.02 to 0.08. well within the range of values thefainter clusters.," The ellipticities of the other brightest clusters, as measured by Staneva, Spassova Golev \shortcite{ssg96}, range from 0.02 to 0.08, well within the range of values for the fainter clusters."
 The remarkable object 037.D327is an M31. globular cluster., The `remarkable object 037–B327' an M31 globular cluster.
 It is extremely reddened. with(2V)=132+ 1.05. and extremely luminous(almost four times as luminous as the brightest Alilky Way globular).," It is extremely reddened, with $E(B-V)=1.32\pm0.05$ , and extremely luminous (almost four times as luminous as the brightest Milky Way globular)."
 However. its racial velocity anc metallicity are entirely unremarkable.," However, its radial velocity and metallicity are entirely unremarkable."
 We use he M31 elobular clusters” reddening values to examine van den Bereh’s (1968). argument than the value of 4 in M31 cillers significantly from that in the Milkv Way.," We use the M31 globular clusters' reddening values to examine van den Bergh's \shortcite{vdb68}
 argument than the value of $R_V$ in M31 differs significantly from that in the Milky Way."
 We ind that the brighter clusters are more heavilv-reddened. out. suggest that this is a combination of two other elfects: selection bias in a magnitude-LIimited. sample. ancl variation in the M31 GCLE with distance from the galaxy centre.," We find that the brighter clusters are more heavily-reddened, but suggest that this is a combination of two other effects: selection bias in a magnitude-limited sample, and variation in the M31 GCLF with distance from the galaxy centre."
 A racial variation in Z in M31 could possibly account for the GCLE variation and the reddening/maesnitude distribution. but there is at present no evidence for such a variation.," A radial variation in $R_V$ in M31 could possibly account for the GCLF variation and the reddening/magnitude distribution, but there is at present no evidence for such a variation."
 We thank M. Lewin for help measuring APAL coordinates. J. luchra and D. Hanes for helpful cliscussions. ane our collaborators on the WYEEOS project for permission o publish the O37D327 data in advance of the main xiblication.," We thank M. Irwin for help measuring APM coordinates, J. Huchra and D. Hanes for helpful discussions, and our collaborators on the WYFFOS project for permission to publish the 037–B327 data in advance of the main publication."
 The Digitized Sky Survey was produced at the Space Telescope Science Institute under. U.S. Government erant NAC W-2166., The Digitized Sky Survey was produced at the Space Telescope Science Institute under U.S. Government grant NAG W-2166.
. The images of these surveys are xwed. On photographic data obtained using the Oschin Schmidt Telescope on Palomar Mountain. ancl the Uly Schmidt Telescope., The images of these surveys are based on photographic data obtained using the Oschin Schmidt Telescope on Palomar Mountain and the UK Schmidt Telescope.
 Lhe plates were processed. into the resent compressed digital form with the permission of these institutions., The plates were processed into the present compressed digital form with the permission of these institutions.
in the FIR.,in the FIR.
 In our case a larger fraction of the absorbed cnerey is radiated at shorter wavelengths because of the sunall particles that are temporarily heated to πιο higher temperatures., In our case a larger fraction of the absorbed energy is radiated at shorter wavelengths because of the small particles that are temporarily heated to much higher temperatures.
 We have calculated FIR cussion aud [CTI] line ‘uuission for tlacedimensional density distributions of compressible maenetolvdrodvuamic turbulent flows with riis sonic Mach uuubers Mg= 0.6. 2.5. and 10.0.," We have calculated FIR emission and [CII] line emission for three–dimensional density distributions of compressible magneto–hydrodynamic turbulent flows with rms sonic Mach numbers $M_{\rm S}=$ 0.6, 2.5, and 10.0."
 The dust cuission. Zgpi. is computed with full radiative transfer caleulatious.," The dust emission, $I_{\rm FIR}$, is computed with full radiative transfer calculations."
 The [CTI] Cluission is estimated assunüug the plotoclectric eating caused by FUVphotous between 0.0912; and 0.2066/20 is balanced by [CTI line enission., The [CII] emission is estimated assuming the photoelectric heating caused by FUV photons between $\mu$ m and $\mu$ m is balanced by [CII] line emission.
 The FUV absorption is determined by the radiative vauster simulations. and is asstmed to be equal o the [CT] line intensity divided by the unkuown cfhicieucy. of the photoclectric heating. Loyp/e.," The FUV absorption is determined by the radiative transfer simulations, and is assumed to be equal to the [CII] line intensity divided by the unknown efficiency of the photoelectric heating, $I_{\rm CII}/\epsilon$."
 The ratio Zegi/(efgi) is in all models yetwoeen 0.50 aud 0.58. showing that its depenudenuce on the density contrast (Mach πο). is weal.," The ratio $I_{\rm CII}/(\epsilon I_{\rm FIR})$ is in all models between 0.85 and 0.88, showing that its dependence on the density contrast (Mach number) is weak."
 However. dense fluueuts are visible iu the maps as regions with lower value of {ο/(efpua).," However, dense filaments are visible in the maps as regions with lower value of $I_{\rm CII}/(\epsilon I_{\rm FIR})$."
 The deeree of correlation between JZeg/(efgig) aud visual extinction decreases in more mlonmogenueous clouds., The degree of correlation between $I_{\rm CII}/(\epsilon I_{\rm FIR})$ and visual extinction decreases in more inhomogeneous clouds.
" Iu the case of simmlated observations convolved to different. resolutions (71"" for (CTI and  for FIR) inmost of the corr‘lation is lost.", In the case of simulated observations convolved to different resolutions $\arcsec$ for [CII] and $\sim$ $\arcmin$ for FIR) most of the correlation is lost.
 The scatter in the observational (Εις.[ο] /ε) uot eau be reproduced by models with rms Mach nunher Ma 72 (supersonic turbulence). showing hat iuost of the scatter may bo due to the inhomogencous nature of the clouds (likely du o the turbulence}.," The scatter in the observational $I_{\rm FIR}$ $I_{\rm CII}/\epsilon$ ) plot can be reproduced by models with rms Mach number $M_{\rm S}\ga$ 2 (supersonic turbulence), showing that most of the scatter may be due to the inhomogeneous nature of the clouds (likely due to the turbulence)."
 Iun subsonic models (Ma. Z1) voth the scatter and the total range of FIR and [CTI] intensities become smaller than in he observed clouds., In subsonic models $M_{\rm S}\la$ 1) both the scatter and the total range of FIR and [CII] intensities become smaller than in the observed clouds.
 Using the empirical value louσι. «10.7? found for high latitude clouds (Iugallsetal.2002) the cfiiciency of the photoelectric reating+ is+ found. to be €—E2.9«10D7., Using the empirical value $I_{\rm CII}/I_{\rm FIR}$ $\times 10^{-2}$ found for high latitude clouds \citep{ingalls02} the efficiency of the photoelectric heating is found to be $\epsilon \sim 2.9\times 10^{-2}$.
 Thed value is very close to the theoretical predictions for the cold neutral mecdimm., The value is very close to the theoretical predictions for the cold neutral medium.
 ALJ acknowledges the support from the Academy of Finlaud Grants no., MJ acknowledges the support from the Academy of Finland Grants no.
 171851 aud 175068., 174854 and 175068.
 The work of PP was partially performed while PP held a National Research Council Associateship Award at the Jet Propulsion Laboratory. California Institute of Technologv.," The work of PP was partially performed while PP held a National Research Council Associateship Award at the Jet Propulsion Laboratory, California Institute of Technology."
 The work of RJ is supported in part by NSF evant AST-0206031., The work of RJ is supported in part by NSF grant AST-0206031.
observationa bandpass.,observational bandpass.
 Note that the Q [actors may cliauge as eas pressure. leigth of liglit. path auc temperaure changes.," Note that the Q factors may change as gas pressure, length of light path and temperature changes."
 The precision also depends on the methods used in tie. RV calibration., The precision also depends on the methods used in the RV calibration.
 We categorized tie calibration methliods into several cases: Suyejniposiug. in whch the calibration spectrum 1s impjuted outo a stellar spectrum: Nou-Comiuo1 Path aid. Brackeing. in which the calibration is coiducted either spatially or temporally.," We categorized the calibration methods into several cases: Superimposing, in which the calibration spectrum is imprinted onto a stellar spectrum; Non-Common Path and Bracketing, in which the calibration is conducted either spatially or temporally."
 The fDu—jer inethod depeids on stellar flux while the latter «yue cau only be applicable for very stable iusI'lments., The former method depends on stellar flux while the latter one can only be applicable for very stable instruments.
 There are other calibratiO1 sources we Lave rot iuclucecd iuto the discussions in this studV. [or example. laser combs (??).. the Fab'v-Perot. calibrator (?) and the Monolithic Michelson Iuterferometer (?)..," There are other calibration sources we have not included into the discussions in this study, for example, laser combs \citep{Steinmetz2008,Li2008}, the Fabry-Perot calibrator \citep{Wildi2010} and the Monolithic Michelson Interferometer \citep{Wan2010}."
 Once they becone More econoluicaly allordable or more technically reads. the RV precision will be greatly improved in the future.," Once they become more economically affordable or more technically ready, the RV precision will be greatly improved in the future."
 For the first tiue we have quantitatively estimated the uncertainty caused by the residu: of telluri¢ contamiuation removal for high resolution echelle spectroscopy method., For the first time we have quantitatively estimated the uncertainty caused by the residual of telluric contamination removal for high resolution echelle spectroscopy method.
 Depencing « the tellric absorplion. different. observational baudgasses are affected. dillerently.," Depending on the telluric absorption, different observational bandpasses are affected differently."
 B. band is t least sersitive to teurie Contamination because there are παον αν telluric absorption featur in B baxl., $B$ band is the least sensitive to telluric contamination because there are barely any telluric absorption features in $B$ band.
 However. the NIB. bands suffer the 1105 in precision RV measurements because t stellar a»sorptioi lies alid telluric liles are mixed logeher severely in this spectral region.," However, the NIR bands suffer the most in precision RV measurements because the stellar absorption lines and telluric lines are mixed together severely in this spectral region."
 Oily when a «0.01. Le.. nore than of streneth of telluri les is reuoved. the advantage of NIB observation of ruiate type M dwars begins to : chi ds a factor of 3 improvement.," Only when $\alpha\leq$ 0.01, i.e., more than of strength of telluric lines is removed, the advantage of NIR observation of mid-late type M dwarfs begins to show, which is a factor of 3 improvement."
 This quantitative met —1 estimatiug t ehVuiceral ced by ellurie Contamination can be easily adapted to ier problems. lor exaiuple. es e moou light coutanmidluatlon.," This quantitative method in estimating the RV uncertainty induced by telluric contamination can be easily adapted to other problems, for example, estimating the moon light contamination."
 Besicles tellu‘ic line removal. tellurie line liassl as also EOLL ciscussecl in several of previous studies (2??)..," Besides telluric line removal, telluric line masking has also been discussed in several of previous studies \citep{Reiners2010, Rodler2011, Wang2011}."
 In ? ellurie absorption with depth more tal all 30 kms! in the vicinity is blocked out when measuriug RV.," In \citet{Reiners2010}, telluric absorption with depth more than and 30 $\rm{km}\cdot\rm{s}^{-1}$ in the vicinity is blocked out when measuring RV."
" Based ou this blocki180 criteriu11. the photou-limited RV uncertainty. Ou, «(refer to Equation (6))). for a1 M9Vstar at R=!LOO.000. is D3.0. 2.2. D+)3.9. n-| in V Y. Ja4 H band respectively (see Table 6 J."," Based on this blocking criterium, the photon-limited RV uncertainty, $\delta v_{rms, S}$ (refer to Equation \ref{eq:simple_example_tulleric_2}) )), for an M9Vstar at $\rm{R}$ =100,000 is 3.9, 2.2, 3.9, 2.2 $\rm{m}\cdot\rm{s}^{-1}$ in $V$, $Y$ , $J$ and $H$ band respectively (see Table \ref{tab:Comp_Reiners}) )."
 In compπο. OUμην IS T1.3. 0.5. 6.5. 3.7 1n-S1 i nV y. J aud A baud respectively.," In comprison, $\delta v_{rms, N}$ is 71.3, 5.8, 6.5, 3.7 $\rm{m}\cdot\rm{s}^{-1}$ in $V$, $Y$, $J$ and $H$ band respectively."
 Excep for V nud. 9csuus axd CrusN are al the same orc ero. uuagnuitude. aud the incertaluly caused by telu‘ic absorption cannot be jegleced even thotwh that the spectral region with auy telluric absorpion of more han Is locked.," Except for $V$ band, $\delta v_{rms, S}$ and $\delta v_{rms, N}$ are at the same order of magnitude, and the uncertainty caused by telluric absorption cannot be neglected even though that the spectral region with any telluric absorption of more than is blocked."
 It more strict criterium of telluric liue maskinο is applied. fewer photous are considered i neasuring the RV which ellectively increases the ploou-limited RV uncedallty.," If more strict criterium of telluric line masking is applied, fewer photons are considered in measuring the RV, which effectively increases the photon-limited RV uncertainty."
 In order to reach jxhotor-limited RV oecisiou predicted by pure couskeration of spectral €) factor. telluric removal should be appliec in which telluric contamination is 1jeasttred. or moclelec all then removed Grom JeastL'ed stellar προστιlu.," In order to reach photon-limited RV precision predicted by pure consideration of spectral Q factor, telluric removal should be applied in which telluric contamination is measured or modeled and then removed from measured stellar spectrum."
 RV uncertaluy due to stellar granulation is taken iito consideration in thispaper., RV uncertainty due to stellar granulation is taken into consideration in thispaper.
 Hie1 requeicy (uin stellar noise such as p-inode oscillations isually lave a RV amplitude of 0.1 to IJO ins alid they can be averaged out within typical 10—15 exposure titje., High frequency $\sim$ min) stellar noise such as p-mode oscillations usually have a RV amplitude of 0.1 to 4.0 $\rm{m}\cdot\rm{s}^{-1}$ \citep{Schrijver2000} and they can be averaged out within typical $-$ 15 exposure time.
 RV uncertaluties ue to low [requeicy (10—LOO day) stellar noise such as stelar spots have been cliscussed in recent papers. lor examje. ? aud 2..," RV uncertainties due to low frequency $10-100$ day) stellar noise such as stellar spots have been discussed in recent papers, for example, \citet{Desort2007} and \citet{Reiners2010}. ."
 The amplitudes of spot-iidlucedRV rauge from oue to several liuuxdred ms fF , The amplitudes of spot-inducedRV range from one to several hundred $\rm{m}\cdot\rm{s}^{-1}$ .
Since stellar spot iuduced RV uucertaiutjes are periodic aud therelore cau be, Since stellar spot induced RV uncertainties are periodic and therefore can be
the wines of the window. depending upon the nature of the orbital parameter uncertainties.,"the wings of the window, depending upon the nature of the orbital parameter uncertainties."
 The described techuiques and scieuce goals are currently being undertaken aud investigated= by the Transit Ephemeris Refinement aud Monitoring Survey (TERMS)., The described techniques and science goals are currently being undertaken and investigated by the Transit Ephemeris Refinement and Monitoring Survey (TERMS).
 Note that the observations from tlis survey will lead. to improved exoplauet orbital parameters aud ephemerides even without au eventual trausit detection for a particular planet., Note that the observations from this survey will lead to improved exoplanet orbital parameters and ephemerides even without an eventual transit detection for a particular planet.
 The results from this survey will provide a complimentary dataset to the fainter magnitude range of the Nepler mission (Boruckietal. 2009).. which is expected to discover niu transiting plauets iucludiug those of intermediate to long-period planets.," The results from this survey will provide a complimentary dataset to the fainter magnitude range of the Kepler mission \citep{bor09}, which is expected to discover many transiting planets including those of intermediate to long-period planets."
 The authors would like to thauk Steven Berukoff for several useful sugeestious., The authors would like to thank Steven Berukoff for several useful suggestions.
 This research has made use of the NASA/IPAC/NExScI Star and Exoplauct Database. which is operated by the Jet Propulsion Laboratory. California Institute of Technology. under coutract with the National Acronautics and Space Adininistration.," This research has made use of the NASA/IPAC/NExScI Star and Exoplanet Database, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration."
"We conclude that uncertainty in the PSF used for the primary deconvolution will lead to uncertainties of only a few percent in the measured flux of point sources, but can become of greater significance for the diffuse background.","We conclude that uncertainty in the PSF used for the primary deconvolution will lead to uncertainties of only a few percent in the measured flux of point sources, but can become of greater significance for the diffuse background."
" While the results show some robustness with respect to PSF errors, great care should be taken, nevertheless, when extracting the primary PSF, particularly its extended wings."," While the results show some robustness with respect to PSF errors, great care should be taken, nevertheless, when extracting the primary PSF, particularly its extended wings."
 This process is unfortunately never free of subjectivity and requires some experience., This process is unfortunately never free of subjectivity and requires some experience.
 It is always recommendable to check the residuals and the diffuse flux related to the area of the image where the PSF reference star(s) is (are) located., It is always recommendable to check the residuals and the diffuse flux related to the area of the image where the PSF reference star(s) is (are) located.
" As an independent check of the photometric accuracy, we compared the photometric uncertainties derived from our algorithm (i.e., formal plus PSF uncertainties) with the uncertainties derived by comparing the measurement of stars present in all four dither positions of the H-band observations."," As an independent check of the photometric accuracy, we compared the photometric uncertainties derived from our algorithm (i.e., formal plus PSF uncertainties) with the uncertainties derived by comparing the measurement of stars present in all four dither positions of the $H$ -band observations."
" We extracted a PSF from the guide star, 77, for each of the images corresponding to the four dither positions."," We extracted a PSF from the guide star, 7, for each of the images corresponding to the four dither positions."
 The images were then deconvolved with the linear Wiener filter algorithm., The images were then deconvolved with the linear Wiener filter algorithm.
" Finally, local PSF fitting was performed on the deconvolved images."," Finally, local PSF fitting was performed on the deconvolved images."
 A scaling factor of 3.3 was applied to the formal uncertainties given by the PSF fitting algorithm to account for the under-estimation of uncertainties in deconvolved images (see refsec:noise))., A scaling factor of $3.3$ was applied to the formal uncertainties given by the PSF fitting algorithm to account for the under-estimation of uncertainties in deconvolved images (see \\ref{sec:noise}) ).
 The lists of detected point sources in the overlapping subframes and the smooth background estimates and residuals for the overlapping subframes were combined as described in refsec:spatial.., The lists of detected point sources in the overlapping subframes and the smooth background estimates and residuals for the overlapping subframes were combined as described in \\ref{sec:spatial}.
 Uncertainties were calculated by quadratically combining the formal fit uncertainties with the PSF uncertainties., Uncertainties were calculated by quadratically combining the formal fit uncertainties with the PSF uncertainties.
 For stars without multiple measurements., For stars without multiple measurements.
 we adopted a PSF uncertainty of 0.02 mmag (see refFig:dphotlinloc))., we adopted a PSF uncertainty of $0.02$ mag (see \\ref{Fig:dphotlinloc}) ).
 The uncertainties derived from the algorithm (formal plus PSF uncertainties) are compared with those obtained from the four independent measurements in the overlapping fields in refFig:dphotcheck.., The uncertainties derived from the algorithm (formal plus PSF uncertainties) are compared with those obtained from the four independent measurements in the overlapping fields in \\ref{Fig:dphotcheck}.
 The uncertainties appear to be uncorrelated and of similar magnitude., The uncertainties appear to be uncorrelated and of similar magnitude.
 More than 91% (50%) of the stars have a photometric uncertainty smaller than 0.05 mmag (0.03 mmag)., More than $91\%$ $50\%$ ) of the stars have a photometric uncertainty smaller than $0.05$ mag $0.03$ mag).
" The bottom panel of refFig:dphotcheck shows plot of the photometric uncertainty versus magnitude for all astars detected in the combined (i.e., all four dither positions) FOV."," The bottom panel of \\ref{Fig:dphotcheck} shows a plot of the photometric uncertainty versus magnitude for all stars detected in the combined (i.e., all four dither positions) FOV."
" To exclude spurious sources that may possibly originate in the deconvolved images, we excluded stars that are not also detected by local PSF fitting without prior deconvolution."," To exclude spurious sources that may possibly originate in the deconvolved images, we excluded stars that are not also detected by local PSF fitting without prior deconvolution."
 The diffuse emission extracted form the entire FOV of the H —band observations is shown in the top panel of refFig:back.., The diffuse emission extracted form the entire FOV of the $H-$ band observations is shown in the top panel of \\ref{Fig:back}.
 The checkerboard pattern is caused by our method because we have partitioned the field into many small overlapping sub-fields., The checkerboard pattern is caused by our method because we have partitioned the field into many small overlapping sub-fields.
 The bottom panel of refFig:back shows the uncertainty in the measured diffuse background determined from the deviation between overlapping fields., The bottom panel of \\ref{Fig:back} shows the uncertainty in the measured diffuse background determined from the deviation between overlapping fields.
 It can again be seen that the applied algorithm appears to work very well., It can again be seen that the applied algorithm appears to work very well.
" No systematicvariations can be seen and the uncertainty is generally < O.1mmagaarcsec?, with the exception of some small patches, where the uncertainty can reach 0.25 aarcsec?."," No systematicvariations can be seen and the uncertainty is generally $\leq 0.1$ $^{-2}$ , with the exception of some small patches, where the uncertainty can reach $\sim 0.25$ $^{-2}$ ."
One of the best wavs (o visualize a vortex in three dimensions is to graph vortex lines. curves that are evervwhere tangent to the vorticitv. vector field.,"One of the best ways to visualize a vortex in three dimensions is to graph vortex lines, curves that are everywhere tangent to the vorticity vector field."
 Vorticity is. by definition. clivergence-free: thus. vortex lines (like magnetic field lines) cannot have beginnings or endings within the fluid. but must extend. to the boundaries. or off to infinitv. or form closed loops.," Vorticity is, by definition, divergence-free; thus, vortex lines (like magnetic field lines) cannot have beginnings or endings within the fluid, but must extend to the boundaries, or off to infinity, or form closed loops."
 The simplest example of a 3D vortex is an infinite column of rotating fluid in which the [Iuid velocity is independent of height., The simplest example of a 3D vortex is an infinite column of rotating fluid in which the fluid velocity is independent of height.
 The core of uniform vorticity is threaded by infinilely-long parallel vortex lines (see Figure laa)., The core of uniform vorticity is threaded by infinitely-long parallel vortex lines (see Figure \ref{F:vortex_lines}a a).
 One might imagine chopping off the ends ol an infinite column to create a finite-height evlinder of rotating fIuid., One might imagine chopping off the ends of an infinite column to create a finite-height cylinder of rotating fluid.
 ILowever. vortex lines cannot have loose ends in (he fluid. ancl imsteacd must. wrap-around ancl form closed loops (see Figure Ibb).," However, vortex lines cannot have loose ends in the fluid, and instead must wrap-around and form closed loops (see Figure \ref{F:vortex_lines}b b)."
 Note that in the core of such a vortex. the vortex lines will be oriented in one direction. whereas in a halo surrounding the core. the vortex lines will be oriented in the opposite direction.," Note that in the core of such a vortex, the vortex lines will be oriented in one direction, whereas in a halo surrounding the core, the vortex lines will be oriented in the opposite direction."
 We now turn to the balance of forces in a 3D vortex., We now turn to the balance of forces in a 3D vortex.
 In anv horizontal plane. the centrifugal force always points racially outward from the vortex center. whereas (he Coriolis force points outward for evclones aud inward for anticvclones.," In any horizontal plane, the centrifugal force always points radially outward from the vortex center, whereas the Coriolis force points outward for cyclones and inward for anticyclones."
 When the Rossby number is much greater than unity. the Coriolis force is negligible.," When the Rossby number is much greater than unity, the Coriolis force is negligible."
 The outward centrifugal force must be balanced by an inward pressure force: such vortices must have low-pressure cores., The outward centrifugal force must be balanced by an inward pressure force; such vortices must have low-pressure cores.
 When the Rossby number is less (han unity. the centrifugal force is small and the Coriolis force is balanced by. the pressure force.," When the Rossby number is less than unity, the centrifugal force is small and the Coriolis force is balanced by the pressure force."
 Cyclones must have low-pressure cores ancl anlicvclones must have high-pressure cores., Cyclones must have low-pressure cores and anticyclones must have high-pressure cores.
 In the vertical direction. the only force that can balance (he pressure lorce is buovaucy.," In the vertical direction, the only force that can balance the pressure force is buoyancy."
 Figure 2aa shows the balance of forces in a low Rosshyv number anticvelone that is vertically centered on (he midplane. whereas figure 2bb shows the same for an anticvelone located completely above the midplane.," Figure \ref{F:force_balance}a a shows the balance of forces in a low Rossby number anticyclone that is vertically centered on the midplane, whereas figure \ref{F:force_balance}b b shows the same for an anticyclone located completely above the midplane."
 In the first case. the high-pressure anlicvelone must have coo]. dense lids to provide a buovant force toward the midplane that balances the pressure force awav from the midplane.," In the first case, the high-pressure anticyclone must have cool, dense lids to provide a buoyant force toward the midplane that balances the pressure force away from the midplane."
 In the second case. the top lid the one farthest from," In the second case, the top lid the one farthest from"
"For each galaxy. we define a critical “central” radius r, by where rar(bulge) is the bulge radius reported in Laurikainenetal.(2004) and {λος is the RCS value of the 25th magnitude D-band isophotal diameter (deVaucouleurs","For each galaxy, we define a critical “central” radius $r_c$ by where $r_{\mbox{\scriptsize eff}}(\mbox{bulge})$ is the bulge radius reported in \citet{laurikainen04} and $D_{25}$ is the RC3 value of the 25th magnitude B-band isophotal diameter \citep{devaucouleurs91}."
"etal.1991).. If Laurikainenetal. eeive no bulge radius. or if the galaxy is completely bulgeless. then r,=0011005."," If \citeauthor{laurikainen04} give no bulge radius, or if the galaxy is completely bulgeless, then $r_c = 0.01 D_{25}$."
 As the bulge will dominate the cirevmnuclear region. the minimum is used in the definition of r. lo guarantee that the central region is no larger than the bulge.," As the bulge will dominate the circumnuclear region, the minimum is used in the definition of $r_c$ to guarantee that the central region is no larger than the bulge."
" Most (about 80%)) of the ealaxies in the final sample have r.,=001120."," Most (about ) of the galaxies in the final sample have $r_c
= 0.01D_{25}$."
" A circle of radius r,. which corresponds to 30550 pe projected. is included on the structure maps used for classification (see re[sec:nuc))."," A circle of radius $r_c$, which corresponds to 30–550 pc projected, is included on the structure maps used for classification (see \\ref{sec:nuc}) )."
 Objects with high inclination (axis ratio Πίος < 0.30) or low signal-to-noise ratio (< 10) are excluded [vom the sample., Objects with high inclination (axis ratio $R_{25}$ $\leq$ $0.30$ ) or low signal-to-noise ratio $\lesssim$ 10) are excluded from the sample.
 We also discard low-resolution objects. given bv 7. < 20 resolution elements. as well as ones with unfavorable location on the chip or hiehlv saturated centers.," We also discard low-resolution objects, given by $r_c$ $\leq$ 20 resolution elements, as well as ones with unfavorable location on the chip or highly saturated centers."
 In general. (he objects failing the resolution or signal-to-noise ratio cuts have no clearly discernible coherent spiral arm structure.," In general, the objects failing the resolution or signal-to-noise ratio cuts have no clearly discernible coherent spiral arm structure."
 All objects are closer than 50 Mpc., All objects are closer than 50 Mpc.
 Our final sample. summarized in Table 1.. consists of the 75 galaxies which pass our resolution ancl signal-Lo-noise ratio cuts: the T-tvpe distribution of the Eskrideeetal. sample is roughly maintained.," Our final sample, summarized in Table \ref{tbl:data}, consists of the 75 galaxies which pass our resolution and signal-to-noise ratio cuts; the T-type distribution of the \citeauthor{eskridge02} sample is roughly maintained."
 We employ (wo methods of examining (he nuclear dust content in galaxies., We employ two methods of examining the nuclear dust content in galaxies.
 The first is to look at what structures the dust forms. ie.. a morphological classification. and the second is to simply study (he amount of dust structure in (he central regions.," The first is to look at what structures the dust forms, i.e., a morphological classification, and the second is to simply study the amount of dust structure in the central regions."
 We describe in how we use the structure map technique of Pogge&Martini(2002). to enhance dust. structures on the scale of 115 pe., We describe in \\ref{sec:smap} how we use the structure map technique of \citet{pogge02} to enhance dust structures on the scale of 1–15 pc.
 We Chen use these structure maps to classify the circumnuclear dust morphology into six classes (four ἵνρος of spirals. plus chaotic and no simmeture). as described in re[sec:nuc..," We then use these structure maps to classify the circumnuclear dust morphology into six classes (four types of spirals, plus chaotic and no structure), as described in \\ref{sec:nuc}."
 In relsecrms we describe how we estimate (he relative amounts of central dust structure in different galaxies., In \\ref{sec:rms} we describe how we estimate the relative amounts of central dust structure in different galaxies.
 Finally. in relsec:monte..we discuss how we statistically compare pairs of distributions of galaxies.," Finally, in \\ref{sec:monte}, we discuss how we statistically compare pairs of distributions of galaxies."
approximately 1000. (Figure 6).,approximately 1000 (Figure 6).
 These orbits pass by the SMDII with eccentricities >0.99. spending only 10? seconds to flv by the SMDII at pericenter distances of about 200 AU.," These orbits pass by the SMBH with eccentricities $> 0.99$, spending only $10^5$ seconds to fly by the SMBH at pericenter distances of about 200 AU."
 This could be a relatively unexplored source of LISA burst signals. assuming that the spacecraft will have the expected sensitivity in the 10? IIz band.," This could be a relatively unexplored source of LISA burst signals, assuming that the spacecraft will have the expected sensitivity in the $10^{-5}$ Hz band."
 These encounters are more likely wilh a triaxial model. due to the increased fraction of centrophilic orbits. though this bees the question of how one produces an O(10*)AL. IMDII in the first place (Gebhardt et al.," These encounters are more likely with a triaxial model, due to the increased fraction of centrophilic orbits, though this begs the question of how one produces an $O(10^3) M_\odot$ IMBH in the first place (Gebhardt et al."
 2000b: Gerssen et al., 2000b; Gerssen et al.
 2003: Taniguchi et al., 2003; Taniguchi et al.
 2000. Miller Hamilton 2002).," 2000, Miller Hamilton 2002)."
 ILowever. even if these were more common LO M. stellar mass black holes. (hey. would still produce a LISA burst signal as they pass through pericenter.," However, even if these were more common 10 $M_\odot$ stellar mass black holes, they would still produce a LISA burst signal as they pass through pericenter."
 During a galaxy merger. each 5MDIL sinks to the center of the new galaxy. potential due to clynamical [rietion ancl eventually becomes a bound SMDII binary (8MDDII.," During a galaxy merger, each SMBH sinks to the center of the new galaxy potential due to dynamical friction and eventually becomes a bound SMBH binary (SMBBH)."
 Dynamical friction still shrinks the SAIBBIT orbit until the binary is hard: thereafter. further decay is mediated by 3-body seattering with the ambient stellar background. until the SAIBBII becomes so close that the orbit can lose energy. via gravitational wave emission. and the SMBBIL can presumably coalesce.," Dynamical friction still shrinks the SMBBH orbit until the binary is hard; thereafter, further decay is mediated by 3-body scattering with the ambient stellar background until the SMBBH becomes so close that the orbit can lose energy via gravitational wave emission, and the SMBBH can presumably coalesce."
" The SMDBDII loss cone is lareer than for single SMIBIL. since stars must only pass within the separation a of the SMBBIL where a=GOAL,+M3)/807~0.05 parsec [or (vo equal LOCAL. SMBIIs."," The SMBBH loss cone is larger than for single SMBH, since stars must only pass within the separation a of the SMBBH, where $a = G (M_1+M_2) /8 \sigma_\star^2 \sim 0.05$ parsec for two equal $10^6 M_\odot$ SMBHs."
 Unfortunately. once the SMDDII has interacted with all the stars within its loss cone. the orbit decay stalls within the center of the galaxy. wilh a separation  parsec.," Unfortunately, once the SMBBH has interacted with all the stars within its loss cone, the orbit decay stalls within the center of the galaxy with a separation $\sim$ parsec."
 This is known as (he final parsec problem: the orbit of a SMDDIL in idealized galaxy models never decavs enough to allow gravitational wave emission to drive the svstem to coalesce., This is known as the 'final parsec problem': the orbit of a SMBBH in idealized galaxy models never decays enough to allow gravitational wave emission to drive the system to coalesce.
 The behavior of stars in angular monmentiun space is deeply connected (o this problem. since an ample supply of low angular momentum stars is Cantamount (o providing a Iresh reservoir of orbits within (he loss cone.," The behavior of stars in angular momentum space is deeply connected to this problem, since an ample supply of low angular momentum stars is tantamount to providing a fresh reservoir of orbits within the loss cone."
 Our results for the relilling rate of the capture and inspiral loss cone imply that it is always full., Our results for the refilling rate of the capture and inspiral loss cone imply that it is always full.
 In other words. (here are many more particles that can flow through (he capture and inspiral loss cone than can be depleted bv gravitational encounters.," In other words, there are many more particles that can flow through the capture and inspiral loss cone than can be depleted by gravitational encounters."
 Hence in principle. the larger loss cone for 3-body scattering by a binary black hole can also remain full in a triaxial potential.," Hence in principle, the larger loss cone for 3-body scattering by a binary black hole can also remain full in a triaxial potential."
 We are developing a fully sell-consistent n-body model with 10* particles, We are developing a fully self-consistent n-body model with $10^7$ particles
The simulations were produced using a auulti-step procedure outlined iu Bialek et al. (,The simulations were produced using a multi-step procedure outlined in Bialek et al. (
2001).,2001).
" The uuderlvius cosmiolosv is a flat. concordance model with 0,,=0.3. Q4= O07. ον= 0,03. σς=1.0. and 7=0.7. where the Tubble coustant is defined as 1002 ni + | and oy is the power spectrum normalization on S1 Mpe scales."," The underlying cosmology is a flat, concordance model with $\Omega_{m} = 0.3$ , $\Omega_{\Lambda} = 0.7$ , $\Omega_{b} =
0.03$ , $\sigma_8 = 1.0$, and $h = 0.7$, where the Hubble constant is defined as $100h$ km $^{-1}$ $^{-1}$ and $\sigma_8$ is the power spectrum normalization on $8h^{-1}$ Mpc scales."
 Details of the full cusemble will be presented im Dialek. Evrard Mohr (2005).," Details of the full ensemble will be presented in Bialek, Evrard Mohr (2005)."
 One member of the eusemble contained a prominent cold frout feature. ecucrated curing a nierecr by the separation aud resultant adiabatie cooling of the core of an intalling satellite. as discussed by Dialek. Evrard Mohr (2002).," One member of the ensemble contained a prominent cold front feature, generated during a merger by the separation and resultant adiabatic cooling of the core of an infalling satellite, as discussed by Bialek, Evrard Mohr (2002)."
 The cosinological values assumed. for the models are in line withWALA allowed paramcters. with the exception of the barvon traction.," The cosmological values assumed for the models are in line with allowed parameters, with the exception of the baryon fraction."
"P The value Q,/2,,=0.1 used im the simulations is lower than theWALA value 0.17£0.01 (Bennett et al.", The value $\Omega_b/\Omega_m \se 0.1$ used in the simulations is lower than the value $0.17 \pm 0.01$ (Bennett et al.
 2003)., 2003).
 The mass fraction im imtrachister eas is expected to be less than the cosmic barvou fraction due to galaxy formation aud energv exchange with dark uatter during mergers (Thomas Couchiman 1992)., The mass fraction in intracluster gas is expected to be less than the cosmic baryon fraction due to galaxy formation and energy exchange with dark matter during mergers (Thomas Couchman 1992).
 The orlmer process removes ~15—20% of the barvous from he hot phase in rich clusters while the latter expels 71054 of the eas from the potential (Freuk et al., The former process removes $\sims 15-20\%$ of the baryons from the hot phase in rich clusters while the latter expels $\sim$ $\%$ of the gas from the potential (Frenk et al.
 1999)., 1999).
 Still. he model gas fractions are likely to be somewhat low compared to current observational estimates.," Still, the model gas fractions are likely to be somewhat low compared to current observational estimates."
 However. in he results presented here. the barvon fraction affects only he normalization of the ICM. X-ray spectrmm.," However, in the results presented here, the baryon fraction affects only the normalization of the ICM X-ray spectrum."
" Our mock spectra are tuned to a fixed line normalization. which at fixed cluster mass scales x(0,OQ,fa. with fa the exposure time."," Our mock spectra are tuned to a fixed line normalization, which at fixed cluster mass scales $\spropto
(\Omega_b/\Omega_m)^2 t_{\rm exp}$, with $t_{\rm exp}$ the exposure time."
 A hieher or lower barvon fraction cau thus © absorbed by appropriate rescaling of the exposure., A higher or lower baryon fraction can thus be absorbed by appropriate rescaling of the exposure.
 The configuration of cach simulation is stored at tweuty output times. spaced equally in time from the initial redshift τες20.82 to the present.," The configuration of each simulation is stored at twenty output times, spaced equally in time from the initial redshift $z_i \se 20.82$ to the present."
 We employ the final niue outputs of the 68 models in this study. corresponding to the redshifts 0.510. 0.£48. 0.365. 0.290. 0.222. 0.160. 0.102. 0.019 and 0.0.," We employ the final nine outputs of the 68 models in this study, corresponding to the redshifts 0.540, 0.448, 0.365, 0.290, 0.222, 0.160, 0.102, 0.049 and 0.0."
 This vields 612 cluster realizatious which we treat. under an creodic hvpothnesis. as statistically incdependcut.," This yields 612 cluster realizations which we treat, under an ergodic hypothesis, as statistically independent."
 The time separation of ~0.7 Cevr between outputs typically exceeds the crossing time αἲ royy. justifvine the ergodic assmuption.," The time separation of $\sims
0.7$ Gyr between outputs typically exceeds the crossing time at $r_{200}$, justifying the ergodic assumption."
 We further cuhance our sample by considering the line of sight (LOS) velocity structure of cach realization along three perpendicular axes., We further enhance our sample by considering the line of sight (LOS) velocity structure of each realization along three perpendicular axes.
 Although these projections ire linked bv dvuamics. the LOS velocity structure is eenuimmcelv incepeudent.," Although these projections are linked by dynamics, the LOS velocity structure is genuinely independent."
 We thus have three projections of cach of the 612 realizations. for a total of 1.836 exposures.," We thus have three projections of each of the 612 realizations, for a total of 1,836 exposures."
" The members of the simulated sample rauge in spectral temperature from 1.5 keV to about 8 keV. with cluster lasses Moog ranging from 0.015-2. 1.«101AZ,"," The members of the simulated sample range in spectral temperature from 1.5 keV to about 8 keV, with cluster masses $M_{200}$ ranging from 0.015-2.4 $\times
10^{15} M_{\odot}$."
 The derived spectra and images. along with associated piuranueters deseribiug the simulations are publiclv available as part ofVCE. the We create mockAstro-E2 spectra of these realizations following two observing programs illustrated in Figure 1..," The derived spectra and images, along with associated parameters describing the simulations are publicly available as part of VCE, the We create mock spectra of these realizations following two observing programs illustrated in Figure \ref{fig:tiles}."
 The first program involves a search for velocity gracicuts bv imeasuniue differences in the mean velocity of the Fe Ko lines for iuultiple poiutiugs of the dstro-E2 instrument., The first program involves a search for velocity gradients by measuring differences in the mean velocity of the Fe $\alpha$ lines for multiple pointings of the instrument.
 This strategy allows one to measure both the magnitude and a crude direction of the velocity eradicut., This strategy allows one to measure both the magnitude and a crude direction of the velocity gradient.
 Multiple poiutiugs are required because the average angular resolution of the XN-rav telescopes onAstro-E 218 —1.9/ (half-power and the detector confieuration is roughly a square with 2.9’ on the side., Multiple pointings are required because the average angular resolution of the X-ray telescopes on is $\sim$ $^\prime$ (half-power and the detector configuration is roughly a square with $^\prime$ on the side.
 Since less than of the encircled energy is contained within 2’. spatially resolved spectroscopy using sub-reeious of the detector will be highly contaminated with photous from ucighhborime regions.," Since less than of the encircled energy is contained within $^\prime$, spatially resolved spectroscopy using sub-regions of the detector will be highly contaminated with photons from neighboring regions."
 Therefore. to carry out this observational strategy. we create four mock spectra of cach cluster projection in a 242 box ceutered ou the cluster.," Therefore, to carry out this observational strategy, we create four mock spectra of each cluster projection in a $\times$ 2 box centered on the cluster."
 The secoucd program involves searching for extra-thermal broadening of the Fe Ίνα Ime using a single. central poutine.," The second program involves searching for extra-thermal broadening of the Fe $\alpha$ line using a single, central pointing."
 -ü.liu 0.051kpe The thermal plasima einission spectra for this study are compiled using the APEC code (Simith et al., -0.1in 0.05in The thermal plasma emission spectra for this study are compiled using the APEC code (Smith et al.
 2001) from the NSPEC 11.3.1 suite of spectral analysis tools (Arnaud 1996)., 2001) from the XSPEC 11.3.1 suite of spectral analysis tools (Arnaud 1996).
 APEC allows us to include thermal broadening of the line spectra by setting the APECTUERMAL togele to wes., APEC allows us to include thermal broadening of the line spectra by setting the APECTHERMAL toggle to `yes'.
 Further. NSPEC allows us to fold in the anticipated XRS response We use NSPEC/APLEC to write a reference table of spectra in flux units at 176 teiiperatures spaced logaritlinically to cover our ranec of interest.," Further, XSPEC allows us to fold in the anticipated XRS response We use XSPEC/APEC to write a reference table of spectra in flux units at 176 temperatures spaced logarithmically to cover our range of interest."
 This spectral table is lnüted to au energv range appropriate for studving the Fe I& complex., This spectral table is limited to an energy range appropriate for studying the Fe K complex.
 The final spectra are limited to theinterval 5.9 keV to 6.1 keV. All spectra are generated with the cluster at a fiducial redshift of 0.1. πο that the FONNYV Ixo line is centered at 6.09 keV aud the FONAVI Ίνα liue at 6.33 keV (the livcdroecu-like iron line is actually two separate lines with centers at 6.32 and 6.31 keV as a result of fine structure (Verner. Verner Ferland 1996)).," The final spectra are limited to theinterval 5.9 keV to 6.4 keV. All spectra are generated with the cluster at a fiducial redshift of 0.1, so that the FeXXV $\alpha$ line is centered at 6.09 keV and the FeXXVI $\alpha$ line at 6.33 keV (the hydrogen-like iron line is actually two separate lines with centers at 6.32 and 6.34 keV as a result of fine structure (Verner, Verner Ferland 1996))."
 Figure 20 shows the Nhe line region of refercuce spectra at a few relevant temperatures., Figure \ref{fig:thermal} shows the $\alpha$ line region of reference spectra at a few relevant temperatures.
 To create a simulated spectrum for a mock observation. we interpolate on the reference flux table to generate au Cluission spectruni for cach gas particle of the simulation contained inthe FOV.," To create a simulated spectrum for a mock observation, we interpolate on the reference flux table to generate an emission spectrum for each gas particle of the simulation contained in the FOV."
 There are typically ~L000 particles in the the FOV. and νο contributions are sununed to obtain the complete spectrum.," There are typically $\sims
1000$ particles in the the FOV, and their contributions are summed to obtain the complete spectrum."
 To convert the resulting flux spectrmu into au NRS count spectrum. we fist define an exposure time that requires either 200 or 100 total counts iu the Fe Ίνα line region within the energy range of interest. 1.0. 6.0-6.2 keV. (The 200 count criterion appliesto thefour-poiutiugmosaic study. while 100 counts are used for the ceutral poiutiug spectra.)," To convert the resulting flux spectrum into an XRS count spectrum, we first define an exposure time that requires either 200 or 400 total counts in the Fe $\alpha$ line region within the energy range of interest, i.e., 6.0-6.2 keV. (The 200 count criterion appliesto thefour-pointingmosaic study, while 400 counts are used for the central pointing spectra.)"
 A single. discrete Poisson realization of cach spectrum is then created. using the routine of Press et al. (," A single, discrete Poisson realization of each spectrum is then created, using the routine of Press et al. ("
1992).,1992).
 0δι, -0.2in
mass of the cloud is much smaller than its Jeans! mass. its ellect will become important locally.,"mass of the cloud is much smaller than its Jeans' mass, its effect will become important locally."
 For example. the high-mass boundary layer clumps of the parallel shock model have masses that exceed their Jeans mass.," For example, the high-mass boundary layer clumps of the parallel shock model have masses that exceed their Jeans mass."
 We will investigate the ellect of seli-gravity on the eloud evolution in a later paper., We will investigate the effect of self-gravity on the cloud evolution in a later paper.
 Our simulations only describe the dynamical evolution of a cloud from warm atomic gas to cold atomic gas., Our simulations only describe the dynamical evolution of a cloud from warm atomic gas to cold atomic gas.
 Figure 11 shows the temporal evolution of the cold gas mass fraction for the parallel and perpendicular shock model., Figure \ref{fig:molecular} shows the temporal evolution of the cold gas mass fraction for the parallel and perpendicular shock model.
 Cold. eas arises earlier in the parallel shock. model than in. the perpendicular one. but after 9 Myr more than of the initial cloud. mass is in the thermally stable cold gas phase.," Cold gas arises earlier in the parallel shock model than in the perpendicular one, but after 9 Myr more than of the initial cloud mass is in the thermally stable cold gas phase."
 Although we have not included a description of molecular cooling. nor do we follow the cloud chemistry. we can roughly estimate how much gas is converted [rom the cold atomic eas to molecular gas.," Although we have not included a description of molecular cooling, nor do we follow the cloud chemistry, we can roughly estimate how much gas is converted from the cold atomic gas to molecular gas."
 Williams.Blitz.&Stark(1995) find that the average number density of Hl» in the CO clumps of the Rosette Molecular. Cloud is z220cm5, \citet{WBS95} find that the average number density of $_2$ in the CO clumps of the Rosette Molecular Cloud is $\approx 220~{\rm cm^{-3}}$.
 With tvpical excitation. temperatures between LO and. 20 Ix. the thermal gas. pressure of these clumps is roughly 2500k.," With typical excitation temperatures between 10 and 20 K, the thermal gas pressure of these clumps is roughly 2500k."
 Thercelore. we assume that any gas. parcel in the shocked clouc with a thermal pressure higher than 2500k and a temperature below LOOK will become molecular given enough time (see below).," Therefore, we assume that any gas parcel in the shocked cloud with a thermal pressure higher than 2500k and a temperature below 100K will become molecular given enough time (see below)."
 Using this criterion. we find that he parallel shock model generates a molecular cloud as half of the cold. eas becomes molecular (sce Fig. 11)).," Using this criterion, we find that the parallel shock model generates a molecular cloud as half of the cold gas becomes molecular (see Fig. \ref{fig:molecular}) )."
 In the »erpendieular cloud model only a small fraction of the cold atomic gas is converted. into molecular gas., In the perpendicular cloud model only a small fraction of the cold atomic gas is converted into molecular gas.
 This suggests hat the perpendicular shock model only produces a ciffuse Η1 cloud., This suggests that the perpendicular shock model only produces a diffuse HI cloud.
 The above result. is only valid i£. the time scale. for he formation of molecules is short anc if the physical xwameters of the. formation process are met., The above result is only valid if the time scale for the formation of molecules is short and if the physical parameters of the formation process are met.
 Gloveretal.(2009) use high-resolution 3D simulations of turbulent interstellar eas to follow the formation and. destruction of molecular hydrogen and €O., \citet{Getal09} use high-resolution 3D simulations of turbulent interstellar gas to follow the formation and destruction of molecular hydrogen and CO.
 Γον find that most CO forms within 2-3 Mr for dense. turbulent gas. while the formation of ο is even faster. Le. within 1-2 Myr.," They find that most CO forms within 2-3 Myr for dense, turbulent gas, while the formation of $_2$ is even faster, i.e. within 1-2 Myr."
 Their results indicate that once large enough spatial and column densities are reached. the conversion from atomic to molecular gas is rapid.," Their results indicate that once large enough spatial and column densities are reached, the conversion from atomic to molecular gas is rapid."
" A eood indictor for the formation of molecules is the visual extinction ;lyo. which can be expressed as (e.g.Cha-puis&Corbel2004) For regions with oh,0.5 and high local densities. we can then expect that molecules are present."," A good indictor for the formation of molecules is the visual extinction $A_V$, which can be expressed as \citep[e.g.][]{CC04}
 For regions with $A_V \gtrsim 0.5$ and high local densities, we can then expect that molecules are present."
 Figure 12 shows that the visual extinction is already high early on in the parallel shock model., Figure \ref{fig:Av_pa} shows that the visual extinction is already high early on in the parallel shock model.
 Phese regions also correspond. to high-densitv regions. as can be seen in Fig. 1..," These regions also correspond to high-density regions, as can be seen in Fig. \ref{fig:paboundary}."
 This model thus most likely produces a molecular cloud., This model thus most likely produces a molecular cloud.
 Also. note the similarity of the column density plot for the parallel shock model with the emission map of the W3 GMC (see Fig.," Also, note the similarity of the column density plot for the parallel shock model with the emission map of the W3 GMC (see Fig."
 6 of Paper D)., 6 of Paper I).
 A more structured inner cloud can be expected with a non-uniform initial condition and a higher resolution., A more structured inner cloud can be expected with a non-uniform initial condition and a higher resolution.
 While the 15° oblique shock model also produces high column densities which coincide with high density regions. the perpendicular and the 45° models do not.," While the $^\circ$ oblique shock model also produces high column densities which coincide with high density regions, the perpendicular and the $^\circ$ models do not."
 Models with large transverse components of the magnetic field. produce diffuse LIL clouds. instead. of molecular clouds., Models with large transverse components of the magnetic field produce diffuse HI clouds instead of molecular clouds.
 However. this conclusion only holds for our current simulations.," However, this conclusion only holds for our current simulations."
 A higher resolution ancl inclusion of small-scale perturbations potentially would produce higher density clumps for these models., A higher resolution and inclusion of small-scale perturbations potentially would produce higher density clumps for these models.
 In this paper we have presented 3D simulations of the interaction of a weak. radiative shock with a magnetisect. diffuse atomic cloud.," In this paper we have presented 3D simulations of the interaction of a weak, radiative shock with a magnetised, diffuse atomic cloud."
 The interaction of the shock induces the transition of the cloud [rom the thermally warm atomic phase to the cold one., The interaction of the shock induces the transition of the cloud from the thermally warm atomic phase to the cold one.
 By modelling the shock-cloud interaction in 3D. we are able to study the ellect of cilferent magnetic field. orientations including parallel. oblique anc perpendicular to the shock normal.," By modelling the shock-cloud interaction in 3D, we are able to study the effect of different magnetic field orientations including parallel, oblique and perpendicular to the shock normal."
 Contrary to the strong. adiabatic shock mocels of Shin.Stone.&Snvder (2008)... we find that the structure of the shocked. cloud cülfers significantly with the magnetic field orientation.," Contrary to the strong, adiabatic shock models of \cite{SSS08}, we find that the structure of the shocked cloud differs significantly with the magnetic field orientation."
 The shock-clouc interaction can be separated into two distinct classes. Le. à quasi-parallel one and a quasi-perpendicular one.," The shock-cloud interaction can be separated into two distinct classes, i.e. a quasi-parallel one and a quasi-perpendicular one."
 In the quasi-parallel shock models high-clensity clumps are generated in the boundary. layer surrounding the cloud., In the quasi-parallel shock models high-density clumps are generated in the boundary layer surrounding the cloud.
 As the visual extinction of the gas is also high. the resulting cloud is most likely molecular.," As the visual extinction of the gas is also high, the resulting cloud is most likely molecular."
 The cquasi-perpendicular shock models. however. only produce low-clensity clouds. resembling. LIE clouds.," The quasi-perpendicular shock models, however, only produce low-density clouds resembling HI clouds."
 This. result. is similar to the one o£ Lleitsch.Stone.&Hartmann(2009)., This result is similar to the one of \cite{HSH09}.
. All our models show that the shocked. cloud. becomes maenctically dominated. after a few Myr., All our models show that the shocked cloud becomes magnetically dominated after a few Myr.
 Although this provides the ideal conditions for the formation of dense clumps and cores (Falle&Lartquist2002:VanLoo.Falle.&Llartquist2006:VanLooetal. 2008).. we do not see this happening in our simulations.," Although this provides the ideal conditions for the formation of dense clumps and cores \citep{FH02, VFH06, VFH08}, we do not see this happening in our simulations."
 This can be partly ascribed. due to the assumption of an initially quiescent. uniform and. spherical cloud.," This can be partly ascribed due to the assumption of an initially quiescent, uniform and spherical cloud."
 From. the colliding, From the colliding
To obtain the magnetic vector potential (which we need for the CODE)). we use the formula For a thin trausitiou laver of thickuess 5=Πίο«Ay. the contributions to the magnetic energy are,"To obtain the magnetic vector potential (which we need for the ), we use the formula For a thin transition layer of thickness $\varepsilon \equiv R_2{-}R_1 \ll R_1$, the contributions to the magnetic energy are"
redshift should not exceed 0.34.,redshift should not exceed $0.34$.
 This conclusion is based on the belief that the initial VIE -raw spectrum cannot be harder than the GeV spectrum measured with Fermi LAT., This conclusion is based on the belief that the initial VHE $\gamma$ -ray spectrum cannot be harder than the GeV spectrum measured with Fermi LAT.
 On the other hand. if the redshift is indeed =0.4. the TeV and GeV parts look quite different. and not part of a single component.," On the other hand, if the redshift is indeed $\gtrsim 0.4$, the TeV and GeV parts look quite different, and not part of a single component."
 Even though. this does not imply that they of different origin.," Even though, this does not imply that they of different origin."
 In. fact. our model can explain both components wilh a single proton population. as parts of the smooth proton svnchrotron spectrum deformed by the enerev-dependent internal absorption.," In fact, our model can explain both components with a single proton population, as parts of the smooth proton synchrotron spectrum deformed by the energy-dependent internal absorption."
" In (his case the de-absorbed TeV spectrum is rather flat. with photon index Ty,1.7. while the HE component is characterized by a similar photon index P1.8 but with ad higher flux."," In this case the de-absorbed TeV spectrum is rather flat, with photon index $\Gamma_{\rm int}\simeq1.7$, while the HE component is characterized by a similar photon index $\Gamma\sim1.8$ but with at higher flux."
 A good agreement between the GeV and TeV spectra can be achieved assuming a proton energy distribution with power-law index p=2., A good agreement between the GeV and TeV spectra can be achieved assuming a proton energy distribution with power-law index $p=2$.
 A weak internal absorption (with maximum optical depth of about 7= 1.6) allows mocdification of the VIIE spectrum to the required photon index (Fit 5 in Fie. 4)).," A weak internal absorption (with maximum optical depth of about $\tau=1.6$ ) allows modification of the VHE spectrum to the required photon index (Fit 5 in Fig. \ref{fig:3c66a}) ),"
 while the IIE part is reproduced bv the unmocdified svnchrotron spectrum., while the HE part is reproduced by the unmodified synchrotron spectrum.
 The svnchrotron emission of secondary pairs can explain (he X-ray spectrum obtained with Swilt but not the optical MDA data. which require an additional radiation component.," The synchrotron emission of secondary pairs can explain the X-ray spectrum obtained with Swift but not the optical MDM data, which require an additional radiation component."
 The physical parameters used in this model may appear quite extreme (see Table 1.. Fit 5).," The physical parameters used in this model may appear quite extreme (see Table \ref{table:parameters}, Fit 5)."
 In particular. the very small value of the Doppler factor has been chosen to avoid -rav excess above 1. TeV. and (his consequently leads to a dramatic increase of (he required enerev budget.," In particular, the very small value of the Doppler factor has been chosen to avoid $\gamma$ -ray excess above $1$ TeV, and this consequently leads to a dramatic increase of the required energy budget."
 In fact. there is a more natural way (o suppress the flux level above 1 TeV. namely assuming a less efficient. acceleration process.," In fact, there is a more natural way to suppress the flux level above $1$ TeV, namely assuming a less efficient acceleration process."
 Ii this wav the Doppler factor and D-field may be increased. while the required οποιον budget will be significantly. reduced.," In this way the Doppler factor and B-field may be increased, while the required energy budget will be significantly reduced."
background structures seen in projection in the PDCS is endemic in optically selected cluster samples.,background structures seen in projection in the PDCS is endemic in optically selected cluster samples.
" Pure projection effects like, e.g., CL02314«0048 (Fig.1,,"," Pure projection effects like, e.g., CL0231+0048 (Fig.\ref{fig:optvsx},"
 left) can be largely eliminated by including information on galaxy colors or redshifts (photometric or spectroscopic) in the original cluster detection phase., left) can be largely eliminated by including information on galaxy colors or redshifts (photometric or spectroscopic) in the original cluster detection phase.
" However, even the latest, state-of-the-art optical cluster samples remain biased, as they are prone to select intrinsically poor systems whose apparently compact cluster core, high optical richness, and high velocity dispersion are inflated by line-of-sight alignment and infall (Hicks et 22008; Horesh et 22009)."," However, even the latest, state-of-the-art optical cluster samples remain biased, as they are prone to select intrinsically poor systems whose apparently compact cluster core, high optical richness, and high velocity dispersion are inflated by line-of-sight alignment and infall (Hicks et 2008; Horesh et 2009)."
" By contrast, X-ray selected cluster samples are almost entirely free of projection effects since they, by virtue of the X-ray selection criteria, comprise exclusively intrinsically massive, gravitationally collapsed systems."," By contrast, X-ray selected cluster samples are almost entirely free of projection effects since they, by virtue of the X-ray selection criteria, comprise exclusively intrinsically massive, gravitationally collapsed systems."
 Enormous progress has been made in the past decade in studies of clusters in the local universe (z< 0.3)., Enormous progress has been made in the past decade in studies of clusters in the local universe $z\le 0.3$ ).
" The availability of large, representative, X-ray selected samples compiled from ROSAT All-Sky Survey (RASS, Trümmper 1983) data (Ebeling et 11996, 1998, 2000; De Grandi et 11999; Ebelling, Mullis Tully 2002; Cruddace et 22002; Bóhhringer et 22004; Kocevski et 22007) has allowed greatly improved, unbiased measurements of the properties of clusters as an astronomical class of objects."," The availability of large, representative, X-ray selected samples compiled from ROSAT All-Sky Survey (RASS, Trümmper 1983) data (Ebeling et 1996, 1998, 2000; De Grandi et 1999; ling, Mullis Tully 2002; Cruddace et 2002; Böhhringer et 2004; Kocevski et 2007) has allowed greatly improved, unbiased measurements of the properties of clusters as an astronomical class of objects."
" Especially the ROSAT Brightest Cluster Sample (BCS, Ebeling et 11998, 2000) and the REFLEX sample (Bóhhringer et 22004) have been used extensively for studies of the local cluster population (e.g., Allen et 11992; Crawford et 11995, 1999; Ebeling et 11997; Hudson Ebeling 1997; Edge et 11999, Smith et 22001; Schuecker et 22001; Allen et 22003; Kocevski et 22004, 2006; Smith et 22005; Stanek et 22006; Kocevski Ebeling 2006; Atrio-Barandela et 22008; Kashlinsky et 22008)."," Especially the ROSAT Brightest Cluster Sample (BCS, Ebeling et 1998, 2000) and the REFLEX sample (Böhhringer et 2004) have been used extensively for studies of the local cluster population (e.g., Allen et 1992; Crawford et 1995, 1999; Ebeling et 1997; Hudson Ebeling 1997; Edge et 1999, Smith et 2001; Schuecker et 2001; Allen et 2003; Kocevski et 2004, 2006; Smith et 2005; Stanek et 2006; Kocevski Ebeling 2006; Atrio-Barandela et 2008; Kashlinsky et 2008)."
" At higher redshift, the Massive Cluster Survey (MACS), launched in 1999, has compiled the first large X-ray selected sample of clusters that are both massive and distant."," At higher redshift, the Massive Cluster Survey (MACS), launched in 1999, has compiled the first large X-ray selected sample of clusters that are both massive and distant."
" Based on sources listed in the RASS Bright Source Catalogue (BSC, Voges et 11999) MACS covers the entire extragalactic sky observable from Mauna Kea (|b|> 20°, —40?<6 80°), aa solid"," Based on sources listed in the RASS Bright Source Catalogue (BSC, Voges et 1999) MACS covers the entire extragalactic sky observable from Mauna Kea $|b|>20^\circ$ , $-40^\circ \leq \delta\leq 80^\circ$ ), a solid"
 Several sources of data were used by two different groups in order to retrieve these volatile abundances., Several sources of data were used by two different groups in order to retrieve these volatile abundances.
 A first set of data was collected by Swain et al., A first set of data was collected by Swain et al.
" 2009 (hereafter S09) from the dayside spectrum of HD 189733b with HST NICMOS spectrophotometry in the 1.5-2.5 wm range, leading them to find subsolar carbon and oxygen abundances."," 2009 (hereafter S09) from the dayside spectrum of HD 189733b with HST NICMOS spectrophotometry in the 1.5–2.5 $\mu$ m range, leading them to find subsolar carbon and oxygen abundances."
" In contrast, from the same set of datamodel, Madhusudhan Seager 2009 (hereafter MS09) found these spectra consistent with supersolar C and O abundances."," In contrast, from the same set of data, Madhusudhan Seager 2009 (hereafter MS09) found these spectra consistent with supersolar C and O abundances."
" However, MS09 also found that these species could be in subsolar abundances from spectra of the planet's atmosphere during secondary eclipses with Spitzer broadband photometry."," However, MS09 also found that these species could be in subsolar abundances from spectra of the planet's atmosphere during secondary eclipses with Spitzer broadband photometry."
 This huge variation of elemental abundances derived by the two groups is due to a wide variety of atmospheric pressure-temperature profiles that are found consistent with the planet's spectra , This huge variation of elemental abundances derived by the two groups is due to a wide variety of atmospheric pressure-temperature profiles that are found consistent with the planet's spectra (S09; MS09).
"Although (S09;consensusMS09). has not yet been reached on the metallicity of HD 189733b, the possibility that this — or potentially other — hot have subsolar metallicity raises the challenging theoretical question of whether and how a giant planet may achieve subsolar metallicity during its formation."," Although consensus has not yet been reached on the metallicity of HD 189733b, the possibility that this -- or potentially other – hot have subsolar metallicity raises the challenging theoretical question of whether and how a giant planet may achieve subsolar metallicity during its formation."
" In order to account for this discrepancy, Mousis et al. "," In order to account for this discrepancy, Mousis et al. ("
"have proposed that gravitational settling, due to (2009b)strong irradiation, could lower the carbon and oxygen abundances in the upper layers of HD189733b's atmosphere.","2009b) have proposed that gravitational settling, due to strong irradiation, could lower the carbon and oxygen abundances in the upper layers of HD189733b's atmosphere."
" However, this possibility has not been yet tested by models detailing the envelope's evolution under the influence of irradiation and might be contradicted by the is required to explain the large radii of irradiated planets (Burrows et al."," However, this possibility has not been yet tested by models detailing the envelope's evolution under the influence of irradiation and might be contradicted by the is required to explain the large radii of irradiated planets (Burrows et al."
 2007)., 2007).
" In this work, we determine the range of volatile abundances in the envelope of HD189733b that matches the 20-80 mass range of heavy elements predicted by the interior models of Guillot (2008)."," In this work, we determine the range of volatile abundances in the envelope of HD189733b that matches the 20–80 mass range of heavy elements predicted by the interior models of Guillot (2008)."
 The latter rejected the models predicting masses of heavy elements lower than 20 in HD189733b on the basis that they are not able Mgto explain in a consistent manner the observed radius measurements of all known transiting giant exoplanets., The latter rejected the models predicting masses of heavy elements lower than 20 in HD189733b on the basis that they are not able to explain in a consistent manner the observed radius measurements of all known transiting giant exoplanets.
" We also use a model describing the formation sequence of planetesimals in the protoplanetary disk and the composition of the incorporated ices, assuming that the distribution of heavy elements is homogeneous within the planet's envelope."," We also use a model describing the formation sequence of planetesimals in the protoplanetary disk and the composition of the incorporated ices, assuming that the distribution of heavy elements is homogeneous within the planet's envelope."
 We then compare the inferred carbon and oxygen abundances to those retrieved from spectroscopy and we infer the range of supersolar values that can directly fit both spectra and internal structure models., We then compare the inferred carbon and oxygen abundances to those retrieved from spectroscopy and we infer the range of supersolar values that can directly fit both spectra and internal structure models.
 We also investigate the role that can be played by carbon molecules in the form of polycyclic aromatic hydrocarbons (PAHs) and soots possibly present in the upper layers of the envelope (Marley et al., We also investigate the role that can be played by carbon molecules in the form of polycyclic aromatic hydrocarbons (PAHs) and soots possibly present in the upper layers of the envelope (Marley et al.
 2009; Zahnle et al., 2009; Zahnle et al.
 2010) in the apparent contradiction between the subsolar elemental abundances and the important mass of heavy elements predicted in HD189733b., 2010) in the apparent contradiction between the subsolar elemental abundances and the important mass of heavy elements predicted in HD189733b.
 We finally discuss the alternative that could explain this possible discrepancy., We finally discuss the alternative that could explain this possible discrepancy.
" Irrespective of the details of their formation, close-in giant planets are thought to have originated in the cold outer region of protoplanetary disks and migrated inwards until they stopped at closer orbital radii to the star (Goldreich Tremaine 1980; Lin et al."," Irrespective of the details of their formation, close-in giant planets are thought to have originated in the cold outer region of protoplanetary disks and migrated inwards until they stopped at closer orbital radii to the star (Goldreich Tremaine 1980; Lin et al."
" 1996; Fogg Nelson 2005, 2007; Mandell et al."," 1996; Fogg Nelson 2005, 2007; Mandell et al."
 2007)., 2007).
" In this context, it has been proposed that core accretion is a method by which planets may form at small distances to the star AU) whilst gravitational instability may be the mechanism(~10 by which planets may form at much larger distances (7100 AU) (Boley 2009; Meru Bate 2010)."," In this context, it has been proposed that core accretion is a method by which planets may form at small distances to the star $\sim$ 10 AU) whilst gravitational instability may be the mechanism by which planets may form at much larger distances $\ge$ 100 AU) (Boley 2009; Meru Bate 2010)."
" Because a bimodal distribution of gas giant planet semi-major axes should remain present after scattering and planet-disk interaction (Boley 2009), implying that giant planets formed by core accretion should migrate closer to the star than those formed by gravitational instability, we follow here the core accretion model to describe the formation of HD189733b."," Because a bimodal distribution of gas giant planet semi-major axes should remain present after scattering and planet-disk interaction (Boley 2009), implying that giant planets formed by core accretion should migrate closer to the star than those formed by gravitational instability, we follow here the core accretion model to describe the formation of HD189733b."
" In this scenario, building blocks accreted by proto-HD 189733b may have formed all along its radial migration pathway in the protoplanetary disk."," In this scenario, building blocks accreted by proto-HD 189733b may have formed all along its radial migration pathway in the protoplanetary disk."
" However, in this work, we assume that only the planetesimals produced beyond the snow line, i.e. those possessing a significant fraction of volatiles, materially affected the observed O and C abundances due to their vaporization when they entered the envelope of the planet."," However, in this work, we assume that only the planetesimals produced beyond the snow line, i.e. those possessing a significant fraction of volatiles, materially affected the observed O and C abundances due to their vaporization when they entered the envelope of the planet."
 This hypothesis is supported by the work of Guillot Gladman (2000) who showed that planetesimals delivered to a planet owning a mass similar or greater than that of Jupiter are rather ejected than accreted., This hypothesis is supported by the work of Guillot Gladman (2000) who showed that planetesimals delivered to a planet owning a mass similar or greater than that of Jupiter are rather ejected than accreted.
 This mechanism should then prevent further noticeable accretion of solids by the planet during its migration below the snow line., This mechanism should then prevent further noticeable accretion of solids by the planet during its migration below the snow line.
inti; rav((r) £O) | 98(0).. where we have introduced the “spherical” total energy = ].,"_0^R (r) (R) + (R), where we have introduced the “spherical” total energy (R)= ."
". Note that £GR) is written in terms of the “spherical” velocity. variance s""(vr). dillerent. in general. from the ordinary velocity variance.e. through the residual 987(r) to be specified. contributing to the residual 5£(r)."," Note that ${\cal E}(R)$ is written in terms of the “spherical” velocity variance $s^2(r)$, different, in general, from the ordinary velocity variance, through the residual $\delta s^2(r)$ to be specified, contributing to the residual $\delta {\cal E}(r)$."
 In other words. there is some freedom in the definition of κέν).," In other words, there is some freedom in the definition of $s^2(r)$."
 We will come back to this point later., We will come back to this point later.
 So far we have considered a system with arbitrary mass clistribution (symmetry). aggregation history and dynamical state.," So far we have considered a system with arbitrary mass distribution (symmetry), aggregation history and dynamical state."
 If the svstem is in addition in equilibrium. then multiplying the steady collisionless Boltzmann equation (e.g. cq. ," If the system is in addition in equilibrium, then multiplying the steady collisionless Boltzmann equation (e.g. eq. ["
"4p-2] in Binney&‘Tremaine 1987)) by the radial particle velocity and. integrating over velocity ancl solid angle. we are led to where ὃν stands for radial partial derivative"".","4p-2] in \citealt{bt87}) ) by the radial particle velocity and integrating over velocity and solid angle, we are led to+ ^2(r) - =, where $\derpr$ stands for radial partial ."
 ‘Taking into account equation (13)). equation (62)) adopts the form radο) (G4) Phi)y((r).. identical to the Jeans equation for spherically svnunetric svstems in equilibrium but. for the last. term on the right.," Taking into account equation \ref{gauss}) ), equation \ref{Jeq1}) ) adopts the form ^2(r) - = -, identical to the Jeans equation for spherically symmetric systems in equilibrium but for the last term on the right."
 Multiplving equation (69)) bv επι and integrating over the sphere of radius £2. the same steps leacing to the scalar virial relation for spherically symmetric self-eravitating svstems now lead to radrune(P r r rav((r)," Multiplying equation \ref{exJeq}) ) by $4\pi r^3$ and integrating over the sphere of radius $R$, the same steps leading to the scalar virial relation for spherically symmetric self-gravitating systems now lead to ^2(R) - r r^3 (r)."
" ""Therefore. defining. the so-called: “spherical” radial velocity variance sz(r) through with osr((r)= πω. the virial relation (521) takes the usual form for spherically svmumiectric systems.M (8S5)rom now on called the “spherical” virial relation."," Therefore, defining the so-called “spherical” radial velocity variance $s^2\rad(r)$ through, with (r)= _0^r ^2 the virial relation \ref{vir1}) ) takes the usual form for spherically symmetric systems, from now on called the “spherical” virial relation."
 Furthermore. defining the “spherical” scaled surface pressure term (from now on simply spherical surface term). SCR). equal to the member on theleft of equation," Furthermore, defining the “spherical” scaled surface pressure term (from now on simply spherical surface term), ${\cal S}(R)$ , equal to the member on theleft of equation"
"and the growth rate, both of which depend on the values of cosmological parameters.","and the growth rate, both of which depend on the values of cosmological parameters."
" The one-halo term is derived from a consideration of the number halos as a function of halo mass, and a match to the redshift distribution of the survey in question."," The one-halo term is derived from a consideration of the number halos as a function of halo mass, and a match to the redshift distribution of the survey in question."
 It was shown in |Schneider&Bridle that the dependence on the survey redshift distribution is weak and thus we neglect it here., It was shown in \citet{schneiderb09} that the dependence on the survey redshift distribution is weak and thus we neglect it here.
" The dependence of both terms on cosmology could be included, and this would make sense if we had complete faith in the models."," The dependence of both terms on cosmology could be included, and this would make sense if we had complete faith in the models."
 We have the alternative of considering the IA power spectra for our fiducial model as a template representing a reasonable but poorly understood guess at the contribution from IAs., We have the alternative of considering the IA power spectra for our fiducial model as a template representing a reasonable but poorly understood guess at the contribution from IAs.
 For this work we use the one-halo term as given in and ignore any cosmology dependence within it., For this work we use the one-halo term as given in \citet{schneiderb09} and ignore any cosmology dependence within it.
 We choose to fix og within the two-halo calculation to the fiducial value., We choose to fix $\sigma_8$ within the two-halo calculation to the fiducial value.
 Therefore the relative amplitude of the one- and two-halo terms stay roughly constant and the overall amplitude of the sum is varied (see below)., Therefore the relative amplitude of the one- and two-halo terms stay roughly constant and the overall amplitude of the sum is varied (see below).
" In this paper we choose to vary the matter density inside the linear theory matter power spectra used in the two-halo terms in equations and and in the €), contribution to the normalised growth in the denominator of these equations.", In this paper we choose to vary the matter density inside the linear theory matter power spectra used in the two-halo terms in equations \ref{eq:PEE2h} and \ref{eq:PdgI2h} and in the $\Omega_{\rm m}$ contribution to the normalised growth in the denominator of these equations.
" 'To include the colour and luminositydependence we generalise our halo model equations [9] and [I0] which scales the amplitude of both one- and two-halo terms by the same factor, given in square brackets."," To include the colour and luminositydependence we generalise our halo model equations \ref{eq:P_II_halo} and \ref{eq:P_GI_halo}
 which scales the amplitude of both one- and two-halo terms by the same factor, given in square brackets."
" The factor in square brackets is squared in the first equation and not in the second equation, to mimic a simultaneous modulation of the one-halo scaling parameter scale and the two-halo amplitude parameter Οι."," The factor in square brackets is squared in the first equation and not in the second equation, to mimic a simultaneous modulation of the one-halo scaling parameter $\gamma_{\rm scale}$ and the two-halo amplitude parameter $C_1$ ."
 Throughout we retain the fiducial values of 4c4j=0.21 following |Schneider&(2010) and C1=5x10(D?MoMpc3) Apa, Throughout we retain the fiducial values of $\gamma_{\rm scale} = 0.21$ following \citet{schneiderb09} and $C_1 = 5\times10^{-14} (h^2 M_{\odot} {\rm Mpc}^{-3})^{-1}$ following \citet{bridleandking}.
 L/Lo is the normalised luminosity of the data bin and fr is the fraction of red galaxies in the data bin., ${L}/{L_0}$ is the normalised luminosity of the data bin and $f_r$ is the fraction of red galaxies in the data bin.
 This power law in luminosity is equivalent to that used in the power law fits of , This power law in luminosity is equivalent to that used in the power law fits of \cite{hirataea07}.
The motivation for multiplication by the red fraction f. is (2007)..that we assume only red galaxies have IAs., The motivation for multiplication by the red fraction $f_r$ is that we assume only red galaxies have IAs.
 These equations could be generalised to have different IA amplitudes for red and blue galaxies by adding a term proportional to the blue fraction (1—f.) with a different variable amplitude parameter., These equations could be generalised to have different IA amplitudes for red and blue galaxies by adding a term proportional to the blue fraction $(1-f_r)$ with a different variable amplitude parameter.
" However, we defer such modelling to future work."," However, we defer such modelling to future work."
 A and f are free parameters., A and $\beta$ are free parameters.
" Note that the above equations reduce to the basic halo model forA=f,=1, 8=0."," Note that the above equations reduce to the basic halo model for $A = f_r = 1$, $\beta = 0$."
 In this Section we summarise the cosmic shear data we use and compare it with predicted correlation functions with the various IÀ models., In this Section we summarise the cosmic shear data we use and compare it with predicted correlation functions with the various IA models.
 We then make first calculation of the impact of the models on constraintsa on the amplitude of matter clustering and the matter density of the Universe., We then make a first calculation of the impact of the models on constraints on the amplitude of matter clustering and the matter density of the Universe.
 The dataset used to constrain models in this paper is the 100 Square Degree weak lensing survey 2007]., The dataset used to constrain models in this paper is the 100 Square Degree weak lensing survey \citep{benjaminea07}.
".. This combines data from the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS)-Wide, the Garching-Bonn Deep Survey (GaBoDS), the Red-sequence Cluster Survey (RCS) and the VIRMOS-DESCART surveys."," This combines data from the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS)-Wide, the Garching-Bonn Deep Survey (GaBoDS), the Red-sequence Cluster Survey (RCS) and the VIRMOS-DESCART surveys."
" The CFHTLS-Wide data included in this compilation covers an area of 22 deg’, reaching a depth of i' = 24.5 (Hoekstraetal.|2006).."," The CFHTLS-Wide data included in this compilation covers an area of 22 $^2$, reaching a depth of i' = 24.5 \citep{Hoekstra:2006cs}."
" There is 13 deg? of data from the GaBoDS survey which uses objects which lie in the interval R € [21.5,24.5] (Hetterscheidtetal.|/2007)."," There is 13 $^2$ of data from the GaBoDS survey which uses objects which lie in the interval R $\in$ [21.5,24.5] \citep{hetterscheidt2007}."
. The RCS data covers 53 deg? with a limiting magnitude of 25.2 in the Rc band (HoekstraetaL.|2002)..., The RCS data covers 53 $^2$ with a limiting magnitude of 25.2 in the $R_C$ band \citep{hoekstraea2002RCS}.
 The VIRMOS-DESCART data has an effective area of 8.5 deg? and a limiting magnitude of 14Η=24.5 (LeFevreetal.|2004)., The VIRMOS-DESCART data has an effective area of 8.5 $^2$ and a limiting magnitude of $I_{AB} = 24.5$ \citep{lefevreea04}.
. Throughout this paper we use the redshift distributions for each data set as given by Eq., Throughout this paper we use the redshift distributions for each data set as given by Eq.
 9 of using the parameters given in the upper section of their Table 2 for the high confidence regime (fittedtophotometricredshiftsintherange0.2«z1.5from, 9 of \citet{benjaminea07} using the parameters given in the upper section of their Table 2 for the high confidence regime \citep[fitted to photometric redshifts in the range $0.2<z<1.5$ from][]{ilbertea06}.
 took into account ∙∙uncertainties in the photometric redshift distributions by sampling from tuples of these parameter values and selecting the best fit values for each of the three parameters., \citet{benjaminea07} took into account uncertainties in the photometric redshift distributions by sampling from tuples of these parameter values and selecting the best fit values for each of the three parameters.
 For computational practicality we here ignore uncertainties in the photometric redshift distributions., For computational practicality we here ignore uncertainties in the photometric redshift distributions.
" We therefore next describe in more detail the relative differences between the redshift distributions of the different surveys, ignoring the uncertainties."," We therefore next describe in more detail the relative differences between the redshift distributions of the different surveys, ignoring the uncertainties."
" Since the impact of IAs on each dataset hinges so much on the redshift distribution we show the redshift distributions and the difference in distribution, with respect to CFHTLS, for each dataset in Fig. [I]. "," Since the impact of IAs on each dataset hinges so much on the redshift distribution we show the redshift distributions and the difference in distribution, with respect to CFHTLS, for each dataset in Fig. \ref{fig:n(z)}. ."
We see that VIRMOS-DESCART and GaBoDS have the greatest number of low redshift galaxies and VIRMOS-DESCARTshows a signifigant excess at z~ 1.4., We see that VIRMOS-DESCART and GaBoDS have the greatest number of low redshift galaxies and VIRMOS-DESCARTshows a signifigant excess at $z\sim1.4$ .
For example. our Galaxy has a distribution of [Fe/1I] which peaks at -1.6 ancl -0.6 and the lowest value is -2.29 (Harris 2001).,"For example, our Galaxy has a distribution of [Fe/H] which peaks at -1.6 and -0.6 and the lowest value is -2.29 (Harris 2001)."
 For M31. M 81 and NGC! 4472. the numbers are respectively: -1.4. -0.6 and -2.18 (Barmby et al.," For M31, M 81 and NGC 4472, the numbers are respectively: -1.4, -0.6 and -2.18 (Barmby et al."
 2000) -1.45. -0.53 and -2.0 (Ala et al.," 2000) -1.45, -0.53 and -2.0 (Ma et al."
 2005) -1.3. -0.1 and -2.0 (Geisler et al.," 2005) -1.3, -0.1 and -2.0 (Geisler et al."
 1996)., 1996).
 While metallicity ancl colors measure the state of evolution of the stellar populations. the structural parameters mainly give indications on the cdvnanmical evolution of the GCs. and (the (vee eroups are markedly different in (his respect as well.," While metallicity and colors measure the state of evolution of the stellar populations, the structural parameters mainly give indications on the dynamical evolution of the GCs, and the three groups are markedly different in this respect as well."
 GCs are predicted to become rounder as (μον lose stars and angular momentum in the course of their evolution., GCs are predicted to become rounder as they lose stars and angular momentum in the course of their evolution.
 In GI the roundest GCs are also the most metal-rich. whereas no such correlation is present in G2 or G3. as shown on Fig.6.," In G1 the roundest GCs are also the most metal-rich, whereas no such correlation is present in G2 or G3, as shown on Fig.6."
 In G2. the rounclest GC's are also the least massive.," In G2, the roundest GCs are also the least massive."
 During the dvnanmical evolution of GCs. their Z2. shrinks and their /2;;; increases.," During the dynamical evolution of GCs, their $R_c$ shrinks and their $R_{tid}$ increases."
 Core collapse occurs when the ratio /og(Ry;4/R.)> 2.5., Core collapse occurs when the ratio $log(R_{tid}/R_c) >$ 2.5.
 As shown on Fig.T. this is the ease for most GC's ol G2 which are thus at an advanced stage of dvnamical evolution. for à minority of GCs in Gl. and for hardly anv in G3.," As shown on Fig.7, this is the case for most GCs of G2 which are thus at an advanced stage of dynamical evolution, for a minority of GCs in G1, and for hardly any in G3."
 A color-color diagram is another wav of examining the properties of the stellar populations of the GC's., A color-color diagram is another way of examining the properties of the stellar populations of the GCs.
" This is done in Fie.&. which shows (C—Ti), vs (M—T3), in the Washington photometric svstem lor our sample. using data frou Πανάς et al. ("," This is done in Fig.8, which shows $(C-T_1)_o$ vs $(M-T_1)_o$ in the Washington photometric system for our sample, using data from Harris et al. ("
2004).,2004).
 For comparison. we also plotted on Fig.8 data for Galactic GCs (open squares. from Harris Canterna 1971) and [ον low surface-brightness (LSB) dwarf galaxies (open (rianeles) [rom Cellone et al. (," For comparison, we also plotted on Fig.8 data for Galactic GCs (open squares, from Harris Canterna 1977) and for low surface-brightness (LSB) dwarf galaxies (open triangles) from Cellone et al. ("
1994).,1994).
 In order to interpret (his Figure. we also plotted several model stellar populations: the thin black solid line is an SSP track of varving metallicity al 15Gvr from Cellone Forte (1996).," In order to interpret this Figure, we also plotted several model stellar populations: the thin black solid line is an SSP track of varying metallicity at 15Gyr from Cellone Forte (1996)."
 The thick short-dashed and dotted lines are (racks of varying age for ellipticals and 5a galaxies [rom Duzzoni (2005)., The thick short-dashed and dotted lines are tracks of varying age for ellipticals and Sa galaxies from Buzzoni (2005).
 The colored grid of models (metallicities z=O0.0004. 0.004. 0.008. 0.02. and 0.04) are GALEV SSP models from Anders Fritze - v. Alvensleben.," The colored grid of models (metallicities z=0.0004, 0.004, 0.008, 0.02, and 0.04) are GALEV SSP models from Anders Fritze - v. Alvensleben,"
"The slopes of the PDMF in the different mass regimes (above and below m., respectively) are notably shallower than the corresponding part of the Kroupa- (Salpeter slope [= —1.35).","The slopes of the PDMF in the different mass regimes (above and below $m_c$, respectively) are notably shallower than the corresponding part of the Kroupa--IMF (Salpeter slope $\Gamma=-1.35$ )."
" However, a source of uncertainty in the derivation of the MF slope are unresolved binaries."," However, a source of uncertainty in the derivation of the MF slope are unresolved binaries."
" Depending on the binary fraction and the intrinsic slope of the stellar MF, the observed slope may deviate from the intrinsic slope by up to AT~210.5 (eg.Sagar&Richtler1991;Kroupa 2001).."," Depending on the binary fraction and the intrinsic slope of the stellar MF, the observed slope may deviate from the intrinsic slope by up to $\Delta \Gamma \sim+0.5$ \cite[e.g.][]{sagar,kroupa}."
 Even with such a large correction our PDMF would appear flatter than a Kroupa-IMF., Even with such a large correction our PDMF would appear flatter than a Kroupa–IMF.
" Considering the rather flat slope of the PDMF of the central region of Tr114 and the unaccounted effect of unresolved binaries, the derived PDMF is in good agreement with the central PDMFs observed in other young and massive clusters."," Considering the rather flat slope of the PDMF of the central region of 14 and the unaccounted effect of unresolved binaries, the derived PDMF is in good agreement with the central PDMFs observed in other young and massive clusters."
" In the very central region in YYC slopes of the MF are found between [ο”—0.31 and -0.91, depending on the stellar population (MS, PMS, PMS plus MS) and area considered in deriving the MF (e.g.Sung&Bessell2004;Stolteetal.2006;Harayama 2008)."," In the very central region in YC slopes of the MF are found between $\Gamma\sim-0.31$ and -0.91, depending on the stellar population (MS, PMS, PMS plus MS) and area considered in deriving the MF \cite[e.g.][]{sung,stolte06,harayama}."
. The different considered mass ranges do not hamper the comparison as above 0.5 the MF is described by a single-power law (Salpeter1955;MeKroupa2001).," The different considered mass ranges do not hamper the comparison as above 0.5 $_{\sun}$ the MF is described by a single-power law \cite{salpeter,kroupa}."
". In the case of 11, Gennaro et al. ("," In the case of 1, Gennaro et al. ("
2011) found a significant flattening of the PDMF towards the centre of the cluster with slopes down to I~—0.7 although the very centre could not be considered due to severe saturation effects.,2011) found a significant flattening of the PDMF towards the centre of the cluster with slopes down to $\Gamma\sim-0.7$ although the very centre could not be considered due to severe saturation effects.
" In the central 0.75 pc, as in our study of 114, Brandner et al. ("," In the central 0.75 pc, as in our study of 14, Brandner et al. ("
2008) could identify a similarly flat PDMF with I'~—0.5.,2008) could identify a similarly flat PDMF with $\Gamma\sim-0.5$.
" However, it should be noted that we have to regard the effect of dynamical mass segregation in case of YYC and 11 flattening the central PDMF because of the significantly higher density in these clusters."," However, it should be noted that we have to regard the effect of dynamical mass segregation in case of YC and 1 flattening the central PDMF because of the significantly higher density in these clusters."
" In contrast, no mass segregation was observed in the centre of Tr114 in the considered mass range."," In contrast, no mass segregation was observed in the centre of 14 in the considered mass range."
" Based on a minimum spanning tree analysis, mass segregation was identified for stars more massive than 10 Mo (Sanaetal.2010).."," Based on a minimum spanning tree analysis, mass segregation was identified for stars more massive than 10 $_{\sun}$ \cite{sana}."
" They have analyzed the same MCAO data of Tr114 but including also the shallower MAD observations of the adjacent fields, such that the analyzed FoV encloses the central 2 arcmin."," They have analyzed the same MCAO data of 14 but including also the shallower MAD observations of the adjacent fields, such that the analyzed FoV encloses the central 2 arcmin."
 À comparable result has, A comparable result has
explosions. the metallicity distribution functüon of the stellar halo. the initial mass Dunction. ihe nature of the Big Bang and the first generation. or Population HI. stars. ete.,"explosions, the metallicity distribution function of the stellar halo, the initial mass function, the nature of the Big Bang and the first generation, or Population III, stars, etc."
 An important place among these fundamental problems is occupied by the questions of the origin. chemical and dynamical evolution of our Galaxy.," An important place among these fundamental problems is occupied by the questions of the origin, chemical and dynamical evolution of our Galaxy."
 The oldest stars with the masses of M<0.8M. are unevolved., The oldest stars with the masses of $M\leqslant0.8\ M_{\odot}$ are unevolved.
 Therefore. the abundance of chemical elements in their atmospheres reproduces the composition of prestellar matter.," Therefore, the abundance of chemical elements in their atmospheres reproduces the composition of prestellar matter."
 Additional information on spatial motions of these stars preserves the possibility to reconstruct the way the Milky Way formed., Additional information on spatial motions of these stars preserves the possibility to reconstruct the way the Milky Way formed.
 The orbital elements of binary. and multiple stellar svstems are an important tool for studying prestellar matter., The orbital elements of binary and multiple stellar systems are an important tool for studying prestellar matter.
 In single low mass stars. (he mass is (he only parameter conserved since the time of star formation.," In single low mass stars, the mass is the only parameter conserved since the time of star formation."
 Binary ancl multiple svstems bear three more conserved. values: the angular momentum. the eccentricity and the mass ratio of their components (Larson2001). in case of detached systems.," Binary and multiple systems bear three more conserved values: the angular momentum, the eccentricity and the mass ratio of their components \citep{larson} in case of detached systems."
 Therefore. binary. and multiple stars carry more information on the process of star Formation than simele stars.," Therefore, binary and multiple stars carry more information on the process of star formation than single stars."
 The study of binary and multiple metal-poor svstems enables us to impose certam restrictions on the physical conditions in prestellar matter at the time of the genesis of our Galaxy., The study of binary and multiple metal-poor systems enables us to impose certain restrictions on the physical conditions in prestellar matter at the time of the genesis of our Galaxy.
 Aletal-poor stars are common in the globular clusters. galactic halo ancl in the galactic field. where an existence of the so-called stellar streams wasrevealed (e.g.. Eggen199Ga.b)).," Metal-poor stars are common in the globular clusters, galactic halo and in the galactic field, where an existence of the so-called stellar streams wasrevealed (e.g., \citealt{eggen_1996a,eggen_1996b}) )."
 The multiplicity and the orbital parameters of binary. and multiple stars in these streams may also provide additional information on (he nature of the streams progenitor and its cdvnamical evolution., The multiplicity and the orbital parameters of binary and multiple stars in these streams may also provide additional information on the nature of the stream's progenitor and its dynamical evolution.
 The problem of stellar multiplicity was widely discussed in (he literature. however. it mostly concerned the thin disc stars with solar-like metalliciGes (Ducquennoy&Mayor1991:Fischer&AMarev1992:Halbwachsetal.," The problem of stellar multiplicity was widely discussed in the literature, however, it mostly concerned the thin disc stars with solar-like metallicities \citep{dm91,fischer_marcy,halbwachs}."
 2003).. Metal-poor stars were studied much less. as their occurrence in the solar neighbourhood is less than 1'4.. according to," Metal-poor stars were studied much less, as their occurrence in the solar neighbourhood is less than , according to"
The EROS experiment has monitored a wider solid angle and less crowed fields in LMC than the MACHO team.,The EROS experiment has monitored a wider solid angle and less crowed fields in LMC than the MACHO team.
 In addition. it has also monitored the SMC.," In addition, it has also monitored the SMC."
 For these reasons. self-lensing of the LMC should be less important in the EROS experiment than in the case of the MACHO collaboration.," For these reasons, self-lensing of the LMC should be less important in the EROS experiment than in the case of the MACHO collaboration."
 Consequently. a smaller value of the optical depth should be expected. and this is indeed the case.," Consequently, a smaller value of the optical depth should be expected, and this is indeed the case."
 The EROS results. adopting a standard halo model and assumingtTsme=].4rj;ic. indicate that the microlensing optical depth is to=0.36x1077 (Tisserand et al.," The EROS results, adopting a standard halo model and assuming$\tau_{\rm
SMC}=1.4\tau_{\rm LMC}$ indicate that the microlensing optical depth is $\tau_0=0.36\times10^{-7}$ (Tisserand et al."
 2007). which is four times smaller than that obtainded by the MACHO team.," 2007), which is four times smaller than that obtainded by the MACHO team."
 We have performed a set of simulations emulating the conditions of the EROS experiment using the same populations described previously., We have performed a set of simulations emulating the conditions of the EROS experiment using the same populations described previously.
 Although only small differences should be expected. this new series of simulations represents a test of the robustness of our numerical procedures.," Although only small differences should be expected, this new series of simulations represents a test of the robustness of our numerical procedures."
 In Table 2 we summarize the results obtained for this set of simulations., In Table 2 we summarize the results obtained for this set of simulations.
 Our simulations show that independently of the adopted model for the spectral type of white dwarfs. the joint population of red dwarfs and white dwarfs of the galactic halo provides at most ~90% of the optical depth estimated by the EROS team.," Our simulations show that independently of the adopted model for the spectral type of white dwarfs, the joint population of red dwarfs and white dwarfs of the galactic halo provides at most $\sim 90\%$ of the optical depth estimated by the EROS team."
 This value represents an increase of ~20% with respect to the one obtained in our previous simulations (Torres et al., This value represents an increase of $\sim 20\%$ with respect to the one obtained in our previous simulations (Torres et al.
 2008)., 2008).
 Obviously. the non-DA white ¢warf population is responsible for this result. and this confirms our previous conclusion that there is à general agreement between the theoretical models and the results of the EROS tean.," Obviously, the non-DA white dwarf population is responsible for this result, and this confirms our previous conclusion that there is a general agreement between the theoretical models and the results of the EROS team."
 Moreover the EROS experiment used a set of selection criteria in. the. search of halo white dwarfs to distinguish halo objects from thick disk stars (Goldman et al., Moreover the EROS experiment used a set of selection criteria in the search of halo white dwarfs to distinguish halo objects from thick disk stars (Goldman et al.
 2002)., 2002).
 For those stars detectable by EROS. namely those with magnitudes brighter than V=21.5 and 7=20.5. the selection criteria are implemented by two cuts.," For those stars detectable by EROS, namely those with magnitudes brighter than $V=21.5$ and $I=20.5$, the selection criteria are implemented by two cuts."
 The first one uses the reduced proper motion and requires that the reduced proper motion of a halo object should be Hy>22.5., The first one uses the reduced proper motion and requires that the reduced proper motion of a halo object should be $H_V>22.5$.
 The second cut is applied to the resulting sample and only selects those stars with large proper motions. jt>0.8” yr!.," The second cut is applied to the resulting sample and only selects those stars with large proper motions, $\mu>0.8''\,{\rm yr^{-1}}$ ."
 In Fig., In Fig.
 3 we present a typical, 3 we present a typical
appears blurred because of its motion during the svuthesis observation.,appears blurred because of its motion during the synthesis observation.
 As shown in the flax curve of AD Leo (Fig. 1..," As shown in the flux curve of AD Leo (Fig. \ref{fig:light97},"
 right plot). the total flux varied bv a factor of 3 during the observations.," right plot), the total flux varied by a factor of 3 during the observations."
 Adding this fact to the high proper motion of the star. if is not surprising that attempts to fit a suele eaussian to the «.c-data did not give consistent results.," Adding this fact to the high proper motion of the star, it is not surprising that attempts to fit a single gaussian to the $u,v$ -data did not give consistent results."
 The weakness aud variability of the star make the estimation of errors on the size difficult., The weakness and variability of the star make the estimation of errors on the size difficult.
 ILoxeever. from he imageoO (see Fie.oO 2)).," However, from the image (see Fig. \ref{fig:cntr}) ),"
 we can note that the appareut FWIIP perpendicular to the motion corresponcs fo he an FWIIP iu this direction., we can note that the apparent FWHP perpendicular to the motion corresponds to the beam FWHP in this direction.
 The intrinsic FWTIP size of the eunüttiug region is therefore likely to be ess tlnm wf the beam EWIIP or about 1 mas. which οςvals he estimated optical diameter of the star (see Table 1)).," The intrinsic FWHP size of the emitting region is therefore likely to be less than half the beam FWHP or about 1 mas, which equals the estimated optical diameter of the star (see Table \ref{tab:sum}) )."
 This wieht incicate a very compact corona or al clit mesyot on the surface of the star., This might indicate a very compact corona or an emitting spot on the surface of the star.
 A very couscrvative upver Liuit ou the size of the corona in the former case wotId be to, A very conservative upper limit on the size of the corona in the former case would be to
νο) has varied by study from 3 (2?) to Gor 8 (2).,"$f_{\nu}$ (LyC) has varied by study from 3 \citep{2001ApJ...546..665S,2006ApJ...651..688S} to 6 or 8 \citep{2007ApJ...668...62S}."
" Since we probe LyC radiation at slightly πα"" wavelengths. at ccolmpared with (??).. we used the spectral energy distributions (SEDs) of ? and estimated the breax amplitude for f,, Fo .)) to be 3.1 based on £,(1500À. ÉL .J)2 3."," Since we probe LyC radiation at slightly bluer wavelengths, at compared with \citep{2001ApJ...546..665S,2006ApJ...651..688S}, we used the spectral energy distributions (SEDs) of \citet{2003MNRAS.344.1000B} and estimated the break amplitude for $f_{\nu}$ $f_{\nu}$ ) to be 3.4 based on $f_{\nu}$ $f_{\nu}$ $=3$ ."
 We assune a factor of —1.2 (ορίτιονο) ) reduction iu [νο fisoy for the neutral hydrogen opacity in the ICM. modeled in the same mauner as ?/ and ?..," We assume a factor of $\sim$ 1.2 $exp(\tau_{\mathrm{IGM,LyC}})$ ) reduction in $f_{\mathrm{LyC}}$ $f_{1500}$ for the neutral hydrogen opacity in the IGM, modeled in the same manner as \citet{1995ApJ...441...18M} and \citet{2007ApJ...668...62S}."
 The SBC spectra measure up to rest frame ~1080 ffor our targets., The SBC spectra measure up to rest frame $\sim1080$ for our targets.
 Therefore. to calculate the escaping UV photons atJ we use the flux within our spectruui between rest frame 1000 and aand apply a scaling factor (5) to estimate the flux at (CCfisoo).," Therefore, to calculate the escaping UV photons at, we use the flux within our spectrum between rest frame 1000 and and apply a scaling factor $S$ ) to estimate the flux at $f_{1500}$ )."
 The sources in our sample are by selection. blue objects with low to moderate levels of extinction.," The sources in our sample are by selection, blue objects with low to moderate levels of extinction."
 Using the SEDs of ?.. aud asstning 0.1 solar inetallicity. constant star formation with a 300 Myr old population. we derive the scaling factor to eo from the fioos to fFisoo to be 1.5 in fy.," Using the SEDs of \citet{2003MNRAS.344.1000B}, and assuming 0.4 solar metallicity, constant star formation with a 300 Myr old population, we derive the scaling factor to go from the $f_{1025}$ to $f_{1500}$ to be 1.5 in $f_{\lambda}$."
 The flux measurement docs not consider the possible effect. if any. of the Ly.) A1026 absorption line as seen in a composite spectrum of 2~3 LBs ?..," The flux measurement does not consider the possible effect, if any, of the $\beta$ $\lambda$ 1026 absorption line as seen in a composite spectrum of $z\sim3$ LBGs \cite{2006ApJ...651..688S}."
 Although the spectral resolution is too low to estimate the strength of this line. it likely has little iupact since our measure of the coutinmun fux is averaged over 50 -Thhe fluxes derived from the spectra are also cousisteut with aperture photometry derived using the FI50LP nuages.," Although the spectral resolution is too low to estimate the strength of this line, it likely has little impact since our measure of the continuum flux is averaged over 50 \\.Thhe fluxes derived from the spectra are also consistent with aperture photometry derived using the F150LP images."
 As we mentioned. earlier. due to the slitless nature ft the spectra there is spectral simcaring along the ispersion direction proportional to the spatial size of the object.," As we mentioned earlier, due to the slitless nature of the spectra there is spectral smearing along the dispersion direction proportional to the spatial size of the object."
 A different red wavelength cutoff was asstmed for cach object based ou the galaxvs size in the SBC irect nuage to cusure that light rechwarcd of the Lyimau lut did not contaminate the LyC flux measurciuent., A different red wavelength cutoff was assumed for each object based on the galaxy's size in the SBC direct image to ensure that light redward of the Lyman limit did not contaminate the LyC flux measurement.
 The sources have typical radii of ~7-20 pixels in FLSOLP correspouding to a red cutoff of rauge of 58520-880AÀ., The sources have typical radii of $\sim$ 7-20 pixels in F150LP corresponding to a red cutoff of range of $\sim$.
ων Furthermore. the seusitivitv drops sharply at the blue end and therefore we cousider ouly the regious at rest waveleugths >TAOAα," Furthermore, the sensitivity drops sharply at the blue end and therefore we consider only the regions at rest wavelengths $>780$."
ν The final spectral region used when estimating the LvC fux is between T80 aud with the red cutoff changing as a function of galaxy size (shaded regions in Figure 5)., The final spectral region used when estimating the LyC flux is between $\sim$ 780 and with the red cutoff changing as a function of galaxy size (shaded regions in Figure 5).
 The coutinumiu is relatively flat avouud ffor ealaxies that are actively forming stars (?).. like those in our sample.," The continuum is relatively flat around for galaxies that are actively forming stars \citep{2003MNRAS.344.1000B}, like those in our sample."
 We therefore iutegrate the observed spectruni over several resolution elemieuts to ducerease the signal-to-noise ratio., We therefore integrate the observed spectrum over several resolution elements to increase the signal-to-noise ratio.
 The wavelength solutions of the SBC are accurate to a few anestroms between observed aud oover the SBC field of view. aud the flux calibrations over this waveleneth range are accurate to approximately 5% (2)..," The wavelength solutions of the SBC are accurate to a few angstroms between observed and over the SBC field of view, and the flux calibrations over this wavelength range are accurate to approximately $5\%$ \citep{2006acs..rept....9L}."
 The flux below the Lyman lait κου) is taken to be the average flux between 780 aud (again the red cutoff depends on the galaxw size)., The flux below the Lyman limit $f_{830}$ ) is taken to be the average flux between 780 and (again the red cutoff depends on the galaxy size).
 The uncertainty iu fssy is derived usine the following equation: where Af is the staudard deviation of the flux iu cach pixel. AA is the size of cach pixel in anestrois (this value changes as a function of waveleneth). aud AA is the total waveleneth rauge beiug averaged.," The uncertainty in $f_{830}$ is derived using the following equation: where $\Delta f_{er}$ is the standard deviation of the flux in each pixel, $\Delta\lambda$ is the size of each pixel in angstroms (this value changes as a function of wavelength), and $\Delta\lambda_{\mathrm{tot}}$ is the total wavelength range being averaged."
" The amount of escaping radiation below the Lyian lanit is typically reported using arelative escape fraction (defined earlier in this section) or through a UV-to-LyC flux density ratio (Ff, ))/f, (830A)).", The amount of escaping radiation below the Lyman limit is typically reported using a escape fraction (defined earlier in this section) or through a UV-to-LyC flux density ratio $f_{\nu}$ $/f_{\nu}$ ).
 The former measure. however. requires an assuniptiou for the intrinsic Lyman break which is not well coustrained.," The former measure, however, requires an assumption for the intrinsic Lyman break which is not well constrained."
 In the next section. we present both the UW-to-LyC fux density ratios aud the inferred relative escape fractions for completeucss.," In the next section, we present both the UV-to-LyC flux density ratios and the inferred relative escape fractions for completeness."
 We find one detection of escapiug LvC radiation in au ACUN stavburst composite. but no direct detections of far-UV flux in our remaining sample of 51 2—0.7 LBC analogs.," We find one detection of escaping LyC radiation in an AGN starburst composite, but no direct detections of far-UV flux in our remaining sample of 31 $z\sim0.7$ LBG analogs."
 Nine galaxies (C-UVLC-3. 9. 10. 13. 11. 16. 22. 31. 32) were not detected in the direct F150LP image or PRIJ0L spectra.," Nine galaxies (C-UVLG-3, 9, 10, 13, 14, 16, 22, 31, 32) were not detected in the direct F150LP image or PR130L spectra."
" Measuring limits on the LyC escape for these objects requires careful cross-calibration between aand ddata due to the significant difference in aneular resolutions ppoiut spread function (PSF) ~5""in the FUV band) aud will be preseuted in a future paper (ILI. Teplitz ct al."," Measuring limits on the LyC escape for these objects requires careful cross-calibration between and data due to the significant difference in angular resolutions point spread function (PSF) $\sim5$ in the FUV band) and will be presented in a future paper (H.I. Teplitz et al.,"
 2010 in preparatio)., 2010 in preparatio).
 The nou-detections are likely due to in part to their large size which resulted in UV surface brightuesses below the scusitivity of our observations., The non-detections are likely due to in part to their large size which resulted in UV surface brightnesses below the sensitivity of our observations.
 Another likely contributing factor is that 7/9 of the udetected galaxies had the larecst extinctious within our suuple E(BVj20.3. based on SED fitting.," Another likely contributing factor is that 7/9 of the undetected galaxies had the largest extinctions within our sample $E(B-V)>0.3$, based on SED fitting."
" The observed flux deusitv ratio. f,15007f;530. i the individual sources range from 20 to 2014 with a median of 73.5 (30 lower linüits)."," The observed flux density ratio, $f_{\nu}{1500}/f_{\nu}{830}$, in the individual sources range from 20 to 204 with a median of 73.5 $3\sigma$ lower limits)."
 In orderto convert these ratios iuto a escape fraction. we apply Equation (13) assundue an average ICAL transmission of 0.85 and a value of 3. Lor 7 for the iutriusic Lyman break (see Table 1))," In orderto convert these ratios into a escape fraction, we apply Equation \ref{eqn: fesc_rel}) ) assuming an average IGM transmission of 0.85 and a value of 3.4 or 7 for the intrinsic Lyman break (see Table \ref{tab:result}) )."
 Our far-UV sensitivities give [νο close to zero. with individual 26 upper limits ranging from 0.010.19.," Our far-UV sensitivities give $f_{\mathrm{esc,rel}}$ close to zero, with individual $3\sigma$ upper limits ranging from $0.01-0.19$."
 Since we have assumed an average IGAL transmission. these upper limits are likely to be even lower in the majority of these objects since the IGAL opacity at low redshift is dominated by very few opaque lines of sight ?," Since we have assumed an average IGM transmission, these upper limits are likely to be even lower in the majority of these objects since the IGM opacity at low redshift is dominated by very few opaque lines of sight \cite{2007ApJ...668...62S}."
 Iu order to mBucrease our sensitivity further. we stacked the nou-detectious with UV sizes 20778 iu diameter. which correspouds to a red cutoff of —860À.," In order to increase our sensitivity further, we stacked the non-detections with UV sizes $\lsim 0\farcs78$ in diameter, which corresponds to a red cutoff of $\sim$."
αν This ved cutoff was chosen to niaxinizing the ΠΡΟ) of galaxies m the stack while probing as closely to the Lyiuaulimit as possible., This red cutoff was chosen to maximizing the number of galaxies in the stack while probing as closely to the Lymanlimit as possible.
" The stack was composed of 15 ealaxies placing a 30 lower linut on f£,15007f,830 =378.7 and a 236 upper huit of fac<0.01 (Figure 6)) ."," The stack was composed of 18 galaxies placing a $3 \sigma$ lower limit on $f_{\nu}{1500}/f_{\nu}{830}=$ 378.7 and a $3\sigma$ upper limit of $f_{\mathrm{esc,rel}}<0.01$ (Figure \ref{fig:stackedfull}) ) ."
 Iu addition to the elobal stack. we separated the sample by inorpholoey. stacking the cight galaxies which were visually classified in the," In addition to the global stack, we separated the sample by morphology, stacking the eight galaxies which were visually classified in the"
where it should be understood that HV;=0 for those time bins that contain no measurements.,where it should be understood that $W_i = 0$ for those time bins that contain no measurements.
 The Τεν are used to weight the time bins in the subsequent analysis., The $W_i$ 's are used to weight the time bins in the subsequent analysis.
 As stated above. a sinoothed version of the light curve Is. da Παν of our analyses. subtracted from the binned data.," As stated above, a smoothed version of the light curve is, in many of our analyses, subtracted from the binned data."
 The sinoothed version is elven by a time bin by time bin ratio m which the wmmerator is computed by convolving a kernel function with a weighted version of the binned light curve., The smoothed version is given by a time bin by time bin ratio in which the numerator is computed by convolving a kernel function with a weighted version of the binned light curve.
 The denominator is computed by convolving the same kernel function with a weighted version of the window function., The denominator is computed by convolving the same kernel function with a weighted version of the window function.
 The value of the ith bin of the zinoothed data is eiven by where AO represents the kernel function. d aud VW are the above defined fuuctious of the time bin index ἐν aud denotes convolution.," The value of the $i$ th bin of the smoothed data is given by where $K$ represents the kernel function, $d$ and $W$ are the above defined functions of the time bin index $i$, and $\otimes$ ” denotes convolution."
 The kernel function A aav be ether a Caussian or a box fuuction., The kernel function $K$ may be either a Gaussian or a box function.
 Iu the case of the Caussian κοπο. the full width at half ανα response is taken to be equal to the sxinoothnius time paraueter.," In the case of the Gaussian kernel, the full width at half maximum response is taken to be equal to the smoothing time parameter."
 The Caussiau is calculated out to E11 standard deviatious frou its center., The Gaussian is calculated out to $\pm 14$ standard deviations from its center.
 In the case of the box function. the box width is taken to be twice the zioothing time parameter.," In the case of the box function, the box width is taken to be twice the smoothing time parameter."
 The convolutiou is accomplished using Fourier transforms., The convolution is accomplished using Fourier transforms.
 We repeated the analyses using sevendiffercut values of the sinoothing time parameter (see Table 2)) to optimize the sensitivity iu each of several different frequency ranges., We repeated the analyses using seven different values of the smoothing time parameter (see Table \ref{tbl:tmscls}) ) to optimize the sensitivity in each of several different frequency ranges.
 Iu each case the sioothed lelt curve was subtracted from the uwnsmoothed light curve. weights were applied. aud the results were Fourier trausformed.," In each case the smoothed light curve was subtracted from the unsmoothed light curve, weights were applied, and the results were Fourier transformed."
 Iu svinbols. this part of the analysis produces a filtered liebt curve described by: where the weights 3; are eiven by and Ap is a second weieliting index.," In symbols, this part of the analysis produces a filtered light curve described by: where the weights $Y_i$ are given by and $k_B$ is a second weighting index."
 Weight iudex values are given iu Table 1.., Weight index values are given in Table \ref{tbl:mthds}.
 We also did the analysis without subtracting a smoothed version of the light curve., We also did the analysis without subtracting a smoothed version of the light curve.
 The unweighted average of the set of F;s which correspond to bins with nouzero exposure is computed ancl then subtracted from each of the £; values for those bius., The unweighted average of the set of $F_i$ 's which correspond to bins with nonzero exposure is computed and then subtracted from each of the $F_i$ values for those bins.
 The resultant arrav is extended with zeroes by a factor of four and Fourier transtormed., The resultant array is extended with zeroes by a factor of four and Fourier transformed.
 The extension of the array viclds oversampling iu the frequency domain., The extension of the array yields oversampling in the frequency domain.
 The oversampled transform is converted iuto a powcr density spectrum which is normalized to have au average value of unity., The oversampled transform is converted into a power density spectrum which is normalized to have an average value of unity.
 The normalized power spectra are conressed by saving the average and iuaxinmun values for sets of contiguous frequeucy bius: the number of contiguous bius depends on the frequeneyv range and smoothing finie parameter (see Table 2))., The normalized power spectra are compressed by saving the average and maximum values for sets of contiguous frequency bins; the number of contiguous bins depends on the frequency range and smoothing time parameter (see Table \ref{tbl:tmscls}) ).
 We found that for the analyses where short z1100thiug time scales were used. Le. time scales of 0.3. 0.9. aud 3.0 days. the compressed power spectra lave a non-white appearance.," We found that for the analyses where short smoothing time scales were used, i.e., time scales of 0.3, 0.9, and 3.0 days, the compressed power spectra have a non-white appearance."
 The effect is strougest for the shortest sanootling time scale. ie... 0.3 days.," The effect is strongest for the shortest smoothing time scale, i.e., 0.3 days."
 It is not clear how o apply a threshold for detection of a periodicity in a jomwhite spectrum., It is not clear how to apply a threshold for detection of a periodicity in a nonwhite spectrum.
" Therefore we added a procedure (to he code that performs the compression described above) ο conrpute a ""background average power around cach conrpressed. frequency bin. and to then obtain whitened uaxinmuni values."," Therefore we added a procedure (to the code that performs the compression described above) to compute a “background” average power around each compressed frequency bin, and to then obtain whitened maximum values."
 Each whitened παΜΗ value is heu the ratio of a maximiin value iu au umvhitened conrpressed. spectrum to the correspondiug background average., Each whitened maximum value is then the ratio of a maximum value in an unwhitened compressed spectrum to the corresponding background average.
 The resulting whitened spectra eeuerallv appear o have little svstematic structure (see Fig. 1))., The resulting whitened spectra generally appear to have little systematic structure (see Fig. \ref{fig:whiten}) ).
 Table 1. lists. at the highest level. the variations of the analvsis method that we have used.," Table \ref{tbl:mthds} lists, at the highest level, the variations of the analysis method that we have used."
" We found hat the results from the methods where both weighting and filtering were applied προς, ονεν τοςvSO. aud “wthbs’) were almost always nearly equal or superior to the results obtained with the other methods (παν wet. “umes”)."," We found that the results from the methods where both weighting and filtering were applied (“wtgs”, “wtgs-v4”, ``wtgs-v8'', and “wtbx”) were almost always nearly equal or superior to the results obtained with the other methods (“unwt”, “wt”, “ungs”)."
 A typical. ies not the extreme best case. of the differences is illustrated iu Figure 2..," A typical, i.e., not the extreme best case, of the differences is illustrated in Figure \ref{fig:pdscalc}."
 Therefore we did not search for significant peaks in the power spectra obtained using the latter methods., Therefore we did not search for significant peaks in the power spectra obtained using the latter methods.
" The ""wtes. vwtes-v wetesvNC. and ους methods were all applied to theE. 1.5-12 keV band light curves. but the results ecnerally produced. power spectra that were quite simular m terms of both detailed appearauce and sensitivity."," The “wtgs”, “wtgs-v4”, “wtgs-v8”, and “wtbx” methods were all applied to the 1.5-12 keV band light curves, but the results generally produced power spectra that were quite similar in terms of both detailed appearance and sensitivity."
 Therefore only the “wtes” method was applied to the other three euergy bauds., Therefore only the “wtgs” method was applied to the other three energy bands.
 The results frou the four energy bands are. in sone cases. quite different from cach other.," The results from the four energy bands are, in some cases, quite different from each other."
 Table 2. lists iuoothiuse time scales and the corresponding bin durations. parameters uxed for conrpression and whitening. aud parameters used im searching for siguificaut peaks.," Table \ref{tbl:tmscls} lists smoothing time scales and the corresponding bin durations, parameters used for compression and whitening, and parameters used in searching for significant peaks."
 The powers iu a spectrum of Caussian white nolse are expected to be well characterized by an exponcutial probability distribution., The powers in a spectrum of Gaussian white noise are expected to be well characterized by an exponential probability distribution.
 We aake the asstuption that the powers iu the whitened spectra computed as described above similarly follow απ exponcutial distribution., We make the assumption that the powers in the whitened spectra computed as described above similarly follow an exponential distribution.
 In the preseut case it is not clear how to precisely compute the nunber of independent bius that we exanined because 1) some of the power spectra for a eivoen source involve the same data and differ only ou account of slight variations in the analysis procedure. aud 2) there is a significant degree of depeudence among the powers in an oversampled power spectrum.," In the present case it is not clear how to precisely compute the number of independent bins that we examined because 1) some of the power spectra for a given source involve the same data and differ only on account of slight variations in the analysis procedure, and 2) there is a significant degree of dependence among the powers in an oversampled power spectrum."
" Although it is uot fully justified on ana priori basis. we simply estimate the umber of independent bins Vj, bv the product of the nuuuber of frequency bins that would have applied if the Fourier spectra had not been oversampled. the uunber of cherey bands analyzed (1: this ucelects the"," Although it is not fully justified on an a priori basis, we simply estimate the number of independent bins $N_{ind}$ by the product of the number of frequency bins that would have applied if the Fourier spectrum had not been oversampled, the number of energy bands analyzed (4; this neglects the"
model a fraction μον0.13 of solar-neighbourhoocl stars belong to the thick disc: it followed that of order one third of the entire disc mass is contributed bv the thick disc.,model a fraction $f_{\rm thick}\sim0.13$ of solar-neighbourhood stars belong to the thick disc; it followed that of order one third of the entire disc mass is contributed by the thick disc.
 These numbers were in good agreement with the conclusions tha Juricetal.(2008) and Ivezicetal.(2008). clrew from SDSS counts of stars zLkpe from the plane., These numbers were in good agreement with the conclusions that \cite{Juric08} and \cite{Ivezic08} drew from SDSS counts of stars $\gta1\kpc$ from the plane.
 Using the presen chemical decomposition into thin and thick disces. we finc πως~0.12.," Using the present chemical decomposition into thin and thick discs, we find $f_{\rm thick}\sim 0.14$."
 In principle this number does not have to agree with the value obtained. from the density. profile., In principle this number does not have to agree with the value obtained from the density profile.
 1 does agree well because at |:lkpe the disc is dominatec by stars that have thick-disc chemistry 7))., It does agree well because at $|z|\gta1\kpc$ the disc is dominated by stars that have thick-disc chemistry ).
 shows the vertical density. profiles of the thin disc (&ereen). thick disc (red) and the entire cise (blue).," shows the vertical density profiles of the thin disc (green), thick disc (red) and the entire disc (blue)."
 Fits of exponentials to the density profiles vield scale wights of 268pe for the thin disc ancl anc S22pe for the hick disc., Fits of exponentials to the density profiles yield scale heights of $268\pc$ for the thin disc and and $822\pc$ for the thick disc.
 The two components of the latter have scale wights 690pe for the metal-poor thick dise and. 890pc or the metal-rich component., The two components of the latter have scale heights $690\pc$ for the metal-poor thick disc and $890 \pc$ for the metal-rich component.
 IE components show more or less exponential profiles., All components show more or less exponential profiles.
 “Phe metal-poor thick disc has he strongest. deviations from an exponential due to its ing a mix of very. old. stars from all over the disc with raclically cillerent intrinsic velocity clispersions., The metal-poor thick disc has the strongest deviations from an exponential due to its being a mix of very old stars from all over the disc with radically different intrinsic velocity dispersions.
 When a sum. of exponentials is fitted to the measured. vertical profile of he Galactic disc. good fits can be obtained with quite a wide range of scale heights on account of a correlation between he scale heights of the two discs and their normalisations.," When a sum of exponentials is fitted to the measured vertical profile of the Galactic disc, good fits can be obtained with quite a wide range of scale heights on account of a correlation between the scale heights of the two discs and their normalisations."
 The fits above to our individual discs are within the range of observationally acceptable scale heights (e.g.Juricet 2008)... consistent with the thick disc identified by Juric et bbeing close to what we have identified in the model using totally cillercnt criteria.," The fits above to our individual discs are within the range of observationally acceptable scale heights \citep[e.g.,][]{Juric08}, consistent with the thick disc identified by Juric et being close to what we have identified in the model using totally different criteria."
" bor simplicity. the SBO9 model does not accelerate the formation of the disc at small radii relative to large racii. as ds required by the popular ""inside-out mocel of. disc formation."," For simplicity the SB09 model does not accelerate the formation of the disc at small radii relative to large radii, as is required by the popular “inside-out” model of disc formation."
 I£ the model were adjusted. to include. out formation. the main change would be to the metal-poor thin disc. which would lose parts of its high-V. wing.," If the model were adjusted to include inside-out formation, the main change would be to the metal-poor thin disc, which would lose parts of its $V$ wing."
 llence the inside-out scenario could. be put. in. doubt. by demonstrating that the V. distribution of the high-a stars extends significantly to 12:0. andthat many high-V. stars have ages in excess of 10vr.," Hence the inside-out scenario could be put in doubt by demonstrating that the $V$ distribution of the $\alpha$ stars extends significantly to $V>0$, andthat many $V$ stars have ages in excess of $10\Gyr$."
 Further inside-out. formation could eive rise to some alpha enhanced. relatively. metal-poor stars vounger than I0Cr by the later onset of star formation in outer rings.," Further inside-out formation could give rise to some alpha enhanced, relatively metal-poor stars younger than $\sim 10 \Gyr$ by the later onset of star formation in outer rings."
 Neither the thin disc nor the metal-rich thick disc would be strongly allected by the introduction of inside-out. formation., Neither the thin disc nor the metal-rich thick disc would be strongly affected by the introduction of inside-out formation.
 Because it ds much easier to measure the velocity of à star than to determine its chemical. composition (particularly its a-enhancement). nearly all analyses select stars kinematically.," Because it is much easier to measure the velocity of a star than to determine its chemical composition (particularly its $\alpha$ -enhancement), nearly all analyses select stars kinematically."
 Our model provides an arena in which we can examine the extent to which kinematically selected samples of each component will be contaminated with stars [rom other components., Our model provides an arena in which we can examine the extent to which kinematically selected samples of each component will be contaminated with stars from other components.
 Samples of local stars such as those of Vennetal.(2004) and Densbvctal.(2005) are kinematically civicecdl into thin and thick-disc stars with the aid of model distribution funetions for cach component: as described in Bensbyctal. (2003).. cach star is assigned. to the component whose DE is largest at the stars velocity.," Samples of local stars such as those of \cite{Venn04} and \cite{Bensby05} are kinematically divided into thin and thick-disc stars with the aid of model distribution functions for each component: as described in \cite{Bensby03}, each star is assigned to the component whose DF is largest at the star's velocity."
 Both DES are of the type introduced by Schwarzschilel(1907).. namely where all components are with respect. to 10. Local Standard of Rest. &=(2x)UVT(mopmemy) tis thestandard normalisation constant. f; is the relative weight of the population.," Both DFs are of the type introduced by \cite{Schwarzschild}, namely where all components are with respect to the Local Standard of Rest, $k=(2\pi)^{-3/2}(\sigma_U\sigma_V\sigma_W)^{-1}$ is the standard normalisation constant, $f_{i}$ is the relative weight of the population."
 The dispersions o; assumed for the thick disc are larger than those assumed for the thin disc. so hieh-velocity stars tend to be assigned to the thick disc.," The dispersions $\sigma_i$ assumed for the thick disc are larger than those assumed for the thin disc, so high-velocity stars tend to be assigned to the thick disc."
 Because View is assumed to be ~30kms| larger for the thick disc than the thin. stars with lageine rotation velocities and therefore guiding centres at 2«f also tend to be assigned to the thick disc.," Because $V_{\rm asymm}$ is assumed to be $\sim30\kms$ larger for the thick disc than the thin, stars with lagging rotation velocities and therefore guiding centres at $R<R_0$ also tend to be assigned to the thick disc."
 This ellect is reinforced by the fact that the dispersions must increase inwards. so stars with guiding centers well inside Z are also likely to be high-velocity stars.," This effect is reinforced by the fact that the dispersions must increase inwards, so stars with guiding centers well inside $R_0$ are also likely to be high-velocity stars."
" Consequently the 7thick disc"" stars in Vennetal.(2004) and DBensbyοἱal.(2005). tend to belong to the inner disc."," Consequently the “thick disc” stars in \cite{Venn04}
 and \cite{Bensby05} tend to belong to the inner disc."
 In the context of our mocel this fact explains why Benshyetal.(2003). found a long tail of “thick disc stars that have higher Fe/L] at a given a/Fe] than the 7thin-disc stars., In the context of our model this fact explains why \cite{Bensby03} found a long tail of “thick disc” stars that have higher $\feh$ at a given $\afe$ than the “thin-disc” stars.
 We examine the effectiveness of kinematic selection in two ways., We examine the effectiveness of kinematic selection in two ways.
 First. in each panel of 12.. we plot the distribution in a Toomre diagram of each of the components," First, in each panel of , we plot the distribution in a Toomre diagram of each of the components"
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 , 
shift sequence can be subtracted from all inputs without altering the solution): PEE anunnnn,shift sequence can be subtracted from all inputs without altering the solution): _0= [0000000000000000].
 Ποιο ὁ; refers to nnnthenond Af-dimensional vector (chaeiaiiuPUY," Here $\vec\phi_j$ refers to the $M$ -dimensional vector $(e^{i\phi_{j1}},e^{i\phi_{j2}},\ldots,e^{i\phi_{jM}})$."
" No can accommodate two more inputs by choosing πα... postenosanna]1112222:588t qus, For these pelsthree input horns. we have six distinct baselines. with masks [equation (8))]—ü.3)."," We can accommodate two more inputs by choosing _1^1= _1=[0000111122223333], _1^0= For these three input horns, we have six distinct baselines, with masks [equation \ref{eq:Phi}) )],."
 These are obtained by subtracting the values iu anele brackets for the two horus modulo [., These are obtained by subtracting the values in angle brackets for the two horns modulo 4.
 for iustance. 91»=OLUS=l.1/iopy. lj.," for instance, $\vec\Phi_{12}=\langle 0,1\rangle-
\langle 1,0\rangle=\langle -1,1\rangle=\langle 3,1\rangle$ ."
 These masks are all cistiuct. aud hence mutually orthogonal. aud furthermore are all orhogonal to the vector (0.0). which is seusitive to the total power.," These masks are all distinct, and hence mutually orthogonal, and furthermore are all orthogonal to the vector $\langle 0,0\rangle$, which is sensitive to the total power."
 This c‘onstruction shows that we can accommodate three horis with a sequence of 16 time steps., This construction shows that we can accommodate three horns with a sequence of 16 time steps.
 We next ask whether it is possible to accomuodate a fourth vector $3; In suc ra wav that the new mezwks $954.du. etc.," We next ask whether it is possible to accommodate a fourth vector $\vec\phi_3$ in such a way that the new masks $\vec\Phi_{03},\vec\Phi_{13},$ etc."
 are iudepenudcnt of the oues we have aready found., are independent of the ones we have already found.
 A search of the 167=9 candidates reveals an affirmative auswer: $4=3.3)ocio works.," A search of the $16-7=9$ candidates reveals an affirmative answer: $\vec\phi_3=\langle 3,3\rangle =
\vec\alpha_2^3\vec\alpha_1^3$ works."
 The value NV= Lis the maxima that cau be achieved for the cwe of AL- fine steps. as is clear from a counting argument: hy5 horus would require at least AL=NUNI—2j steps.," The value $N=4$ is the maximum that can be achieved for the case of $M=4^2$ time steps, as is clear from a counting argument: $N=5$ horns would require at least $M=N(N-1)+1=21$ steps."
 Table shows the maximum nuniber of horus that can be acconirnorated for various vahes of AL., Table \ref{table:nvsm} shows the maximum number of horns that can be accommodated for various values of $M$.
 These were fou by rectuwsvev searching the space of possible phase shifts in the manner described above., These were found by recursively searching the space of possible phase shifts in the manner described above.
 The last coluin slic»vs the uaxinmui value that would be possible according to he simple counting argument that the mimver of nne steps must exceed the umber of baselines., The last column shows the maximum value that would be possible according to the simple counting argument that the number of time steps must exceed the number of baselines.
 We lave repeaed his analvsis for the case P=2. where the phase shifters are capable of oulv 0 aud 1807. shifts. ancl ound very similar results for the rclationship between Alaια NV," We have repeated this analysis for the case $P=2$, where the phase shifters are capable of only 0 and $180^\circ$ shifts, and found very similar results for the relationship between $M$ and $N$."
 As noted in the introduction. extremely large values of AM are practical.," As noted in the introduction, extremely large values of $M$ are impractical."
 This is one reason that a bolometric iuterforonjeter with a large number of horus should surely be designed with a hieh deeree of sviuuetry. so that there are many equivalent basclines that can be read pnt cobyreutly. (," This is one reason that a bolometric interferometer with a large number of horns should surely be designed with a high degree of symmetry, so that there are many equivalent baselines that can be read out coherently. ("
The other reason is the signal-to-noise advantage.},The other reason is the signal-to-noise advantage.)
 f sununary. this. section. las presented a procedure for selecting $; that yields fully orthogonal masks.," In summary, this section has presented a procedure for selecting $\vec\phi_j$ that yields fully orthogonal masks."
 This means that the result of applying the mask for a given baseline will ouly be scusitive to the signal from the desired. baseline. or equivalently that the reconstruction of all visibilitics is accomplished with iininal noise.," This means that the result of applying the mask for a given baseline will only be sensitive to the signal from the desired baseline, or equivalently that the reconstruction of all visibilities is accomplished with minimal noise."
 We now consider the case where the input horus are arrange In a square array with ας horus ou a side., We now consider the case where the input horns are arranged in a square array with $N_{\rm side}$ horns on a side.
 Iutus case. inany cdiffercut baselines (1.0... pairs of lorus) sauuple he same visibility.," In this case, many different baselines (i.e., pairs of horns) sample the same visibility."
 We wish to apply identical phase shifts to suc1 equivaleut baselines. so that a single mas; reads out their sum.," We wish to apply identical phase shifts to such equivalent baselines, so that a single mask reads out their sum."
 Naturally. we also require that equivaent baselije have orthogonal masks.," Naturally, we also require that inequivalent baselines have orthogonal masks."
 This is the Case considered iu detail bv Charlassier et al. (, This is the case considered in detail by Charlassier et al. (
C08).,C08).
" Our method. xwallels tleis dn many respects but refines if in SOLO Wars,", Our method parallels theirs in many respects but refines it in some ways.
 Followiis the rotation of COS. we paraneterize theposition of horus in the arrav iu units of ΓΕ horn separation as a vector d;=(/).17;).," Following the notation of C08, we parameterize theposition of horns in the array in units of the minimum horn separation as a vector $\vec d_j=(l_j,m_j)$."
 Mere Pj.10; are integers rumune from 0 to Nau1. labeling the position of the horn iu along the c aud. y directions.," Here $l_j,m_j$ are integers running from 0 to $N_{\rm side}-1$, labeling the position of the horn in along the $x$ and $y$ directions."
 The iudex / runs froili ! to N24.l according to j=Fj|Nam., The index $j$ runs from 0 to $N_{\rm side}^2-1$ according to $j=l_j+N_{\rm side}m_j$.
 We can costruct a set of phase shifts for all horus that satisty the desired criteria using the basis described iu the previous section with j;= 2., We can construct a set of phase shifts for all horns that satisfy the desired criteria using the basis described in the previous section with $\mu=2$ .
 We let the phase shift sequence for horn j be a, We let the phase shift sequence for horn $j$ be .
 We let the phase shift sequence for horn j be an, We let the phase shift sequence for horn $j$ be .
 We let the phase shift sequence for horn j be ang, We let the phase shift sequence for horn $j$ be .
 We let the phase shift sequence for horn j be angi, We let the phase shift sequence for horn $j$ be .
"propagated into the mass error bars, ey, and thus impacts directly the estimated intrinsic scatter, 7j [10)).","propagated into the mass error bars, $\mscat_{Y}$, and thus impacts directly the estimated intrinsic scatter, $\hat{\iscat}$ )."
" This results in a degeneracy between and5o;; however, is not coupled to the other fit parameters, and so we can take its systematic uncertainty into account simply by increasing the width of the likelihood function forgo."," This results in a degeneracy between and; however, is not coupled to the other fit parameters, and so we can take its systematic uncertainty into account simply by increasing the width of the likelihood function for."
. We therefore replace the chi-square likelihood discussed above by the gamma distribution (of which the chi-square distribution is a special case)., We therefore replace the chi-square likelihood discussed above by the gamma distribution (of which the chi-square distribution is a special case).
" Fixing the location of the distribution's peak and augmenting its variance by a factor of F', the shape and scale parameters of the gamma distribution, k and 0, can be determined by solving the system of equations In practice, the value F=14 approximately corresponds to the desired 20 per cent uncertainty ins,."," Fixing the location of the distribution's peak and augmenting its variance by a factor of $F$, the shape and scale parameters of the gamma distribution, $k$ and $\theta$, can be determined by solving the system of equations In practice, the value $F=14$ approximately corresponds to the desired 20 per cent uncertainty in."
". Finally, we account for a 20 per cent systematic uncertainty in the mean bias,b,, by straightforwardly marginalizing over an appropriate prior."," Finally, we account for a 20 per cent systematic uncertainty in the mean bias, by straightforwardly marginalizing over an appropriate prior."
" In detail, we parametrize the mean bias through B=—log,o(1—5)log,9(Mbruc/Mest), since this quantity is added to the log-masses, Y."," In detail, we parametrize the mean bias through $B=-\log_{10}(1-\meanbias)=\log_{10}(\mysub{M}{true}/\mysub{M}{est})$, since this quantity is added to the log-masses, $Y$."
" Confidence regions for o and ( obtained with cosmological parameters fixed at our reference and using uniform priors on a, f and are displayed in (solid lines)."," Confidence regions for $\alpha$ and $\beta$ obtained with cosmological parameters fixed at our reference and using uniform priors on $\alpha$, $\beta$ and are displayed in (solid lines)."
" The best-fitting values and marginal 68.3 igure}per cent confidence intervals are a=14.49+0.04, 8=0.677906 and no=0.127393."," The best-fitting values and marginal 68.3 per cent confidence intervals are $\alpha=14.49\pm 0.04$, $\beta=0.67^{+0.04}_{-0.06}$ and $\iscat=0.12^{+0.04}_{-0.03}$."
" A quantile-quantile plot of the residuals in Xi for the best fit confirms that the distribution of luminosities for a given (Figure[4))mass is reasonably approximated by the log-normal In order to verify the appropriateness of the hydrostatic bias correction applied to the masses, we compare the results of with the data of(2006), for which masses were measured using weak [Dahle]gravitational lensing."," A quantile-quantile plot of the residuals in $X_1$ for the best fit ) confirms that the distribution of luminosities for a given mass is reasonably approximated by the log-normal In order to verify the appropriateness of the hydrostatic bias correction applied to the masses, we compare the results of with the data of, for which masses were measured using weak gravitational lensing."
" These masses, with associated luminosities taken from the BCS and extended BCS (eBCS) catalogs, are shown in (black points)."," These masses, with associated luminosities taken from the BCS and extended BCS (eBCS) catalogs, are shown in (black points)."
" In contrast to the data, the Malmquist[5| bias due to the (e)BCS flux limit is clearly evident; in particular, the least massive clusters in this data set are very likely to represent the upper tail of the distribution of luminosities for given mass."," In contrast to the data, the Malmquist bias due to the (e)BCS flux limit is clearly evident; in particular, the least massive clusters in this data set are very likely to represent the upper tail of the distribution of luminosities for given mass."
" Although the simple methods described above are unsuitable for fitting the mass-luminosity relation when the data are subject to significant Malmquist bias, the intersection of these two data sets near the highest observed masses indicates qualitatively that they are compatible."," Although the simple methods described above are unsuitable for fitting the mass–luminosity relation when the data are subject to significant Malmquist bias, the intersection of these two data sets near the highest observed masses indicates qualitatively that they are compatible."
" We can quantify this observation by using the data to fit for the normalization, o, by minimizingX, while leaving the slope, 8, fixed at the best-fitting value from"," We can quantify this observation by using the data to fit for the normalization, $\alpha$, by minimizing, while leaving the slope, $\beta$, fixed at the best-fitting value from."
 The resulting one-dimensional 68.3 per cent confidence B.T.1].interval is a=14.46*005 Bp. in agreement with the corrected data.," The resulting one-dimensional 68.3 per cent confidence interval is $\alpha=14.46^{+0.04}_{-0.05}$ ), in agreement with the corrected data."
" In contrast, the lensing constraint is incompatible at the 68 per cent confidence level with the confidence regions that would have"," In contrast, the lensing constraint is incompatible at the 68 per cent confidence level with the confidence regions that would have"
"for the faint eud slope ijs &αν one finds that the fraction F(:) of the flux observed above a even flux limit f,,;, from the sources at redshift 5 is F(:)zexptfinin/fe). where f. is the flux received from an £. galaxy lviug at redshift :.","for the faint end slope is $a\simeq -1$, one finds that the fraction $F(z)$ of the flux observed above a given flux limit $f_{min}$ from the sources at redshift $z$ is $F(z)\simeq \exp(-f_{min}/f_*)$, where $f_*$ is the flux received from an $L_*$ galaxy lying at redshift $z$."
" Iu the scenarios in which one assumes that the cosmic rav luminosities are proportional to the observed catalog Iuninosities (flux weighted scenarios) the fraction jj of the total cose ray flax which is accounted by the model will then be Defining the characteristic depth of the survey. z« as that correspondiug to the redshift at which fe=μμ one fads for iustance that for the representative value τν=0.3 (1.0. about 130 Alpe). the fraction jj turus out to be if one uses the GZI& attenuation factor corresponding to Ey,=δ EeV. while it is if one adopts Ey,=60 EeV. For +.=0.05 (corresponding to a survey depth of about 200 AIpe). the corresponding fractions are and respectively,"," In the scenarios in which one assumes that the cosmic ray luminosities are proportional to the observed catalog luminosities (flux weighted scenarios) the fraction $\eta$ of the total cosmic ray flux which is accounted by the model will then be Defining the characteristic depth of the survey $z_*$ as that corresponding to the redshift at which $f_*=f_{min}$, one finds for instance that for the representative value $z_*=0.3$ (i.e. about 130 Mpc), the fraction $\eta$ turns out to be if one uses the GZK attenuation factor corresponding to $E_{th}=80$ EeV, while it is if one adopts $E_{th}=60$ EeV. For $z_*=0.05$ (corresponding to a survey depth of about 200 Mpc), the corresponding fractions are and respectively."
 Moreover. these fractious become larger im models in which the cosmic ray sources are restricted to those with absolute huuinosities above a certain threshold. as was the case for the IHTIPASS based models restricted to galaxies more massive than a certain Εππιο mass.," Moreover, these fractions become larger in models in which the cosmic ray sources are restricted to those with absolute luminosities above a certain threshold, as was the case for the HIPASS based models restricted to galaxies more massive than a certain limiting mass."
 Let us now illustrate the possible discrimination power of the 2DISS test with future increased data samples., Let us now illustrate the possible discrimination power of the 2DKS test with future increased data samples.
" For definiteness we use in these examples the CZs factor corresponding to EZ,=8S0 ΤΟΝ. for which sources bevoud LOO Mpc have essentially a negligible coutribution aud closer ones are weighted non-trivially, and weight the SWIFT aud HIPASS sources by their respective fluxes."," For definiteness we use in these examples the GZK factor corresponding to $E_{th}=80$ EeV, for which sources beyond 100 Mpc have essentially a negligible contribution and closer ones are weighted non-trivially, and weight the SWIFT and HIPASS sources by their respective fluxes."
 We consider the HIPASS galaxies (both the northern and southern ones) with ρε>7.1Jvlaus! aud Mj;>LOM’AL..., We consider the HIPASS galaxies (both the northern and southern ones) with $S_{int}>7.4\ {\rm Jy\ km\ s^{-1}}$ and $M_{HI}>10^{10}\ M_\odot$.
 The left panels in fie., The left panels in fig.
 1 show the distribution of D values expected for v=50 and 100 events using as reference catalog the SWIFT one. aud the right panels show the results using the HIPASS reference catalog.," 4 show the distribution of $D$ values expected for $n=50$ and 100 events using as reference catalog the SWIFT one, and the right panels show the results using the HIPASS reference catalog."
 As a general trend. one can see that the D distribution of the data sampled according to the reference catalog considered just scales as à.1/2. peaking at about [δρα&0.24725/n. being quite independent from the particular catalog adopted (sce also fies.," As a general trend, one can see that the $D$ distribution of the data sampled according to the reference catalog considered just scales as $n^{-1/2}$, peaking at about $D_{peak}\simeq 0.2\sqrt{25/n}$, being quite independent from the particular catalog adopted (see also figs."
 l and 2)., 1 and 2).
" On the other laud. for the scenarios differing from the reference one (either one based ou a differeut catalog or the isotropic hypothesis). the distribution of D values teuds to a eiven non-zero average value. with the associated dispersion decreastug as à.17, as is also seen iu fig."," On the other hand, for the scenarios differing from the reference one (either one based on a different catalog or the isotropic hypothesis), the distribution of $D$ values tends to a given non-zero average value, with the associated dispersion decreasing as $n^{-1/2}$, as is also seen in fig."
 1., 4.
 It is clear that for 100 events the distributions of the differeut models become quite separated from cach other. aud hence this method will have the ability to couficleutly tell apart these scenarios after a few vears of operation of the Auger Observatory.," It is clear that for 100 events the distributions of the different models become quite separated from each other, and hence this method will have the ability to confidently tell apart these scenarios after a few years of operation of the Auger Observatory."
 However. as was apparent from figs.," However, as was apparent from figs."
 1 and 2. according to the IKolinosorov-Siiiruov test the Auger Observatory data analyzed are still cousisteut with many differeut possible scenarios (except isotropy to a certain level).," 1 and 2, according to the Kolmogorov-Smirnov test the Auger Observatory data analyzed are still consistent with many different possible scenarios (except isotropy to a certain level)."
 Oue las to keep in mind however that the cnerev threshold for this dataset was selected by the Auger Collaboration as that maximizing the correlation with ACN from the VC catalog. and heuce although the discrepancy with isotropy iu some of the tests is reassunnue. it does uot provide a totally indepencent test of aulsotropy.," One has to keep in mind however that the energy threshold for this dataset was selected by the Auger Collaboration as that maximizing the correlation with AGN from the VC catalog, and hence although the discrepancy with isotropy in some of the tests is reassuring, it does not provide a totally independent test of anisotropy."
 Finally. it is also useful to consider how would the different sky distributious look for a large uunuber of simulated events. in which case the effects of sampling fluctuations teud to vanish.," Finally, it is also useful to consider how would the different sky distributions look for a large number of simulated events, in which case the effects of sampling fluctuations tend to vanish."
 Ideutifving the quadraut responsible for the largest fractional differeuce D will heuce characterize the most iuportanut feature discriminating among alternative scenarios in these tests., Identifying the quadrant responsible for the largest fractional difference $D$ will hence characterize the most important feature discriminating among alternative scenarios in these tests.
" In particular. when comparing the isotropic and ACN based distributions we find that the lareest value of D arises. in the large data size μμ, most frequently from the fourth quadrant. measured iu a counter clockwise order starting from the top-right one. with respect to the direction (116°.117). for which of the weighted AGN lie while only of the isotropic events are found."," In particular, when comparing the isotropic and AGN based distributions we find that the largest value of $D$ arises, in the large data size limit, most frequently from the fourth quadrant, measured in a counter clockwise order starting from the top-right one, with respect to the direction $(146^\circ, -14^\circ)$, for which of the weighted AGN lie while only of the isotropic events are found."
" Ou the other haud for the HIPASS (north aud south with 5;,,77.1Jvhans 1) fux woighted catalog aud the isotropic", On the other hand for the HIPASS (north and south with $S_{int}>7.4\ {\rm Jy\ km\ s^{-1}}$ ) flux weighted catalog and the isotropic
lgT5000€ 1.,$\lg\tau_{5000}<1$ .
" While turbulent pressure is naturally included in the RHD simulations, it is modeled in 1D models assuming a parameterisation as where p is the density, νι the characteristic velocity, and P is approximatively 1 and depends on whether the motions occur more or less isotropically."," While turbulent pressure is naturally included in the RHD simulations, it is modeled in 1D models assuming a parameterisation as where $\rho$ is the density, $v_{\rm{t}}$ the characteristic velocity, and $\beta$ is approximatively 1 and depends on whether the motions occur more or less isotropically."
" This pressure is measuring the force produced by the kinetic movements of the gas, whether due to convective or other turbulent gas motions."," This pressure is measuring the force produced by the kinetic movements of the gas, whether due to convective or other turbulent gas motions."
" In 1D models, assuming spherical symmetry, the equation of hydrostatic equilibrium is solved for where g(r)=oy (being r the radius, Μ the mass of the star and G the Newton's constant of gravity), Py=RpoT[mol the gas pressure (Ἂ, being the gas constant, (mo, the molecular weight, and T the temperature), and P,aq the radiative pressure."," In 1D models, assuming spherical symmetry, the equation of hydrostatic equilibrium is solved for where $g\left(r\right)=\frac{GM}{r^{2}}$ (being $r$ the radius, $M$ the mass of the star and $G$ the Newton's constant of gravity), $P_{\rm{g}}=\Re \rho T/\mu_{\rm{mol}}$ the gas pressure $\Re$ being the gas constant, $\mu_{\rm{mol}}$ the molecular weight, and $T$ the temperature), and $P_{\rm{rad}}$ the radiative pressure."
" ? and? showed that, assuming Praq=0 like in 3D simulations, they could mimic the turbulent pressure on the models by using models with those effects neglected with an adjusted gravity: Eventually, ? chose to set v, = 0 for all 1D models in their grid, advicing those who would have liked a different choice"," \cite{2008A&A...486..951G} and \cite{1992iesh.conf...86G} showed that, assuming $P_{\rm{rad}}=0$ like in 3D simulations, they could mimic the turbulent pressure on the models by using models with those effects neglected with an adjusted gravity: Eventually, \cite{2008A&A...486..951G} chose to set $v_{\rm{t}}$ = 0 for all 1D models in their grid, advicing those who would have liked a different choice"
whereas the value deduced in Morandictal.(2011) was Hoste=237OLLI.,"whereas the value deduced in \cite{morandi2011a} was $\eta_{\rm{DM},c'}=2.37\pm 0.11$."
 In Table we present the best-fit model. parameters for our analysis of Abell 1689., In Table \ref{tabdon} we present the best-fit model parameters for our analysis of Abell 1689.
 Errors in the individual parameters (q.a..) have been evaluated by considering the average value and the mean absolute deviation. of the marginal probability istribution of each parameter.," Errors in the individual parameters $({\bf q},
\sigma_{\rm sys})$ have been evaluated by considering the average value and the mean absolute deviation of the marginal probability distribution of each parameter."
" Note that we list the axis ratio along the line of sight ""psp,"" rather than the eccentricity."," Note that we list the axis ratio along the line of sight $\eta_{\rm{DM},c'}$ rather than the eccentricity."
 Our work shows that Abell 1689 is a triaxial galaxy cluster with DAL halo axis ratios pras=1.24ck0.13 anc ipa=2.02+0.01. where oat is the axis ratio on the plane of the sky inferred fron SL measurements. and apype ds the axis ratio along the line of sight inferred through our joint analysis.," Our work shows that Abell 1689 is a triaxial galaxy cluster with DM halo axis ratios $\eta_{\rm{DM},b'}=1.24\pm 0.13$ and $\eta_{\rm{DM},c'}=2.02\pm 0.01$, where $\eta_{\rm{DM},b'}$ is the axis ratio on the plane of the sky inferred from SL measurements, and $\eta_{\rm{DM},c'}$ is the axis ratio along the line of sight inferred through our joint analysis."
 Note that these elongations are statistically significant. ie. our results disprove the spherical geometry assumption.," Note that these elongations are statistically significant, i.e., our results disprove the spherical geometry assumption."
 The axis ratio ol the gas is i.av~ld1.06 (on the plane of the sky) and thease~15109 (along the line of sight). moving from the center toward the X-ray. boundary.," The axis ratio of the gas is $\eta_{\rm{gas},b'}\sim 1.1-1.06$ (on the plane of the sky) and $\eta_{\rm{gas},c'}\sim 1.5-1.3$ (along the line of sight), moving from the center toward the X-ray boundary."
" In Table 1 we also report the value of Mog: wherep, is the critical density of the Universe at. the redshift z of the cluster. e=Peggfr. and (fe, and 6,./¢, are the minor-major and intermeciate-major axis ratios of the DM halo. respectively."," In Table \ref{tabdon} we also report the value of $M_{200}$: where$\rho_c$ is the critical density of the Universe at the redshift $z$ of the cluster, $c = {R_{200}}/{r_{\rm s}}$, and $a_r/c_r$ and $b_r/c_r$ are the minor-major and intermediate-major axis ratios of the DM halo, respectively."
 The second main result. from ourwork is the need. for a appreciable non-thermal pressure support. formally at à level of ~20%..," The second main result from ourwork is the need for a appreciable non-thermal pressure support, formally at a level of $\sim$."
 In Figure 2 we present the joint probability distribution of ἠυνιω and €," In Figure \ref{entps3xkn} we present the joint probability distribution of $\eta_{\rm{DM},c'}$ and $\xi$."
" Note the positive correlation between£ and ""pron be. the N-rav/Lensing mass discrepancy in clusters with prominent strong lensing features can be explained via a combination of both triaxiality ancl non-thermal support."," Note the positive correlation between $\xi$ and $\eta_{\rm{DM},c'}$, i.e. the X-ray/Lensing mass discrepancy in clusters with prominent strong lensing features can be explained via a combination of both triaxiality and non-thermal support."
 This expected. in light of the following considerations: (1) the observed temperature profile and projected mass prolile are both sensitive to triaxialitv. specifically HausesZBgps;=1) and SUR)xμονο (Morandictal. 2010).. so that the cependency of MCA?) on triaxiality is stronger than that of Z(H). (remembering that generally NAc!7 Haase): (2) the non-thermal pressure support alfects only the X-ray data via Equation 4.. i.c.. neglecting u systematically lowers the determination. of cluster masses based on X-ray. data roughly by the factor £.," This expected in light of the following considerations: (1) the observed temperature profile and projected mass profile are both sensitive to triaxiality, specifically $T(R,\eta_{\rm
DM}) \sim \eta_{\rm{gas},c'} \, T(R,\eta_{\rm DM}=1)$ and $\Sigma(R)
\propto \eta_{\rm{DM},c'}$ \citep{morandi2010a}, , so that the dependency of $\Sigma(R)$ on triaxiality is stronger than that of $T(R)$ (remembering that generally $\eta_{\rm{DM},c'} > \eta_{\rm{gas},c'}$ ); (2) the non-thermal pressure support affects only the X-ray data via Equation \ref{aa4}, i.e., neglecting $P_{\rm nt}$ systematically lowers the determination of cluster masses based on X-ray data roughly by the factor $\xi$."
 A precise determination of cluster masses is crucial for he use of clusters as cosmological probes., A precise determination of cluster masses is crucial for the use of clusters as cosmological probes.
 However. there are discrepancies between cluster masses determined. based on gravitational lensing and on X-rav observations. the ormer being significantly higher than the latter in many clusters with prominent lensing features.," However, there are discrepancies between cluster masses determined based on gravitational lensing and on X-ray observations, the former being significantly higher than the latter in many clusters with prominent lensing features."
 Indeed. Oguri&DBlandford.(2000). showed that SL clusters with the largest Einstein radii constitute a highly biased. population with major axes preferentially aligned with the line of sight thus increasing the magnitude of lensing.," Indeed, \cite{Oguri2009} showed that SL clusters with the largest Einstein radii constitute a highly biased population with major axes preferentially aligned with the line of sight thus increasing the magnitude of lensing."
 Given that. lensing depends on the integrated. mass along the line of sight. either fortuitous alignments with mass concentrations that are not physically related to the galaxy cluster or departures of the DAL halo from spherical symmetry can bias upwards the three-climensional mass with respect to the X-ray. mass (Gavazzi2005): on the other hand. X-rav-only masses hinge on the accuracy of the assumption of strict hydrostatic equilibrium: the presence. of bulk motions in the gas can bias low the three-dimensional mass profile between 5 and (Moeneghettietal.2010)..," Given that lensing depends on the integrated mass along the line of sight, either fortuitous alignments with mass concentrations that are not physically related to the galaxy cluster or departures of the DM halo from spherical symmetry can bias upwards the three-dimensional mass with respect to the X-ray mass \citep{Gavazzi2005}; on the other hand, X-ray-only masses hinge on the accuracy of the assumption of strict hydrostatic equilibrium: the presence of bulk motions in the gas can bias low the three-dimensional mass profile between 5 and \citep{meneghetti2010b}."
 Ogurietal.(2005) concluded that weak lensing measurements in Abell 1689 are indeed compatible with the CDALbasecd triaxial halo mocel if Abell 1689 represents a rare population (~6% by number) of cluster-seale halos. ancl Morandictal.(2011). demonstrated that triaxiality allows us to remove the mass discrepancy between the strong lensing and X-ray estimates in Abell L689.," \cite{Oguri2005} concluded that weak lensing measurements in Abell 1689 are indeed compatible with the CDM-based triaxial halo model if Abell 1689 represents a rare population $\sim$ by number) of cluster-scale halos, and \cite{morandi2011a} demonstrated that triaxiality allows us to remove the mass discrepancy between the strong lensing and X-ray estimates in Abell 1689."
 Molnaretal.(2010). suggested an alternative explanation for the mass discrepancy. due to violations of strict. hydrostatic equilibrium in Abell 1689: they found that a contribution of about from non-thermal pressure within the core region of Abell 1689 can explain the mass discrepancy. provided ju the spherical geometry assumption holds.," \cite{molnar2010} suggested an alternative explanation for the mass discrepancy, due to violations of strict hydrostatic equilibrium in Abell 1689: they found that a contribution of about from non-thermal pressure within the core region of Abell 1689 can explain the mass discrepancy, provided that the spherical geometry assumption holds."
 Aloreover. recent work investigating the mass istributions of individual galaxy clusters (Abell 1689 and others) based on gravitational lensing and. emploving standard. spherical modeling have found a potential inconsistency compared. to the predictions of the CDM scenario relating halo mass to the concentration parameter c.," Moreover, recent work investigating the mass distributions of individual galaxy clusters (Abell 1689 and others) based on gravitational lensing and employing standard spherical modeling have found a potential inconsistency compared to the predictions of the CDM scenario relating halo mass to the concentration parameter $c$ ."
 ln particular. relatively high values of e (~— 8-14) have been derived from lensing analysis of Abell 1689 (Broaclhurstetal.2005:Limousin 2007)...," In particular, relatively high values of $c$ $\sim 8$ $14$ ) have been derived from lensing analysis of Abell 1689 \citep{broadhurst2005,Limousin2007}. ."
 Thesevalues are outside the range predicted. from. simulations of the standard CDM moclel (e~4:Netoetal.2007 ).., Thesevalues are outside the range predicted from simulations of the standard CDM model \citep[$c\sim 4$;][]{neto2007}. .
histories.,histories.
 We present the basic properties of each galaxy in Table 1.., We present the basic properties of each galaxy in Table \ref{tab:setparam}. .
" ? studied cluster populations in a set of 21 galaxies, including the four included here."," \citet{LR99} studied cluster populations in a set of 21 galaxies, including the four included here."
" Using ground-based multiband (UBVRI and Ha) observations they estimated the total number of young massive clusters in each galaxy, using a magnitude limit of My< -—8.5."," Using ground-based multiband $UBVRI$ and $\alpha$ ) observations they estimated the total number of young massive clusters in each galaxy, using a magnitude limit of $M_V\le-8.5$ ."
" In a further work, ? estimated the star formation rate density (SgrrR) and the specific U-band luminosity, Tr(U)= 100xL(clusters,U)/L(galaxy,U), for each galaxy."," In a further work, \citet{LR00} estimated the star formation rate density $\Sigma_{\rm SFR}$ ) and the specific $U$ -band luminosity, $T_L(U) = 100\times$ L(clusters,U)/L(galaxy,U), for each galaxy."
 The TL(U) was found to correlate with Xgpn., The $T_L(U)$ was found to correlate with $\Sigma_{\rm SFR}$.
" Taking Tz(U) as a proxy for the cluster formation efficiency, these data thus suggested an increase in the cluster formation efficiency with Mgpr."," Taking $T_L(U)$ as a proxy for the cluster formation efficiency, these data thus suggested an increase in the cluster formation efficiency with $\Sigma_{\rm SFR}$."
" It is worth noting here that the “grr values were derived by normalizing the total star formation rates, obtained from IRAS far-infrared fluxes, to the optical galaxy diameters obtained from the RC3 catalog."," It is worth noting here that the $\Sigma_{\rm SFR}$ values were derived by normalizing the total star formation rates, obtained from IRAS far-infrared fluxes, to the optical galaxy diameters obtained from the RC3 catalog."
" Therefore, while these numbers were useful for studying trends and correlations, they should not be taken as reliable absolute values."," Therefore, while these numbers were useful for studying trends and correlations, they should not be taken as reliable absolute values."
" More recent estimates of Ugpr have been made by ? for the galaxies NGC 5236 and NGC 7793, where they found similar values to ?.."," More recent estimates of $\Sigma_{\rm SFR}$ have been made by \citet{calzetti10}
 for the galaxies NGC 5236 and NGC 7793, where they found similar values to \citet{LR00}."
 ? present a photometric observation of clusters in the center (inner 300 pc.), \citet{harris01} present a photometric observation of clusters in the center (inner 300 pc.)
 of NGC 5236., of NGC 5236.
 Harris et al., Harris et al.
" find a large number of young and massive clusters, consistent with a burst of star formation that began around 10 Myr ago, but note that the apparent absence of older clusters might also be due to rapid disruption."," find a large number of young and massive clusters, consistent with a burst of star formation that began around 10 Myr ago, but note that the apparent absence of older clusters might also be due to rapid disruption."
 ? used the new Wide Field Camera 3 (WFC3) on HST to analyze the cluster system of NGC 5236., \citet{chandarwhitmore10} used the new Wide Field Camera 3 (WFC3) on HST to analyze the cluster system of NGC 5236.
 Theyfind that luminosity functions and age distributions are consistent with previous work on galaxies of different morphological types (e.g.?).., Theyfind that luminosity functions and age distributions are consistent with previous work on galaxies of different morphological types \citep[e.g.][]{fall04}.
" ?? studied the cluster system for the same set of galaxies used in this work, based on the same HST images."," \citet{mora07,mora09} studied the cluster system for the same set of galaxies used in this work, based on the same HST images."
" They present detailed estimates of the sizes, ages, and masses for the clusters detected."," They present detailed estimates of the sizes, ages, and masses for the clusters detected."
 Mora et al., Mora et al.
" conclude that the age distributions are consistent with a ~80% MID per decade in age up to 1 Gyr, but could not make a distinction between different models (MDD MMID) of cluster disruption."," conclude that the age distributions are consistent with a $\sim$ MID per decade in age up to 1 Gyr, but could not make a distinction between different models (MDD MID) of cluster disruption."
" In the galaxy NGC 45 they found a large number of old globular clusters, of which 8 were spectroscopically confirmed to be ancient and metal-poor (?).."," In the galaxy NGC 45 they found a large number of old globular clusters, of which 8 were spectroscopically confirmed to be ancient and metal-poor \citep{mora08}."
 The five galaxies studied in this series of papers were selected for detailed observations with the (ACS) and2 (WPFC2) onboard HST from the work of ??..," The five galaxies studied in this series of papers were selected for detailed observations with the (ACS) and (WPFC2) onboard HST from the work of \citet{LR99,LR00}."
" The two instruments have a resolution of 0.05 and 0""046,071 for ACS and WFPC2 (PC,WFs), respectively."," The two instruments have a resolution of $0\farcs05$ and $0\farcs046,0\farcs1$ for ACS and WFPC2 (PC,WFs), respectively."
 At the distance of our galaxies (~4 Mpc) the ACS pixel scale corresponds to 1 pc., At the distance of our galaxies $\sim4$ Mpc) the ACS pixel scale corresponds to $\sim1$ pc.
" Besides NGC 1313, which has three different fields observed, the rest of the galaxies were covered using two pointings (see Fig. 1))"," Besides NGC 1313, which has three different fields observed, the rest of the galaxies were covered using two pointings (see Fig. \ref{fig:set}) )."
" The bands used for the observations were F336W(— U), F435W(~ B), F555W(~ V), and F814W(~ I), with the exposure times listed in 'Table 2.."," The bands used for the observations were $\sim U$ ), $\sim B$ ), $\sim V$ ), and $\sim I$ ), with the exposure times listed in Table \ref{tab:journal}."
 The standard STScI pipeline was used for the initial data processing., The standard STScI pipeline was used for the initial data processing.
" ACS images were drizzled using the multidrizzle task (7?) in the STSDAS package in IRAF using the default parameters, but disabling the automatic sky subtraction."," ACS images were drizzled using the multidrizzle task \citep{koekemoer02} in the STSDAS package in IRAF using the default parameters, but disabling the automatic sky subtraction."
 WFPC2 images were combined andcorrectedfor cosmic rays using the task using the default parameters., WFPC2 images were combined andcorrectedfor cosmic rays using the task using the default parameters.
for some NV—2 form A.,for some $N-2$ form ${\cal A}$.
 Equivalently: Assuming p=exp(—Q) aud A=£exp(—Q). where ( is a polynomial aud € is a polynomial AN—2 form. becomes The case £20 is well known to quantum field theorists auc arises in the context of stochastic quantization of a field theory with action Q [0]..," Equivalently; Assuming $\rho = \exp(-Q)$ and ${\cal A} = \xi \exp(-Q)$, where $Q$ is a polynomial and $\xi$ is a polynomial $N-2$ form, becomes The case $\xi=0$ is well known to quantum field theorists and arises in the context of stochastic quantization of a field theory with action $Q$ \cite{ParisiWu}."
 The dynamical system in this case has fixed poluts where dQ=0 with qu:uium fluctuations arising from Gaussian noise., The dynamical system in this case has fixed points where $dQ=0$ with quantum fluctuations arising from Gaussian noise.
 Allowing choices [or £ gives a inliuite class of possible quantizatious., Allowing non-trivial choices for $\xi$ gives a infinite class of possible quantizations.
 Iu the cdetermiulstic case. D—60. one must take care that & is chosen such that the the dynamical system is chaotic.," In the deterministic case, $\Gamma=0$, one must take care that $\xi$ is chosen such that the the dynamical system is chaotic."
 As a highlye speculative remark iuteuded for Τquanti field theorists. we suggestMO that there uay be an advantage to cousideriuig deterministic chaotic quautizatious for which the distributioi exp(—Q) is not ereodic.," As a highly speculative remark intended for quantum field theorists, we suggest that there may be an advantage to considering deterministic chaotic quantizations for which the distribution $\exp(-Q)$ is not ergodic."
 It has been noted earlier. in section 3. that tle initia istribution p usec iu tle inverse metloc may have syimuiuetries which are not reflected by the dyuamics.," It has been noted earlier, in section 3, that the initial distribution $\rho$ used in the inverse method may have symmetries which are not reflected by the dynamics."
 Phenomena iu quautum field theory such as spontaneous syiumetry breaking might be naturally eucoded ii he two-form *£. whereas stochastic quantizatiou (with £= 0) does not naturally give rise to synunetry breaking (see [8.9] for potentially related cdiscussious).," Phenomena in quantum field theory such as spontaneous symmetry breaking might be naturally encoded in the two-form ${}^*\xi$, whereas stochastic quantization (with $\xi=0$ ) does not naturally give rise to symmetry breaking (see \cite{GP,ZG} for potentially related discussions)."
 If exp(—Q) is uot ergodic. one must make sure that the 5chwiuger action principle equations which defiue quantum fiel heories are still satisfiecl.," If $\exp(-Q)$ is not ergodic, one must make sure that the Schwinger action principle equations which define quantum field theories are still satisfied."
 We have ceimonstrated ani iuverse method to construct chaotic dyuamical systems starting [rom analvtie expressious for au invariant. probability distribution aud a two-form., We have demonstrated an inverse method to construct chaotic dynamical systems starting from analytic expressions for an invariant probability distribution and a two-form.
 In. principle. the inverse method can be used to generate au uulimited uumber of chaotic systems together with very well inotivated coujectures for their exact statistics.," In principle, the inverse method can be used to generate an unlimited number of chaotic systems together with very well motivated conjectures for their exact statistics."
 Al present. the examples of¢Iyvnaimical systems we lave considered are not pluysically motivated aud in some cases are very Couples. having a large number of teris in the compouents of the velocity field.," At present, the examples of dynamical systems we have considered are not physically motivated and in some cases are very complex, having a large number of terms in the components of the velocity field."
 The next challenge is to attempt to reverse engineeres systems close to ones of johwsical interest., The next challenge is to attempt to reverse engineer systems close to ones of physical interest.
 It would ultimately be very interesting to apply the inverse method to plivsica systems witli a very large number of degrees of freecom. such as fluids.," It would ultimately be very interesting to apply the inverse method to physical systems with a very large number of degrees of freedom, such as fluids."
 The most difficult part of 'everse engineering a plivsical systems seems to lie in choosing the two-form. which lias uo direc johwsical interpretation.," The most difficult part of reverse engineering a physical system seems to lie in choosing the two-form, which has no direct physical interpretation."
 Cloosiig a probability distribution is easier: oue could. for iustauce. choose a distribution resembling that of a fluid with some mean shear.," Choosing a probability distribution is easier; one could, for instance, choose a distribution resembling that of a fluid with some mean shear."
 Thus far. we have studied systems with ouly three or four degrees of freedom.," Thus far, we have studied systems with only three or four degrees of freedom."
 Equations of he form eau be evaluatec very quickly by haud or by computer. depeudiug on the systeui. even for very large numbers of ¢legrees of freedom.," Equations of the form can be evaluated very quickly by hand or by computer, depending on the system, even for very large numbers of degrees of freedom."
 Poteutial computational problems arise ouly when trying to determine the domain of support of the ergodic distribution., Potential computational problems arise only when trying to determine the domain of support of the ergodic distribution.
 At present. we do uot have a way to clo this besices direct numerical simulation of the dyuaiical system. which requires more computer time.," At present, we do not have a way to do this besides direct numerical simulation of the dynamical system, which requires more computer time."
 However. allowing for this computer time. one should also be able to make very well motivated coijectures about the exact statistics of eliaotie dynamical systems with a very large nunber of deg»rees of freedom.," However, allowing for this computer time, one should also be able to make very well motivated conjectures about the exact statistics of chaotic dynamical systems with a very large number of degrees of freedom."
relevance for representing true star formation processes in real galaxies.,relevance for representing true star formation processes in real galaxies.
 The first issue we address is whether the star ormation rates we obtain are consistent with the Kennicutt relation., The first issue we address is whether the star formation rates we obtain are consistent with the Kennicutt relation.
 In section 4. we scaled the mass in our simulation volume to that of the Alilky Way. finding that our star ormation rates and surface densities were consistent with star formation occuring in the starburst regime.," In section \ref{detailedpics}
 we scaled the mass in our simulation volume to that of the Milky Way, finding that our star formation rates and surface densities were consistent with star formation occuring in the starburst regime."
 Lowe do not scale our SE5 and gas densities to a Milky Way type galaxy rut instead take them at lace value we find that our initial latom/cm? gas density in a (1.28 kpc)* volume vields in xojection about a 30 M. /pc column density which lies at he boundary between Ixennicutts normal clisks and centers of normal disks (Ixennicutt 1998)., If we do not scale our SFRs and gas densities to a Milky Way type galaxy but instead take them at face value we find that our initial 1 $^3$ gas density in a (1.28 $^3$ volume yields in projection about a 30 $_\odot$ $^2$ column density which lies at the boundary between Kennicutt's normal disks and centers of normal disks (Kennicutt 1998).
 Transforming our average star formation rate of 0.2-0.3. M. /vr into a star formation rate per unit volume leads us to an average star formation rate density of about 0.1 M. Κρο on the high side but in fair agreement with Ixennicutt's measurements for our computed. surface density (Ixennicutt. 1998. Ligure 6).," Transforming our average star formation rate of 0.2-0.3 $_\odot$ /yr into a star formation rate per unit volume leads us to an average star formation rate density of about 0.1 $_\odot$ $^2$, on the high side but in fair agreement with Kennicutt's measurements for our computed surface density (Kennicutt 1998, figure 6)."
 We note that Wennicutt’s law is a static relation as it concerns space averaged quantities in local galaxies. and a moment in the history of these galaxies is bound to exist when their main progenitor will be entirely gaseous (i.c. with no stars vet formed) anc the Kennicutt relation will break.," We note that Kennicutt's law is a static relation as it concerns space averaged quantities in local galaxies, and a moment in the history of these galaxies is bound to exist when their main progenitor will be entirely gaseous (i.e. with no stars yet formed) and the Kennicutt relation will break."
 2S OUL simulations start from an exclusively gaseous medium. we do not expect our simulation to follow the Ixennicutt relation from the very beginning. but to move towards it as it does.," As our simulations start from an exclusively gaseous medium, we do not expect our simulation to follow the Kennicutt relation from the very beginning, but to move towards it as it does."
 We nevertheless consider our simulations to be in a starburst mode because the duration of the star formation. episode is much shorter than that of what one expects in either a disk or spheroidal galaxy., We nevertheless consider our simulations to be in a starburst mode because the duration of the star formation episode is much shorter than that of what one expects in either a disk or spheroidal galaxy.
 But this is not. unusual since we are only modeling a chunk of a galaxy. anc are therefore neglecting ellects on larger length and therefore timescales., But this is not unusual since we are only modeling a chunk of a galaxy and are therefore neglecting effects on larger length and therefore timescales.
 The second issue we address is whether periodic bouncary conditions drive the high star formation rates seen in our simulations., The second issue we address is whether periodic boundary conditions drive the high star formation rates seen in our simulations.
 When hot gas starts to fill the bulls of the simulation volume. because the boundary. conditions trap the hot gas. conditions in the simulation may be viewed as à pressure cooker and the increased. pressure may. drive higher star formation rates.," When hot gas starts to fill the bulk of the simulation volume, because the boundary conditions trap the hot gas, conditions in the simulation may be viewed as a pressure cooker and the increased pressure may drive higher star formation rates."
 In our simulation by the time the pressure cooker is operative. the SEIs are already at starburst levels as seen when one scales the SEIts ancl σας densities to à Milkv Way type galaxy as we do in section 4..," In our simulation by the time the pressure cooker is operative, the SFRs are already at starburst levels as seen when one scales the SFRs and gas densities to a Milky Way type galaxy as we do in section \ref{detailedpics}."
 ‘To be more specific. for the pressure cooker to be operative we have to wait  10 Myr for the first supernovae to go olf and then we have to wait for the volume to become significantly filled by this supernovae generated hot gas for the hot gas to be able to traverse the volume unobstructe bv cold. dense gas.," To be more specific, for the pressure cooker to be operative we have to wait $\sim$ 10 Myr for the first supernovae to go off and then we have to wait for the volume to become significantly filled by this supernovae generated hot gas for the hot gas to be able to traverse the volume unobstructed by cold, dense gas."
 According to figure 15. it takes on the order of 50 Myr for the hot eas filling fraction to be approximately4.. corresponding to à porosity of abou 0.7.," According to figure 15, it takes on the order of 50 Myr for the hot gas filling fraction to be approximately, corresponding to a porosity of about 0.7."
 Hence boundary ellects are not dominant in shaping the star formation rate until after that time., Hence boundary effects are not dominant in shaping the star formation rate until after that time.
 We also point ou that the limitations of the boundary. conditions should no obfuscate the point that the manner in which we implemen supernovae is a more important factor leading to the builc up of large quantities of hot eas in the medium., We also point out that the limitations of the boundary conditions should not obfuscate the point that the manner in which we implement supernovae is a more important factor leading to the build up of large quantities of hot gas in the medium.
 When we perform simulations in all points identical to those presentec in this paper but with supernovae going olf instantaneously. as opposed to exploding with a more realistic LO Myr time delay used in the work presented in this paper. we ge extremely low star formation rates (a few hundred. times smaller than those we get in our simulation here). because," When we perform simulations in all points identical to those presented in this paper but with supernovae going off instantaneously, as opposed to exploding with a more realistic 10 Myr time delay used in the work presented in this paper, we get extremely low star formation rates (a few hundred times smaller than those we get in our simulation here), because"
When we insert these values into we obtain the radial velocity of alow redshift supernova In this approximation the distance modulus. :—M]. is given by where the Hubble constant as usual is given as 100/kms! Mpc.,"When we insert these values into we obtain the radial velocity of a low redshift supernova In this approximation the distance modulus, $m - M$, is given by where the Hubble constant as usual is given as $H_0 = 100 h\kms{\rm Mpc}^{-1}$ ."
 The distance modulus defined in should be compared with the distance modulus. 77—M. as measured in a frame at rest with respect to the CMB.," The distance modulus defined in should be compared with the distance modulus, $\tilde{m}-M$, as measured in a frame at rest with respect to the CMB."
 The difference between the apparent magnitude 77 and the one measured by the observer. η. is according to(15).. The approximate equation (25)) ts sufficient for the low redshifts that we are considering. while at higher redshifts one has to use the correct form Eq. (21)).," The difference between the apparent magnitude $\tilde{m}$ and the one measured by the observer, $m$, is according to, The approximate equation \ref{eq:approxvr}) ) is sufficient for the low redshifts that we are considering, while at higher redshifts one has to use the correct form Eq. \ref{eq:vr1}) ),"
 and also take into account other contributions to 77—(2). such as lensing.," and also take into account other contributions to $\tilde m - \bar m(\tilde z)$, such as lensing."
 We analyse both the mock catalogues discussed in the next section and the real data set (see section ??)) using the same technique., We analyse both the mock catalogues discussed in the next section and the real data set (see section \ref{sec:data}) ) using the same technique.
 In practice we decompose the field into spherical harmonics., In practice we decompose the field into spherical harmonics.
" The radial velocity is a real scalar field. and on a spherical shell of a given redshift it can be decomposed into spherical harmonics Using «oy—CD"" for the expansion of a real function and Y;4,2(-D""Y,, we aj,obtain However. this applies strictly only if the field can be measured on the entire sphere."," The radial velocity is a real scalar field, and on a spherical shell of a given redshift it can be decomposed into spherical harmonics Using $a_{l,-m}=(-1)^{m}a_{lm}^{*}$ for the expansion of a real function and $Y_{l,-m}=(-1)^{m}Y_{lm}^{*}$ we obtain However, this applies strictly only if the field can be measured on the entire sphere."
" In our case the radial velocity field is measured for a finite number of directions. so we can only hope to determine a finite number of «aj, coefficients by fitting a truncated multipole expansion by the method of weighted linear least squares using [Yio(ZR).2:4Kind}mde.|| as basis functions."," In our case the radial velocity field is measured for a finite number of directions, so we can only hope to determine a finite number of $a_{lm}$ coefficients by fitting a truncated multipole expansion by the method of weighted linear least squares using $[Y_{l0}, \lbrace 2\Re(Y_{lm}), -2
\Im(Y_{lm})\rbrace , m=1,\ldots,l]$ as basis functions."
 Specifically. we solved the problem by a singular value decomposition.," Specifically, we solved the problem by a singular value decomposition."
" We follow the procedure by Copi.Huterer.Schwarz.and and represent the /'th multipole in terms of a sealar. A‘? and / unit vectors, [v7jiaLis.lj: where e=(sincoso.sinsino.cos). and 7; is the sum of all possible traces of the first term."," We follow the procedure by \citet*{copi06} and represent the $l$ 'th multipole in terms of a scalar, $A^{(l)}$ and $l$ unit vectors, $\lbrace \hat{v}^{(l,m)}, m=1,\ldots,l \rbrace$: where $\hat{e} =
(\sin\theta\cos\phi,\sin\theta\sin\phi,\cos\theta)$, and $\mathcal{T}_l$ is the sum of all possible traces of the first term."
 In this representation the multipole expansion up to and including the quadrupole term takes the following form: Note that P and iC are “headless” vectors only defining a line. not a direction.," In this representation the multipole expansion up to and including the quadrupole term takes the following form: Note that $\hat{v}^{(2,1)}$ and $\hat{v}^{(2,2)}$ are “headless” vectors only defining a line, not a direction."
 Equivalently they define a plane. but they do not define a rotation in that plane. so the normal to the plane is also headless.," Equivalently they define a plane, but they do not define a rotation in that plane, so the normal to the plane is also headless."
 By convention we choose as the first vector. ej. the one with the largest absolute z-coordinate.," By convention we choose as the first vector, $\hat{e}_1$, the one with the largest absolute z-coordinate."
" We can choose e, to point to the hemisphere near the pole without introducing a negative amplitude A''. if both οι and e» have their sign changed."," We can choose $\hat{e}_1$ to point to the hemisphere near the pole without introducing a negative amplitude $A^{(2)}$, if both $\hat{e}_1$ and $\hat{e}_2$ have their sign changed."
" Finally we define the normal to the plane spanned by the two vectors as e,\e».", Finally we define the normal to the plane spanned by the two vectors as $\hat{e}_1\times\hat{e}_2$.
 This is thevector., This is the.
 From the αμ coefficients the monopole amplitude can be found as and the dipole amplitude and direction can be found as This is the direction of the maximum of the dipole., From the $a_{lm}$ coefficients the monopole amplitude can be found as and the dipole amplitude and direction can be found as This is the direction of the maximum of the dipole.
 All the higher order multipole vectors are found by using the program ddecomp by Copietal.(2006)., All the higher order multipole vectors are found by using the program decomp by \citet{copi06}.
". For the lowest /-values the amplitudes in the multipole vector expansion are related to the usual power C, as (Coptetal.2006) It should be noted that in general the individual multipole coefficients obtained in the fit to data can be strongly dependent on the number of modes included."," For the lowest $l$ -values the amplitudes in the multipole vector expansion are related to the usual power $C_l$ as \citep{copi06}
 It should be noted that in general the individual multipole coefficients obtained in the fit to data can be strongly dependent on the number of modes included."
 The reason for this is that the window function does not cover the entire sky. rather there are patches with zero coverage.," The reason for this is that the window function does not cover the entire sky, rather there are patches with zero coverage."
 This means that the spherical harmonics are no longer orthogonal. and shows up as a leakage of power between different /.," This means that the spherical harmonics are no longer orthogonal, and shows up as a leakage of power between different $l$."
 In fact. this is predicted to be a significant problem for any harmonic analysis with limited sampling because the higher order multipoles do contribute significantly to the rms velocity.," In fact, this is predicted to be a significant problem for any harmonic analysis with limited sampling because the higher order multipoles do contribute significantly to the rms velocity."
 In Section ?? we discuss the implications of sampling for the JRK sample., In Section \ref{sec:window} we discuss the implications of sampling for the JRK sample.
 Before analysing existing data we make mock catalogues of supernova data based on dark matter N-body simulations., Before analysing existing data we make mock catalogues of supernova data based on dark matter N-body simulations.
 This is done in order to get an estimate of the various sources of error in such measurements., This is done in order to get an estimate of the various sources of error in such measurements.
 The N-body simulations were done using the Gadget-2 code, The N-body simulations were done using the Gadget-2 code
Unlike the deep NICMOS observations in the NIIDE. the HIST secondary mirror was not adjusted to bring the camera 3 images into sharp focus.,"Unlike the deep NICMOS observations in the NHDF, the HST secondary mirror was not adjusted to bring the camera 3 images into sharp focus."
 The photometric gain. was nol considered high enough to request the adjustment which would have put the parallel ACS Images significantly out of focus., The photometric gain was not considered high enough to request the adjustment which would have put the parallel ACS images significantly out of focus.
 The PSF at the focal plane of camera 3 is therelore broader than the diffraction limited PSF observed by NICMOS cameras | and 2., The PSF at the focal plane of camera 3 is therefore broader than the diffraction limited PSF observed by NICMOS cameras 1 and 2.
 To determine the PSFs of the UDF images (wo measuremenis were performed., To determine the PSFs of the UDF images two measurements were performed.
 The first was to measure the PSF of the bright star alt x = 1897.26. v = 1610.34 with Gaussian fitting.," The first was to measure the PSF of the bright star at x = 1897.26, y = 1610.34 with Gaussian fitting."
 The second bright star al x = 1246.12. v = 1420.42 appears to be double with a faint companion.," The second bright star at x = 1246.12, y = 1420.42 appears to be double with a faint companion."
 The second measurement involved 42 camera 3 images in FLIOW and FIGOW of the photometric calibration star P330-E taken alter the NCS saline event., The second measurement involved 42 camera 3 images in F110W and F160W of the photometric calibration star P330-E taken after the NCS safing event.
 These were part of the Prop., These were part of the Prop.
 9995 calibration program of Mark Dickinson., 9995 calibration program of Mark Dickinson.
 These images were drizzled in (he same manner as ihe UDF images., These images were drizzled in the same manner as the UDF images.
 The PSF of the drizzled F110W and FIGOW images were measured by the same Gaussian fitting as for the UDF stellar images., The PSF of the drizzled F110W and F160W images were measured by the same Gaussian fitting as for the UDF stellar images.
 The results are listed in Table 6. which gives (he measured major and minor axis FEWIIM values., The results are listed in Table \ref{tab-psf} which gives the measured major and minor axis FWHM values.
 Table ο also gives the results of performing the same exercise on svntletic images produced with the Tinv Tim software (IxristanclHook2004) [or the camera 3 focus utilized in the UDF observations., Table \ref{tab-psf} also gives the results of performing the same exercise on synthetic images produced with the Tiny Tim software \citep{kri04} for the camera 3 focus utilized in the UDF observations.
 The Tiny Tin and calibration star PSFs agree quit well but the measured UDF stellar values are between 0.06 and 0.1 arc seconds wider., The Tiny Tim and calibration star PSFs agree quit well but the measured UDF stellar values are between 0.06 and 0.1 arc seconds wider.
 This may reflect the accuracy of the mosaic position calculations., This may reflect the accuracy of the mosaic position calculations.
 The widths measured in an independently reduced image (see 7.4)) are very similar to our UDF image widths., The widths measured in an independently reduced image (see \ref{ss-igi}) ) are very similar to our UDF image widths.
 Any researcher that. requires extremely accurate object shapes. such as lor weak lensing. may wish (o go to the original single images for size ancl shape measurements.," Any researcher that requires extremely accurate object shapes, such as for weak lensing, may wish to go to the original single images for size and shape measurements."
 Those researchers should apply (he geometric distortion. corrections listed in Table 4.., Those researchers should apply the geometric distortion corrections listed in Table \ref{tb-dis}.
 The full drizzled image does not have a unilorm integration time over the image., The full drizzled image does not have a uniform integration time over the image.
 In parücular the edges of the image have only one integration as opposed to the average 16 integrations for the interior of the image., In particular the edges of the image have only one integration as opposed to the average 16 integrations for the interior of the image.
" The full drizzled image has a size of 3500 by 3500 pixels. the same size ancl orientation as the ACS images reduced to 0.09"" pixels."," The full drizzled image has a size of 3500 by 3500 pixels, the same size and orientation as the ACS images reduced to $0.09 \arcsec$ pixels."
 Experience with the NIIDE images indicated that source extraction in regions with less (han half of the average integration (ime was not profitable except in special cases where a particular object near (he edge of the total image required. analvsis., Experience with the NHDF images indicated that source extraction in regions with less than half of the average integration time was not profitable except in special cases where a particular object near the edge of the total image required analysis.
 Users of (he treasury image should be aware that the edges of the image have roughly a V2 lower signal to noise than the central regions., Users of the treasury image should be aware that the edges of the image have roughly a $\sqrt{2}$ lower signal to noise than the central regions.
 The exact weight for all pixels is given by the weight images included in (he treasury, The exact weight for all pixels is given by the weight images included in the treasury
Strong magnetic fields on large scales may play an essential. active role in the formation and evolution of jet-like outflows.,"Strong magnetic fields on large scales may play an essential, active role in the formation and evolution of jet-like outflows."
" The general idea ts that a poloidal magnetic field. embedded in à plasma and anchored e.g. in an accretion disk or a black hole. is forced into rotation at the anchor point. a toroidal field develops and the plasma is accelerated by what can be interpreted as a centrifugal force in a corotating frame (???).,"," The general idea is that a poloidal magnetic field, embedded in a plasma and anchored e.g. in an accretion disk or a black hole, is forced into rotation at the anchor point, a toroidal field develops and the plasma is accelerated by what can be interpreted as a centrifugal force in a corotating frame \citep{1982Blandford,1996Spruit,2000Koenigl}."
 However. this magnetocentrifugal acceleration is only effective up until the surface. defined as the surface where the flow velocity equals the velocity.," However, this magnetocentrifugal acceleration is only effective up until the surface, defined as the surface where the flow velocity equals the velocity."
 Beyond this point. the magnetic field will be strongly wound-up.," Beyond this point, the magnetic field will be strongly wound-up."
 Such a field configuration 1s potentially unstable with respect to certain MHD instabilities., Such a field configuration is potentially unstable with respect to certain MHD instabilities.
 MHD jets are susceptible to a variety of instabilities., MHD jets are susceptible to a variety of instabilities.
 Kelvin-Helmholtz (KH) instabilities are fed by the relative kinetic energy between the jet and the ambient medium., Kelvin-Helmholtz (KH) instabilities are fed by the relative kinetic energy between the jet and the ambient medium.
 They can distort the jet surface only (ordinary modes) or the whole beam (e.g.?).. provoking shocks. mixing with ambient material and possibly a disruption of the jet (??)..," They can distort the jet surface only (ordinary modes) or the whole beam \citep[e.g.][]{1991Birkinshaw}, provoking shocks, mixing with ambient material and possibly a disruption of the jet \citep{1995Bodo,1998Bodo}."
 The presence of strong magnetic fields. poloidal or toroidal. is expected to hamper the growth of KH instabilities (??)..," The presence of strong magnetic fields, poloidal or toroidal, is expected to hamper the growth of KH instabilities \citep{1992Appl,1999Keppens}."
 The free energy associated with the toroidal magnetic field is responsible for another class of instabilities. which ts traditionally known as current-driven (CD) and of notorious importance in controlled fusion devices (foranintroduction.see.e.g. ?2?).," The free energy associated with the toroidal magnetic field is responsible for another class of instabilities, which is traditionally known as current-driven (CD) and of notorious importance in controlled fusion devices \citep[for an
introduction, see, e.g.][]{1987Freidberg,1978Bateman}."
 The relevance for magnetized astrophysical Jets has been pointed out by ??? and others.," The relevance for magnetized astrophysical jets has been pointed out by \citet{1993Eichler,1997Spruit,1998Begelman} and others."
 Among CD instabilities. #7=| kink instabilities are the most effective.," Among CD instabilities, $m=1$ kink instabilities are the most effective."
 An ideal kink mode ts characterized by helical displacements of the cylindrical cross sections of a plasma column., An ideal kink mode is characterized by helical displacements of the cylindrical cross sections of a plasma column.
 It is expected to grow on a dynamical time scale with respect to an wave crossing the unstable column., It is expected to grow on a dynamical time scale with respect to an wave crossing the unstable column.
 The susceptibility is strongly dependent on the magnetic pitch. a measure for the degree of wind-up.," The susceptibility is strongly dependent on the magnetic pitch, a measure for the degree of wind-up."
 Kink instabilities might destroy the ordered. symmetric state of a jet. leading to its disruption or. through magnetic reconnection. the associated dissipation of magnetic fields and steepening of the magnetic pressure gradient. to its acceleration (??)..," Kink instabilities might destroy the ordered, symmetric state of a jet, leading to its disruption or, through magnetic reconnection, the associated dissipation of magnetic fields and steepening of the magnetic pressure gradient, to its acceleration \citep{2002Drenkhahn,2006Giannios}."
 Different kinds of instability can mix and interact., Different kinds of instability can mix and interact.
 For example. ? show how CD instabilities can stabilize KH vortices at the jet surface.," For example, \citet{2002Baty} show how CD instabilities can stabilize KH vortices at the jet surface."
 For this work. we used conditions under which CD kink instabilities are expected to dominate (low plasma-f. small magnetic pitch).," For this work, we used conditions under which CD kink instabilities are expected to dominate (low $\beta$, small magnetic pitch)."
 For a self-consistent study of kink instabilities. numerical simulations need to be carried out in 3D. ? did so using a simple model in which a toroidal magnetic field configuration was allowed to expand into a uniform atmosphere.," For a self-consistent study of kink instabilities, numerical simulations need to be carried out in 3D. \citet{1996Lucek} did so using a simple model in which a toroidal magnetic field configuration was allowed to expand into a uniform atmosphere."
 This generated a jet which was subject to kink instabilities., This generated a jet which was subject to kink instabilities.
 ? performed 3D simulations of MHD jets in variously stratified atmospheres. finding that they can develop kink-like distortions in the region.," \citet{2004Nakamura} performed 3D simulations of MHD jets in variously stratified atmospheres, finding that they can develop kink-like distortions in the region."
 Laboratory experiments of MHD jets have been performed by ?.. confirming that the magnetic pitch plays a crucial role for the formation of kink instabilities.," Laboratory experiments of MHD jets have been performed by \citet{2005Hsu}, confirming that the magnetic pitch plays a crucial role for the formation of kink instabilities."
 Jets from protostars. and especially AGN and microquasars. expand in width d by orders of magnitude after passing through their radius.," Jets from protostars, and especially AGN and microquasars, expand in width $d$ by orders of magnitude after passing through their radius."
 In an expanding flow there is no clean separation between time dependence due to instability and that due to the expansion itself. making the question of stability less well defined.," In an expanding flow there is no clean separation between time dependence due to instability and that due to the expansion itself, making the question of stability less well defined."
" Analytical studies thus tend to focus on instabilities in a cylindrical geometry. with constant diameter (such as in the ""magnetic tower"" picture of ?))."," Analytical studies thus tend to focus on instabilities in a cylindrical geometry, with constant diameter (such as in the “magnetic tower” picture of \citealt{2003Lynden}) )."
 Expansion has strong consequences on the behavior of instabilities. however. compared with jets modeled as cylinders of constant width.," Expansion has strong consequences on the behavior of instabilities, however, compared with jets modeled as cylinders of constant width."
 First. there is the tendency for the toroidal (azimuthal. around the jet axis) component of the magnetic field to dominate m an expandingjet.," First, there is the tendency for the toroidal (azimuthal, around the jet axis) component of the magnetic field to dominate in an expanding jet."
 From the induction equation. the poloidal and toroidal components of the field vary as Bp.-1A. and B.~l|/d respectively (for constant jet velocity).," From the induction equation, the poloidal and toroidal components of the field vary as $B_\mathrm{p}\sim 1/d^2$ and $B_\varphi\sim 1/d$ respectively (for constant jet velocity)."
 Expansion thus causes a continual increase of the ratio διΕν., Expansion thus causes a continual increase of the ratio $B_\varphi/B_\mathrm{p}$.
 Even when dissipation were to decrease the toroidal field at some point. the ratio increases again on further expansion.," Even when dissipation were to decrease the toroidal field at some point, the ratio increases again on further expansion."
 Free energy available in the toroidal field thus remains the dominant form of magnetic energy. and one may expect the question of stability and dissipation to remain relevant on all length scales.," Free energy available in the toroidal field thus remains the dominant form of magnetic energy, and one may expect the question of stability and dissipation to remain relevant on all length scales."
 It also follows that the nonlinear development of instabilities in an expending jet is expected to be very different from the constant-diameter case., It also follows that the nonlinear development of instabilities in an expending jet is expected to be very different from the constant-diameter case.
Note that Milgrom(2009). predicts LO7<—g0.3 for the relevant range of values for the Galactic field at the Suns location. and for a variety of interpolating Dunctions: thus. tell us that the upper bound is less tight being It must be noted (hat Milgrom(2009) made certain simplifications in his calculations that should be taken into account when comparing hiis results with ours.,"Note that \citet{Mil09} predicts $10^{-2}\leq-q\leq 0.3$ for the relevant range of values for the Galactic field at the Sun's location, and for a variety of interpolating functions; thus, tell us that the upper bound is less tight being It must be noted that \citet{Mil09} made certain simplifications in his calculations that should be taken into account when comparing his results with ours."
 Indeed. in addition lo λος=1807.σος07. he assumed perfectly ecliptic orbits. ie. with £=0°. obtaining only radial and (ransverse components of the perturbing acceleration.," Indeed, in addition to $\lambda_{\rm GC}=180^{\circ},\beta_{\rm GC}=0^{\circ}$, he assumed perfectly ecliptic orbits, i.e. with $I=0^{\circ}$, obtaining only radial and transverse components of the perturbing acceleration."
 Thus. his precession of the longitude of perihelion a reduces to that of the argument of perihelion w because there is no precession of the node O.," Thus, his precession of the longitude of perihelion $\varpi$ reduces to that of the argument of perihelion $\omega$ because there is no precession of the node $\Omega$."
 Milerom(2009) himself acknowledees that such an approximation is not valid for bodies like Plito and Icarus showing high inclinations to the ecliptie., \citet{Mil09} himself acknowledges that such an approximation is not valid for bodies like Pluto and Icarus showing high inclinations to the ecliptic.
 Actually. the quadrupolar field of X/EFE does induce a secular precession on O as well. as we will see in Section ??..," Actually, the quadrupolar field of X/EFE does induce a secular precession on $\Omega$ as well, as we will see in Section \ref{nodo}."
 Let us. now. reason in terms of a rock-ice planetary body.," Let us, now, reason in terms of a rock-ice planetary body."
 By assuming for it a mass as largee as that of Mars we have for its distance An Earth-sized body. would be a while a gaseous giant like Jupiter would be αἱ The distance of a brown dwarf with Af=SOA‘) would be while an object with the mass of the Sun would be al, By assuming for it a mass as large as that of Mars we have for its distance An Earth-sized body would be at while a gaseous giant like Jupiter would be at The distance of a brown dwarf with $M=80M_{\rm J}$ would be while an object with the mass of the Sun would be at
After decomposing the ASAI light curve into IMFEs. the normalized Iilbert transform (Iluang&Long2003) was applied on the ΙΔΙΕΣ to obtain the instantaneous Irequencies and amplitudes.,"After decomposing the ASM light curve into IMFs, the normalized Hilbert transform \citep{Huang2003} was applied on the IMFs to obtain the instantaneous frequencies and amplitudes."
 The normalized Hilbert transform was proposed to overcome the limitation of absence of strong amplitude modulations imposed by (he Bedrosian theorem 1963)., The normalized Hilbert transform was proposed to overcome the limitation of absence of strong amplitude modulations imposed by the Bedrosian theorem \citep{Bedrosian1963}.
. The resultant Hilbert spectrum is a three-dimensional map which displays how the modulation period and amplitude vary. with lime., The resultant Hilbert spectrum is a three-dimensional map which displays how the modulation period and amplitude vary with time.
 Figure 3. shows the result. in which the frequency range is divided into 3000 bins and the spectrum is smoothed bv a Gaussian filter for clarity.," Figure \ref{hilbert_dynamic} shows the result, in which the frequency range is divided into 3000 bins and the spectrum is smoothed by a Gaussian filter for clarity."
 The color map represents the Hilbert energy spectrum with the magnitude of energy defined as square of the amplitude., The color map represents the Hilbert energy spectrum with the magnitude of energy defined as square of the amplitude.
 For comparison. the dvnamic power spectral technique. as described in Clarksonetal.(2003a).. was also applied on the ASAI light curve.," For comparison, the dynamic power spectral technique, as described in \citet{Clarkson2003}, was also applied on the ASM light curve."
 We first caleulated the Lomb-Scarele power spectrum (Scargle1982) of the first 200 d of the ASAI data. then successively moved the 200 d data window forward by a step size of 10 d and applied the Lomb-Scarele algorithm on each segment (o obtain a series of power spectra.," We first calculated the Lomb-Scargle power spectrum \citep{Scargle1982} of the first 200 d of the ASM data, then successively moved the 200 d data window forward by a step size of 10 d and applied the Lomb-Scargle algorithm on each segment to obtain a series of power spectra."
 The power spectra are plotted in Figure 3. in the contour form with the spectral power as defined in the Lomb-Scargle periodogram (Scarele1932)., The power spectra are plotted in Figure \ref{hilbert_dynamic} in the contour form with the spectral power as defined in the Lomb-Scargle periodogram \citep{Scargle1982}.
. It i8 obvious that the IHilbert energy spectrum is consistent. with (he dynamic power spectrum., It is obvious that the Hilbert energy spectrum is consistent with the dynamic power spectrum.
 Decause the spectral analysis based on LIT is independent of window size. more detailed structures in the light curve data can be observed from (he high-resolution Hilbert spectrum (han the dynamic power spectrum.," Because the spectral analysis based on HHT is independent of window size, more detailed structures in the light curve data can be observed from the high-resolution Hilbert spectrum than the dynamic power spectrum."
suggestive.,suggestive.
 Neither source is strougly variable al 5—ray euergies. although iu the case of WR LIT the natural time scale of the binary period is shorter than the variability analysis is seusitive to.," Neither source is strongly variable at $\gamma-$ ray energies, although in the case of WR 141 the natural time scale of the binary period is shorter than the variability analysis is sensitive to."
 However. both of these sources cannot be cousidered stroug candidates since one is outsile the coulidence contour aud the other has another equally bright. and hence equally viable. N-ray point source cousistent with the GeV position.," However, both of these sources cannot be considered strong candidates since one is outside the confidence contour and the other has another equally bright, and hence equally viable, X-ray point source consistent with the GeV position."
 LSI+61 303 is auother caucliclate. but iu this case the particle acceleration mechauisu is less clear.," LSI+61 303 is another candidate, but in this case the particle acceleration mechanism is less clear."
 If the companion to tlie B star is a neutrou star. the 5 —rays could be produced through an accretion process. colliding winds. or even standard pulsation mechanisms.," If the companion to the B star is a neutron star, the $\gamma-$ rays could be produced through an accretion process, colliding winds, or even standard pulsation mechanisms."
 Is moderate variability would suggest that some of the emission could be due to interactions of the neutroncstar with its environment., Its moderate variability would suggest that some of the emission could be due to interactions of the neutron-star with its environment.
 The Vela pulsar is in the X-ray. moclerate. low-variability group.," The Vela pulsar is in the X-ray moderate, low-variability group."
 When the binary sources are eliminated. ouly four sources are in this region of the plot. although there are au additional four potential members of this eroup which were not tested [or variability.," When the binary sources are eliminated, only four sources are in this region of the plot, although there are an additional four potential members of this group which were not tested for variability."
 Of these. two sources are weak upper-lituits on nouthermal fux hiddeu in thermal SNR. auc are therefore. if pulsars. likely to be X-ray faint.," Of these, two sources are weak upper-limits on non-thermal flux hidden in thermal SNR, and are therefore, if pulsars, likely to be X-ray faint."
 The best cauclidates for Vela-like raclio-quiet. pulsars are therefore INXNJOOQ0T.02-1302 in CTA I. aud sre? iu GeV J20204-3658.," The best candidates for Vela-like radio-quiet pulsars are therefore RXJ0007.0+7302 in CTA 1, and src2 in GeV J2020+3658."
 Src2 in GeV J2035+1211 and the double source in GeV JI1907-2-00T are reasonable candidates among the sources with unknown variability., Src2 in GeV J2035+4214 and the double source in GeV J1907+097 are reasonable candidates among the sources with unknown variability.
 Predictious of the majority of unideutilied GeV sources beiug radio-quiet. Vela-type pulsars by some outer-gap models of pulsar emission (eg.," Predictions of the majority of unidentified GeV sources being radio-quiet, Vela-type pulsars by some outer-gap models of pulsar emission (eg."
 Yadigaroglu aud Romani 1997) are therefore not well supported by the X-ray data., Yadigaroglu and Romani 1997) are therefore not well supported by the X-ray data.
 The most intriguing sources are the X- . ⋅⋅⋅ ↥⋅⋜↕⊽∖⊽⋯⋯⇂≺↵↕⋅⋜↕↕≺↵⋅∐↥∑≟∐∖⇁⋜∐⋅↥⋜↕∣≻⊔↕⊽∖⊽⋯⊔≺⇂≺↵∐⋃∐≺↲≺⇂⋅⋅⋅ sources.," The most intriguing sources are the X-ray moderate, high variability unidentified sources."
 Although cousistent⋅ with⋅ the blazars in the survey. uoue have bright. compact radio sources coiucklent with the X-ray source.," Although consistent with the blazars in the survey, none have bright, compact radio sources coincident with the X-ray source."
 What is most remarkable is that all four sources in this category seem (o coltain extended. syuchrotron uebulae.," What is most remarkable is that all four sources in this category seem to contain extended, synchrotron nebulae."
 Two of these. GeV J1856401125 aud GeV J1117-6100. have nebulae associated with the high E pulsars PSR B1853+01 aud the Ixookaburra Pulsar PSR J1120-6015.," Two of these, GeV J1856+0115 and GeV J1417-6100, have nebulae associated with the high $\dot E$ pulsars PSR B1853+01 and the Kookaburra Pulsar PSR J1420-6048."
 The other two. GeV JI8500-2327 and GeV 1825-1310. are in star forming 'eglons providing potential pulsar birtli-sites. with the latter haviug as a secoucdary source caudilate PSR BIS23-13.," The other two, GeV J1809-2327 and GeV J1825-1310, are in star forming regions providing potential pulsar birth-sites, with the latter having as a secondary source candidate PSR B1823-13."
 GeV. JOQOS+730L. he source associated with CTA 1 which also las a syuchrotron X-ray spectrum. shows inclicatious of ?—ray variability aud could also e included in this group.," GeV J0008+7304, the source associated with CTA 1 which also has a synchrotron X-ray spectrum, shows indications of $\gamma-$ ray variability and could also be included in this group."
 The most likely explanation [or these sources are wind nebulae around young pulsars., The most likely explanation for these sources are wind nebulae around young pulsars.
 The variability would iudicate that a substautial fraction of the +—ray flux is syuchrotron/C'ompton emission geuerated by particles in tlie pulsar wind., The variability would indicate that a substantial fraction of the $\gamma-$ ray flux is synchrotron/Compton emission generated by particles in the pulsar wind.
 Depending ou the local magnetic field strength. the syuchrotron. cooling timescale could be ou the order of a few months. similar to the variability time scale.," Depending on the local magnetic field strength, the synchrotron cooling timescale could be on the order of a few months, similar to the variability time scale."
 De Jager et al. (, De Jager et al. (
1996) have suggested a similar explanation for a possible variation seen in the Crab at 70-150 Mev.,1996) have suggested a similar explanation for a possible variation seen in the Crab at 70-150 Mev.
 If this is the case. the svnchrotror spectrum would mostly donunate the lower energies. aud the y-ray pulse fraction shouk increase with enerey uutil the pulsar emission cuts off at several GeV. Oka et al. (," If this is the case, the synchrotron spectrum would mostly dominate the lower energies, and the $\gamma-$ ray pulse fraction should increase with energy until the pulsar emission cuts off at several GeV. Oka et al. ("
1999 oropose that in the case of GeV J1809-232T. he 5 —ray euission is bremsstrahlung pliotons rom a pulsar wind collidiug with target yaryous iu the molecular cloud Lyucs 227.,"1999) propose that in the case of GeV J1809-2327, the $\gamma-$ ray emission is bremsstrahlung photons from a pulsar wind colliding with target baryons in the molecular cloud Lynds 227."
 In this case. the variability could be due to iustabilities in the interaction layer.," In this case, the variability could be due to instabilities in the interaction layer."
 . ∖↖≺↵∐⋜↕∖⇁≺↵↥↽∐⋅≺↵⊳∖↩∐↕≺↵≺⇂⋜↕∐≺↵⋜↕↓⋅↥⊽∖⊽∢∙∩⋯↥↽≻↥≺↲↕≺↵−≻− . keV eovX-ray image⋅ catalog of⋅ potential⋅ counterparts to the brightest⋅ sources of DEMCteV ⋅⋅ ⋅ ↩∐∐⊳, We have presented a nearly complete 2-10 keV X-ray image catalog of potential counterparts to the brightest sources of GeV emission.
∖⊳∖↓∩∐⋅↕∐↕∐≺↵∐∐⋜↕∑∸≺↲⊳∖∩⊔∐↩⋯⊔≺⇂≺↵∐, In the images of the unidentified
∖⊳∖↓∩∐⋅↕∐↕∐≺↵∐∐⋜↕∑∸≺↲⊳∖∩⊔∐↩⋯⊔≺⇂≺↵∐⋃, In the images of the unidentified
∖⊳∖↓∩∐⋅↕∐↕∐≺↵∐∐⋜↕∑∸≺↲⊳∖∩⊔∐↩⋯⊔≺⇂≺↵∐⋃∐, In the images of the unidentified
∖⊳∖↓∩∐⋅↕∐↕∐≺↵∐∐⋜↕∑∸≺↲⊳∖∩⊔∐↩⋯⊔≺⇂≺↵∐⋃∐≺, In the images of the unidentified
∖⊳∖↓∩∐⋅↕∐↕∐≺↵∐∐⋜↕∑∸≺↲⊳∖∩⊔∐↩⋯⊔≺⇂≺↵∐⋃∐≺↲, In the images of the unidentified
∖⊳∖↓∩∐⋅↕∐↕∐≺↵∐∐⋜↕∑∸≺↲⊳∖∩⊔∐↩⋯⊔≺⇂≺↵∐⋃∐≺↲≺, In the images of the unidentified
∖⊳∖↓∩∐⋅↕∐↕∐≺↵∐∐⋜↕∑∸≺↲⊳∖∩⊔∐↩⋯⊔≺⇂≺↵∐⋃∐≺↲≺⇂, In the images of the unidentified
∖⊳∖↓∩∐⋅↕∐↕∐≺↵∐∐⋜↕∑∸≺↲⊳∖∩⊔∐↩⋯⊔≺⇂≺↵∐⋃∐≺↲≺⇂⋅, In the images of the unidentified
∖⊳∖↓∩∐⋅↕∐↕∐≺↵∐∐⋜↕∑∸≺↲⊳∖∩⊔∐↩⋯⊔≺⇂≺↵∐⋃∐≺↲≺⇂⋅ , In the images of the unidentified
∖⊳∖↓∩∐⋅↕∐↕∐≺↵∐∐⋜↕∑∸≺↲⊳∖∩⊔∐↩⋯⊔≺⇂≺↵∐⋃∐≺↲≺⇂⋅ ⋅, In the images of the unidentified
∖⊳∖↓∩∐⋅↕∐↕∐≺↵∐∐⋜↕∑∸≺↲⊳∖∩⊔∐↩⋯⊔≺⇂≺↵∐⋃∐≺↲≺⇂⋅ ⋅⋅, In the images of the unidentified
∖⊳∖↓∩∐⋅↕∐↕∐≺↵∐∐⋜↕∑∸≺↲⊳∖∩⊔∐↩⋯⊔≺⇂≺↵∐⋃∐≺↲≺⇂⋅ ⋅⋅⋅, In the images of the unidentified
Fanaroll-Rilev tvpe Ll radio galaxies. (EIE: 2)) are well-known for the cjection of highly collimated jets from a central. nucleus.,Fanaroff-Riley type II radio galaxies (FRII; \citealt{fr74}) ) are well-known for the ejection of highly collimated jets from a central nucleus.
 ποσο jets subsequently inflate a pair of radio svnchrotron-emitting lobes where the jets are decelerated by the ran-pressure of the intergalactie medium (1GM). “, These jets subsequently inflate a pair of radio synchrotron-emitting lobes where the jets are decelerated by the ram-pressure of the intergalactic medium (IGM). “
Double-double radio galaxies” (DDRGs) form a sub-class of PRU objects in which there are multiple pairs of obes. all strongly coaligned to within a few degrees of each other.,"Double-double radio galaxies” (DDRGs) form a sub-class of FRII objects in which there are multiple pairs of lobes, all strongly coaligned to within a few degrees of each other."
 There are currently ~ 1217 such systems known. identified anc studied by ?.. 2.. 2.. 2.0 7.. 7.. 7. and ?)).," There are currently $\sim$ 12–17 such systems known, identified and studied by \citet{sbrlk00}, , \citet{sbrl00}, \citet*{ksr00}, \citet{ksj06}, \citet*{skk06}, \citet*{ms09}, \citet*{mjk10} and \citet*{sj09}) )."
 tecently the first. 7double-double radio quasar. 4€ 02.27 ias been discovered. (7)). showing that the properties. of DDIG are not purely. phenomena of giant radio sources and may even be a common. but short-lived. phase of active ealaxy evolution.," Recently the first “double-double radio quasar”, 4C 02.27 has been discovered \citealt*{jsk09}) ), showing that the properties of DDRG are not purely phenomena of giant radio sources and may even be a common, but short-lived, phase of active galaxy evolution."
 The second. inner pair of lobes in cach DDRG/Q was interpreted as evidence for a second. episode of jet activity. within the remnant cocoon of the original jet. as opposed to knots in an underlying jet.," The second, inner pair of lobes in each DDRG/Q was interpreted as evidence for a second episode of jet activity, within the remnant cocoon of the original jet, as opposed to knots in an underlying jet."
" Support for this conclusion was increased significantly by the discovery by ? ofafhird pair of closely. aligned lobes in the first known ""triple-double radio ealaxv. BO925|420."," Support for this conclusion was increased significantly by the discovery by \citet{bks07} of a pair of closely aligned lobes in the first known “triple-double radio galaxy”, B0925+420."
 Such objects therefore eive us rare and invaluable opportunities to study the cuty-eveles of Iarge-scale racio galaxies. despite their episodes of jet activity taking place on timescales of millions of vears.," Such objects therefore give us rare and invaluable opportunities to study the duty-cycles of large-scale radio galaxies, despite their episodes of jet activity taking place on timescales of millions of years."
 2? modelled the three pairs of lobes of D0925|420 in terms of their cynamical evolution in order to determine the permitted. ranges of jet. power as a function of age of the source and density of the surrounding medium. thereby testing the hypothesis that the subsequent pairs of lobes were indeed. forming within the cocoon of the original jet.," \citet{bks07} modelled the three pairs of lobes of B0925+420 in terms of their dynamical evolution in order to determine the permitted ranges of jet power as a function of age of the source and density of the surrounding medium, thereby testing the hypothesis that the subsequent pairs of lobes were indeed forming within the cocoon of the original jet."
 They found that the formation of the inner pair of lobes was indeed: consistent with the outer pair having been clisplaced buovanthy by the ambient medium., They found that the formation of the inner pair of lobes was indeed consistent with the outer pair having been displaced buoyantly by the ambient medium.
 The middle lobes were more problematic. requiring higher densities than those found within the outer lobes.," The middle lobes were more problematic, requiring higher densities than those found within the outer lobes."
 An alternative model (2)) was sugeested. interpreting the inner and. middle lobes as driven bow-shocks within the outer lobes.," An alternative model \citealt{cb91}) ) was suggested, interpreting the inner and middle lobes as jet-driven bow-shocks within the outer lobes."
 In order to further line-tune the mechanisms by which the observed characteristics of the lobes canbe reproduced.it is necessary to model more lobes from other. DDRG," In order to further fine-tune the mechanisms by which the observed characteristics of the lobes canbe reproduced,it is necessary to model more lobes from other DDRG"
for lensing in our survey Apu11410%.075L1294.10+ based on the Wambsganss et al.,for lensing in our survey $P_{CDM}\sim1.14\times10^{-3}\times0.75\times1.1=9.4\times10^{-4}$ based on the Wambsganss et al.
 simulations., simulations.
 We note that the magnification bias we found in this paper is based on a SiS [lux ratio distribution - an assumption that is not necessarily compatible with the Wambseanss et al. (, We note that the magnification bias we found in this paper is based on a SIS flux ratio distribution - an assumption that is not necessarily compatible with the Wambsganss et al. (
1995. 1998) simulations.,"1995, 1998) simulations."
 However. Figure 5 in Wambseanss et al. (," However, Figure 5 in Wambsganss et al. ("
1998) shows that the magnification probability found in their simulations is not very. dillerent [rom the PCL)~AI expected. from the SIS model we assumed in our maegnification-bias calculation.,1998) shows that the magnification probability found in their simulations is not very different from the $P(A)\sim A^{-3}$ expected from the SIS model we assumed in our magnification-bias calculation.
 Dased on the calculation described. above. 7.5 lenses are expected in our survey for an 0=1 CDM model.," Based on the calculation described above, 7.5 lenses are expected in our survey for an $\Omega_{0}=1$ CDM model."
 We can therefore reject the Wambseanss et al. (, We can therefore reject the Wambsganss et al. (
1995. 1998). model at 99.9% CL.,"1995, 1998) model at $99.9\%$ CL."
 We note that. since Figure 2 in Wambsganss et al. (," We note that, since Figure 2 in Wambsganss et al. ("
1995) eives the splitting angle probability for image [ux ratios smaller than 1.5 mag. our conclusion is conservative.,"1995) gives the splitting angle probability for image flux ratios smaller than 1.5 mag, our conclusion is conservative."
 Note. that the simulations of Wambseanss et al.," Note, that the simulations of Wambsganss et al."
 use the CODE normalization. v=1.05. which predicts an excess of high-mass clusters at the present epoch. and slower evolution of the mass function.," use the COBE normalization, $\sigma_{8}=1.05$, which predicts an excess of high-mass clusters at the present epoch, and slower evolution of the mass function."
 In this sense. our results do not reject the O4=1 modelse. but the combination of the cosmology and the high normalization.," In this sense, our results do not reject the $\Omega_{0}=1$ model, but the combination of the cosmology and the high normalization."
 The results. presented here. constitute one. of. the tightest and well-defined limits on large separation lensing to date., The results presented here constitute one of the tightest and well-defined limits on large separation lensing to date.
 Clearly. we have now reached a level where the non-detections are becoming interesting cosmological constraints.," Clearly, we have now reached a level where the non-detections are becoming interesting cosmological constraints."
 Lt is) probable that actual cases of large-separation eravitationally Lensecl quasars will be found soon using one of the large area surveys (c.g... SDSS. 2DE: see Croom et al.," It is probable that actual cases of large-separation gravitationally lensed quasars will be found soon using one of the large area surveys (e.g., SDSS, 2DF; see Croom et al."
 1998)., 1998).
 Llowever. in order to use such large separation lenses to constrain the cluster mass function and mass profile parameter space. we need to: (i) understand the selection effects and effectiveness of these surveys for large separation lensing: (ii) have a realistic estimate of the cross section for large separation lensing. taking into account the substructure of clusters.," However, in order to use such large separation lenses to constrain the cluster mass function and mass profile parameter space, we need to: (i) understand the selection effects and effectiveness of these surveys for large separation lensing; (ii) have a realistic estimate of the cross section for large separation lensing, taking into account the substructure of clusters."
 These points will be addressed in luture papers., These points will be addressed in future papers.
 ‘To summarize our main results. we have derived a lower limit to the magnification bias in our survey. Dc1.1. an we have also found that the median photometric-redshift of quasars in our sample is z;í4; ld. ," To summarize our main results, we have derived a lower limit to the magnification bias in our survey, $B\geq1.1$, and we have also found that the median photometric-redshift of quasars in our sample is $\bar z_{source}\sim1.4$ ."
Using the redshift distribution from the FBOS faint extension. we determine jiu fo<00018 with 95% CL (assuming a SIS moclel anc an Og=0.3. O4=0.7 cosmology).," Using the redshift distribution from the FBQS faint extension, we determine that $F<0.018$ with $95\%$ CL (assuming a SIS model and an $\Omega_{0}=0.3$, $\Omega_{\Lambda}=0.7$ cosmology)."
 Our non-detection of sed FERS quasars is consistent. with expectations. if clusters can be represented. by a non-evolving population OF SIS masses with the mass function of the observed cluster »opulation.," Our non-detection of lensed FIRST quasars is consistent with expectations, if clusters can be represented by a non-evolving population of SIS masses with the mass function of the observed cluster population."
 H£ so. moderately larger surveys will discover the irst exemples of large separation quasar lensing.," If so, moderately larger surveys will discover the first examples of large separation quasar lensing."
" Our survey already has the ability to reject some models with concrete oedictions. namelv the 4,=1 COBL-normalized CDM model. whose excess of power on large scales is well known."," Our survey already has the ability to reject some models with concrete predictions, namely the $\Omega_{0}=1$ COBE-normalized CDM model, whose excess of power on large scales is well known."
 We thank Eric Richards for sending us a digital. version of his deep radio catalogue of the HIDE region. and an anonymous referee. for useful. comments.," We thank Eric Richards for sending us a digital version of his deep radio catalogue of the HDF region, and an anonymous referee for useful comments."
 EOO wishes to thank the Alax-Planek-lnstitut (rr Astronomie. for its hospitality. and financial support: the Deutscher Akademischer Austauschelienst for financial. support: ane Orly Gnat and Avishay GalYan for fruitful discussions., EOO wishes to thank the Max-Planck-Institut fürr Astronomie for its hospitality and financial support; the Deutscher Akademischer Austauschdienst for financial support; and Orly Gnat and Avishay Gal-Yam for fruitful discussions.
 This research has made use of the Sloan Digital Sky Survey., This research has made use of the Sloan Digital Sky Survey.
 Funding for the creation and. distribution. of the SDSS Archive has been provided by the Alfred. P. Sloan Foundation. the Participating Institutions. the National Aeronautics and Space Xdministration. the National Science Foundation. the U.S. Department of Energy. the Japanese AMonbukagakusho. andthe Max Planck Society.," Funding for the creation and distribution of the SDSS Archive has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, andthe Max Planck Society."
 The SDSS Web site is httpz/www.sdss.org, The SDSS Web site is http://www.sdss.org/.
"Using the conclusions of a recent study of the influence of the gas expulsion phase on the shape of the resulting CIMF (?)., we infer that the empirical CIMF derived in the present paper is compatible with the scenario of a low, randomly distributed star formation efficiency with an average of and a dispersion of3%.","Using the conclusions of a recent study of the influence of the gas expulsion phase on the shape of the resulting CIMF \citep{parea08}, we infer that the empirical CIMF derived in the present paper is compatible with the scenario of a low, randomly distributed star formation efficiency with an average of and a dispersion of."
. The evolution of the luminosity function of Galactic star clusters is shown in Fig. 8.., The evolution of the luminosity function of Galactic star clusters is shown in Fig. \ref{fig:fulu}.
" Similar to the mass function, the CLF apparently includes two regimes (although less clearly distinguishable from each other than in the CMF case)."," Similar to the mass function, the CLF apparently includes two regimes (although less clearly distinguishable from each other than in the CMF case)."
" The dominant feature is the linear regime of the CLF, occupying the bulk of brighter magnitudes up to Ty,~—2.5, and a minor detail is a tail at fainter magnitudes."," The dominant feature is the linear regime of the CLF, occupying the bulk of brighter magnitudes up to $I_{M_V} \approx -2.5$, and a minor detail is a tail at fainter magnitudes."
" However, since the evolution of the luminosity function is governed mainly by stellar evolution, and only at the end of cluster life by dynamical effects, there is no direct correspondence between absolute magnitude and mass of clusters."," However, since the evolution of the luminosity function is governed mainly by stellar evolution, and only at the end of cluster life by dynamical effects, there is no direct correspondence between absolute magnitude and mass of clusters."
" In most of the CLF bins of absolute magnitude, we find a mixture of masses and evolutionary states."," In most of the CLF bins of absolute magnitude, we find a mixture of masses and evolutionary states."
" Only at the extremes of the magnitude scale, there are clusters of more or less “pure” evolutionary status."," Only at the extremes of the magnitude scale, there are clusters of more or less “pure” evolutionary status."
" As a result, the initial luminosity function of open clusters can be taken from the distribution of the youngest clusters (logt<6.9) at Iy,<—5.5 where the clusters belong to the massive portion of the CIMF (logM.>3.3), and the tail of the CPDLF at /y,>—2 consists mainly of decaying clusters with masses less than ~100Mo i.e., after the CPDMF maximum."," As a result, the initial luminosity function of open clusters can be taken from the distribution of the youngest clusters $\log t \leqslant6.9$ ) at $I_{M_V}<-5.5$ where the clusters belong to the massive portion of the CIMF $\log M_c>3.3$ ), and the tail of the CPDLF at $I_{M_V}>-2$ consists mainly of decaying clusters with masses less than $\approx 100 M_\odot$ i.e., after the CPDMF maximum."
" Contrary to the CMF, the luminosity function at —8.0<Iy,«—5.5 does not show any evolution of the slope with time."," Contrary to the CMF, the luminosity function at $-8.0<I_{M_V}<-5.5$ does not show any evolution of the slope with time."
" It seems that, with increasing age, the CLF is just moving along the ordinate due to the arrival of newborn clusters without changing the shape and extends to fainter magnitudes due to the aging effect (fading of the brightest stars)."," It seems that, with increasing age, the CLF is just moving along the ordinate due to the arrival of newborn clusters without changing the shape and extends to fainter magnitudes due to the aging effect (fading of the brightest stars)."
" Based on this study on local Galactic clusters, we find that, in the immediate vicinity of the Sun, young (logt«6.9) open clusters are present within a wide range of masses."," Based on this study on local Galactic clusters, we find that, in the immediate vicinity of the Sun, young $\log t \leqslant $ 6.9) open clusters are present within a wide range of masses."
 The mass range extends from the highest masses - observed also in other galaxies - to a few tens of solar mass., The mass range extends from the highest masses - observed also in other galaxies - to a few tens of solar mass.
 This is a strong hint that the population in the solar neighbourhood is typical of spiral galaxies., This is a strong hint that the population in the solar neighbourhood is typical of spiral galaxies.
" In quite a natural way, cluster-like associations (see."," In quite a natural way, cluster-like associations (see."
 Sect. ??)), Sect. \ref{sec:dadef}) )
" form the high-mass end of the CPDMF; in other words, they represent the same population of the Galactic disc as young open clusters."," form the high-mass end of the CPDMF; in other words, they represent the same population of the Galactic disc as young open clusters."
" A comparison of our luminosity and mass functions of star clusters with those in other galaxies, which we discussed in Sect.??,, strongly indicates a universal law of cluster formation, which is only weakly dependent on the environment."," A comparison of our luminosity and mass functions of star clusters with those in other galaxies, which we discussed in \ref{sec:lmf}, strongly indicates a universal law of cluster formation, which is only weakly dependent on the environment."
 The issue of the universality of the cluster initial mass function in different galaxies is discussed in more detail by ?.., The issue of the universality of the cluster initial mass function in different galaxies is discussed in more detail by \citet{grijs03}. .
" Studying the CPDLF of extragalactic clusters, ? notes a depletion of the CPDLF at Jy,«-δ in three galaxies."," Studying the CPDLF of extragalactic clusters, \citet{slars} notes a depletion of the CPDLF at $I_{M_V}<-8$ in three galaxies."
 The author explains this effect by a possible increase in the steepness of the CPDLF., The author explains this effect by a possible increase in the steepness of the CPDLF.
" ? confirm the existence of this precipitous drop in the cluster luminosity functions of the spiral galaxies NGC 6946 and M51 and explain this by assuming two-segment-, or Schechter CIMFs, in these galaxies."," \citet{giel06} confirm the existence of this precipitous drop in the cluster luminosity functions of the spiral galaxies NGC 6946 and M51 and explain this by assuming two-segment-, or Schechter CIMFs, in these galaxies."
" We observe the same feature in the luminosity function of Galactic clusters, too."," We observe the same feature in the luminosity function of Galactic clusters, too."
" Unfortunately, the sample is restricted to the solar neighbourhood and does not include enough of the brightest clusters to be compared with the brightest limit of the extragalactic CPDLFs."," Unfortunately, the sample is restricted to the solar neighbourhood and does not include enough of the brightest clusters to be compared with the brightest limit of the extragalactic CPDLFs."
" As noted at the end of the last section, the parallel slope of the CPDLF for samples of different ages in the range -8<Iy,€—5 is a consequence of the continuity equation."," As noted at the end of the last section, the parallel slope of the CPDLF for samples of different ages in the range $-8 \leq I_{M_V}
\leq -5$ is a consequence of the continuity equation."
" A depletion at Jy,«-—8 suggests that no open clusters are born (or leave their parental cloud) with an absolute integrated magnitude much brighter than /y,=—8.", A depletion at $I_{M_V}<-8$ suggests that no open clusters are born (or leave their parental cloud) with an absolute integrated magnitude much brighter than $I_{M_V}=-8$.
 A caveat is the poor statistics (only a few extragalactic clusters and no Galactic ones)., A caveat is the poor statistics (only a few extragalactic clusters and no Galactic ones).
" From the physical point of view, the observed deficiency might correspond to a gap caused by so-called ""type II embedded clusters” (?),, which are massive enough to produce plenty of O stars providing fast gas expulsion and parent cluster decay."," From the physical point of view, the observed deficiency might correspond to a gap caused by so-called “type II embedded clusters” \citep{krobo02}, which are massive enough to produce plenty of O stars providing fast gas expulsion and parent cluster decay."
" The low-mass limitof this cluster family should be in the vicinity of logM,=4.5 in this case.", The low-mass limitof this cluster family should be in the vicinity of $\log M_c=4.5$ in this case.
located in a galaxy cluster.,located in a galaxy cluster.
 The question arises of whether most radio relics and halos are indeed located in massive galaxy clusters or whether they also occur in poor clusters and galaxy groups., The question arises of whether most radio relics and halos are indeed located in massive galaxy clusters or whether they also occur in poor clusters and galaxy groups.
" None of the sources in our sample, with a«-—1.35 (between 74 and 1400 MHZ), are located in massive known galaxy clusters."," None of the sources in our sample, with $\alpha<-1.35$ (between 74 and 1400 MHz), are located in massive known galaxy clusters."
 Only VLSS J1515.1+0424 (in Abell 2048) and VLSS J1431.8+1331 (in MaxBCG J217.95869+13.53470) are found in clusters detected in the ROSAT All-Sky Survey., Only VLSS J1515.1+0424 (in Abell 2048) and VLSS J1431.8+1331 (in MaxBCG J217.95869+13.53470) are found in clusters detected in the ROSAT All-Sky Survey.
" The X-ray luminosities of these clusters are moderate, with values between 1-2 x10“ erg s!."," The X-ray luminosities of these clusters are moderate, with values between 1–2 $\times 10^{44}$ erg $^{-1}$."
" Therefore, our observations indicate that diffuse steep-spectrum sources do also occur in less massive clusters and galaxy groups."," Therefore, our observations indicate that diffuse steep-spectrum sources do also occur in less massive clusters and galaxy groups."
 Most of the sources seem to be radio relics related to previous episodes of AGN activity: either AGN relics or radio phoenices., Most of the sources seem to be radio relics related to previous episodes of AGN activity: either AGN relics or radio phoenices.
" Some other sources in our sample can be classified as core-halo or candidates, where the radio emission surrounds a central galaxy of a poor cluster or galaxy group."," Some other sources in our sample can be classified as core-halo or candidates, where the radio emission surrounds a central galaxy of a poor cluster or galaxy group."
" In our case, they are not found in massive cool-core clusters."," In our case, they are not found in massive cool-core clusters."
" Amongst the sources in our sample, there are also a number of more distant (z~ 1) filamentary radio sources related to AGN activity."," Amongst the sources in our sample, there are also a number of more distant $z \sim 1$ ) filamentary radio sources related to AGN activity."
" These could be relatively “nearby” ultra-steep spectrum (USS) sources (e.g.,see?,forareview).."," These could be relatively “nearby” ultra-steep spectrum (USS) sources \citep[e.g., see ][for a review]{2008A&ARv..15...67M}."
" As they are relatively nearby, they are clearly extended in for example the 1.4 GHz FIRST survey images resolution) and therefore included in our sample."," As they are relatively nearby, they are clearly extended in for example the 1.4 GHz FIRST survey images resolution) and therefore included in our sample."
 We did not detect any ultra-steep spectrum radio halos (?) in our sample., We did not detect any ultra-steep spectrum radio halos \citep{2008Natur.455..944B} in our sample.
 This could be because the surface brightness of these objects is too low for them to be detectedin the 74 MHz VLSS survey (??).. ," This could be because the surface brightness of these objects is too low for them to be detectedin the 74 MHz VLSS survey \citep{2008Natur.455..944B, 2010A&A...517A..43M}."
The 74 MHz VLSS survey is relatively shallow with an average rms noise of 0.1 Jy beam™!., The 74 MHz VLSS survey is relatively shallow with an average rms noise of 0.1 Jy $^{-1}$ .
svstematic errors to the simulated radial velocities. subtract the error-weighted mean. and calculate the RAIS.,"systematic errors to the simulated radial velocities, subtract the error-weighted mean, and calculate the RMS."
 To filler binary stars. we remove observed and predicted svstems whose RAS exceeds a specified οπίου.," To filter binary stars, we remove observed and predicted systems whose RMS exceeds a specified cutoff $B$."
 The model and observed distributions are compared using the two-sided Ixolmogorov-Smürnov (IX-5) test and the two-sample Ixuiper test: the latter is sensitive to the tails of a distribution as opposed to the median., The model and observed distributions are compared using the two-sided Kolmogorov-Smirnov (K-S) test and the two-sample Kuiper test; the latter is sensitive to the tails of a distribution as opposed to the median.
 The four parameters of the model are (he MRR parameter a. Πίο magnitude op). binary. cutoff D. ancl completeness C.," The four parameters of the model are the MRR parameter $\alpha$, jitter magnitude $\sigma_0$ , binary cutoff $B$, and completeness $C$."
 In Section 4. we introduce a fifth parameter + Chat describes a mixed population of rocky and Neptune-like planets.," In Section \ref{sec.results}
 we introduce a fifth parameter $\gamma$ that describes a mixed population of rocky and Neptune-like planets."
" A bvproduet of our analvsis is an estimate ofthe average number of planets per star: SOs, ' ", A byproduct of our analysis is an estimate ofthe average number of planets per star: $\sum_i s_i^{-1}$ .
We find that ofKepler stars with 7; = 3660-4660 Xv have planets with Π>2R and P<50 cl. This is in agreement with the findings of of Lowardetal.(2011).," We find that of stars with $T_e$ = 3660-4660 K have planets with $R_e >
2$ and $P < 50$ d. This is in agreement with the findings of of \citet{Howard2011}."
". The frequency of giant planets (2, 0.91) in our sample is2.4%... close to that estimated in Doppler surveys (Johnsonetal.2010)."," The frequency of giant planets $R_p >
0.8R_J$ ) in our sample is, close to that estimated in Doppler surveys \citep{Johnson2010}."
. This indicates minimal bias in our Monte Carlo reconstruction of the discreteAepler saniple because any effect should be most pronounced for the rarest (largest) planets., This indicates minimal bias in our Monte Carlo reconstruction of the discrete sample because any effect should be most pronounced for the rarest (largest) planets.
 The observed cumulative distribution of RV RMS (points in Figure 4)) has an accelerating rise below 3 [rom gaussian noise. a logarithmic increase over [rom the combined effect of svstematic error and planets not resolved bv Doppler observations. and a tail bevond 10 from giant planets and low-inclination binary stars.," The observed cumulative distribution of RV RMS (points in Figure \ref{fig.rmsdist}) ) has an accelerating rise below 3 from gaussian noise, a logarithmic increase over 3-10 from the combined effect of systematic error and planets not resolved by Doppler observations, and a tail beyond 10 from giant planets and low-inclination binary stars."
 The best-fit models (e.g.. solid line) agree with the observed distribution with a IxX-Sprobability >90%.," The best-fit models (e.g., solid line) agree with the observed distribution with a K-Sprobability $>$ ."
. TheIX-S and Ixuiper statistics are largely congruent and hereafter. we, TheK-S and Kuiper statistics are largely congruent and hereafter we
suuple the dust at z 50-100. I& (typically Lo100 AU radius) so these are also biased towards warm. dust disks.,"sample the dust at $\approx$ 50-100 K (typically 40–100 AU radius), so these are also biased towards warm dust disks."
 Yet we know cool debris disks do exist: Figure 2. shows the SED of the bright nearby disk around ε Dridani and Figure 3. shows the fitted temperatures of known debris disks versus stellar hunuinositv for stars of differing spectral classes;," Yet we know cool debris disks do exist; Figure \ref{epsiloneri} shows the SED of the bright nearby disk around $\epsilon$ Eridani, and Figure \ref{lum.v.T} shows the fitted temperatures of known debris disks versus stellar luminosity for stars of differing spectral classes."
 Disks around lower mass stars tend to be significantly: cooler than their counterparts around A stars. with virtually all such disks exhibiting temperatures of «70 EK. This is consistent with the findings of Wyattetal.(2003) and Rheeetal.(2007) of a disk population below the sensitivities of IRAS observations.," Disks around lower mass stars tend to be significantly cooler than their counterparts around A stars, with virtually all such disks exhibiting temperatures of $< 70$ K. This is consistent with the findings of \cite{wdg03} and \cite{rhe07} of a disk population below the sensitivities of IRAS observations."
 To sample the cool dust. we must eo to submillimeter wavelengths.," To sample the cool dust, we must go to submillimeter wavelengths."
 The umuuber of unbiased surveys conducteck in the submillimeter. however. is very lianuted (see Table 1).," The number of unbiased surveys conducted in the submillimeter, however, is very limited (see Table \ref{surveys}) )."
 Iu most cases. once the submillimeter detectious were made. onlv a few subsequent detailed analysis of far-IR data showed detections (Zuckerman2001).. indicatiug that the dust is indeed cool.," In most cases, once the submillimeter detections were made, only a few subsequent detailed analysis of far-IR data showed detections \citep{zuc01}, indicating that the dust is indeed cool."
 A further point illustrated iu Table 1 is that the percentage detection rate increases sharply with sensitivitv. frou in the least sensitive survey up to in deep searches (and higher im the ο) Pic eroup. perhaps because these stars are voung).," A further point illustrated in Table \ref{surveys} is that the percentage detection rate increases sharply with sensitivity, from in the least sensitive survey up to in deep searches (and higher in the $\beta$ Pic group, perhaps because these stars are young)."
 Extrapolatiug to still deeper survevs. we nieht expect a substantially higher detection vate of about," Extrapolating to still deeper surveys, we might expect a substantially higher detection rate of about."
 Iu sumnnuiuw. there is growing evidence of a significant population of submilhneter-brieht disks with Fo<10 Ik. The final coluun in Table 1. shows depths reached thus far (where equivalent flux limits of other wavelengths have beeu corrected to 850 422)).," In summary, there is growing evidence of a significant population of submillimeter-bright disks with $T \le 40$ K. The final column in Table \ref{surveys} shows depths reached thus far (where equivalent flux limits of other wavelengths have been corrected to 850 )."
 The SUNS survey. with au ris sensitivity of1o=0.7 11Jv willbe deeperin fiux than the only previous large scale survey (Carpenterct 2005).," The SUNS survey, with an rms sensitivity of $1 \ \sigma = 0.7$ mJy will be in flux than the only previous large scale survey \citep{car05}."
. This is the equivalent depth to the observation of the disk around the 1 Cyr old star 7 Ceti (Figure 1))., This is the equivalent depth to the observation of the disk around the 1 Gyr old star $\tau$ Ceti (Figure \ref{tauceti}) ).
 Below. woe discuss the effective Πιτ on the subinillimeter survey compared to the current eeneratiou of far-IR detectors onSpitcer.," Below, we discuss the effective limits on the submillimeter survey compared to the current generation of far-IR detectors on."
 For the nearby stars where photospheric ciission dominates (Figure 2)). the dust detection linüt of far-IR iustruuents are set by the accuracy with which a disk excess can be discriminated from plotospheric contributions.," For the nearby stars where photospheric emission dominates (Figure \ref{epsiloneri}) ), the dust detection limit of far-IR instruments are set by the accuracy with which a disk excess can be discriminated from photospheric contributions."
 The limits on the detectability of a, The limits on the detectability of a
"Solving (3)) in this regime we find the time scale /4400;:0,) to grow the grains from o; lo oy Is for Epstein drag and for Stokes drag.","Solving \ref{main}) ) in this regime we find the time scale $t_{1.1}(\phi_i, \phi_f)$ to grow the grains from $\phi_i$ to $\phi_f$ is for Epstein drag and for Stokes drag."
" Note that these values for /4,4 are not strongly dependent on or. allowing us to use the approximations implicit in (25))."," Note that these values for $t_{1.1}$ are not strongly dependent on $\phi_f$, allowing us to use the approximations implicit in \ref{vc1}) )."
 Once the damping time grows long enough such that then the “Goldilocks” turbulent scale exists. ος=Όρο (24)) applies aud the regime 1.1 progresses to regime 2.1.," Once the damping time grows long enough such that then the ""Goldilocks"" turbulent scale exists, $v_c=v_{c, 2}$ \ref{vc2}) ) applies and the regime 1.1 progresses to regime 2.1."
 This occurs for with Epstein drag ancl for with Stokes drag., This occurs for with Epstein drag and for with Stokes drag.
 In regime 2.1. the dust grows to couple will progressively larger and larger scale eddies that determine the collisional velocity e...," In regime $2.1$, the dust grows to couple with progressively larger and larger scale eddies that determine the collisional velocity $v_c$."
 For the range of a and HR that we consider. the erains still remain small enough (o avoid settling. (," For the range of $\alpha$ and $R$ that we consider, the grains still remain small enough to avoid settling. ("
For smaller a and larger A. even the largest ecdcdies would be be too weak to prevent settling and an additional Regime 1.2 would OCCUL.),"For smaller $\alpha$ and larger $R$, even the largest eddies would be be too weak to prevent settling and an additional Regime $1.2$ would occur.)"
" In regime 2.1. we have v0.» from (24)) ancl fy, from (33))."," In regime $2.1$, we have $v_{c, 2}$ from \ref{vc2}) ) and $H_{d, 1}$ from \ref{hd1}) )."
 Solving (3)) we find the growth time scale in this regime (o be, Solving \ref{main}) ) we find the growth time scale in this regime to be
As the result. we have an adaptively configured SNR seed in the 3D simulation.,"As the result, we have an adaptively configured SNR seed in the 3D simulation."
 This seed has a yuatiically self-consistent structure expected for the SNR evolving in the local ambient meciuu. which is pa‘ticularly important lor accurately tracing the SNB structures aud SN ejecta (see 833.1).," This seed has a dynamically self-consistent structure expected for the SNR evolving in the local ambient medium, which is particularly important for accurately tracing the SNR structures and SN ejecta (see 3.4)."
 We can therefore incorporate the sub-erid evolution of the SNR into the large-scale 3D simulation. wlich optitσος the use of the computational time aud enlarges the covered dynamical rauge )..," We can therefore incorporate the sub-grid evolution of the SNR into the large-scale 3D simulation, which optimizes the use of the computational time and enlarges the covered dynamical range \citep{Tang09}."
 It is not clear how such realisin of the SNR seed aud the adaptiveness of its plautiug Ca1 be realized in other simple way (e.g.. assuming a uuilorm thermal energy depositiou or other arbitrary pκMiles).," It is not clear how such realism of the SNR seed and the adaptiveness of its planting can be realized in other simple way (e.g., assuming a uniform thermal energy deposition or other arbitrary profiles)."
 When au SNB is young. the mass of he SN ejecta cau be considerable.," When an SNR is young, the mass of the SN ejecta can be considerable."
 Asstumine that Inass is the salue for the SNRs iu the coisideration. we have /3;—0 as well as {ως aud 7p— as in the previous case.," Assuming that the mass is the same for the SNRs in the consideration, we have $i_M$ =0 as well as $i_E$ =0 and $i_{\rho}$ =0, as in the previous case."
 The SNR evolutio Lis not self-similar and asyinptotically approaches he Sedov-Taylor solution ouly when the swep-up mass is much greater than the ejecta mass (M.;) aud the swept-up euerey is still ueelieible., The SNR evolution is not self-similar and asymptotically approaches the Sedov-Taylor solution only when the swept-up mass is much greater than the ejecta mass $M_{ej}$ ) and the swept-up energy is still negligible.
 But. the solution 1yay still be scalable (rom oue 5di to another.," But, the solution may still be scalable from one SNR to another."
 From Eqs. (29))-(33)).," From Eqs. \ref{eq:a1begin}) \ref{eq:a1end}) ),"
" we also lave η EUN4 ‘pal pai,f3.", we also have $i_T$ =0 and $i_L$ $i_t$ $i_\rho$ /3.
" This means that oue 5di evolving within a1 ambient. mecitun of deiIsity Py ancl lempe‘ature Ty, can be scaled to anotler SNR o “the densiVv ph=paA8 but) oftle salie tempe‘ature: these two SNRs have their ages linked N fy—LA!£ and have the same swept-up passes aud elereies.", This means that one SNR evolving within an ambient medium of density $\rho_a$ and temperature $T_a$ can be scaled to another SNR of the density $\rho_b = \rho_a \lambda^{-3i_L}$ but of the same temperature; these two SNRs have their ages linked by $t_b = t_a \lambda^{i_L}$ and have the same swept-up masses and energies.
 ΤΙe saLe screme introduced in the previous section cal also be used lor embeddiug $ seeds ilicing tlje ejecta., The same scheme introduced in the previous section can also be used for embedding SNR seeds including the ejecta.
 But in tus case the library o “SNR templates needs to be expauk because the scaling is now only accurate for SNRs evolving uuder the same ambient temperat, But in this case the library of SNR templates needs to be expanded because the scaling is now only accurate for SNRs evolving under the same ambient temperature.
 We can tablate : vseries of SNRs simulated for a eimperaure erid., We can tabulate a series of SNRs simulated for a temperature grid.
 An interpolation may be usec to generate any needed seed for a particular auljent gas temperature., An interpolation may be used to generate any needed seed for a particular ambient gas temperature.
 If the eric is sufficiettly fine. then stch interpolation may not even be neeed.," If the grid is sufficiently fine, then such interpolation may not even be needed."
 For example. a logarithiuical grid interva of 0.02 (Le.. ouly 50 SNB simulations are ueeded to cover au order of magnitude temperature rauge," For example, a logarithmical grid interval of 0.02 (i.e., only 50 SNR simulations are needed to cover an order of magnitude temperature range)"
(emperature. S/N ratio. or resolution.,"temperature, S/N ratio, or resolution."
 The three stars in Table 8 with upper limits are indeed Abnormal to Al-poor.," The three stars in Table \ref{tab:t08}
 with upper limits are indeed Al-normal to Al-poor."
 The intent of this research is to discover the nature of the [Al/Fe] distribution in these two Custers. aud we can make some observatious despite the limited sample size.," The intent of this research is to discover the nature of the [Al/Fe] distribution in these two clusters, and we can make some observations despite the limited sample size."
 Figure 3... which shows [Al/Fe] as a function of theTa. demonstrates that there is a broad distribution along the RGB with no cliscernible trends in the Al ratio for either cluster.," Figure \ref{fig:f03}, which shows [Al/Fe] as a function of the, demonstrates that there is a broad distribution along the RGB with no discernible trends in the Al ratio for either cluster."
 As shown in Table 10.. which sSumimarizes the 1uean abundances by cluster. alumiuum is enlianced in both clusters aud slows lie. largest. clistriltition among the elements studied. suggesting that the abuudance spread is uot statistical.," As shown in Table \ref{means}, which summarizes the mean abundances by cluster, aluminum is enhanced in both clusters and shows the largest distribution among the elements studied, suggesting that the abundance spread is not statistical."
 That the variations are real is further supported in Figure [. which shows the spectra ¢M two stars witl very similar atinospheric parameters from each cluster having largely varying Al I liines.," That the variations are real is further supported in Figure \ref{fig:f04}, which shows the spectra of two stars with very similar atmospheric parameters from each cluster having largely varying Al I lines."
 Our results are consisteut with the giants studied by Norris&DaCosta(1995) aud (2002).. aud. with the subgiauts of Cirattouetal.(2001).," Our results are consistent with the giants studied by \citet{ND95}
 and \citet{GBNF2002}, and with the subgiants of \citet{GratAl2001}."
. It would be useful to know low (us distribution ¢angesDm with magultudee by usingOm the data of Grattonetal.(2001). and (2002).. but theirs were purposely choseu in a biased manuer according to c4 indices aud are understaudably. iucomplete. given the large number of stars iu the maguitude rauges where (ley were operatiug. so that the data are insullicient to reveal any evolution of the Al ratio.," It would be useful to know how this distribution changes with magnitude by using the data of \citet{GratAl2001} and \citet{GBNF2002}, but theirs were purposely chosen in a biased manner according to $c_{1}$ indices and are understandably incomplete, given the large number of stars in the magnitude ranges where they were operating, so that the data are insufficient to reveal any evolution of the Al ratio."
 If our results are representative of the clusters’ [Al/Fe] distributions in general. then one would have to rile out the connection between the Al ratio aud the HB morphology. since we expect any ongoing mixiug to create an upward trend in [Al/Fe] with decreasingTey. which is not seen here for this Snall sample.," If our results are representative of the clusters' [Al/Fe] distributions in general, then one would have to rule out the connection between the Al ratio and the HB morphology, since we expect any ongoing mixing to create an upward trend in [Al/Fe] with decreasing, which is not seen here for this small sample."
 Whether these [Al/Fe] distributions truly represent the actual distributions in these Custers needs to be demonstrated with larger datasets., Whether these [Al/Fe] distributions truly represent the actual distributions in these clusters needs to be demonstrated with larger datasets.
 We look briely at the other elements that bad lines present in our spectra., We look briefly at the other elements that had lines present in our spectra.
 Consistent witli other clusters. calcium. au o-elemenut. is euliaucecl by ~0.25 dex relative to solar for both clusters.," Consistent with other clusters, calcium, an ${\alpha}$ -element, is enhanced by ${\sim}$ 0.25 dex relative to solar for both clusters."
 ()n the other haid. titamitum is difficult to interpret: the ueutral lines do not always agree well with the results fi'om the ionized lines.," On the other hand, titanium is difficult to interpret; the neutral lines do not always agree well with the results from the ionized lines."
 On average the ο] abundances are higher than the ueutral-Hine abundances. possibly indicating miscalculated) eravities. NLTE ellects. poor oscillator Streneths. or a coubination of any of these.," On average the $_{\rm II}$ abundances are higher than the neutral-line abundances, possibly indicating miscalculated gravities, NLTE effects, poor oscillator strengths, or a combination of any of these."
 With regarde to the eeravities. we show in Table 7 that eveu a Q.2 dex change in results in less than a 0.1 dex change in [Ti/Fe] as determined from the Ti HE lines. iudicaine that the discrepaucy from the various lites probably has some other source.," With regard to the gravities, we show in Table \ref{tab:t07}
 that even a 0.2 dex change in results in less than a 0.1 dex change in [Ti/Fe] as determined from the Ti II lines, indicating that the discrepancy from the various lines probably has some other source."
 Tie. Fe-peak elements chromium and nickel track irou with uo unusual treucls., The Fe-peak elements chromium and nickel track iron with no unusual trends.
he LV (see Figs.,the LV (see Figs.
 |. and 2))°.., \ref{Fig:LVxy} and \ref{Fig:LVxz}).
 We place the centre of the Local Void in the plane of the Galactic equator. in accordance with observations. which additionally maximizes the studied effect.," We place the centre of the Local Void in the plane of the Galactic equator, in accordance with observations, which additionally maximizes the studied effect."
 The .r and y axes of he coordinate system lie in the Galactic plane. with the origin in the centre of the LV (Fig. |».," The $x$ and $y$ axes of the coordinate system lie in the Galactic plane, with the origin in the centre of the LV (Fig. \ref{Fig:LVxy}) )."
 As the latter is situated at ἐν=307.O°. this means that our coordinate system is shifted with respect to the Galactic one and rotated by 210° in the MilkyWay plane (our 2 axis is parallel to τομ).," As the latter is situated at $l_\mathrm{LV}=30\degr$, this means that our coordinate system is shifted with respect to the Galactic one and rotated by $210\degr$ in the MilkyWay plane (our $z$ axis is parallel to $z_\mathrm{Gal}$ )."
 The part missed in all-sky surveys due to the Zone of Avoidance is a spherical section bounded by two planes (Fig. 2)):, The part missed in all-sky surveys due to the Zone of Avoidance is a spherical section bounded by two planes (Fig. \ref{Fig:LVxz}) );
 the angle between them. a. depends on the survey. but for our purposes a20 (we consider near-infrared wavelengths. as is explained hereafter).," the angle between them, $\alpha$, depends on the survey, but for our purposes $\alpha\simeq 20\degr$ (we consider near-infrared wavelengths, as is explained hereafter)."
 Owing to the smallness ofthis angle (6.20.35 rac). we treat the masked region as a thin wedge.," Owing to the smallness of this angle $\alpha\simeq0.35\,\mathrm{rad}$ ), we treat the masked region as a thin wedge."
 We additionally include a at the edge of the LV. of width AZ? ," We additionally include a at the edge of the LV, of width $\Delta R$."
According to the standard picture of void formation. where such structures are grown from initial underdensities and gradually expand. the matter expelled from inside of the void creates a layer at the edge. of density higher than the average background one.," According to the standard picture of void formation, where such structures are grown from initial underdensities and gradually expand, the matter expelled from inside of the void creates a layer at the edge, of density higher than the average background one."
 This is supported by both simulations (see e.g. vandeWeygaert&Schaap 2009)) and observations (cf., This is supported by both simulations (see e.g. \citealt{vdWSch}) ) and observations (cf.
" Fairall1998 and. references therein): voids are usually bounded by ""filaments"" and “walls” of high density contrast.", \citealt{Fairall} and references therein): voids are usually bounded by `filaments' and `walls' of high density contrast.
 In our cosmic neighbourhood. a part of such a shell is probably the Local Sheet and the Local Group is located at its inner edge (Tully 2010. private communication).," In our cosmic neighbourhood, a part of such a shell is probably the Local Sheet and the Local Group is located at its inner edge (Tully 2010, private communication)."
 A mass element cLA/ contributing to the spurious acceleration is where 2ar is the height of the wedge at a distance + from the LG and c5 is a surface element.," A mass element $\de M$ contributing to the spurious acceleration is V =S =, where $h\simeq\alpha\,r$ is the height of the wedge at a distance $r$ from the LG and $\de S$ is a surface element."
" The differential acceleration ""measured! due to random filling of theZoA will beqii. with dS=φας. q=(qcoss.qsins). Ro—(2.0) and ds the azimuthal angle."," The differential acceleration `measured' due to random filling of theZoA will be, with $\de S = q\, \de q\, \de \varphi$, $\bmath{q}=(q\cos\varphi,q\sin\varphi) $, $\bmath{R}=(R,0) $ and is the azimuthal angle."
" It is easy to check that from symmetry g,=0.", It is easy to check that from symmetry $g_y=0$.
 The .c-component of the spurious acceleration is given bynz. where limils:2xudg limilsg'due—," The $x$ -component of the spurious acceleration is given by, where _0 ^1_0."
— Thus the value of the peculiar velocity caused by the spurious acceleration is (in linear theory), Thus the value of the peculiar velocity caused by the spurious acceleration is (in linear theory).
 It is interesting to compare this value with the one induced by a sphere of radius /? and density pi., It is interesting to compare this value with the one induced by a sphere of radius $R$ and density $\rho_\mathrm{b}$.
 The peculiar acceleration at the the is spherethen.g.= srk. which gives the linear peculiar surfieo.ofvelocity of ing.," The peculiar acceleration at the surface of the sphere is then $g_\bullet=\frac{4}{3}\pi G \rho_\mathrm{b} R$ , which gives the linear peculiar velocity of ."
 We thus have, We thus have .
 The above calculation applied to an isolated void without any, The above calculation applied to an isolated void without any
Although the determination of the fundamental paranietors of Rit Lyrae (RR) stars is interesting in itself. it) is also important [rom a practical point of view because RR stars plav a considerable role in establishing Calactic ancl extragalactic distance scales.,"Although the determination of the fundamental parameters of RR Lyrae (RR) stars is interesting in itself, it is also important from a practical point of view because RR stars play a considerable role in establishing Galactic and extragalactic distance scales."
 The Preston index and spectroscopic observations are used το determine their atmospheric metallicity AZ] and. interstellar reddening E(DV)., The Preston index and spectroscopic observations are used to determine their atmospheric metallicity $[M]$ and interstellar reddening $E(B-V)$.
 Since confirmed. RR-type components are not known in binary svstemis. the mass determination is based on both stellar evolution and pulsation theories.," Since confirmed RR-type components are not known in binary systems, the mass determination is based on both stellar evolution and pulsation theories."
 Due to the uncertainty of parallax data. the Baacle-Wesselink (BW) method. is mostly usec to infer their distance d. 1995)..," Due to the uncertainty of parallax data, the Baade-Wesselink (BW) method is mostly used to infer their distance $d$ \citep{smit1}."
 In the BW analysis. and to determine. M] and E(B V. the quasi-static atmosphere approximation (QSAA) is emploved to interpret photometry ancl spectroscopy.," In the BW analysis, and to determine $[M]$ and $E(B-V)$ , the quasi-static atmosphere approximation (QSAA) is employed to interpret photometry and spectroscopy."
" The QSAA was. introduced. by Ledoux& \Whit- (LOGO): ""phe simplest approach is to assume that at each phase. the atmosphere adjusts. itself practically. instantancously to the radiative. flux. coming from. the interior and to the elfective gravity. ος where #2.and# ore the instantaneous values of the radius and acceleration. which is supposed uniform throughout the/ atmosphere’. € is the Newtonian eravitational constant. Vf is the stellar mass and clot is a differentiation with respect to time £."," The QSAA was introduced by \citet{ledo1}: `The simplest approach is to assume that at each phase, the atmosphere adjusts itself practically instantaneously to the radiative flux coming from the interior and to the effective gravity $g_{\rm e}$ where $R,\: \mbox{and}\: {\ddot R}$ are the instantaneous values of the radius and acceleration, which is supposed uniform throughout the atmosphere', $G$ is the Newtonian gravitational constant, ${\cal M}$ is the stellar mass and dot is a differentiation with respect to time $t$."
" ""One may then build a series of static model atmospheres.” and select one of them at each phase by spectroscopic or photometric observations."," `One may then build a series of static model atmospheres,' and select one of them at each phase by spectroscopic or photometric observations."
 ts lux. colours. effective temperature 7; and surface gravity ge ave accepted as the atmospheric parameters of that phase providing a basis for the determination of other parameters such as angular radius. mass. distance. etc.," Its flux, colours, effective temperature $T_{\rm e}$ and surface gravity $g_{\rm e}$ are accepted as the atmospheric parameters of that phase providing a basis for the determination of other parameters such as angular radius, mass, distance, etc."
 The subject of the this paper is the QSAA and its generalization to a non-uniform atmosphere., The subject of the this paper is the QSAA and its generalization to a non-uniform atmosphere.
 We will investigate the QSAA from the point of view of atmospheric emerecnt flux. and. hydrodynamics., We will investigate the QSAA from the point of view of atmospheric emergent flux and hydrodynamics.
 By comparing the observed. colour indices with those of static moclel atmospheres (Castelli.Gratton&Ixurucz.1997... Ixurucz 19972) we select the phases when they coincide.," By comparing the observed colour indices with those of static model atmospheres \citealt{cast1}, \citealt{kuru1}) ) we select the phases when they coincide."
 Considering hivelrodyvnamics. we do not construct a consistent. civnanic model of an Itt atmosphere.," Considering hydrodynamics, we do not construct a consistent dynamic model of an RR atmosphere."
 However. we find a better description of the pulsating atmosphere if we characterize it by pressure anc density stratifications in addition to the iwo parameters A? and. 2.," However, we find a better description of the pulsating atmosphere if we characterize it by pressure and density stratifications in addition to the two parameters $R$ and ${\ddot R}$."
 We determine the fundamental parameters t and d from the hydrodynamic considerations without using the BW method. or. theories of. stellar evolution and pulsation at all., We determine the fundamental parameters ${\cal M}$ and $d$ from the hydrodynamic considerations without using the BW method or theories of stellar evolution and pulsation at all.
 Our method uses photometry as observational input: spectroscopy. ancl radial velocity observations are not. needed., Our method uses photometry as observational input; spectroscopy and radial velocity observations are not needed.
 Quasars at hieh redshift are excellent tools to investisate the formation of galaxies and supermassive black holes in the carly universe. and to probe the physical state of their galactic euvironmenut up to carly cosmic epochs.," Quasars at high redshift are excellent tools to investigate the formation of galaxies and supermassive black holes in the early universe, and to probe the physical state of their galactic environment up to early cosmic epochs."
 Iu receut vears there ds erowing evidence that quasar activity and the formation of their host galaxies. in particular of massive spheroidal svstcms. are closely related.," In recent years there is growing evidence that quasar activity and the formation of their host galaxies, in particular of massive spheroidal systems, are closely related."
 The presence of dark massive objects (DAIOs) in the center of uearly every galaxw with a sienificant spheroidal component supports models that connect the formation and evolution of ealaxies with quasar activity., The presence of dark massive objects (DMOs) in the center of nearly every galaxy with a significant spheroidal component supports models that connect the formation and evolution of galaxies with quasar activity.
 It has been shown that the mass of the DMOs. ecnerally regarded as supermassive black holes. is closely correlated with the spheroidal mass of the host-galaxy (e.g. Isormendy Richstone 1995: Magorriau et al.11998: Richstone et 11998: Gebhardt et 22000: Mexritt Ferrarese 2001: Tremaine et 22002).," It has been shown that the mass of the DMOs, generally regarded as super-massive black holes, is closely correlated with the spheroidal mass of the host-galaxy (e.g., Kormendy Richstone 1995; Magorrian et 1998; Richstone et 1998; Gebhardt et 2000; Merritt Ferrarese 2001; Tremaine et 2002)."
 Iu the contest of galaxw evolution. the conditious that eive rise tfo quasars and massive black holes will also vield solar or super-solar ποιαποιος on time scales shorter than ~ [Gyr (Arimoto Yoshii 1987: IEuuaun Ferland 1993: Cuedin Ostriker 1997: Friacaa Terlevich 1998: Con Ostriker 1999: Romano et 22002).," In the context of galaxy evolution, the conditions that give rise to quasars and massive black holes will also yield solar or super-solar metallicities on time scales shorter than $\sim 1$ Gyr (Arimoto Yoshii 1987; Hamann Ferland 1993; Gnedin Ostriker 1997; Friaçaa Terlevich 1998; Cen Ostriker 1999; Romano et 2002)."
 Additional strong evidence for the relationship between quasar activity. lost galaxy formation. and inteuse star formation episodes is provided by the detection of huge amounts of dust (~—105 NINE.) and molecular pas (~1059 NINE.) measured in high redshift quasars (Andreani. LaFFranca. Cristiani 1993: Isaals 1199: Omout et 22001: Carilli et 22001).," Additional strong evidence for the relationship between quasar activity, host galaxy formation, and intense star formation episodes is provided by the detection of large amounts of dust $\sim 10^8$ $_\odot$ ) and molecular gas $\sim 10^{10}$ $_\odot$ ) measured in high redshift quasars (Andreani, Franca, Cristiani 1993; Isaak et 1994; Omont et 2001; Carilli et 2001)."
 The coanoviug uuuber density of quasars and the cosmic star formation rate are both at leas ie order of magnitude larger for epochs with +2X1 than in the local wuiiverse (e.g. Callego et 11995: Lilly et 11996: Connolly et al.11997: Tresse Maddox 1998: Steidel et .11999: Lauzetta et 22002).," The co-moving number density of quasars and the cosmic star formation rate are both at least one order of magnitude larger for epochs with $z\ga 1$ than in the local universe (e.g., Gallego et 1995; Lilly et 1996; Connolly et 1997; Tresse Maddox 1998; Steidel et 1999; Lanzetta et 2002)."
 The evolution of —ie space densities of quasars aud galaxies with starburst activity are also very simular., The evolution of the space densities of quasars and galaxies with starburst activity are also very similar.
 Finally. there may be a relation between the bhuuinositv functions of normal galaxies and quasars (6.8.. Dickinson 1998: Pettini et 11998: Dovle Terlevich 1905).," Finally, there may be a relation between the luminosity functions of normal galaxies and quasars (e.g., Dickinson 1998; Pettini et 1998; Boyle Terlevich 1998)."
 Quasars at hieh vedshitt are therefore of interest as Valuable probes to date the beginning of the first star formation episodes in the carly universe (αιμα Ferland 11999: Dietrich oet 11999.22000)., Quasars at high redshift are therefore of interest as valuable probes to date the beginning of the first star formation episodes in the early universe (Hamann Ferland 1999; Dietrich et 2000).
 Currently. about 350 quasars with redshifts 2.=1 are known (e.g. Schneider et bb: Storrie-Lonibixdi et 11996: Andersou et 22001: Djorgovski 2002). and several quasars with :25 and even 2>6 have been recently discovered (Fan et 22001: Stern ct 22000: Zheng et 22000: Sharp ct 22001: Decker ct 22001).," Currently, about 350 quasars with redshifts $z \geq 4$ are known (e.g., Schneider et b; Storrie-Lombardi et 1996; Anderson et 2001; Djorgovski 2002), and several quasars with $z \ga 5$ and even $z > 6$ have been recently discovered (Fan et 2001; Stern et 2000; Zheng et 2000; Sharp et 2001; Becker et 2001)."
" The redshift range :ZL| correspouds to an epoch when the universe was less than ~10 (IL,=65 ! Mpe1. Qyy=0.3. Q4=0.7: Carroll. Press. Turner 1992)."," The redshift range $z \ga 4$ corresponds to an epoch when the universe was less than $\sim 10$ $_o = 65$ $^{-1}$ $^{-1}$, $\Omega _M = 0.3$, $\Omega _\Lambda = 0.7$; Carroll, Press, Turner 1992)."
 The chemical composition of the gas associated with quasars can be estimated using the broad cluission lines in the ultraviolet spectral rauge (for a review. sce Wamanun Ferland 1999).," The chemical composition of the gas associated with quasars can be estimated using the broad emission lines in the ultraviolet spectral range (for a review, see Hamann Ferland 1999)."
to observe true nanolensing caustic crossings. we use light curves from the map of width 0.2 Eh. created with small objects of 2.510 M...,"to observe true nanolensing caustic crossings, we use light curves from the map of width 0.2 ER, created with small objects of $2.5\times 10^{-5}$ $_\odot$."
 We use two source sizes. an aeeretion disk. of 0.002 IER. and the smallest. source size used previously: 0.0001 LEAR.," We use two source sizes, an accretion disk of 0.002 ER, and the smallest source size used previously: 0.0001 ER."
 Light curves are cut horizontally across the map and a representative segment. extracted. showing nanolensing events due to nanolensine caustics.," Light curves are cut horizontally across the map and a representative segment extracted, showing nanolensing events due to nanolensing caustics."
 These are in Figure 9.. where the top row is for image M. the bottom for image S: the left column is the source of 0.002 ER. the right column is 0.0001 Eh.," These are in Figure \ref{cadence}, where the top row is for image M, the bottom for image S; the left column is the source of 0.002 ER, the right column is 0.0001 ER."
 Phe time span is 1. vear in. the left⋅ column. and 4 weeks in. the right. column.," The time span is 1 year in the left column, and 4 weeks in the right column."
 qsThe light. curves are sampled at 14 davs (left column) and 2 days (right column) which we suggest is the longest sampling time that will accurately reconstruct these light curves., The light curves are sampled at 14 days (left column) and 2 days (right column) which we suggest is the longest sampling time that will accurately reconstruct these light curves.
 Only the right column shows true (albeit smoothed) nanolensing caustic crossings — the left column does not., Only the right column shows true (albeit smoothed) nanolensing caustic crossings – the left column does not.
 In the left column. nanolensing caustics have been smoothed. and combined.," In the left column, nanolensing caustics have been smoothed and combined."
 Therefore the source of 0.002 ER is still too large to truly resolve the nanolensing caustics a size of order 0.0001 El is needed., Therefore the source of 0.002 ER is still too large to truly resolve the nanolensing caustics – a size of order 0.0001 ER is needed.
" At Sl4 nm (271a- nm in. the rest. frame).⋅ the predicted. flux size of the aceretion disk in MO 0414|0534 is0.002 Eh = 2.10"" em (Alosquera&Ixochanek 2011).."," At 814 nm (271 nm in the rest frame), the predicted flux size of the accretion disk in MG 0414+0534 is0.002 ER = $\times 10^{14}$ cm \citep{mosquera2011}. ."
 We assume, We assume
Tn Figue 1 owe show (from top to bottom) the WILC map. the best-&t Dianchi iiodoel. aud the ditference between the two.,"In Figure \ref{fig:maps} we show (from top to bottom) the WILC map, the best-fit Bianchi model, and the difference between the two."
 It should be apparent that the “Bianchi corrected” imap exhibits ereater isotropy than the WILC data., It should be apparent that the “Bianchi corrected” map exhibits greater isotropy than the WILC data.
 In Figure 2 we compare the power spectra of the original and the Biauchi-corrected V|W linear combination(Llinshaw €«100. (ITivonctal.2002) (215. Tausenetal.(200la) o the northern hemisphere data (defined iu the reference παλιο Which maximises the power asvuumetry) which avours a lower value for 7.aimplitude:, In Figure \ref{fig:spectrum} we compare the power spectra of the original and the Bianchi-corrected V+W linear combination $\ell < 100$ \citep{hivon:2002} $\ell > 15$ \citet{hansen:2004a} to the northern hemisphere data (defined in the reference frame which maximises the power asymmetry) which favours a lower value for $\tau$.:
: The team sugecstCoco that the quadrupole amplitude is significautly low. although other analyses have found it to be quite acceptable (Slosar Seljak 2001; O'Dwyer oet al.," The team suggest that the quadrupole amplitude is significantly low, although other analyses have found it to be quite acceptable (Slosar Seljak 2004; O'Dwyer et al."
 2001)., 2004).
 As seen in Fiewe 2.. the Biauchi-correcte« VIW aap has a quadrupole amplitue of SOLμι”. compared to the uncorrected amplitude of 137ps7 and the theoretical best-fit spectrum value of 869μι”.," As seen in Figure \ref{fig:spectrum}, the Bianchi-corrected V+W map has a quadrupole amplitude of $504\,\mu\textrm{K}^2$, compared to the uncorrected amplitude of $137\,\mu\textrm{K}^2$ and the theoretical best-fit spectrum value of $869\,\mu\textrm{K}^2$."
 Tu this context. the quadrupole auplitude should no longer be considered anomalous.," In this context, the quadrupole amplitude should no longer be considered anomalous."
 Whether the amplitude euhaucenieut itself requires an unmsua cancelation between the intrinsic aud Bianchiiuduce quadrupoles. which could also be considered a tuningof the model. is deferred to a later analysis4. ," Whether the amplitude enhancement itself requires an unusual cancelation between the intrinsic and Bianchi–induced quadrupoles, which could also be considered a fine-tuning'of the model, is deferred to a later analysis. :"
An alignment between the quadrupole and the octopole has been claimed by deOliveira-Costaetal.(2001). and Copictal.(200L)., An alignment between the quadrupole and the octopole has been claimed by \citet{de Oliveira-Costa:2004} and \citet{copi:2004}.
. Quantitative caleulatious similar to those of deOliveira-Costaetal.(2001). and. Exiksenetal.(20015). slow that a strouger planarity is expected by chance with a probability of for both the (2 aud 3 modes after subtracting the Bianchi template.," Quantitative calculations similar to those of \citet{de
Oliveira-Costa:2004} and \citet{eriksen:2004b} show that a stronger planarity is expected by chance with a probability of for both the $\ell=2$ and 3 modes after subtracting the Bianchi template."
" The angle between the preferred directions of the (=2 aud 3 modes is 70"" after subtracting the Bianchi template. compared to 127 before."," The angle between the preferred directions of the $\ell=2$ and 3 modes is $70\degr$ after subtracting the Bianchi template, compared to $12\degr$ before."
 Adcitionally the (=5 and 6 modes (Exrikseu et al.," Additionally, the $\ell=5$ and 6 modes (Eriksen et al."
 200Lb) become less anomalous. with significances dropping to 1.50 in both cases.a," 2004b) become less anomalous, with significances dropping to $1.5\sigma$ in both cases.:"
symunetry:: Eriksenotal.(2001a) reported that the large-scale power (6= 10) in the data isanisotropicallydistributed over two opposing hemispheres. with a significance of 36 conrpared with simulations.," \citet{eriksen:2004a} reported that the large-scale power $\ell \lesssim 40$ ) in the data isanisotropicallydistributed over two opposing hemispheres, with a significance of $3\sigma$ compared with simulations."
 Repeating the analysisaudadoptingthe Np2 «ky coverage. we compare the corrected," Repeating the analysisandadoptingthe Kp2 sky coverage, we compare the corrected"
is difficult to identify with visual inspection alone.,is difficult to identify with visual inspection alone.
 Images affected in this way were detected and removed by the facto calibration procedure (see §8.4))., Images affected in this way were detected and removed by the post-facto calibration procedure (see $\S$ \ref{sec:post_facto_calibration}) ).
 The standard MOST image reduction pipeline assumes default values for calibration parameters if none are supplied., The standard MOST image reduction pipeline assumes default values for calibration parameters if none are supplied.
" Inspection of image headers revealed that over 600 images had been reduced with default calibration values, rather than the measured values."," Inspection of image headers revealed that over 600 images had been reduced with default calibration values, rather than the measured values."
 We were able to re-reduce these images with the same calibration measurements used to produce the results of ?.., We were able to re-reduce these images with the same calibration measurements used to produce the results of \citet{gaensler2000most}.
" In spite of this effort, we found large variations in the flux density scale on some occasions, which we attribute to the variable calibrators, wrongly applied calibration and interference during calibrator observations."," In spite of this effort, we found large variations in the flux density scale on some occasions, which we attribute to the variable calibrators, wrongly applied calibration and interference during calibrator observations."
" Rather than discarding images that appeared good apart from flux density scale, we included them in our analysis and calibrated with the post-facto calibration procedure (see Ga)."," Rather than discarding images that appeared good apart from flux density scale, we included them in our analysis and calibrated with the post-facto calibration procedure (see $\S$ \ref{sec:post_facto_calibration}) )."
 , 
"]t is well known that the acoustic power computed from solar intensitverams is less stronger than that computed from Dopplergrams, thus time-distance measurements from intensitygrams are noisier (c.g..Sekietal.2001).","It is well known that the acoustic power computed from solar intensitygrams is less stronger than that computed from Dopplergrams, thus time-distance measurements from intensitygrams are noisier \citep[e.g.,][]{sek01}."
". However, although the travel time maps computed from the intensitygrams are noisier for short distances (small annuli), the signatures of active regions and supergranulations are still clear, and such measurements are sufficiently good to perform the analysis similar to Section 2.1. in order to evaluate travel time variations with the azimuthal angle inside the sunspot penumbra."," However, although the travel time maps computed from the intensitygrams are noisier for short distances (small annuli), the signatures of active regions and supergranulations are still clear, and such measurements are sufficiently good to perform the analysis similar to Section \ref{sec2p1} in order to evaluate travel time variations with the azimuthal angle inside the sunspot penumbra."
 Figure 3 shows the measurement results., Figure \ref{fg3} shows the measurement results.
" The averages of the mean travel times inside the sunspot penumbra measured trom the two datasets are different, so that the travel time measured from the continuum intensitygrams about 0.5 minutes longer than that the corresponding travel times from the Dopplergrams."," The averages of the mean travel times inside the sunspot penumbra measured from the two datasets are different, so that the travel time measured from the continuum intensitygrams about 0.5 minutes longer than that the corresponding travel times from the Dopplergrams."
" This is probably caused by the different acoustic power distributions in the /:—& diagrams of these two kinds of observations, which is well known in helioseismology."," This is probably caused by the different acoustic power distributions in the $k-\omega$ diagrams of these two kinds of observations, which is well known in helioseismology."
" For example, the ratios of acoustic powers in higher frequency and lower frequency are different, and power spectra from Dopplergrams and intensitygrams display different line asymmetries"," For example, the ratios of acoustic powers in higher frequency and lower frequency are different, and power spectra from Dopplergrams and intensitygrams display different line asymmetries"
of LO! I was imposed.,of $10^4$ K was imposed.
 We plot vertical profiles of density and. for the runs with cooling. teniperature. at a point 20° downstream of the stream impact poiut just interior to the disk ria.," We plot vertical profiles of density and, for the runs with cooling, temperature, at a point $^\circ$ downstream of the stream impact point just interior to the disk rim."
 The density profiles show that the low density wake belind the overflowing stream persists in all three runs., The density profiles show that the low density wake behind the overflowing stream persists in all three runs.
 Iu the ruus incorporating cooling the density at high + can be two to three orders of magnitude higher than for the isothermal case — this is a consequence of the overspill of disk gasabove the stream mentioned earlier., In the runs incorporating cooling the density at high $z$ can be two to three orders of magnitude higher than for the isothermal case – this is a consequence of the overspill of disk gas the stream mentioned earlier.
 The absolute density though is very low in all cases., The absolute density though is very low in all cases.
 Wiel temperatures of 10° IS and above are seeu in a laver above the disk surface. this is material that has been shock heated by tle interaction with the stream and which has passed beneath the overflowing gas.," High temperatures of $10^5$ K and above are seen in a layer above the disk surface, this is material that has been shock heated by the interaction with the stream and which has passed beneath the overflowing gas."
 This feature is not adequately resolved in these simulations., This feature is not adequately resolved in these simulations.
 Fig., Fig.
 6 sunmniarizes the results for a simulation with au adiabatic equation of state aud no radiative cooling., 6 summarizes the results for a simulation with an adiabatic equation of state and no radiative cooling.
 The grid was again 1287.lO cells. and ΠΠ.Πα=2.," The grid was again $128^2 \times 40$ cells, and $H_{\rm s} / H_{\rm d} = 2$."
 The reaming initial conditions were as for the isothermal anc radiative cooling runs. except that the stream injection point was moved slightly further from the c=0 boundary in order to reduce effects arising from the fuite volume of the computational box.," The remaining initial conditions were as for the isothermal and radiative cooling runs, except that the stream injection point was moved slightly further from the $x=0$ boundary in order to reduce effects arising from the finite volume of the computational box."
 Qualitatively. the distinction from the isotherma calculations is that in this simulation the hot shock-heatc« eas expands in all directions and disrupts the cobhereu overflowiue stream seen previously.," Qualitatively, the distinction from the isothermal calculations is that in this simulation the hot shock-heated gas expands in all directions and disrupts the coherent overflowing stream seen previously."
 In the disk midplauc. ‘splashing of hot material dowustreamn of the mipac point is evident. though the velocities of this eas are substantially less than those of the disk.," In the disk midplane, `splashing' of hot material downstream of the impact point is evident, though the velocities of this gas are substantially less than those of the disk."
" Αι=322, there is overflow in a broad fan over the disk surface.", At $z=3 H_{\rm d}$ there is overflow in a broad fan over the disk surface.
" Most of this material appears to be stream gas that has suffered a strong deflection upon reaching the disk οσο, though au exanuuation of the velocity field also shows disk materia at hieh + that is being deflected iuwurds as a result of the stream interaction."," Most of this material appears to be stream gas that has suffered a strong deflection upon reaching the disk edge, though an examination of the velocity field also shows disk material at high $z$ that is being deflected inwards as a result of the stream interaction."
 A slice alone the initial stream flow direction now resolves clearly the shocks in the stream ando disk eas., A slice along the initial stream flow direction now resolves clearly the shocks in the stream and disk gas.
 The overflowing component has a velocity that is predominantly inthe. y plane. with a small (a few times es) vertical component.," The overflowing component has a velocity that is predominantly in the $x-y$ plane, with a small (a few times $c_s$ ) vertical component."
 Further from the disk midplane sienificant vertical velocity away from the diskis seen. sugecsting that with this equation of state a substantially ercater absorption coluun will be generated for Hues-of-sight well away from the disk plane.," Further from the disk midplane significant vertical velocity away from the disk seen, suggesting that with this equation of state a substantially greater absorption column will be generated for lines-of-sight well away from the disk plane."
 As shown later. the actual fraction of the stream overflowing the disk rim is comparable to that in the isothermal case. but the structure of the flow is here very clistiuct.," As shown later, the actual fraction of the stream overflowing the disk rim is comparable to that in the isothermal case, but the structure of the flow is here very distinct."
 The ZEUS simulations discussed in this paper sugecst a picture in which efficient radiative cooling leads to a coherent stream overflowing the disk iu a manucr verv stuuilar to that deserbed by Lubow (1989)., The ZEUS simulations discussed in this paper suggest a picture in which efficient radiative cooling leads to a coherent stream overflowing the disk in a manner very similar to that described by Lubow (1989).
" Conversely. if cooling is imeffücieunt. there is a plashius of stream material off the disk οσο,"," Conversely, if cooling is inefficient, there is a `splashing' of stream material off the disk edge."
 Similar quautities of material can flow nmsvard iu this regine. but there is no coliercut stream and gas is also thrown outwards aud upwards.," Similar quantities of material can flow inward in this regime, but there is no coherent stream and gas is also thrown outwards and upwards."
 Iu order to examine the qualitative differences in global effects between the isothermal and inefficient cooling cases. we performed two threc-dimensional smooth particle livdrodyuauies (SPIT) calculations.," In order to examine the qualitative differences in global effects between the isothermal and inefficient cooling cases, we performed two three-dimensional smooth particle hydrodynamics (SPH) calculations."
 The results are shown in Fie., The results are shown in Fig.
 7., 7.
 These caleulatious have vastly lower resolution of the impact region than the ZEUS simulations. but cover the whole disk and have been evolved for long enough (10 binary orbits) to allow the disk to relax iu the binary potential.," These calculations have vastly lower resolution of the impact region than the ZEUS simulations, but cover the whole disk and have been evolved for long enough $\sim 10$ binary orbits) to allow the disk to relax in the binary potential."
 We show au isothermal calculation (similar to that described in Armitage Livio 1996). and a calculation with a polvtropic equation of state (>=1.1) and system parameters appropriate to the supersoft source CALST (Callanau Charles 1989: Could 1995).," We show an isothermal calculation (similar to that described in Armitage Livio 1996), and a calculation with a polytropic equation of state $\gamma = 1.1$ ) and system parameters appropriate to the supersoft source CAL87 (Callanan Charles 1989; Gould 1995)."
 Similar features are evident in the SPI calculations as in the fuite difference simulations., Similar features are evident in the SPH calculations as in the finite difference simulations.
 The isothermal run shows a narrow overflowing stream. while the polvtropic calculation leads to a 10nch more vertically extended spray of material and a bulee of outflowing eas ucar the impact point.," The isothermal run shows a narrow overflowing stream, while the polytropic calculation leads to a much more vertically extended spray of material and a bulge of outflowing gas near the impact point."
 Negligible masses of material escape the accreting stirs Roche lobe in either simulation., Negligible masses of material escape the accreting star's Roche lobe in either simulation.
 Although the choice ofa value for 5 insuch a calculation is essentially arbitrary. it is clear from Figure 7 that the trend is such that svstenis where cooling is inefiicicut should display absorption at much higher clevations above the disk plane than those well described by au isothermal equation of state.," Although the choice of a value for $\gamma$ in such a calculation is essentially arbitrary, it is clear from Figure 7 that the trend is such that systems where cooling is inefficient should display absorption at much higher elevations above the disk plane than those well described by an isothermal equation of state."
 To quantify the deeree of stream overflow in the siuulatiouns. we compute the integrated radial mass flux through vertical «2 slices which has a radial velocity CR5Cor ," To quantify the degree of stream overflow in the simulations, we compute the integrated radial mass flux through vertical $x-z$ slices which has a radial velocity $v_R \ge v_{\rm cut}$."
"For Carc220, the initial inflow velocity of the stream gas at the eril boundary — this quautity is conserved in the absence of interaction with the disk."," For $v_{\rm cut} <
22 c_s$ – the initial inflow velocity of the stream gas at the grid boundary – this quantity is conserved in the absence of interaction with the disk."
 Fig., Fig.
 δ shows the radial mass flux as a function of AR Gvhere the Π for cache + slice is evaluated along the line of the initial stream flow direction). for a variety of threshold radial velocities.," 8 shows the radial mass flux as a function of $R / R_{\rm out}$ (where the $R$ for each $x-z$ slice is evaluated along the line of the initial stream flow direction), for a variety of threshold radial velocities."
 Outside the outer edge of the disk. all the curves coimcide and are flat. reflecting steady-state undisturbed stream flow.," Outside the outer edge of the disk, all the curves coincide and are flat, reflecting steady-state undisturbed stream flow."
" For the ruus with au isothermal or cooling equation of state. the amount of material flowing wird at the fastest velocity. z20e¢,. drops sharply as the disk ria is reached. and the central portions of the eas stream are stopped by he denser disk gas."," For the runs with an isothermal or cooling equation of state, the amount of material flowing inward at the fastest velocity, $\ge 20 c_s$, drops sharply as the disk rim is reached, and the central portions of the gas stream are stopped by the denser disk gas."
 In this case. aud as noted previously. he main interaction occurs close to the disk rim. after which the highest velocity curve remains fairly flat at a ower level than initially.," In this case, and as noted previously, the main interaction occurs close to the disk rim, after which the highest velocity curve remains fairly flat at a lower level than initially."
 This mass fiux is comprised of uaterial that has overflowed the disk at large enough + to avoid strong interaction with the disk., This mass flux is comprised of material that has overflowed the disk at large enough $z$ to avoid strong interaction with the disk.
 For the illustrated case with 1Πα=2. this is around of the stream nlass transfer rate.," For the illustrated case with $H_{\rm s} / H_{\rm d} = 2$, this is around of the stream mass transfer rate."
 From the Figure. it is evident that a significautlv arecry quantity of mmass flows νάνο at velocities that are sanaller than the ballistic stream velocity. but still highly supersonic.," From the Figure, it is evident that a significantly larger quantity of mass flows inward at velocities that are smaller than the ballistic stream velocity, but still highly supersonic."
 This is either stream material slowed by strong interaction with the disk. or disk eas eutrained by the overflowing stream.," This is either stream material slowed by strong interaction with the disk, or disk gas entrained by the overflowing stream."
 For the case shown in Fig., For the case shown in Fig.
" 8. a radial lnass flux of around of the initial stream. uass transter rate is flowing inward with eg>Se, at the inrermmost boundary of the sinmlatiou voluue. at ~0.6R,a "," 8, a radial mass flux of around of the initial stream mass transfer rate is flowing inward with $v_R \ge 5 c_s$ at the innermost boundary of the simulation volume, at $\sim 0.6 \ R_{\rm out}$."
We analyze the observational signatures of this maerial more fully in the following Section., We analyze the observational signatures of this material more fully in the following Section.
 We also note that close to the rim. the total mass of gas flowing mud supersonically exceeds the stream," We also note that close to the rim, the total mass of gas flowing inward supersonically exceeds the stream"
 We also note that close to the rim. the total mass of gas flowing mud supersonically exceeds the streams," We also note that close to the rim, the total mass of gas flowing inward supersonically exceeds the stream"
aas eiven in reftabome are more accurate than previously published positions. and may be used to search for optical counterparts.,"as given in \\ref{tabomc} are more accurate than previously published positions, and may be used to search for optical counterparts."
 We lave done this among the variables (contact binaries. detached binaries. and suspected RS οδα stars) found ince bby Kaluzux et ((1996. 1997): no counterpart is alone these stars. (," We have done this among the variables (contact binaries, detached binaries, and suspected RS CVn stars) found in by Kaluzny et (1996, 1997): no counterpart is among these stars. ("
Onlv one of these variables is in the area shown in rofüeonic.. tthe contact binary 113.),"Only one of these variables is in the area shown in \\ref{figomc}, the contact binary 13.)"
 Our nou-detection of these biuaries is uot surprising. considering that our detection uit is above 1tyueres: all of the contact binaries hitherto detected in X- (AIcCGale et 11996). aud many RS οδα svstenis (Deipsev ct 11993) are less luminous than this.," Our non-detection of these binaries is not surprising, considering that our detection limit is above $10^{31}$: all of the contact binaries hitherto detected in X-rays (McGale et 1996), and many RS CVn systems (Dempsey et 1993) are less luminous than this."
 Cool et ((1995a) argue that N77/B is au extended source., Cool et (1995a) argue that 7/B is an extended source.
 This source is detected im the ROSAT PSPC observation (Johustou et 11991) and in the ROSAT IIRI observations of 1991. 1995 Jauuary aud July. aud 1996.," This source is detected in the ROSAT PSPC observation (Johnston et 1994) and in the ROSAT HRI observations of 1994, 1995 January and July, and 1996."
 All ofthese observations are nore sensitive than the 1992 and 1993 observatious used by Cool et al. (, All of these observations are more sensitive than the 1992 and 1993 observations used by Cool et al. (
"19952): in all of thems 77/D is compatible with beiug a point ποιος,",1995a); in all of them 7/B is compatible with being a point source.
 With the identification of sources N33 and Xl with foreground stars. we cau reiuvestieate the suggested identification of 55/E with a foreground [E star. as sugeestedee w Margou BBolte (1987).," With the identification of sources 3 and 4 with foreground stars, we can reinvestigate the suggested identification of 5/E with a foreground K star, as suggested by Margon Bolte (1987)."
 We use the optical positions of A aud D to determine the offset between the N-rav positions of the PSPC observation as listed in Joluston et al. (, We use the optical positions of A and D to determine the offset between the X-ray positions of the PSPC observation as listed in Johnston et al. (
1991) aud the optical positions.,1994) and the optical positions.
 We then apply this offset to the position of N55. and find that the resulting position is a G5 arcsecouds from the optical star.," We then apply this offset to the position of 5, and find that the resulting position is at $\pm$ 5 arcseconds from the optical star."
 We take the position of the optical star reftabome)) frou 00375-18331783 CMonet e 11998)., We take the position of the optical star \\ref{tabomc}) ) from 0375-18334783 (Monet et 1998).
 Identification of N55 with the foreground star is therefore a distinct possibility., Identification of 5 with the foreground star is therefore a distinct possibility.
 66397 is à nearby cluster. with a collapsed core. iu or close to which Cool et ((1993) detected. with a ROSAT URI observation.," 6397 is a nearby cluster, with a collapsed core, in or close to which Cool et (1993) detected with a ROSAT HRI observation."
 Photometiv with the Dubble Space Telescope enabled Cool et ((1995b) to find cight candidate counterparts for these sources. on the basis of high ultraviolet flux or of IIo enmusson.," Photometry with the Hubble Space Telescope enabled Cool et (1995b) to find eight candidate counterparts for these sources, on the basis of high ultraviolet flux or of $\alpha$ emission."
 The Ta cussion of three stars has been confirmed spectroscopically by Caiudlay ct ((1995) who argue that these stars are cataclvsuie variables. and responsible for the N-ray cinission close to the core.," The $\alpha$ emission of three stars has been confirmed spectroscopically by Grindlay et (1995) who argue that these stars are cataclysmic variables, and responsible for the X-ray emission close to the core."
 We analyse first the ongest observation. obtained im 1995. ancl use this as a reference for our discussion of the earlier. shorter observatious.," We analyse first the longest observation, obtained in 1995, and use this as a reference for our discussion of the earlier, shorter observations."
" The standard analysis provides 11 sources, listed in roeftaba.."," The standard analysis provides 14 sources, listed in \\ref{taba}."
 Identifications with carlicr XN-raw sources or optical objects are indicated: 7 sources are new., Identifications with earlier X-ray sources or optical objects are indicated; 7 sources are new.
 X66 has been ilenutifie bv Cool et (1993) as 2211911., 6 has been identified by Cool et (1993) as 244944.
 This star ds identical to1G0177.. aud is in the Ilpparcos Catalogue as IIP556569.," This star is identical to, and is in the Hipparcos Catalogue as 86569."
 Its position and proper motion are lus very accurately know. aud we use it to deteriune the bore sight correction.," Its position and proper motion are thus very accurately known, and we use it to determine the bore sight correction."
 This bore seht correction is given in rofta.. and is applied to the N-ray positions: the resulting positions are given in roftaba..," This bore sight correction is given in \\ref{ta}, and is applied to the X-ray positions; the resulting positions are given in \\ref{taba}."
" The statistical uuncertaimtv in the X-ray position of X66 is about (0.57: we therefore estimate that systematic error of the A-ray positions listed in reftaba is better than 1"": this error should be added in quadrature to the statistical error for each individual source position.", The statistical uncertainty in the X-ray position of 6 is about $''$; we therefore estimate that systematic error of the X-ray positions listed in \\ref{taba} is better than $''$; this error should be added in quadrature to the statistical error for each individual source position.
 The quasar identified by Cool et ((1993) with X55 coiucides within the error with our position for X55., The quasar identified by Cool et (1993) with 5 coincides within the error with our position for 5.
" Iowever. the active galaxy. identified bv Cool et ((1993) with X22 is 10"" from our N-ray position. mainly in right ascension: aud we conchide that it is not the N-ray source."," However, the active galaxy identified by Cool et (1993) with 2 is $''$ from our X-ray position, mainly in right ascension; and we conclude that it is not the X-ray source."
 The explanation probably lies in the new scale for the size of the IIRI pixel that we use (see 22). which moclifies positions of sources at large distance from the center of the ITRI image.," The explanation probably lies in the new scale for the size of the HRI pixel that we use (see 2), which modifies positions of sources at large distance from the center of the HRI image."
 The flux. detection luit 1 alout Oa« outside the blended ceutral region. shuilar to that obtained for Cen.," The flux detection limit is about $0.8\times10^{-14}\,\ergcms$ outside the blended central region, similar to that obtained for ."
" Analogous to our arguinent for«ο, we find that all objects detected within 0/5 are probably cluster ποος, whereas we expect L.1 background sources within 3’frou the center of of 66397: the sources at 0/5<r<3 therefore nav be background sources."," Analogous to our argument for, we find that all objects detected within $0\farcm5$ are probably cluster members, whereas we expect 1.4 background sources within $3'$from the center of of 6397; the sources at $0\farcm5<r<3'$ therefore may be background sources."
 We thus cannot decide, We thus cannot decide
The approach described above also allows one to determine the spatial distribution of the electrons in the downstream and upstream regions. through Eqs.,"The approach described above also allows one to determine the spatial distribution of the electrons in the downstream and upstream regions, through Eqs."
 7 and 8.., \ref{eq:N1} and \ref{eq:N2}.
 This information is important for the determination of (he spectrum of the radiation emitted bv the accelerated electrons., This information is important for the determination of the spectrum of the radiation emitted by the accelerated electrons.
 In Fig., In Fig.
" 2 we show the spatial distribution of the electrons upstream (left panel) and downstream (right panel) for constant dilfusion coefficient ancl for three values ofthe momentum of particles: p=O.1p,;4, (solid line). p=pyro, (dashed line) and p=2p,,,; (dash-dotted line)."," \ref{fig:space4_const} we show the spatial distribution of the electrons upstream (left panel) and downstream (right panel) for constant diffusion coefficient and for three values of the momentum of particles: $p=0.1 p_{max}$ (solid line), $p=p_{max}$ (dashed line) and $p=2 p_{max}$ (dash-dotted line)."
 On the v-axis we plot. p?.NGr.p).," On the y-axis we plot $p^2 N(x,p)$."
" On the x-axis there is the distance from the shock in units of L4,5,,=Do/uy upstream and La,,,,=usTioiolpass) downstream."," On the x-axis there is the distance from the shock in units of $L_{1,max}=D_{0}/u_{1}$ upstream and $L_{2,max}=u_{2}\tau_{loss,2}(p_{max})$ downstream."
 In all cases a compression [actor r=4 has been adopted., In all cases a compression factor $r=4$ has been adopted.
 It should be noticed that the diffusion length is independent of momentum in (his case. therefore the size of the upstream region is basically independent of p at low momenta (compare (he dashed and solid lines).," It should be noticed that the diffusion length is independent of momentum in this case, therefore the size of the upstream region is basically independent of $p$ at low momenta (compare the dashed and solid lines)."
 At momenta close to (he maximum momentum. losses become important. but by definition of maximum momentum the acceleration time and the loss time are comparable at that point. therefore the size of the diffusionregion in the upstream [Iuid is roughly the same also for pp~pray.," At momenta close to the maximum momentum, losses become important, but by definition of maximum momentum the acceleration time and the loss time are comparable at that point, therefore the size of the diffusionregion in the upstream fluid is roughly the same also for $p\sim p_{max}$."
" AM p29puo, the density of particles is suppressed exponentially. as shown in Fig."," At $p>p_{max}$ the density of particles is suppressed exponentially, as shown in Fig."
 2. (dash-dotted Ime)., \ref{fig:space4_const} (dash-dotted line).
" In the downstream region (he situation is more interesting: (here are (wo relevant spatial scales, ri!"" ιο αμ=V2DiTcL/p'?."," In the downstream region the situation is more interesting: there are two relevant spatial scales, $x_{loss}^{adv}=u_2\tau_{loss}\sim 1/p$ and $x_{loss}^{diff}= \sqrt{2 D_0\tau_{loss}}\sim 1/p^{1/2}$."
" For a diffusion coefficient constant with momentum. the (wo spatial scales are equal at p,= u5/(2ADp)."," For a diffusion coefficient constant with momentum, the two spatial scales are equal at $p_*=u_2^2/(2AD_0)$ ."
 Comparing this with the maximum momentum. one obtains:," Comparing this with the maximum momentum, one obtains:"
fuelling the prodigious AGNjet activity in strong-lined radio galaxies.,fuelling the prodigious AGN/jet activity in strong-lined radio galaxies.
 Llowever. in cases in which the merging nuclei have significant bulges (highly likely in the case of racio ealaxies). only a relatively low level of star formation is expected at this stage.," However, in cases in which the merging nuclei have significant bulges (highly likely in the case of radio galaxies), only a relatively low level of star formation is expected at this stage."
 This mechanism may be supported by the finding of a relatively high incidence of tidal bridge features and tidally distorted. companion galaxies in deep imagine observations of non-starburst radio galaxies in the 2Jy sample (RamosAlmeida.ctal.2010): it is further supported: by. detailed: studies of individual radio galaxies in interacting groups (Inskipctal.2007.3005)...," This mechanism may be supported by the finding of a relatively high incidence of tidal bridge features and tidally distorted companion galaxies in deep imaging observations of non-starburst radio galaxies in the 2Jy sample \citep{ramos10}; it is further supported by detailed studies of individual radio galaxies in interacting groups \citep{inskip07,inskip08}."
 A final possibility is that nonestarburst radio galaxies are triggered in relatively minor mergers (1:3 or less). or in major mergers that are relatively gas poor (πάν).," A final possibility is that non-starburst radio galaxies are triggered in relatively minor mergers (1:3 or less), or in major mergers that are relatively gas poor (“dry”)."
 In such cases relatively low levels of star formation are expected. which are likely to be dillicult to detect against the light of the old. stellar populations in the host galaxies.," In such cases relatively low levels of star formation are expected, which are likely to be difficult to detect against the light of the old stellar populations in the host galaxies."
 Llowever. without further theoretical work. it is not clear whether minor or gas-poor mergers would be capable of delivering sullicient gas to the nuclear regions to fuel the quasar-Ike levels of nuclear activity detected. in. some non-starburst radio galaxies.," However, without further theoretical work, it is not clear whether minor or gas-poor mergers would be capable of delivering sufficient gas to the nuclear regions to fuel the quasar-like levels of nuclear activity detected in some non-starburst radio galaxies."
 An interesting aspect of starburst radio galaxies is that they show a high incidence of unusual radio structures: our sample includes several compact CSS/GPS sources. as well as sources with relatively bright. steep spectrum core structures. dilluse outer haloes and. double-double structures.," An interesting aspect of starburst radio galaxies is that they show a high incidence of unusual radio structures: our sample includes several compact CSS/GPS sources, as well as sources with relatively bright steep spectrum core structures, diffuse outer haloes and double-double structures."
 What (if anv) is the relationship between these unusual radio structures and the presence of voung stellar populations in the host. galaxies?, What (if any) is the relationship between these unusual radio structures and the presence of young stellar populations in the host galaxies?
 As already discussed: above. couble-double sources. and sources with compact high surface. brightness. inner structures combined with dilluse outer haloes. may represent cases in which the radio jet activity has been re-trigeered (but see Morganti et al.," As already discussed above, double-double sources, and sources with compact high surface brightness inner structures combined with diffuse outer haloes, may represent cases in which the radio jet activity has been re-triggered (but see Morganti et al."
.. 1999 and. Wise et al., 1999 and Wise et al.
 2007 [for counter-arguments in the cases of Centaurus A and. Hydra A)., 2007 for counter-arguments in the cases of Centaurus A and Hydra A).
 Given the complexity of the gas infall histories of major eas rich mergers. it is certainly plausible that cach merging system undergoes more than one phase of ACN/jet activity. thus explaining the presence of such sources in our sample.," Given the complexity of the gas infall histories of major gas rich mergers, it is certainly plausible that each merging system undergoes more than one phase of AGN/jet activity, thus explaining the presence of such sources in our sample."
 Considering the compact (CSS/GPS) radio. sources. there is direct. observational evidence fron measurements of hotspot. advance speeds that CSS/CGPS radio sources are relatively vouthful (Ot 10° vr).," Considering the compact (CSS/GPS) radio sources, there is direct observational evidence from measurements of hotspot advance speeds that CSS/GPS radio sources are relatively youthful $10^4$ – $10^6$ yr)."
 However. since the CSS/GPS radio sources are generally estimated to be much vounger than the YSPs detected. in their. host. galaxies (uus 105—107 vr). the vouth of the compact sources does not necessarilv help to explain their relatively high rate of occurrence in our sample of starburst radio galaxies.," However, since the CSS/GPS radio sources are generally estimated to be much younger than the YSPs detected in their host galaxies $t_{ysp} \sim 10^7$ – $10^9$ yr), the youth of the compact sources does not necessarily help to explain their relatively high rate of occurrence in our sample of starburst radio galaxies."
 Alternatively. the high incidence ofCSS/€DPS sources in the starburst radio galaxies sample may be the consequence of an observational selection effect as follows.," Alternatively, the high incidence of CSS/GPS sources in the starburst radio galaxies sample may be the consequence of an observational selection effect as follows."
 We expect a relatively rich. and. dense LSAL to be present in the nuclear regions of merging systems. especially around. the time of nuclear coalescence.," We expect a relatively rich and dense ISM to be present in the nuclear regions of merging systems, especially around the time of nuclear coalescence."
 A radio source triggered in à merger will interact particularly strongly with this rich LSAL in the carly stages of the radio source history. as the jets expand through the central regions of the host. galaxies: direct. evidence for strong jet-cloud interactions in. voung radio sources is provided by their extreme emission. line kinematics (Holt.Fadhunter&Morganti2008).," A radio source triggered in a merger will interact particularly strongly with this rich ISM in the early stages of the radio source history, as the jets expand through the central regions of the host galaxies; direct evidence for strong jet-cloud interactions in young radio sources is provided by their extreme emission line kinematics \citep{holt08}."
. Phe strong interactions between the jets ancl the rich ISM. associated with the mergers will not only result in extreme emission line kinematics. but may also alfect the conversion of jet. power into radio luminosity. boosting the radio luminosities of sources.," The strong interactions between the jets and the rich ISM associated with the mergers will not only result in extreme emission line kinematics, but may also affect the conversion of jet power into radio luminosity, boosting the radio luminosities of sources."
 There is already evidence that interaction with the relatively dense. hot X-ray. haloes associated with clusters of galaxies boosts the radio luminosities of jets for a given jet power (Barthel&ArnauclL99G).. ancl it is plausible that there will be a similar boosting clleet when the jets strongly interact with the (cooler) ISAL in the central regions of merger remnants.," There is already evidence that interaction with the relatively dense, hot X-ray haloes associated with clusters of galaxies boosts the radio luminosities of jets for a given jet power \citep{barthel96}, and it is plausible that there will be a similar boosting effect when the jets strongly interact with the (cooler) ISM in the central regions of merger remnants."
 Indeed. strong enhancements in the racio emission are observed. at the sites of interactions between radio jets and warm emission line clouds in the haloes of radio galaxies in the local Universe (c.g.vanDreugelοἱal.1985.1986:Fosburvetal.1998:Tadhunter 2000).," Indeed, strong enhancements in the radio emission are observed at the sites of interactions between radio jets and warm emission line clouds in the haloes of radio galaxies in the local Universe \citep[e.g.][]{vanbreugel85,vanbreugel86,fosbury98,tadhunter00}."
. For a given intrinsic jet power. this Hux boosting will lead to the compact radio sources that are trigeered in voung. star forming merger remnants being preferentially selected in [ux-limited radio surveys.," For a given intrinsic jet power, this flux boosting will lead to the compact radio sources that are triggered in young, star forming merger remnants being preferentially selected in flux-limited radio surveys."
 This in turn could explain the relatively high rate of occurrence of compact radio sources amongst the starburst radio galaxies. as well as the bias of the compact sources towards relatively voung YSDP! ages (usp0.1 Cover see section 4.1).," This in turn could explain the relatively high rate of occurrence of compact radio sources amongst the starburst radio galaxies, as well as the bias of the compact sources towards relatively young YSP ages $t_{ysp} < 0.1$ Gyr; see section 4.1)."
 The interaction of the jets with the richer gaseous environments present in merger remnants could also help to explain the relatively high. incidence of extended: radio sources with compact steep spectrum cores in our sample. since such interactions have the potential to boost the radio emission from the jets. even if the radio lobes are well ouside the central regions of the galaxies.," The interaction of the jets with the richer gaseous environments present in merger remnants could also help to explain the relatively high incidence of extended radio sources with compact steep spectrum cores in our sample, since such interactions have the potential to boost the radio emission from the jets, even if the radio lobes are well ouside the central regions of the galaxies."
 1n this paper we have discussed the properties of the voung stellar populations (YSP) in the 15 of powerful radio galaxies that show strong evidence for recent star ormation activity at optical wavelengths., In this paper we have discussed the properties of the young stellar populations (YSP) in the $\sim$ 15 – of powerful radio galaxies that show strong evidence for recent star formation activity at optical wavelengths.
 Combined: with information about the morphologies of the host galaxies. he YSP properties of most of these starburst radio galaxies are consistent with the triggering of both starburst and AGN/jet activity in galaxy mergers in whieh at least one of he merging galaxies is gas-rich.," Combined with information about the morphologies of the host galaxies, the YSP properties of most of these starburst radio galaxies are consistent with the triggering of both starburst and AGN/jet activity in galaxy mergers in which at least one of the merging galaxies is gas-rich."
 However. the triggering of he AGN/jet activity is not confined to a single evolutionary hase of galaxv mergers.," However, the triggering of the AGN/jet activity is not confined to a single evolutionary phase of galaxy mergers."
 While in a significant. subset of objects the Αλλο activity has been triggered within LI] Gyr of the coalescence of merging nuclei. close to the expected. peaks of the merger-induced: starbursts.. many objects are observed in the post-coalescence phase. 20.2 Gyr alter the starburst peaks.," While in a significant subset of objects the AGN/jet activity has been triggered within 0.1 Gyr of the coalescence of merging nuclei, close to the expected peaks of the merger-induced starbursts, many objects are observed in the post-coalescence phase, $>$ 0.2 Gyr after the starburst peaks."
 In the former group the triggering of the activity can be readily. identified. with the major infalls of gas that are predicted to occur around the time of coalescence., In the former group the triggering of the activity can be readily identified with the major infalls of gas that are predicted to occur around the time of coalescence.
 On the other hand. in the latter group the nature of the link between the triggering of the AGN/jct and the original starburst-inducing mergers is less clear: late-time infall of merger debris. settling of the debris disks to an equilibrium configuration. and perturbation of the debris disks by minor mergers and encounters. are all possibilities," On the other hand, in the latter group the nature of the link between the triggering of the AGN/jet and the original starburst-inducing mergers is less clear: late-time infall of merger debris, settling of the debris disks to an equilibrium configuration, and perturbation of the debris disks by minor mergers and encounters, are all possibilities"
bright structures.,bright structures.
 The fact that we image a complete loop structure aud monitor part of its evolution provide further constraints of coherence for the data iuterpretation., The fact that we image a complete loop structure and monitor part of its evolution provide further constraints of coherence for the data interpretation.
 Siuce the loo> fades out at the end of the TRACE and Yohlkoh observations aud is absent in the secoud CDS raster. we could àse the final TRACE aud Yohsoli friunes aud the secoud CDS raster as backeround to be subtractec Xxel-by-pixel from the other frames.," Since the loop fades out at the end of the TRACE and Yohkoh observations and is absent in the second CDS raster, we could use the final TRACE and Yohkoh frames and the second CDS raster as background to be subtracted pixel-by-pixel from the other frames."
 The advantages iux disadvantages of this method of background subtraction are listed nu Section 2: a siuple inspection of the vackeround-subtracted images supports that the methoc oovides sound results., The advantages and disadvantages of this method of background subtraction are listed in Section \ref{sec:data}; a simple inspection of the background-subtracted images supports that the method provides sound results.
 The background is indeed a sjeuificaut fraction (> 50)) of the total signal for al iustruineuts (Fig. 5)).," The background is indeed a significant fraction $> 50$ ) of the total signal for all instruments (Fig. \ref{fig:profbk}) ),"
 aud its accurate subtraction is herefore critical for any subsequent analysis and for determining any physical parameter of a specific structure., and its accurate subtraction is therefore critical for any subsequent analysis and for determining any physical parameter of a specific structure.
 Tn fact. we fiud differences between indicators obtained roni subtracted aud unsubtracted data (Fie 8)). the ormer beius less uuiform aud more evolving.," In fact, we find differences between indicators obtained from subtracted and unsubtracted data (Fig \ref{fig:hrlc}) ), the former being less uniform and more evolving."
 The loop is best visible aud lives longer in the TRACE 171 aud 195 fiter passbands., The loop is best visible and lives longer in the TRACE 171 and 195 filter passbands.
 It is instead quite faint and decays rapidly in the 281 filter passbaucd., It is instead quite faint and decays rapidly in the 284 filter passband.
 A simple superposition of the images. using the loop outlines. shows that the loop inthe 171 filter passband reasonably overlaps the loop in the 195 filter passband.," A simple superposition of the images, using the loop outlines, shows that the loop in the 171 filter passband reasonably overlaps the loop in the 195 filter passband."
 The good correspondence is also supported by he oop aspect in the 195/171 filter ratio maps., The good correspondence is also supported by the loop aspect in the 195/171 filter ratio maps.
 The aligumeut is not as eood with the loop in the 281 filter passband., The alignment is not as good with the loop in the 284 filter passband.
 The SXT loop is more diffuse: the right leg appears to overlap that oftιο TRACE 171 À//195 loop., The SXT loop is more diffuse: the right leg appears to overlap that of the TRACE 171 /195 loop.
 This may indicate the presence of relatively hot plasma iu the right lee of the loop., This may indicate the presence of relatively hot plasma in the right leg of the loop.
 The eusssion evolution in the SNT band appears to be cuite coherent with that iu the TRACE 195 baud., The emission evolution in the SXT band appears to be quite coherent with that in the TRACE 195 band.
 However. because of the lower spatial resolution. uo οςnclusive statement can be made ou the correspondence between the SXT aud the TRACE loop.," However, because of the lower spatial resolution, no conclusive statement can be made on the correspondence between the SXT and the TRACE loop."
 With the same limitations. the TRACE loop overlaps well with the loop as visible in a few SoIIO/CDS spectral lines.," With the same limitations, the TRACE loop overlaps well with the loop as visible in a few SoHO/CDS spectral lines."
 The loop is best visible in the Me IX 368 line. but well visible also in the Mg X 625A.. in the Si X 317 and 356 lines. less in the Fe NTT 361 line.," The loop is best visible in the Mg IX 368 line, but well visible also in the Mg X 625, in the Si X 347 and 356 lines, less in the Fe XII 364 line."
 All these Hues have temperature of asian formation about logT~6.06.1. which is also around the temperature of inaxiuun sensitivity of both the TRACE 171 auc 195 filter passbands.," All these lines have temperature of maximum formation about $\log T \sim 6.0 - 6.1$, which is also around the temperature of maximum sensitivity of both the TRACE 171 and 195 filter passbands."
 Thus. there is a quaitative coherence of he data frou the different instruments.," Thus, there is a qualitative coherence of the data from the different instruments."
 Limited parts of he loop seem to be visible in a few spectral lines with other formation temperature. e.g. the lef leg in the cooler Ca X line (logZz 5.9). the lower part of the right lee in the hotter Fe lines.," Limited parts of the loop seem to be visible in a few spectral lines with other formation temperature, e.g. the left leg in the cooler Ca X line $\log T \approx 5.9$ ), the lower part of the right leg in the hotter Fe lines."
 This suggests that. diving the first CDS raster. in the right leg there is hotter plasima than in the left leg.," This suggests that, during the first CDS raster, in the right leg there is hotter plasma than in the left leg."
 This is confirmed by the EAT) reconstructed at five locations along the loop. after renoving the Meg X 625 line.," This is confirmed by the EM(T) reconstructed at five locations along the loop, after removing the Mg X 625 line."
 In the coo ο V line. we may be seeing ouly the footpoiuts of the loyp.," In the cool O V line, we may be seeing only the footpoints of the loop."
 We will not connrent here about the structures surrotmiddling the selectec loop., We will not comment here about the structures surrounding the selected loop.
 We only mention that there Is ALLOther bright structire which apparently intersects the loop and which may have importance because it apCaS to evolve coherently with the loop., We only mention that there is another bright structure which apparently intersects the loop and which may have importance because it appears to evolve coherently with the loop.
 This may be taken as evidence of au interaction of this structure with the loop., This may be taken as evidence of an interaction of this structure with the loop.
 Tl1C TRACE lhiages show that the loop Is1 substructured imu severa strands. as are niuiv other Oops observed with TRACE.," The TRACE images show that the loop is substructured in several strands, as are many other loops observed with TRACE."
 This work analyzes the loop as a sinele aud cohereut structure. aud we will not comnent further on the substictudug of the loop. which iav deser(oa further separate work.," This work analyzes the loop as a single and coherent structure, and we will not comment further on the substructuring of the loop, which may deserve a further separate work."
 We ouly note that TRACE appears to be detecting a thermal structuriug across the loop better han other imustrunents. as shown by he filter ratio maps.," We only note that TRACE appears to be detecting a thermal structuring across the loop better than other instruments, as shown by the filter ratio maps."
" Since amvway. the loop appears to hax“oa colerent evolition. the finer substructurmgniav not be crucial for the description of average properties of theαπο,"," Since anyway, the loop appears to have a coherent evolution, the finer substructuring may not be crucial for the description of average properties of the system."
 The coherent evolution may sugeest a cohernf heating acreISS the structure., The coherent evolution may suggest a coherent heating across the structure.
 TRAC'E and Yoikoh data alow us to analyze the evoution of the loop., TRACE and Yohkoh data allow us to analyze the evolution of the loop.
 Uufortiliaolv. CDS data ire not able to ovile analogous 1formation because there is Ollv one relevait raster. d.e. a single suapshot. ching the loop evohtiou.," Unfortunately, CDS data are not able to provide analogous information because there is only one relevant raster, i.e. a single snapshot, during the loop evolution."
 Wieh αιality spectrolelioerams intrinsicaly require relatively ong acquisilon fines., High quality spectroheliograms intrinsically require relatively long acquisition times.
 Iu the analyzed iue sequence the loop evoves., In the analyzed time sequence the loop evolves.
 The TRACT Tl filter detects an evolution bo1 of the Cluission intensity and « fits distribution aloug he loop., The TRACE 171 filter detects an evolution both of the emission intensity and of its distribution along the loop.
 Iu particilav. the right lee of the oop is brigit at the beeiuuiug of the observation. while the left lee )Oconues the brighter laer on.," In particular, the right leg of the loop is bright at the beginning of the observation, while the left leg becomes the brighter later on."
 Tje bright lef leg is cohereut with the brehtuess distribujon iu the relevant CDS lines. taken int10 Satie fime Jiod.," The bright left leg is coherent with the brightness distribution in the relevant CDS lines, taken in the same time period."
 Fig., Fig.
 13. shows au image of the loop region obtain from the TRACE 171 images with :v procedure which ninics the CDS rasteriug (with COLTCSponding time ste]ping) and «ceraded to the CDS aneular resolution. coniwed to the CDS raster inage i- he Ae IX 368 liuc.," \ref{fig:trace_cds}
 shows an image of the loop region obtained from the TRACE 171 images with a procedure which mimics the CDS rastering (with corresponding time stepping) and degraded to the CDS angular resolution, compared to the CDS raster image in the Mg IX 368 line."
 The figure coufixiis a very good COLTCSpondenuce o: the oop appearance m both iuages., The figure confirms a very good correspondence of the loop appearance in both images.
 The :uwvnsnietrv along the loop both iu space aud in nne uav be aniidication of an asviuauetrc distributio- of the| heatingc» alonec» ti6 loop aud a time variation of he heating inteisity. to be checked through detailed nodeine.," The asymmetry along the loop both in space and in time may be an indication of an asymmetric distribution of the heating along the loop and a time variation of the heating intensity, to be checked through detailed modeling."
 In the SNT :ud the other TRACE filters the Cluission distrinions is more uniforiu aud evolves more uniforiulv., In the SXT and the other TRACE filters the emission distributions is more uniform and evolves more uniformly.
 Tlιο SoIIO canalenu covers mostlv the loop decay., The SoHO campaign covers mostly the loop decay.
 This js clear roni the relevant light curves (shown iu Fie. { ME, This is clear from the relevant light curves (shown in Fig. \ref{fig:lcbk}) ):
 they have a decreasing trend. with c-folding times between 0.7 aud 1.7 h. with the oulv exception of the TRACE 171 filter.," they have a decreasing trend, with e-folding times between 0.7 and 1.7 h, with the only exception of the TRACE 171 filter."
 In this filter. the ligi curve has a peak about one hour after the observation starts aud then decays steadily," In this filter, the light curve has a peak about one hour after the observation starts and then decays steadily."
 This is coherent with other TRACE observations of loops (Winebarger et al., This is coherent with other TRACE observations of loops (Winebarger et al.
 20035)., 2003b).
i. integrated above e; —100 MeV. along the line of sight into a solid angle dO and is given bv the expression The total emission [rom the polar cap for a particular phase bin o is obtained bv integrating over parameter € to include the contributions of all the open field lines along a line of sight defined bv the viewing angle ¢.,"$\eta$, integrated above $\epsilon_\gamma$ =100 MeV, along the line of sight into a solid angle $d\Omega$ and is given by the expression The total emission from the polar cap for a particular phase bin $\phi$ is obtained by integrating over parameter $\xi$ to include the contributions of all the open field lines along a line of sight defined by the viewing angle $\zeta$."
 The total emission in (ie phase bin is given bv llaving calculated (he s-ray pulse profile for each MSP [or a given viewing geometry. we average (he profile to obtain the average photon flux. aud compare it to the instrument threshold.," The total emission in the phase bin is given by Having calculated the $\gamma$ -ray pulse profile for each MSP for a given viewing geometry, we average the profile to obtain the average photon flux, and compare it to the instrument threshold."
 Our resulting 5-rav efficienev. (7)) lor the total spectrum and. profiles for the nearby AISP PSR are in agreement with those obtained by (2005)., Our resulting $\gamma$ -ray efficiency ) for the total spectrum and profiles for the nearby MSP PSR are in agreement with those obtained by \citet{Vent05}.
 From the simulated y-ray pulse profile. we obtain an average [lux thal we compare {ο all skv threshold maps lor EGRET. AGILE and GLAST Large Area Telescope (LAT).," From the simulated $\gamma$ -ray pulse profile, we obtain an average flux that we compare to all sky threshold maps for EGRET, AGILE and GLAST Large Area Telescope (LAT)."
 We use (he recently revised EGRET map that includes the dark clouds 2007).. which has led to a radical reassessment of the EGRET unidentifiel sources.," We use the recently revised EGRET map that includes the dark clouds \citep{Casand07}, which has led to a radical reassessment of the EGRET unidentified sources."
 The GLAST threshold has been improved and updated (Grenier Casandjian private communication) as à 1 vear GLAST LAT threshold map., The GLAST threshold has been improved and updated (Grenier Casandjian private communication) as a 1 year GLAST LAT threshold map.
 The all skv map for AGILE (Pellizzoni private communication) has not been recently updated in our computer code., The all sky map for AGILE (Pellizzoni private communication) has not been recently updated in our computer code.
 The detection of radio and οταν point sources within the code are independent of each other. allowing the tagging of radio-equiet (below the survey flux thresholds) and radio-loud 5-rav. MSPs.," The detection of radio and $\gamma$ -ray point sources within the code are independent of each other, allowing the tagging of radio-quiet (below the survey flux thresholds) and radio-loud $\gamma$ -ray MSPs."
 To improve the simulated statistics. we run the simulation to obtain ten (imes the number of detected MSPs and then normalize the distributions accordingly.," To improve the simulated statistics, we run the simulation to obtain ten times the number of detected MSPs and then normalize the distributions accordingly."
 In Figure 4. we," In Figure 4, we"
"kpc, but our targets are expected to lie beyond this point where it begins to taper off reffig,xtinction)).","kpc, but our targets are expected to lie beyond this point where it begins to taper off \\ref{fig_extinction}) )."
T hegoodagreementbetweentheT¢ values derived from near-IR data and those determined from the optical photometric data in the Harris BV and Sloan-Gunn r'i' filters available in Exo-Dat suggests that this estimate is appropriate., The good agreement between the $T_{\rm eff}$ values derived from near-IR data and those determined from the optical photometric data in the Harris $BV$ and Sloan-Gunn $r^{\prime}i^{\prime}$ filters available in Exo-Dat suggests that this estimate is appropriate.
" The extinction in the J, H, and Ks bandpasses were determined following ? assuming the spectral energy distribution of a K1 giant."," The extinction in the $J$, $H$, and $K_S$ bandpasses were determined following \citet{Fiorucci03} assuming the spectral energy distribution of a K1 giant."
 We adopt the unweighted mean of Teg(J— H) and Teg(J Ks) as the final Τομ values., We adopt the unweighted mean of $T_{\rm eff}$ $J-H$ ) and $T_{\rm eff}$ $J-K_S$ ) as the final $T_{\rm eff}$ values.
" A typical value forthe uncertainty on these temperatures is 4150 KK. Their distribution, shown in reffig,effaistribution, , iscenteredon-4500K, which is about, but slightly lower than, the value expected for stars pertaining to the red clump, which are supposed to be representative of most of the red-giant stars observed here (?).."," A typical value forthe uncertainty on these temperatures is $\sim$ K. Their distribution, shown in \\ref{fig_teff_distribution}, is centered on $\sim$ 4500K, which is about, but slightly lower than, the value expected for stars pertaining to the red clump, which are supposed to be representative of most of the red-giant stars observed here \citep{Miglio09}."
" Another characteristic of interest is the luminosity-to-mass ratio, L/M."," Another characteristic of interest is the luminosity-to-mass ratio, $L/M$."
" However, this ratio cannot generally be derived from observations in a straightforward and accurate manner."," However, this ratio cannot generally be derived from observations in a straightforward and accurate manner."
" A scaling law can be derived to directly estimate L/M from observables, namely Teg and Vmax."," A scaling law can be derived to directly estimate $L/M$ from observables, namely $T_{\rm eff}$ and $\nu_{\rm max}$."
" First, we consider that Vmax, the frequency at which the modes have maximum amplitude, scales as the cut-off frequency νς, which itself varies as g/VTeg (where g is the surface gravity)."," First, we consider that $\nu_{\rm max}$, the frequency at which the modes have maximum amplitude, scales as the cut-off frequency $\nu_c$ , which itself varies as $g/\sqrt{T_{\rm eff}}$ (where $g$ is the surface gravity)."
" Then, as the L/M ratio scales"," Then, as the $L/M$ ratio scales"
L(FIR)/M(H»2) as a tracer.,$L(FIR)/M(H_2)$ as a tracer.
 A similar result has been obtained by Bosellietal.(2001) and Boissieretal. who obtain a nearly constant SFE in a sample of normal spirals., A similar result has been obtained by \citet{Boselli2001} and \citet{Boissier2001} who obtain a nearly constant SFE in a sample of normal spirals.
" More recently, Bothwell,Kennicutt,&Lee(2009) suggested that the SFE is slowly increasing with galaxy luminosity (implying that more luminous galaxies have shorter gas consumption timescales), but those data, which only include r--detected galaxies, are nearly consistent with the constant values we have derived for the GASS sample."," More recently, \citet{Bothwell2009} suggested that the SFE is slowly increasing with galaxy luminosity (implying that more luminous galaxies have shorter gas consumption timescales), but those data, which only include -detected galaxies, are nearly consistent with the constant values we have derived for the GASS sample."
 We return to the comparative question: Why does the drop sharply with and µι while the SFE remains constant?, We return to the comparative question: Why does the drop sharply with and $\mu_\star$ while the SFE remains constant?
 Here we consider two different scenarios and leave a more detailed analysis for future work., Here we consider two different scenarios and leave a more detailed analysis for future work.
" One possibility is that star formation is inhibited within the gas reservoir, at the sink point rather than the supply location."," One possibility is that star formation is inhibited within the gas reservoir, at the sink point rather than the supply location."
" Under the assumption that the efficiency of conversion of molecular gas into stars is nearly constant (e.g.Bigieletal.2008;Leroy 2008),, regulation would then occur at the interface between the atomic and molecular phase."," Under the assumption that the efficiency of conversion of molecular gas into stars is nearly constant \citep[e.g.][]{Bigiel2008,Leroy2008}, regulation would then occur at the interface between the atomic and molecular phase."
" Processes that can stabilize a gaseous disk, such as those proposed by Martigetal.(2009) are possible examples."," Processes that can stabilize a gaseous disk, such as those proposed by \citet{Martig2009} are possible examples."
" As discussed in the introduction, although such a process can explain a decreasing iit may also result in a large reservoir of cold gas, leading to a decreasing SFE for galaxies that are actively being quenched."," As discussed in the introduction, although such a process can explain a decreasing it may also result in a large reservoir of cold gas, leading to a decreasing SFE for galaxies that are actively being quenched."
 Therefore it appears hard to reconcile internal, Therefore it appears hard to reconcile internal
 Gamma-Ray Bursts (GRBs) are powerful brief transient phenomena of high-energy radiation that appear randomly in the sky., Gamma-Ray Bursts (GRBs) are powerful brief transient phenomena of high-energy radiation that appear randomly in the sky.
 They were first detected in 1969 by the satellites (Klebesadel et al., They were first detected in 1969 by the satellites (Klebesadel et al.
 1973) and have remained for many years one of the most elusive mysteries in astrophysics., 1973) and have remained for many years one of the most elusive mysteries in astrophysics.
 Before the launch of the andRossiXTE satelllites in 1996. they had not been detected in any other wavelength region. and their distance scale remained unknown.," Before the launch of the and llites in 1996, they had not been detected in any other wavelength region, and their distance scale remained unknown."
" The discovery of X-ray afterglows by both satellites revolutionized the field. because they are able to provide very accurate GRB error boxes within a few hours (circular error boxes with radius up to 50""). which enables very rapid follow up observations at longer wavelengths."," The discovery of X-ray afterglows by both satellites revolutionized the field, because they are able to provide very accurate GRB error boxes within a few hours (circular error boxes with radius up to $50^{\prime \prime}$ ), which enables very rapid follow up observations at longer wavelengths."
 Eight GRBs detected byBeppoSAX have been detected at optical and infrared wavelengths: GRB 970228 (Guarmniert et al., Eight GRBs detected by have been detected at optical and infrared wavelengths; GRB 970228 (Guarnieri et al.
 19972. van Paradijs et al.," 1997a, van Paradijs et al."
 1997). GRB 970508 (Bond 1997. Djorgovski et al.," 1997), GRB 970508 (Bond 1997, Djorgovski et al."
 1997. Castro-Tirado et al.," 1997, Castro-Tirado et al."
 19983). GRB 971214 (Halpern et al.," 1998a), GRB 971214 (Halpern et al."
 1997. Gorosabel et al.," 1997, Gorosabel et al."
 1998. Ramapprakash et al.," 1998, prakash et al."
 1998). GRB 980326 (Groot et al.," 1998), GRB 980326 (Groot et al."
 1998). GRB 980329 (Klose 1998.," 1998), GRB 980329 (Klose 1998,"
rises by a factor of 5 between 150 and LOkkpe. unlike any observed. cluster.,"rises by a factor of 5 between 150 and kpc, unlike any observed cluster."
" The emissivity profile. shown in 5.. has 19 bins of width S arcsec. with 912 bins interior to the cooling radius (roan,7150 kkpc)."," The emissivity profile, shown in \ref{fig:a745xi}, has 19 bins of width 8 arcsec, with 9–12 bins interior to the cooling radius $r_{\rm cool}\approx180$ kpc)."
 The first thing to note is that £ flattens considerably in the innermost bin., The first thing to note is that $\xi$ flattens considerably in the innermost bin.
 This is incompatible with density distributions with small values of k., This is incompatible with density distributions with small values of $k$.
 1n Fact the fit shown by the solid line. acmits solutions which extend tor—0 only for &—x.," In fact the fit shown by the solid line, + admits solutions which extend to $r=0$ only for $k=\infty$."
 Unfortunately. just as for SS5. large values of & eive steeply rising dark-matter density and tempoerature profiles at small raclii," Unfortunately, just as for 85, large values of $k$ give steeply rising dark-matter density and temperature profiles at small radii."
 IE we ignore the inner bin. however. then it is possible to find solutions for all values of &.," If we ignore the inner bin, however, then it is possible to find solutions for all values of $k$."
 The dotted line in 5 shows the enissivity. profile which corresponds to a mass densityb, The dotted line in \ref{fig:a745xi} shows the emissivity profile which corresponds to a mass density.
"e, and &=I.", and $k=1$.
 For 22029 there are 79 bins of width 12 aresec. within the cooling radius. μαυροτὸ 210kkpe.," For 2029 there are 7–9 bins of width 12 arcsec within the cooling radius, $r_{\rm cool}approx170$ kpc."
 The eniissivity prolile ⊽, The emissivity profile +.
 shown in 6. is again too shallow in the central jn. but the inconsistencey. is this time so slight. that it strenethens the case for &=1 (as discussed in 3.2 the slope of the emissivity. profile within the cluster core wovicles a measure of 4).," shown in \ref{fig:a2029xi} is again too shallow in the central bin, but the inconsistency is this time so slight that it strengthens the case for $k=1$ (as discussed in \ref{sec:behaviour} the slope of the emissivity profile within the cluster core provides a measure of $k$ )."
 Taa shows that X crops to a value close to zero within 30kkpc., \ref{fig:a2029k001}a a shows that $\Sigma$ drops to a value close to zero within kpc.
 This indicates that the virial temperature ms sunk well below the gas temperature the flow is isobaric within this radius)., This indicates that the virial temperature has sunk well below the gas temperature the flow is isobaric within this radius).
 This is reflected in Thb which. shows the corresponding density profile., This is reflected in \ref{fig:a2029k001}b b which shows the corresponding density profile.
 Lhe latter is well-fit at radii ereater than kkpe by a massedensity, The latter is well-fit at radii greater than kpc by a mass-density
"Astrophysical > ray sources are often subject to the so-caled conmpactuess problem: when the fux at longer wavelengths is combined with the dimensions of the source, Which are interred frou helit-crossing time areuients. a hieh optical thickness to photon-photou anunihilation aud effecive absorption of 35 Paves are nuplied.","Astrophysical $\gamma-$ ray sources are often subject to the so-called `compactness' problem: when the flux at longer wavelengths is combined with the dimensions of the source, which are inferred from light-crossing time arguments, a high optical thickness to photon-photon annihilation and effective absorption of $\gamma-$ rays are implied."
 The possibility that lieh-enerev photous could pair-produce on soft targe photons instead of escape in conrpact sources was first discussed by 7.. while the ratio of the huuimositv to the size of the source. LR. CliOrYgSos as d ctermuning factor of whether or not a ügl-enerev photon wil acually be absorbed (7)..," The possibility that high-energy photons could pair-produce on soft target photons instead of escape in compact sources was first discussed by \cite{jelley66}, while the ratio of the luminosity to the size of the source, $L/R$, emerges as a determining factor of whether or not a high-energy photon will actually be absorbed \citep{herterich74}."
. This was followed by work tha took iuto account ploton-xXioton anmililation not onlv as a sin zof5 rays. but also as a source of clectrou-YONIron pairs inside uon-theriual conrpact sources (77777η]..," This was followed by work that took into account photon-photon annihilation not only as a sink of $\gamma-$ rays, but also as a source of electron-positron pairs inside non-thermal compact sources \citep{bonometto71, guilbert83,
kazanas84, zdziarski85, svensson87}."
 The aiio| these models was o calculate self-cousiseutv the photon flux escapiugroni the sources by aki18o iuto account the energv redistribution caused by the  aunuiliation-induced pair cascades., The aim of these models was to calculate self-consistently the photon flux escapingfrom the sources by taking into account the energy redistribution caused by the $\gamma-$ annihilation-induced pair cascades.
 The assuuptiou was hat Hel-cnerey particles Or 5 ravs were injectce| uuiforuly in a source that also contains soft photons. aud the svstcui was followed to its flnal steady-state through the solution of a set of kinetic equations describiug ιο physical processes at work.," The assumption was that high-energy particles or $\gamma-$ rays were injected uniformly in a source that also contains soft photons, and the system was followed to its final steady-state through the solution of a set of kinetic equations describing the physical processes at work."
 Several groups lave also ¢eveloped umuuerical codes for the computation of time«cpendent solutions to the kinetic equations taking photon-photon aunihilation iuto account (2777?3..," Several groups have also developed numerical codes for the computation of time-dependent solutions to the kinetic equations taking photon-photon annihilation into account \citep{coppi92, mastkirk95, stern95, boettcherchiang02}."
 These algoritlns are conunonlv used iu source modelling (2777?)..," These algorithms are commonly used in source modelling \citep{mastkirk97, kataoka00, konopelko03, katarz05}."
 One of the assuuptiois of these models. as stated above. is the presence of soft protons in the source. which serve as targets for the ES rav annibhilation.," One of the assumptions of these models, as stated above, is the presence of soft photons in the source, which serve as targets for the $\gamma-$ ray annihilation."
 À different approach has beeu receutvo presented bv ?.. henceforth SI.," A different approach has been recently presented by \cite{SK07}, henceforth SK."
 These authors focused Ol the non-linear effects induced by photou-plioton annibilation aud mvestisated the necessary concitions 1udder which 5-rav photons ca- cause ruuawav pairp, These authors focused on the non-linear effects induced by photon-photon annihilation and investigated the necessary conditions under which $\gamma$ -ray photons can cause runaway pair.
roduction. 7 showed that there is a limit to the +rav huninositv escapiug from a source. which docs not rely ou the existing soft photon population mit is instead a theoretical lait depending oulv on »uwnneters such as the source size and its magnetic Ποια streneth.," \cite{SK07} showed that there is a limit to the $\gamma-$ ray luminosity escaping from a source, which does not rely on the existing soft photon population but is instead a theoretical limit depending only on parameters such as the source size and its magnetic field strength."
 Violation of this Iiuit leads to automatic quenching of the + rave., Violation of this limit leads to automatic quenching of the $\gamma-$ rays.
" This involves a network of Xocesses, nanielv photon-ohiotou :uinilhilaion and lepon svuchrotrou radiation. which cau become ron-linear ouce certain criteria are satisfie"," This involves a network of processes, namely photon-photon annihilation and lepton synchrotron radiation, which can become non-linear once certain criteria are satisfied."
 επι this case clectron-positrou airs grow spontancouxlv i the svsteni ane the excessive  ravs are absorbed on the svuchrotron protous enited wv the pairs., In this case electron-positron pairs grow spontaneously in the system and the `excessive' $\gamma-$ rays are absorbed on the synchrotron photons emitted by the pairs.
 As a resu the system reaches a fiial steady state where the 7 raves. soft photons. aud electrou-)ositron pairs iive all reacred equilibrmu.," As a result the system reaches a final steady state where the $\gamma-$ rays, soft photons, and electron-positron pairs have all reached equilibrium."
 Therefore this Cul occur even in the livpohetical case when there are no soft photons in the source. at least initially.," Therefore this can occur even in the hypothetical case when there are no soft photons in the source, at least initially."
 Tudeed. piotol qlenchiug las solue juterestine Huplicatious for ciissionu models of 5 ravs because. it eves a robust upper limit ol. he 5 rav lDunuinosity.," Indeed, photon quenching has some interesting implications for emission models of $\gamma-$ rays because it gives a robust upper limit on the $\gamma-$ ray luminosity."
 The aim of the preseut paper is to investigate the Huplicatiois of this network for the high - energy compact astrophysical sources., The aim of the present paper is to investigate the implications of this network for the high - energy compact astrophysical sources.
 Iu 822 woe Wi] expauid the analvtical xoach. of SI. who sudied tlic| ανασα. syste of photous aud relativistic pairs usiig ὁ functions for the photon-photou annililaOW Cross section and for the svuchroron enüsvitv. while they treaed svuchrotron losses as catastrophic.," In 2 we will expand the analytical approach of SK, who studied the dynamical system of photons and relativistic pairs using $\delta-$ functions for the photon-photon annihilation cross section and for the synchrotron emissivity, while they treated synchrotron losses as catastrophic."
 Iu 50:X) we will use a nunerical approaci that will allow us to study fιο properties of quenching using fie. full cross section for 55 absorption aud the full svwchrotron cuussivity., In 3 we will use a numerical approach that will allow us to study the properties of quenching using the full cross section for $\gamma\gamma$ absorption and the full synchrotron emissivity.
 As an example. iu Sli the above wil be applied to the 2016 MTACIC TeV observations ofcuasar 30€279 to extract a parameter space of allowed valies for the source parameters. ic. the radius R and the magneic field streneth DB. as well as for the Doppler factor ó of the flaw.," As an example, in 4 the above will be applied to the 2006 MAGIC TeV observations of quasar 3C279 to extract a parameter space of allowed values for the source parameters, i.e, the radius $R$ and the magnetic field strength $B$ , as well as for the Doppler factor $\delta$ of the flow."
 Fimally im 855 we couclude ixd eive a brief iscussion of the main poiuts of the present work., Finally in 5 we conclude and give a brief discussion of the main points of the present work.
We have investigated structure functions and distributions of flux. factors produced. by models with m=LAL. for mass function psioqr ancl by models with Ga)=LAL. for miatss functions ΣΣ AMO Poueprh WIL wi=10 and —=100.,"We have investigated structure functions and distributions of flux factors produced by models with $m =1M_{\odot}$ for mass function $p_{Single}$ and by models with $\langle m\rangle =1M_{\odot}$ for mass functions $p_{Ndense}$ , $p_{Salpeter}$ and $p_{Odepth}$ with $\frac{m_{2}}{m_{1}}=10$ and $\frac{m_{2}}{m_{1}}=100$."
 For each model. 500 point source lDight-curves were produced (one per random starfield). each with a length of 60 using the contouring method of Lewis et al. (," For each model, 500 point source light-curves were produced (one per random starfield), each with a length of 60 $_{1M_{\odot}}$ using the contouring method of Lewis et al. ("
1993) and Witt (1993).,1993) and Witt (1993).
 The number of stars in cach mocdoel was determined. from the description of Lewis Lewin (1095) (using the formalism of Ixatz. Balbus Paczenski (1986)).," The number of stars in each model was determined from the description of Lewis Irwin (1995) (using the formalism of Katz, Balbus Paczynski (1986))."
 Table 3. shows the number of stars and the mean magnification for cach model together with the theoretical magnification., Table \ref{tab3} shows the number of stars and the mean magnification for each model together with the theoretical magnification.
 The resulting magnification distributions are shown in Fig. 4.., The resulting magnification distributions are shown in Fig. \ref{magdist}.
 Note that we confirm the finding of Lewis Irwin (1995) that the magnification distribution is independent of mass function., Note that we confirm the finding of Lewis Irwin (1995) that the magnification distribution is independent of mass function.
 Eqn., Eqn.
 S suggests that the structure function has a shape that reflects the microlens mass distribution., \ref{psf} suggests that the structure function has a shape that reflects the microlens mass distribution.
 Small masses produce more rapid. variability anc therefore a faster rise in the structure function at small Ay., Small masses produce more rapid variability and therefore a faster rise in the structure function at small $\Delta y$.
 Larger masses cause the asymptotic behaviour of the structure function at large Ay do slow., Larger masses cause the asymptotic behaviour of the structure function at large $\Delta y$ to slow.
Fig.,Fig.
 5. shows structure functions corresponding to microlens mass functions of the form pxaesescs Psotpeter- Podepih With =100.," \ref{sf} shows structure functions corresponding to microlens mass functions of the form $p_{Ndense}$, $p_{Salpeter}$, $p_{Odepth}$, with $\frac{m_{2}}{m_{1}}=100$."
 These demonstrate the effect of à varving massi function on the structure function. of a microlensed. light-curve. as well as the applicability of Eqn S..," These demonstrate the effect of a varying mass function on the structure function of a microlensed light-curve, as well as the applicability of Eqn \ref{psf}."
 In. cach case 4 curves are shown in the left-hand figure., In each case 4 curves are shown in the left-hand figure.
 The solid light ancl solid. clark lines correspond to structure functions. computed directly. from. models and from Eqn., The solid light and solid dark lines correspond to structure functions computed directly from models and from Eqn.
 S respectively., \ref{psf} respectively.
 For comparison. the structure function corresponding to the single mass microlensing model (psinge) is shown by the dot-dashed line.," For comparison, the structure function corresponding to the single mass microlensing model $p_{Single}$ ) is shown by the dot-dashed line."
 Lig., Fig.
 5. shows that Eqn., \ref{sf} shows that Eqn.
 8 provides a significantly better approximation to the microlensing statistics than Eqn. 12.., \ref{psf} provides a significantly better approximation to the microlensing statistics than Eqn. \ref{sinsf}.
 'To quantify the success of the approximation we have fitted or the three [ree parameters of pl) in Eqn. ὃν.," To quantify the success of the approximation we have fitted for the three free parameters of $p(m)$ in Eqn. \ref{psf},"
 ie. tm Ll," ie. $\langle m \rangle$,"
 and pony) or the index a (For fits corresponding input mass unctions pages. UML Podopb OL Psatpeter respectively)., $\frac{m_{2}}{m_{1}}$ and $p(m_{1})$ or the index $\alpha$ (for fits corresponding input mass functions $p_{Ndense}$ and $p_{Odepth}$ or $p_{Salpeter}$ respectively).
 The input mass weighted number densities (those used to compute the model lisht-curves) are shown as the light ustograms in the right hand panels of Figs. 5.., The input mass weighted number densities (those used to compute the model light-curves) are shown as the light histograms in the right hand panels of Figs. \ref{sf}.
 In each case. he fitted mpm) is overlaved (dark histogram).," In each case, the fitted $mp(m)$ is overlayed (dark histogram)."
 The fitting »ocedure. using Eqn.," The fitting procedure, using Eqn."
 Sis far more successful for mass functions which provide significant fractions of optical depth over a large mass range., \ref{psf} is far more successful for mass functions which provide significant fractions of optical depth over a large mass range.
 This is because the dimensions of the magnification pattern only scale with m (so that very dillerent. masses are needed to clleet the scale of the magnification map). ancl also because (from Eqn. NJ) ," This is because the dimensions of the magnification pattern only scale with $\sqrt{m}$ (so that very different masses are needed to effect the scale of the magnification map), and also because (from Eqn. \ref{psf}) )"
the mass function contributes to the dillerent scales (m) of the caustic network in proportion to the optical depth associated with mass m (ie., the mass function contributes to the different scales $\sqrt{m}$ ) of the caustic network in proportion to the optical depth associated with mass $m$ (ie.
 απ ηλ)., $\kappa(m)dm$ ).
" The input and fitted parameters [or pom) with ""m=10.100 are summarised in Tab. 4.."," The input and fitted parameters for $p(m)$ with $\frac{m_{2}}{m_{1}}=10,100$ are summarised in Tab. \ref{tab4}."
 Fig., Fig.
 r5 shows excellent agreement between the directly calculated. predicted: and fitted structurefunctions in the case Of pasos. Llowever the mass function corresponding to the best fit is not in agreement. with the input mass function.," \ref{sf} shows excellent agreement between the directly calculated, predicted and fitted structurefunctions in the case of $p_{Ndense}$ However the mass function corresponding to the best fit is not in agreement with the input mass function."
The reason is that the mass weighted. number density Lor py.Hon is approximately that of mass function,The reason is that the mass weighted number density for $p_{Ndense}$ is approximately that of mass function
spheroid could not all have been formed. in. the same kind of event. but must. have formed. in. different events which cepend on the past history of the merging galaxies.,"spheroid could not all have been formed in the same kind of event, but must have formed in different events which depend on the past history of the merging galaxies."
 Since merger simulations indicate that violent relaxation is not complete and that the stars manage to remember their initial energv and orbital angular momentum 19058).. it is necessary to take into account the past history of a galaxy.," Since merger simulations indicate that violent relaxation is not complete and that the stars manage to remember their initial energy and orbital angular momentum \citep{ba98}, it is necessary to take into account the past history of a galaxy."
 The main task now is to connect these past histories with the properties of merger remnants., The main task now is to connect these past histories with the properties of merger remnants.
 Large observational studies that collect. data. from several thousands of galaxies. like the Sloan Digital Sky Survey. reveal that the galaxy population follows remarkable trencs: e.g. the surface mass density of galaxies. increases . . ∖∖⋎↓↿↓↕⊔⋯⊳∖⊳∖⊔⊔↿↓↓⋜↧≼↛↓↥⋜⊔⋅⋯∼∩⋅↓⋅↓⊳∖∣⊔⇍⊔↓⋜↧⊳∖⊳∖⊳∖≼∼⋜↧↓∢⋅∪⇀∪≺∣∶⇀∫≻↓∪⊔20. ⋅⊏ Al. at which it becomes constant (Ixaullmannetal.2003).," Large observational studies that collect data from several thousands of galaxies, like the Sloan Digital Sky Survey, reveal that the galaxy population follows remarkable trends: e.g. the surface mass density of galaxies increases with mass until a characteristic mass scale of $M_C=3 \times 10^{10}$ $_{\odot}$ at which it becomes constant \citep{k03}."
. The constant surface mass density is mainly associated with elliptical galaxies and galaxies having significant bulges., The constant surface mass density is mainly associated with elliptical galaxies and galaxies having significant bulges.
 Furthermore. detailed: studies of the size distribution. of elliptical galaxies reveal that the scatter in sizes of elliptical ealaxies of a given mass is log-normal distributed: with a scatter which decreases for larger galaxy masses (Shenetal. 2003).," Furthermore, detailed studies of the size distribution of elliptical galaxies reveal that the scatter in sizes of elliptical galaxies of a given mass is log-normal distributed with a scatter which decreases for larger galaxy masses \citep{sh03}."
. Those authors could. explain the evolution of the sizes by assuming continued mergers of galaxies which had initially all the same mass but. sizes that followed an appropriate distribution., Those authors could explain the evolution of the sizes by assuming continued mergers of galaxies which had initially all the same mass but sizes that followed an appropriate distribution.
 The origin of this distribution however remains unsolved., The origin of this distribution however remains unsolved.
 Another interesting observed: correlation is that the surface. mass clensity of ealaxies in different environments only cillers at low masses (Ixaulfmannetal.2004)., Another interesting observed correlation is that the surface mass density of galaxies in different environments only differs at low masses \citep{k04}.
. In this paper. we address the question of where stars hat end up in spheroids were formed.," In this paper, we address the question of where stars that end up in spheroids were formed."
 The paper is structured as follows: we begin bv explaining the mocel ingredients we use. followed by a section on the past merging ustory of galaxies.," The paper is structured as follows: we begin by explaining the model ingredients we use, followed by a section on the past merging history of galaxies."
 Then we introduce our definition of the wo stellar components found in spheroids and discuss how hese components evolve in the simulated galaxy population., Then we introduce our definition of the two stellar components found in spheroids and discuss how these components evolve in the simulated galaxy population.
 In section five we present our conclusions., In section five we present our conclusions.
 The main strategy behind the modelling approach we follow is first to caleulate the collapse ancl merging history. of individual dark matter halos. which is governed purely. by eravitational interactions. and secondly to calculate. the more complex physies of the barvons inside these dark matter halos. including e.g. radiative cooling of the gas. star formation. and feedback from supernovae by. simplified prescriptions on top of the dark matter evolution.," The main strategy behind the modelling approach we follow is first to calculate the collapse and merging history of individual dark matter halos, which is governed purely by gravitational interactions, and secondly to calculate the more complex physics of the baryons inside these dark matter halos, including e.g. radiative cooling of the gas, star formation, and feedback from supernovae by simplified prescriptions on top of the dark matter evolution."
 Each of the dark matter halos will consist of three main components which are distributed among individual galaxies inside then: a stellar. cold. and hot gas component. where the latter is only attributed toοσα galaxies. which are the most massive galaxies inside individual halos.," Each of the dark matter halos will consist of three main components which are distributed among individual galaxies inside them: a stellar, cold, and hot gas component, where the latter is only attributed to galaxies, which are the most massive galaxies inside individual halos."
 In. the following sections. we will describe brielly the recipes used to calculate these different components which are mainly based on recipes presented in e.g. Colectal.(1994.2000).. etal.(1999). (hereafter. IX99) ancl Springeletal.(2001) (hereafter. SOL). anc we refer readers for more details on model implementations to their work and references therein.," In the following sections, we will describe briefly the recipes used to calculate these different components which are mainly based on recipes presented in e.g. \citet{c94,c00}, \citet{k99} (hereafter, K99) and \citet{spr01} (hereafter, S01), and we refer readers for more details on model implementations to their work and references therein."
" Throughout this paper we use the following set of cosmological parameters: Qy=0.3. ο.»IlE HeX""eIl-—m ay—0.9 and fp=0.65."," Throughout this paper we use the following set of cosmological parameters: $\Omega_0=0.3$, $\Omega_{\Lambda}=0.7$, $\Omega_b/\Omega_0=0.15$, $\sigma_8=0.9$ and $h=0.65$."
 We calculate the merging. history of dark matter halos according to the prescription presented in Somerville&Ixo-(αι (19992)., We calculate the merging history of dark matter halos according to the prescription presented in \citet{som99a}.
.. This approach has been shown to produce merging histories and progenitor distributions in reasonable agreement with results from. N-body simulations of. cold dark matter structure formation in a cosmological context (Somervilleetal.2000)., This approach has been shown to produce merging histories and progenitor distributions in reasonable agreement with results from N-body simulations of cold dark matter structure formation in a cosmological context \citep{som00}.
. The merging history of dark matter halos is reconstructed by breaking cach halo up into progenitors above a limiting minimum progenitor mass Ανν, The merging history of dark matter halos is reconstructed by breaking each halo up into progenitors above a limiting minimum progenitor mass $M_{min}$.
 This mass cut needs to be chosen carefully as it ensures that the right galaxy population ancl merging ustories are produced. within the model., This mass cut needs to be chosen carefully as it ensures that the right galaxy population and merging histories are produced within the model.
" Progenitor halos with masses below Adj, are declared as events and their histories are not followed. further back in time.", Progenitor halos with masses below $M_{min}$ are declared as events and their histories are not followed further back in time.
 'rogenitors labelled as accretion events should. ideally not rost any significant galaxies in them and be composed mainly of primordial hot eas at the progenitor halo's virial emperature., Progenitors labelled as accretion events should ideally not host any significant galaxies in them and be composed mainly of primordial hot gas at the progenitor halo's virial temperature.
 The mass scale at which this is the case can in xinciple be estimated. from the prescriptions of supernova vedback and reionization presented in section ?2?.., The mass scale at which this is the case can in principle be estimated from the prescriptions of supernova feedback and reionization presented in section \ref{cool}.
" Llowever. o achieve à good compromise between accuracy anc computational time. we instead estimated A,,;; by running several simulations with cifferent resolutions and chose the resolution for which results in the galaxy mass range of interest. are. independent. of the specifie choice of ALi."," However, to achieve a good compromise between accuracy and computational time, we instead estimated $M_{min}$ by running several simulations with different resolutions and chose the resolution for which results in the galaxy mass range of interest are independent of the specific choice of $M_{min}$."
 Changing the mass resolution mainly alfects our results a low galaxv mass scales as shown in Fig.l. leaving massive galaxies nearly unallected.," Changing the mass resolution mainly affects our results at low galaxy mass scales as shown in Fig.1, leaving massive galaxies nearly unaffected."
" Throughout this paper we wil use Mui—210° M. which produces numerically stable results for galaxies with stellar masses AJ;10"" ML.", Throughout this paper we will use $M_{min}=2 \times 10^{9}$ $_{\odot}$ which produces numerically stable results for galaxies with stellar masses $M_{*} \geq 10^9$ $_{\odot}$ .
Dark matter accounts for the majority of the mass in the Universe. vet its identitv remains elusive.,"Dark matter accounts for the majority of the mass in the Universe, yet its identity remains elusive."
 Candidates include weakly interacting massive particles (WIAIPs) like the neutralino (4). the supersvyimmietric partner of the neutrino (Pagels&Primack19352). alihough their properties are only loosely constrained by theory. and experiment.," Candidates include weakly interacting massive particles (WIMPs) like the neutralino $\chi$ ), the supersymmetric partner of the neutrino \citep{PagPri82}, although their properties are only loosely constrained by theory and experiment."
 In some cases. plausible values of (he mass and cross section suggest that sell-annihilation signatures may be detectable in regions where the densitv of dark matter is high 2004).," In some cases, plausible values of the mass and cross section suggest that self-annihilation signatures may be detectable in regions where the density of dark matter is high \citep{BerGurZyb92,BerGon96,BerHooSil04}."
. For example. Dergstrón calculate the eamma ray “ax from neutralino sellannibilation in the citep|seealso] ZahlIoo06.. while Tyler(2002) and Dergstiróm&Llooper(2006) provide estimates of the annihilation signal from the nearby Draco dwarf galaxy.," For example, \citet{BerUllBuc98} calculate the gamma ray flux from neutralino self-annihilation in the \\citep[see also][]{ZahHoo06}, while \citet{Tyl02} and \citet{BerHoo06} provide estimates of the annihilation signal from the nearby Draco dwarf galaxy."
 Intermecdiate-mass black holes may vield a WIMP annihilation signal (Bertoneetal. 2005).. as may remnant dark," Intermediate-mass black holes may yield a WIMP annihilation signal \citep{BerZenSil05}, , as may remnant dark"
The discrepancy between the hJuuinous mass and the classical dyvnanuical mass was first identified im clusters of galaxies. the largest virialized svsteuis in the Universe (Zwickv 1933).,"The discrepancy between the luminous mass and the classical dynamical mass was first identified in clusters of galaxies, the largest virialized systems in the Universe (Zwicky 1933)."
 This discrepancy has been only partially alleviated by the subsequent detection of a substantial conrponeut of hot N-ray cutting intrachister eax a conrponeut with a total mass which iav. in rich clusters. exceed the stellar mass in galaxies by a factor of four or five (Jones Forman 1981. David et al.," This discrepancy has been only partially alleviated by the subsequent detection of a substantial component of hot X-ray emitting intracluster gas– a component with a total mass which may, in rich clusters, exceed the stellar mass in galaxies by a factor of four or five (Jones Forman 1984, David et al."
 1990. Bolhrinecr et al.," 1990, Böhhringer et al."
 1993)., 1993).
" Even considering the contribution of this diffuse eas, the mass of detectable matter fails by at least a actor of three more typically a factor of 10. to account for the Newtoman dvuanücal mass of clusters."," Even considering the contribution of this diffuse gas, the mass of detectable matter fails by at least a factor of three– more typically a factor of 10– to account for the Newtonian dynamical mass of clusters."
" The traditional solution to this problem is to postulate the presence of ""useen niatter which is most often assumed to be non-dissipative and nonu-barvonic.", The traditional solution to this problem is to postulate the presence of unseen matter which is most often assumed to be non-dissipative and non-baryonic.
 Another solution lies in the possibility that there is no substautial quantity of dark matter but that Nowtoniai eravity or dvuaiics is uot valid ou the scale of lavee astronomical systems., Another solution lies in the possibility that there is no substantial quantity of dark matter but that Newtonian gravity or dynamics is not valid on the scale of large astronomical systems.
" Of several suggested alternatives to dark matter on extragalactic scales, Mileroii's phenomenologically motivated modified Newtoman dynamics (MOND) is the most) successful ii accounting for the systematics aud details of the discrepancy in galaxies."," Of several suggested alternatives to dark matter on extragalactic scales, Milgrom's phenomenologically motivated modified Newtonian dynamics (MOND) is the most successful in accounting for the systematics and details of the discrepancy in galaxies."
" The basic idea is that. below a critical acceleration. ανz10* ήν, the magnitude of the gravitational acceleration is given by gτναμήν where gu Is the Newtonian eravitational acceleration (AUlerom 1983a)."," The basic idea is that, below a critical acceleration, $a_o\approx 10^{-8}$ $^2$, the magnitude of the gravitational acceleration is given by $g=\sqrt{g_na_o}$ where $g_n$ is the Newtonian gravitational acceleration (Milgrom 1983a)."
" At higher accelerations. y=yg, as usual."," At higher accelerations, $g = g_n$ as usual."
 The low acceleration lit directly iuplies the Iunuimositv-velocity correlations observe’ for galaxies (ZLxci) the Tulh-Fisher relation for spirals and the Faber-Jackson relation for cllipticals as well as predicting that galaxy rotation curves become asvinptotically flat in the limit of large distance from the visible galaxy (Milgroià 19835)., The low acceleration limit directly implies the luminosity-velocity correlations observed for galaxies $L\propto v^4$ )– the Tully-Fisher relation for spirals and the Faber-Jackson relation for ellipticals– as well as predicting that galaxy rotation curves become asymptotically flat in the limit of large distance from the visible galaxy (Milgrom 1983b).
 The success Of he simple MOND prescription iu xedietiugC» the detailed shape of the rotation curves of spiral galaxies frou the observed distribution of detectable matter is well-doctmented (DBegeman et al., The success of the simple MOND prescription in predicting the detailed shape of the rotation curves of spiral galaxies from the observed distribution of detectable matter is well-documented (Begeman et al.
 1991. Sanders 1996. MeCaugh de Blok 1998a. b. Sanders Verbeijeu 1998).," 1991, Sanders 1996, McGaugh de Blok 1998a, b, Sanders Verheijen 1998)."
" But MOND. as a modification of Newtonian gravity or inertia, nius also account for the observed properties of arecr virnalized svstenis which lie iu the low-acceleration ποσο groups ai clusters of galaxies."," But MOND, as a modification of Newtonian gravity or inertia, must also account for the observed properties of larger virialized systems which lie in the low-acceleration regime– groups and clusters of galaxies."
 \Glerom (1998) as recently reconsidered simall groups iu the coutext of MOND and finds that the statistically averaged mass-to-ight ratio in groups is on the order of unity. removing he necessity of dark matter CMileroii 1998).," Milgrom (1998) has recently reconsidered small groups in the context of MOND and finds that the statistically averaged mass-to-light ratio in groups is on the order of unity, removing the necessity of dark matter (Milgrom 1998)."
 [previously considered 200 Nav enüttiug clusters (Saucers 1991. Paper 1). and found that. for these objects. the mass medicicted by. MOND from the observed temperature of he hot gas is consistent with the inferred mass of hot eas.," I previously considered 20 X-ray emitting clusters (Sanders 1994, Paper 1), and found that, for these objects, the mass predicted by MOND from the observed temperature of the hot gas is consistent with the inferred mass of hot gas."
" Moreover. MOND predicts the observed gas nasscluperature relation for clusters (M,κ T?) which is. in effect. the high mass continuation of the Eaber-Jacksou relation for elliptical galaxies."," Moreover, MOND predicts the observed gas mass-temperature relation for clusters $M_g\propto T^2$ ) which is, in effect, the high mass continuation of the Faber-Jackson relation for elliptical galaxies."
 This originalOo sample of N-rav cuttingC» clusters was roni the early analysis of satellite data by Joues Forman (1981) with temperature determinations by David et al. (, This original sample of X-ray emitting clusters was from the early analysis of satellite data by Jones Forman (1984) with temperature determinations by David et al. (
1993).,1993).
 Beceutlv. data for a much arecr sample of 207 clusters has been compiled by White. Jones Forman (1997) who are interested primarily in he properties of clusters with cooling flows.," Recently, data for a much larger sample of 207 clusters has been compiled by White, Jones Forman (1997) who are interested primarily in the properties of clusters with cooling flows."
 The purpose of the preseut note is to consider this larecr sample iu he context of MOND., The purpose of the present note is to consider this larger sample in the context of MOND.
 I deinoustrate below that. with," I demonstrate below that, with"
redshilt-argument or xX-subscript in the rest of the paper. this should be regarded as referring to a single redshift plane.,"redshift-argument or $\infty$ -subscript in the rest of the paper, this should be regarded as referring to a single redshift plane."
 Assuming that we can unambiguously distinguish the cluster galaxies from the population of background galaxies. we calculated the average image ellipticity € for the latter on a 30« erid using a Gaussian smoothing procedure with variable smoothing length in order to account for the varving strength. of the distortion ellects.," Assuming that we can unambiguously distinguish the cluster galaxies from the population of background galaxies, we calculated the average image ellipticity $\overline\epsilon$ for the latter on a $30\times 30$ grid using a Gaussian smoothing procedure with variable smoothing length in order to account for the varying strength of the distortion effects."
 For simplicity. this smoothing length was adjusted linearly [rom 072 at the cluster centre to 1/70 at the boundary of the field of view. although in principle objective strategies could be developed [or its optimal choice.," For simplicity, this smoothing length was adjusted linearly from $0\farcm2$ at the cluster centre to $1\farcm0$ at the boundary of the field of view, although in principle objective strategies could be developed for its optimal choice."
 refeluster displavs πο gridded distortion pattern determined in this way. as well as the reconstruction of the cluster surface mass density calculated [rom it by applying the non-linear finite-field inversion method described in Seitz Schneider (1996). and taking into account the redshift distribution of the sources as explained in Seitz Schneider (1997).," \\ref{cluster} displays the gridded distortion pattern determined in this way, as well as the reconstruction of the cluster surface mass density calculated from it by applying the non-linear finite-field inversion method described in Seitz Schneider (1996), and taking into account the redshift distribution of the sources as explained in Seitz Schneider (1997)."
 Llere we assumed the true redshift distribution to be, Here we assumed the true redshift distribution to be
A key ingredient of the analysis of bulge profiles. overlooked in the HS7-based studies of bulges cited above. is the modeling of the extended bulge and disk light distributions when fitting analytic functions to the bulge light.,"A key ingredient of the analysis of bulge profiles, overlooked in the -based studies of bulges cited above, is the modeling of the extended bulge and disk light distributions when fitting analytic functions to the bulge light."
 Here. composite profiles linkingHST profiles with ground-based K-band profiles are used so that bulge-disk decompositions can be performed.," Here, composite profiles linking profiles with ground-based $K$ -band profiles are used so that bulge-disk decompositions can be performed."
 We assume a Hubble constant of Hy=75 .MMpe!., We assume a Hubble constant of $H_{0} = 75$ $^{-1}$.
 We work with a subset of the BP94 diameter-limited sample of inclined. early-to-intermediate type disk galaxies classified as unbarred in the UGC (Nilson 1973): see Paper | and references therein.," We work with a subset of the BP94 diameter-limited sample of inclined, early-to-intermediate type disk galaxies classified as unbarred in the UGC (Nilson 1973); see Paper I and references therein."
 None has a Seyfert or starburst nucleus., None has a Seyfert or starburst nucleus.
 Ground-based surface brightness profiles in the K-band for the BP94 sample. derived from ellipse fits to UKIRT/IRCAM3 images. are given in Peletier Balcells (1997). while two-dimensional bulge-disk decomposition and Sérrsic fits to the K-band bulge profiles are published in APB95.," Ground-based surface brightness profiles in the $K$ -band for the BP94 sample, derived from ellipse fits to UKIRT/IRCAM3 images, are given in Peletier Balcells (1997), while two-dimensional bulge-disk decomposition and Sérrsic fits to the $K$ -band bulge profiles are published in APB95."
" The subsample studied here comprises 19 galaxies of types SO to Sbe that were imaged with NICMOS onHST (camera 2. ος19""., 0.075 aresec/pixel)."," The subsample studied here comprises 19 galaxies of types S0 to Sbc that were imaged with NICMOS on (camera 2, $\times$, 0.075 arcsec/pixel)."
 Data reduction is described in Paper I. while details of the data analysis are given in. Paper III.," Data reduction is described in Paper I, while details of the data analysis are given in Paper III."
" We derive elliptically-averaged surface brightness profiles and isophotal shapes. from 0.075""to typically10"".. using the package Jorgensen et 11992)."," We derive elliptically-averaged surface brightness profiles and isophotal shapes, from to typically, using the package rgensen et 1992)."
 We keep the centers fixed and allow the ellipticity and position angles of the isophotes to vary., We keep the centers fixed and allow the ellipticity and position angles of the isophotes to vary.
 Linking the HS7-FI60W and ground-based K profiles is done following Paper I. with details given in Paper IH.," Linking the -F160W and ground-based $K$ profiles is done following Paper I, with details given in Paper III."
 The combinedZST plus ground-based profiles. corrected for foreground Galactic. extinction. (Schlegel et 11998). (142) cosmological dimming and K-correction. were fitted with a PSF-convolved. Sérrsic-plus-exponential model using the code from Graham (2001) modified to use a Moffat PSFjo. ft bul gei. Rz).," The combined plus ground-based profiles, corrected for foreground Galactic extinction (Schlegel et 1998), $(1+z)^4$ cosmological dimming and $K$ -correction, were fitted with a PSF-convolved Sérrsic-plus-exponential model using the code from Graham (2001) modified to use a Moffat PSF, h; bulge $\mu_{e},
R_{e}, n$ )."
 Each fit was individually inspected., Each fit was individually inspected.
 When an obvious local minimum was found. the code was run agam with new initial. conditions; when the apparent global minimum was found. the code was also again run with different initial conditions to. provide confirmation.," When an obvious local minimum was found, the code was run again with new initial conditions; when the apparent global minimum was found, the code was also again run with different initial conditions to provide confirmation."
 The final fits for every galaxy are shown in Paper III., The final fits for every galaxy are shown in Paper III.
" Such Sérrsic-exponential bulge-disk fits. covering the entire radial range down to0.075"".. tend to show strong residuals. up to 0.3mag. over the entire bulge."," Such Sérrsic-exponential bulge-disk fits, covering the entire radial range down to, tend to show strong residuals, up to 0.3mag, over the entire bulge."
 A typical example is shown in Figure laa. The residual profile shows a characteristic wave pattern., A typical example is shown in Figure \ref{Fig:ExampleProfile}a a. The residual profile shows a characteristic wave pattern.
 This is caused by a strong central light excess. as inferred from fits excluding the central 1-2 aresec.," This is caused by a strong central light excess, as inferred from fits excluding the central 1-2 arcsec."
 We then run the fitting code including either an additional central delta function point source (PS); a central exponential: a point source plus an exponential: or a central Gaussian component with free FWHM to the fitting function., We then run the fitting code including either an additional central delta function point source (PS); a central exponential; a point source plus an exponential; or a central Gaussian component with free FWHM to the fitting function.
 In all cases each component is PSF-convolved before fitting., In all cases each component is PSF-convolved before fitting.
 For each galaxy we select the simplest fit. i.e. minimum number of components. for which the residual profile falls below an amplitude of 0.1 ," For each galaxy we select the simplest fit, i.e. minimum number of components, for which the residual profile falls below an amplitude of 0.1 $^2$."
mag/aresee)-. Figure [bb shows the profile from Figure laa fitted with an additional central PS. which yields an excellent fit.," Figure \ref{Fig:ExampleProfile}b b shows the profile from Figure \ref{Fig:ExampleProfile}a a fitted with an additional central PS, which yields an excellent fit."
" The total light in the inner 1-2"" can also be approximated with power laws (Balcells et 22001: Bókker et al."," The total light in the inner 1-2"" can also be approximated with power laws (Balcells et 2001; Bökker et al."
 2002)., 2002).
 The Nuker model also fits the inner few arcsec of the early-type galaxy profiles well (Byun et 11996)., The Nuker model also fits the inner few arcsec of the early-type galaxy profiles well (Byun et 1996).
 However. these approaches break down further out (e.g. Lauer et 11995). do not allow a bulge-disk decomposition. and are not discussed further here.," However, these approaches break down further out (e.g. Lauer et 1995), do not allow a bulge-disk decomposition, and are not discussed further here."
 Our fits extend over 2.5 decades in radius. and deseribe both bulge and disk.," Our fits extend over 2.5 decades in radius, and describe both bulge and disk."
 Of the 19 galaxies. 12 yield a satisfactory fit with the addition of a single PS. 2 with the addition of a single nuclear exponential. 4 with a PS plus an exponential. and one with a pure Sérrsic bulge.," Of the 19 galaxies, 12 yield a satisfactory fit with the addition of a single PS, 2 with the addition of a single nuclear exponential, 4 with a PS plus an exponential, and one with a pure Sérrsic bulge."
 The frequency of PS is thus 84+8%.. and that of inner exponentials is 32+11%.," The frequency of PS is thus $84 \pm 8$, and that of inner exponentials is $32 \pm 11$."
. Only one galaxy (NGC 5577. Sbe) does not require an unresolved source and can be fit with a simple Sérrsic bulge plus exponential disk: however. the profile for this galaxy has lower S/N than the others owing to its lower surface brightness.," Only one galaxy (NGC 5577, Sbc) does not require an unresolved source and can be fit with a simple Sérrsic bulge plus exponential disk; however, the profile for this galaxy has lower S/N than the others owing to its lower surface brightness."
 Most galaxies with PSs yield a good fit with a Gaussian inner component instead; in those cases. the FWHM of the inner Gaussian. before PSF convolution. is generally well below the PSF FWHM. recovering the PS solution.," Most galaxies with PSs yield a good fit with a Gaussian inner component instead; in those cases, the FWHM of the inner Gaussian, before PSF convolution, is generally well below the PSF FWHM, recovering the PS solution."
 Some galaxies with inner exponential components also admit a good fit with a marginally resolved Gaussian instead., Some galaxies with inner exponential components also admit a good fit with a marginally resolved Gaussian instead.
 Because these galaxies show high ellipticity and pointy isophotes in the nuclear region. we choose the PS-plus-exponential fit instead of the Gaussian inner component.," Because these galaxies show high ellipticity and pointy isophotes in the nuclear region, we choose the PS-plus-exponential fit instead of the Gaussian inner component."
 Nuclear isophotes are described in Paper III., Nuclear isophotes are described in Paper III.
 The Sérrsic index Που the bulges ranges from 0.5 to 3.0. with a mean of <n>= 1.7+0.7.," The Sérrsic index for the bulges ranges from 0.5 to 3.0, with a mean of $<$ $> = 1.7 \pm 0.7$ ."
" The range is significantly lower than that obtainec by ΑΡΒΟΣ using ground-based data alone. which reaches 71=6: Figure Ibb shows that lis systematically lower than,,.. especially for galaxies with Ha,2 3."," The range is significantly lower than that obtained by APB95 using ground-based data alone, which reaches $n=6$: Figure \ref{Fig:NvsTvsBDvsMKdeJ}b b shows that is systematically lower than, especially for galaxies with $n_{gb}>3$ ."
 None of our bulges reaches the de Vaucouleurs bbehaviour., None of our bulges reaches the de Vaucouleurs behaviour.
 It appears that fits to ground-based profiles reach Sérrsic indices n74 because the light from HST- central sources. plus in some instances nuclear disks or bars. when convolved with typical ground-based seeing. link smoothly with the the extended bulge profile and mimic n Sérrsic profiles.," It appears that fits to ground-based profiles reach Sérrsic indices $n\geq 4$ because the light from }-unresolved central sources, plus in some instances nuclear disks or bars, when convolved with typical ground-based seeing, link smoothly with the the extended bulge profile and mimic $n$ Sérrsic profiles."
 Figures 1cc.d plot the distribution of tthe bulge-to-disk luminosity ratio (B/D) and bulge K- absolute magnitude. respectively.," Figures \ref{Fig:NvsTvsBDvsMKdeJ}c c,d plot the distribution of the bulge-to-disk luminosity ratio (B/D) and bulge $K$ -band absolute magnitude, respectively."
 B/D are derived from the best-fit parameters., B/D are derived from the best-fit parameters.
 Bulge absolute magnitudes are derived from the galaxy K-band magnitude given in APB95 and our computed B/D. As noted by APB9S. some of the galaxy magnitudes are probably slightly underestimated when the galaxy overtills the frame.," Bulge absolute magnitudes are derived from the galaxy $K$ -band magnitude given in APB95 and our computed B/D. As noted by APB95, some of the galaxy magnitudes are probably slightly underestimated when the galaxy overfills the frame."
 Figures Ice.d show that logGij4 correlates with log(B/D) and with the bulge absolute K-band magnitude (Spearman rank-order correlation coefficients -0.52 and -O.51. significances and 97.4%.. respectively).," Figures \ref{Fig:NvsTvsBDvsMKdeJ}c c,d show that ) correlates with log(B/D) and with the bulge absolute $K$ -band magnitude (Spearman rank-order correlation coefficients -0.52 and -0.51, significances and , respectively)."
 Thus. the correlation of Sérrsic index #with B/D and bulge luminosity," Thus, the correlation of Sérrsic index $n$with B/D and bulge luminosity"
rest of the shell. with some material near the axis IHlowing back towards the rear of the cloud. (seealsoNittmann.Falle&Gaskell1982:Tenorio-lagleRozvezka 1984a).,"rest of the shell, with some material near the axis flowing back towards the rear of the cloud \citep*[see
 also][]{Nittmann:1982,Tenorio-Tagle:1984a}."
. This material is subseequentIy: compressed. against the axis bv the hot. subsonic Low which overtakes it.," This material is subsequently compressed against the axis by the hot, subsonic flow which overtakes it."
 Phe pressure &eracient across the face of the shell diminishes as the shell moves Further downstream. and the focusing becomes more &eraciual.," The pressure gradient across the face of the shell diminishes as the shell moves further downstream, and the focusing becomes more gradual."
 A 3D simulation of this interaction reveals the same features (see Fig. 4)).," A 3D simulation of this interaction reveals the same features (see Fig. \ref{fig:3d}) ),"
 indicating that this is a robust result which is not dependent on the assumed. axisvometry., indicating that this is a robust result which is not dependent on the assumed axisymmetry.
 The high shear around the cloud causes a turbulent. boundary laver at the edge of the tail which grows with an opening angle of =3.4°., The high shear around the cloud causes a turbulent boundary layer at the edge of the tail which grows with an opening angle of $\approx3-4^{\circ}$.
" The interior parts of the tail also contain some turbulence. though the central part of the cloud has none,"," The interior parts of the tail also contain some turbulence, though the central part of the cloud has none."
 ‘The tails in these models exhibit a large leneth-to-width ratio which can reach nearly 50:1 at late times (/= 2.1/4).," The tails in these models exhibit a large length-to-width ratio which can reach nearly 50:1 at late times $t = 2.1\,t_{\rm cc}$ )."
 Fig., Fig.
 5 shows the velocity. profile along the symmetry. axis through the core of the tail at /=0.806foo for the interaction shown in Fig. 2..," \ref{fig:vel_profile} shows the velocity profile along the symmetry axis through the core of the tail at $t = 0.806\,t_{\rm cc}$ for the interaction shown in Fig. \ref{fig:rz12}."
" Phe acceleration is approximately constant along the tail. with the velocity. reaching =10kms (AL,= OS) at z=IOr.."," The acceleration is approximately constant along the tail, with the velocity reaching $\approx 10\,\kmps$ $M_{\rm a} = 0.8$ ) at $z
= 10\,r_{\rm c}$."
 Due to the lack of material being stripped olf the cloud. the tail eventually clissipates as it thins and then detaches from the cloud (by f~ 344).," Due to the lack of material being stripped off the cloud, the tail eventually dissipates as it thins and then detaches from the cloud (by $t \sim 3\,t_{\rm cc}$ )."
 The axial velocity. profile perpendicular to the tail shows a near Constant speed at a given downstream: position. which indicates cllicient momentum transfer across the tail.," The axial velocity profile perpendicular to the tail shows a near constant speed at a given downstream position, which indicates efficient momentum transfer across the tail."
 We have performed. a series. of models. designed to explore parameter space to determine the conditions necessary for tail production (see Fig. 6))., We have performed a series of models designed to explore parameter space to determine the conditions necessary for tail production (see Fig. \ref{fig:various}) ).
 Decreasing the thickness of the shell (ie. σ.µ/σοι) Heads to a thinner tail (lig., Decreasing the thickness of the shell (i.e. $\sigma_{\rm sh}/\sigma_{\rm cl}$ ) leads to a thinner tail (Fig.
 6aa)., \ref{fig:various}a a).
 Increasing the thickness of the shell enhances the stripping of material from the eloud. which causes oscillations in the tail width (Pies.," Increasing the thickness of the shell enhances the stripping of material from the cloud, which causes oscillations in the tail width (Figs."
 6bb and c)., \ref{fig:various}b b and c).
 Interactions at higher Mach number enhance the growth of instabilities in the shear laver surrounding the tail (Eig., Interactions at higher Mach number enhance the growth of instabilities in the shear layer surrounding the tail (Fig.
 6dd)., \ref{fig:various}d d).
 A model with a lower cloud density contrast (4=125 instead of 107) still produces a tail (Figs., A model with a lower cloud density contrast $\chi=125$ instead of $10^{3}$ ) still produces a tail (Figs.
 6ec-g)., \ref{fig:various}e e-g).
 Tails still form. behind clouds with smoother density. profiles and when the shell is curved (not shown), Tails still form behind clouds with smoother density profiles and when the shell is curved (not shown).
 The crushing of clouds by isothermal shells has been investigated only a few times in the literature (Tenorio-Tagleal.2009).," The crushing of clouds by isothermal shells has been investigated only a few times in the literature \citep{Tenorio-Tagle:1984b,Rozyczka:1987,Leao:2009}."
. While these works have demonstrated that a tail composed of shell material can form in an interaction with a cloud. the shell. and consequently the focussed tail. is always much thinner than the cloud radius.," While these works have demonstrated that a tail composed of shell material can form in an interaction with a cloud, the shell, and consequently the focussed tail, is always much thinner than the cloud radius."
 Furthermore. some of the tails are short-Hived while others are soon dominated by ablatecd material.," Furthermore, some of the tails are short-lived while others are soon dominated by ablated material."
 In contrast. we emphasize that the models presented here have long-lived tails of thickness comparable to the size of the cloud.," In contrast, we emphasize that the models presented here have long-lived tails of thickness comparable to the size of the cloud."
 Cometary taiklike structures. formed. behind. dense molecular clouds. are seen in many PNe.," Cometary tail-like structures, formed behind dense molecular clouds, are seen in many PNe."
 The best. studied are those of the highly evolved. PNe 77293 (the Llelix Nebula)., The best studied are those of the highly evolved PNe 7293 (the Helix Nebula).
 The clouds. are ionized on the parts of their surfaces exposed to the ionizing Dux from the central star. and the tails point racially away from it.," The clouds are ionized on the parts of their surfaces exposed to the ionizing flux from the central star, and the tails point radially away from it."
 The tails often contain molecular material (Alatsuuractal.2009.6.," The tails often contain molecular material \citep[e.g.,]{Matsuura:2009}."
$..).. Two different models have been proposed. to explain the tails., Two different models have been proposed to explain the tails.
" In ""shadow"" models the tail forms due to the shielding of the direct ionizing radiation field of the central star (e.g..Lopez-Alartinetal.2001:O'Dell 2005)."," In “shadow” models the tail forms due to the shielding of the direct ionizing radiation field of the central star \citep[e.g.,][]{Lopez-Martin:2001,ODell:2005}."
. In contrast. κο models assume that the tail forms [rom material photoahblated from the cloud (Dyson.Llartquist&al. 2006).," In contrast, “stream-source” models assume that the tail forms from material photoablated from the cloud \citep*{Dyson:1993,Falle:2002,Pittard:2005,Dyson:2006}."
. The correct. model is still. disputed (e.g...Dysoneal.2006:O'Dell.Lenney&Ferland|007 ).," The correct model is still disputed \citep*[e.g.,][]{Dyson:2006,ODell:2007}."
. llowever. observations of the dynamics of the tails favour stream-source models: i) there is no evidence for significant ionizec eas velocities perpendicular to the tails 1998).. in contrast to the shadow mocel of López-al. (2001): ii) the How accelerates along the tails (bvabou 2010).," However, observations of the dynamics of the tails favour stream-source models: i) there is no evidence for significant ionized gas velocities perpendicular to the tails \citep{Meaburn:1998}, in contrast to the shadow model of \citet{Lopez-Martin:2001}; ii) the flow accelerates along the tails \citep[by about $8-14\,\kmps$, see][]{Meaburn:2010}."
. While our models are not specifically of the 1ος tails. the velocity increase along the tail is similar to the observations. which are suggestive ofa linear velocity πμ private communication)," While our models are not specifically of the Helix tails, the velocity increase along the tail is similar to the observations, which are suggestive of a linear velocity gradient (Meaburn, private communication)."
potential to open a new frontier in constraints on local dynamics.,potential to open a new frontier in constraints on local dynamics.
 We may hope this frontier will be opened far more widely by new advances in the optical (the GAIA Science Mission) and VLBI (Reid et al., We may hope this frontier will be opened far more widely by new advances in the optical (the GAIA Science Mission) and VLBI (Reid et al.
 2009b)., 2009b).
 A group of ten LG galaxies emanate from high redshift along similar paths., A group of ten LG galaxies emanate from high redshift along similar paths.
" This is seen in Figures 3 to 5,, and it is illustrated in another way in Figure 7,, which shows physical positions at the starting time of the computation, at expansion factor 14-z;=10."," This is seen in Figures \ref{Fig:3} to \ref{Fig:5}, and it is illustrated in another way in Figure \ref{Fig:7}, which shows physical positions at the starting time of the computation, at expansion factor $1+z_i=10$."
" The external actors are not shown in this figure, the initial positions of MW and M31 are plotted in red, and the LG galaxies not in the group of ten are shown as filled circles."," The external actors are not shown in this figure, the initial positions of MW and M31 are plotted in red, and the LG galaxies not in the group of ten are shown as filled circles."
" The ten with similar initial positions, shown as filled squares, are in order of increasing present distance from MW the galaxies NGC 6822, NGC 185, NGC 147, Leo A, Andromeda XIV, Cassiopeia dwarf spheroidal, Pegasis dwarf, UGC 4879, and Sextans A and B. One might include a more distant eleventh member of the group, Andromeda XII."," The ten with similar initial positions, shown as filled squares, are in order of increasing present distance from MW the galaxies NGC 6822, NGC 185, NGC 147, Leo A, Andromeda XIV, Cassiopeia dwarf spheroidal, Pegasis dwarf, UGC 4879, and Sextans A and B. One might include a more distant eleventh member of the group, Andromeda XII."
" It is plotted as the filled circle at largest SGX and SGY in Figure 7,, and has the label 17 in Figs."," It is plotted as the filled circle at largest SGX and SGY in Figure \ref{Fig:7}, and has the label 17 in Figs."
 3 to 5.., \ref{Fig:3} to \ref{Fig:5}.
" The initial positions of the inner ten are in a band of physical length 400 kpc that is close to perpendicularto the supergalactic plane, and centered at SGL ~70°, SGB~0."," The initial positions of the inner ten are in a band of physical length $\sim 400$ kpc that is close to perpendicularto the supergalactic plane, and centered at SGL $\sim 70^\circ$, $\sim0$."
 The narrow dimension is less than 75 kpc., The narrow dimension is less than $75$ kpc.
 If this distinct early concentration had been a little tighter the group could have merged into a protogalaxy., If this distinct early concentration had been a little tighter the group could have merged into a protogalaxy.
" It might prove interesting to check whether these ten parts of a possible failed protogalaxy have more in common among themselves than among the other low mass LG members, perhaps in the mass fraction or the distributions of metallicity or"," It might prove interesting to check whether these ten parts of a possible failed protogalaxy have more in common among themselves than among the other low mass LG members, perhaps in the mass fraction or the distributions of metallicity or"
superclusters).,superclusters).
 We also give morphological descriptions of superclusters and notes., We also give morphological descriptions of superclusters and notes.
 Table 4 shows that superclusters with a smaller number of galaxies also contain. as expected. a smaller number of rich groups and Abell clusters.," Table \ref{tab:sclothermorf} shows that superclusters with a smaller number of galaxies also contain, as expected, a smaller number of rich groups and Abell clusters."
 Among them less elongated superclusters dominate over more elongated superclusters there are 16 systems from set 2 and 10 from set | among them., Among them less elongated superclusters dominate over more elongated superclusters -- there are 16 systems from set 2 and 10 from set 1 among them.
 The morphology of 14 of them can be deseribed as simple spider or simple filament. and 12 of them are either multispiders or multibranching filaments.," The morphology of 14 of them can be described as simple spider or simple filament, and 12 of them are either multispiders or multibranching filaments."
 In contrast. of 10 superclusters with at least 950 member galaxies 7 can be described as multispiders of multibranching filaments. two of them are simple spiders and one is a simple filament.," In contrast, of 10 superclusters with at least 950 member galaxies 7 can be described as multispiders of multibranching filaments, two of them are simple spiders and one is a simple filament."
 The main selection effect in our study comes from the use of the flux-limited sample of galaxies to determine the luminosity density field and superclusters., The main selection effect in our study comes from the use of the flux-limited sample of galaxies to determine the luminosity density field and superclusters.
 To keep the luminosity-dependent selection effects as small as possible. we used data on galaxies and galaxy systems for a distance interval 90—32041 Mpc.," To keep the luminosity-dependent selection effects as small as possible, we used data on galaxies and galaxy systems for a distance interval 90--320 ."
. In this interval these effects are the smallest (we refer to T10 for details)., In this interval these effects are the smallest (we refer to T10 for details).
 We calculate Minkowski functionals οἱ individual superclusters from volume limited samples., We calculate Minkowski functionals of individual superclusters from volume limited samples.
 This approach makes the calculations of morphology insensitive to luminosity dependent selection effects., This approach makes the calculations of morphology insensitive to luminosity dependent selection effects.
 Another selection. effect comes from the choice of the density level used to determine superclusters., Another selection effect comes from the choice of the density level used to determine superclusters.
 At the density, At the density
where gc;deo. is the volume occupied by the radiating particles.,where $\eta_G R_{LC}^3$ is the volume occupied by the radiating particles.
" Replacing B with a dipole field Ds*(Ray/R)* at the light evlinder 2=Rye. it follows that NEL where f)2B.απEuRS.NS""*01 js. (he pulsar spin-down. power."," Replacing $B$ with a dipole field $B_{NS} * (R_{NS}/R)^3 $ at the light cylinder $R=R_{LC}$, it follows that L_c _G _G where $\dot{E}_{SD} \approx { B_{NS}^2 R_{NS}^6 \Omega^4 \over 2 \pi c^3} $, is the pulsar spin-down power."
 Thus.power. L.x Esp.," Thus, $L_c \propto \dot{E}_{SD} $ ."
" This differs from the commonly used L,xvEsp scaling. which results if the maximum particle energy is not limited by radiation reaction but by the electric potential and most of (he energy is radiated away once the particle is outside of the accelerating region."," This differs from the commonly used $L_c \propto \sqrt{ \dot{E}_{SD}} $ scaling, which results if the maximum particle energy is not limited by radiation reaction but by the electric potential and most of the energy is radiated away once the particle is outside of the accelerating region."
 This is the case in polar cap models., This is the case in polar cap models.
 In these models a beam with a particle density. equal to the Goldreich-Julian densitw loses energy NxorbexvEsp (seeο.Zhang&lIlarding2000).. where rpe is the radius of the polar cap.," In these models a beam with a particle density equal to the Goldreich-Julian density loses energy $\dot{N} \propto n_{GJ} r_{PC}^2 \propto \sqrt{\dot{E}_{SD}}$ \citep[see \eg][]{2000ApJ...532.1150Z}, where $ r_{PC} $ is the radius of the polar cap."
 The same square-root scaling has been extended (o outer gaps. assuming that (he emitting volume is proportional to the volume within the light evlinder radius (Ilirotanietal.2003)..," The same square-root scaling has been extended to outer gaps, assuming that the emitting volume is proportional to the volume within the light cylinder radius \citep{2003ApJ...591..334H}."
 The expected linear proportionality (5)) of (he οταν Iuminosity is valid in the radiation reaction limit. if the dominant radiation processes depend on the particle energy.," The expected linear proportionality \ref{11}) ) of the $\gamma$ -ray luminosity is valid in the radiation reaction limit, if the dominant radiation processes depend on the particle energy."
 This is (he case. for exaniple. lor curvature radiation or inverse-Compton (IC) scattering in the Thompson regime.," This is the case, for example, for curvature radiation or inverse-Compton (IC) scattering in the Thompson regime."
 And it is not the case for IC scattering in the Ixlein-Nishina regime. where (he radiative losses are independent of the particle energy. (see Eq. 6)).," And it is not the case for IC scattering in the Klein-Nishina regime, where the radiative losses are independent of the particle energy (see Eq. \ref{gKN}) ),"
 and. therefore. the acceleration is not limited by radiation losses.," and, therefore, the acceleration is not limited by radiation losses."
 ILowever. as we argued in 83.. there are good reasons to believe that particle acceleration is indeed. limited by radiation reaction.," However, as we argued in \ref{IC}, there are good reasons to believe that particle acceleration is indeed limited by radiation reaction."
 We note that testing our prediction is complicated bv the laree uncertainty of the geometrical parameter ης. the effective emission volume. which depends on the pulsar inclination angle. (he angle between the rotation axis. ancl the line of sight.," We note that testing our prediction is complicated by the large uncertainty of the geometrical parameter $\eta_G$, the effective emission volume, which depends on the pulsar inclination angle, the angle between the rotation axis, and the line of sight."
 It may also depend on the period of the pulsar through the microphivsies of the acceleration., It may also depend on the period of the pulsar through the microphysics of the acceleration.
Array ()) and in the 843 MHz Molonglo Galactic Plane Survey (MGPS: ).,Array \cite{esg01}) ) and in the 843 MHz Molonglo Galactic Plane Survey (MGPS; \cite{gcl98}) ).
 Although these observations are all of poorer sensitivity than the data presented here. the presence and morphology of this source ts clearly apparent in all three sets.," Although these observations are all of poorer sensitivity than the data presented here, the presence and morphology of this source is clearly apparent in all three data-sets."
 In future discussion. we refer to this source as1.. corresponding to the position of its approximate center of curvature.," In future discussion, we refer to this source as, corresponding to the position of its approximate center of curvature."
 An examination of the GGalaxy Atlas () shows no counterpart to aat wavelengths of 60 sm| or 100 j/m. nor in a map of the ratio 60 i my100 μπι. We also have found no X-ray emission from this source in archival oor ddata.," An examination of the Galaxy Atlas \cite{ctpb97}) ) shows no counterpart to at wavelengths of 60 $\mu$ m or 100 $\mu$ m, nor in a map of the ratio 60 $\mu$ m/100 $\mu$ m. We also have found no X-ray emission from this source in archival or data."
 We have searched for radio emission from itself by making a 1.4 GHz image using only data from the higher-resolution CnB array., We have searched for radio emission from itself by making a 1.4 GHz image using only data from the higher-resolution CnB array.
 No emission ts seen at the position of iin this image down to 10a 5a upper limit of 3 mJy., No emission is seen at the position of in this image down to a $5\sigma$ upper limit of 3 mJy.
 We have determined approximate spectral indices for the emission seen in Fig ??. by comparing our 1.4 GHz image to a 843 MHz MGPS image of the same region ())., We have determined approximate spectral indices for the emission seen in Fig \ref{fig_rxj} by comparing our 1.4 GHz image to a 843 MHz MGPS image of the same region \cite{gcl98}) ).
 In order to make a proper comparison of the images. we first applied to the 843 MHz data the mosaicing pattern. primary beam attenuation and 4—v coverage of the 1.4 GHz VLA observations so às to produce two data-sets which were identical except in their brightness distributions.," In order to make a proper comparison of the images, we first applied to the 843 MHz data the mosaicing pattern, primary beam attenuation and $u-v$ coverage of the 1.4 GHz VLA observations so as to produce two data-sets which were identical except in their brightness distributions."
 We then applied to this spatially-filtered 843 MHz data the same deconvolution process as was required to produce the 1.4 GHz image shown in Fig ??.., We then applied to this spatially-filtered 843 MHz data the same deconvolution process as was required to produce the 1.4 GHz image shown in Fig \ref{fig_rxj}.
" Images at both frequencies were then smoothed to a resolution of G0""«60"". and compared using the technique of spectral tomography. whereby scaled versions of the 843-MHz image are subtracted from the 1.4-GHz image. and the scaling factor for which a given feature merges into the background is used to compute that feature's spectral index ())."," Images at both frequencies were then smoothed to a resolution of $60'' \times 60''$, and compared using the technique of spectral tomography, whereby scaled versions of the 843-MHz image are subtracted from the 1.4-GHz image, and the scaling factor for which a given feature merges into the background is used to compute that feature's spectral index \cite{kr97}) )."
 An accurate spectral index for us difficult to determine because it is so faint and diffuse., An accurate spectral index for is difficult to determine because it is so faint and diffuse.
" However. for the brightest region along its extent. we estimate a spectral index a2—0.4+0.2 (where S,x 17)."," However, for the brightest region along its extent, we estimate a spectral index $\alpha = -0.4\pm0.2$ (where $S_\nu \propto \nu^\alpha$ )."
 Of the other main sources seen in Fig ??.. we find that SNR G346.6-0.2 has a spectral index à2—0.630.1. in good agreement with the value a2—0.5 tabulated by Green (2000)) in his SNR catalog.," Of the other main sources seen in Fig \ref{fig_rxj}, we find that SNR G346.6–0.2 has a spectral index $\alpha = -0.6\pm0.1$, in good agreement with the value $\alpha = -0.5$ tabulated by Green \nocite{gre00}) ) in his SNR catalog."
 G346.52+0.08 and IRAS 17056-4004 both have relative flat spectra (—0.15+0.1 and —0.1+0.1 respectively). consistent with their interpretations as thermal sources.," G346.52+0.08 and IRAS 17056–4004 both have relative flat spectra $-0.15\pm0.1$ and $-0.1\pm0.1$ respectively), consistent with their interpretations as thermal sources."
 G346.47240.053 has a steeper spectrum. a=—0.9 0.1. indicating that it is probably a background radio galaxy.," G346.472+0.053 has a steeper spectrum, $\alpha = -0.9\pm0.1$ , indicating that it is probably a background radio galaxy."
 The CGPS image of the region surrounding ts shown in Fig ??:: no extended structure can be seen anywhere near the position of the AXP., The CGPS image of the region surrounding is shown in Fig \ref{fig_4u}; no extended structure can be seen anywhere near the position of the AXP.
 The RMS sensitivity of the image is 0.2 mJy beam!., The RMS sensitivity of the image is 0.2 mJy $^{-1}$.
" Assuming a typical SNR spectral index a2—0.5. this corresponds to a lo surface brightness limit on any SNR of ©;cu,=3.5«1077? W m7 Hz! sr!"," Assuming a typical SNR spectral index $\alpha = -0.5$, this corresponds to a $1\sigma$ surface brightness limit on any SNR of $\Sigma_{\rm 1\, GHz} = 3.5 \times 10^{-23}$ W $^{-2}$ $^{-1}$ $^{-1}$."
 We can use our VLA observations to search for emission from 0142+61u itself., We can use our VLA observations to search for emission from u itself.
 Using these data. we find no point source at the position of ddown to a 5o limit of 0.27 mJy.," Using these data, we find no point source at the position of down to a $5\sigma$ limit of 0.27 mJy."
 The are of emission wwhich we have identified in Fig 2? has à partial-shell morphology. a high radio/IR flux ratio. and a spectral index which suggests non-thermal emission.," The arc of emission which we have identified in Fig \ref{fig_rxj} has a partial-shell morphology, a high radio/IR flux ratio, and a spectral index which suggests non-thermal emission."
 We thus suggest that us potentially a previously-unidentified SNR. although confirmation of this possibility will require a detection of linear polarization and/or a more accurate determination of its spectral index.," We thus suggest that is potentially a previously-unidentified SNR, although confirmation of this possibility will require a detection of linear polarization and/or a more accurate determination of its spectral index."
 It is certainly not unusual for deep imaging to reveal previously-unidentified faint SNRs in complex regions of the Galactic Plane ἐν 5: ) — these results underscore the incompleteness of current SNR samples., It is certainly not unusual for deep imaging to reveal previously-unidentified faint SNRs in complex regions of the Galactic Plane \cite{fgw94}; \cite{ggv99}; \cite{cgk+00}) ) — these results underscore the incompleteness of current SNR samples.
 Of the nearby sources in the field. SNR G346.6-0.2 is at à distance of either 5.5 or 11 kpe 0). while the ultra-compact rregion G346.5240.08 is at a distance of ~17 kpe (6: ).," Of the nearby sources in the field, SNR G346.6–0.2 is at a distance of either 5.5 or 11 kpc \cite{kfg+98}) ), while the ultra-compact region G346.52+0.08 is at a distance of $\sim$ 17 kpc \cite{ch87b}; \cite{cvew+95}) )."
 Thus even if the case can be made that lis associated with one of these nearby sources. its distance is still highly uncertain.," Thus even if the case can be made that is associated with one of these nearby sources, its distance is still highly uncertain."
 We assume in future discussion that the distance to iis I0d1o kpe with 0.5xdio<2., We assume in future discussion that the distance to is $10d_{10}$ kpc with $0.5 \la d_{10} \la 2$.
 If iis indeed a SNR. could it be associated with4," If is indeed a SNR, could it be associated with?"
0091033 The hydrogen column density towards the latter as inferred from its X-ray spectrum suggests that dio>| for the AXP ())., The hydrogen column density towards the latter as inferred from its X-ray spectrum suggests that $d_{10} \ga 1$ for the AXP \cite{snt+97}) ).
 So while the distance to neither object is known. there is nothing to suggest they are inconsistent.," So while the distance to neither object is known, there is nothing to suggest they are inconsistent."
" If we assume that the AXP was born at the center of 107r, years ago. we can infer a projected velocity for the AXP of 2300416/t;s7!."," If we assume that the AXP was born at the center of $10^4t_4$ years ago, we can infer a projected velocity for the AXP of $2300d_{10}/t_4$."
. If we assume £i>5 (as suggested by the faint and ragged appearance of aand the lack of any X-ray emission from it) and djs=I. we obtain a projected velocity of <460s. which is comparable to that inferred for other AXPs (see discussion in Section 4.4. below).," If we assume $t_4 \ga 5$ (as suggested by the faint and ragged appearance of and the lack of any X-ray emission from it) and $d_{10} = 1$, we obtain a projected velocity of $\la460$, which is comparable to that inferred for other AXPs (see discussion in Section \ref{sec_axp_overall} below)."
 However. we also need to consider the possibility that the AXP and candidate SNR lie near each other only through random alignment along the line-of-sight.," However, we also need to consider the possibility that the AXP and candidate SNR lie near each other only through random alignment along the line-of-sight."
 We can estimate such a probability by noting that there are 12 SNRs in the catalog of Whiteoak Green (1996)) within a representative area bounded by 340°«/<<350°. |b]<075.," We can estimate such a probability by noting that there are 12 SNRs in the catalog of Whiteoak Green \nocite{wg96}) ) within a representative area bounded by $340^\circ \le l \le 350^\circ$, $|b| \le 0\fdg5$."
 To calculate the probability of an AXP lying within 2’ of the rim of an unrelated SNR. we inflate the radius of each of these 12 SNRs by 2’.," To calculate the probability of an AXP lying within $2'$ of the rim of an unrelated SNR, we inflate the radius of each of these 12 SNRs by $2'$."
 The chance of an alignment is then just the ratio of the area of these 12 sub-regions to the total 10 square degrees under consideration ()). corresponding to a probability of οσο," The chance of an alignment is then just the ratio of the area of these 12 sub-regions to the total 10 square degrees under consideration \cite{sbl99}) ), corresponding to a probability of $\sim$."
 However. this value is certainly an underestimate. as we have carried out a targeted observation of greater sensitivity than the survey of Whiteoak Green (1996)). and the probability of finding a nearby SNR will thus be higher than inferred from this catalog.," However, this value is certainly an underestimate, as we have carried out a targeted observation of greater sensitivity than the survey of Whiteoak Green \nocite{wg96}) ), and the probability of finding a nearby SNR will thus be higher than inferred from this catalog."
 The catalog of Whiteoak Green (1996)) is complete to a I-GHz surface brightness of Xz8«107! W m Hz. about 10 times poorer than the 3o sensitivity of the VLA observations presented here.," The catalog of Whiteoak Green \nocite{wg96}) ) is complete to a 1-GHz surface brightness of $\Sigma \approx 8\times 10^{-21}$ W $^{-2}$ $^{-1}$, about 10 times poorer than the $\sigma$ sensitivity of the VLA observations presented here."
 Gaensler Johnston (1995)) simulate the Galactic SNR population. and find that for a search 10 times deeper than that of Whiteoak Green (1996). one would find approximately twice as many SNRs.," Gaensler Johnston \nocite{gj95c}) ) simulate the Galactic SNR population, and find that for a search 10 times deeper than that of Whiteoak Green (1996), one would find approximately twice as many SNRs."
 Similarly. Helfand ((1989)) argue that about of SNRs in this direction are still to be discovered.," Similarly, Helfand \nocite{hvbl89}) ) argue that about of SNRs in this direction are still to be discovered."
 We thus conclude that for our targeted search. the probability," We thus conclude that for our targeted search, the probability"
that the photons above the lonizatiou edge that intercept the material are absorbed aud ultimately reemittec as 1’ecombinatjon line photons.,that the photons above the ionization edge that intercept the material are absorbed and ultimately reemitted as recombination line photons.
 Expressiug tliis in terms of the number (hus. as ZNéoutinuun*recombined - and ΑΝrecombined*lineMine. where 5j is the efficiency of cascade through the line we cai caleulate the solid augle subtennclect.," Expressing this in terms of the number flux, as $N_{\rm continuum}*\Omega/(4\pi)=N_{\rm absorbed}=N_{\rm recombined}$ , and $N_{\rm recombined}*\eta_{\rm line}=N_{\rm line}$, where $\eta$ is the efficiency of cascade through the line we can calculate the solid angle subtended, $\Omega$."
 Usiug the spectrum [rom the o=0.25 phase bin we find a solid angle of /(1x)=(1.8+0.)x107., Using the spectrum from the $\phi=0.25$ phase bin we find a solid angle of $\Omega/(4\pi)=(1.8 \pm 0.7) \times 10^{-2}$.
 For the 1U 1822—37 eeometry this correspotrds to au illuminated surface area of (1.0dE0.Dx102!em. or a vertical scale heielt o [~~(ο)0.7) ," For the 4U $-$ 37 geometry this corresponds to an illuminated surface area of $(1.0\pm 0.4) \times 10^{21}\, {\rm cm^{2}}$, or a vertical scale height of $\sim (3.3\pm 0.7) \times10^{10}\, {\rm cm}$."
The presence of a oulge at the stream impact point in. [fU 1822—3T was first. suggested by Masonetal.(1980). to explain the siuusoidal modulation iu the optical ligliteurve., The presence of a bulge at the stream impact point in 4U $-$ 37 was first suggested by \citet{Mason} to explain the sinusoidal modulation in the optical lightcurve.
 Usiug detailed mocleling of the X-ray. UV. optical. aud UR lighteurves White&Holt(1982).. Mason&Córdova (1982b).. and Hellier&Mason(1989). all inferred a plase-¢epeudent vertical structure along the edge of the disk that is dominated by a bulge arouud plane ¢)—(0.85. which extends from o=0.70 too=0.0 with πο vertical height between 0.6 aud 1.6x1010em depending on the model.," Using detailed modeling of the X-ray, UV, optical, and IR lightcurves \citet{WhiteHolt}, \citet{MasonCordovaB}, and \citet{HellierMason} all inferred a phase-dependent vertical structure along the edge of the disk that is dominated by a bulge around phase $\phi=0.85$, which extends from $\phi=0.70$ to $\phi=0.0$ with a maximum vertical height between $0.6$ and $1.6 \times 10^{10}\, {\rm cm}$ depending on the model."
 This is cousiseut with the pliase location aud the vertical |elelt that we measure here to within a factor of twO., This is consistent with the phase location and the vertical height that we measure here to within a factor of two.
 We can tse the details of he HETGS spectra to further constralu the psical parameters of tlie emitti netjaterial., We can use the details of the HETGS spectra to further constrain the physical parameters of the emitting material.
 The widh of the RRC feature is a direct ineasure of the plasma temperature., The width of the RRC feature is a direct measure of the plasma temperature.
" Fo ""the cleanly resolved RRC we find a temperature of 137eV—(1.50.s)xLOK."," For the cleanly resolved RRC we find a temperature of $13\pm 7\, {\rm eV} = (1.5\pm 0.8) \times 10^{5}\, {\rm K}$."
 We can esimate the dlasina deusity o the emitting material using the emission measure. EM=fdV.," We can estimate the plasma density of the emitting material using the emission measure, ${\rm EM}=\int{dV n_{\rm e}^2}$."
 ΤΙe eimnission imneasure is cleteruined by divicing the line huminositv by the line powers. which are aled usine HULLAC (BaShalometal.," The emission measure is determined by dividing the line luminosity by the line powers, which are calculated using HULLAC \citep{BarShalom}."
1995).. For all ions except oxyeen. we meantre EM~5 ⋅≻↕⊊↥↽⋊∙⋝−∢∙⋯∌∩“QO ," For all ions except oxygen, we measure ${\rm EM} \sim 5 \times 10^{56}\, (D/2.5\, {\rm kpc})^{2}\, {\rm cm^{-3}}$ ."
aud we easwe EM~2.5x10°?(D/2.5ipe)en? COLlc iniply a relative urderabuidaice of oxvgeu by a [actor of ~20.," For and we measure ${\rm EM} \sim 2.5 \times 10^{55}\, (D/2.5\, {\rm kpc})^{2}\, {\rm cm^{-3}}$, which could imply a relative underabundance of oxygen by a factor of $\sim 20$."
" Estlating ile volume by taking the vertical height tLat we infer |iere, the azimutlal extent from previots Hioce——ug of the lie""urves. aud assuimiug that the emissio1 measure Is dorinated by material wΠΜ :|Thoimpsou T clenth οἱ τ-1, we find an aveage electroi1 density of ~IxI0!ci.7."," Estimating the volume by taking the vertical height that we infer here, the azimuthal extent from previous modeling of the lightcurves, and assuming that the emission measure is dominated by material within a Thompson depth of $\tau=1$, we find an average electron density of $\sim 1 \times 10^{11}\, {\rm cm^{-3}}$."
 Such a hieh de15ity would have been discerniable in the He-like line alios if he UV plOlOex(jtatiou bac lol sauratec the trausitious., Such a high density would have been discernable in the He-like line ratios if the UV photoexcitation had not saturated the transitions.
" The persisteice of the [Iuorescence enission t]roughout the bina'"" phases with a ecrease in tlje 11teusity only during phase o=0.75 suggests that the fluoresci emaerial comes TOW al extelded inner region of the system. which is visible a all times. but parially blocked from “lew at that [OL1 by the bulge."," The persistence of the fluorescence emission throughout the binary phases with a decrease in the intensity only during phase $\phi=0.75$ suggests that the fluorescing material comes from an extended inner region of the system, which is visible at all times, but partially blocked from view at that point by the bulge."
 The width of the lije constrains the racial location of he emitting jaterial., The width of the line constrains the radial location of the emitting material.
 Fron the measured ipper-lunit to the velocity broaceuit& we find a owel unit for the juner radius ¢ ffQ51x10!em.," From the measured upper-limit to the velocity broadening we find a lower limit for the inner radius of $R \geq 1\times 10^{10}\, {\rm cm}$."
 According to mocels for tle formaion of the e«rona. it should be ighlv ionizec txd optically thick (White&Holt1982).," According to models for the formation of the corona, it should be highly ionized and optically thick \citep{WhiteHolt}."
. The observed Lite Callοἱ originate in such a corona or else it woudhave a higher eleley celtroic aid would appear broadened by Compton scatering in the hot (ο1.8 keV) corona material.," The observed line cannot originate in such a corona or else it wouldhave a higher energy centroid and would appear broadened by Compton scattering in the hot $\sim 1.8\, {\rm keV}$ ) coronal material."
 We can estimate the relative eeometry of the luorescing material aud the illuminating central, We can estimate the relative geometry of the fluorescing material and the illuminating central
Since the pioneering observational. detection. of the first Galactic. gravitational. microlensing events by the MACHO team (Alcock et al.,Since the pioneering observational detection of the first Galactic gravitational microlensing events by the MACHO team (Alcock et al.
" 1997, 2000). many efforts have been devoted to this issue."," 1997, 2000), many efforts have been devoted to this issue."
 In fact. after these preliminary discoveries. many other teams pursued similar studies to either confirm or discard their results.," In fact, after these preliminary discoveries, many other teams pursued similar studies to either confirm or discard their results."
 Among these observational studies we mention those performed by the EROS (Lasserre et al., Among these observational studies we mention those performed by the EROS (Lasserre et al.
 2001: Goldman et al., 2001; Goldman et al.
 2002: Tisserand et al., 2002; Tisserand et al.
 2007). OGLE (Udalski et al.," 2007), OGLE (Udalski et al."
 1994). MOA (Muraki et al.," 1994), MOA (Muraki et al."
 1999) and SuperMACHO (Becker et al., 1999) and SuperMACHO (Becker et al.
 2005) teams., 2005) teams.
 All of them have nonitored millions of stars during several years in both the Large Magellanic Cloud (LMC) and the Small Magellante Cloud (SMC) to search for microlensing events., All of them have monitored millions of stars during several years in both the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC) to search for microlensing events.
 One of the nain results of these searches is that none of the microlensing events found so far has durations between a few hours and 20 days., One of the main results of these searches is that none of the microlensing events found so far has durations between a few hours and 20 days.
 This inmediately translates into tight contraints on the nature of the objects responsible for the microlensing events., This inmediately translates into tight contraints on the nature of the objects responsible for the microlensing events.
 Today it is known that most likely the objects responsible of the reported gravitational microlensing events are stars with nasses ranging from ~0.1]Mc; and ~1.0Me.," Today it is known that most likely the objects responsible of the reported gravitational microlensing events are stars with masses ranging from $\sim 0.1\, M_{\sun}$ and $\sim 1.0\, M_{\sun}$."
 Thus. for this reason and because of their intrinsical faintness. white dwarfs seem to be the best candidates to explain the observed nicrolensing events and. consequently. they would also be obvious candidates to build up the baryonic dark matter content of the Galaxy.," Thus, for this reason and because of their intrinsical faintness, white dwarfs seem to be the best candidates to explain the observed microlensing events and, consequently, they would also be obvious candidates to build up the baryonic dark matter content of the Galaxy."
 In a series of previous papers we have exhaustively analyzed the contributions of the halo populations of carbon-oxygen (CO) and oxygen-neon (ONe) white dwarfs with pure hydrogen atmospheres (Garefaa—Berro et al., In a series of previous papers we have exhaustively analyzed the contributions of the halo populations of carbon-oxygen (CO) and oxygen-neon (ONe) white dwarfs with pure hydrogen atmospheres a–Berro et al.
 2004: Camacho et al., 2004; Camacho et al.
 2007)., 2007).
 We have also extended our previous studies to include the population of halo red dwarfs (Torres et al., We have also extended our previous studies to include the population of halo red dwarfs (Torres et al.
 2008)., 2008).
 Thus. these studies covered the full range of initial masses able to produce microlensing events compatible with the required durations. and nearly 90% of the stellar content.," Thus, these studies covered the full range of initial masses able to produce microlensing events compatible with the required durations, and nearly $90\%$ of the stellar content."
 The main conclusion of these papers is that the entire population of these stars can account at most for ~0.3 of the optical depth found by the MACHO team., The main conclusion of these papers is that the entire population of these stars can account at most for $\sim 0.3$ of the optical depth found by the MACHO team.
 This in turn implies that the contribution of the full range of masses between 0.08 and 10Mq represents €556t of the halo dark matter. with an average mass of 0.4Mo.," This in turn implies that the contribution of the full range of masses between $0.08$ and $10\, M_{\sun}$ represents $\la 5\%$ of the halo dark matter, with an average mass of $0.4\, M_{\sun}$."
 Even though. we also found that the expected number of events obtained in our simulations (three events at the 95% confidence level) is substantially below the number of events detected by the MACHO team.," Even though, we also found that the expected number of events obtained in our simulations (three events at the $95\%$ confidence level) is substantially below the number of events detected by the MACHO team."
 Thus these results support the idea previously pointed out in several other studies. that the optical depth found by the MACHO team ts probably an overstimate. possibly due to contamination of self-lensing objects. variable stars and others.," Thus these results support the idea previously pointed out in several other studies, that the optical depth found by the MACHO team is probably an overstimate, possibly due to contamination of self-lensing objects, variable stars and others."
 In all previous studies in which the contribution. of white dwarfs to the dark matter. content of the Galaxy was analyzed. white-dwarf evolutionary sequences with pure hydrogen atmospheres (white dwarfs of the DA type) were employed. and the contribution of non-DA white dwarfs was disregarded.," In all previous studies in which the contribution of white dwarfs to the dark matter content of the Galaxy was analyzed, white-dwarf evolutionary sequences with pure hydrogen atmospheres (white dwarfs of the DA type) were employed, and the contribution of non-DA white dwarfs was disregarded."
 However. non-DA white dwarfs represent roughly of the entire white dwarf population and consequently their contribution cannot be considered a priori negligible.," However, non-DA white dwarfs represent roughly of the entire white dwarf population and consequently their contribution cannot be considered a priori negligible."
 Moreover. there is strong observational evidence that non-DA white dwarfs respresent an even more important fraction of the cool white dwarf population (Bergeron. Legget Ruiz 2001). but the current simulations of the halo white dwarf population do not take this fact into account.," Moreover, there is strong observational evidence that non-DA white dwarfs respresent an even more important fraction of the cool white dwarf population (Bergeron, Legget Ruiz 2001), but the current simulations of the halo white dwarf population do not take this fact into account."
 Additionally. the colors and magnitudes of cool white dwarfs depend on their atmospheric composition — see Fig.," Additionally, the colors and magnitudes of cool white dwarfs depend on their atmospheric composition — see Fig."
 1., 1.
 Indeed. it has beer demonstrated (Hansen 1998) that white dwarfs with hydrogen-rich atmospheres experience a blue tur at low luminosities. which is the result of extremely strong H» molecular absorptior features in the infrared.," Indeed, it has been demonstrated (Hansen 1998) that white dwarfs with hydrogen-rich atmospheres experience a blue turn at low luminosities, which is the result of extremely strong ${\rm H}_2$ molecular absorption features in the infrared."
 This blue hook prevents DA white dwarts from reaching very faint magnitudes., This blue hook prevents DA white dwarfs from reaching very faint magnitudes.
 On the contrary. white dwarfs of the non-DA types cool as blackbodies anc hence can reach extremely faint magnitudes within the age of the Galaxy.," On the contrary, white dwarfs of the non-DA types cool as blackbodies and hence can reach extremely faint magnitudes within the age of the Galaxy."
 Again. this important fact has been overlooked i the most up-to-date models of the population of halo white dwarfs.," Again, this important fact has been overlooked in the most up-to-date models of the population of halo white dwarfs."
 Finally. the rate of cooling of white dwarfs is controllec by the thickness and composition of the atmospheric layers.," Finally, the rate of cooling of white dwarfs is controlled by the thickness and composition of the atmospheric layers."
 It turns out that non-DA white dwarfs cool faster than their corresponding DA counterparts. another fact that has not beer taken into account in previous simulations.," It turns out that non-DA white dwarfs cool faster than their corresponding DA counterparts, another fact that has not been taken into account in previous simulations."
 Another point which deserves attention 1s whether the lenses belong to the halo or to an extended thick disk, Another point which deserves attention is whether the lenses belong to the halo or to an extended thick disk
SSP spectra ave given in Luminosity units per one solar mass.,SSP spectra are given in luminosity units per one solar mass.
" We also account. for the fact that a certain percentage of stars. depending on the SSDP’s age. has evolved ancl is not shining anvmore. so the mass value we provide is actually ""luminous mass”. Fig."," We also account for the fact that a certain percentage of stars, depending on the SSP's age, has evolved and is not shining anymore, so the mass value we provide is actually “luminous mass”, Fig."
 Ll shows a comparison of the stellar mass computed in this worκ and that provided in the narrow line AGN catalogue Ixaulfnjuinetal.(2003)., \ref{fig:kauff_mstars} shows a comparison of the stellar mass computed in this work and that provided in the narrow line AGN catalogue \cite{kauffmann03}.
". The line shows the linear correlation between the two quantities. Aj, 1.59 | (1.06A/&)."," The line shows the linear correlation between the two quantities, $M^*_{here}$ = 1.59 + $M^*_{\bf K}$ )."
 Notetiab the svstematic cillerences in the mass values are the result. of the clilferent LATE used by Ixaulfmannetal.2(2003)... a Ixroupa (2001) EME. which differs from ours both in t1e slope and in the mass limits.," Note that the systematic differences in the mass values are the result of the different IMF used by \cite{kauffmann03}, a Kroupa (2001) IMF, which differs from ours both in the slope and in the mass limits."
 We now compute 1ie star formation rate (SER) according to Ixennicutt(1998). as where £Lpyp is the infrared. luminosity of the SB component. integrated between S and. 1000 micron.," We now compute the star formation rate (SFR) according to \cite{kennicutt98} as where $L_{FIR}$ is the infrared luminosity of the SB component, integrated between 8 and 1000 micron."
 Fig., Fig.
 shows the distribution of the SEIts for all objects with an SD component and 47«16.0 (black histogram). with the eraved region corresponding to the objects without an ACN component.," \ref{fig:SFRkauff}
 shows the distribution of the SFRs for all objects with an SB component and $\chi^2 < 16.0$ (black histogram), with the grayed region corresponding to the objects without an AGN component."
 The average SET. of the entire sample without imposing a eut on the X7 values is of 2.8 A. /vr. and drops 10 2.2 when only objects with 47«16.0 are consider. and to 1.855 when objects with an AGN component are excluded.," The average SFR of the entire sample without imposing a cut on the $\chi^2$ values is of 2.8 $M_{\odot}$ /yr, and drops to 2.2 when only objects with $\chi^2 <16.0$ are consider, and to 1.85 when objects with an AGN component are excluded."
 Note that all objects with a torus component. are, Note that all objects with a torus component are
and >=3.3 lieht curves is Nay=0.34. placing the +=3.3 light curve between the 0.5-1.0 keV (λαμκοςξ 0.25) and 1.0-2.0 keV (Negxoc= 0.54) bands.,"and $\gamma=3.3$ light curves is $\Delta\alpha_{\rm H}=-0.34$, placing the $\gamma=3.3$ light curve between the 0.5-1.0 keV $\Delta \alpha_{\rm H, NGC}=-0.25$ ) and 1.0-2.0 keV $\Delta \alpha_{\rm H, NGC}=-0.54$ ) bands."
 To check the consistency of the time-scales. we compared the bend frequeney fiverc: measured by etal. (2004)... using the combined and Ilight. curves. to model light curves covering a similar range in frequencies.," To check the consistency of the time-scales, we compared the bend frequency $f_{b, NGC}$ measured by \citet{McHardy4051}, using the combined and light curves, to model light curves covering a similar range in frequencies."
 As the clelata used for this fit corresponded to the 4LO keV bband. we used the shard’ simulated. light. curves with > between 5.5 and oc.," As the data used for this fit corresponded to the 4–10 keV band, we used the `hard' simulated light curves with $\gamma$ between 5.5 and $\infty$."
" Phe best fit bend frequencies for 7,=!ut and xX. respectively, ave 4.6101 and 210ος."," The best fit bend frequencies for $\gamma=5.5 $ and $ \infty$, respectively, are $4.6\times 10^{-4}$ and $2 \times 10^{-3} c/R_{\rm
g}$."
 Equating these values to fi—5.10! Lz vields a mass of 200810AL... consistent with the rreverberation mapping mass of 5.5LOAL. (Shemumoeral. 2003).," Equating these values to $f_{b, NGC}=5\times 10^{-4}$ Hz yields a mass of $2 - 8\times10^5 M_\odot$, consistent with the reverberation mapping mass of $5^{+6}_{-3}\times10^5 M_\odot$ \citep{Shemmer}."
. A similar energy dependence of the PSD has been found in other AGN., A similar energy dependence of the PSD has been found in other AGN.
 As an example. the PSD of the Sevfert 1 ealaxy ccan also be fit with a bending power law model obtaining Hatter high-frequency. slopes for higher energy. light curves (Vaughanctal.," As an example, the PSD of the Seyfert 1 galaxy can also be fit with a bending power law model obtaining flatter high-frequency slopes for higher energy light curves \citep{VaughanMCG}."
2003).. Phe energy dependence in this case is less pronounced than in4051... possibly. suggesting that the energy. bands used have closer emissivity indices.," The energy dependence in this case is less pronounced than in, possibly suggesting that the energy bands used have closer emissivity indices."
 Incidentallv. emissivity inclices that are closer in value would also produce smaller. time lags. as observed. in.," Incidentally, emissivity indices that are closer in value would also produce smaller time lags, as observed in."
30-15.. Llowever. more parameters contribute to celine the observed. lags. for example. the mass of the central object changes the frequency range probed. in terms of the light crossing times.," However, more parameters contribute to define the observed lags, for example, the mass of the central object changes the frequency range probed in terms of the light crossing times."
 A comparison of the fractional lags at. for example. the PSD bend frequency in cach case gives à mass-independent measure. so an extrapolation of the lag spectra in ppublished by Al’Lardyetal.(2004) down to the break time-scale would suggest that the lags in this case are indeed systematically larger than in6-30-15.," A comparison of the fractional lags at, for example, the PSD bend frequency in each case gives a mass-independent measure, so an extrapolation of the lag spectra in published by \citet{McHardy4051}
 down to the break time-scale would suggest that the lags in this case are indeed systematically larger than in."
. We now apply our simple model to data from the well-studied. persistent black hole Χο νο N-1. in the high/soft state.," We now apply our simple model to data from the well-studied, persistent black hole XRB Cyg X-1, in the high/soft state."
 Our model. produces light curves with a ~1/f PSD shape down to low frequencies., Our model produces light curves with a $\sim1/f$ PSD shape down to low frequencies.
 This is because we assume that the input signals originate at many different. raclii throughout the aceretion disc. are equally separated in the logarithm of [requeney and have identical rms amplitudes of variability.," This is because we assume that the input signals originate at many different radii throughout the accretion disc, are equally separated in the logarithm of frequency and have identical rms amplitudes of variability."
 PSDs of this shape are seen for several AGN (see previous section) and Cve X-1 in its high/soft state., PSDs of this shape are seen for several AGN (see previous section) and Cyg X-1 in its high/soft state.
 We will. use cata from ai short. (2.5. ks)RATE observation of (νο X-1 in the high/soft state. Observation ID. 10512-01-09-01. obtained on 1996 June187.," We will use data from a short (2.3 ks) observation of Cyg X-1 in the high/soft state, Observation ID 10512-01-09-01, obtained on 1996 June."
. Using Proportional Counter Array (PCA) light curves with 27s resolution. we measured the [ag spectrum and PSD in two bands. 25.1 keV. (soft. band) and S.13 keV. (hard. band)," Using Proportional Counter Array (PCA) light curves with $2^{-8}$ s resolution, we measured the lag spectrum and PSD in two bands, 2–5.1 keV (soft band) and 8–13 keV (hard band)."
 We subtracted Poisson noise. including the appropriate deadtime correction. e.g. Itevnivtsev.Gilfanov&Churazov(2000).. before calculating the ratio of the PSDs.," We subtracted Poisson noise, including the appropriate deadtime correction, e.g. \citet{RevHifreq}, before calculating the ratio of the PSDs."
 To keep the fitting simple. we consider only the ratio of the PSDs. and not the cnerev-depencent PSD shapes themselves. so we do not attempt to match the PSD shape by assuming any particular input signal.," To keep the fitting simple, we consider only the ratio of the PSDs, and not the energy-dependent PSD shapes themselves, so we do not attempt to match the PSD shape by assuming any particular input signal."
 This approach allows us to estimate the laes and filtering elfect in a simple analytical wav. by assuming that cach frequency. contributing to the lag spectrum and PSD ratio corresponds to a single radius. so input signal PSDs do not overlap in frequency. with the lags anc PSD filtering determined. using the analytical expressions given in Appendix A. We note that M*LIardyetal.(2004). do not claim any evidence of energy. dependence of the PSD in their fitting of the same data used here. but we do find a significant energy. dependence using the PSD ratio (sce below).," This approach allows us to estimate the lags and filtering effect in a simple analytical way, by assuming that each frequency contributing to the lag spectrum and PSD ratio corresponds to a single radius, so input signal PSDs do not overlap in frequency, with the lags and PSD filtering determined using the analytical expressions given in Appendix A. We note that \citet{McHardy4051} do not claim any evidence of energy dependence of the PSD in their fitting of the same data used here, but we do find a significant energy dependence using the PSD ratio (see below)."
 The discrepancy may result [rom the fact that the measured PSD ratio is. in fact. more sensitive than independent fits to the PSD. because the light curves in different bands are correlated. so that statistical scatter in the PSD due to the stochastic nature of the light curves is in the same cirection in both bands. and its elfect on the PSD ratio is therefore mitigatecd.," The discrepancy may result from the fact that the measured PSD ratio is, in fact, more sensitive than independent fits to the PSD, because the light curves in different bands are correlated, so that statistical scatter in the PSD due to the stochastic nature of the light curves is in the same direction in both bands, and its effect on the PSD ratio is therefore mitigated."
 We first stress that due to the complexity of fitting even our relatively simple model to the data. and the dilficulty of quantifving certain measurement uncertainties (see below). we will only test the broad consistency of our model with he data.," We first stress that due to the complexity of fitting even our relatively simple model to the data, and the difficulty of quantifying certain measurement uncertainties (see below), we will only test the broad consistency of our model with the data."
 Therefore. we will not quote statistical errors on xwameters derived. here. which should. be treated. as only indicative of the underlving physical parameters.," Therefore, we will not quote statistical errors on parameters derived here, which should be treated as only indicative of the underlying physical parameters."
 Since our model contains many parameters with complex degeneracies tween them. we only fit the model with a few parameters," Since our model contains many parameters with complex degeneracies between them, we only fit the model with a few parameters"
filaments are oriented racially from the umbral core which sugecst the presence of a inoat flow in the erantlation region iu the direct vicinity.,filaments are oriented radially from the umbral core which suggest the presence of a moat flow in the granulation region in the direct vicinity.
 Even with a ower velocity threshold. wo moat flow cau be discerned in this region.," Even with a lower velocity threshold, no moat flow can be discerned in this region."
 Nevertheless. when comparing with the magnetoeram (see lower pancl of Figure 9)). we fouud an inversion m maeuctic polarity just outside the right border of the sunspot: the magnetoeram displays positive polarity (n white) for the sunspot but neeative polarity for the samall magnetic elements aud pore just outside the peuuubra.," Nevertheless, when comparing with the magnetogram (see lower panel of Figure \ref{F:9}) ), we found an inversion in magnetic polarity just outside the right border of the sunspot: the magnetogram displays positive polarity (in white) for the sunspot but negative polarity for the small magnetic elements and pore just outside the penumbra."
 The reversal of polarity (or neutral line) is confined to a narrow region that roughly coimcides with the sunspot border., The reversal of polarity (or neutral line) is confined to a narrow region that roughly coincides with the sunspot border.
 The absence of large outflows, The absence of large outflows
hand simply do not allow accurate curveπο)”.,hand simply do not allow accurate curve.
 If we guess that the distributions shown actually contain most of the peculiar velocity dispersion. (alternatively. that the Hubble constant is not biased verv much). then 200 kin FH forms a rough limit to the observed dispersion and the rms value is something over halfthat’.," If we guess that the distributions shown actually contain most of the peculiar velocity dispersion (alternatively, that the Hubble constant is not biased very much), then 200 km $^{-1}$ forms a rough limit to the observed dispersion and the rms value is something over half."
 A substantially unbiased sample must then include radial velocities out to about 700 km sec.! [or 5 Mpc and 1000 kin see+ [or 10 Mpe., A substantially unbiased sample must then include radial velocities out to about 700 km ${\rm sec}^{-1}$ for 5 Mpc and 1000 km ${\rm sec}^{-1}$ for 10 Mpc.
 Usine a sample of nine galaxies extending to about 8 Alpe. Sancdage(1986). concluded that the velocity field in the Local Volume was extremely quiet. the velocity dispersion being about equal to the observational errors in distance. near GO km sec!.," Using a sample of nine galaxies extending to about 8 Mpc, \citet{S86} concluded that the velocity field in the Local Volume was extremely quiet, the velocity dispersion being about equal to the observational errors in distance, near 60 km ${\rm sec}^{-1}$."
 Ekholmοἱ repeated the calculation with 14 galaxies having Cepheid distances. obtaining a similar dispersion of 40-60 km sec4.," \citet{EBT01}
 repeated the calculation with 14 galaxies having Cepheid distances, obtaining a similar dispersion of 40-60 km ${\rm sec}^{-1}$."
 A flow this cold is difficult to explain theoretically. recent attempts including those of Daryvshev.Chernin.&Teerikorpi(2001) and &Perivolaropoulos (2002).," A flow this cold is difficult to explain theoretically, recent attempts including those of \citet{BCT01} and \citet{AP02}."
. However. the fact. of a cold flow has been disputed. by cde [or instance. ancl the present study indicates a dispersion twice that of Ekholmοἱal.(2001) even ignoring the sample incompleteness at high racial velocity.," However, the fact of a cold flow has been disputed, by \citet{VB79} for instance, and the present study indicates a dispersion twice that of \citet{EBT01} even ignoring the sample incompleteness at high radial velocity."
 In any investigation of kinematics in (he Local Volume this disagreement requires some explanation., In any investigation of kinematics in the Local Volume this disagreement requires some explanation.
 The non-Local Group galaxies used bv Ekhohlmοἱal.(2001) in their study are shown in Figure 15.. as thev fall in (he 35-galaxy. anisotropic solution.," The non-Local Group galaxies used by \citet{EBT01} in their study are shown in Figure \ref{coldflow}, as they fall in the 35-galaxy anisotropic solution."
 They clearly do not explore the full width of the velocity dispersion., They clearly do not explore the full width of the velocity dispersion.
 ‘This is easily explained if the Cepheicl galaxies are more massive than the average. and thus harder to disturb by gravitational interaction (andpriori plausible. given that Cephleids are easier to find in massive spirals).," This is easily explained if the Cepheid galaxies are more massive than the average, and thus harder to disturb by gravitational interaction (and plausible, given that Cepheids are easier to find in massive spirals)."
 ILowever. in the right hand side of the same figure several galaxies are singled out whieh are about as massive as the Cepheid set. perhaps more so. and show a much greater dispersion.," However, in the right hand side of the same figure several galaxies are singled out which are about as massive as the Cepheid set, perhaps more so, and show a much greater dispersion."
 It appears that the various cold-flow groups have been misled by small number s, It appears that the various cold-flow groups have been misled by small number .
 It appears that the various cold-flow groups have been misled by small number st, It appears that the various cold-flow groups have been misled by small number .
 It appears that the various cold-flow groups have been misled by small number sta, It appears that the various cold-flow groups have been misled by small number .
 It appears that the various cold-flow groups have been misled by small number stat, It appears that the various cold-flow groups have been misled by small number .
 It appears that the various cold-flow groups have been misled by small number stati, It appears that the various cold-flow groups have been misled by small number .
 It appears that the various cold-flow groups have been misled by small number statis, It appears that the various cold-flow groups have been misled by small number .
 It appears that the various cold-flow groups have been misled by small number statist, It appears that the various cold-flow groups have been misled by small number .
 It appears that the various cold-flow groups have been misled by small number statisti, It appears that the various cold-flow groups have been misled by small number .
 It appears that the various cold-flow groups have been misled by small number statistic, It appears that the various cold-flow groups have been misled by small number .
 It appears that the various cold-flow groups have been misled by small number statistics, It appears that the various cold-flow groups have been misled by small number .
 It appears that the various cold-flow groups have been misled by small number statistics!, It appears that the various cold-flow groups have been misled by small number .
Based on the spatial coincidence between the two objects. suggested an association of IGR J1]3000+2529 withO-379-0073388.. an AGN listed in the NED database.,"Based on the spatial coincidence between the two objects, \cite{bassani06} suggested an association of IGR $+$ 2529 with, an AGN listed in the NED database."
 The XRT position is consistent with that of MAPS-NGP O-379-0073388. which the high energy souree and the AGN are the same.," The XRT position is consistent with that of MAPS-NGP O-379-0073388, which the high energy source and the AGN are the same."
 We found a single 2MASS source within the XRT error circle. and although the source is not reported as extended it lies only ffrom the position of the AGN reported in NED. which indicates the two objects are probably the same.," We found a single 2MASS source within the XRT error circle, and although the source is not reported as extended it lies only from the position of the AGN reported in NED, which indicates the two objects are probably the same."
 As the source is very weak. we extracted an average spectrum from the two ppointings.," As the source is very weak, we extracted an average spectrum from the two pointings."
 The spectrum has too few counts for a spectral analysis to be possible., The spectrum has too few counts for a spectral analysis to be possible.
 Although this source 1s the faintest from our sample that we detect with XRT. and the very low flux could indicate a lower probability that it is associated with the IGR source. the good spatial coincidence with the AGN along withcandidate.," Although this source is the faintest from our sample that we detect with XRT, and the very low flux could indicate a lower probability that it is associated with the IGR source, the good spatial coincidence with the AGN along with."
. This source was first mentioned in 9 and was classified as a pulsar/HMXB in ?.. probably based on the positional coincidence withJ130159.6—6358006.. which indeed is an HMXB containing a pulsar (2)..," This source was first mentioned in \citet{bird06} and was classified as a pulsar/HMXB in \citet{bird07}, probably based on the positional coincidence with, which indeed is an HMXB containing a pulsar \citep{chernyak05}."
 ?. further report a distance to the source of about 5.5 kpe., \citet{bodaghee07} further report a distance to the source of about 5.5 kpc.
 We find a single XRT source within the IBIS error circle at a position compatible with that of 2RXP J130159.6—6358006., We find a single XRT source within the IBIS error circle at a position compatible with that of 2RXP $-$ 635806.
 This renders the association even more likely., This renders the association even more likely.
 It is unfortunate that due to its off-axis position (the pointings were aimed at PSR BI259—-63). none of the UVOT exposures contains the source.," It is unfortunate that due to its off-axis position (the pointings were aimed at PSR $-$ 63), none of the UVOT exposures contains the source."
 There is no USNO-BI.O source within the eerror circle., There is no USNO-B1.0 source within the error circle.
 We estimate a lower limit Vz21. for the magnitude of an optical counterpart., We estimate a lower limit $\gtrsim$ 21 for the magnitude of an optical counterpart.
 As the source may be significantly variable (?).. we fitted each spectrum from each independent pointing separately.," As the source may be significantly variable \citep{chernyak05}, we fitted each spectrum from each independent pointing separately."
 An absorbed power-law fits all spectra rather well iin the range 0.6 to 1.40 for 30 to 13 dof)., An absorbed power-law fits all spectra rather well in the range 0.6 to 1.40 for 30 to 13 dof).
 Since the absorption is poorly constrained and given that ? mention a relatively stable value of 2.48x107 οι”. we froze tto this value in all our fits.," Since the absorption is poorly constrained and given that \citet{chernyak05} mention a relatively stable value of $\times10^{22}$ $^{-2}$, we froze to this value in all our fits."
 Note that for all pointings the value obtained for wwhen it ts allowed to vary is in good agreement. or compatible with 2..," Note that for all pointings the value obtained for when it is allowed to vary is in good agreement, or compatible with \citet{chernyak05}."
 The spectral results reported in Table 5 show some slight variability especially between the first pointing and the following ones. which are slightly softer.," The spectral results reported in Table \ref{tab:spectral} show some slight variability especially between the first pointing and the following ones, which are slightly softer."
" The spectral parameters are those expected for an accreting pulsar and. assuming a distance of 5.5 kpe. lead to a 2-10 keV luminosity of about οκ10"" erg/s. typical for these objects."," The spectral parameters are those expected for an accreting pulsar and, assuming a distance of 5.5 kpc, lead to a 2–10 keV luminosity of about $\times10^{34}$ erg/s, typical for these objects."
 Based on the positional coincidence of IGR 115161—3827 and2816946.. ? suggested that the latter. an AGN. is the counterpart of the high energy source.," Based on the positional coincidence of IGR $-$ 3827 and, \citet{masetti06b} suggested that the latter, an AGN, is the counterpart of the high energy source."
 The AGN type ts intermediate between a Liner and a Sey 2 at zz0.0365 (?).., The AGN type is intermediate between a Liner and a Sey 2 at $z$ =0.0365 \citep{masetti06b}.
 The mmosaic image revealed four possible X-ray counterparts within the IBIS error circle of IGR 715161—3827..," The mosaic image revealed four possible X-ray counterparts within the IBIS error circle of IGR $-$ 3827.,"
 J151559.3-382548..J151630.0-382656..J151612.2-383102.. and are labeled source #11. #22. #33. and #44. respectively in Tables 2. and 3..," and are labeled source 1, 2, 3, and 4, respectively in Tables \ref{tab:position} and \ref{tab:ircounterparts}."
 It 1s not possible to say which (1f any) is the true counterpart., It is not possible to say which (if any) is the true counterpart.
 Two of these are compatible with IR counterparts found in the 2MASS and 2MASX catalogs. although 2MASX J15155970-3825468 slightly outside the XRT error circle of source ΠΤΙ.," Two of these are compatible with IR counterparts found in the 2MASS and 2MASX catalogs, although 2MASX $-$ 3825468 slightly outside the XRT error circle of source 1."
 This source is the one suggested by ? as the counterpart to the IGR source., This source is the one suggested by \citet{masetti06b} as the counterpart to the IGR source.
 Source #33 has à position compatible with an IR point source. which is consistent with being TYC 7822-2179-] catalogued as a star in SIMBAD There are no UVOT data available for either of the two XRT pointings.," Source 3 has a position compatible with an IR point source, which is consistent with being TYC 7822-2179-1 catalogued as a star in SIMBAD There are no UVOT data available for either of the two XRT pointings."
This user software must be capable of supporting both expert users and those (hat are new to using the EVLA. or anv radio interferometer.,"This user software must be capable of supporting both expert users and those that are new to using the EVLA, or any radio interferometer."
 As such. it often has two interface stvles. expert and novice.," As such, it often has two interface styles, expert and novice."
 In most cases. these interfaces are GUIs. either web-based. or stand-alone. using modern software tools (for instance. most of the web-based GUIs are written within the JavaServer Faces (JSF) framework).," In most cases, these interfaces are GUIs, either web-based, or stand-alone, using modern software tools (for instance, most of the web-based GUIs are written within the JavaServer Faces (JSF) framework)."
 The EVLA is a major expansion to the highly flexible and productive VLA., The EVLA is a major expansion to the highly flexible and productive VLA.
 The expansion includes new or upgraded receivers (hal enable continuous frequency coverage from 1 to 50 GllIz. a new broadband LO/IF svstem. a new fiber optic-based data transmission svslenm. a new correlator (o process the wideband data. à new monitor ancl control svstem. and new software that provides telescope ease of use.," The expansion includes new or upgraded receivers that enable continuous frequency coverage from 1 to 50 GHz, a new broadband LO/IF system, a new fiber optic-based data transmission system, a new correlator to process the wideband data, a new monitor and control system, and new software that provides telescope ease of use."
 The expansion provides order of magnitude. or greater. improvements over existing capabilities with the VLA.," The expansion provides order of magnitude, or greater, improvements over existing capabilities with the VLA."
 Observations with the VLA have been ongoing as the expansion has progressed., Observations with the VLA have been ongoing as the expansion has progressed.
 The project is scheduled for completion in 2012., The project is scheduled for completion in 2012.
 The expansion will enable new investigations into celestial radio transients. the evolution of objects in the universe. and the structure and strength of celestial magnetic fields.," The expansion will enable new investigations into celestial radio transients, the evolution of objects in the universe, and the structure and strength of celestial magnetic fields."
 The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities. Inc. The Dominion Radio Astrophysical Observatory is a National Facility operated by the National Research Council Canacla.," The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. The Dominion Radio Astrophysical Observatory is a National Facility operated by the National Research Council Canada."
Our results show that mass loss. irradiation and tidal interactions all have a profound effect on the observable properties of long period X-ray transients.,"Our results show that mass loss, irradiation and tidal interactions all have a profound effect on the observable properties of long period X-ray transients."
 In particular. the interplay of all of these effects in the outer regions of the accretion dise is able to drive long time-scale (i.e. months to years) variability is these objects. and is a possible origin for some of the extreme variability of GRS 191541085.," In particular, the interplay of all of these effects in the outer regions of the accretion disc is able to drive long time-scale (i.e. months to years) variability is these objects, and is a possible origin for some of the extreme variability of GRS 1915+105."
 The physical process that drives these variations occurs in hree main stages., The physical process that drives these variations occurs in three main stages.
 In the first stage. after the onset of an outburst. he mass accretion rate rises and the dise becomes irradiated out oa certain radius #2).," In the first stage, after the onset of an outburst, the mass accretion rate rises and the disc becomes irradiated out to a certain radius $R_{\rmn{h}}$."
 If the Eddington limit holds. this radius is limited to a maximum value corresponding to accretion at the Eddington rate at the inner boundary of the disc.," If the Eddington limit holds, this radius is limited to a maximum value corresponding to accretion at the Eddington rate at the inner boundary of the disc."
 We have shown hat the flow through a fixed hot/cold boundary is neither steady nor smooth., We have shown that the flow through a fixed hot/cold boundary is neither steady nor smooth.
 Gas in the unirradiated part of the dise rapidly crosses he critical threshold for the dise instability and the remainder of the accretion dise now makes the transition to the hot. high viscosity state.," Gas in the unirradiated part of the disc rapidly crosses the critical threshold for the disc instability and the remainder of the accretion disc now makes the transition to the hot, high viscosity state."
 In the third and final stage. the interaction of non-axisymmetric structure (here. the spiral waves induced by the tidal stresses of the companion star on the disc) with the unsteady 10t/cold. boundary produces a rather inhomogeneous flow.," In the third and final stage, the interaction of non-axisymmetric structure (here, the spiral waves induced by the tidal stresses of the companion star on the disc) with the unsteady hot/cold boundary produces a rather inhomogeneous flow."
 The ocal variations in density and mass accretion rate produce the variations in accretion rate seen in our models., The local variations in density and mass accretion rate produce the variations in accretion rate seen in our models.
 A further layer of complexitv in the variations is added when local mass loss from he dise there assumed to be in the form of a wind) is taken into account., A further layer of complexity in the variations is added when local mass loss from the disc (here assumed to be in the form of a wind) is taken into account.
" The variable which has the most impact on the variability hat is predicted by this model is the magnitude of /?4,44. the radius to which the dise can be irradiated for accretion at the Eddington limit."," The variable which has the most impact on the variability that is predicted by this model is the magnitude of $R_{\rmn{h,max}}$, the radius to which the disc can be irradiated for accretion at the Eddington limit."
 This is sensitive to the geometry of the dise and he illuminating X-ray source and to the accretion efficiency., This is sensitive to the geometry of the disc and the illuminating X-ray source and to the accretion efficiency.
 It is orobable that self-shadowing and radiative warping of the dise will jay some part in the behaviour. which we have not considered jere.," It is probable that self-shadowing and radiative warping of the disc will play some part in the behaviour, which we have not considered here."